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http://aas.org/archives/cdrom/volume5/volume5/aj/v110/p1083/table1.tex	aas.org	CC-MAIN-2014-52	text/x-tex	null	crawl-data/CC-MAIN-2014-52/segments/1418802768397.103/warc/CC-MAIN-20141217075248-00143-ip-10-231-17-201.ec2.internal.warc.gz	4,238,647	19,989	\documentstyle[aj_pt]{article} \begin{document} \begin{planotable}{rrrrcccccccc} \tablewidth{0pt} \tablecaption{The Photoelectric Data} \tablehead{ \multicolumn{2}{c}{R.A.}&\multicolumn{2}{c}{Dec}&\colhead{m$_{z}$}&\colhead{Other}&\colhead{V}&\colhead{B}&\colhead{B$-$V}&\colhead{$\delta$m}&\colhead{R}&\colhead{Date}\\ \colhead{$^{hr}$}&\colhead{$^{min}$}&\colhead{$^{\circ}$}&\colhead{$'$}&\colhead{}&\colhead{Name}&\colhead{}&\colhead{}&\colhead{}&\colhead{}&\colhead{$''$}&\colhead{}} \startdata $ 0$ & 0.7 & 15 & 42 & 14.9 & IC5381 & 14.30 & 15.43 & 1.13 & -0.062 & 25.5 & 10/22/65 \nl $ $ & & & & & & 14.16 & 15.34 & 1.18 & 0.049 & 38.0 & \nl $ 0$ & 1.2 & 7 & 11 & 14.0 & NGC7816 & 13.29 & 14.30 & 1.01 & -0.254 & 26.0 & 10/25/65 \nl $ $ & & & & & & 13.06 & 13.83 & 0.77 & -0.176 & 39.0 & \nl $ $ & & & & & & 12.84 & 13.55 & 0.71 & -0.083 & 57.0 & \nl $ $ & & & & & & 12.68 & 13.46 & 0.78 & 0.030 & 84.5 & \nl $ 0$ & 2.6 & 6 & 38 & 14.5 & NGC7824 & 13.41 & 14.34 & 0.93 & -0.246 & 26.0 & 10/25/65 \nl $ $ & & & & & & 13.20 & 14.22 & 1.02 & -0.108 & 39.0 & \nl $ $ & & & & & & 13.09 & 14.01 & 0.92 & -0.013 & 57.0 & \nl $ $ & & & & & & 13.05 & 14.12 & 1.07 & 0.115 & 84.5 & \nl $ 0$ & 4.2 & 8 & 21 & 15.0 & $\cdots$ & 13.94 & 14.77 & 0.83 & -0.172 & 25.5 & 10/21/65 \nl $ $ & & & & & & 13.66 & 14.54 & 0.88 & -0.066 & 38.0 & \nl $ $ & & & & & & 13.28 & 14.31 & 1.03 & 0.029 & 57.0 & \nl $ 0$ & 6.2 & 4 & 20 & 14.5 & NGC0012 & 13.82 & 14.59 & 0.77 & -0.198 & 26.0 & 10/25/65 \nl $ $ & & & & & & 13.38 & 14.15 & 0.77 & -0.120 & 39.0 & \nl $ $ & & & & & & 13.32 & 14.07 & 0.75 & -0.004 & 57.0 & \nl $ $ & & & & & & 13.23 & 13.86 & 0.63 & 0.082 & 84.5 & \nl $ 0$ & 7.8 & 11 & 52 & 15.7 & $\cdots$ & 15.30 & 16.05 & 0.75 & 0.028 & 25.5 & 10/ 4/64 \nl $ 0$ &10.4 & 14 & 08 & 14.2 & $\cdots$ & 14.19 & 14.72 & 0.53 & -0.182 & 25.5 & 10/ 4/64 \nl $ 0$ &10.8 & 17 & 13 & 14.2 & IC0004 & 13.84 & 14.48 & 0.64 & -0.227 & 25.5 & 10/22/65 \nl $ $ & & & & & & 13.66 & 14.43 & 0.77 & -0.083 & 38.0 & \nl $ $ & & & & & & 13.71 & 14.39 & 0.68 & 0.040 & 57.0 & \nl $ 0$ &13.6 & 10 & 03 & 14.7 & $\cdots$ & 13.94 & 15.03 & 1.09 & -0.127 & 25.5 & 10/ 4/64 \nl $ 0$ &16.5 & 15 & 28 & 15.3 & $\cdots$ & 14.70 & 15.39 & 0.69 & 0.056 & 38.0 & 10/ 4/64 \nl $ 0$ &22.4 & 6 & 23 & 15.4 & $\cdots$ & 14.46 & 15.44 & 0.98 & -0.061 & 25.5 & 10/21/65 \nl $ $ & & & & & & 14.41 & 15.57 & 1.16 & 0.079 & 38.0 & \nl $ 0$ &22.8 & 19 & 56 & 14.3 & $\cdots$ & 13.64 & 14.39 & 0.75 & -0.244 & 25.5 & 10/22/65 \nl $ $ & & & & & & 13.48 & 14.20 & 0.72 & -0.121 & 38.0 & \nl $ $ & & & & & & 13.42 & 14.00 & 0.58 & -0.015 & 57.0 & \nl $ 0$ &25.4 & 2 & 14 & 14.9 & $\cdots$ & 14.06 & 14.55 & 0.49 & -0.064 & 38.0 & 10/ 3/64 \nl $ 0$ &27.6 & 1 & 49 & 13.8 & NGC0132 & 12.76 & 13.36 & 0.60 & -0.277 & 38.0 & 10/ 3/64 \nl $ 0$ &31.9 & 3 & 18 & 15.7 & $\cdots$ & 14.98 & 15.84 & 0.86 & -0.001 & 25.5 & 10/ 3/64 \nl $ 0$ &35.7 & 2 & 27 & 13.8 & NGC0182 & 13.25 & 14.19 & 0.94 & -0.285 & 25.5 & 10/ 3/64 \nl $ 0$ &39.3 & -2 & 00 & 15.3 & $\cdots$ & 14.36 & 15.29 & 0.93 & -0.228 & 17.5 & 10/ 3/64 \nl $ 0$ &40.9 & -0 & 24 & 13.6 & NGC0237 & 13.18 & 13.91 & 0.73 & -0.171 & 38.0 & 10/ 3/64 \nl $ 0$ &42.5 & 5 & 52 & 14.8 & NGC0240 & 13.53 & 14.52 & 0.99 & -0.219 & 25.5 & 10/21/65 \nl $ $ & & & & & & 13.33 & 14.39 & 1.06 & -0.090 & 38.0 & \nl $ 0$ &44.7 & 14 & 26 & 15.2 & UGC00488 & 14.56 & 15.41 & 0.85 & -0.065 & 25.5 & 10/ 4/64 \nl $ 0$ &45.5 & -1 & 49 & 14.6 & UGC00492 & 13.51 & 14.50 & 0.99 & -0.223 & 25.5 & 10/20/65 \nl $ $ & & & & & & 13.48 & 14.37 & 0.89 & -0.093 & 38.0 & \nl $ 0$ &48.1 & 10 & 20 & 15.5 & IC0053 & 14.33 & 15.51 & 1.18 & -0.187 & 17.5 & 10/ 4/64 \nl $ 0$ &48.2 & -2 & 09 & 13.2 & NGC0271 & 12.71 & 13.80 & 1.09 & -0.370 & 25.5 & 10/ 3/64 \nl $ 0$ &50.9 & 2 & 30 & 15.4 & $\cdots$ & 14.89 & 15.54 & 0.65 & -0.045 & 25.5 & 10/ 3/64 \nl $ 0$ &52.2 & 11 & 34 & 15.7 & IC0057 & 14.88 & 15.96 & 1.08 & -0.108 & 17.5 & 10/ 4/64 \nl $ 0$ &54.0 & -2 & 02 & 14.1 & NGC0307 & 13.17 & 14.15 & 0.98 & -0.293 & 25.5 & 10/ 3/64 \nl $ $ & & & & & & 13.39 & 14.25 & 0.86 & -0.272 & 25.5 & 10/20/65 \nl $ $ & & & & & & 13.10 & 14.03 & 0.93 & -0.150 & 38.0 & \nl $ 0$ &54.4 & -1 & 28 & 15.3 & UGC00587 & 14.78 & 15.61 & 0.83 & -0.035 & 25.5 & 10/ 3/64 \nl $ $ & & & & & & 15.05 & 15.64 & 0.59 & -0.030 & 25.5 & 10/20/65 \nl $ 0$ &56.3 & 0 & 20 & 14.5 & IC1607 & 13.88 & 14.42 & 0.54 & -0.085 & 38.0 & 10/ 3/64 \nl $ 0$ &59.0 & -1 & 33 & 15.7 & $\cdots$ & 15.29 & 15.77 & 0.48 & -0.011 & 25.5 & 10/ 3/64 \nl $ 1$ & 0.4 & -1 & 49 & 15.7 & $\cdots$ & 14.83 & 15.75 & 0.92 & -0.014 & 25.5 & 10/20/65 \nl $ $ & & & & & & 14.79 & 15.70 & 0.91 & 0.096 & 38.0 & \nl $ 1$ & 0.5 & 6 & 34 & 15.5 & $\cdots$ & 15.04 & 15.61 & 0.57 & -0.035 & 25.5 & 10/21/65 \nl $ $ & & & & & & 15.12 & 15.78 & 0.66 & 0.105 & 38.0 & \nl $ 1$ & 0.6 & -1 & 22 & 15.6 & $\cdots$ & 15.05 & 15.86 & 0.81 & -0.125 & 17.5 & 10/ 3/64 \nl $ 1$ & 4.7 & 16 & 25 & 14.5 & UGC00685 & 13.81 & 14.39 & 0.58 & 0.040 & 57.0 & 10/ 4/64 \nl $ 1$ & 6.8 & 2 & 18 & 15.7 & IC1629 & 14.75 & 15.90 & 1.15 & -0.118 & 17.5 & 10/ 3/64 \nl $ 1$ &13.4 & 4 & 55 & 13.9 & NGC0455 & 13.02 & 13.97 & 0.95 & -0.151 & 39.0 & 10/25/65 \nl $ $ & & & & & & 12.88 & 13.77 & 0.89 & -0.049 & 57.0 & \nl $ $ & & & & & & 12.71 & 13.68 & 0.97 & 0.059 & 84.5 & \nl $ 1$ &14.1 & 16 & 08 & 14.7 & $\cdots$ & 13.94 & 14.76 & 0.82 & -0.032 & 38.0 & 10/ 4/64 \nl $ 1$ &16.3 & 16 & 03 & 15.2 & NGC0463 & 14.40 & 15.48 & 1.08 & -0.054 & 25.5 & 10/ 4/64 \nl $ 1$ &18.0 & 18 & 15 & 15.6 & $\cdots$ & 15.28 & 15.80 & 0.52 & -0.007 & 25.5 & 10/ 4/64 \nl $ 1$ &20.6 & -0 & 54 & 15.2 & UGC00928 & 14.43 & 15.35 & 0.92 & -0.075 & 25.5 & 10/ 3/64 \nl $ $ & & & & & & 14.31 & 15.40 & 1.09 & -0.067 & 25.5 & 10/20/65 \nl $ $ & & & & & & 14.21 & 15.23 & 1.02 & 0.035 & 38.0 & \nl $ 1$ &20.7 & 9 & 10 & 14.7 & NGC0509 & 13.83 & 14.62 & 0.79 & -0.045 & 39.0 & 10/25/65 \nl $ $ & & & & & & 13.62 & 14.45 & 0.83 & 0.048 & 57.0 & \nl $ $ & & & & & & 13.64 & 14.40 & 0.76 & 0.148 & 84.5 & \nl $ 1$ &22.3 & 15 & 35 & 15.4 & $\cdots$ & 15.21 & 15.54 & 0.33 & -0.045 & 25.5 & 10/ 4/64 \nl $ 1$ &22.6 & 2 & 02 & 15.5 & UGC00981 & 15.05 & 15.65 & 0.60 & -0.029 & 25.5 & 10/ 3/64 \nl $ 1$ &23.0 & -1 & 45 & 14.8 & UGC00996 & 14.26 & 15.29 & 1.03 & -0.084 & 25.5 & 10/ 3/64 \nl $ 1$ &23.1 & 0 & 55 & 15.4 & $\cdots$ & 14.92 & 15.47 & 0.55 & -0.056 & 25.5 & 10/20/65 \nl $ $ & & & & & & 14.84 & 15.28 & 0.44 & 0.041 & 38.0 & \nl $ 1$ &24.8 & 18 & 55 & 13.8 & UGC01032 & 13.78 & 14.49 & 0.71 & -0.225 & 25.5 & 10/ 4/64 \nl $ 1$ &26.2 & 2 & 10 & 15.0 & IC0123 & 14.42 & 15.36 & 0.94 & -0.073 & 25.5 & 10/ 3/64 \nl $ 1$ &26.4 & -0 & 49 & 14.0 & UGC01062 & 13.21 & 14.25 & 1.04 & -0.113 & 38.0 & 10/ 3/64 \nl $ 1$ &29.1 & -1 & 11 & 14.2 & NGC0585 & 13.53 & 14.58 & 1.05 & -0.207 & 25.5 & 10/20/65 \nl $ $ & & & & & & 13.32 & 14.39 & 1.07 & -0.090 & 38.0 & \nl $ 1$ &30.0 & 18 & 04 & 14.3 & UGC01104 & 14.03 & 14.50 & 0.47 & -0.072 & 38.0 & 10/ 4/64 \nl $ 1$ &30.9 & 12 & 19 & 14.5 & IC1715 & 14.27 & 14.72 & 0.45 & -0.038 & 38.0 & 10/ 4/64 \nl $ 1$ &35.1 & -0 & 12 & 15.5 & UGC01159 & 15.29 & 15.82 & 0.53 & -0.004 & 25.5 & 10/20/65 \nl $ $ & & & & & & 15.09 & 15.79 & 0.70 & 0.107 & 38.0 & \nl $ 1$ &35.5 & 20 & 10 & 15.5 & $\cdots$ & 15.21 & 15.88 & 0.67 & 0.005 & 25.5 & 10/ 4/64 \nl $ 1$ &40.3 & 13 & 23 & 12.8 & NGC0660 & 12.04 & 13.14 & 1.10 & -0.152 & 57.0 & 10/ 4/64 \nl $ 1$ &41.6 & 17 & 13 & 13.6 & UGC01219 & 13.33 & 14.05 & 0.72 & -0.007 & 57.0 & 10/ 4/64 \nl $ 1$ &42.3 & 10 & 10 & 13.5 & NGC0665 & 12.40 & 13.51 & 1.11 & -0.090 & 57.0 & 10/ 4/64 \nl $ 1$ &44.3 & 12 & 52 & 14.3 & NGC0671 & 13.82 & 14.67 & 0.85 & -0.191 & 25.5 & 10/ 4/64 \nl $ 1$ &46.3 & 12 & 57 & 14.6 & UGC01271 & 13.69 & 14.68 & 0.99 & -0.189 & 25.5 & 10/ 4/64 \nl $ 1$ &46.5 & 20 & 27 & 13.8 & IC0163 & 13.52 & 14.09 & 0.57 & -0.140 & 38.0 & 10/ 4/64 \nl $ 1$ &48.3 & 13 & 03 & 15.1 & UGC01312 & 14.71 & 15.40 & 0.69 & -0.067 & 25.5 & 10/ 4/64 \nl $ 1$ &51.5 & 17 & 51 & 14.9 & UGC01369 & 14.40 & 14.61 & 0.21 & -0.055 & 38.0 & 10/ 4/64 \nl $ 1$ &51.8 & 39 & 08 & 13.8 & NGC0721 & 12.68\tablenotemark{e} & 13.36\tablenotemark{e} & 0.68 & -0.114 & 57.0 & 9/11/64 \nl $ 1$ &52.8 & 21 & 05 & 15.1 & UGC01396 & 14.40 & 15.40 & 1.00 & -0.207 & 17.5 & 10/ 4/64 \nl $ 2$ &22.7 & 20 & 10 & 15.3 & IC1797 & 14.78 & 15.79 & 1.01 & -0.008 & 25.5 & 10/ 4/64 \nl $ 2$ &26.4 & 0 & 09 & 14.6 & UGC01962 & 13.80 & 14.51 & 0.71 & -0.071 & 38.0 & 10/ 3/64 \nl $ 2$ &30.1 & 0 & 03 & 14.3 & UGC02018 & 13.50 & 14.50 & 1.00 & -0.072 & 38.0 & 10/ 3/64 \nl $ 2$ &30.1 & 0 & 24 & 14.4 & UGC02019 & 14.40 & 14.82 & 0.42 & -0.164 & 25.5 & 10/ 3/64 \nl $ 2$ &31.2 & 20 & 45 & 12.9 & NGC0976 & 12.66 & 13.46 & 0.80 & -0.257 & 38.0 & 10/ 4/64 \nl $ 2$ &32.6 & 19 & 43 & 15.6 & UGC02071 & 14.96 & 15.66 & 0.70 & -0.027 & 25.5 & 10/ 4/64 \nl $ 2$ &34.6 & 20 & 53 & 13.5 & NGC0992 & 13.49 & 14.17 & 0.68 & -0.289 & 25.5 & 10/ 4/64 \nl $ 2$ &35.4 & 1 & 28 & 15.0 & UGC02121 & 14.38 & 14.90 & 0.52 & -0.012 & 38.0 & 10/ 3/64 \nl $ 2$ &35.6 & -1 & 32 & 13.5 & NGC1015 & 13.08 & 13.99 & 0.91 & -0.327 & 25.5 & 10/ 3/64 \nl $ 2$ &37.7 & 19 & 05 & 13.5 & NGC1036 & 13.54 & 14.10 & 0.56 & -0.304 & 25.5 & 10/ 4/64 \nl $ 2$ &39.1 & 18 & 49 & 15.1 & IC1832 & 14.44 & 15.59 & 1.15 & -0.038 & 25.5 & 10/ 4/64 \nl $ 2$ &39.4 & 18 & 00 & 14.6 & NGC1054 & 14.13 & 14.86 & 0.73 & -0.156 & 25.5 & 10/ 4/64 \nl $ 2$ &41.4 & 5 & 13 & 14.9 & $\cdots$ & 14.46 & 14.86 & 0.40 & -0.009 & 39.0 & 1/13/66 \nl $ $ & & & & & & 14.02 & 14.53 & 0.51 & 0.059 & 57.0 & \nl $ $ & & & & & & 13.46 & 14.08 & 0.62 & 0.110 & 84.5 & \nl $ 2$ &42.1 & 5 & 08 & 15.0 & $\cdots$ & 14.95 & 15.46 & 0.51 & -0.196 & 17.5 & 1/13/66 \nl $ $ & & & & & & 14.88 & 15.50 & 0.62 & -0.045 & 26.0 & \nl $ $ & & & & & & 14.88 & 15.34 & 0.46 & 0.057 & 39.0 & \nl $ 2$ &45.0 & 4 & 26 & 14.2 & NGC1095 & 14.14 & 14.76 & 0.62 & -0.167 & 26.0 & 1/13/66 \nl $ $ & & & & & & 13.96 & 14.54 & 0.58 & -0.057 & 39.0 & \nl $ $ & & & & & & 13.94 & 14.47 & 0.53 & 0.051 & 57.0 & \nl $ 2$ &46.7 & 7 & 54 & 14.1 & NGC1107 & 13.39 & 14.67 & 1.28 & -0.183 & 26.0 & 1/13/66 \nl $ $ & & & & & & 13.18 & 14.42 & 1.24 & -0.076 & 39.0 & \nl $ $ & & & & & & 12.90 & 14.19 & 1.29 & 0.013 & 57.0 & \nl $ $ & & & & & & 12.69 & 13.90 & 1.21 & 0.088 & 84.5 & \nl $ $ & & & & & & 12.74 & 13.75 & 1.01 & 0.173 & 126.5 & \nl $ 2$ &54.0 & 7 & 08 & 14.8 & UGC02419 & 14.15 & 14.86 & 0.71 & -0.149 & 26.0 & 1/13/66 \nl $ $ & & & & & & 14.05 & 15.00 & 0.95 & 0.011 & 39.0 & \nl $ $ & & & & & & 13.88 & 15.03 & 1.15 & 0.121 & 57.0 & \nl $ 3$ & 5.6 & 20 & 35 & 15.1 & UGC02553 & 14.19 & 15.04 & 0.85 & 0.008 & 38.0 & 10/ 4/64 \nl $ 3$ & 5.8 & 3 & 55 & 14.0 & NGC1218 & 13.50 & 14.90\tablenotemark{e} & 1.40 & -0.004 & 39.0 & 1/13/66 \nl $ $ & & & & & & 13.22 & 14.29 & 1.07 & 0.026 & 57.0 & \nl $ $ & & & & & & 13.11 & 14.19 & 1.08 & 0.123 & 84.5 & \nl $ $ & & & & & & 13.08 & 14.29 & 1.21 & 0.230 & 126.5 & \nl $ 3$ & 5.9 & 1 & 57 & 13.5 & NGC1219 & 13.20 & 14.01 & 0.81 & -0.154 & 38.0 & 10/ 3/64 \nl $ 3$ & 6.6 & 15 & 55 & 15.7 & $\cdots$ & 14.14 & 15.30 & 1.16 & -0.083 & 25.5 & 10/ 4/64 \nl $ 3$ & 9.0 & -0 & 55 & 15.7 & $\cdots$ & 15.74 & 16.10 & 0.36 & 0.035 & 25.5 & 10/ 3/64 \nl $ 3$ & 9.2 & -0 & 35 & 14.4 & UGC02585 & 13.93 & 14.79 & 0.86 & -0.169 & 25.5 & 10/ 3/64 \nl $ 3$ & 9.6 & 19 & 03 & 15.1 & $\cdots$ & 14.27 & 15.21 & 0.94 & -0.097 & 25.5 & 10/ 4/64 \nl $ 3$ &10.2 & 4 & 31 & 14.0 & IC0302 & 13.78 & 14.76 & 0.98 & -0.024 & 39.0 & 1/13/66 \nl $ $ & & & & & & 13.43 & 14.30 & 0.87 & 0.028 & 57.0 & \nl $ $ & & & & & & 13.42 & 14.18 & 0.76 & 0.011 & 57.0 & \nl $ $ & & & & & & 13.46 & 14.22 & 0.76 & 0.127 & 84.5 & \nl $ 3$ &11.4 & 16 & 18 & 15.0 & UGC02602 & 14.35 & 15.03 & 0.68 & -0.127 & 25.5 & 10/ 4/64 \nl $ 3$ &15.4 & -0 & 20 & 13.9 & NGC1280 & 13.54 & 14.26 & 0.72 & -0.111 & 38.0 & 10/ 3/64 \nl $ 3$ &16.5 & 18 & 01 & 15.7 & $\cdots$ & 15.38 & 16.09 & 0.71 & 0.034 & 25.5 & 10/ 4/64 \nl $ 3$ &17.5 & 1 & 11 & 15.4 & $\cdots$ & 14.44 & 15.31 & 0.87 & 0.045 & 38.0 & 10/ 3/64 \nl $ 3$ &18.8 & -2 & 30 & 14.8 & NGC1305 & 13.36 & 14.43 & 1.07 & -0.083 & 38.0 & 10/ 3/64 \nl $ 3$ &20.2 & -0 & 01 & 15.0 & $\cdots$ & 14.35 & 15.00 & 0.65 & 0.003 & 38.0 & 10/ 3/64 \nl $ 3$ &21.2 & 16 & 00 & 14.8 & $\cdots$ & 14.64 & 15.29 & 0.65 & -0.084 & 25.5 & 10/ 4/64 \nl $ 3$ &28.8 & 4 & 12 & 15.0 & NGC1349 & 14.20 & 15.30 & 1.10 & -0.076 & 26.0 & 1/13/66 \nl $ $ & & & & & & 13.91 & 15.10 & 1.19 & 0.024 & 39.0 & \nl $ $ & & & & & & 13.97 & 14.83 & 0.86 & 0.097 & 57.0 & \nl $ 3$ &36.0 & 20 & 15 & 15.1 & $\cdots$ & 14.98 & 15.60 & 0.62 & -0.036 & 25.5 & 10/ 4/64 \nl $ 3$ &36.4 & 15 & 40 & 15.6 & NGC1384 & 14.56 & 15.35 & 0.79 & -0.216 & 17.5 & 10/ 4/64 \nl $ 3$ &37.9 & 17 & 35 & 14.6 & IC1977 & 14.04 & 14.94 & 0.90 & -0.142 & 25.5 & 10/ 4/64 \nl $ 3$ &39.2 & 15 & 50 & 15.7 & $\cdots$ & 15.01 & 16.24 & 1.23 & -0.063 & 17.5 & 10/ 4/64 \nl $ 3$ &51.4 & 15 & 47 & 15.3 & $\cdots$ & 14.57 & 15.47 & 0.90 & -0.056 & 25.5 & 10/ 9/64 \nl $ 3$ &55.3 & 18 & 26 & 15.5 & NGC1488 & 15.24 & 15.97 & 0.73 & 0.017 & 25.5 & 10/ 4/64 \nl $ 3$ &59.7 & 21 & 25 & 15.7 & $\cdots$ & 14.31 & 15.68 & 1.37 & -0.156 & 17.5 & 9/10/64 \nl $ $ & & & & & & 14.36 & 15.58 & 1.22 & -0.174 & 17.5 & 9/11/64 \nl $ $ & & & & & & 14.27 & 15.47 & 1.20 & -0.194 & 17.5 & 10/ 4/64 \nl $ 4$ & 0.0 & 21 & 20 & 15.5 & $\cdots$ & 14.83 & 16.00 & 1.17 & 0.021 & 25.5 & 10/ 4/64 \nl $ 4$ & 0.8 & 19 & 45 & 15.3 & IC0358 & 14.40 & 15.55 & 1.15 & -0.044 & 25.5 & 10/ 4/64 \nl $ 4$ &28.5 & -2 & 07 & 14.9 & $\cdots$ & 14.56 & 14.87 & 0.31 & -0.155 & 25.5 & 10/ 3/64 \nl $ 4$ &28.5 & 7 & 31 & 14.6 & NGC1590 & 13.94 & 14.69 & 0.75 & -0.034 & 39.0 & 1/12/66 \nl $ $ & & & & & & 13.79 & 14.60 & 0.81 & 0.068 & 57.0 & \nl $ $ & & & & & & 14.03 & 14.76 & 0.73 & 0.188 & 84.5 & \nl $ 4$ &28.5 & 8 & 24 & 14.8 & $\cdots$ & 14.30 & 14.88 & 0.58 & -0.146 & 26.0 & 1/12/66 \nl $ $ & & & & & & 14.31 & 14.81 & 0.50 & -0.017 & 39.0 & \nl $ $ & & & & & & 14.19 & 14.84 & 0.65 & 0.098 & 57.0 & \nl $ 4$ &29.3 & 6 & 40 & 14.9 & $\cdots$ & 14.26\tablenotemark{a} & 15.00\tablenotemark{a} & 0.74 & -0.125 & 26.0 & 1/12/66 \nl $ $ & & & & & & 14.38 & 15.01 & 0.63 & 0.012 & 39.0 & \nl $ 4$ &29.6 & 16 & 32 & 15.7 & IC0374 & 14.31 & 15.52 & 1.21 & -0.048 & 25.5 & 10/ 4/64 \nl $ 4$ &33.0 & 19 & 50 & 15.0 & NGC1615 & 13.86\tablenotemark{e} & 14.61\tablenotemark{e} & 0.75 & -0.202 & 25.5 & 10/ 4/64 \nl $ 4$ &33.1 & 2 & 09 & 15.6 & $\cdots$ & 14.97 & 15.76 & 0.79 & -0.142 & 17.5 & 9/20/63 \nl $ $ & & & & & & 14.97 & 15.72 & 0.75 & -0.149 & 17.5 & 9/10/64 \nl $ 4$ &36.2 & 2 & 44 & 15.1 & $\cdots$ & 14.12 & 14.99 & 0.87 & -0.134 & 25.5 & 10/ 3/64 \nl $ 4$ &37.2 & 6 & 57 & 14.8 & $\cdots$ & 13.83 & 14.66 & 0.83 & -0.039 & 39.0 & 1/12/66 \nl $ $ & & & & & & 13.71 & 14.53 & 0.82 & 0.059 & 57.0 & \nl $ 4$ &37.5 & -0 & 40 & 13.5 & NGC1635 & 12.95 & 13.82 & 0.87 & -0.365 & 25.5 & 10/ 3/64 \nl $ 4$ &39.2 & -1 & 24 & 14.4 & $\cdots$ & 13.86 & 14.56 & 0.70 & -0.211 & 25.5 & 10/ 3/64 \nl $ 4$ &49.1 & 6 & 45 & 15.7 & $\cdots$ & 14.72 & 15.51 & 0.79 & -0.050 & 25.5 & 10/17/63 \nl $ $ & & & & & & 15.08 & 15.80 & 0.72 & -0.007 & 25.5 & 9/11/64 \nl $ 4$ &51.3 & 1 & 36 & 15.7 & $\cdots$ & 14.79 & 15.86 & 1.07 & -0.125 & 17.5 & 9/20/63 \nl $ $ & & & & & & 14.85 & 15.53 & 0.68 & -0.183 & 17.5 & 9/11/64 \nl $ 4$ &51.7 & 3 & 59 & 15.2 & $\cdots$ & 14.83 & 15.36 & 0.53 & -0.066 & 26.0 & 1/12/66 \nl $ $ & & & & & & 14.60 & 15.18 & 0.58 & 0.035 & 39.0 & \nl $ 4$ &52.0 & 3 & 11 & 13.2 & NGC1691 & 12.81 & 13.63 & 0.82 & -0.400 & 26.0 & 1/12/66 \nl $ $ & & & & & & 12.66 & 13.46 & 0.80 & -0.246 & 39.0 & \nl $ 4$ &55.3 & 5 & 47 & 15.7 & $\cdots$ & 14.93 & 16.05 & 1.12 & -0.094 & 17.5 & 2/18/64 \nl $ $ & & & & & & 15.14 & 16.32 & 1.18 & -0.051 & 17.5 & 9/11/64 \nl $ 4$ &55.5 & 3 & 55 & 15.1 & $\cdots$ & 14.18 & 15.24 & 1.06 & -0.085 & 26.0 & 1/12/66 \nl $ $ & & & & & & 14.22 & 14.95 & 0.73 & 0.004 & 39.0 & \nl $ $ & & & & & & 14.09 & 15.17 & 1.08 & 0.138 & 57.0 & \nl $ 5$ & 6.3 & -0 & 38 & 15.1 & $\cdots$ & 14.36 & 15.37 & 1.01 & -0.072 & 25.5 & 10/ 3/64 \nl $ 5$ & 7.1 & -0 & 18 & 15.6 & $\cdots$ & 14.10 & 15.41 & 1.31 & -0.065 & 25.5 & 10/ 3/64 \nl $ 5$ & 7.5 & 0 & 52 & 15.4 & $\cdots$ & 15.32 & 15.81 & 0.49 & -0.005 & 25.5 & 10/ 3/64 \nl $ 5$ & 7.6 & 0 & 50 & 14.6 & $\cdots$ & 14.00 & 14.78 & 0.78 & -0.171 & 25.5 & 10/ 3/64 \nl $ 5$ & 7.9 & -0 & 47 & 15.7 & $\cdots$ & 14.77 & 15.87 & 1.10 & 0.003 & 25.5 & 10/ 3/64 \nl $ 5$ & 7.9 & 16 & 25 & 15.7 & $\cdots$ & 14.29 & 15.56 & 1.27 & -0.177 & 17.5 & 10/ 4/64 \nl $ 5$ & 8.3 & -2 & 45 & 14.0 & $\cdots$ & 14.30 & 14.75 & 0.45 & -0.176 & 25.5 & 10/ 3/64 \nl $ 5$ & 9.0 & -0 & 38 & 14.7 & $\cdots$ & 13.79 & 14.86 & 1.07 & -0.156 & 25.5 & 10/ 3/64 \nl $ 5$ &11.6 & 1 & 50 & 15.5 & $\cdots$ & 14.06 & 15.17 & 1.11 & 0.026 & 38.0 & 10/ 3/64 \nl $ 7$ & 6.4 & 20 & 43 & 12.6 & NGC2342 & 12.97 & 13.44 & 0.47 & -0.250 & 39.0 & 1/13/66 \nl $ $ & & & & & & 12.64 & 13.34 & 0.70 & -0.118 & 57.0 & \nl $ $ & & & & & & 12.59 & 13.14 & 0.55 & -0.015 & 84.5 & \nl $ 7$ &29.0 & 18 & 27 & 14.9 & NGC2407 & 14.20 & 15.30 & 1.10 & -0.076 & 26.0 & 1/13/66 \nl $ $ & & & & & & 13.91 & 15.10 & 1.19 & 0.024 & 39.0 & \nl $ $ & & & & & & 13.97 & 14.84 & 0.87 & 0.098 & 57.0 & \nl $ 7$ &49.2 & 2 & 57 & 14.7 & $\cdots$ & 13.58\tablenotemark{a,b} & 14.60\tablenotemark{a,b} & 1.02 & -0.374 & 17.5 & 2/18/64 \nl $ 8$ & 0.1 & 16 & 27 & 14.7 & $\cdots$ & 13.81 & 14.92 & 1.11 & -0.139 & 26.0 & 1/13/66 \nl $ $ & & & & & & 13.68 & 14.68 & 1.00 & -0.036 & 39.0 & \nl $ $ & & & & & & 13.69 & 14.64 & 0.95 & 0.073 & 57.0 & \nl $ 8$ & 4.0 & 18 & 53 & 15.0 & $\cdots$ & 14.09\tablenotemark{a,b} & 15.01\tablenotemark{a,b} & 0.92 & -0.284 & 17.5 & 2/18/64 \nl $ 8$ & 5.8 & 18 & 14 & 15.3 & $\cdots$ & 14.14\tablenotemark{a,b} & 15.17\tablenotemark{a,b} & 1.03 & -0.252 & 17.5 & 2/18/64 \nl $10$ &53.0 & 30 & 06 & 15.7 & $\cdots$ & 14.93\tablenotemark{b} & 15.73\tablenotemark{b} & 0.80 & -0.147 & 17.5 & 2/18/64 \nl $11$ & 6.6 & 29 & 50 & 15.0 & $\cdots$ & 14.28\tablenotemark{a,b} & 15.11\tablenotemark{a,b} & 0.83 & -0.264 & 17.5 & 2/18/64 \nl $11$ & 8.0 & 28 & 33 & 15.7 & $\cdots$ & 14.63\tablenotemark{a,b} & 15.64\tablenotemark{a,b} & 1.01 & -0.163 & 17.5 & 2/18/64 \nl $11$ & 8.2 & 27 & 22 & 15.5 & $\cdots$ & 14.94\tablenotemark{a,b} & 16.08\tablenotemark{a,b} & 1.14 & -0.089 & 17.5 & 3/13/64 \nl $11$ &10.5 & 28 & 05 & 14.7 & $\cdots$ & 13.97\tablenotemark{a,b} & 14.97\tablenotemark{a,b} & 1.00 & -0.292 & 17.5 & 2/18/64 \nl $11$ &11.6 & 28 & 25 & 15.6 & $\cdots$ & 15.06\tablenotemark{a,b} & 15.87\tablenotemark{a,b} & 0.81 & -0.123 & 17.5 & 2/18/64 \nl $11$ &11.9 & 30 & 35 & 14.6 & $\cdots$ & 14.25\tablenotemark{a,b} & 14.90\tablenotemark{a,b} & 0.65 & -0.149 & 25.5 & 2/18/64 \nl $11$ &12.2 & 31 & 47 & 15.3 & $\cdots$ & 14.48\tablenotemark{a,b} & 15.48\tablenotemark{a,b} & 1.00 & -0.192 & 17.5 & 2/18/64 \nl $11$ &12.4 & 31 & 18 & 14.4 & $\cdots$ & 13.91\tablenotemark{a,b} & 14.98\tablenotemark{a,b} & 1.07 & -0.290 & 17.5 & 2/18/64 \nl $11$ &12.6 & 27 & 40 & 15.2 & $\cdots$ & 14.82\tablenotemark{a} & 15.54\tablenotemark{a} & 0.72 & -0.181 & 17.5 & 2/18/64 \nl $11$ &14.2 & 32 & 52 & 15.5 & $\cdots$ & 14.52\tablenotemark{a} & 15.54\tablenotemark{a} & 1.02 & -0.181 & 17.5 & 2/18/64 \nl $12$ & 0.8 & 44 & 48 & 11.5 & NGC4051 & 13.14 & 13.75 & 0.61 & -0.929 & 11.5 & 5/12/67 \nl $ $ & & & & & & 13.12 & 13.74 & 0.62 & -0.934 & 11.5 & \nl $ $ & & & & & & 12.69 & 13.36 & 0.67 & -0.726 & 17.5 & \nl $ $ & & & & & & 12.27 & 12.94 & 0.67 & -0.584 & 26.0 & \nl $12$ & 1.6 & 20 & 38 & 14.4 & NGC4066 & 13.40 & 14.35 & 0.95 & -0.244 & 26.0 & 4/ 7/67 \nl $ $ & & & & & & 13.09 & 14.22 & 1.13 & -0.108 & 39.0 & \nl $ $ & & & & & & 13.11 & 14.18 & 1.07 & -0.115 & 39.0 & \nl $ $ & & & & & & 13.13 & 14.07 & 0.94 & -0.004 & 57.0 & \nl $12$ & 2.7 & 21 & 30 & 14.9 & NGC4084 & 13.78 & 14.82 & 1.04 & -0.156 & 26.0 & 4/ 7/67 \nl $ $ & & & & & & 13.64 & 14.59 & 0.95 & -0.049 & 39.0 & \nl $12$ & 6.6 & 31 & 51 & 14.4 & $\cdots$ & 13.62\tablenotemark{a,b} & 14.68\tablenotemark{a,b} & 1.06 & -0.356 & 17.5 & 3/13/64 \nl $12$ & 8.2 & 24 & 00 & 15.7 & $\cdots$ & 14.31 & 15.36 & 1.05 & -0.066 & 26.0 & 4/ 7/67 \nl $ $ & & & & & & 14.07 & 15.18 & 1.11 & 0.035 & 39.0 & \nl $12$ & 9.4 & 27 & 55 & 15.3 & $\cdots$ & 14.16\tablenotemark{b} & 15.17\tablenotemark{b} & 1.01 & -0.104 & 25.5 & 3/13/64 \nl $12$ & 9.7 & 29 & 27 & 12.9 & NGC4169 & 12.47\tablenotemark{a,b} & 13.44\tablenotemark{a,b} & 0.97 & -0.458 & 25.5 & 3/13/64 \nl $12$ &10.3 & 1 & 35 & 12.8 & NGC4179 & 11.42 & 12.36 & 0.94 & -0.514 & 38.0 & 2/18/64 \nl $ $ & & & & & & 11.52 & 12.45 & 0.93 & -0.490 & 38.0 & 5/ 2/65 \nl $ $ & & & & & & 11.38 & 12.32 & 0.94 & -0.311 & 57.0 & \nl $ $ & & & & & & 11.32 & 12.26 & 0.94 & -0.173 & 81.0 & \nl $12$ &11.6 & 32 & 43 & 15.1 & $\cdots$ & 14.21\tablenotemark{a,b} & 15.26\tablenotemark{a,b} & 1.05 & -0.234 & 17.5 & 3/13/64 \nl $12$ &11.8 & 32 & 42 & 14.6 & $\cdots$ & 13.91 & 14.92 & 1.01 & -0.303 & 17.5 & 3/13/64 \nl $12$ &12.1 & -2 & 10 & 14.6 & $\cdots$ & 14.26 & 14.82 & 0.56 & -0.023 & 38.0 & 2/18/64 \nl $ $ & & & & & & 14.30 & 14.82 & 0.52 & -0.164 & 25.5 & 5/ 2/65 \nl $ $ & & & & & & 14.31 & 14.80 & 0.49 & -0.026 & 38.0 & \nl $12$ &13.1 & 27 & 17 & 15.4 & $\cdots$ & 14.76 & 15.75 & 0.99 & -0.144 & 17.5 & 3/13/64 \nl $12$ &14.4 & 13 & 54 & 14.1 & IC3094 & 14.19 & 14.77 & 0.58 & -0.031 & 38.0 & 6/25/63 \nl $12$ &14.6 & 30 & 55 & 15.7 & $\cdots$ & 15.21\tablenotemark{a,b} & 16.02\tablenotemark{a,b} & 0.81 & -0.098 & 17.5 & 3/13/64 \nl $ $ & & & & & & 15.14 & 15.88 & 0.74 & -0.122 & 17.5 & 4/ 3/64 \nl $12$ &15.3 & 11 & 07 & 14.5 & IC3107 & 13.98 & 14.75 & 0.77 & -0.176 & 25.5 & 6/25/63 \nl $12$ &17.2 & 2 & 22 & 14.6 & $\cdots$ & 14.64 & 15.15 & 0.51 & -0.107 & 25.5 & 2/18/64 \nl $12$ &17.2 & 9 & 26 & 15.0 & IC3156 & 14.73 & 15.22 & 0.49 & 0.033 & 38.0 & 6/25/63 \nl $12$ &17.2 & 29 & 00 & 15.5 & $\cdots$ & 14.70\tablenotemark{a,b} & 15.69\tablenotemark{a,b} & 0.99 & -0.154 & 17.5 & 3/13/64 \nl $12$ &17.2 & 29 & 07 & 15.4 & $\cdots$ & 14.80\tablenotemark{a,b} & 15.70\tablenotemark{a,b} & 0.90 & -0.153 & 17.5 & 3/13/64 \nl $12$ &17.3 & 30 & 37 & 14.2 & NGC4272 & 13.75\tablenotemark{a,b} & 14.81\tablenotemark{a,b} & 1.06 & -0.327 & 17.5 & 3/13/64 \nl $12$ &17.4 & 26 & 03 & 14.5 & IC0780 & 13.55 & 14.40 & 0.85 & -0.079 & 39.0 & 4/ 7/67 \nl $ $ & & & & & & 13.29 & 14.36 & 1.07 & 0.036 & 57.0 & \nl $12$ &17.4 & 28 & 40 & 15.6 & $\cdots$ & 14.80\tablenotemark{a,b} & 15.30\tablenotemark{a,b} & 0.50 & -0.226 & 17.5 & 3/13/64 \nl $12$ &17.8 & 29 & 35 & 13.1 & NGC4283 & 12.63\tablenotemark{a,b} & 13.58\tablenotemark{a,b} & 0.95 & -0.422 & 25.5 & 3/13/64 \nl $12$ &18.7 & 28 & 26 & 15.0 & NGC4295 & 14.21\tablenotemark{a,b} & 15.25\tablenotemark{a,b} & 1.04 & -0.236 & 17.5 & 3/13/64 \nl $ $ & & & & & & 14.13 & 15.25 & 1.12 & -0.236 & 17.5 & 4/ 3/64 \nl $12$ &19.4 & 30 & 20 & 14.3 & NGC4308 & 13.78\tablenotemark{a} & 14.64\tablenotemark{a} & 0.86 & -0.365 & 17.5 & 3/13/64 \nl $ $ & & & & & & 13.70 & 14.54 & 0.84 & -0.388 & 17.5 & 4/ 3/64 \nl $12$ &21.3 & 27 & 40 & 15.3 & IC3262 & 14.72 & 15.70 & 0.98 & -0.153 & 17.5 & 3/13/64 \nl $12$ &23.2 & 0 & 52 & 13.4 & NGC4385 & 13.13 & 13.71 & 0.58 & -0.391 & 25.5 & 2/18/64 \nl $ $ & & & & & & 13.29 & 13.75 & 0.46 & -0.382 & 25.5 & 5/ 2/65 \nl $ $ & & & & & & 12.84 & 13.42 & 0.58 & -0.265 & 38.0 & \nl $ $ & & & & & & 12.72 & 13.30 & 0.58 & -0.124 & 57.0 & \nl $12$ &24.3 & -0 & 35 & 14.2 & NGC4418 & 13.37 & 14.21 & 0.84 & -0.280 & 25.5 & 2/18/64 \nl $ $ & & & & & & 13.38 & 14.06 & 0.68 & -0.145 & 38.0 & 5/ 2/65 \nl $ $ & & & & & & 13.30 & 13.98 & 0.68 & -0.017 & 57.0 & \nl $12$ &25.1 & 31 & 13 & 15.3 & $\cdots$ & 15.41\tablenotemark{a,b} & 15.81\tablenotemark{a,b} & 0.40 & -0.133 & 17.5 & 3/13/64 \nl $ $ & & & & & & 14.97 & 15.32 & 0.35 & -0.222 & 17.5 & 4/ 3/64 \nl $12$ &26.4 & 8 & 08 & 15.2 & $\cdots$ & 14.85 & 15.33 & 0.48 & -0.078 & 25.5 & 6/24/63 \nl $12$ &28.0 & 19 & 56 & 15.0 & IC3436 & 14.20\tablenotemark{b} & 14.98\tablenotemark{b} & 0.78 & -0.136 & 25.5 & 4/ 3/64 \nl $12$ &32.3 & 18 & 05 & 15.2 & $\cdots$ & 14.40\tablenotemark{b} & 15.35\tablenotemark{b} & 0.95 & -0.075 & 25.5 & 4/ 3/64 \nl $12$ &32.6 & 0 & 03 & 14.0 & NGC4541 & 13.33 & 14.01 & 0.68 & -0.154 & 38.0 & 2/18/64 \nl $12$ &33.3 & 27 & 12 & 14.4 & NGC4556 & 13.64\tablenotemark{b} & 14.59\tablenotemark{b} & 0.95 & -0.206 & 25.5 & 4/ 3/64 \nl $12$ &33.6 & 27 & 11 & 15.7 & IC3561 & 14.88\tablenotemark{b} & 15.67\tablenotemark{b} & 0.79 & -0.158 & 17.5 & 4/ 3/64 \nl $12$ &34.5 & 2 & 05 & 15.5 & $\cdots$ & 14.55 & 15.63 & 1.08 & -0.165 & 17.5 & 2/18/64 \nl $ $ & & & & & & 14.73 & 15.75 & 1.02 & -0.144 & 17.5 & 5/ 2/65 \nl $ $ & & & & & & 14.42 & 15.53 & 1.11 & -0.047 & 25.5 & \nl $ $ & & & & & & 14.25 & 15.37 & 1.12 & 0.053 & 38.0 & \nl $12$ &35.1 & 8 & 50 & 15.1 & $\cdots$ & 14.77 & 15.18 & 0.41 & -0.102 & 25.5 & 6/25/63 \nl $12$ &39.6 & 12 & 52 & 14.7 & IC0810 & 13.96 & 14.81 & 0.85 & -0.025 & 38.0 & 6/25/63 \nl $12$ &40.2 & 20 & 12 & 13.7 & NGC4635 & 13.49 & 13.94 & 0.45 & -0.156 & 39.0 & 4/ 9/67 \nl $ $ & & & & & & 13.27 & 13.74 & 0.47 & -0.053 & 57.0 & \nl $ $ & & & & & & 13.04 & 13.53 & 0.49 & 0.039 & 84.5 & \nl $12$ &40.4 & 3 & 57 & 15.1 & $\cdots$ & 14.23 & 14.93 & 0.70 & -0.144 & 25.5 & 5/21/63 \nl $12$ &40.6 & 3 & 51 & 15.4 & $\cdots$ & 15.36 & 15.88 & 0.52 & 0.005 & 25.5 & 5/21/63 \nl $12$ &42.6 & 21 & 27 & 15.3 & $\cdots$ & 14.53\tablenotemark{b} & 15.08\tablenotemark{b} & 0.55 & -0.270 & 17.5 & 4/ 3/64 \nl $12$ &43.2 & 19 & 27 & 15.0 & IC3745 & 14.34\tablenotemark{b} & 15.19\tablenotemark{b} & 0.85 & -0.248 & 17.5 & 4/ 3/64 \nl $12$ &44.7 & 19 & 44 & 13.8 & NGC4685 & 13.30 & 14.11 & 0.81 & -0.496 & 17.5 & 4/ 3/64 \nl $ $ & & & & & & 13.38 & 14.24 & 0.86 & -0.266 & 26.0 & 4/ 9/67 \nl $ $ & & & & & & 13.42 & 14.43 & 1.01 & -0.074 & 39.0 & \nl $12$ &45.6 & -3 & 03 & 12.0 & NGC4691 & 11.68 & 12.15 & 0.47 & -0.574 & 38.0 & 5/ 2/65 \nl $ $ & & & & & & 11.43 & 11.94 & 0.51 & -0.397 & 57.0 & \nl $12$ &46.6 & 17 & 17 & 15.5 & $\cdots$ & 15.10 & 15.43 & 0.33 & -0.201 & 17.5 & 4/ 9/67 \nl $ $ & & & & & & 14.60 & 15.29 & 0.69 & -0.078 & 26.0 & \nl $ $ & & & & & & 14.40 & 15.17 & 0.77 & 0.034 & 39.0 & \nl $12$ &46.7 & 17 & 58 & 15.7 & $\cdots$ & 15.11\tablenotemark{b} & 16.01\tablenotemark{b} & 0.90 & -0.100 & 17.5 & 4/ 3/64 \nl $12$ &49.0 & 14 & 03 & 15.4 & $\cdots$ & 14.81 & 15.83 & 1.02 & -0.003 & 25.5 & 6/25/63 \nl $12$ &49.0 & 18 & 20 & 15.3 & $\cdots$ & 14.93 & 15.38 & 0.45 & -0.211 & 17.5 & 4/ 3/64 \nl $12$ &49.5 & 16 & 33 & 15.0 & IC0827 & 14.32 & 15.01 & 0.69 & -0.123 & 26.0 & 4/ 9/67 \nl $ $ & & & & & & 14.29 & 15.04 & 0.75 & 0.016 & 39.0 & \nl $12$ &57.9 & 13 & 57 & 15.4 & $\cdots$ & 15.54 & 15.83 & 0.29 & -0.003 & 25.5 & 6/25/63 \nl $13$ & 2.0 & 8 & 15 & 15.6 & $\cdots$ & 15.24 & 16.19 & 0.95 & -0.071 & 17.5 & 5/21/63 \nl $13$ & 5.4 & 18 & 41 & 14.4 & NGC4978 & 13.57 & 14.68 & 1.11 & -0.181 & 26.0 & 4/ 9/67 \nl $ $ & & & & & & 13.51 & 14.56 & 1.05 & -0.054 & 39.0 & \nl $ $ & & & & & & 13.36 & 14.41 & 1.05 & 0.043 & 57.0 & \nl $13$ & 6.2 & -0 & 32 & 14.6 & $\cdots$ & 13.84 & 14.71 & 0.87 & -0.183 & 25.5 & 5/20/63 \nl $13$ & 6.3 & -0 & 31 & 15.1 & $\cdots$ & 14.51 & 15.61 & 1.10 & -0.035 & 25.5 & 5/20/63 \nl $13$ & 7.5 & 11 & 43 & 15.5 & $\cdots$ & 15.77 & 16.42 & 0.65 & 0.077 & 25.5 & 6/25/63 \nl $13$ & 8.8 & 0 & 01 & 14.3 & $\cdots$ & 13.93 & 14.76 & 0.83 & -0.338 & 17.5 & 5/20/63 \nl $13$ & 9.6 & 3 & 28 & 15.0 & NGC5013 & 14.90 & 15.50 & 0.60 & -0.188 & 17.5 & 5/21/63 \nl $13$ &10.2 & 5 & 00 & 14.5 & NGC5019 & 14.29 & 14.43 & 0.14 & -0.083 & 38.0 & 5/21/63 \nl $13$ &11.8 & -1 & 52 & 15.7 & $\cdots$ & 15.55 & 16.40 & 0.85 & -0.039 & 17.5 & 5/20/63 \nl $13$ &13.2 & 3 & 08 & 14.7 & NGC5050 & 13.73 & 14.57 & 0.84 & -0.209 & 25.5 & 5/21/63 \nl $13$ &13.5 & 18 & 01 & 15.7 & $\cdots$ & 16.04 & 16.43 & 0.39 & 0.084 & 26.0 & 4/ 9/67 \nl $ $ & & & & & & 15.10 & 15.85 & 0.75 & 0.121 & 39.0 & \nl $13$ &14.3 & -2 & 48 & 15.5 & $\cdots$ & 15.18 & 15.97 & 0.79 & -0.107 & 17.5 & 5/20/63 \nl $13$ &19.6 & -2 & 50 & 15.5 & $\cdots$ & 14.82 & 15.92 & 1.10 & 0.010 & 25.5 & 5/20/63 \nl $13$ &20.9 & 6 & 39 & 14.4 & NGC5118 & 14.02 & 14.52 & 0.50 & -0.219 & 25.5 & 6/24/63 \nl $13$ &21.0 & 14 & 02 & 15.5 & $\cdots$ & 14.93 & 15.68 & 0.75 & -0.024 & 25.5 & 6/25/63 \nl $13$ &27.2 & 13 & 34 & 14.7 & NGC5181 & 13.79 & 14.79 & 1.00 & -0.169 & 25.5 & 6/25/63 \nl $13$ &29.5 & 20 & 15 & 13.8 & $\cdots$ & 13.72 & 14.16 & 0.44 & -0.282 & 26.0 & 4/ 9/67 \nl $ $ & & & & & & 13.54 & 14.04 & 0.50 & -0.139 & 39.0 & \nl $ $ & & & & & & 13.54 & 14.10 & 0.56 & 0.000 & 57.0 & \nl $13$ &31.5 & 5 & 00 & 15.3 & $\cdots$ & 14.89 & 15.45 & 0.56 & -0.059 & 25.5 & 6/24/63 \nl $13$ &36.7 & 9 & 09 & 15.7 & $\cdots$ & 15.91 & 16.21 & 0.30 & 0.050 & 25.5 & 6/25/63 \nl $13$ &40.0 & 3 & 19 & 15.7 & $\cdots$ & 15.66 & 16.17 & 0.51 & 0.045 & 25.5 & 6/24/63 \nl $13$ &44.4 & 11 & 53 & 15.1 & $\cdots$ & 15.09 & 15.68 & 0.59 & -0.024 & 25.5 & 6/25/63 \nl $13$ &48.0 & 3 & 26 & 14.8 & IC0943 & 14.23 & 14.90 & 0.67 & -0.149 & 25.5 & 6/24/63 \nl $13$ &54.7 & 12 & 15 & 14.9 & $\cdots$ & 14.53 & 15.28 & 0.75 & -0.086 & 25.5 & 6/25/63 \nl $13$ &55.5 & 7 & 25 & 15.2 & $\cdots$ & 14.83 & 15.21 & 0.38 & 0.142 & 57.0 & 6/24/63 \nl $13$ &58.7 & 8 & 51 & 15.3 & $\cdots$ & 14.57 & 15.61 & 1.04 & -0.035 & 25.5 & 6/25/63 \nl $14$ & 1.7 & -1 & 24 & 15.7 & $\cdots$ & 15.55 & 16.54 & 0.99 & -0.018 & 17.5 & 5/20/63 \nl $14$ & 4.4 & -1 & 21 & 15.1 & $\cdots$ & 14.73 & 15.55 & 0.82 & -0.179 & 17.5 & 5/20/63 \nl $14$ & 6.1 & -0 & 55 & 14.1 & IC0976 & 13.40 & 14.18 & 0.78 & -0.287 & 25.5 & 5/20/63 \nl $14$ &10.1 & 13 & 32 & 14.1 & NGC5505 & 13.72 & 14.33 & 0.61 & -0.099 & 38.0 & 6/25/63 \nl $14$ &10.7 & -2 & 59 & 13.6 & NGC5506 & 12.41 & 13.34 & 0.93 & -0.118 & 57.0 & 5/20/63 \nl $14$ &12.6 & 25 & 33 & 13.4 & NGC5523 & 12.98 & 13.57 & 0.59 & -0.235 & 38.0 & 7/ 5/64 \nl $14$ &15.0 & 8 & 17 & 15.5 & $\cdots$ & 14.96 & 15.99 & 1.03 & -0.103 & 17.5 & 6/24/63 \nl $14$ &15.7 & 25 & 22 & 13.1 & NGC5548 & 13.08 & 13.82 & 0.74 & -0.365 & 25.5 & 7/ 5/64 \nl $14$ &17.5 & 12 & 12 & 15.7 & $\cdots$ & 16.09 & 16.65 & 0.56 & 0.210 & 39.0 & 6/25/63 \nl $14$ &18.4 & 22 & 10 & 14.7 & $\cdots$ & 13.90 & 14.49 & 0.59 & -0.074 & 38.0 & 7/ 5/64 \nl $14$ &19.4 & 8 & 07 & 15.4 & $\cdots$ & 14.68 & 15.75 & 1.07 & -0.144 & 17.5 & 6/24/63 \nl $14$ &19.6 & 23 & 45 & 15.6 & $\cdots$ & 14.58 & 15.47 & 0.89 & -0.194 & 17.5 & 7/ 5/64 \nl $14$ &23.2 & 25 & 45 & 15.1 & IC4418 & 14.36 & 15.26 & 0.90 & -0.234 & 17.5 & 7/ 5/64 \nl $14$ &30.8 & 14 & 02 & 15.5 & $\cdots$ & 15.36 & 16.18 & 0.82 & 0.153 & 38.0 & 6/25/63 \nl $14$ &31.1 & 20 & 13 & 15.0 & $\cdots$ & 14.64 & 15.26 & 0.62 & -0.082 & 26.0 & 4/ 9/67 \nl $ $ & & & & & & 14.50 & 15.33 & 0.83 & 0.055 & 39.0 & \nl $14$ &33.8 & 22 & 01 & 14.6 & $\cdots$ & 13.42 & 14.48 & 1.06 & -0.227 & 25.5 & 7/ 5/64 \nl $14$ &36.6 & 20 & 43 & 14.5 & NGC5702 & 13.78 & 14.83 & 1.05 & -0.322 & 17.5 & 7/ 5/64 \nl $14$ &36.9 & 20 & 15 & 14.3 & NGC5710 & 13.82 & 14.84 & 1.02 & -0.153 & 26.0 & 4/ 9/67 \nl $ $ & & & & & & 13.44 & 14.43 & 0.99 & -0.074 & 39.0 & \nl $14$ &37.1 & 3 & 22 & 14.9 & $\cdots$ & 13.92 & 14.93 & 1.01 & -0.144 & 25.5 & 6/24/63 \nl $14$ &39.3 & 23 & 09 & 15.3 & $\cdots$ & 14.64 & 15.65 & 1.01 & -0.161 & 17.5 & 7/ 5/64 \nl $14$ &39.7 & 9 & 36 & 15.7 & $\cdots$ & 15.83 & 16.44 & 0.61 & 0.182 & 38.0 & 6/25/63 \nl $14$ &40.3 & 9 & 02 & 15.6 & $\cdots$ & 15.41 & 15.89 & 0.48 & -0.120 & 17.5 & 6/24/63 \nl $14$ &40.7 & 21 & 38 & 15.7 & $\cdots$ & 15.26 & 16.23 & 0.97 & -0.065 & 17.5 & 7/ 5/64 \nl $14$ &44.2 & 16 & 21 & 14.9 & IC4503 & 14.14 & 15.10 & 0.96 & 0.130 & 57.0 & 4/ 3/64 \nl $ $ & & & & & & 14.32 & 15.19 & 0.87 & -0.248 & 17.5 & 5/ 2/65 \nl $ $ & & & & & & 14.15 & 15.16 & 1.01 & -0.105 & 25.5 & \nl $ $ & & & & & & 14.09 & 15.00 & 0.91 & 0.003 & 38.0 & \nl $ $ & & & & & & 14.21 & 15.16 & 0.95 & 0.137 & 57.0 & \nl $14$ &46.8 & 17 & 14 & 14.8 & IC1058 & 14.29 & 15.31 & 1.02 & -0.224 & 17.5 & 5/ 2/65 \nl $ $ & & & & & & 14.24 & 15.20 & 0.96 & -0.246 & 17.5 & \nl $ $ & & & & & & 14.13 & 15.06 & 0.93 & -0.122 & 25.5 & \nl $ $ & & & & & & 13.97 & 14.95 & 0.98 & -0.005 & 38.0 & \nl $ $ & & & & & & 13.99 & 14.84 & 0.85 & 0.098 & 57.0 & \nl $14$ &52.5 & 24 & 17 & 15.2 & $\cdots$ & 14.68 & 15.26 & 0.58 & -0.089 & 25.5 & 7/ 5/64 \nl $14$ &52.6 & 18 & 14 & 13.9 & IC1076 & 13.96 & 14.52 & 0.56 & -0.219 & 25.5 & 4/ 3/64 \nl $ $ & & & & & & 14.07 & 14.59 & 0.52 & -0.206 & 25.5 & 5/ 2/65 \nl $ $ & & & & & & 13.98 & 14.49 & 0.51 & -0.074 & 38.0 & \nl $ $ & & & & & & 13.86 & 14.39 & 0.53 & 0.040 & 57.0 & \nl $14$ &55.0 & 19 & 52 & 14.0 & $\cdots$ & 13.89 & 14.31 & 0.42 & -0.260 & 25.5 & 4/ 3/64 \nl $ $ & & & & & & 13.96 & 14.53 & 0.57 & -0.217 & 25.5 & 5/ 2/65 \nl $ $ & & & & & & 13.79 & 14.34 & 0.55 & -0.098 & 38.0 & \nl $ $ & & & & & & 13.73 & 14.33 & 0.60 & 0.032 & 57.0 & \nl $14$ &57.8 & 10 & 08 & 15.5 & $\cdots$ & 15.57 & 16.12 & 0.55 & 0.038 & 25.5 & 7/ 2/62 \nl $14$ &58.9 & 16 & 58 & 15.7 & $\cdots$ & 15.09 & 16.17 & 1.08 & -0.074 & 17.5 & 4/ 3/64 \nl $ $ & & & & & & 15.25 & 16.18 & 0.93 & -0.073 & 17.5 & 5/ 2/65 \nl $ $ & & & & & & 15.01 & 16.13 & 1.12 & 0.039 & 25.5 & \nl $ $ & & & & & & 15.04 & 16.08 & 1.04 & 0.141 & 38.0 & \nl $14$ &59.6 & 26 & 10 & 13.7 & NGC5827 & 13.25 & 13.90 & 0.65 & -0.173 & 38.0 & 7/ 5/64 \nl $14$ &59.9 & 5 & 51 & 14.6 & $\cdots$ & 13.62 & 14.62 & 1.00 & -0.200 & 25.5 & 6/25/63 \nl $14$ &59.9 & 12 & 07 & 15.0 & $\cdots$ & 14.24 & 15.35 & 1.11 & -0.075 & 25.5 & 6/24/63 \nl $15$ & 3.1 & 8 & 42 & 14.5 & $\cdots$ & 13.83 & 14.49 & 0.66 & -0.225 & 25.5 & 6/24/63 \nl $15$ & 4.1 & 2 & 12 & 14.8 & NGC5848 & 13.80 & 14.66 & 0.86 & -0.193 & 25.5 & 5/20/63 \nl $15$ & 5.2 & 16 & 23 & 15.6 & $\cdots$ & 14.82 & 15.88 & 1.06 & -0.122 & 17.5 & 4/ 3/64 \nl $ $ & & & & & & 14.90 & 15.90 & 1.00 & -0.118 & 17.5 & 5/ 2/65 \nl $ $ & & & & & & 14.76 & 15.94 & 1.18 & 0.013 & 25.5 & \nl $ $ & & & & & & 14.63 & 15.74 & 1.11 & 0.101 & 38.0 & \nl $15$ & 5.2 & 19 & 47 & 13.6 & NGC5857 & 13.02 & 13.81 & 0.79 & -0.190 & 38.0 & 4/ 3/64 \nl $15$ & 5.6 & 14 & 04 & 15.3 & $\cdots$ & 15.30 & 15.81 & 0.51 & -0.005 & 25.5 & 6/24/63 \nl $15$ & 6.1 & 19 & 24 & 15.1 & IC1096 & 14.32 & 15.32 & 1.00 & -0.222 & 17.5 & 4/ 3/64 \nl $15$ & 6.2 & 19 & 22 & 14.7 & IC1097 & 14.79 & 15.47 & 0.68 & -0.194 & 17.5 & 4/ 3/64 \nl $15$ & 7.9 & -1 & 59 & 14.9 & $\cdots$ & 14.16 & 15.29 & 1.13 & -0.084 & 25.5 & 5/20/63 \nl $15$ & 9.5 & -3 & 03 & 15.0 & $\cdots$ & 14.81 & 15.43 & 0.62 & -0.201 & 17.5 & 5/20/63 \nl $15$ &10.1 & 18 & 50 & 15.2 & $\cdots$ & 14.98 & 15.68 & 0.70 & -0.156 & 17.5 & 4/ 3/64 \nl $ $ & & & & & & 15.12 & 15.67 & 0.55 & -0.158 & 17.5 & 5/ 2/65 \nl $ $ & & & & & & 14.85 & 15.57 & 0.72 & -0.041 & 25.5 & \nl $ $ & & & & & & 14.83 & 15.51 & 0.68 & 0.072 & 38.0 & \nl $15$ &15.7 & 5 & 30 & 14.7 & $\cdots$ & 14.45 & 15.01 & 0.56 & 0.004 & 38.0 & 6/25/63 \nl $15$ &15.7 & 13 & 42 & 14.9 & $\cdots$ & 14.19 & 14.96 & 0.77 & -0.139 & 25.5 & 6/24/63 \nl $15$ &17.0 & 11 & 14 & 14.7 & $\cdots$ & 14.51 & 15.07 & 0.56 & 0.126 & 57.0 & 6/24/63 \nl $15$ &18.3 & -2 & 25 & 14.6 & NGC5913 & 13.28 & 14.33 & 1.05 & -0.099 & 38.0 & 5/20/63 \nl $15$ &20.6 & 15 & 11 & 15.0 & $\cdots$ & 14.51 & 15.26 & 0.75 & -0.089 & 25.5 & 4/ 3/64 \nl $ $ & & & & & & 14.45 & 15.22 & 0.77 & -0.096 & 25.5 & 5/ 2/65 \nl $ $ & & & & & & 14.45 & 15.15 & 0.70 & 0.024 & 38.0 & \nl $ $ & & & & & & 14.40 & 15.15 & 0.75 & 0.135 & 57.0 & \nl $15$ &21.2 & 9 & 10 & 15.7 & $\cdots$ & 15.27 & 16.36 & 1.09 & -0.045 & 17.5 & 6/24/63 \nl $15$ &21.8 & 8 & 44 & 15.6 & $\cdots$ & 15.37 & 16.22 & 0.85 & -0.066 & 17.5 & 6/24/63 \nl $15$ &23.2 & 18 & 27 & 14.6 & $\cdots$ & 13.99 & 14.97 & 0.98 & -0.002 & 38.0 & 4/ 3/64 \nl $15$ &30.5 & -1 & 28 & 14.5 & IC1125 & 13.66 & 14.24 & 0.58 & -0.114 & 38.0 & 5/20/63 \nl $15$ &30.8 & 4 & 38 & 15.6 & $\cdots$ & 15.38 & 16.23 & 0.85 & -0.065 & 17.5 & 6/25/63 \nl $15$ &31.7 & 21 & 19 & 14.9 & $\cdots$ & 14.18 & 15.09 & 0.91 & -0.117 & 25.5 & 7/ 5/64 \nl $15$ &31.9 & 23 & 05 & 14.6 & $\cdots$ & 14.21 & 14.90 & 0.69 & -0.149 & 25.5 & 7/ 5/64 \nl $15$ &34.2 & 16 & 46 & 12.2 & NGC5962 & 12.01 & 12.63 & 0.62 & -0.443 & 38.0 & 4/ 3/64 \nl $15$ &35.2 & 9 & 29 & 15.5 & $\cdots$ & 15.38 & 16.42 & 1.04 & -0.036 & 17.5 & 6/24/63 \nl $15$ &35.2 & 20 & 43 & 14.7 & $\cdots$ & 13.71 & 14.59 & 0.88 & -0.058 & 38.0 & 7/ 5/64 \nl $15$ &36.6 & 17 & 12 & 14.8 & NGC5972 & 14.27 & 15.21 & 0.94 & -0.244 & 17.5 & 4/ 3/64 \nl $15$ &36.7 & 10 & 58 & 15.5 & $\cdots$ & 14.95 & 15.97 & 1.02 & -0.274 & 11.5 & 7/ 2162 \nl $15$ &37.9 & 20 & 51 & 14.4 & IC1132 & 13.57 & 14.19 & 0.62 & -0.123 & 38.0 & 7/ 5/64 \nl $15$ &38.2 & 16 & 52 & 15.6 & $\cdots$ & 15.48 & 16.11 & 0.63 & -0.084 & 17.5 & 4/ 3/64 \nl $15$ &38.2 & 17 & 17 & 15.1 & NGC5977 & 14.53 & 15.51 & 0.98 & -0.043 & 26.0 & 4/ 9/67 \nl $ $ & & & & & & 14.21 & 15.28 & 1.07 & 0.049 & 39.0 & \nl $15$ &39.1 & 15 & 57 & 13.3 & NGC5980 & 12.99 & 13.67 & 0.68 & -0.216 & 38.0 & 4/ 3/64 \nl $15$ &40.5 & 23 & 02 & 15.3 & $\cdots$ & 14.96 & 15.84 & 0.88 & -0.128 & 17.5 & 7/ 5/64 \nl $15$ &41.2 & 17 & 28 & 15.5 & $\cdots$ & 15.06 & 15.82 & 0.76 & -0.004 & 25.5 & 4/ 3/64 \nl $15$ &44.5 & -0 & 50 & 15.4 & $\cdots$ & 14.24 & 15.19 & 0.95 & -0.100 & 25.5 & 5/20/63 \nl $15$ &46.1 & 0 & 25 & 15.7 & $\cdots$ & 15.23 & 16.11 & 0.88 & 0.036 & 25.5 & 5/20/63 \nl $15$ &47.1 & 19 & 11 & 14.4 & NGC6003 & 13.70 & 14.60 & 0.90 & -0.204 & 25.5 & 4/ 3/64 \nl $15$ &47.5 & 12 & 33 & 14.5 & IC1141 & 13.84 & 14.58 & 0.74 & -0.207 & 25.5 & 6/24/63 \nl $15$ &48.1 & 19 & 05 & 13.4 & NGC6004 & 12.76 & 13.59 & 0.83 & -0.077 & 57.0 & 4/ 9/67 \nl $ $ & & & & & & 11.92\tablenotemark{d} & 12.80\tablenotemark{d} & 0.88 & -0.067 & 84.5 & \nl $15$ &48.7 & 9 & 53 & 15.5 & $\cdots$ & 15.72 & 16.30 & 0.58 & -0.054 & 17.5 & 7/ 2/62 \nl $15$ &48.9 & 18 & 43 & 15.2 & $\cdots$ & 14.34 & 15.52 & 1.18 & -0.048 & 25.5 & 4/ 3/64 \nl $15$ &49.9 & 2 & 36 & 15.3 & $\cdots$ & 14.97 & 16.02 & 1.05 & 0.024 & 25.5 & 6/25/63 \nl $15$ &50.7 & 21 & 16 & 14.2 & NGC6008 & 13.61 & 14.44 & 0.83 & -0.234 & 25.5 & 7/ 5/64 \nl $15$ &51.9 & 14 & 44 & 13.1 & NGC6012 & 12.72 & 13.47 & 0.75 & -0.255 & 38.0 & 4/ 3/64 \nl $15$ &52.3 & 16 & 45 & 14.5 & $\cdots$ & 14.62 & 15.11 & 0.49 & 0.018 & 38.0 & 4/ 3/64 \nl $15$ &54.0 & 9 & 13 & 15.5 & $\cdots$ & 14.99 & 15.78 & 0.79 & -0.139 & 17.5 & 6/24/63 \nl $16$ & 2.3 & 17 & 36 & 15.7 & $\cdots$ & 15.55 & 16.27 & 0.72 & -0.059 & 17.5 & 5/21/66 \nl $ $ & & & & & & 15.52 & 16.27 & 0.75 & 0.063 & 26.0 & \nl $16$ & 2.3 & 17 & 51 & 14.9 & IC1170 & 15.07 & 16.22 & 1.15 & -0.066 & 17.5 & 5/23/66 \nl $ $ & & & & & & 14.83 & 15.86 & 1.03 & 0.008 & 26.0 & \nl $16$ & 2.5 & 17 & 35 & 15.7 & $\cdots$ & 15.03 & 15.73 & 0.70 & -0.011 & 26.0 & 5/21/66 \nl $ $ & & & & & & 14.93 & 15.62 & 0.69 & 0.093 & 39.0 & \nl $ $ & & & & & & 14.98 & 15.57 & 0.59 & 0.183 & 57.0 & \nl $16$ & 2.7 & 17 & 55 & 15.4 & NGC6043 & 14.57 & 15.66 & 1.09 & -0.160 & 17.5 & 5/23/66 \nl $ $ & & & & & & 14.50 & 15.64 & 1.14 & -0.024 & 26.0 & \nl $ $ & & & & & & 14.46 & 15.58 & 1.12 & -0.033 & 26.0 & 6/ 2/67 \nl $ $ & & & & & & 14.27 & 15.53 & 1.26 & 0.081 & 39.0 & \nl $16$ & 2.7 & 18 & 00 & 15.3 & NGC6044 & 14.69 & 15.72 & 1.03 & -0.149 & 17.5 & 5/21/66 \nl $ $ & & & & & & 14.67 & 15.63 & 0.96 & -0.025 & 26.0 & \nl $ $ & & & & & & 14.55 & 15.38 & 0.83 & 0.062 & 39.0 & \nl $ $ & & & & & & 14.49 & 15.34 & 0.85 & 0.157 & 57.0 & \nl $16$ & 2.9 & 17 & 53 & 14.8 & NGC6045 & 14.31 & 15.18 & 0.87 & -0.095 & 26.0 & 5/23/66 \nl $ $ & & & & & & 14.21 & 15.18 & 0.97 & 0.035 & 39.0 & \nl $ $ & & & & & & 14.12 & 14.90 & 0.78 & 0.106 & 57.0 & \nl $16$ & 3.0 & 17 & 33 & 15.3 & IC1173 & 14.96 & 15.57 & 0.61 & -0.034 & 26.0 & 5/24/66 \nl $ $ & & & & & & 14.36 & 15.12 & 0.76 & 0.027 & 39.0 & \nl $ $ & & & & & & 14.26 & 15.19 & 0.93 & 0.140 & 57.0 & \nl $ $ & & & & & & 14.83 & 15.69 & 0.86 & -0.017 & 26.0 & 6/ 2/67 \nl $ $ & & & & & & 14.70 & 15.73 & 1.03 & 0.106 & 39.0 & \nl $16$ & 3.1 & 17 & 53 & 14.9 & NGC6050 & 14.15 & 14.82 & 0.67 & -0.015 & 39.0 & 5/23/66 \nl $ $ & & & & & & 13.91 & 14.84 & 0.93 & 0.098 & 57.0 & \nl $ $ & & & & & & 13.95 & 14.68 & 0.73 & 0.179 & 84.5 & \nl $ $ & & & & & & 14.34 & 15.17 & 0.83 & 0.034 & 39.0 & 6/ 2/67 \nl $ $ & & & & & & 14.02 & 14.61 & 0.59 & 0.069 & 57.0 & \nl $16$ & 3.3 & 17 & 54 & 15.4 & NGC6054 & 15.25 & 16.13 & 0.88 & 0.045 & 26.0 & 5/24/66 \nl $ $ & & & & & & 15.52 & 16.41 & 0.89 & 0.185 & 39.0 & \nl $ $ & & & & & & 15.47 & 16.26 & 0.79 & 0.062 & 26.0 & 6/ 2/67 \nl $ $ & & & & & & 15.58 & 16.42 & 0.84 & 0.186 & 39.0 & \nl $16$ & 3.3 & 18 & 05 & 15.1 & NGC6056 & 14.22 & 15.49 & 1.27 & -0.046 & 26.0 & 5/22/66 \nl $ $ & & & & & & 14.09 & 15.21 & 1.12 & 0.039 & 39.0 & \nl $ $ & & & & & & 14.22 & 15.58 & 1.36 & 0.184 & 57.0 & \nl $ $ & & & & & & 13.98 & 15.39 & 1.41 & -0.062 & 26.0 & 5/24/66 \nl $ $ & & & & & & 13.94 & 15.02 & 1.08 & 0.013 & 39.0 & \nl $ $ & & & & & & 14.05 & 14.83 & 0.78 & 0.097 & 57.0 & \nl $16$ & 3.3 & 17 & 44 & 15.0 & IC1178 & 14.34 & 15.35 & 1.01 & -0.216 & 17.5 & 5/24/66 \nl $ $ & & & & & & 14.00 & 14.90 & 0.90 & -0.142 & 26.0 & \nl $ $ & & & & & & 13.60 & 14.71 & 1.11 & -0.031 & 39.0 & \nl $ $ & & & & & & 13.39 & 14.41 & 1.02 & 0.043 & 57.0 & \nl $16$ & 3.3 & 18 & 17 & 15.4 & NGC6055 & 14.33 & 15.46 & 1.13 & -0.196 & 17.5 & 5/21/66 \nl $ $ & & & & & & 13.95 & 15.38 & 1.43 & -0.063 & 26.0 & \nl $ $ & & & & & & 14.15 & 15.52 & 1.37 & 0.080 & 39.0 & \nl $16$ & 3.3 & 17 & 43 & 15.0 & IC1181 & 15.62 & 16.78 & 1.16 & -0.124 & 11.5 & 5/24/66 \nl $ $ & & & & & & 15.14 & 16.30 & 1.16 & -0.054 & 17.5 & \nl $16$ & 3.4 & 17 & 56 & 15.2 & IC1182 & 14.77 & 15.73 & 0.96 & -0.147 & 17.5 & 5/24/66 \nl $ $ & & & & & & 14.44 & 15.52 & 1.08 & -0.042 & 26.0 & \nl $ $ & & & & & & 14.36 & 15.30 & 0.94 & 0.052 & 39.0 & \nl $16$ & 3.4 & 17 & 54 & 15.6 & IC1183 & 14.66 & 15.79 & 1.13 & -0.137 & 17.5 & 5/24/66 \nl $ $ & & & & & & 14.47 & 15.52 & 1.05 & -0.042 & 26.0 & \nl $ $ & & & & & & 14.39 & 15.43 & 1.04 & 0.069 & 39.0 & \nl $16$ & 3.4 & 18 & 17 & 15.7 & NGC6057 & 14.70\tablenotemark{a} & 15.79\tablenotemark{a} & 1.09 & -0.002 & 26.0 & 5/22/66 \nl $ $ & & & & & & 14.86\tablenotemark{a} & 15.92\tablenotemark{a} & 1.06 & 0.129 & 39.0 & \nl $16$ & 3.5 & 17 & 51 & 15.1 & IC1185 & 13.92\tablenotemark{a} & 14.88\tablenotemark{a} & 0.96 & -0.146 & 26.0 & 5/24/66 \nl $ $ & & & & & & 13.85 & 14.80 & 0.95 & -0.018 & 39.0 & \nl $ $ & & & & & & 13.65\tablenotemark{a} & 14.68\tablenotemark{a} & 1.03 & 0.078 & 57.0 & 5/12/67 \nl $ $ & & & & & & 13.85\tablenotemark{a} & 14.96\tablenotemark{a} & 1.11 & 0.005 & 39.0 & \nl $16$ & 3.5 & 18 & 09 & 15.7 & $\cdots$ & 15.32\tablenotemark{a} & 16.32\tablenotemark{a} & 1.00 & 0.070 & 26.0 & 5/22/66 \nl $ $ & & & & & & 15.09\tablenotemark{a} & 16.06\tablenotemark{a} & 0.97 & 0.145 & 39.0 & \nl $16$ & 3.6 & 18 & 21 & 15.7 & UGC10195 & 14.78 & 15.85 & 1.07 & 0.006 & 26.0 & 5/22/66 \nl $ $ & & & & & & 14.60 & 15.57 & 0.97 & 0.086 & 39.0 & \nl $ $ & & & & & & 14.52 & 15.54 & 1.02 & 0.180 & 57.0 & \nl $16$ & 4.0 & 18 & 18 & 15.5 & IC1189 & 14.63 & 15.47 & 0.84 & -0.050 & 26.0 & 5/23/66 \nl $ $ & & & & & & 14.81 & 15.51 & 0.70 & -0.043 & 26.0 & 6/ 1/67 \nl $ $ & & & & & & 14.46 & 15.09 & 0.63 & 0.023 & 39.0 & \nl $16$ & 4.0 & 18 & 23 & 15.0 & NGC6061 & 13.98 & 14.87 & 0.89 & -0.147 & 26.0 & 5/23/66 \nl $ $ & & & & & & 13.70 & 14.82 & 1.12 & -0.015 & 39.0 & \nl $ $ & & & & & & 13.58 & 14.52 & 0.94 & 0.057 & 57.0 & \nl $ $ & & & & & & 13.17 & 14.11 & 0.94 & 0.113 & 84.5 & \nl $ $ & & & & & & 13.74 & 14.78 & 1.04 & -0.021 & 39.0 & 6/ 1/67 \nl $ $ & & & & & & 13.77 & 14.79 & 1.02 & 0.092 & 57.0 & \nl $16$ & 4.2 & 6 & 43 & 15.3 & $\cdots$ & 15.03 & 15.50 & 0.47 & -0.051 & 25.5 & 6/25/63 \nl $16$ & 4.3 & 18 & 01 & 15.7 & $\cdots$ & 15.44\tablenotemark{a} & 16.32\tablenotemark{a} & 0.88 & 0.070 & 26.0 & 5/21/66 \nl $ $ & & & & & & 15.31 & 16.14 & 0.83 & 0.155 & 39.0 & \nl $ $ & & & & & & 15.34 & 16.27 & 0.93 & 0.063 & 26.0 & 5/12/67 \nl $ $ & & & & & & 15.22 & 16.37 & 1.15 & 0.180 & 39.0 & \nl $16$ & 4.4 & 17 & 53 & 15.5 & IC1194 & 14.50 & 15.62 & 1.12 & -0.167 & 17.5 & 5/21/66 \nl $ $ & & & & & & 14.53 & 15.67 & 1.14 & -0.020 & 26.0 & \nl $ $ & & & & & & 14.36 & 15.52 & 1.16 & 0.080 & 39.0 & \nl $ $ & & & & & & 14.37 & 15.53 & 1.16 & -0.040 & 26.0 & 5/12/67 \nl $ $ & & & & & & 14.47 & 15.53 & 1.06 & 0.081 & 39.0 & \nl $16$ & 6.3 & 12 & 28 & 14.9 & IC1198 & 14.30 & 15.05 & 0.75 & -0.124 & 25.5 & 6/24/63 \nl $16$ & 8.1 & 12 & 57 & 15.1 & $\cdots$ & 15.01 & 15.60 & 0.59 & -0.036 & 25.5 & 6/24/63 \nl $16$ & 9.7 & 14 & 20 & 14.6 & NGC6078 & 13.71 & 14.80 & 1.09 & -0.167 & 25.5 & 6/24/63 \nl $16$ &10.1 & 3 & 08 & 15.7 & $\cdots$ & 15.64 & 16.63 & 0.99 & 0.103 & 25.5 & 6/25/63 \nl $16$ &13.0 & 1 & 39 & 15.2 & $\cdots$ & 15.14 & 15.89 & 0.75 & -0.120 & 17.5 & 5/20/63 \nl $16$ &15.8 & 11 & 17 & 15.7 & $\cdots$ & 15.29 & 16.25 & 0.96 & 0.055 & 25.5 & 6/24/63 \nl $16$ &20.0 & 13 & 57 & 15.7 & $\cdots$ & 15.64 & 16.62 & 0.98 & 0.102 & 25.5 & 6/24/63 \nl $16$ &33.1 & 0 & 25 & 14.9 & $\cdots$ & 13.86 & 14.97 & 1.11 & -0.137 & 25.5 & 5/20/63 \nl $16$ &45.0 & -1 & 20 & 15.6 & $\cdots$ & 14.76 & 15.87 & 1.11 & -0.123 & 17.5 & 5/20/63 \nl $16$ &48.2 & 4 & 41 & 15.5 & NGC6230 & 15.28 & 16.29 & 1.01 & -0.211 & 11.5 & 7/ 2/62 \nl $16$ &48.4 & 8 & 53 & 15.0 & IC4621 & 14.42 & 15.20 & 0.78 & -0.099 & 25.5 & 6/25/63 \nl $ $ & & & & & & 14.64 & 15.32 & 0.68 & -0.222 & 17.5 & 7/ 5/64 \nl $ $ & & & & & & 14.52 & 15.16 & 0.64 & -0.105 & 25.5 & \nl $16$ &51.7 & 10 & 39 & 15.6 & $\cdots$ & 15.58 & 16.14 & 0.56 & 0.040 & 25.5 & 6/24/63 \nl $16$ &52.3 & 26 & 38 & 15.7 & $\cdots$ & 14.54 & 15.55 & 1.01 & -0.179 & 17.5 & 8/ 3/64 \nl $16$ &54.6 & 26 & 55 & 15.5 & $\cdots$ & 14.53 & 15.65 & 1.12 & -0.161 & 17.5 & 8/ 3/64 \nl $16$ &56.0 & 23 & 03 & 14.0 & NGC6267 & 12.97 & 13.57 & 0.60 & -0.235 & 38.0 & 8/ 3/64 \nl $16$ &57.2 & 2 & 34 & 15.3 & $\cdots$ & 15.04 & 15.89 & 0.85 & -0.120 & 17.5 & 5/20/63 \nl $16$ &58.7 & 23 & 05 & 13.8 & NGC6278 & 12.68 & 13.67 & 0.99 & -0.401 & 25.5 & 8/ 3/64 \nl $16$ &59.5 & 6 & 44 & 15.5 & NGC6280 & 14.88 & 15.96 & 1.08 & -0.276 & 11.5 & 7/ 2/62 \nl $17$ & 3.4 & 11 & 41 & 15.3 & $\cdots$ & 15.18 & 15.87 & 0.69 & 0.003 & 25.5 & 6/24/63 \nl $17$ & 3.9 & 10 & 28 & 14.5 & $\cdots$ & 14.08 & 14.78 & 0.70 & -0.171 & 25.5 & 6/24/63 \nl $17$ & 5.2 & 11 & 31 & 15.3 & $\cdots$ & 15.64 & 16.09 & 0.45 & 0.034 & 25.5 & 6/24/63 \nl $17$ & 6.3 & 9 & 40 & 15.5 & $\cdots$ & 15.21 & 15.77 & 0.56 & -0.011 & 25.5 & 6/24/63 \nl $17$ & 6.3 & 25 & 35 & 14.2 & $\cdots$ & 13.30 & 13.85 & 0.55 & -0.182 & 38.0 & 8/ 3/64 \nl $17$ & 9.1 & 8 & 03 & 14.8 & $\cdots$ & 13.96 & 14.96 & 1.00 & -0.139 & 25.5 & 7/ 5/64 \nl $ $ & & & & & & 14.15 & 14.87 & 0.72 & -0.016 & 38.0 & 6/25/63 \nl $17$ & 9.8 & 23 & 26 & 14.4 & NGC6308 & 13.41 & 14.23 & 0.82 & -0.276 & 25.5 & 8/ 3/64 \nl $17$ &10.5 & 23 & 20 & 14.3 & NGC6314 & 13.45 & 14.35 & 0.90 & -0.252 & 25.5 & 8/ 3/64 \nl $17$ &10.8 & 21 & 22 & 15.4 & $\cdots$ & 14.27 & 15.55 & 1.28 & -0.179 & 17.5 & 8/ 3/64 \nl $17$ &18.0 & 23 & 53 & 14.5 & $\cdots$ & 13.89 & 14.84 & 0.95 & -0.320 & 17.5 & 8/ 3/64 \nl $17$ &19.8 & 2 & 03 & 15.1 & $\cdots$ & 14.76 & 15.77 & 1.01 & -0.011 & 25.5 & 5/20/63 \nl $17$ &19.8 & 18 & 37 & 15.2 & $\cdots$ & 14.87 & 15.44 & 0.57 & -0.200 & 17.5 & 6/10/64 \nl $17$ &21.9 & 21 & 11 & 15.6 & $\cdots$ & 14.68 & 15.65 & 0.97 & -0.029 & 25.5 & 8/ 3/64 \nl $17$ &22.5 & 29 & 26 & 14.4 & NGC6364 & 13.48 & 14.47 & 0.99 & -0.405 & 17.5 & 8/ 3/64 \nl $17$ &22.7 & 23 & 47 & 14.9 & $\cdots$ & 14.18 & 15.20 & 1.02 & -0.246 & 17.5 & 8/ 3/64 \nl $17$ &23.3 & 26 & 47 & 15.6 & $\cdots$ & 15.86 & 16.36 & 0.50 & -0.045 & 17.5 & 8/ 3/64 \nl $17$ &25.5 & 6 & 31 & 15.5 & $\cdots$ & 15.09 & 16.14 & 1.05 & 0.040 & 25.5 & 6/25/63 \nl $ $ & & & & & & 15.09 & 16.13 & 1.04 & 0.039 & 25.5 & 7/ 5/64 \nl $17$ &26.1 & 14 & 13 & 14.3 & $\cdots$ & 13.49 & 14.37 & 0.88 & -0.248 & 25.5 & 6/24/63 \nl $17$ &26.7 & 24 & 26 & 15.7 & $\cdots$ & 15.39 & 16.37 & 0.98 & -0.043 & 17.5 & 8/ 3/64 \nl $17$ &27.1 & 16 & 14 & 14.5 & NGC6375 & 13.46 & 14.62 & 1.16 & -0.369 & 17.5 & 6/10/64 \nl $17$ &27.2 & 24 & 55 & 14.8 & $\cdots$ & 13.96 & 14.93 & 0.97 & -0.301 & 17.5 & 8/ 3/64 \nl $17$ &28.2 & 6 & 19 & 15.1 & NGC6378 & 13.92 & 14.86 & 0.94 & -0.156 & 25.5 & 6/25/63 \nl $ $ & & & & & & 13.90 & 14.81 & 0.91 & -0.165 & 25.5 & 7/ 5/64 \nl $17$ &30.1 & 3 & 41 & 15.6 & $\cdots$ & 14.53 & 15.33 & 0.80 & -0.078 & 25.5 & 6/25/63 \nl $ $ & & & & & & 14.45 & 15.19 & 0.74 & -0.100 & 25.5 & 7/ 5/64 \nl $17$ &30.5 & 16 & 26 & 13.6 & NGC6389 & 13.50 & 14.47 & 0.97 & -0.405 & 17.5 & 8/ 2/64 \nl $17$ &31.3 & -0 & 34 & 15.6 & $\cdots$ & 15.04 & 16.36 & 1.32 & -0.045 & 17.5 & 5/20/63 \nl $17$ &32.8 & 6 & 12 & 14.8 & $\cdots$ & 14.13 & 14.75 & 0.62 & -0.176 & 25.5 & 6/25/63 \nl $ $ & & & & & & 14.16 & 14.55 & 0.39 & -0.213 & 25.5 & 7/ 5/64 \nl $17$ &35.3 & 17 & 34 & 14.5 & $\cdots$ & 13.93 & 14.60 & 0.67 & -0.204 & 25.5 & 8/ 2/64 \nl $17$ &36.2 & 28 & 29 & 15.3 & $\cdots$ & 14.71 & 15.65 & 0.94 & -0.161 & 17.5 & 8/ 3/64 \nl $17$ &36.6 & 18 & 54 & 14.0 & NGC6408 & 13.82 & 14.82 & 1.00 & -0.325 & 17.5 & 6/10/64 \nl $ $ & & & & & & 13.35 & 14.25 & 0.90 & -0.272 & 25.5 & 8/ 2/64 \nl $17$ &37.4 & 2 & 51 & 15.3 & $\cdots$ & 14.73 & 15.69 & 0.96 & -0.023 & 25.5 & 5/20/63 \nl $17$ &39.7 & 23 & 42 & 14.4 & NGC6417 & 13.89 & 14.77 & 0.88 & -0.336 & 17.5 & 9/10/64 \nl $17$ &39.9 & 18 & 02 & 15.7 & $\cdots$ & 15.32 & 16.32 & 1.00 & -0.051 & 17.5 & 8/ 2/64 \nl $17$ &40.5 & 19 & 30 & 15.6 & $\cdots$ & 14.68 & 15.64 & 0.96 & -0.163 & 17.5 & 6/10/64 \nl $ $ & & & & & & 14.78 & 15.73 & 0.95 & -0.147 & 17.5 & 8/ 2/64 \nl $17$ &41.4 & 4 & 34 & 15.7 & $\cdots$ & 14.28 & 15.41 & 1.13 & -0.065 & 25.5 & 6/25/63 \nl $ $ & & & & & & 14.20 & 15.31 & 1.11 & -0.081 & 25.5 & 7/ 5/64 \nl $17$ &42.0 & 25 & 23 & 14.3 & NGC6429 & 13.38 & 14.27 & 0.89 & -0.268 & 25.5 & 8/ 2/64 \nl $17$ &42.7 & 19 & 33 & 15.5 & $\cdots$ & 15.63 & 16.34 & 0.71 & -0.048 & 17.5 & 8/ 2/64 \nl $17$ &44.0 & 32 & 54 & 15.3 & $\cdots$ & 14.67 & 15.68 & 1.01 & -0.156 & 17.5 & 8/ 3/64 \nl $17$ &44.7 & 20 & 47 & 14.5 & $\cdots$ & 13.36 & 14.44 & 1.08 & -0.412 & 17.5 & 6/10/64 \nl $17$ &46.6 & 24 & 40 & 15.6 & $\cdots$ & 15.00 & 16.06 & 1.06 & -0.092 & 17.5 & 9/10/64 \nl $17$ &47.9 & 14 & 18 & 14.4 & $\cdots$ & 13.87 & 14.42 & 0.55 & 0.044 & 57.0 & 6/24/63 \nl $17$ &48.6 & 23 & 09 & 15.3 & $\cdots$ & 14.33 & 15.25 & 0.92 & -0.236 & 17.5 & 9/10/64 \nl $17$ &48.7 & 17 & 09 & 15.3 & $\cdots$ & 14.59 & 15.62 & 1.03 & -0.349 & 11.5 & 6/10/64 \nl $17$ &49.7 & 24 & 30 & 13.5 & NGC6484 & 12.92 & 13.78 & 0.86 & -0.375 & 25.5 & 8/ 2/64 \nl $17$ &49.8 & 5 & 27 & 15.5 & $\cdots$ & 15.28 & 15.89 & 0.61 & 0.006 & 25.5 & 6/25/63 \nl $ $ & & & & & & 15.80 & 16.13 & 0.33 & 0.039 & 25.5 & 7/ 5/64 \nl $17$ &50.0 & 21 & 35 & 14.5 & IC1269 & 14.18 & 15.00 & 0.82 & -0.286 & 17.5 & 8/ 2/64 \nl $17$ &50.0 & 31 & 28 & 14.2 & NGC6485 & 13.71 & 14.41 & 0.70 & -0.240 & 25.5 & 8/ 3/64 \nl $17$ &50.6 & 29 & 50 & 15.0 & NGC6486 & 14.28 & 15.31 & 1.03 & -0.224 & 17.5 & 8/ 3/64 \nl $17$ &50.8 & 23 & 14 & 15.0 & $\cdots$ & 14.08 & 15.08 & 1.00 & -0.270 & 17.5 & 9/10/64 \nl $17$ &52.1 & 2 & 53 & 14.9 & $\cdots$ & 14.37 & 14.95 & 0.58 & -0.005 & 38.0 & 5/20/63 \nl $17$ &52.3 & 18 & 23 & 14.7 & NGC6490 & 13.56 & 14.56 & 1.00 & -0.383 & 17.5 & 6/10/64 \nl $ $ & & & & & & 13.66 & 14.70 & 1.04 & -0.351 & 17.5 & 8/ 2/64 \nl $17$ &52.6 & 18 & 20 & 13.8 & NGC6495 & 13.16 & 14.20 & 1.04 & -0.472 & 17.5 & 6/10/64 \nl $ $ & & & & & & 13.05 & 14.09 & 1.04 & -0.306 & 25.5 & 8/ 2/64 \nl $17$ &53.1 & 6 & 12 & 15.5 & $\cdots$ & 15.12 & 15.96 & 0.84 & -0.108 & 17.5 & 7/ 2/62 \nl $ $ & & & & & & 14.88 & 15.74 & 0.86 & -0.146 & 17.5 & \nl $17$ &55.7 & 3 & 44 & 15.4 & $\cdots$ & 14.86 & 15.71 & 0.85 & 0.097 & 38.0 & 6/25/63 \nl $ $ & & & & & & 14.53 & 15.35 & 0.82 & 0.051 & 38.0 & 7/ 5/64 \nl $17$ &55.9 & 21 & 17 & 15.0 & $\cdots$ & 14.44 & 15.21 & 0.77 & -0.244 & 17.5 & 8/ 2/64 \nl $17$ &58.6 & 23 & 03 & 15.1 & $\cdots$ & 14.67 & 15.69 & 1.02 & -0.154 & 17.5 & 8/ 2/64 \nl $17$ &59.5 & 26 & 15 & 14.8 & $\cdots$ & 14.11 & 14.92 & 0.81 & -0.303 & 17.5 & 9/10/64 \nl $18$ & 0.9 & 29 & 18 & 15.2 & $\cdots$ & 14.92 & 15.65 & 0.73 & -0.161 & 17.5 & 8/ 3/64 \nl $18$ & 2.8 & 17 & 16 & 15.6 & $\cdots$ & 14.86 & 15.65 & 0.79 & -0.161 & 17.5 & 6/10/64 \nl $ $ & & & & & & 14.64 & 15.39 & 0.75 & -0.068 & 25.5 & 8/ 2/64 \nl $18$ & 3.1 & 25 & 13 & 14.3 & NGC6547 & 13.10 & 14.14 & 1.04 & -0.295 & 25.5 & 8/ 2/64 \nl $18$ & 3.3 & 23 & 08 & 15.7 & $\cdots$ & 15.06 & 15.67 & 0.61 & -0.158 & 17.5 & 8/ 2/64 \nl $18$ & 4.0 & 22 & 39 & 15.7 & $\cdots$ & 15.12 & 16.04 & 0.92 & -0.260 & 11.5 & 9/10/64 \nl $18$ & 4.0 & 23 & 28 & 15.1 & $\cdots$ & 14.06 & 14.91 & 0.85 & -0.148 & 25.5 & 8/ 2/64 \nl $18$ & 5.8 & 11 & 41 & 14.7 & IC4688 & 13.68 & 14.44 & 0.76 & -0.082 & 38.0 & 6/25/63 \nl $ $ & & & & & & 13.96 & 14.80 & 0.84 & -0.167 & 25.5 & 7/ 5/64 \nl $18$ & 6.4 & 11 & 49 & 15.5 & IC4691 & 14.53 & 15.67 & 1.14 & -0.338 & 11.5 & 7/ 2/62 \nl $18$ & 6.8 & 28 & 02 & 14.8 & $\cdots$ & 14.30 & 14.77 & 0.47 & -0.172 & 25.5 & 7/ 5/64 \nl $18$ & 7.2 & 19 & 06 & 15.1 & $\cdots$ & 14.42 & 15.29 & 0.87 & -0.228 & 17.5 & 8/ 2/64 \nl $18$ & 8.6 & 28 & 55 & 15.6 & $\cdots$ & 14.38 & 15.28 & 0.90 & -0.086 & 25.5 & 8/ 3/64 \nl $18$ & 9.0 & 31 & 05 & 14.4 & NGC6575 & 13.20 & 14.27 & 1.07 & -0.268 & 25.5 & 7/ 5/64 \nl $18$ & 9.6 & 21 & 25 & 15.5 & NGC6576 & 14.73 & 15.61 & 0.88 & -0.168 & 17.5 & 9/10/64 \nl $18$ &10.1 & 21 & 53 & 14.9 & $\cdots$ & 14.21 & 14.98 & 0.77 & -0.290 & 17.5 & 9/10/64 \nl $18$ &10.2 & 29 & 08 & 14.9 & $\cdots$ & 13.58 & 14.59 & 1.01 & -0.206 & 25.5 & 8/ 3/64 \nl $18$ &10.5 & 25 & 25 & 15.5 & $\cdots$ & 14.29 & 15.02 & 0.73 & -0.129 & 25.5 & 9/10/64 \nl $18$ &10.5 & 25 & 31 & 14.7 & $\cdots$ & 13.72 & 14.84 & 1.12 & -0.320 & 17.5 & 9/10/64 \nl $18$ &11.1 & 28 & 25 & 15.7 & $\cdots$ & 15.64 & 16.43 & 0.79 & -0.034 & 17.5 & 7/ 5/64 \nl $18$ &11.6 & 18 & 49 & 14.3 & NGC6587 & 12.98\tablenotemark{b} & 14.04\tablenotemark{b} & 1.06 & -0.515 & 17.5 & 6/10/64 \nl $18$ &11.7 & 13 & 15 & 14.2 & $\cdots$ & 13.41 & 14.08 & 0.67 & -0.308 & 25.5 & 6/25/63 \nl $ $ & & & & & & 13.04 & 13.78 & 0.74 & -0.195 & 38.0 & \nl $18$ &11.9 & 10 & 05 & 15.5 & $\cdots$ & 14.20 & 15.23 & 1.03 & -0.094 & 25.5 & 6/25/63 \nl $ $ & & & & & & 13.91 & 14.87 & 0.96 & -0.155 & 25.5 & 7/ 5/64 \nl $18$ &12.0 & 9 & 59 & 15.5 & $\cdots$ & 14.51 & 15.61 & 1.10 & -0.352 & 11.5 & 7/ 2/62 \nl $18$ &13.6 & 6 & 44 & 15.5 & $\cdots$ & 14.44 & 15.35 & 0.91 & -0.216 & 17.5 & 7/ 2/62 \nl $ $ & & & & & & 14.17 & 15.14 & 0.97 & -0.109 & 25.5 & 6/25/63 \nl $ $ & & & & & & 13.91 & 14.87 & 0.96 & -0.155 & 25.5 & 7/ 5/64 \nl $18$ &13.6 & 24 & 54 & 13.7 & NGC6599 & 12.99 & 14.02 & 1.03 & -0.321 & 25.5 & 8/ 2/64 \nl $18$ &14.0 & 28 & 42 & 15.2 & $\cdots$ & 14.36 & 14.95 & 0.59 & -0.141 & 25.5 & 8/ 3/64 \nl $18$ &14.5 & 29 & 53 & 15.5 & $\cdots$ & 14.68 & 15.69 & 1.01 & -0.154 & 17.5 & 8/ 3/64 \nl $18$ &15.0 & 12 & 56 & 15.5 & $\cdots$ & 15.24 & 16.07 & 0.83 & 0.031 & 25.5 & 7/ 2/62 \nl $18$ &16.8 & 23 & 38 & 14.3 & NGC6619 & 13.12 & 14.17 & 1.05 & -0.480 & 17.5 & 9/10/64 \nl $18$ &21.1 & 29 & 53 & 14.9 & $\cdots$ & 14.73 & 15.49 & 0.76 & -0.190 & 17.5 & 8/ 3/64 \nl $18$ &23.0 & 27 & 30 & 13.2 & NGC6632 & 12.67 & 13.54 & 0.87 & -0.241 & 38.0 & 7/ 5/64 \nl $18$ &24.0 & 23 & 17 & 15.1 & $\cdots$ & 13.93 & 14.85 & 0.92 & -0.318 & 17.5 & 9/10/64 \nl $18$ &26.8 & 22 & 52 & 14.3 & NGC6641 & 13.51 & 14.29 & 0.78 & -0.449 & 17.5 & 9/10/64 \nl $18$ &29.0 & 22 & 23 & 15.5 & $\cdots$ & 14.95 & 15.59 & 0.64 & -0.172 & 17.5 & 9/10/64 \nl $18$ &29.8 & 31 & 02 & 15.2 & $\cdots$ & 14.93 & 15.46 & 0.53 & -0.058 & 25.5 & 7/ 5/64 \nl $18$ &30.2 & 31 & 00 & 14.9 & $\cdots$ & 13.89 & 14.79 & 0.90 & -0.169 & 25.5 & 7/ 5/64 \nl $18$ &30.9 & 32 & 00 & 15.6 & $\cdots$ & 15.00 & 15.83 & 0.83 & -0.003 & 25.5 & 8/ 3/64 \nl $18$ &32.3 & 18 & 56 & 15.2 & $\cdots$ & 14.87 & 16.12 & 1.25 & -0.082 & 17.5 & 6/10/64 \nl $18$ &32.3 & 32 & 01 & 14.9 & $\cdots$ & 13.92 & 14.92 & 1.00 & -0.146 & 25.5 & 7/ 5/64 \nl $18$ &32.3 & 32 & 08 & 15.6 & $\cdots$ & 15.19 & 16.14 & 0.95 & 0.040 & 25.5 & 7/ 5/64 \nl $18$ &32.5 & 22 & 52 & 14.1 & NGC6661 & 12.53 & 13.65 & 1.12 & -0.405 & 25.5 & 8/ 2/64 \nl $18$ &33.2 & 32 & 57 & 15.4 & $\cdots$ & 14.09 & 15.42 & 1.33 & -0.064 & 25.5 & 7/ 5/64 \nl $18$ &35.2 & 32 & 58 & 15.6 & $\cdots$ & 15.83 & 16.93 & 1.10 & 0.037 & 17.5 & 7/ 5/64 \nl $18$ &35.4 & 26 & 22 & 13.8 & NGC6671 & 13.03 & 14.05 & 1.02 & -0.513 & 17.5 & 8/ 2/64 \nl $18$ &36.5 & 25 & 20 & 13.7 & NGC6674 & 13.30 & 14.37 & 1.07 & -0.429 & 17.5 & 9/10/64 \nl $18$ &38.2 & 24 & 09 & 14.2 & $\cdots$ & 12.83 & 13.92 & 1.09 & -0.343 & 25.5 & 8/ 2/64 \nl $18$ &38.5 & 28 & 34 & 15.5 & $\cdots$ & 14.93 & 15.69 & 0.76 & -0.154 & 17.5 & 8/ 2/64 \nl $18$ &38.7 & 23 & 38 & 15.3 & $\cdots$ & 14.38 & 15.48 & 1.10 & -0.054 & 25.5 & 8/ 2/64 \nl $18$ &39.6 & 32 & 18 & 15.7 & $\cdots$ & 15.10 & 16.31 & 1.21 & -0.207 & 11.5 & 8/ 2/64 \nl $18$ &43.2 & 25 & 27 & 14.5 & NGC6697 & 13.25 & 14.32 & 1.07 & -0.442 & 17.5 & 8/ 2/64 \nl $18$ &44.2 & 32 & 13 & 14.2 & NGC6700 & 13.25 & 14.31 & 1.06 & -0.260 & 25.5 & 7/ 5/64 \nl $18$ &45.6 & 23 & 17 & 15.0 & $\cdots$ & 13.46 & 14.53 & 1.07 & -0.217 & 25.5 & 8/ 2/64 \nl $18$ &46.3 & 23 & 06 & 15.6 & $\cdots$ & 15.06 & 15.70 & 0.64 & -0.153 & 17.5 & 9/10/64 \nl $18$ &48.6 & 26 & 46 & 14.6 & NGC6710 & 13.23 & 14.41 & 1.18 & -0.240 & 25.5 & 9/11/64 \nl $ $ & & & & & & 13.09 & 14.25 & 1.16 & -0.113 & 38.0 & \nl $18$ &49.5 & 23 & 34 & 15.2 & $\cdots$ & 14.24 & 15.05 & 0.81 & -0.276 & 17.5 & 8/ 2/64 \nl $18$ &52.2 & 24 & 35 & 15.6 & $\cdots$ & 14.50 & 15.25 & 0.75 & -0.091 & 25.5 & 8/ 2/64 \nl $19$ &36.8 & -1 & 41 & 15.7 & $\cdots$ & 14.86 & 16.05 & 1.19 & -0.094 & 17.5 & 10/ 3/64 \nl $19$ &37.2 & -0 & 37 & 15.7 & $\cdots$ & 14.48 & 15.72 & 1.24 & -0.149 & 17.5 & 10/ 3/64 \nl $19$ &40.9 & -1 & 17 & 15.1 & $\cdots$ & 13.65 & 14.65 & 1.00 & -0.194 & 25.5 & 10/ 3/64 \nl $19$ &48.8 & -2 & 23 & 15.4 & $\cdots$ & 14.69 & 15.98 & 1.29 & -0.105 & 17.5 & 10/ 3/64 \nl $19$ &56.9 & 0 & 57 & 14.8 & $\cdots$ & 14.11 & 15.27 & 1.16 & -0.232 & 17.5 & 10/ 3/64 \nl $19$ &59.9 & 1 & 30 & 15.2 & $\cdots$ & 14.56 & 15.61 & 1.05 & -0.168 & 17.5 & 10/ 3/64 \nl $20$ & 2.2 & 12 & 35 & 14.4 & $\cdots$ & 13.59 & 14.61 & 1.02 & -0.202 & 25.5 & 10/ 4/64 \nl $20$ & 6.1 & 14 & 52 & 15.5 & $\cdots$ & 14.19 & 15.08 & 0.89 & -0.119 & 25.5 & 10/ 4/64 \nl $20$ & 8.3 & 1 & 59 & 14.9 & $\cdots$ & 13.91 & 14.93 & 1.02 & -0.144 & 25.5 & 10/ 3/64 \nl $20$ & 9.8 & 1 & 48 & 15.4 & $\cdots$ & 14.11 & 15.24 & 1.13 & -0.092 & 25.5 & 10/ 3/64 \nl $20$ &20.2 & 9 & 59 & 15.0 & $\cdots$ & 14.47\tablenotemark{a} & 15.11\tablenotemark{a} & 0.64 & -0.264 & 17.5 & 8/14/63 \nl $20$ &25.5 & 13 & 21 & 15.4 & $\cdots$ & 14.84 & 15.38 & 0.54 & -0.070 & 25.5 & 10/ 4/64 \nl $20$ &25.9 & 10 & 35 & 15.0 & $\cdots$ & 13.51 & 14.62 & 1.11 & -0.053 & 38.0 & 10/ 4/64 \nl $20$ &27.8 & -1 & 10 & 15.2 & $\cdots$ & 14.24 & 15.43 & 1.19 & -0.201 & 17.5 & 9/10/64 \nl $ $ & & & & & & 14.06 & 15.26 & 1.20 & -0.234 & 17.5 & 8/23/65 \nl $ $ & & & & & & 13.84 & 14.99 & 1.15 & -0.134 & 25.5 & \nl $ $ & & & & & & 13.64 & 14.74 & 1.10 & -0.035 & 38.0 & \nl $20$ &28.0 & -1 & 10 & 15.5 & $\cdots$ & 14.64 & 16.04 & 1.40 & -0.095 & 17.5 & 9/10/64 \nl $ $ & & & & & & 14.49 & 15.81 & 1.32 & -0.133 & 17.5 & 8/23/65 \nl $ $ & & & & & & 14.54 & 15.84 & 1.30 & -0.001 & 25.5 & \nl $ $ & & & & & & 14.52 & 15.66 & 1.14 & 0.091 & 38.0 & \nl $20$ &28.9 & -2 & 07 & 15.5 & $\cdots$ & 14.41 & 15.52 & 1.11 & -0.185 & 17.5 & 9/11/64 \nl $ $ & & & & & & 14.29 & 15.40 & 1.11 & -0.207 & 17.5 & 8/23/65 \nl $ $ & & & & & & 14.05 & 15.08 & 1.03 & -0.119 & 25.5 & \nl $ $ & & & & & & 13.90 & 15.16 & 1.26 & 0.025 & 38.0 & \nl $20$ &29.9 & 11 & 12 & 14.7 & $\cdots$ & 13.12 & 14.20 & 1.08 & -0.121 & 38.0 & 8/14/63 \nl $ $ & & & & & & 13.12 & 14.24 & 1.12 & -0.114 & 38.0 & 9/21/63 \nl $20$ &30.2 & 9 & 45 & 15.6 & NGC6927 & 14.74 & 15.75 & 1.01 & -0.144 & 17.5 & 8/14/63 \nl $ $ & & & & & & 14.70 & 15.84 & 1.14 & -0.128 & 17.5 & 9/21/63 \nl $ $ & & & & & & 14.70 & 15.72 & 1.02 & -0.149 & 17.5 & 10/ 4/64 \nl $20$ &30.5 & 9 & 45 & 13.7 & NGC6928 & 12.70 & 13.78 & 1.08 & -0.047 & 57.0 & 9/11/64 \nl $20$ &30.6 & 9 & 41 & 14.3 & NGC6930 & 14.01 & 14.96 & 0.95 & -0.139 & 25.5 & 9/11/64 \nl $20$ &34.2 & 11 & 20 & 14.0 & $\cdots$ & 13.28 & 14.26 & 0.98 & -0.270 & 25.5 & 10/ 4/64 \nl $20$ &36.3 & 9 & 33 & 15.1 & $\cdots$ & 14.53 & 14.96 & 0.43 & -0.139 & 25.5 & 8/14/63 \nl $ $ & & & & & & 14.44 & 15.01 & 0.57 & -0.130 & 25.5 & 9/21/63 \nl $ $ & & & & & & 14.65 & 15.12 & 0.47 & -0.262 & 17.5 & 8/23/65 \nl $ $ & & & & & & 14.56 & 15.06 & 0.50 & -0.122 & 25.5 & \nl $ $ & & & & & & 14.39 & 15.00 & 0.61 & 0.003 & 38.0 & \nl $20$ &36.9 & 10 & 37 & 15.2 & $\cdots$ & 13.62 & 14.75 & 1.13 & -0.340 & 17.5 & 10/ 4/64 \nl $20$ &37.2 & 10 & 37 & 15.7 & $\cdots$ & 15.11\tablenotemark{a} & 16.10\tablenotemark{a} & 0.99 & 0.035 & 25.5 & 8/15/63 \nl $20$ &38.3 & 10 & 37 & 15.5 & $\cdots$ & 14.35 & 15.44 & 1.09 & -0.200 & 17.5 & 10/ 4/64 \nl $20$ &41.6 & 3 & 02 & 14.2 & NGC6954 & 13.32 & 14.36 & 1.04 & -0.250 & 25.5 & 9/11/64 \nl $20$ &41.8 & 12 & 14 & 14.5 & $\cdots$ & 13.87 & 14.57 & 0.70 & -0.209 & 25.5 & 10/ 4/64 \nl $20$ &44.4 & 11 & 06 & 15.5 & $\cdots$ & 15.37 & 16.04 & 0.67 & 0.027 & 25.5 & 8/15/63 \nl $20$ &44.9 & 0 & 07 & 14.2 & NGC6964 & 13.10 & 14.12 & 1.02 & -0.299 & 25.5 & 10/ 3/64 \nl $20$ &45.1 & 12 & 54 & 14.7 & $\cdots$ & 14.45 & 15.07 & 0.62 & -0.120 & 25.5 & 10/ 4/64 \nl $20$ &47.5 & 9 & 46 & 15.5 & $\cdots$ & 15.00\tablenotemark{a} & 15.58\tablenotemark{a} & 0.58 & -0.174 & 17.5 & 8/14/63 \nl $ $ & & & & & & 15.04 & 15.65 & 0.61 & -0.161 & 17.5 & 9/21/63 \nl $20$ &47.6 & 9 & 43 & 14.3 & NGC6972 & 13.40 & 14.27 & 0.87 & -0.454 & 17.5 & 8/ 3/64 \nl $ $ & & & & & & 13.25 & 14.13 & 0.88 & -0.297 & 25.5 & 10/04 64 \nl $20$ &47.9 & 13 & 10 & 15.6 & $\cdots$ & 14.86 & 15.49 & 0.63 & -0.053 & 25.5 & 10/04 64 \nl $20$ &51.6 & 0 & 35 & 15.2 & $\cdots$ & 14.38 & 15.23 & 0.85 & 0.035 & 38.0 & 10/ 3/64 \nl $20$ &52.9 & -1 & 25 & 14.5 & $\cdots$ & 13.61 & 14.54 & 0.93 & -0.215 & 25.5 & 10/ 3/64 \nl $20$ &56.1 & 0 & 43 & 15.4 & $\cdots$ & 14.67 & 15.82 & 1.15 & -0.132 & 17.5 & 10/ 3/64 \nl $21$ & 0.5 & 15 & 12 & 14.9 & $\cdots$ & 14.76 & 15.35 & 0.59 & -0.075 & 25.5 & 10/ 4/64 \nl $21$ & 1.6 & 12 & 56 & 15.6 & $\cdots$ & 14.54 & 15.46 & 0.92 & -0.058 & 25.5 & 10/ 4/64 \nl $21$ & 3.3 & 11 & 13 & 13.2 & NGC7015 & 12.79 & 13.58 & 0.79 & -0.233 & 38.0 & 10/ 4/64 \nl $21$ & 5.2 & 12 & 07 & 15.4 & $\cdots$ & 14.87 & 15.77 & 0.90 & -0.140 & 17.5 & 8/14/63 \nl $21$ & 8.4 & 4 & 52 & 15.6 & IC1360 & 14.52 & 15.53 & 1.01 & -0.047 & 25.5 & 10/21/65 \nl $ $ & & & & & & 14.52 & 15.45 & 0.93 & 0.064 & 38.0 & \nl $21$ &14.3 & 14 & 50 & 15.3 & $\cdots$ & 14.39\tablenotemark{a} & 15.47\tablenotemark{a} & 1.08 & -0.194 & 17.5 & 7/ 5/64 \nl $21$ &18.5 & 3 & 47 & 15.1 & IC1375 & 14.03 & 15.11 & 1.08 & -0.114 & 25.5 & 10/21/65 \nl $ $ & & & & & & 13.97 & 14.94 & 0.97 & -0.006 & 38.0 & \nl $21$ &19.8 & 18 & 27 & 13.8 & NGC7056 & 13.23 & 14.10 & 0.87 & -0.304 & 25.5 & 10/22/65 \nl $ $ & & & & & & 13.04 & 13.89 & 0.85 & -0.175 & 38.0 & \nl $ $ & & & & & & 13.07 & 13.91 & 0.84 & -0.028 & 57.0 & \nl $21$ &20.1 & 15 & 04 & 14.9 & $\cdots$ & 14.01\tablenotemark{a} & 15.09\tablenotemark{a} & 1.08 & -0.268 & 17.5 & 8/ 3/64 \nl $21$ &21.2 & 17 & 22 & 15.0 & $\cdots$ & 14.40 & 15.46 & 1.06 & -0.058 & 25.5 & 10/22/65 \nl $ $ & & & & & & 14.49 & 15.26 & 0.77 & 0.039 & 38.0 & \nl $21$ &21.5 & 17 & 21 & 15.0 & $\cdots$ & 14.56 & 15.53 & 0.97 & -0.047 & 25.5 & 10/22/65 \nl $ $ & & & & & & 14.45 & 15.36 & 0.91 & 0.052 & 38.0 & \nl $21$ &29.0 & 15 & 35 & 15.7 & $\cdots$ & 14.72 & 15.69 & 0.97 & -0.023 & 25.5 & 10/22/65 \nl $ $ & & & & & & 14.70 & 15.84 & 1.14 & 0.113 & 38.0 & \nl $21$ &29.2 & 2 & 15 & 14.6 & $\cdots$ & 13.95 & 14.51 & 0.56 & -0.071 & 38.0 & 10/ 3/64 \nl $21$ &32.5 & 14 & 14 & 15.6 & $\cdots$ & 15.64\tablenotemark{a} & 16.12\tablenotemark{a} & 0.48 & -0.082 & 17.5 & 8/03/64 \nl $21$ &40.0 & 13 & 40 & 15.4 & $\cdots$ & 14.34\tablenotemark{a} & 15.35\tablenotemark{a} & 1.01 & -0.216 & 17.5 & 8/14/63 \nl $21$ &43.3 & 15 & 04 & 15.7 & $\cdots$ & 15.09 & 15.72 & 0.63 & -0.018 & 25.5 & 8/14/63 \nl $21$ &47.6 & 13 & 51 & 15.7 & $\cdots$ & 15.20 & 15.80 & 0.60 & -0.135 & 17.5 & 8/14/63 \nl $ $ & & & & & & 15.28 & 15.94 & 0.66 & -0.112 & 17.5 & 9/21/63 \nl $21$ &48.1 & 0 & 41 & 15.4 & $\cdots$ & 14.49 & 15.55 & 1.06 & -0.044 & 25.5 & 10/ 3/64 \nl $21$ &48.3 & 1 & 47 & 15.0 & IC1405 & 14.26 & 15.11 & 0.85 & -0.114 & 25.5 & 10/ 3/64 \nl $21$ &50.2 & 12 & 17 & 15.6 & $\cdots$ & 14.49\tablenotemark{a} & 15.62\tablenotemark{a} & 1.13 & -0.167 & 17.5 & 9/20/63 \nl $21$ &50.5 & 3 & 28 & 15.6 & $\cdots$ & 14.68 & 15.56 & 0.88 & 0.078 & 38.0 & 10/ 3/64 \nl $21$ &52.0 & 2 & 42 & 13.5 & NGC7156 & 12.73 & 13.44 & 0.71 & -0.261 & 38.0 & 10/ 3/64 \nl $21$ &55.9 & 8 & 11 & 14.9 & IC1414 & 14.34 & 15.29 & 0.95 & -0.084 & 25.5 & 10/21/65 \nl $ $ & & & & & & 14.40 & 15.17 & 0.77 & 0.026 & 38.0 & \nl $21$ &56.2 & 8 & 13 & 15.5 & $\cdots$ & 15.08 & 15.60 & 0.52 & -0.036 & 25.5 & 10/21/65 \nl $ $ & & & & & & 14.93 & 15.65 & 0.72 & 0.089 & 38.0 & \nl $21$ &58.2 & 11 & 08 & 15.6 & $\cdots$ & 15.09 & 15.81 & 0.72 & -0.133 & 17.5 & 9/20/63 \nl $21$ &59.3 & 11 & 37 & 15.6 & $\cdots$ & 14.40 & 15.46 & 1.06 & -0.058 & 25.5 & 9/20/63 \nl $22$ & 0.0 & 18 & 05 & 14.8 & $\cdots$ & 14.08 & 14.64 & 0.56 & -0.188 & 26.0 & 10/12/66 \nl $ $ & & & & & & 13.96 & 14.42 & 0.46 & -0.076 & 39.0 & \nl $ $ & & & & & & 13.46 & 14.14 & 0.68 & 0.006 & 57.0 & \nl $ $ & & & & & & 13.43 & 13.98 & 0.55 & 0.097 & 84.5 & \nl $22$ & 2.4 & 15 & 33 & 15.5 & $\cdots$ & 14.60 & 15.16 & 0.56 & -0.105 & 25.5 & 10/22/65 \nl $ $ & & & & & & 14.48 & 15.11 & 0.63 & 0.018 & 38.0 & \nl $22$ & 4.2 & 17 & 13 & 15.4 & $\cdots$ & 14.60 & 15.45 & 0.85 & -0.198 & 17.5 & 10/22/65 \nl $ $ & & & & & & 14.44 & 15.12 & 0.68 & -0.112 & 25.5 & \nl $ $ & & & & & & 14.34 & 15.18 & 0.84 & 0.028 & 38.0 & \nl $22$ & 9.1 & 10 & 38 & 15.5 & $\cdots$ & 14.90 & 15.98 & 1.08 & -0.105 & 17.5 & 9/20/63 \nl $22$ &13.9 & 16 & 13 & 14.9 & NGC7244 & 14.28 & 14.95 & 0.67 & -0.297 & 17.5 & 10/22/65 \nl $ $ & & & & & & 14.20 & 14.82 & 0.62 & -0.164 & 25.5 & \nl $ $ & & & & & & 14.14 & 14.82 & 0.68 & -0.023 & 38.0 & \nl $22$ &19.2 & 6 & 40 & 15.1 & $\cdots$ & 14.82 & 15.40 & 0.58 & -0.067 & 25.5 & 10/21/65 \nl $ $ & & & & & & 14.76 & 15.44 & 0.68 & 0.062 & 38.0 & \nl $22$ &22.0 & 17 & 50 & 15.3 & $\cdots$ & 14.96 & 15.60 & 0.64 & -0.170 & 17.5 & 10/22/65 \nl $ $ & & & & & & 15.15 & 15.59 & 0.44 & -0.038 & 25.5 & \nl $22$ &24.1 & 15 & 54 & 13.6 & NGC7280 & 12.51 & 13.44 & 0.93 & -0.250 & 39.0 & 10/14/66 \nl $ $ & & & & & & 12.29 & 13.27 & 0.98 & -0.129 & 57.0 & \nl $ $ & & & & & & 12.33 & 13.17 & 0.84 & -0.011 & 84.5 & \nl $22$ &24.5 & 19 & 17 & 15.1 & $\cdots$ & 14.43 & 15.49 & 1.06 & -0.046 & 26.0 & 10/14/66 \nl $ $ & & & & & & 14.17 & 15.15 & 0.98 & 0.031 & 39.0 & \nl $ $ & & & & & & 14.17 & 15.20 & 1.03 & 0.141 & 57.0 & \nl $22$ &26.0 & 16 & 53 & 13.8 & NGC7290 & 13.61 & 14.07 & 0.46 & -0.133 & 39.0 & 10/11/66 \nl $ $ & & & & & & 13.55 & 14.00 & 0.45 & -0.015 & 57.0 & \nl $ $ & & & & & & 13.27 & 13.85 & 0.58 & 0.081 & 84.5 & \nl $ $ & & & & & & 13.28 & 13.99 & 0.71 & 0.099 & 84.5 & \nl $22$ &26.1 & 11 & 47 & 15.4 & $\cdots$ & 14.80 & 15.47 & 0.67 & -0.056 & 25.5 & 10/ 4/64 \nl $22$ &29.4 & 19 & 25 & 14.6 & $\cdots$ & 14.19 & 14.71 & 0.52 & -0.176 & 26.0 & 10/11/66 \nl $ $ & & & & & & 14.05 & 14.54 & 0.49 & -0.057 & 39.0 & \nl $ $ & & & & & & 13.99 & 14.55 & 0.56 & 0.061 & 57.0 & \nl $22$ &30.6 & 7 & 50 & 14.2 & $\cdots$ & 13.92 & 14.66 & 0.74 & -0.193 & 25.5 & 10/21/65 \nl $ $ & & & & & & 13.92 & 14.61 & 0.69 & -0.055 & 38.0 & \nl $ $ & & & & & & 13.68 & 14.51 & 0.83 & 0.056 & 57.0 & \nl $ $ & & & & & & 14.21 & 14.83 & 0.62 & -0.322 & 17.5 & 10/25/65 \nl $ $ & & & & & & 14.44 & 14.79 & 0.35 & -0.161 & 26.0 & \nl $ $ & & & & & & 14.08 & 14.72 & 0.64 & -0.030 & 39.0 & \nl $22$ &31.6 & 5 & 19 & 13.4 & NGC7311 & 13.02 & 14.20 & 1.18 & -0.274 & 26.0 & 10/25/65 \nl $ $ & & & & & & 12.78 & 13.72 & 0.94 & -0.196 & 39.0 & \nl $ $ & & & & & & 12.68\tablenotemark{c} & 13.70\tablenotemark{c} & 1.02 & -0.060 & 57.0 & \nl $22$ &33.0 & 19 & 25 & 15.2 & $\cdots$ & 14.57 & 15.35 & 0.78 & 0.058 & 39.0 & 10/14/66 \nl $ $ & & & & & & 14.38 & 15.19 & 0.81 & 0.140 & 57.0 & \nl $22$ &33.5 & 20 & 04 & 13.7 & NGC7316 & 13.31 & 13.89 & 0.58 & -0.349 & 25.5 & 10/22/65 \nl $ $ & & & & & & 13.23 & 13.85 & 0.62 & -0.182 & 38.0 & \nl $ $ & & & & & & 13.29 & 13.89 & 0.60 & -0.031 & 57.0 & \nl $22$ &34.4 & 14 & 07 & 15.7 & $\cdots$ & 14.87 & 15.85 & 0.98 & -0.127 & 17.5 & 10/ 4/64 \nl $22$ &35.1 & 10 & 16 & 14.3 & NGC7328 & 13.10 & 14.06 & 0.96 & -0.145 & 38.0 & 10/ 4/64 \nl $22$ &37.1 & 11 & 31 & 14.9 & $\cdots$ & 13.97 & 14.75 & 0.78 & -0.034 & 38.0 & 10/ 4/64 \nl $22$ &38.1 & 11 & 39 & 14.8 & NGC7348 & 14.18 & 14.71 & 0.53 & -0.040 & 38.0 & 10/ 4/64 \nl $22$ &38.9 & 9 & 29 & 15.1 & $\cdots$ & 14.27 & 15.23 & 0.96 & -0.240 & 17.5 & 10/ 4/64 \nl $22$ &41.0 & 3 & 53 & 14.5 & NGC7360 & 14.40 & 15.28 & 0.88 & -0.230 & 17.5 & 10/25/65 \nl $ $ & & & & & & 14.09 & 14.98 & 0.89 & -0.128 & 26.0 & \nl $ $ & & & & & & 14.20 & 15.19 & 0.99 & 0.037 & 39.0 & \nl $22$ &41.5 & 1 & 26 & 15.7 & $\cdots$ & 14.95 & 15.89 & 0.94 & 0.006 & 25.5 & 10/ 3/64 \nl $22$ &43.6 & 10 & 35 & 14.9 & NGC7374 & 14.03 & 14.79 & 0.76 & -0.028 & 38.0 & 10/ 4/64 \nl $22$ &44.2 & 20 & 49 & 14.9 & NGC7375 & 14.07 & 15.08 & 1.01 & -0.112 & 26.0 & 10/11/66 \nl $ $ & & & & & & 13.69 & 14.50 & 0.81 & -0.063 & 39.0 & \nl $ $ & & & & & & 13.56 & 14.57 & 1.01 & 0.064 & 57.0 & \nl $ $ & & & & & & 13.17 & 14.30 & 1.13 & 0.136 & 84.5 & \nl $22$ &46.9 & 19 & 01 & 14.8 & $\cdots$ & 14.06\tablenotemark{b} & 14.88\tablenotemark{b} & 0.82 & -0.146 & 26.0 & 10/11/66 \nl $ $ & & & & & & 13.91 & 14.65 & 0.74 & -0.040 & 39.0 & \nl $ $ & & & & & & 14.19 & 14.92 & 0.73 & 0.108 & 57.0 & \nl $22$ &47.4 & 11 & 20 & 14.4 & NGC7385 & 12.90 & 13.96 & 1.06 & -0.334 & 25.5 & 10/ 4/64 \nl $22$ &47.6 & 11 & 25 & 14.6 & NGC7386 & 13.16 & 14.22 & 1.06 & -0.278 & 25.5 & 10/ 4/64 \nl $22$ &49.9 & 0 & 50 & 14.1 & NGC7396 & 12.48 & 13.58 & 1.10 & -0.233 & 38.0 & 10/ 3/64 \nl $22$ &52.6 & 12 & 56 & 15.2 & NGC7413 & 14.37 & 15.39 & 1.02 & -0.209 & 17.5 & 10/ 4/64 \nl $22$ &54.7 & -1 & 18 & 13.8 & NGC7428 & 12.86 & 13.81 & 0.95 & -0.190 & 38.0 & 10/ 3/64 \nl $22$ &56.9 & 14 & 53 & 15.7 & $\cdots$ & 15.23 & 15.85 & 0.62 & 0.000 & 25.5 & 10/ 4/64 \nl $22$ &56.9 & 15 & 17 & 14.2 & NGC7442 & 13.62 & 14.25 & 0.63 & -0.272 & 25.5 & 10/ 4/64 \nl $22$ &57.8 & 1 & 22 & 15.5 & $\cdots$ & 14.48 & 15.24 & 0.76 & -0.092 & 25.5 & 10/ 3/64 \nl $22$ &58.6 & 19 & 20 & 15.2 & $\cdots$ & 15.47\tablenotemark{b} & 15.87\tablenotemark{b} & 0.40 & 0.009 & 26.0 & 10/15/66 \nl $ $ & & & & & & 14.85\tablenotemark{b} & 15.44\tablenotemark{b} & 0.59 & 0.070 & 39.0 & \nl $ $ & & & & & & 14.99\tablenotemark{b} & 15.59\tablenotemark{b} & 0.60 & 0.089 & 39.0 & \nl $ $ & & & & & & 15.36\tablenotemark{b} & 16.13\tablenotemark{b} & 0.77 & 0.241 & 57.0 & \nl $ $ & & & & & & 15.26\tablenotemark{b} & 16.14\tablenotemark{b} & 0.88 & 0.242 & 57.0 & \nl $22$ &58.9 & 1 & 29 & 13.9 & NGC7458 & 12.90 & 13.93 & 1.03 & -0.341 & 25.5 & 10/ 3/64 \nl $23$ & 0.5 & 16 & 20 & 14.0 & NGC7468 & 13.77 & 14.27 & 0.50 & -0.260 & 26.0 & 10/14/66 \nl $ $ & & & & & & 13.59 & 14.17 & 0.58 & -0.117 & 39.0 & \nl $ $ & & & & & & 13.80 & 14.19 & 0.39 & 0.013 & 57.0 & \nl $23$ & 2.3 & 16 & 24 & 15.0 & $\cdots$ & 14.66 & 15.34 & 0.68 & -0.070 & 26.0 & 10/14/66 \nl $ $ & & & & & & 14.30 & 15.03 & 0.73 & 0.015 & 39.0 & \nl $ $ & & & & & & 14.07 & 14.73 & 0.66 & 0.084 & 57.0 & \nl $ $ & & & & & & 14.06 & 14.58 & 0.52 & 0.168 & 84.5 & \nl $23$ & 2.7 & 2 & 16 & 15.1 & NGC7480 & 13.36 & 14.51 & 1.15 & -0.071 & 38.0 & 10/ 3/64 \nl $23$ & 5.3 & 0 & 40 & 14.9 & NGC7488 & 14.18 & 15.21 & 1.03 & -0.244 & 17.5 & 10/ 3/64 \nl $23$ & 8.6 & -0 & 25 & 15.4 & $\cdots$ & 14.86 & 15.79 & 0.93 & -0.137 & 17.5 & 9/20/63 \nl $ $ & & & & & & 14.81 & 15.83 & 1.02 & -0.130 & 17.5 & 9/10/64 \nl $23$ & 9.2 & -2 & 26 & 14.3 & NGC7506 & 12.93 & 14.01 & 1.08 & -0.154 & 38.0 & 10/ 3/64 \nl $23$ &12.1 & 15 & 40 & 15.7 & NGC7540 & 14.27 & 15.36 & 1.09 & -0.066 & 26.0 & 10/11/66 \nl $ $ & & & & & & 14.12 & 15.11 & 0.99 & 0.026 & 39.0 & \nl $ $ & & & & & & 14.06 & 15.01 & 0.95 & 0.119 & 57.0 & \nl $23$ &12.8 & 18 & 41 & 13.9 & NGC7550 & 12.93 & 13.99 & 1.06 & -0.318 & 26.0 & 10/11/66 \nl $ $ & & & & & & 12.64 & 13.82 & 1.18 & -0.177 & 39.0 & \nl $ $ & & & & & & 12.49 & 13.62 & 1.13 & -0.072 & 57.0 & \nl $ $ & & & & & & 12.37 & 13.43 & 1.06 & 0.026 & 84.5 & \nl $ $ & & & & & & 12.36 & 13.34 & 0.98 & 0.126 & 126.5 & \nl $23$ &13.4 & 6 & 24 & 13.0 & NGC7562 & 12.50 & 13.57 & 1.07 & -0.415 & 26.0 & 10/25/65 \nl $ $ & & & & & & 12.30 & 13.42 & 1.12 & -0.254 & 39.0 & \nl $ $ & & & & & & 12.08 & 13.15 & 1.07 & -0.150 & 57.0 & \nl $ $ & & & & & & 12.00 & 12.97 & 0.97 & -0.040 & 84.5 & \nl $23$ &15.8 & 0 & 00 & 15.4 & NGC7589 & 14.62 & 15.50 & 0.88 & -0.188 & 17.5 & 10/ 3/64 \nl $23$ &16.4 & 16 & 21 & 15.2 & $\cdots$ & 14.81 & 15.30 & 0.49 & -0.083 & 25.5 & 10/22/65 \nl $ $ & & & & & & 14.68 & 15.13 & 0.45 & 0.021 & 38.0 & \nl $23$ &17.6 & 15 & 41 & 14.3 & $\cdots$ & 13.84 & 14.35 & 0.51 & 0.035 & 57.0 & 10/12/66 \nl $ $ & & & & & & 13.76 & 14.27 & 0.51 & 0.132 & 84.5 & \nl $ $ & & & & & & 13.47 & 14.26 & 0.79 & 0.227 & 126.5 & \nl $23$ &18.6 & 0 & 07 & 15.7 & $\cdots$ & 14.86\tablenotemark{a} & 15.98\tablenotemark{a} & 1.12 & -0.105 & 17.5 & 9/20/63 \nl $ $ & & & & & & 14.88 & 15.98 & 1.10 & -0.105 & 17.5 & 9/10/64 \nl $23$ &19.3 & -0 & 57 & 15.0 & $\cdots$ & 14.50 & 15.10 & 0.60 & 0.017 & 38.0 & 10/ 3/64 \nl $23$ &19.8 & 18 & 27 & 15.4 & $\cdots$ & 15.24 & 15.90 & 0.66 & -0.118 & 17.5 & 10/12/66 \nl $ $ & & & & & & 15.10 & 15.92 & 0.82 & 0.016 & 26.0 & \nl $ $ & & & & & & 14.88 & 15.93 & 1.05 & 0.130 & 39.0 & \nl $23$ &20.1 & -1 & 15 & 15.6 & $\cdots$ & 15.12\tablenotemark{a} & 16.22\tablenotemark{a} & 1.10 & -0.066 & 17.5 & 9/20/63 \nl $ $ & & & & & & 15.14 & 16.14 & 1.00 & -0.079 & 17.5 & 9/10/64 \nl $23$ &20.9 & 20 & 53 & 15.1 & IC5317 & 14.24 & 15.43 & 1.19 & -0.056 & 26.0 & 10/12/66 \nl $ $ & & & & & & 13.94 & 14.98 & 1.04 & 0.008 & 39.0 & \nl $ $ & & & & & & 13.57 & 14.87 & 1.30 & 0.102 & 57.0 & \nl $ $ & & & & & & 13.67 & 14.95 & 1.28 & 0.112 & 57.0 & \nl $ $ & & & & & & 13.78 & 15.00 & 1.22 & 0.213 & 84.5 & \nl $23$ &21.5 & 16 & 31 & 15.2 & NGC7647 & 14.00 & 15.17 & 1.17 & -0.097 & 26.0 & 10/12/66 \nl $ $ & & & & & & 13.86 & 15.02 & 1.16 & 0.013 & 39.0 & \nl $ $ & & & & & & 13.39 & 14.54 & 1.15 & 0.060 & 57.0 & \nl $ $ & & & & & & 13.08 & 14.24 & 1.16 & 0.129 & 84.5 & \nl $23$ &26.4 & 17 & 03 & 14.2 & $\cdots$ & 12.79 & 13.77 & 0.98 & -0.187 & 39.0 & 10/15/66 \nl $ $ & & & & & & 12.69 & 13.82 & 1.13 & -0.041 & 57.0 & \nl $ $ & & & & & & 12.69 & 13.69 & 1.00 & 0.061 & 84.5 & \nl $23$ &29.7 & 2 & 08 & 15.0 & $\cdots$ & 15.00\tablenotemark{a} & 15.59\tablenotemark{a} & 0.59 & -0.172 & 17.5 & 9/20/63 \nl $23$ &31.0 & 14 & 05 & 15.3 & $\cdots$ & 14.57 & 15.46 & 0.89 & -0.196 & 17.5 & 10/ 4/64 \nl $23$ &32.8 & 12 & 40 & 14.9 & $\cdots$ & 14.12 & 14.82 & 0.70 & -0.164 & 25.5 & 10/ 4/64 \nl $23$ &32.4 & 17 & 57 & 14.7 & $\cdots$ & 13.82 & 14.31 & 0.49 & -0.093 & 39.0 & 10/12/66 \nl $ $ & & & & & & 13.79 & 14.17 & 0.38 & 0.010 & 57.0 & \nl $ $ & & & & & & 13.84 & 14.12 & 0.28 & 0.115 & 84.5 & \nl $23$ &32.7 & 4 & 43 & 14.6 & NGC7706 & 13.90 & 14.90 & 1.00 & -0.149 & 25.5 & 10/21/65 \nl $23$ &32.7 & 21 & 21 & 15.2 & $\cdots$ & 14.47 & 15.39 & 0.92 & -0.209 & 17.5 & 10/12/66 \nl $ $ & & & & & & 14.39 & 15.54 & 1.15 & -0.039 & 26.0 & \nl $ $ & & & & & & 14.02 & 15.04 & 1.02 & 0.016 & 39.0 & \nl $ $ & & & & & & 14.17 & 15.44 & 1.27 & 0.169 & 57.0 & \nl $23$ &33.0 & 4 & 57 & 14.5 & $\cdots$ & 13.84 & 14.88 & 1.04 & -0.015 & 38.0 & 10/21/65 \nl $ $ & & & & & & 13.78 & 14.88 & 1.10 & 0.103 & 57.0 & \nl $23$ &33.2 & 9 & 53 & 15.6 & $\cdots$ & 15.43 & 15.92 & 0.49 & -0.115 & 17.5 & 10/ 4/64 \nl $23$ &33.3 & 16 & 06 & 15.3 & $\cdots$ & 14.34 & 15.51 & 1.17 & -0.043 & 26.0 & 10/12/66 \nl $ $ & & & & & & 14.08 & 15.39 & 1.31 & 0.063 & 39.0 & \nl $ $ & & & & & & 14.02 & 15.06 & 1.04 & 0.125 & 57.0 & \nl $ $ & & & & & & 14.08 & 15.32 & 1.24 & 0.245 & 84.5 & \nl $23$ &34.0 & 0 & 02 & 12.9 & NGC7716 & 12.54 & 13.26 & 0.72 & -0.298 & 38.0 & 10/ 3/64 \nl $23$ &34.2 & 17 & 15 & 15.0 & $\cdots$ & 14.44 & 14.78 & 0.34 & -0.021 & 39.0 & 10/15/66 \nl $ $ & & & & & & 14.23 & 14.46 & 0.23 & 0.049 & 57.0 & \nl $23$ &35.7 & 7 & 32 & 15.3 & $\cdots$ & 14.89 & 15.79 & 0.90 & -0.008 & 25.5 & 10/21/65 \nl $ $ & & & & & & 14.59 & 15.45 & 0.86 & 0.064 & 38.0 & \nl $ $ & & & & & & 14.60 & 15.69 & 1.09 & 0.196 & 57.0 & \nl $23$ &38.0 & 2 & 30 & 15.1 & $\cdots$ & 14.33 & 15.22 & 0.89 & -0.096 & 25.5 & 10/ 3/64 \nl $23$ &41.0 & 11 & 23 & 15.5 & $\cdots$ & 14.83 & 15.47 & 0.64 & -0.056 & 25.5 & 10/ 4/64 \nl $23$ &41.0 & 12 & 55 & 15.1 & $\cdots$ & 13.48 & 14.43 & 0.95 & -0.083 & 38.0 & 10/ 4/64 \nl $23$ &41.4 & 2 & 28 & 15.5 & $\cdots$ & 14.81 & 15.58 & 0.77 & -0.039 & 25.5 & 10/ 3/64 \nl $23$ &41.7 & 2 & 00 & 15.2 & $\cdots$ & 14.75 & 15.46 & 0.71 & -0.196 & 17.5 & 10/ 3/64 \nl $23$ &41.8 & 2 & 32 & 15.7 & $\cdots$ & 14.86 & 15.76 & 0.90 & 0.110 & 39.0 & 10/ 3/64 \nl $23$ &41.8 & 9 & 39 & 12.9 & NGC7743 & 11.74 & 12.67 & 0.93 & -0.239 & 57.0 & 10/ 4/64 \nl $23$ &42.6 & 19 & 37 & 15.2 & $\cdots$ & 14.80 & 15.53 & 0.73 & -0.040 & 26.0 & 10/14/66 \nl $ $ & & & & & & 14.57 & 15.28 & 0.71 & 0.049 & 39.0 & \nl $23$ &42.8 & -1 & 57 & 14.5 & NGC7746 & 13.58 & 14.57 & 0.99 & -0.209 & 25.5 & 10/ 3/64 \nl $23$ &43.4 & 11 & 47 & 14.6 & IC1508 & 13.60 & 14.23 & 0.63 & -0.116 & 38.0 & 10/ 4/64 \nl $23$ &44.1 & 3 & 30 & 13.8 & NGC7750 & 13.00 & 13.57 & 0.57 & -0.235 & 38.0 & 10/ 3/64 \nl $23$ &47.6 & 36 & 35 & 15.5 & $\cdots$ & 14.65\tablenotemark{a} & 15.81\tablenotemark{a} & 1.16 & -0.005 & 25.5 & 10/17/63 \nl $23$ &48.9 & 20 & 18 & 14.9 & $\cdots$ & 13.81 & 14.67 & 0.86 & -0.183 & 26.0 & 10/15/66 \nl $ $ & & & & & & 13.81 & 14.86 & 1.05 & -0.009 & 39.0 & \nl $ $ & & & & & & 13.30 & 14.27 & 0.97 & 0.024 & 57.0 & \nl $23$ &50.0 & 14 & 17 & 15.0 & $\cdots$ & 13.81 & 14.84 & 1.03 & -0.020 & 38.0 & 10/ 4/64 \nl $23$ &52.8 & 21 & 19 & 13.9 & NGC7786 & 14.23 & 14.91 & 0.68 & -0.140 & 26.0 & 10/14/66 \nl $ $ & & & & & & 13.81 & 14.42 & 0.61 & 0.044 & 57.0 & \nl $ $ & & & & & & 13.72 & 14.47 & 0.75 & -0.068 & 39.0 & \nl $23$ &56.0 & 10 & 26 & 13.8 & NGC7794 & 13.23 & 13.89 & 0.66 & -0.175 & 38.0 & 10/ 4/64 \nl $23$ &57.0 & 14 & 32 & 13.4 & NGC7800 & 13.15 & 13.58 & 0.43 & -0.233 & 38.0 & 10/ 4/64 \nl $23$ &59.4 & 36 & 22 & 15.4 & $\cdots$ & 14.84 & 15.63 & 0.79 & -0.032 & 25.5 & 10/17/63 \nl \tablenotetext{a}{Data marked with ``x" in original data sheets.} \tablenotetext{b}{Data marked with ``?" in original data sheets.} \tablenotetext{c}{Missing computer log entry.} \tablenotetext{d}{Perhaps 1/2 mag shunt error.} \tablenotetext{e}{$\|$mag$-$mag$_{rc3}\|>0.75$} \end{planotable} \end{document}
https://www.coaps.fsu.edu/bibliography/search.php?sqlQuery=SELECT%20author%2C%20title%2C%20type%2C%20year%2C%20publication%2C%20abbrev_journal%2C%20volume%2C%20issue%2C%20pages%2C%20keywords%2C%20abstract%2C%20thesis%2C%20editor%2C%20publisher%2C%20place%2C%20abbrev_series_title%2C%20series_title%2C%20series_editor%2C%20series_volume%2C%20series_issue%2C%20edition%2C%20language%2C%20author_count%2C%20online_publication%2C%20online_citation%2C%20doi%2C%20serial%2C%20area%20FROM%20refs%20WHERE%20serial%20%3D%2066%20ORDER%20BY%20first_author%2C%20author_count%2C%20author%2C%20year%2C%20title&client=&formType=sqlSearch&submit=Cite&viewType=&showQuery=0&showLinks=1&showRows=10&rowOffset=&wrapResults=1&citeOrder=&citeStyle=APA&exportFormat=RIS&exportType=html&exportStylesheet=&citeType=LaTeX&headerMsg=	fsu.edu	CC-MAIN-2023-14	application/x-latex	application/x-latex	crawl-data/CC-MAIN-2023-14/segments/1679296950110.72/warc/CC-MAIN-20230401160259-20230401190259-00386.warc.gz	806,577,734	1,455	%&LaTeX \documentclass{article} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} \usepackage{textcomp} \begin{document} \begin{thebibliography}{1} \bibitem{MacKinnon_etal2017} MacKinnon, J. A., Alford, M. H., Ansong, J. K., Arbic, B. K., Barna, A., Briegleb, B. P., et al. (2017). Climate Process Team on Internal-Wave Driven Ocean Mixing. \textit{Bull. Amer. Meteor. Soc.}, \textit{98}(11), 2429--2454. \end{thebibliography} \end{document}
https://fr.theanarchistlibrary.org/library/xavier-bekaert-l-anarchisme-une-ideologie-ou-une-methodologie.tex	theanarchistlibrary.org	CC-MAIN-2022-40	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2022-40/segments/1664030337398.52/warc/CC-MAIN-20221003035124-20221003065124-00770.warc.gz	307,527,170	11,932	\documentclass[DIV=12,% BCOR=0mm,% headinclude=false,% footinclude=false,open=any,% fontsize=10pt,% twoside,% paper=a4]% {scrbook} \usepackage{fontspec} \setmainfont[Script=Latin]{Linux Libertine O} \setsansfont[Script=Latin,Scale=MatchLowercase]{CMU Sans Serif} \setmonofont[Script=Latin,Scale=MatchLowercase]{CMU Typewriter Text} % global style \pagestyle{plain} \usepackage{microtype} % you need an updated texlive 2012, but harmless \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} \usepackage[shortlabels]{enumitem} \usepackage{tabularx} \usepackage[normalem]{ulem} \def\hsout{\bgroup \ULdepth=-.55ex \ULset} % https://tex.stackexchange.com/questions/22410/strikethrough-in-section-title % Unclear if \protect \hsout is needed. Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand{\captionformat}{} \renewcommand{\figureformat}{} \renewcommand{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} \usepackage{polyglossia} \setmainlanguage{french} % footnote handling \usepackage[fragile]{bigfoot} \usepackage{perpage} \DeclareNewFootnote{default} \DeclareNewFootnote{B} \MakeSorted{footnoteB} \renewcommand\thefootnoteB{(\arabic{footnoteB})} \deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand{\forcelinebreak}{\strut\\{}} \newcommand{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand{\Slash}{\slash\hspace{0pt}} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} % forbid widows/orphans \frenchspacing \sloppy \clubpenalty=10000 \widowpenalty=10000 % http://tex.stackexchange.com/questions/304802/how-not-to-hyphenate-the-last-word-of-a-paragraph \finalhyphendemerits=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{L’anarchisme : une idéologie ou une méthodologie ?} \date{} \author{Xavier Bekaert} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={anarchisme : une idéologie ou une méthodologie ?},% pdfauthor={Bekaert Xavier},% pdfsubject={},% pdfkeywords={idéologie; méthodologie; anarchisme}% } \begin{document} \begin{titlepage} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge L’anarchisme : une idéologie ou une méthodologie ?\par}}% \vskip 1em \vskip 2em {\usekomafont{author}{Xavier Bekaert\par}}% \vskip 1.5em \vfill \strut\par \end{center} \end{titlepage} \cleardoublepage \tableofcontents % start a new right-handed page \cleardoublepage \emph{Comment définir l'anarchisme ? Comme un projet de société future ? Une idéologie ? Ou comme une technique d'action dans le présent ? Une méthodologie ? En d'autres termes : L'anarchie est-elle une fin ou un moyen ?} \hairline La définition usuelle de l'anarchisme, rencontrée dans les dictionnaires, est toujours centrée sur le projet de société future de l'anarchisme : l'anarchie, dont la définition est bien entendu souvent burlesque. Par exemple, dans le Littré on trouve : \emph{Anarchie : absence de gouvernement, et par suite désordre et confusion}. Certaines sont cependant moins risibles et se rapprochent d'avantage d'une définition qui pourrait sembler acceptable par les anarchistes eux-mêmes. Par exemple, l'encyclopédie Larousse reprend la définition du Littré mais propose également la définition suivante de l'anarchie : \emph{système politique ou social suivant lequel tout individu doit être émancipé de toute tutelle gouvernementale}. Par suite, l'anarchisme est défini comme une \emph{idéologie ou doctrine qui préconise la suppression de l'État, quelles que soient les conditions historiques}. Ce type de définition, centrée uniquement sur le projet social, amène souvent l'anarchisme à être catalogué comme étant une idéologie, à classer parmi tant d'autres. Hélas, procéder ainsi revient à manquer, voire détourner complètement, l'essence profonde de l'anarchisme qui s'étend certainement au-delà du cadre restreint d'une idéologie. C'est ce que je voudrais tenter de montrer ici, pour ensuite proposer un autre type d'approche qui se voudrait plus en rapport avec la spécificité de l'anarchisme.\footnote{Je précise immédiatement que je ne prétends nullement être détenteur d'aucune vérité révélée. Cette autre approche n'est nullement novatrice, tout au plus tente-t-elle de souligner et de correspondre à l'originalité propre à l'anarchisme depuis ses origines, hélas trop souvent dissimulée derrière un paravent idéologique par ses détracteurs et par ses partisans\dots{} Je ne suis pas non plus un expert en histoire de l'anarchisme et j'espère avoir limité au maximum les inexactitudes en présentant le socialisme libertaire et le syndicalisme révolutionnaire.} \subsection{L'anarchisme, une idéologie ?} Tout d'abord, l'anarchisme n'est certainement pas un système de pensée figé, ni une théorie unique relevant d'un penseur bien particulier, il se caractérise au contraire par une pensée en constante évolution, et par la grande diversité de courants qui le composent. N'étant pas une théorie sociale fixe et bien déterminée, l'anarchisme ne se prête pas facilement à l'analyse systématique (au contraire du marxisme plus souvent formalisé, quoique lui aussi fort multiple), ce qui amène bon nombre de commentateurs à la congédier comme étant utopique, primitive, et incompatible avec la complexité des réalités sociales. Mais ce qui est considéré en général comme une preuve de faiblesse théorique, se révèle en réalité une des preuves de la cohérence, de la souplesse et de la richesse de l'idée anarchiste. Comme le faisait remarquer l'anarcho-syndicaliste allemand Rudolf Rocker (1873-1958) : \begin{quote} \emph{L'anarchisme n'est pas une solution brevetée pour tous les problèmes humains, ni une Utopie ou un ordre social parfait, ainsi qu'il a souvent été appelé, puisqu'il rejette en principe tout schéma et concept absolus. Il ne croit en aucune vérité absolue, ou but final défini pour le développement humain, mais dans la perfectibilité illimitée des arrangements sociaux et des conditions de vie humaines, qui sont toujours tirées vers de plus hautes formes d'expression, et auxquels pour cette raison on ne peut assigner aucun fin déterminée ni poser aucun but fixé. Le pire crime de n'importe quel type d'état est justement qu'il essaye toujours de forcer la riche diversité de la vie sociale à des formes définies, et de l'ajuster à une forme particulière qui ne permet pas de perspective plus large, et considère les excitants états précédents comme terminés}.\footnote{Rudolf Rocker, \emph{Anarcho-Syndicalism : Theory and Practice}, Secker and Warburg, 1938.} \end{quote} On constate donc que l'anarchisme ne peut donc pas être défini comme une doctrine sociale censée apporter \emph{la} solution à tous les problèmes de la société, ce qui l'éloigne d'une définition idéologique. Ceci pourrait suffire, mais il est intéressant d'approfondir encore un peu la nature de l'idéologie et les rapports qu'elle entretient avec le pouvoir avant d'affirmer que l'anarchisme \emph{ne peut être} une idéologie. \subsection{Idéologie et pouvoir} La point de départ est le constat qu'\emph{il n'y a pas de pouvoir sans nécessité de justification et, donc} (\dots{}) \emph{d'idéologie} comme le souligne A. G. Calvo pour qui l'idéologie est simplement \emph{la forme froide et détachée de la justification}.\footnote{Agustin Garcia Calvo, \emph{Qu'est-ce que l'État ?}, Atelier de Création Libertaire, 1992.} La nature de l'idéologie serait donc d'être un discours au service du pouvoir (du pouvoir en place ou de ceux qui ambitionnent d'y accéder) : \begin{quote} \emph{L'idéologie est une condition indispensable de l'État. Non seulement l'idéologie qu'émettent directement les organes du Pouvoir, mais aussi celle que développent les militants contre le Pouvoir, intégrés dans l'ordre}.\footnote{Agustin Garcia Calvo, \emph{Qu'est-ce que l'État ?}, Atelier de Création Libertaire, 1992.} \end{quote} En effet, toute idéologie, quelle que soit sa forme, s'accorde avec l'idéologie de l'État et la consolide, de par sa prétention à une explication totale, qui aboutit nécessairement (comme l'État) à vouloir figer la riche diversité de la vie sociale à une forme unique figée dans le temps. Dès lors, il serait plus approprié de considérer l'anarchisme comme étant une anti-idéologie, puisqu'au lieu d'avoir comme fonction de légitimer le pouvoir, l'anarchisme a pour principe de renier la légitimité de toute forme de pouvoir. \subsection{Anarchie et idéologie} De toute manière, savoir si l'anarchisme est ou n'est pas une idéologie revient à poser une mauvaise question, car l'anarchie \emph{n'a pas besoin} d'idéologie, seule l'autorité nécessite une justification, lorsqu'elle tente de légitimer les limites qu'elle impose à la liberté de chacun. Selon le célèbre linguiste Noam Chomsky, l'anarchisme est même \emph{une expression de l'idée que le fardeau de la preuve est toujours sur ceux qui défendent que l'autorité et la domination sont nécessaires}. L'anarchie n'a pas besoin d'idéologie mais cela ne signifie bien entendu pas qu'elle n'a pas besoin d'idées. L'anarchisme est entre autre un courant de pensée étendu et varié. Le rejet de l'idéologie ne revient certainement pas à refuser les discours théoriques ou les tentatives d'analyses globales. La contamination des idées est telle que certains oublient parfois que l'idéologie n'est pas la seule forme possible de discours rationnel sur le monde et sur les manières de l'appréhender. Cette idée erronée est directement reliée à cette, toute faite, selon laquelle l'État est la seule forme possible d'organisation de la société. Notons que la contamination idéologique et le malentendu au sujet de la nature de l'anarchisme sont tels que même les libertaires sont souvent eux-mêmes victimes sans le savoir du paradigme idéologique lorsqu'ils tentent de définir l'anarchisme. \subsection{L'anarchisme, un mouvement historique ?} Une fois rejetée la définition idéologique, on est souvent amené à rencontrer une définition plus concrète de l'anarchisme, comme mouvement historique. Par exemple, dans l'Encyclopédie Universalis on trouve : \begin{quote} \emph{L'anarchisme est un mouvement d'idées et d'action qui} (\dots{}) \emph{se propose de reconstruire la vie en commun sur la base de la volonté individuelle autonome}. \end{quote} C'est un chemin semblable qui est suivi par Rudolf Rocker pour qui l'anarchisme est \emph{une tendance définie dans le développement historique de l'humanité, qui} (\dots{}) \emph{s'efforce d'obtenir le libre déploiement de toutes les forces individuelles et sociales de la vie}.\footnote{Rudolf Rocker, \emph{Anarcho-Syndicalism : Theory and Practice}, Secker and Warburg, 1938.} Mais comment unifier les idées contenues dans les diverses définitions précédentes (projet social, corps d'idées, mouvement historique) qui contiennent toutes des fragment de la nature profonde de l'anarchisme ? \subsection{L'anarchisme, vu comme une méthodologie} Une manière de procéder pour unifier ces divers éléments est de définir l'anarchisme non comme une \emph{idéologie} (c'est-à-dire un système d'interprétation du monde à prétention totale dont découle une doctrine sociale déterminée), mais comme une \emph{méthodologie} (c'est-à-dire une réflexion générale sur la fin et les moyens aboutissant à une méthode d'action). Procéder ainsi a pour but de souligner et d'extraire ce qui constitue la force, la vitalité et la pertinence actuelle de l'idée anarchiste.\footnote{Dave Neal, \emph{Anarchism : Ideology or Methodology ?}, The Spunk Press Archive, 1997.} Définir l'anarchisme comme une méthodologie n'est pas une simple question de subtilité sémantique, c'est une distinction fondamentale très concrète, qui remonte aux origines de l'anarchisme lors de la scission du mouvement socialiste en deux courants : autoritaire et antiautoritaire. \subsection{Fondements historiques} \subsubsection{Le socialisme antiautoritaire} Le socialisme libertaire (ou antiautoritaire) trouve sa source dans la célèbre querelle entre Marx et Bakounine au sein de la Ière Internationale, qui aboutit à l'expulsion de Bakounine en 1872. De ce débat, toujours d'actualité, deux modèles de mouvements sociaux ont émergés. \begin{itemize} \item\relax Le \emph{modèle Marxiste} selon lequel : une avant-garde doit guider les masses vers le socialisme futur, le rôle des masses se réduisant à amener cette avant-garde au pouvoir (par le vote ou par la révolution armée selon que ce modèle soit réformiste ou révolutionnaire), le passage au socialisme devant se faire avec une période de transition étatique (succession de réformes de l'"État bourgeois" pour les sociaux-démocrates ; "dictature du prolétariat" pour les marxistes-léninistes) \item\relax Le \emph{modèle Bakouninien :} toute autorité politique doit être rejetée, l'action directe des masses librement organisées sans hiérarchie étant le moyen de réaliser le socialisme ici et maintenant, sans phase de transition. \end{itemize} Avant tout, l'antagonisme entre socialisme autoritaire et antiautoritaire est donc méthodologique. En effet, ces deux mouvements partagent une critique commune du capitalisme et un même projet social, la société socialiste sans État, ce sont les moyens proposés pour le réaliser qui les opposent. Et c'est le choix de la méthode (ou plus exactement les principes méthodologiques qui déterminent et constituent ce choix) qui fonde le socialisme libertaire, historiquement et ontologiquement (au sens où, défini comme une méthodologie, l'\emph{être} du socialisme libertaire c'est sa méthode). Cette déchirure voue toute alliance à l'échec, la profondeur de leurs divergences ne concernant pas uniquement le futur (transition ou passage immédiat vers le socialisme) ou le passé (de cruels souvenirs, hélas très révélateurs), mais surtout le présent (accepter ou rejeter l'État comme moyen comme modèle pour la transformation sociale). Des idéologies différentes, voire opposées, réussissent couramment à faire alliance dans un combat politique particulier pour le contrôle du pouvoir (exemple évident : les élections), par contre des divergences méthodologiques sont de nature inconciliables (le drame des révolutions russe et espagnole est suffisamment claire là-dessus). Puisque la fin concerne le futur mais les moyens résident dans le présent, ils entrent donc directement en conflit. On peut tricher avec la fin, pas avec les moyens. \subsubsection{L'anarchie, une idée en action} L'exemple du socialisme antiautoritaire montre que, contrairement à une idée répandue, ce n'est pas uniquement le rejet de l'État pour la société future qui caractérise l'anarchisme (l'entièreté du courant socialiste partage en principe cet objectif), mais surtout les pratiques développées dans le présent. Selon l'historien libertaire Georges Woodcock (1912-1995), \emph{l'anarchisme ne se limite pas un projet de société future}, il revient plutôt à \emph{soutenir pratiquement les idées et modèles libertaires aussi loin que cela peut être fait ici et maintenant}.\footnote{Georges Woodcock, \emph{Tradition and Revolution}, Kick it Over nE19-20, été et hiver 1987.} Au lieu d'attendre passivement la révolution, qui peut très bien ne jamais venir ou dégénérer en un simple changement de maîtres si la société n'est pas suffisamment préparée, l'anarchisme revient d'après lui à \emph{renforcer et encourager toutes les impulsions libertaires et mutualistes, qu'elles soient constructives au sens où elles créent de nouvelles organisations libertaires, ou rebelles au sens où elles résistent aux nouvelles attaques sur la liberté ou cherchent à mettre fin aux vieilles tyrannies et discriminations.}\footnote{Georges Woodcock, \emph{Tradition and Revolution}, Kick it Over nE19-20, été et hiver 1987.} \subsubsection{L'anarcho-syndicalisme} Définir l'anarchisme comme une méthodologie permet également de comprendre la raison fondamentale des multiples succès historiques de l'anarcho-syndicalisme. Ce dernier trouve son origine dans le constat effectué vers 1894 par la majorité des anarchistes de l'échec de la tactique de la "propagande par le fait". Contrairement aux espoirs immenses que les attentats individuels avaient pu soulever chez certains militants, aucune prise de conscience collective ne s'était produite au sein des masses ouvrières. Pire, la répression qui suivit les attentats, loin de constituer le prélude de la révolution sociale, marqua bien plus la fin d'une époque. Un grand nombre d'anarchistes rejoignirent alors les organisations syndicales naissantes (les Bourses du Travail) dans lesquelles ils jouèrent un grand rôle en y ravivant les principes méthodologiques du socialisme libertaire, c'est-à-dire l'indépendance vis-à-vis des organisations politiques (autonomie syndicale, anti-parlementarisme\dots{}), la pratique de l'action directe (grèves "sauvages", boycotts, occupations, sabotages techniques, grève générale\dots{}), l'organisation autonome et fédérée du mouvement social\dots{} L'anarcho-syndicalisme est souvent défini comme un \emph{anarchisme qui attribue aux syndicats l'organisation de la société} (Larousse). À nouveau, une définition de type "doctrine sociale" manque sa cible et appauvrit, voire détourne, la signification réelle. En effet, les organisations anarcho-syndicalistes ne sont pas des organisations spécifiquement anarchistes, même si bon nombre d'anarchistes y participent (la dénomination syndicalisme révolutionnaire, souvent synonyme d'anarcho-syndicalisme, ne contient d'ailleurs pas de référence explicite à l'anarchisme). Plutôt qu'une doctrine sociale, le syndicalisme révolutionnaire revient à \emph{pratiquer} les principes et méthodes libertaires au sein du mouvement social, par le biais du syndicat. Une définition méthodologique comme celle-là rend probablement mieux compte de sa nature et des raisons de son succès. L'anarcho-syndicalisme correspond donc à l'essence profonde de la propagande par le fait (propager les idées libertaires par l'action), avant qu'elle ne dégénère dans un nihilisme destructeur, source et conséquence de l'isolement révolutionnaire conduisant les plus impatients à de tragiques actes de désespoir. \subsection{Principes fondateurs} \subsubsection{Adéquation entre la fin et les moyens} Pour conclure cette recherche de la nature de l'anarchisme, il est indispensable d'analyser le principe fondateur de la méthode anarchiste : la \emph{nécessaire adéquation} entre la fin et les moyens. Des moyens en contradiction avec la fin amènent inévitablement à un résultat opposé aux objectifs poursuivis. L'idée de vouloir utiliser l'État pour amener la société socialiste sans État contient sa propre contradiction et ne pouvait que mener aux échecs les plus tragiques. Pour s'en convaincre, il suffit d'observer les échecs du socialisme autoritaire, qu'il soit réformiste ou révolutionnaire. L'adéquation des moyens avec la fin est par contre un principe positif amenant à développer \emph{aujourd'hui} des pratiques préfigurant la société de \emph{demain}. En effet, la société à venir n'est pas indépendante des moyens utilisés pour la créer, mais le reflet du combat social qui l'a précédée et des idées qui l'ont sous-tendue. Ce principe méthodologique d'adéquation des moyens avec la fin aboutit donc à trois principes méthodiques : ! rejet de la politique ! action directe ! auto-organisation du mouvement social. Les deux premiers sont parfois sources de confusion, c'est pourquoi ils sont commentés plus en détail. \subsubsection{Rejet de la politique} Le rejet du parlementarisme et de l'action politique par l'anarchisme est très souvent mal compris, et interprété par ses détracteurs comme la preuve d'un désintérêt pour la chose publique, d'une incapacité à infléchir sur le cours de la société, ou d'un refus de prendre ses responsabilités lorsque des décisions doivent être prises. Mais d'abord, qu'est-ce que la politique ? Le sens donné à ce mot varie énormément. En se limitant à la définition donnée par le philosophe André Comte-Sponville, on découvre que la politique, \emph{c'est la vie commune et conflictuelle, sous la domination de l'État et pour son contrôle : c'est l'art de prendre, de garder, et d'utiliser le pouvoir}.\footnote{André Comte-Sponville, \emph{Pensées sur la politique}, Albin Michel, 1998.} Entendue dans ce sens-là (sens auquel se réfèrent les anarchistes lorsqu'ils rejettent l'action politique), la politique ne se limite pas à la gestion de la vie commune et conflictuelle (qui est \emph{le} centre d'intérêt de l'anarchisme), elle est sa monopolisation par le pouvoir. Cette monopolisation a entre autres pour effet de détourner l'action politique de son but avoué : la gestion de la vie sociale, vers un but inavoué : le contrôle du pouvoir. En effet : \begin{quote} \emph{Tout homme qui fait de la politique aspire au pouvoir - soit parce qu'il le considère comme un moyen au service d'autres fins, idéales ou égoïstes, soit parce qu'il le désire "pour lui-même" en vue de jouir du sentiment de prestige qu'il confère.}\footnote{Max Weber, \emph{Le savant et le philosophe}, Librairie Plon, 1959.} \end{quote} C'est ainsi que l'anarchisme n'est pas un mouvement \emph{politique} mais un mouvement \emph{social} dans la mesure où il ne lutte pas pour prendre le pouvoir mais tente de mettre fin à toute forme de pouvoir. En d'autres termes, il vise la \emph{transformation} de la société, et non son \emph{contrôle} (même au nom d'une noble fin). Et c'est pourquoi, le mouvement anarchiste n'a pas besoin d'idéologie. La conquête du pouvoir nécessite une idéologie, pour justifier l'accaparement de la gestion de la société par une minorité imposant à tous un modèle social déterminé censé garantir le bonheur de chacun. L'anarchisme vise par contre à restituer la gestion de la vie commune à la société elle-même, et cette restitution ne nécessite pas de justification, elle lui revient de droit. \subsubsection{Action directe} Mais le rejet de l'action politique et les raisons de ce rejet ne suffisent pas à caractériser la méthodologie anarchiste, car elle détermine une technique d'action et non d'inaction. Chez les anarchistes, l'action directe remplace l'action politique. L'action directe consiste \emph{à intervenir directement dans la société, sans passer par l'intermédiaire des institutions}.\footnote{Jean-Marie Muller, \emph{Lexique de la non-violence}, Alternatives non-violentes n°68, 1988.} Elle vise à réaliser nos buts à travers notre propre activité plutôt qu'à travers celle des autres, particulièrement celle de "représentants" surtout soucieux de la préservation du statu-quo. Elle se base sur une critique radicale de la démocratie formelle parlementaire dans laquelle le citoyen délègue son pouvoir au lieu de l'exercer. L'action directe est souvent associée, dans l'opinion publique, à la violence mais cette technique d'action est entièrement indépendante du choix ou du rejet de la violence, elle peut tout aussi bien avoir un caractère violent que non-violent (sur l'action directe non-violente voir l'article du numéro précédent d'AL.\footnote{Claudio, \emph{Voor Moeder Aarde}, Alternative Libertaire n°216, 1999.} En revanche, \emph{le vrai non-violent peut seulement croire en l'action directe, jamais en l'action politique} car \emph{la base de toute action politique est la contrainte ; même lorsque l'État fait de bonnes choses, cela repose finalement sur une matraque, un revoler, ou une prison}, souligna l'anarchiste américaine Voltairine de Cleyre (1866-1912). Pour les anarchistes, l'action directe n'est pas seulement une méthode de protestation, c'est aussi une école libertaire, dans laquelle les individus retrouvent leur dignité en se réapropriant le pouvoir d'agir sur leur propre existence et en renouant avec les liens sociaux d'entraide et de solidarité. Conçue ainsi, l'action directe c'est l'anarchie en action, ici et maintenant. Le principe méthodologique d'adéquation des moyens avec la fin permet donc d'ancrer dans le présent un projet de société qui, sans cela, pourrait paraître fort lointain voire franchement inaccessible, alors qu'au sein de la société actuelle existe déjà, en germes, la société de demain, dans les nombreuses associations d'individus basées sur la coopération volontaire et l'aide mutuelle. En conséquence, ce principe méthodologique va au-delà d'une simple réconciliation entre la fin et les moyens, il vise à opérer une réelle fusion entre eux. \subsection{Les moyens sont la fin, la fin est le moyen} Toutes les idéologies ont en commun de séparer les moyens de la fin, ce qui les conduit soit à\dots{} \begin{itemize} \item\relax \emph{Subordonner la fin aux moyens}. C'est la tare fondamentale du réformisme. Son défaut incurable n'est pas tant de vouloir une transformation progressive de la société, mais de se concentrer sur l'action politique. Les moyens (les luttes du pouvoir) deviennent alors vite une fin en soi, et la nécessité de prendre des décisions en accord avec les "dures contraintes de la réalité" aboutit rapidement à renoncer aux principes initiaux \item\relax \emph{Subordonner les moyens à la fin.} C'est la tare des révolutions autoritaires. Ses partisans considèrent que, pourvu que la fin soit bonne et qu'on la garde toujours à l'esprit, les moyens importent peu (la fin possède la capacité de transcender les moyens), seul compte le critère de l'efficacité, assimilée à la prise en main du pouvoir. \end{itemize} Pour être plus précis, réformistes comme révolutionnaires adoptent les deux positions à des degrés divers et selon les circonstances, mais quoiqu'il en soit, ces deux attitudes séparent les moyens de la fin et subordonnent l'un par rapport à l'autre. L'anarchisme, en tant que méthodologie, considère au contraire que les moyens et la fin sont indissolublement liés. Séparer artificiellement la fin des moyens revient à nier la relation organique qui les unit. Chaque moyen est étroitement lié à un but. Les moyens contiennent et engendrent inévitablement la fin qui leur est propre. Par exemple, il est de la nature même de l'État de maintenir la division de la société en classes antagonistes dont l'une exerce sa domination sur l'autre. L'État utilisé comme un moyen (par ex., pour aboutir à la société sans classes et sans État) ne peut aboutir qu'à la fin qui lui est propre, c'est à dire l'État, qui est sa propre fin. Mais l'idée anarchiste va plus loin que la nécessaire adéquation entre les moyens et la fin déjà évoquée précédemment, elle consiste réellement à \emph{fusionner les moyens et la fin}. D'une part, l'objectif poursuivi par l'anarchisme est précisément de mettre en pratique l'anarchie ici et maintenant, en développant les formes d'organisations libertaires au sein de la société, et en luttant contre la domination exercée par les forces du désordre établi. D'autre part, le projet social libertaire n'est pas une abstraction toute faite, c'est dans les luttes et les alternatives vécues concrètement que l'anarchie prend forme et s'élabore progressivement, au contact de la réalité. La fin indique les moyens, et en retour, les moyens construisent la fin. \subsection{Conclusion} La question de départ \emph{L'anarchie : une fin ou un moyen ?} semble posséder une réponse : l'anarchie est simultanément la fin et le moyen de l'anarchisme. Alors que le propre des idéologies de tous bords est de séparer la fin des moyens, l'anarchisme tente de les fusionner en une anarchie qui ne serait pas une utopie pour demain mais une idée en action ici et maintenant. % begin final page \clearpage % if we are on an odd page, add another one, otherwise when imposing % the page would be odd on an even one. \ifthispageodd{\strut\thispagestyle{empty}\clearpage}{} % new page for the colophon \thispagestyle{empty} \begin{center} Bibliothèque Anarchiste \smallskip Anti-copyright \bigskip \includegraphics[width=0.25\textwidth]{logo-sv.pdf} \bigskip \end{center} \strut \vfill \begin{center} Xavier Bekaert L’anarchisme : une idéologie ou une méthodologie ? \bigskip Consulté le 15 octobre 2016 de \href{http://libertaire.pagesperso-orange.fr/anar3.htm}{libertaire.pagesperso-orange.fr} \bigskip \textbf{fr.theanarchistlibrary.org} \end{center} % end final page with colophon \end{document}
http://voodoo-circle.sourceforge.net/doc_for_developers/latex/c__procedure_8h_source.tex	sourceforge.net	CC-MAIN-2018-13	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2018-13/segments/1521257648178.42/warc/CC-MAIN-20180323044127-20180323064127-00118.warc.gz	296,104,097	3,407	\hypertarget{c__procedure_8h}{ \section{c\_\-procedure.h} \label{c__procedure_8h}\index{c\_\-procedure.h@{c\_\-procedure.h}} } \begin{DoxyCode} 00001 \textcolor{comment}{/*************************************************************************} 00002 \textcolor{comment}{ c\_procedure.h - description} 00003 \textcolor{comment}{ -------------------} 00004 \textcolor{comment}{ begin : Thu May 10 2007} 00005 \textcolor{comment}{ copyright : (C) 2004-2010 Marian VooDooMan Meravy} 00006 \textcolor{comment}{ email : ghostvoodooman -a.T= users (dot) sourceforge.net} 00007 \textcolor{comment}{ ***********************************************************************/} 00008 00009 \textcolor{comment}{/***********************************************************************} 00010 \textcolor{comment}{} 00011 \textcolor{comment}{VooDoo cIRCle - an IRC (ro)bot} 00012 \textcolor{comment}{Copyright (C) 2004-2010 Marian VooDooMan Meravy} 00013 \textcolor{comment}{ (ghostvoodooman -a.T= users (dot) sourceforge.net)} 00014 \textcolor{comment}{} 00015 \textcolor{comment}{This program is free software; you can redistribute it and/or} 00016 \textcolor{comment}{modify it under the terms of the GNU General Public License} 00017 \textcolor{comment}{as published by the Free Software Foundation; either version 2} 00018 \textcolor{comment}{of the License, or (at your option) any later version.} 00019 \textcolor{comment}{} 00020 \textcolor{comment}{This program is distributed in the hope that it will be useful,} 00021 \textcolor{comment}{but WITHOUT ANY WARRANTY; without even the implied warranty of} 00022 \textcolor{comment}{MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the} 00023 \textcolor{comment}{GNU General Public License for more details.} 00024 \textcolor{comment}{} 00025 \textcolor{comment}{You should have received a copy of the GNU General Public License} 00026 \textcolor{comment}{along with this program; if not, write to the Free Software} 00027 \textcolor{comment}{Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.} 00028 \textcolor{comment}{} 00029 \textcolor{comment}{*************************************************************************/} 00030 \textcolor{comment}{} 00031 \textcolor{comment}{/!} 00032 \textcolor{comment}{ $\backslash$file} 00033 \textcolor{comment}{ $\backslash$brief Class 'c\_procedure'} 00034 \textcolor{comment}{/} 00035 00036 \textcolor{preprocessor}{#ifndef C\_PROCEDURE\_H\_\_} 00037 \textcolor{preprocessor}{}\textcolor{preprocessor}{#define C\_PROCEDURE\_H\_\_} 00038 \textcolor{preprocessor}{} 00039 \textcolor{preprocessor}{#if defined(HAVE\_CONFIG\_H)} 00040 \textcolor{preprocessor}{}\textcolor{preprocessor}{# include <config.h>} 00041 \textcolor{preprocessor}{#endif} 00042 \textcolor{preprocessor}{} 00043 \textcolor{preprocessor}{#include <string>} 00044 \textcolor{preprocessor}{#include <vector>} 00045 \textcolor{preprocessor}{#include <stack>} 00046 \textcolor{preprocessor}{#include <list>} 00047 \textcolor{preprocessor}{#include <map>} 00048 \textcolor{preprocessor}{#include <algorithm>} 00049 00050 \textcolor{preprocessor}{#include "../utils/memleak.h"} 00051 00052 \textcolor{preprocessor}{#include "../params.h"} 00053 00054 \textcolor{preprocessor}{#include "\hyperlink{c__proc__command_8h}{c_proc_command.h}"} 00055 \textcolor{preprocessor}{#include "../logic/c\_rproc.h"} 00056 \textcolor{preprocessor}{#include "../botnet/c\_replication.h"} 00057 \textcolor{comment}{} 00058 \textcolor{comment}{/!} 00059 \textcolor{comment}{ $\backslash$brief Stores procedure implementation and its properties} 00060 \textcolor{comment}{ $\backslash$author VooDooMan} 00061 \textcolor{comment}{ $\backslash$version 1} 00062 \textcolor{comment}{ $\backslash$date 2004} 00063 \textcolor{comment}{/} \hypertarget{c__procedure_8h_source_l00064}{}\hyperlink{classc__procedure}{00064} \textcolor{keyword}{class }\hyperlink{classc__procedure}{c_procedure} 00065 \{ 00066 \textcolor{keyword}{public}: \hypertarget{c__procedure_8h_source_l00067}{}\hyperlink{classc__procedure_afa0ff6cbb7a91dd934c2e40a4c71fce8_afa0ff6cbb7a91dd934c2e40a4c71fce8}{00067} \textcolor{keywordtype}{string} \hyperlink{classc__procedure_afa0ff6cbb7a91dd934c2e40a4c71fce8_afa0ff6cbb7a91dd934c2e40a4c71fce8}{name}; \textcolor{comment}{//!< Declaration string of pr ocedure} \hypertarget{c__procedure_8h_source_l00068}{}\hyperlink{classc__procedure_a6b03d3c5594682beae01f72da5d392f2_a6b03d3c5594682beae01f72da5d392f2}{00068} \textcolor{comment}{} deque<c\_proc\_command> \hyperlink{classc__procedure_a6b03d3c5594682beae01f72da5d392f2_a6b03d3c5594682beae01f72da5d392f2}{commands}; \textcolor{comment}{//!< Commands of procedure} \hypertarget{c__procedure_8h_source_l00069}{}\hyperlink{classc__procedure_ac1b6c214bd03aab33adbdc0b2aecc180_ac1b6c214bd03aab33adbdc0b2aecc180}{00069} \textcolor{comment}{} vector<string> \hyperlink{classc__procedure_ac1b6c214bd03aab33adbdc0b2aecc180_ac1b6c214bd03aab33adbdc0b2aecc180}{groups}; \textcolor{comment}{//!< List of groups that proc edure is member of} \hypertarget{c__procedure_8h_source_l00070}{}\hyperlink{classc__procedure_aaba2c2db69d46d68ce838a01f29ecb83_aaba2c2db69d46d68ce838a01f29ecb83}{00070} \textcolor{comment}{} vector<c\_rproc> \hyperlink{classc__procedure_aaba2c2db69d46d68ce838a01f29ecb83_aaba2c2db69d46d68ce838a01f29ecb83}{rproc}; \textcolor{comment}{//!< List of bot which can ca ll this procedure remotely (BOTNET)} 00071 \textcolor{comment}{} \hypertarget{c__procedure_8h_source_l00072}{}\hyperlink{classc__procedure_aea8d1d604a8e1c6e67c8f57ec1059af0_aea8d1d604a8e1c6e67c8f57ec1059af0}{00072} vector<c\_replication> \hyperlink{classc__procedure_aea8d1d604a8e1c6e67c8f57ec1059af0_aea8d1d604a8e1c6e67c8f57ec1059af0}{replication}; \textcolor{comment}{//!< Informations of replicat ion} \hypertarget{c__procedure_8h_source_l00073}{}\hyperlink{classc__procedure_a4753245bd9288aea42f1e561f479d1f4_a4753245bd9288aea42f1e561f479d1f4}{00073} \textcolor{comment}{} \hyperlink{utils_8h_a3ad7b00f971eb60ce4d6b176d8e9d767_a3ad7b00f971eb60ce4d6b176d8e9d767}{my_time_t} \hyperlink{classc__procedure_a4753245bd9288aea42f1e561f479d1f4_a4753245bd9288aea42f1e561f479d1f4}{last_changed}; \textcolor{comment}{//!< Time of last change} 00074 \textcolor{comment}{} \hypertarget{c__procedure_8h_source_l00075}{}\hyperlink{classc__procedure_a63014f07a2c8186b3b7f76237349fbd9_a63014f07a2c8186b3b7f76237349fbd9}{00075} \textcolor{keywordtype}{int} \hyperlink{classc__procedure_a63014f07a2c8186b3b7f76237349fbd9_a63014f07a2c8186b3b7f76237349fbd9}{minimal_botnet_version}; \textcolor{comment}{//!< Number of minimal BOTNET protocol version (for replication)} 00076 \textcolor{comment}{} \hypertarget{c__procedure_8h_source_l00077}{}\hyperlink{classc__procedure_adc240c9d0807cb1b9eca5d167062654b_adc240c9d0807cb1b9eca5d167062654b}{00077} \textcolor{keywordtype}{bool} \hyperlink{classc__procedure_adc240c9d0807cb1b9eca5d167062654b_adc240c9d0807cb1b9eca5d167062654b}{parsed_call_string}; \textcolor{comment}{//!< If we have parsed call s tring} \hypertarget{c__procedure_8h_source_l00078}{}\hyperlink{classc__procedure_aa65a15ceb877b2bf45be3b83a3504610_aa65a15ceb877b2bf45be3b83a3504610}{00078} \textcolor{comment}{} \textcolor{keywordtype}{string} \hyperlink{classc__procedure_aa65a15ceb877b2bf45be3b83a3504610_aa65a15ceb877b2bf45be3b83a3504610}{name_only}; \textcolor{comment}{//!< Only name of procedure} \hypertarget{c__procedure_8h_source_l00079}{}\hyperlink{classc__procedure_a1963cdb90f098d3cfbd05c3da1241b68_a1963cdb90f098d3cfbd05c3da1241b68}{00079} \textcolor{comment}{} vector<string> \hyperlink{classc__procedure_a1963cdb90f098d3cfbd05c3da1241b68_a1963cdb90f098d3cfbd05c3da1241b68}{args}; \textcolor{comment}{//!< List of arguments} 00080 \textcolor{comment}{} \hypertarget{c__procedure_8h_source_l00081}{}\hyperlink{classc__procedure_ab224e36ee4ee31d6342154e9441ea0f5_ab224e36ee4ee31d6342154e9441ea0f5}{00081} \textcolor{keywordtype}{int} \hyperlink{classc__procedure_ab224e36ee4ee31d6342154e9441ea0f5_ab224e36ee4ee31d6342154e9441ea0f5}{lock_cnt}; \textcolor{comment}{//!< If we are executing this procedure} 00082 \textcolor{comment}{}\textcolor{comment}{} 00083 \textcolor{comment}{ /!} 00084 \textcolor{comment}{ $\backslash$brief Constructor} 00085 \textcolor{comment}{ $\backslash$author VooDooMan} 00086 \textcolor{comment}{ $\backslash$version 1} 00087 \textcolor{comment}{ $\backslash$date 2005} 00088 \textcolor{comment}{ /} 00089 \hyperlink{classc__procedure_ac1989445454952e75e1dac2fb64a417f_ac1989445454952e75e1dac2fb64a417f}{c_procedure}(); 00090 \textcolor{comment}{} 00091 \textcolor{comment}{ /!} 00092 \textcolor{comment}{ $\backslash$brief Parses call string} 00093 \textcolor{comment}{ $\backslash$author VooDooMan} 00094 \textcolor{comment}{ $\backslash$version 1} 00095 \textcolor{comment}{ $\backslash$date 2005} 00096 \textcolor{comment}{ /} 00097 \textcolor{keywordtype}{void} \hyperlink{classc__procedure_a00dfd25303556416f56bbe36c67c7d7a_a00dfd25303556416f56bbe36c67c7d7a}{parse_call_string}(); 00098 \textcolor{comment}{} 00099 \textcolor{comment}{ /!} 00100 \textcolor{comment}{ $\backslash$brief Returns last changed attribute} 00101 \textcolor{comment}{ $\backslash$author VooDooMan} 00102 \textcolor{comment}{ $\backslash$version 1} 00103 \textcolor{comment}{ $\backslash$date 2005} 00104 \textcolor{comment}{ /} \hypertarget{c__procedure_8h_source_l00105}{}\hyperlink{classc__procedure_a23b6cbb95908ddb96c9434cee09373f0_a23b6cbb95908ddb96c9434cee09373f0}{00105} \hyperlink{utils_8h_a3ad7b00f971eb60ce4d6b176d8e9d767_a3ad7b00f971eb60ce4d6b176d8e9d767}{my_time_t} \hyperlink{classc__procedure_a23b6cbb95908ddb96c9434cee09373f0_a23b6cbb95908ddb96c9434cee09373f0}{get_last_changed}() \{ \textcolor{keywordflow}{return} \hyperlink{classc__procedure_a4753245bd9288aea42f1e561f479d1f4_a4753245bd9288aea42f1e561f479d1f4}{last_changed}; \} 00106 \textcolor{comment}{} 00107 \textcolor{comment}{ /!} 00108 \textcolor{comment}{ $\backslash$brief Sets last changed attribute} 00109 \textcolor{comment}{ $\backslash$author VooDooMan} 00110 \textcolor{comment}{ $\backslash$version 1} 00111 \textcolor{comment}{ $\backslash$date 2005} 00112 \textcolor{comment}{ $\backslash$param when Last changed} 00113 \textcolor{comment}{ /} \hypertarget{c__procedure_8h_source_l00114}{}\hyperlink{classc__procedure_a614f9a77f2370d68bc0fe16f9939e470_a614f9a77f2370d68bc0fe16f9939e470}{00114} \textcolor{keywordtype}{void} \hyperlink{classc__procedure_a614f9a77f2370d68bc0fe16f9939e470_a614f9a77f2370d68bc0fe16f9939e470}{set_last_changed}(\hyperlink{utils_8h_a3ad7b00f971eb60ce4d6b176d8e9d767_a3ad7b00f971eb60ce4d6b176d8e9d767}{my_time_t} when) \{ \hyperlink{classc__procedure_a4753245bd9288aea42f1e561f479d1f4_a4753245bd9288aea42f1e561f479d1f4}{last_changed}=when; \} 00115 \textcolor{comment}{} 00116 \textcolor{comment}{ /!} 00117 \textcolor{comment}{ $\backslash$brief Gets minimal botnet version (for replication)} 00118 \textcolor{comment}{ $\backslash$author VooDooMan} 00119 \textcolor{comment}{ $\backslash$version 1} 00120 \textcolor{comment}{ $\backslash$date 2005} 00121 \textcolor{comment}{ /} \hypertarget{c__procedure_8h_source_l00122}{}\hyperlink{classc__procedure_a2b1ffd98693650ba5d6483e6cad38b58_a2b1ffd98693650ba5d6483e6cad38b58}{00122} \textcolor{keywordtype}{int} \hyperlink{classc__procedure_a2b1ffd98693650ba5d6483e6cad38b58_a2b1ffd98693650ba5d6483e6cad38b58}{get_minimal_botnet_version}() \{ \textcolor{keywordflow}{return} \hyperlink{classc__procedure_a63014f07a2c8186b3b7f76237349fbd9_a63014f07a2c8186b3b7f76237349fbd9}{minimal_botnet_version}; \} 00123 \textcolor{comment}{} 00124 \textcolor{comment}{ /!} 00125 \textcolor{comment}{ $\backslash$brief Gets name of procedure} 00126 \textcolor{comment}{ $\backslash$author VooDooMan} 00127 \textcolor{comment}{ $\backslash$version 1} 00128 \textcolor{comment}{ $\backslash$date 2005} 00129 \textcolor{comment}{ */} \hypertarget{c__procedure_8h_source_l00130}{}\hyperlink{classc__procedure_a3d64e4b5d57956db0dc5e58c271af45b_a3d64e4b5d57956db0dc5e58c271af45b}{00130} \textcolor{keywordtype}{string} \hyperlink{classc__procedure_a3d64e4b5d57956db0dc5e58c271af45b_a3d64e4b5d57956db0dc5e58c271af45b}{get_name}() \{ \textcolor{keywordflow}{return} \hyperlink{classc__procedure_afa0ff6cbb7a91dd934c2e40a4c71fce8_afa0ff6cbb7a91dd934c2e40a4c71fce8}{name}; \} 00131 \}; 00132 00133 \textcolor{preprocessor}{#endif} 00134 \textcolor{preprocessor}{} \end{DoxyCode}
https://mirror.aut.ac.nz/CTAN/graphics/mcf2graph/mcf_manual.tex	aut.ac.nz	CC-MAIN-2021-21	application/x-tex	text/x-matlab	crawl-data/CC-MAIN-2021-21/segments/1620243991829.45/warc/CC-MAIN-20210514214157-20210515004157-00104.warc.gz	413,131,819	13,078	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Molecular Coding Format manual by Akira Yamaji 2021.05.05 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \documentclass[a4paper]{article} \usepackage[pdftex]{graphicx} \usepackage[pdftex]{hyperref} \usepackage{makeidx} \makeindex \hypersetup{colorlinks=true,linkcolor=blue} \makeatletter \usepackage{mcf_setup} %---------------------------------------------------------------------------- %%%%\pdfpkresolution=1200 %---------------------------------------------------------------------------- %%%%\edef\fext{pk}% ** for proof print (fast) \edef\fext{mps}% for final print (it takes long time) %---------------------------------------------------------------------------- %%%%\edef\fext{png}% %%%%\edef\fext{svg}% %%%%\edef\fext{eps}% %---------------------------------------------------------------------------- \topmargin=-18mm \textheight=254mm \textwidth=168mm \oddsidemargin=0mm %%%%\oddsidemargin=7mm %%%%\evensidemargin=-7mm \unitlength=1mm% %---------------------------------------------------------------------------- \newcount \fnum% \newdimen \htman% \newdimen \wdman% \newdimen \htmans% \newbox \fbox% %---------------------------------------------------------------------------- \htman=45mm% \wdman=94mm% \htmans=42mm% \fnum=1% %---------------------------------------------------------------------------- \edef\MCFjobname{mcf_man_soc}% %---------------------------------------------------------------------------- \font\@strufont=\MCFjobname\relax% %---------------------------------------------------------------------------- \def\MCFgraph{% \ifx\fext\@pk{\@strufont\char\fnum}% \else% \edef\file@name{\MCFjobname-\z@num\fnum.\fext}% \setbox\fbox=\hbox{\@strufont\char\fnum}% \includegraphics[width=\wd\fbox,height=\ht\fbox]{\file@name}% %%%%%%\includegraphics{\file@name}% \fi% \global\advance\fnum\@ne\relax% }% %--------------------------------------------------------------------------- \def\put@char{% \begin{picture}(75,100)% \put(0,95){\bf [\NO]\EN}% \put(5,90){\small\tt FM:\fm{ }MW:\mw}% \put(5,0){\MCFgraph}% \end{picture}% }% %---------------------------------------------------------------------------- \def\INFO#1{\@for\@temp:=#1\do{\tag@var\@temp}\put@char}% %---------------------------------------------------------------------------- \begin{document} \title{\Huge\sf Molecular Coding Format manual} \author{Akira Yamaji} \date{\today} \maketitle \begin{center} Located at http://www.ctan.org/pkg/mcf2graph \end{center} \begin{center} Suggestion or request mail to: [email protected] \end{center} %----------------------------------------------------------------------------- \thispagestyle{empty} \vspace{5mm}% \MCFgraph\MCFgraph\MCFgraph\MCFgraph\\ \MCFgraph\MCFgraph\MCFgraph\MCFgraph\\ \MCFgraph\MCFgraph\MCFgraph\MCFgraph\\ \MCFgraph\MCFgraph\MCFgraph\MCFgraph\\ \MCFgraph\MCFgraph\MCFgraph\MCFgraph\\ \MCFgraph\MCFgraph\MCFgraph\MCFgraph\\ \MCFgraph\MCFgraph\MCFgraph\MCFgraph %----------------------------------------------------------------------------- \twocolumn \thispagestyle{empty} \tableofcontents %----------------------------------------------------------------------------- \linethickness{0.08mm}% %---------------------------------------------------------------------------- \newpage \twocolumn \section{Introduction} Molecular Coding Format(MCF) is new linear notation represent chemical structure diagrams. This Coding is named from programing technique such as operator, array, scope, macro, adressing, etc. mcf2graph convert from MCF to pk font, PNG, SVG, EPS, MOL file. It is also able to calculate molecular weight, exact mass, molecular formula. %----------------------------------------------------------------------------- \section{MCF syntax} \subsection{Make bond} \subsubsection{Chain} \begin{verbatim} real number plus (+): counterclockwize real number minus(-): clockwize $n (0<=n<360): absolute angle <10,-30,45,-45,60,$300,$0 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Chain use !,!n} \index{"!}% \begin{verbatim} ! : take value 60 or -60 depend on current angle and environment !6 : !,!,!,!,!,! <-30,!6 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Jump to atom} \index{"@}% \begin{verbatim} @n : Jump to An An: atom number(-999<=n<=4095) <-30,!6,@3,0,!,@5,-30 \end{verbatim} \MCFgraph %------------------------------------ \subsubsection{Branch bond} \index{\textbackslash}% \begin{verbatim} \ : 0 <-30,!6,@3,\,! \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Branch modified bond} \index{\textbackslash}% \index{\textbackslash}% \index{\textbackslash\textbackslash}% \index{\textbackslash}% \begin{verbatim} \ : 0 \ : 0~wf \ : 0~zf \\ : 0~dm \ : 0~wv <30,!8, @2,\,!,@4,\,!,@6,\,!,@8,\\,!,@10,\,! \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \index{\textasciicircum}% ^ \index{\textasciitilde}% ~ \index{`}% \begin{verbatim} <30,!6, \~dr,!, : 0~dr,! \`1.5,-90 : 0`1.5,-90 \^15,-60 : 0^15,-60 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Connect atom} \index{\&}% \begin{verbatim} &n : Connect to An <-30,!6,@3,\,!3,&6~bd,@9,&4~bz \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Ring} \index{?}% \begin{verbatim} ?n : n membered ring(3<=n<=20) ?6 : <-120,60,60,60,60,60,&1 ?6 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Rotate current angle} \index{\textgreater}% \begin{verbatim} <angle : rotate current angle 0,0,<90,0,<-90,0,<$315,0,<$90,0,<$0,0 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Change bond type} \subsubsection{Double,triple,wedge,vector} \index{\textasciitilde}% \index{\textasciitilde\textasciitilde}% \index{"!"!}% \index{"!"!"!}% \index{dm}% \index{dl}% \index{dr}% \index{db}% \index{tm}% \begin{verbatim} (Double,triple) a~type : ~~type,a dm : double middle dl : double left side dr : double right side db : double left or right side tm : triple !! : !~db / !!! : !~tm <-30,!~dm,!,!~dl,!,!~dr,!~db,!~db,!,!~tm <-30,!~dm,!,!~dl,!,!~dr,!! ,!! ,!,!!! \end{verbatim} \MCFgraph \vspace{-3mm}% %----------------------------------------------------------------------------- %%\subsubsection{Wedge} \index{wf}% \index{wb}% \index{zf}% \index{zb}% \begin{verbatim} (Wedge) wf: wedge forward wb: wedge backward zf: hashed(zebra stripe) wedge foward zb: hashed(zebra stripe) wedge backward <-30,!~wf,!,!~wb,!,!~zf,!,!~zb \end{verbatim} \MCFgraph \vspace{-3mm}% %----------------------------------------------------------------------------- %%\subsubsection{Vector} \index{vf}% \index{vb}% \begin{verbatim} (Vector) vf:vector forward vb:vector backward <-30,!~vf,!,!~vb \end{verbatim} \MCFgraph \vspace{-3mm}% %----------------------------------------------------------------------------- %%\subsubsection{Dotted,wave} \index{dt}% \index{wv}% \index{bd}% \index{bz}% \begin{verbatim} (Dotted,wave) Bn=bond type : change bond type at Bn dt : dotted wv : wave bd : broad bz : broad dotted <-30,!7,1=dt,3=wv,5=bd,7=bz \end{verbatim} \MCFgraph \vspace{-3mm}% %----------------------------------------------------------------------------- \subsubsection{Change multiple bond type} \index{vf}% \begin{verbatim} {2,4,6}=dr : 2=dr,4=dr,6=dr <30,!7,{2,4,6}=dr \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Over line} \index{si\_}% \index{wf\_}% \index{wb\_}% \index{zf\_}% \index{zb\_}% \index{bd\_}% \index{dl\_}% \index{dr\_}% \index{dm\_}% \begin{verbatim} si_ : single over line wf_ : wedge forward over line wb_ : wedge backward over line zf_ : hashed wedge forward over line zb_ : hashed wedge backward over line bd_ : broad over line dl_ : duble left over line dr_ : duble right over line dm_ : duble over line <30,!8,!,60,90`18, {2~si_,4~wf_,6~wb_,8~zf_,10~zb_, 12~bd_,14~dl_,16~dr_,18~dm_}:/_`2 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Change bond length} \subsubsection{Chain length} \index{`}% \begin{verbatim} (!,!n)`length : change length of !,!n <-30,!2,!4`1.2,!2 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \index{\#}% \index{\#\#}% \begin{verbatim} #n : bond length=n ## : reset bond length <-30,!2,#1.2,!4,##,!2 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Ring length} \begin{verbatim} ?n`length : change ring length ?6,@4,\,?6`1.2 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Change atom} \subsubsection{Insert atom} \begin{verbatim} Insert hetero atom <-30,!2,O,!2,N,!2 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Addressed atom} \index{:}% \begin{verbatim} 2:O : change A2 C to O {3,4}:N : change A3,A4 C to N <30,!4,2:O,{3,4}:N \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Brock address} \index{\textbar}% \| \begin{verbatim} \| : divide brock ?6,@4,\,\|,?6,2:O \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Reset brock address} \index{\textbar\textbar}% \|\| \begin{verbatim} \|\| : reset brock adress ?6,@4,\,\|,?6,\|\|,2:N \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Absolute address} \index{\$}% $ \begin{verbatim} $2:N : change A$2 C to N 1<=n<=3095 ?6,@4,\,\|,?6,$2:N \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Relative address} \begin{verbatim} -2:N : change A(-2) C to N -999<=n<=-1 ?6,@4,\,?6,-2:N \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Charged atom} \begin{verbatim} p_ : positive / n_ : negative <-30,!2,N,??,p_,!2,S,n_^180, !6,7:N,7:??,9:S,7:n_,9:n_^180 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Fuse ring} \subsubsection{Attached 1 bond} \begin{verbatim} ?6,3=?6 : fuse ?6 at B3 Bn(n:-999<=n<=4095): bond number ?6,3=?6 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \begin{verbatim} fused ring size depend on attached bond length ?6,@4,\,?6`1.2,5=?6,11=?6 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \begin{verbatim} ?6,3=?6[13] : fuse ?6[13] at B3 ?6[13]: 6 membered ring scaled 13/10 ?m[n] (5<=m<=8,11<=n<=15) ?6,3=?6[13] \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \begin{verbatim} ?6,{-3,-4,-4,-2,-2,-4,-4}=?6 ?6,{4,8,13,20,25,28,33}=?6 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Attached 2 bond} \begin{verbatim} (4,11)=?6[4] : fuse 4/6 ring to B11..B4 (4,11)=?5[3] : fuse 3/5 ring to B11..B4 (4,11)=?4[2] : fuse 2/4 ring to B11..B4 ?m[n] (4<=m<=6,n=m-2) 1:<30,?6,3=?6,(11,4)=?6[4] 2:<30,?6,3=?6,(11,4)=?5[3] 3:<30,?6,3=?6,(11,4)=?4[2] \end{verbatim} \MCFgraph \vspace{-3mm}% \begin{verbatim} \end{verbatim} %----------------------------------------------------------------------------- \subsubsection{Attached 3 bond} \begin{verbatim} (16,4)=?6[3] : fuse 3/6 ring to B16..B4 (16,4)=?5[2] : fuse 2/5 ring to B16..B4 ?m[n] (5<=m<=6,n=m-3) 1:?6,{3,10}=?6,(16,4)=?6[3] 2:?6,{3,10}=?6,(16,4)=?5[2] \end{verbatim} \MCFgraph \vspace{-3mm}% \begin{verbatim} \end{verbatim} %----------------------------------------------------------------------------- \subsubsection{Attached 4 bond} \begin{verbatim} (21,4)=?6[2] : fuse 2/6 ring to B21..B4 MC(<-30,?6,{3,10,15}=?6,(21,4)=?6[2]) ?m[n] (m=6,n=2) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Spiro ring} \begin{verbatim} @4,?5 : add ?5 at A4 <30,!6,@4,?5 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Group} \subsubsection{Insert group} \index{/}% \index{Ph}% \begin{verbatim} / : single <-30,!,/_,!,/!,!3,/!2,!,/?!, !3,/??!,!,/Ph^-30,! ** /_ : methyl /! : ethyl /!2 : propyl /?! : isopropyl /??! : tert-butyl /Ph : phenyl \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Insert modified group} \index{//}% \index{/}% \index{/}% \index{/}% \index{*}% \begin{verbatim} // : double (double middle) / : wedge forward /* : hashed wedge forward / : wave ** : direct <30,!,//O,!2,/H,!2,/H,!2,/H,!2,*?3,! \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \index{\textasciicircum}% ^ \index{\textasciitilde}% ~ \index{`}% \index{\textless}% \begin{verbatim} ~ : change type ^ : change angle ` : change length > : change environment <-30,``1,!, /_`2^30,!2,/!2>lr,!2,/!2>rl,!) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Add group} \begin{verbatim} <30,!17,2:/_,4:/!,6:/!2, 10:/?!,14:/??!,16:/Ph^-60 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Add modified group} \begin{verbatim} ~,^,` : change type,angle,length <30,!6,{2~wf,4~zf,6^-30,8^$120}:/_ \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \begin{verbatim} ^,`,> : change angle,length,environment <-30,!7`1,3:/_`2^30,5:/!2>lr,7:/!2>rl \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Chain environment} \subsubsection{Horizontal,vertical} \index{hz}% \index{vt}% \index{"'}% \begin{verbatim} >hz : horizontal environment (default) >vt : vertical environment ?4, {3^-90,3^-30,3^90}:/'(!3,"{hz}")>hz, {1^-60,1,1^60}:/'(!3,"{vt}")>vt \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Left-right,right-left} \index{lr}% \index{rl}% \begin{verbatim} >lr : left-right environment >rl : right-left environment <-30,!6, {3^-30,3,3^30}:/'(!3,"{lr}")>lr, {5^-30,5,5^30}:/'(!3,"{rl}")>rl \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Fixed rotate angle} \index{\textgreater}% \begin{verbatim} >n : rotate n <30,!4, 2:/!6>30, % 2:\,30,30,30,30,30,30 4:/!4>-45 % 4:\,-45,-45,-45,-45 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Multi rotate angle} \begin{verbatim} >'(90,-90,...) : rotate 90,-90,... <30,!6,6>'(90,-90,90,-90,90):/!5 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Miscellaneous} %----------------------------------------------------------------------------- \subsubsection{Abbreviated parts} \index{NH}% \index{N"!}% \index{N"!2}% \index{SO}% \index{SOO}% \begin{verbatim} NH : N,/H~nl N! : N,/_ N!2 : N,/! SO : S,//O SOO : S,//O^35,//^-35 <-30,!2,NH,!2,N!,!2,N!2,SO,!2,SOO,! \end{verbatim} \MCFgraph \index{?"!}% \index{??}% \index{??"!}% \index{N?"!}% \begin{verbatim} ?! : /_,! ?? : /_^35,/_-35 /?! : isopropyl /??! : tert-butyl /N?! : dimethylamino <30,!9`1,?!,!,??,!, 2:??,4:/??,6:/??!,8:/N?! \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Parts definition} \begin{verbatim} '(..) : user defined parts iBuOH:='(!,/_,!,OH); MC(<30,?6,{4,6}:/iBuOH) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Parts inline definition} \begin{verbatim} <30,!, /'(!,/_,!,OH),! <30,!8,{2,6}:/'(!,/_,!,OH) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Move position} \index{"@()}% \begin{verbatim} @(x,y) : Move to (lx,ly) from origin * l=bond length of ring <30,?6,@3,!4,//O,!,O,n_^60,@(6,1),H,p_^15 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Change color} \index{red}% \index{blue}% \index{green}% \begin{verbatim} (use with metapost only) beginfont() MC(<30,Ph,{2,5}:N,3:/NH2,4:/COOH, %--------------------- 2:red, % red A2 5:blue, % blue A5 3=green % green B3 %--------------------- ) endfont \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Change font} \index{atomfont}% \begin{verbatim} (use with metapost only) beginfont() %---------------- atomfont:="cmr8"; %---------------- MC(<30,Ph,{2,5}:N,3:/NH2,4:/COOH) endfont \end{verbatim} \MCFgraph %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Option parameter} %------------------------------------------------------------------------------ \subsection{Angle parameter} \index{mangle}% \begin{verbatim} mangle=0 default MCat(0.2,0.5)(Ph) mangle:=30; MCat(0.8,0.5)(Ph) \end{verbatim} \MCFgraph %------------------------------------------------------------------------------ \subsection{Size/Ratio parameter} %----------------------------------------------------------------------------- \subsubsection{Bond length} \index{blength}% \begin{verbatim} (fit to font size) blength=0 default \end{verbatim} \MCFgraph %----------------------------------------- \begin{verbatim} (ratio bond/font width) blength=0.1 ** (0<blength<=1) blength=60mm(width)0.1=6mm \end{verbatim} \MCFgraph %----------------------------------------- \begin{verbatim} (bond length) blength=9mm * (blength>1) ignore msize(w,h) \end{verbatim} \MCFgraph %------------------------------------------------------------------------------ \subsubsection{Molecular size} \index{msize}% \begin{verbatim} msize=(1,1) ** default \end{verbatim} \MCFgraph %----------------------------------------------------------- \begin{verbatim} msize=(0.25,1) msize=40mm-4mm0.25=9mm \end{verbatim} \MCFgraph %----------------------------------------------------------- \begin{verbatim} msize=(11mm,11mm) \end{verbatim} \MCFgraph %------------------------------------------------------------------------------ \subsubsection{Molecular position} \index{mposition}% \begin{verbatim} mposition=(0.5,0.5) * default \end{verbatim} \MCFgraph %-------------------------------------------------------------- \begin{verbatim} mposition=(1,0) \end{verbatim} \MCFgraph %-------------------------------------------------------------- \begin{verbatim} mposition=(10mm,4mm) \end{verbatim} \MCFgraph %------------------------------------------------------------------------------ \subsection{Size parameter} %----------------------------------------------------------------------------- \subsubsection{Font size} \index{fsize}% \begin{verbatim} fsize=(font width,font height) default: (30mm,20mm) fsize=(40mm,15mm) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Font margin} \index{fmargin}% \begin{verbatim} fmargin=(margin left rigth,top bottom) default: (0.4mm,0.4mm) fmargin=(10mm,2mm) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Offset thickness of bond} \index{offset\_thickness}% \begin{verbatim} default: offset_thickness=0.2pt \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Offset of double bond gap} \index{offset\_bond\_gap}% \begin{verbatim} default: offset_bond_gap=0.3pt \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Offset of atom width} \index{offset\_atom}% \begin{verbatim} default: offset_atom=0.8pt \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Offset of wedge width} \index{offset\_wedge}% \begin{verbatim} default: offset_wedge=0.4pt \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Max bond length} \index{max\_blength}% \begin{verbatim} default: max_blength=10mm \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Ratio parameter} %----------------------------------------------------------------------------- \subsubsection{Thickness/bond length} \index{ratio\_thickness\_bond}% \begin{verbatim} default: ratio_thickness_bond=0.015 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Char/bond thickness} \index{ratio\_char\_bond}% \begin{verbatim} default: ratio_char_bond=1.5 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Bond gap/bond length} \index{ratio\_bondgap\_bond}% \begin{verbatim} default: ratio_bondgap_bond= 0.15 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Atom/bond length} \index{ratio\_atom\_bond}% \begin{verbatim} default: ratio_atom_bond= 0.36 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Wedge/bond length} \index{ratio\_wedge\_bond}% \begin{verbatim} default: ratio_wedge_bond=0.12 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Font atom gap/atom length} \index{ratio\_atomgap\_atom}% \begin{verbatim} default: ratio_atomgap_atom= 0.050 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Chain/ring length} \index{ratio\_chain\_ring}% \begin{verbatim} default: ratio_chain_ring= 0.66 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Hash gap/bond length} \index{ratio\_hashgap\_bond}% \begin{verbatim} default: ratio_hashgap_bond=0.12 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- %%%%\newpage %----------------------------------------------------------------------------- \subsection{Drawing mode} %----------------------------------------------------------------------------- \subsubsection{Numbering atom} \index{numberA}% \index{numberA\_start}% \index{numberA\_end}% \begin{verbatim} numberA_start:=3; numberA_end:=8; default: sw_numberA=0 : numberA_start=1 numberA_end=4095 \end{verbatim} \MCFgraph \begin{picture}(5,20) \put(0,14){\makebox[5mm]{\tt 1}} \put(0, 8){\makebox[5mm]{\tt 2}} \put(0, 2){\makebox[5mm]{\tt 3}} \end{picture} %----------------------------------------------------------------------------- \subsubsection{Numbering bond} \index{numberB}% \index{numberB\_start}% \index{numberB\_end}% \begin{verbatim} numberB_start:=3; numberB_end:=8; default: sw_numberB=0 : numberB_start=1 numberB_end=4095 \end{verbatim} \MCFgraph \begin{picture}(5,20) \put(0,14){\makebox[5mm]{\tt 1}} \put(0, 8){\makebox[5mm]{\tt 2}} \put(0, 2){\makebox[5mm]{\tt 3}} \end{picture} %----------------------------------------------------------------------------- \subsubsection{Trimming mode} \index{sw\_trimming}% \begin{verbatim} sw_trimming:=0; default msize:=(1,0.7); MCat(0.2,0.3)(Ph) MCat(0.8,0.7)(Ph) \end{verbatim} \MCFgraph \begin{verbatim} sw_trimming:=1; MCat(0.2,0.3)(Ph) MCat(0.8,0.7)(Ph) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Expand mode} \index{sw\_expand}% \begin{verbatim} MCat(0, .5)(<30,Ph,4:/COOH,3:/NH2) sw_expand:=1; MCat(1, .5)(<30,Ph,4:/COOH,3:/NH2) default: sw_expand=0 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Group off mode} \index{sw\_group\_off}% \begin{verbatim} default: sw_group_off=0 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Single bond mode} \index{sw\_single}% \begin{verbatim} default: sw_single=0 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Frame} %----------------------------------------------------------------------------- \subsubsection{Font frame} \index{sw\_fframe}% \begin{verbatim} default:sw_fframe=0 (Draw font frame) fmargin:=(5mm,2mm); sw_fframe=1 \end{verbatim} \MCFgraph \begin{verbatim} (Frame inside margin) sw_fframe=2 \end{verbatim} \MCFgraph \begin{verbatim} (Draw both frame) sw_fframe=3 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Molecular frame} \index{sw\_mframe}% \begin{verbatim} sw_mframe=1 default:sw_mframe=0 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Atom frame} \index{sw\_aframe}% \begin{verbatim} sw_aframe=1 default: sw_aframe=0 MC(<30,COOH,!,COOH) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Parameter setting} \subsubsection{Local parameter setting} \index{beginfont()}% \index{endfont}% \begin{verbatim} beginfont() MC(Ph) endfont beginfont() %-------------------------- ratio_thickness_bond:=0.05; %-------------------------- MC(Ph) endfont beginfont() MC(Ph) endfont \end{verbatim} \MCFgraph\MCFgraph\MCFgraph %----------------------------------------------------------------------------- \subsubsection{Global parameter setting} \begin{verbatim} beginfont() MC(Ph) endfont %-------------------------- ratio_thickness_bond:=0.05; %-------------------------- beginfont() MC(Ph) endfont beginfont() MC(Ph) endfont \end{verbatim} \MCFgraph\MCFgraph\MCFgraph %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Function} %----------------------------------------------------------------------------- \subsection{Function MC()} \index{MC()}% \begin{verbatim} (Draw molecule) msize=(a,b) default (1,1) mposition=(c,d) default (0.5,0.5) a: ratio molecular width/font width b: ratio molecular hight/font hight c: x axis position d: y axis position beginfont() MC(<30,Ph,3:/F,4:/Cl) endfont \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Function MCat()} \index{MCat()}% \begin{verbatim} (Draw molecule at mposition) MCat(c,d)(....) : mposition:=(c,d); MC(....) c: x axis position d: y axis position defaultsize:=5bp; fsize:=(60mm,40mm); fmargin:=(3mm,3mm); blength:=0.07; sw_fframe:=1; mangle:=0; for i=1 step -0.5 until 0: for j=0 step 0.33 until 1: MCat(j,i)(Ph,4:N) add(drawarrow((A1+A1upaw)..A1); label(decimal(mangle), p0+(0.5w,0.5h)); ) mangle:=mangle+30; endfor endfor \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Function check()} \index{check()}% \begin{verbatim} (immediately compile) beginfont("EN:Pyridine") MC(<30,Ph,2:N) endfont (check mcf and compile) check(mc) : error count beginfont("EN:Pyridine", ":<30,Ph,}2:N") % extra '}' if check(mc)=0: MC(scantokens(mc)) fi endfont \end{verbatim} \MCFgraph\hspace{22mm}\MCFgraph \begin{verbatim} check(mc)=0 check(mc)>=1 \end{verbatim} %=============================================================================== \newpage \subsection{Function add()} \index{add()}% \index{plus}% \index{minus}% \index{lonepair}% \index{lonepairdiam}% \index{lonepairspace}% \index{circlediam}% \index{circlepen}% \index{w}% \index{h}% \index{aw}% \index{em}% \index{p0}% \index{l}% \index{/}% \index{}% \index{\textgreater\textgreater}% \index{An}% \index{A[]}% \index{A[]ang}% \index{A[]up}% \index{A[]left}% \index{A[]right}% \index{A[]down}% \index{Bn}% \index{B[]}% \index{B[]s}% \index{B[]m}% \index{B[]e}% \index{B[]ang}% \index{B[]up}% \index{B[]left}% \index{B[]right}% \index{B[]down}% \index{defaultscale}% \index{labeloffset}% \begin{verbatim} (Add label to molecule) w: molecular width h: molecular height aw: atom font size em: label font size p0: origin of molecular structure l: bond length An: atom number A[m]: atom position A[m]ang: branch angle of A[m] A[m]up: dir A[m]ang A[m]left: dir A[m]ang+90 A[m]right: dir A[m]ang-90 A[m]down: dir A[m]ang+180 Bn: bond number B[m]: bond(path) B[m]s: bond start position B[m]m: bond middle position B[m]e: bond end position B[m]ang: bond angle B[m]up: dir B[m]ang B[m]left: dir B[m]ang+90 B[m]right: dir B[m]ang-90 B[m]down: dir B[m]ang+180 plus : '+' circled minus : '-' circled circlediam = 0.6aw (default) circlepen = 0.2bp (default) lonepair r: ':' rotated r lonepairdiam = 0.3aw (default) lonepairspace = 0.7aw (default) * : scaled << : rotated a /* b : point b of a beginfont("EN:add() 1") fsize:=(70mm,40mm); sw_aframe:=sw_mframe:=1; max_blength:=10mm; msize:=(.91,.9); MCat(.5,.85)(<30,?6,{2,5}:O) add( defaultscale:=.8; labeloffset:=.3aw; dotlabel.lft("p0",p0); dotlabel.rt( "p0+(w,h)",p0+(w,h)); dotlabel.ulft("A1",A1); drawarrow A1..A1+__l<<A1ang; dotlabel.lrt( "B3s",B3s); dotlabel.rt("B3m",B3m); drawarrow B3m..B3m+__l<<(B3ang+90); dotlabel.ulft("A6",A6); drawarrow A1{A1down}..A6; dotlabel.urt( "B3e",B3e); label.rt( "An="&decimal(An)& " Bn="&decimal(Bn)& " aw="&decimal(aw)& " em="&decimal(em), p0+(-9em,-1.5em)); label.rt( "w="&decimal(w)& " h="&decimal(h)& " l="&decimal(l), p0+(-9em,-3em)); ) endfont \end{verbatim} \MCFgraph \begin{verbatim} beginfont("EN:add() 2") fsize:=(60mm,20mm); msize:=(1,0.85); %--------------------------------------- MCat(0,0)(<30,Ph,3=dl,4:/NH2) %--------------------------------------- add( labeloffset:=.7aw; label.top(lone_pair 90,A7); drawarrow (A7+up*1.2aw){A7left} ..{B7right}B7/0.3; drawarrow B3m..A3+B2up1.5aw..{A3down}A3; ) %--------------------------------------- MCat(1,0)(<30,?6,{1,5}=dl,4://NH2) %--------------------------------------- add( labeloffset:=.7aw; label.top(plus,A7); label.urt(minus,A3); label(lonepair A3ang,A3+A3up.7aw); ) %--------------------------------------- ext(drawdblarrow (.4w,.4h)..(.55w,.4h);) %--------------------------------------- endfont \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \newpage \subsection{Function ext()} \index{ext()}% \index{w0}% \index{h0}% \index{aw}% \index{em}% \index{n}% \index{ratio\_thickness\_char}% \index{defaultscale}% \begin{verbatim} (Extra label to font) w: font width h: font height w0: font width-2xpart(fmargin) h0: font height-2ypart(fmargin) aw: atom font size em: label font size p0: fmargin n: molecular number p[m]: molecular origin position w[m]: molecular width h[m]: molecular height ratio_thickness_char: pen thickness / char width %---------------------------------------- beginfont() fsize:=(70mm,30mm;); blength:=0.065; %--------------------------------------- MCat(0.1,0.5)( <-210,60`1,60`1,60`1,{1,3}=dl, 1:/R1,4:/R2^-60 ) add( defaultscale:=0.6; label.bot("Diene",p0+(0.5w,0)); ) MCat(0.4,0.5)( <-30,-60`1,1=dl,1:/R3,2:/R4^60) add(defaultscale:=0.6; label.bot("Dienophile",p0+(.5w,0)); ) MCat(0.9,0.5)( <30,?6,6=dl,2:/R2,3:/R4,4:/R3,5:/R1 ) %--------------------------------------- ext( drawarrow (.52w,.5h)..(.6w,.5h); defaultscale:=0.7; label("+",(0.25w,0.5h)); ratio_thickness_char:=0.125; label.bot("Diels-Alder Reaction", (.5w,h)); ) %--------------------------------------- endfont \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Local ext() setting} \begin{verbatim} beginfont("EN:?3") fsize:=(12mm,15mm); MCat(0.5,1)(<30,?3) endfont beginfont("EN:?4") fsize:=(12mm,15mm); MCat(0.5,1)(?4) %------------------------------- ext(label.top(inf_EN,(0.5w,0));) %------------------------------- endfont beginfont("EN:?5") fsize:=(12mm,15mm); MCat(0.5,1)(?5) endfont beginfont("EN:?5") fsize:=(12mm,15mm); MCat(0.5,1)(?6) endfont \end{verbatim} \MCFgraph\MCFgraph\MCFgraph\MCFgraph \subsubsection{Global ext() setting} \index{ext\_clear}% \begin{verbatim} ext_clear: reset global ext() beginfont("EN:?3") fsize:=(12mm,15mm); MCat(0.5,1)(<30,?3) endfont %------------------------------- ext(label.top(inf_EN,(0.5w,0));) %------------------------------- beginfont("EN:?4") fsize:=(12mm,15mm); MCat(0.5,1)(?4) endfont beginfont("EN:?5") fsize:=(12mm,15mm); MCat(0.5,1)(?5) endfont %--------- ext_clear; %--------- beginfont("EN:?6") fsize:=(12mm,15mm); MCat(0.5,1)(?6) endfont \end{verbatim} \MCFgraph\MCFgraph\MCFgraph\MCFgraph %----------------------------------------------------------------------------- \newpage %----------------------------------------------------------------------------- \section{MCF example} %----------------------------------------------------------------------------- \subsection{Luciferin} \index{check()}% \begin{verbatim} (use data base file 'mcf_data_base') beginfont("f:mcf_data_base", "t:EN","v:Luciferin") fsize:=(50mm,15mm); if check(mc)=0: MC(scantokens(mc)) fi endfont \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Colchicine} \begin{verbatim} beginfont("EN:Colchicine","MW:385.41", %------------------------------------- ": <30,Ph,{1,2,6}:/O!,-4=?7,-5=?7, ", ": {-1,-4,-6}=dl,-2://O,-3:/O!, ", ": @9,\,NH,!,//O,! ") %------------------------------------- fsize:=(50mm,20mm); if check(mc)=0: MC(scantokens(mc)) fi endfont \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Paclitaxel} \begin{verbatim} beginfont("EN:Paclitaxel","MW:853.91", %------------------------------------ ": ?6,5=dl,@3,#1,36,45,45,45,45,##, ", ": &5", ", ": -4=?6,-4=?4,-1=wb,-3=wf,-1:O,\|\|, ", ": 4:??,6:/_,{3^-60,15}:/OH, ", ": 8:/H^-60,", ", ": 9:/_^60,10://O, ", ": @1,\,O,!,//O,!,/OH,!,/Ph,60~wf, ", ": NH,-60,//O,60,Ph, ", ": @7,\,O,-45,//O,60,Ph, ", ": @11,\,O,-60,//O,60, ", ": @12,\^-15,O,60,//O,-60 ") %------------------------------------ fsize:=(50mm,25mm); if check(mc)=0: MC(scantokens(mc)) fi endfont \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Lycorine} \begin{verbatim} beginfont("EN:Lycorine","MW:287.31", %-------------------------------------- ": Ph,-4=?6,-2=?6,6=?5,(9,12)=?5[3], ", ": 13=dl,8:N,{15,17}:O, ", ": 9:/H^180,10:/H^60, ", ": 13:/OH,14:/OH ") %-------------------------------------- fsize:=(50mm,20mm); if check(mc)=0: MC(scantokens(mc)) fi endfont \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Gibberellin} \begin{verbatim} beginfont("EN:Gibberellin A3","MW:346.37", %---------------------------------------- ": <18,?5,3=?7,5=?6[12],@8,160`1.3,&3, ", ": 13=dl,6=wf,8=wb, ", ": @5,40~zf`1,O,50,//O^180,&14~zb, ", ": 2:/COOH,7://_,13:/OH,8:/OH, ", ": 14:/_,{1,4}:/H^60 ") %---------------------------------------- fsize:=(50mm,18mm); if check(mc)=0: MC(scantokens(mc)) fi endfont \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Quinine} \begin{verbatim} beginfont("EN:Quinine","MW:324.42", %------------------------------- ": <30,Ph,3=Ph,7:N,6:/O!, ", ": @10,\,/OH,/H~zf^-60,!, ", ": \|,?6,2:N,1:/H^60,4:/!!, ", ": @2,165~zf,60,&5~zb ") %------------------------------- fsize:=(50mm,20mm); if check(mc)=0: MC(scantokens(mc)) fi endfont \end{verbatim} \MCFgraph %------------------------------------------------------------------------ \onecolumn \section{Example to use mcf2graph} \subsection{Metafont/Metapost souce file} \index{mcf2graph.mf}% \index{sw\_output}% \index{tag}% \index{var}% \begin{verbatim} %------------------------------------------------------------------------- input mcf2graph.mf; > input main macro %------------------------------------------------------------------------- sw_output:=Info1; % aux(information) file output on > global setting %%%% sw_output:=Report; > report output %%%% sw_output:=MOL2k; > MOL file output fsize:=(60mm,40mm); % (font width,font height) > tag1:="J"; > jobname tag2:="C"; > char No tag3:="mw"; % calculated molecular weight > tag4:="fm"; % calculated molecular formula > outputformat:="png"; hppp:=vppp:=0.1; > PNG output outputtemplate:="%j-%3c.png"; > %------------------------------------------------------------------------- beginfont("EN:Ampicillin","MW:349.405") > information MC(<45,?4,-3=?5,2:N,7:S, > immediately compile 3^45:/H,1://O^15,5:/COOH^-18,6:??, > @4,\^15,NH,!,//O,!,/NH2,!,Ph) > endfont > %------------------------------------------------------------------------ beginfont("EN:Cholesterol","MW:386.65", >information %---------------------------------------- > ": <30,?6,{-4,-2}=?6,-4=?5,7=dl, ", > mc1 ": 10:/H^180,11:/H^-60,17:/H^-54, ", > mc2 ": {4,12}:/_^60, ", > mc3 ": @-1,18,/_,-60,!3,?! ") > mc4 %---------------------------------------- > if check(mc)=0: MC(scantokens(mc)) fi > mc=mc1 - mc4 endfont > %------------------------------------------------------------------------------ beginfont("f:mcf_data_base","t:EN","v:Adenine") > from mcf_data_base.mcf if check(mc)=0: MC(scantokens(mc)) fi > select EN="Adenine" endfont > %------------------------------------------------------------------------------ beginfont("f:mcf_data_base","t:EN","v:Guanine") > from mcf_data_base.mcf if check(mc)=0: MC(scantokens(mc)) fi > select EN="Guanine" endfont %------------------------------------------------------------------------------ beginfont("f:mcf_data_base","t:EN","v:Cytosine") > from mcf_data_base.mcf if check(mc)=0: MC(scantokens(mc)) fi > select EN="Cytosine" endfont > %------------------------------------------------------------------------------ beginfont("f+:mcf_data_base","t:n","v:4") > from mcf_data_base.mcf if check(mc)=0: MC(scantokens(mc)) fi > v:4 select No.4 endfont > 'f+' keep file open %------------------------------------------------------------------------------ for i=5 upto 155: > from mcf_data_base.mcf beginfont("f+:mcf_data_base","v:") > v:* no selection if check(mc)=0: MC(scantokens(mc)) fi > No.5 - No.155 endfont > 'f+' keep file open endfor > %------------------------------------------------------------------------------ bye \end{verbatim} %------------------------------------------------------------------------ \noindent% \newpage \subsection{Molecular data base file} \begin{verbatim} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % molecular data base file mcf_data_base.mcf by Akira Yamaji 2021.04.18 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % tag1:var1;tag2:var2;tag3:var3 .... % first character of line '%' comment out % first character of line '+' begin MCF , end MCF %------------------------------------------------------------------------------ Cat:biological;EN:Adenine;MW:135.13 + <30,?6,3=?5,{1,3,5,9}=dl,{2,6,9}:N,5:/NH2,7:NH +------------------------------------------------------------------------------ Cat:biological;EN:Guanine;MW:151.13 + <30,?6,3=?5,{1,3,9}=dl,{2,9}:N,{6,7}:NH,5://O,1:/NH2 +------------------------------------------------------------------------------ Cat:biological;EN:Cytosine;MW:111.10 + <30,?6,{4,6}=dl,4:N,3://O,2:NH,5:/NH2 +------------------------------------------------------------------------------ Cat:biological;EN:Thymine;MW:126.11 + <30,?6,3=dl,{2,6}:NH,{1,5}://O,4:/_ +------------------------------------------------------------------------------ Cat:biological;EN:Uracil;MW:112.09 + <30,?6,6=dl,{3,5}://O,{2,4}:NH +------------------------------------------------------------------------------ Cat:biological;EN:Geraniol;MW:154.25 + <30,!8,OH,{2,6}=dr,{2,6}:/_ +------------------------------------------------------------------------------ Cat:biological;EN:Limonene;MW:136.24 + <30,?6,2=dl,2:/_,@5,\,/_,!! +------------------------------------------------------------------------------ Cat:biological;EN:l-Menthol;MW:156.27 + <30,?6,2:/?!,5:/_,3:/OH +------------------------------------------------------------------------------ Cat:biological;EN:Vanillin;MW:152.15 + <30,Ph,2:/OH,3:/O!,5:/CHO +------------------------------------------------------------------------------ Cat:biological;EN:Allicin;MW:162.28 + <-30,!!,!2,SO,!,S,!2,!! +------------------------------------------------------------------------------ Cat:biological;EN:Stearic acid;MW:284.48 + <30,!17,COOH +------------------------------------------------------------------------------ Cat:biological;EN:Linoleic acid;MW:280.45 + <30,!5,-30,-30,!,-30,-30,!7,COOH,{6,9}=dr +------------------------------------------------------------------------------ \end{verbatim} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \noindent% \newpage \subsection{Information aux file output} \paragraph{(Insert option parameter setting)} \index{J}% \index{C}% \index{NO}% \index{MW}% \index{MI}% \index{EN}% \index{JN}% \index{FM}% \index{USE}% \index{mw}% \index{fm}% \index{mi}% \index{w}% \index{h}% \index{Info1}% \index{Info2}% \index{Info\_t}% \begin{verbatim} sw_output:=Info1; % tag1:var1;tag2:var2 sw_output:=Info2; % tag1;tag2 var1;var2 sw_output:=Info_t; % tag1:var1;tag2:var2 / output 'temp-info.aux' \end{verbatim} \paragraph{(Command line)} \begin{verbatim} >mpost -s ahlength=1 FILENAME (sw_output=Info1) >mpost -s ahlength=2 FILENAME (sw_output=Info2) \end{verbatim} \paragraph{(Sourse)} \begin{verbatim} beginfont("EN:Ampicillin") .... endfont beginfont("EN:Cholesterol") .... endfont beginfont("EN:Limonin") .... endfont beginfont("EN:beta-Carotene") .... endfont \end{verbatim} \paragraph{(Setting)} \begin{verbatim} tag1:="J"; tag2:="C"; tag3:="mw"; tag4:="fm"; tag5:="EN"; \end{verbatim} \paragraph{(Output)} \index{aux\_delimiter}% \begin{verbatim} (sw_output=Info1) F:mcf_man_soc;C:1;mw:349.40462;fm:C16H19N3O4S;EN:Ampicillin F:mcf_man_soc;C:2;mw:386.6532;fm:C27H46O;EN:Cholesterol F:mcf_exa_soc;C:3;mw:470.5113;fm:C26H30O8;EN:Limonin F:mcf_exa_soc;C:4;mw:536.8722;fm:C40H56;EN:beta-Carotene (sw_output=Info2) F;C;mw;fm mcf_man_soc;1;349.40462;C16H19N3O4S;Ampicillin mcf_man_soc;2;386.6532;C27H46O;Cholesterol mcf_exa_soc;3;470.5113;C26H30O8;Limonin mcf_exa_soc;4;536.8722;C40H56;beta-Carotene (aux_delimiter="/") F:mcf_man_soc/C:1/mw:349.40462/fm:C16H19N3O4S/EN:Ampicillin F:mcf_man_soc/C:2/mw:386.6532/fm:C27H46O/EN:Cholesterol F:mcf_exa_soc/C:3/mw:470.5113/fm:C26H30O8/EN:Limonin F:mcf_exa_soc/C:4/mw:536.8722/fm:C40H56/EN:beta-Carotene \end{verbatim} \paragraph{(Tag)} \begin{verbatim} J : jobname C : char number NO : serial number EN : english name JN : japanese name FM : formula from literature data MW : molecular weight from literature data MI : monoisotopic mass from literature data USE : the use mw : molecular weight calculated mi : monoisotopic mass calculated fm : molecular formula calculated w : font width h : font height \end{verbatim} %------------------------------------------------------------------------ \noindent% \newpage \subsection{Metafont aux file output} \index{Mfont}% \paragraph{(Insert option parameter setting)} \begin{verbatim} sw_output:=Mfont; \end{verbatim} \paragraph{(Command line)} \begin{verbatim} >mpost -s ahlength=7 FILENAME (sw_output=Mfont) \end{verbatim} \paragraph{(Output)} \begin{verbatim} beginfont("Cat:biological","EN:Adenine","MW:135.13", ": <30,?6,3=?5,{1,3,5,9}=dl,{2,6,9}:N,5:/NH2,7:NH") if check(mc)=0: MC(scantokens(mc)) fi endfont beginfont("Cat:biological","EN:Guanine","MW:151.13", ": <30,?6,3=?5,{1,3,9}=dl,{2,9}:N,{6,7}:NH,5://O,1:/NH2") if check(mc)=0: MC(scantokens(mc)) fi endfont beginfont("Cat:biological","EN:Cytosine","MW:111.10", ": <30,?6,{4,6}=dl,4:N,3://O,2:NH,5:/NH2") if check(mc)=0: MC(scantokens(mc)) fi endfont beginfont("Cat:biological","EN:Thymine","MW:126.11", ": <30,?6,3=dl,{2,6}:NH,{1,5}://O,4:/_") if check(mc)=0: MC(scantokens(mc)) fi endfont beginfont("Cat:biological","EN:Adenine","MW:135.13", ": <30,?6,3=?5,{1,3,5,9}=dl,{2,6,9}:N,5:/NH2,7:NH") if check(mc)=0: MC(scantokens(mc)) fi endfont beginfont("Cat:biological","EN:Guanine","MW:151.13", ": <30,?6,3=?5,{1,3,9}=dl,{2,9}:N,{6,7}:NH,5://O,1:/NH2") if check(mc)=0: MC(scantokens(mc)) fi endfont beginfont("Cat:biological","EN:Cytosine","MW:111.10", ": <30,?6,{4,6}=dl,4:N,3://O,2:NH,5:/NH2") if check(mc)=0: MC(scantokens(mc)) fi endfont beginfont("Cat:biological","EN:Thymine","MW:126.11", ": <30,?6,3=dl,{2,6}:NH,{1,5}://O,4:/_") if check(mc)=0: MC(scantokens(mc)) fi endfont beginfont("Cat:biological","EN:Uracil","MW:112.09", ": <30,?6,6=dl,{3,5}://O,{2,4}:NH") if check(mc)=0: MC(scantokens(mc)) fi endfont beginfont("Cat:biological","EN:Geraniol","MW:154.25", ": <30,!8,OH,{2,6}=dr,{2,6}:/_") if check(mc)=0: MC(scantokens(mc)) fi endfont beginfont("Cat:biological","EN:Limonene","MW:136.24", ": <30,?6,2=dl,2:/_,@5,\,/_,!!") if check(mc)=0: MC(scantokens(mc)) fi endfont beginfont("Cat:biological","EN:l-Menthol","MW:156.27", ": <30,?6,2:/?!,5:/_,3:/OH") if check(mc)=0: MC(scantokens(mc)) fi endfont \end{verbatim} %------------------------------------------------------------------------ \noindent% \newpage \subsection{MCF aux file output(1)} \paragraph{(Insert option parameter setting)} \index{Mcode}% \begin{verbatim} sw_output:=Mcode; \end{verbatim} \paragraph{(Command line)} \index{Mcode\_t}% \begin{verbatim} >mpost -s ahlength=8 FILENAME (sw_output=Mcode) \end{verbatim} \paragraph{(Output)} \begin{verbatim} file name = 'mcf_exa_soc-001-Adenine-mc.aux' <30,?6,3=?5,{1,3,5,9}=dl,{2,6,9}:N,5:/NH2,7:NH \end{verbatim} %------------------------------------------------------------------------ \subsection{MCF aux file output(2)} \paragraph{(Insert option parameter setting)} \begin{verbatim} beginfont("f:mcf_data_base","t:EN","v:Adenine") sw_output:=Mcode_t; endfont \end{verbatim} %----------------------------------------------------------------------- \paragraph{(Lualatex example)} %----------------------------------------------------------------------- \begin{verbatim} %----------------------------------------------------------------------- \begin{mplibcode} beginfont("f:mcf_data_base","t:EN","v:Vancomycin") sw_output:=Mcode_t; %%%% output temp-mc.aux %%%% endfont; \end{mplibcode} %----------------------------------------------------------------------- \verbatiminput{temp-mc.aux} %----------------------------------------------------------------------- \end{verbatim} %----------------------------------------------------------------------- \paragraph{(Output)} %----------------------------------------------------------------------- \begin{verbatim} file name = 'temp-mc.aux' <-30,#1,!12,{1,3,12}=zf,7=wf,/H^-60,60,/OH,60, Ph,-4:/Cl,@-3,\,O,!,Ph,@-4,\,O,!,Ph,-1^15:/Cl,@-3,\,/OH,/H^-60,&1, @7,&26,@$1,60,//O,60,NH,60,/H,/COOH^180,-60, Ph,{-2,-4}:/OH,@-1,\,Ph,-5:/OH,@-2,&4,##, {3^40,6,9,12}://O,{2,5,8,11}:NH,{1,4^180}:/H,{7^-60,10^60,14^60}:/H, @10,\^-60,60,//O,!,NH2,@13,\,NH,!,//O,!,/??!,/H^60,!~zf,NH,!, @23,\,O,!,\|,?6`.7,2:O,3^10:/!OH,{4,5}:/OH, @-1,\,O,!,\|,?6`.7,6:O,{3^35,5}:/_,3^-35:/NH2,4:/OH \end{verbatim} %------------------------------------------------------------------------ \newpage \noindent% \subsection{Report output} \paragraph{(Insert option parameter setting)} \index{sw\_output}% \index{Report}% \begin{verbatim} sw_output:=Report; \end{verbatim} \paragraph{(Command line)} \begin{verbatim} >mpost -s ahlength=3 FILENAME \end{verbatim} \paragraph{(Output)} \begin{verbatim} =========================================================================== No. 3 / Name = Cytosine --------------------------------------------------------------------------- <30,?6,{4,6}=dl,4:N,3://O,2:NH,5:/NH2 --------------------------------------------------------------------------- row= 1 / length= 37 / commands= 7 {}=X = 1 / {}:X = 0 / '() = 0 / @ = 0 / & = 0 / < = 1 --------------------------------------------------------------------------- Warnings = 0 / Code= 60 Width * Height = 34.68852 * 47.4036 Shift width * height = 0 * -14.46167 Bond length = 12.75589 Atom size = 5.38914 Atom count= 9 Bond count= 9 Ring count= 1 Hide H count= 2 --------------------------------------------------------------------------- < NO. ><atom(s) >( x axis , y axis )<bond><hideH><chg> A1 C ( 0 , 0 ) 3 1 A2 N ( 0.866 , -0.5 ) 3 A3 C ( 1.732 , 0 ) 4 A4 N ( 1.732 , 1 ) 3 A5 C ( 0.866 , 1.5 ) 4 A6 C ( 0 , 1 ) 3 1 A7 O ( 2.508 , -0.448 ) 2 A8 H ( 0.866 , -0.922 ) 1 A9 NH2 ( 0.866 , 2.371 ) 1 --------------------------------------------------------------------------- < NO. >< bond (sdt)><angle +( +- )><length ( pt )> B1 1 -> 2 ( 1) 330 ( -30) 1 ( 12.76) B2 2 -> 3 ( 1) 30 ( 30) 1 ( 12.76) B3 3 -> 4 ( 1) 90 ( 90) 1 ( 12.76) B4 4 -> 5 ( 2) 150 ( 150) 1 ( 12.76) B5 5 -> 6 ( 1) 210 ( -150) 1 ( 12.76) B6 6 -> 1 ( 2) 270 ( -90) 1 ( 12.76) B7 3 -> 7 ( 2) 330 ( -30) 0.66 ( 8.42) B8 2 -> 8 ( 1) 270 ( -90) 0.36 ( 4.59) B9 5 -> 9 ( 1) 90 ( 90) 0.66 ( 8.42) --------------------------------------------------------------------------- <atom>( atom wt )[ mi wt ] < cnt > < sum wt >[ sum mi wt ] C ( 12.0107)[ 12] * 4 48.04279[ 48] H ( 1.00793)[ 1.00783] * 5 5.03967[ 5.03914] N ( 14.0067)[ 14.00307] * 3 42.0201[ 42.0092] O ( 15.9994)[ 15.99492] * 1 15.9994[ 15.99492] Molecular Weight [Mono Isotopic] = 111.1019[ 111.04326] --------------------------------------------------------------------------- Weight Calc: 111.1019 / Input: 111.10 / weight gap= 0.00195 Fomula Calc: C4H5N3O / Input: =========================================================================== \end{verbatim}% \newpage %------------------------------------------------------------------------ \noindent% \subsection{MOL file output} \paragraph{(Insert option parameter setting)} \index{sw\_output}% \index{MOL2k}% \index{MOL3k}% \begin{verbatim} sw_output:=MOL2k; % MOL(V2000) sw_output:=MOL3k; % MOL(V3000) \end{verbatim} \paragraph{(Command line)} \begin{verbatim} >mpost -s ahlength=5 FILENAME % MOL(V2000) >mpost -s ahlength=6 FILENAME % MOL(V3000) \end{verbatim} \paragraph{(Output)} \begin{verbatim} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -MCFtoMOL- EN:Caffeine 14 15 0 0 0 0 0 0 0 0999 V2000 0 0 0 C 0 0 0 0 0.86603 -0.5 0 N 0 0 0 0 1.73206 0 0 C 0 0 0 0 1.73206 1 0 C 0 0 0 0 0.86603 1.5 0 C 0 0 0 0 0 1 0 N 0 0 0 0 2.6831 -0.30902 0 N 0 0 0 0 3.27089 0.5 0 C 0 0 0 0 2.6831 1.30902 0 N 0 0 0 0 0.86603 -1.36383 0 C 0 0 0 0 -0.76894 1.44394 0 C 0 0 0 0 -0.76894 -0.44394 0 O 0 0 0 0 0.86603 2.36383 0 O 0 0 0 0 2.95299 2.1396 0 C 0 0 0 0 1 2 1 0 0 0 2 3 1 0 0 0 3 4 2 0 0 0 4 5 1 0 0 0 5 6 1 0 0 0 6 1 1 0 0 0 3 7 1 0 0 0 7 8 2 0 0 0 8 9 1 0 0 0 9 4 1 0 0 0 2 10 1 0 0 0 6 11 1 0 0 0 1 12 2 0 0 0 5 13 2 0 0 0 9 14 1 0 0 0 M END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{verbatim}% %---------------------------------------------------------------------------- \newpage \subsection{LuaTeX file example} \index{None}% %############################################################################ \begin{verbatim} \documentclass{article} \usepackage{luamplib}% \usepackage[T1]{fontenc}% \usepackage{textcomp}% \mplibcodeinherit{enable}% \mplibverbatim{enable}% \mplibnumbersystem{double}% \everymplib{% if unknown Ph1: input mcf2graph.mf; fi sw_output:=None; sw_fframe:=4; max_blength:=4.5mm; defaultfont:="uhvr8r"; defaultsize:=8bp; defaultscale:=1; }% \begin{document} \noindent% %-------------------------------------------------------------------- \begin{mplibcode} fsize:=(50mm,50mm); beginfont("NO:1","EN:Limonin","MW:470.51", %---------------------------------------- ": <30,?6,{-3,-4}=?6, ", ": -5=?3,-2=wf,-1=wb,6=?5,-4=?6,-5=wf, ", ": {13,15,17,20}:O,{3,12,21}://O, ", ": {4~wf^60,8~zf^60,18^35,18^-35}:/_, ", ": {1^60,5^180,16^60}:/H, ", ": @14,\,\|,?5,{1,4}=dl,3:O ") %---------------------------------------- if check(mc)=0: MC(scantokens(mc)) fi endfont \end{mplibcode}\\ %-------------------------------------------------------------------- \begin{mplibcode} fsize:=(80mm,50mm); beginfont("NO:2","EN:beta-carotene","MW:536.87", %------------------------------------------ ": <30,?6,3=dl,{3,5^35,5^-35}:/_, ", ": @4,\,\|,!18,{1,3,5,7,9,11,13,15,17}=dr, ", ": {3,7,12,16}:/_, ", ": \|,?6,6=dl,{6,2^35,2^-35}:/_ ") %------------------------------------------ if check(mc)=0: MC(scantokens(mc)) fi endfont \end{mplibcode}\\ %-------------------------------------------------------------------- \begin{mplibcode} fsize:=(50mm,50mm); beginfont("NO:3","EN:Gibberellin A3","MW:346.37", %------------------------------------ ": <18,?5,3=?7,5=?6[12], ", ": @8,160`1.3,&3,13=dl,6=wf,8=wb, ", ": @5,40~zf`1,O,60,//O^180,&14~zb, ", ": 2:/COOH,7://_,13:/OH,8:/OH, ", ": 14:/_,{1^60,4^60}:/H ") %------------------------------------ if check(mc)=0: MC(scantokens(mc)) fi endfont; %-------------------------------------------------------------------- \end{mplibcode}\\ \end{document} \end{verbatim}% %############################################################################ %------------------------------------------------------------------------ \newpage \subsection{LaTeX file example} %############################################################################ \index{mcf\_setup.sty}% \begin{verbatim} %-------------------------------------------------------------------- \documentclass[a4paper]{article} \usepackage{graphicx} \makeatletter% %--------------------- \usepackage{mcf_setup} %--------------------- \pagestyle{empty} %-------------------------------------------------------------------- \def\put@char{% \begin{picture}(84,42)% \put(0,38){\bf [\MOLnum]\EN{ }\small\tt/FM:\fm/MW:\mw}% \put(10,0){\font\@strufont=\File\relax% \hbox{\@strufont\char\Char}}% \end{picture}% }% \def\INFO#1{\@for\@temp:=#1\do{\tag@var\@temp}\put@char}% \makeatother %-------------------------------------------------------------------- \begin{document} \unitlength=1mm% \INFO{J:mcf_man_soc,C:141,NO:1,mw:349.40462,fm:C16H19N3O4S,EN:Ampicillin}% \INFO{J:mcf_man_soc,C:142,NO:2,mw:386.6532,fm:C27H46O,EN:Cholesterol}% \end{document} %-------------------------------------------------------------------- \end{verbatim}% %############################################################################ %------------------------------------------------------------------------ \INFO{J:mcf_man_soc,C:141,NO:1,mw:349.40462,fm:C16H19N3O4S,EN:Ampicillin}% \INFO{J:mcf_man_soc,C:142,NO:2,mw:386.6532,fm:C27H46O,EN:Cholesterol}% %------------------------------------------------------------------------ \texttt{\printindex} %------------------------------------------------------------------------ \end{document}
https://lib.anarhija.net/library/benjamin-tucker-my-reasons-for-favoring-the-allies.tex	anarhija.net	CC-MAIN-2021-39	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2021-39/segments/1631780057083.64/warc/CC-MAIN-20210920161518-20210920191518-00032.warc.gz	420,380,319	2,875	\documentclass[DIV=12,% BCOR=0mm,% headinclude=false,% footinclude=false,% fontsize=10pt,% oneside,% paper=a5]% {scrartcl} \usepackage{fontspec} \setmainfont[Script=Latin]{Alegreya} \setsansfont[Script=Latin,Scale=MatchLowercase]{Alegreya Sans} \setmonofont[Script=Latin,Scale=MatchLowercase]{Space Mono} \let\chapter\section % global style \pagestyle{plain} \usepackage{microtype} % you need an updated texlive 2012, but harmless \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} \usepackage[shortlabels]{enumitem} \usepackage{tabularx} \usepackage[normalem]{ulem} \def\hsout{\bgroup \ULdepth=-.55ex \ULset} % https://tex.stackexchange.com/questions/22410/strikethrough-in-section-title % Unclear if \protect \hsout is needed. Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand{\captionformat}{} \renewcommand{\figureformat}{} \renewcommand{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} \usepackage{polyglossia} \setmainlanguage{english} % footnote handling \usepackage[fragile]{bigfoot} \usepackage{perpage} \DeclareNewFootnote{default} \DeclareNewFootnote{B} \MakeSorted{footnoteB} \renewcommand\thefootnoteB{(\arabic{footnoteB})} \deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand{\forcelinebreak}{\strut\\{}} \newcommand{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand{\Slash}{\slash\hspace{0pt}} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} % forbid widows/orphans \frenchspacing \sloppy \clubpenalty=10000 \widowpenalty=10000 % http://tex.stackexchange.com/questions/304802/how-not-to-hyphenate-the-last-word-of-a-paragraph \finalhyphendemerits=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{“My Reasons for Favoring the Allies”} \date{Dec 23, 1914} \author{Benjamin Tucker} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={“My Reasons for Favoring the Allies”},% pdfauthor={Benjamin Tucker},% pdfsubject={},% pdfkeywords={letter}% } \begin{document} \thispagestyle{empty} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge “My Reasons for Favoring the Allies”\par}}% \vskip 1em \vskip 2em {\usekomafont{author}{Benjamin Tucker\par}}% \vskip 1.5em {\usekomafont{date}{Dec 23, 1914\par}}% \end{center} \vskip 3em \par Dec 23, 1914 Dear Labadie; Bool says that you wish to know my reasons for favoring the Allies. I favor the Allies because I pity the Belgian people, because I admire the British influences that make or liberty, because I feel some (tho I regret to say a decreasing) concern for the future of the American people, because I have considerable sympathy or the \emph{people} of Russia, and because I hate and fear the German people as a nation of domineering brutes bent on turning the whole world into a police-ridden paradise of the Prussian pattern. I have numerous other reasons for favoring the allies, but the above is the main reason and a sufficient one. You see, I don’t love everybody as you and Bool do. My love is limited in quantity, and goes out in special directions. However, much as it is, here’s a goodly share of it for \emph{you}. Cordially yours, Benj. R. Tucker Feb 19, 1907 % begin final page \clearpage % new page for the colophon \thispagestyle{empty} \begin{center} Library.Anarhija.Net \bigskip \includegraphics[width=0.25\textwidth]{logo-yu.pdf} \bigskip \end{center} \strut \vfill \begin{center} Benjamin Tucker “My Reasons for Favoring the Allies” Dec 23, 1914 \bigskip Retrieved on 2016-10-28 from http:\Slash{}\Slash{}marxists.architexturez.net\Slash{}archive\Slash{}tucker\Slash{}1914\Slash{}allies.htm Source: Benjamin R. Tucker Papers, New York Public Library; Transcribed: by Mitchell Abidor. \bigskip \textbf{lib.anarhija.net} \end{center} % end final page with colophon \end{document}
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https://alco.centre-mersenne.org/article/10.5802/alco.19/file/src/tex/ALCO_2018__1_4_501_0.tex	centre-mersenne.org	CC-MAIN-2021-39	text/x-tex	text/x-matlab	crawl-data/CC-MAIN-2021-39/segments/1631780057033.33/warc/CC-MAIN-20210920070754-20210920100754-00519.warc.gz	145,791,585	23,188	%~Mouliné par MaN_auto v.0.17.2 2018-06-25 16:28:55 \documentclass[ALCO,Unicode,ThmDefs]{cedram} \OneNumberAllTheorems %\usepackage{latexsym} %\usepackage{mathrsfs} \usepackage{tikz} \usepackage{mathtools} \usetikzlibrary{shapes} \newcommand\Q{{\mathbf Q}} \newcommand\R{{\mathbf R}} \newcommand\Z{{\mathbf Z}} \renewcommand\C{{\mathbf C}} \newcommand\OO{\mathcal{O}} \newcommand\m{\mathfrak m} \newcommand{\F}{\mathbf{F}} \newcommand{\map}[4]{ \begin{array}{ccc} #1 & \longrightarrow & #2 \\ #3 & \longmapsto & #4 \end{array} } \renewcommand{\geq}{\geqslant} \renewcommand{\leq}{\leqslant} \graphicspath{{./figures/}} \newcommand{\mk}{\mkern -1mu} \newcommand{\Mk}{\mkern -2mu} \newcommand{\mK}{\mkern 1mu} \newcommand{\MK}{\mkern 2mu} \title{Towards a function field version of Freiman's Theorem} \author{\firstname{Christine} \lastname{Bachoc}} \address{Institut de Mathématiques de Bordeaux, CNRS UMR 5251, Université de Bordeaux, 351 cours de la Libération, 33400 Talence, France} \email{[email protected]} \author{\firstname{Alain} \lastname{Couvreur}} \address{INRIA \& Laboratoire LIX, CNRS UMR 7161, École Polytechnique, Université Paris Saclay, 91128 Palaiseau Cedex, France} \email{[email protected]} \author{\firstname{Gilles} \lastname{Zémor}} \address{Institut de Mathématiques de Bordeaux, CNRS UMR 5251, Université de Bordeaux, 351 cours de la Libération, 33400 Talence, France} \email{[email protected]} \thanks{The authors are supported by French \emph{Agence nationale de la recherche} grant ANR-15-CE39-0013-01 \emph{Manta}.} \keywords{Additive combinatorics, function fields} \subjclass{11R58, 11P99, 05E40, 14H05} \begin{abstract} We discuss a multiplicative counterpart of Freiman's $3k-4$ theorem in the context of a function field $F$ over an algebraically closed field $K$. Such a theorem would give a precise description of subspaces $S$, such that the space $S^2$ spanned by products of elements of $S$ satisfies $\dim S^2\leq3 \dim S-4$. We make a step in this direction by giving a complete characterisation of spaces $S$ such that $\dim S^2=2 \dim S$. We show that, up to multiplication by a constant field element, such a space $S$ is included in a function field of genus $0$ or $1$. In particular if the genus is $1$ then this space is a Riemann--Roch space. \end{abstract} \begin{document} \maketitle \section{Introduction} We are interested in linear analogues of addition theorems that occur in field extensions $F/K$ of a base field $K$. If $S$ and $T$ are finite-dimensional $K$-vector subspaces of $F$, we denote by $ST$ the $K$-linear span of the set of all products $st$, $s\in S$, $t\in T$. The general purpose of this area of research is to characterise subspaces $S$ and $T$ whose product $ST$ has unusually small dimension: it is naturally inspired by one of the goals of additive combinatorics which is to characterise subsets $A,B$ of elements of a group that have sumsets $A+B$ of small cardinality, where $A+B$ denotes the set of elements $a+b$, $a\in A$, $b\in B$. The first significant result in this direction is arguably due to Hou, Leung and Xiang~\cite{hlx02} and generalises the classical addition theorem of Kneser~\cite{kneser}. It essentially states that if $\dim ST < \dim S + \dim T -1$, then the space $ST$ must be stabilised by a non-trivial subfield of $F$. A welcome feature of Hou et~al.'s theorem is that Kneser's original theorem can be recovered from it, so that it is not only a transposition to the linear setting of its additive counterpart, but it can also be seen as a generalisation. Hou's Theorem was finally proved for all field extensions in~\cite{bszKneser}, and also studied in other algebras than field extensions~\cite{bl15,mz15}. Linear versions of addition theorems were also studied in the somewhat broader context of skew field extensions in~\cite{el09}. Many applications of the theory of products of spaces in the algebra $\F_q^n$ with componentwise multiplication are discussed in~\cite{hugues}. A common feature of {many of} the above works is that they tend to focus on highlighting the existence of finite dimensional subfields or subalgebras, whenever $\dim ST < \dim S + \dim T -1$. In contrast, in~\cite{bszVosper} field extensions $F/K$ are studied where there are no subextensions of $K$ in $F$ ($K$ is algebraically closed in $F$) in which case one always has $\dim ST\geq\dim S +\dim T -1$ whenever $ST\neq F$~\cite{el09}. The goal of~\cite{bszVosper} was to prove that the equality $\dim ST=\dim S +\dim T -1$ essentially implies that $S$ and $T$ have bases in geometric progression: this is a linear equivalent of Vosper's Theorem~\cite{Vosper} which states that in a group of prime order, or more generally an abelian group with no finite subgroups, $\|A+B\|=\|A\|+\|B\|-1$ implies that $A$ and $B$ are arithmetic progressions (with some degenerate cases ruled out). It is proved in~\cite{bszVosper} that a linear version of Vosper's theorem holds when the base field $K$ is finite, and for a number of other base fields, but not for every field $K$, even if it is assumed to be algebraically closed in $F$. This theory of subspaces with products of small dimension in field extensions has also recently found applications to coding theory in~\cite{RRT18}. A particularly simple case for which a linear version of Vosper's Theorem can be derived from an addition theorem, is when the base field $K$ is itself assumed to be algebraically closed. The linear theorem then follows almost directly from considering sets $A$ and $B$ of valuations of the field elements in $S$ and $T$ and arguing that $A$ and $B$ must satisfy an addition theorem. From this perspective it becomes very natural to ask what can be said of the structure of spaces $S$ such that \begin{equation}\label{eq:cgenus} \dim S^2=2\dim S -1 +\gamma \end{equation} for increasing values of $\gamma$. We have switched to the symmetric situation $S=T$ for the sake of simplicity. In the additive case, recall Freiman's ``$3k-4$'' Theorem~\cite{Freiman}, \cite[Theorem~5.11]{TaoVu}, which says that in a torsion-free abelian group, \[ \|A+A\|=2\|A\|-1+\gamma \] implies, when $\gamma\leq\|A\|-3$, that $A$ is included in an arithmetic progression of length $\|A\|+\gamma$ (i.e. $A$ is a progression with at most $\gamma$ missing elements). The full Freiman Theorem, which extends the above $3k-4$ version, is arguably a cornerstone of additive combinatorics and has inspired a lot of subsequent work (see e.g.~\cite{TaoVu}). In this light, tackling the characterisation of spaces satisfying~\eqref{eq:cgenus} would be a welcome addition to the burgeoning theory of space products in extension fields. Candidates for spaces $S$ satisfying~\eqref{eq:cgenus} are of course subspaces (of codimension at most $\gamma$) inside a space that has a basis in geometric progression. However, some thought yields alternative spaces that do not have an additive analogue when $\gamma\geq1$: namely Riemann--Roch spaces $L(D)$ of an algebraic curve of genus $\gamma$, which {can be} seen to satisfy~\eqref{eq:cgenus}. It is tempting to conjecture that, in the case when the base field $K$ is algebraically closed, any space satisfying~\eqref{eq:cgenus} {with $\gamma\leq\dim S-3$} is, up to multiplication by a constant, a subspace of codimension $t$ inside a Riemann--Roch space of an algebraic curve of genus $g$, with $t+g\leq\gamma$. With this in mind, let us call the quantity $\gamma$ in~\eqref{eq:cgenus} the \emph{combinatorial genus} of $S$. In the present paper we make a modest contribution towards this hypothesis by proving it in the case when $\gamma=1$. We will use a blend of combinatorial and algebraic methods. The paper is organised as follows: {Section~\ref{sec:examples} starts with a discussion of concrete examples of spaces with small products.} Section~\ref{sec:valuations} recalls basic properties of valuations that will in particular associate sets of integers with small sumsets to subspaces with products of small dimension. Section~\ref{sec:freiman} proves {Theorem~\ref{thm:freiman_field}}, an extension field version of ``Freiman's Lemma'' where the transcendence degree plays a role analogous to the rank of a set of elements of a torsion-free abelian group. Section~\ref{sec:products} introduces a lattice of subspaces that we shall rely on heavily, and illustrates its usefulness by characterising spaces with combinatorial genus equal to zero. Section~\ref{sec:divisors} recalls basic properties of Riemann--Roch spaces and states the paper's main result, Theorem~\ref{thm:main}. Section~\ref{sec:proof_main} proves Theorem~\ref{thm:main}. Section~\ref{sec:genus0} complements Theorem~\ref{thm:main} by giving a precise characterisation of those subspaces of Riemann--Roch spaces that have combinatorial genus equal to $1$. Finally, Section~\ref{sec:perfect} extends Theorems~\ref{thm:freiman_field} and~\ref{thm:main} to the case when the base field is perfect rather than algebraically closed. \section{{Motivating Examples}}\label{sec:examples} Let $K$ be a field and consider the field $F=K(x)$ of rational functions over $K$. Suppose we want a $K$-vector subspace $S$ of dimension $k$ such that $S^2$ has the smallest possible dimension. A natural candidate is the space $S$ generated by the geometric progression $1,x,x^2,\ldots,x^{k-1}$ for which we have $\dim S^2=2k-1$. We notice that the set $A$ of degrees of the rational functions (in this example polynomials in $x$) of $S$ is an arithmetic progression. More generally, the set of degrees of the functions in $S^2$ must contain $A+A$, so that $\dim S^2\geq\|A+A\|$. This remark may be used to claim that if $\dim S^2$ is the smallest possible, namely $2k-1$, then $\|A+A\|$ must be as small as possible, which implies that $A$ must be an arithmetic progression of integers, from which it is fairly straightforward to deduce that $S$ must have a basis of elements in geometric progression. We will make the point below that this line of reasoning extends to other extension fields $F$ of $K$, provided we have \emph{valuations} at our disposal to generalise degrees of rational functions. Next relax slightly the condition on $\dim S^2$ to $\dim S^2\leq2k$. To construct examples of such spaces we may consider $S$ in the rational function field $K(x)$ generated by $1,x^2,x^3,\ldots,x^k$. These spaces are directly inspired from the sets of integers $A=\{0,2,3,\ldots,k\}$ such that $\|A+A\|=2\|A\|$. However, we have additional examples of such spaces that have no direct additive counterpart: take $K$ to be the field of complex numbers (say) and take $F$ to be the algebraic extension $K(x,y)$ of the rational function field $K(x)$ where $y$ satisfies the equation $y^2-x^3+x=0$. Now consider the space $S$ of dimension~$5$ generated by $1,x,y,x^2,xy$. It is readily checked that we have $\dim S^2=2\dim S$. The space $S$ is an example of a Riemann--Roch space of the algebraic curve of equation $y^2-x^3+x=0$ which is elliptic or of genus $1$. Our main result, namely Theorem~\ref{thm:main}, will tell us that these two examples are in some sense generic. This has motivated the following definition, and also the conjecture below: \begin{defi}\label{def:gamma} Let $K$ be a field and $F$ be a $K$--algebra. Let $S \subset F$ be a finite dimensional $K$--subspace of $F$. The \emph{combinatorial genus of $S$} is defined as the integer $\gamma$ such that \[ \dim S^2=2\dim S - 1 + \gamma. \] \end{defi} \begin{conj}\label{conj} Let $K$ be an algebraically closed field and let $F$ be an extension field of $K$. Let $S$ be a $K$-subspace of finite dimension in $F$ such that $K\subset S$. Let the combinatorial genus $\gamma$ of $S$ satisfy $\gamma\leq\dim S -3$. Then the genus $g$ of the field $K(S)$ satisfies $g\leq\gamma$ and there exists a Riemann--Roch space $L(D)$ that contains $S$ and such that $\dim L(D)\leq\dim S +\gamma -g$. \end{conj} The next section recalls some background on valuations with which we will derive our first results on spaces with small combinatorial genus. \section{{Function fields, valuations}}\label{sec:valuations} We start by recalling some basic facts about valuations in function fields that will be crucial to transferring additive statements to the extension field setting. We refer the reader to~\cite[Chapter~6]{Bourbaki_AlgComm5-6} for further details. Let $K$ be a field, a \emph{function field in $m$ variables over $K$} is a field $F$ which is a finitely generated algebra of transcendence degree $m$. Equivalently it is a finite extension of the field $K(X_1, \ldots, X_m)$ of rational functions in $m$ variables. We recall that such fields have \emph{valuations} that map $F^{\times}$ to the elements of some ordered group. Valuations are multiplicative, i.e. $v(xy)= v(x) + v(y)$ and satisfy the ultrametric inequality, $v(x+y)\geq\min \{v(x), v(y)\}$ with equality when $v(x) \neq v(y)$. The map $v$ is extended to $F$ with the convention $v(0)=\infty$. A valuation comes with \emph{a valuation ring} $\OO \subset F$ which is defined as the set of functions of non-negative valuation, together with addition and multiplication inherited from $F$. A valuation ring has a unique maximal ideal $\m$ equal to the set of elements of positive valuation. The quotient $\OO/\m$ is called the \emph{residue field} of the valuation ring. Let $S \subseteq F$ be a finite dimensional $K$--vector space of dimension $n>0$. Given a valuation $v$ on $F$ with residue field $K$, we denote by $v(S)$ the set of valuations of the non-zero elements of $S$. We recall the following classical result, and give a proof for the sake of self--containedness. \begin{prop}\label{prop:filtered_basis} The set $v(S)$ is finite and its cardinality equals $\dim S$. Moreover, there exists a basis $(e_1, \ldots, e_n)$ of $S$ such that \[ v(e_1) > v(e_2) > \dots > v(e_n) \quad \text{and} \quad \{v(e_1), \ldots, v(e_n)\}= v(S). \] Such a basis is referred to as a \emph{filtered basis}. In addition, $S$ has a natural filtration \[ \{0\} \subset S_1 \subset \cdots \subset S_{n-1} \subset S_n \] such that \begin{equation}\label{eq:ineq_valuations} \min v(S_1) > \cdots > \min v(S_{n-1}) > \min v (S). \end{equation} For every $i=1,\dots, n$, the space $S_i$ is generated by $e_1,\ldots ,e_i$, but the filtration is uniquely defined and does not depend on the choice of a filtered basis. \end{prop} \begin{proof} First notice that elements of $F$ with distinct finite valuations are linearly independent. Indeed, if $x_1, \ldots, x_k$ have distinct valuations, then so do $a_1x_1,\ldots,a_kx_k$ for non-zero $a_i\in K$, since non-zero elements of $K$ have valuation $0$, so that $v(a_1 x_1 + \cdots + a_k x_k)=\min(v(x_1),\ldots, v(x_k))$ must be finite, meaning $a_1 x_1 + \cdots + a_k x_k$ must be non-zero. This shows that $\|v(S)\|\leq\dim S$. Now let $E$ be a subspace of $S$ such that $v(E)=v(S)$ and suppose $E\subsetneqq S$. Let $x$ be an element of $S\setminus E$ with maximal valuation in $\{v(s), s\in S\setminus E\}$. Let $e\in E$ be such that $v(e)=v(x)$. Then, $xe^{-1} \in \OO^\times$ and since the residue field is $K$, there exists $\lambda \in K$ such that $xe^{-1} \equiv \lambda \mod \m$. Therefore, $x -\lambda e$ has a valuation larger than $v(x)$, a contradiction. Therefore $E=S$, meaning that we have $\dim S=\|v(S)\|$. Choosing any $n$ elements of $S$ with distinct finite valuations yields a filtered basis. Finally, the filtration $S_1 \subset \cdots \subset S_n= S$ is iteratively constructed as follows, \[ S_{i-1}=\{x \in S_i~\|~v(x) > \min v(S_i)\}. \] Note that this definition is independent of the choice of a filtered basis, however one checks easily that $S_{i-1}$ is spanned by $e_1, \ldots, e_{i-1}$. This shows that the space $S_{i-1}$ has codimension~$1$ in $S_i$ and the sequence of inequalities~\eqref{eq:ineq_valuations} follows immediately from the definition of the $S_i$'s. \end{proof} The following lemma is elementary but fundamental to the study of the structure of products $S^2$ of small dimension. It enables us to involve theorems from additive combinatorics. \begin{lemm}\label{lem:v(H^2)} For any valuation $v$ on $F$, and any $K$--subspace $S$, \begin{equation}\label{eq:valuation_product} v(S)+v(S) \subseteq v(S^2). \end{equation} \end{lemm} \begin{rema} Note that this inclusion is not necessarily an equality. For instance, consider the subspace $H$ of $K(x)$ of basis $1, x, x^2, x^3 + \frac 1 x$ and the valuation $v$ at infinity. Then $v(H)=\{0,-1,-2,-3\}$ while $H^2=\langle \frac 1 x, 1, x, x^2, \ldots, x^5, x^6+\frac 1 {x^2} \rangle$ whose valuation set contains $v(1/x)=1$ which is not in $v(H)+v(H)$. \end{rema} From now on and until the end of Section~\ref{sec:genus0} (with a temporary exception in \S \ref{subsec:divisors}), we suppose that the base field $K$ is algebraically closed. Note that this assumption entails that any valuation on $F$ has residue field $K$, which will therefore enable us to apply Proposition~\ref{prop:filtered_basis}. Only in Section~\ref{sec:perfect} will we consider what becomes of our results when the base field $K$ is not algebraically closed. \section{Transposing Freiman's Lemma in field extensions}\label{sec:freiman} Recall the following result of Freiman~\cite{Freiman}, named ``Freiman's Lemma'' by Tao and Vu~\cite[Lemma~5.13]{TaoVu}. \begin{theo}\label{thm:freiman} Let $A$ be a finite subset of $\R^d$ such that no hyperplane of $\R^d$ contains a translate of $A$. Then \[ \|A+A\|\geq(d+1)\|A\| -d(d+1)/2. \] \end{theo} Let $S$ be a $K$-vector space inside a field extension $L$ of a field $K$. We remark that for a non-zero element $s$ of $S$, the field subextension $K(Ss^{-1})$ of $L$ is independent of the choice of the element $s$. Let us call the \emph{transcendence degree of $S$} the transcendence degree of $K(Ss^{-1})$ over $K$. Similarly, by the \emph{genus of $S$} we will mean the genus of the field extension $K(Ss^{-1})/K$ (see Theorem~\ref{thm:main} in Section~\ref{sec:Vosper+1}). We have the extension field analogue of Theorem~\ref{thm:freiman}. \begin{theo}\label{thm:freiman_field} Let $K$ be {an algebraically closed} field and let $F \supseteq K$ be an extension field of $K$. Let $S$ be a $K$-vector subspace of $F$ of finite dimension and of transcendence degree $d$. Then \[ \dim S^2\geq(d+1)\dim S -d(d+1)/2. \] \end{theo} The proof of Theorem~\ref{thm:freiman_field} rests upon the following lemma. \begin{lemm}\label{lem:val} If $F/K$ is a field extension over an algebraically closed field $K$, and if $x_1,\ldots,x_d$ are $K$-algebraically independent elements of $F$ such that $F$ is an algebraic extension of $K(x_1,\ldots,x_d)$, then there exists a valuation $v$ of~$F$, such that the associated valuation ring has residue field isomorphic to $K$ and such that the valuation values $v(x_1),v(x_2),\ldots,v(x_d)$ generate a group isomorphic to~$\Z^d$. \end{lemm} \begin{proof} It is standard to construct a valuation $v$ from $K(x_1,x_2,\ldots ,x_d)$ to $\Z^d$ such that $v(x_1)=(1,0,\ldots,0), v(x_2)=(0,1,\ldots,0),\ldots, v(x_d)=(0,\ldots,0,1)$ and with associated residue field isomorphic to $K$ (see e.g.~\cite[Chapter~6, \S 3.4, Example~6]{Bourbaki_AlgComm5-6}). This valuation can then be extended to the whole of $F$~\cite[Chapter~6, \S 3.3, Proposition~5]{Bourbaki_AlgComm5-6} with its residue field necessarily becoming an algebraic extension of the original residue field associated to $v$~\cite[Chapter~6, \S 8.1, Proposition~1]{Bourbaki_AlgComm5-6}. Since~$K$ is algebraically closed, the residue field associated to the extended valuation must therefore also be isomorphic to $K$. \end{proof} \begin{proof}[Proof of Theorem~\ref{thm:freiman_field}] Without loss of generality we may suppose $K\subset S$ and $F=K(S)$. Let $x_1,\ldots,x_d$ be $d$ algebraically independent elements of $F$. Choose for $v$ a valuation given by Lemma~\ref{lem:val}. Then, since the residue field associated to $v$ is $K$, by Proposition~\ref{prop:filtered_basis} we know that $\dim S=\|v(S)\|$ and $\dim S^2=\|v(S^2)\|$. From~\eqref{eq:valuation_product} we have $\dim S^2\geq\|v(S)+v(S)\|$ and Theorem~\ref{thm:freiman} now gives us \[ \|v(S)+v(S)\|\geq(d+1)\|v(S)\|-d(d+1)/2=(d+1)\dim S-d(d+1)/2 \] which proves the theorem. \end{proof} \begin{enonce}[remark]{Consequence} When one considers a space $S$, $K\subset S \subset F$, with $\dim S^2\leq3\dim S - 4$, and $F= K(S)$, then $F$ is a function field in one variable. In particular, from~\cite[Theorem~1.1.16]{Stichtenoth}, every valuation on $F$ is discrete and its set of values is $\Z$. \end{enonce} For the rest of this article we will assume this setting, namely a sufficiently small combinatorial genus $\gamma$, so that the transcendence degree of $S$ can only be equal to $1$. The term \emph{function field} will consequently always mean from now on \emph{function field in one variable}. Since the multiplicative properties of $S$ that we wish to study are invariant by multiplication by a constant non-zero element, it will also be convenient to systematically assume $1\in S$, so that $K(S)$ is a function field (in one variable). \section{Products of spaces, the lattice of subspaces and characterising spaces with combinatorial genus \texorpdfstring{$\gamma=0$}{gamma=0}}\label{sec:products} In order to study the structure of a product set $S^2$, the lattice of subspaces that we introduce below will be particularly useful. Its structure will enable us to almost immediately characterise spaces with the smallest possible combinatorial genus. \subsection{The lattice of subspaces}\label{sec:lattice} Let $(e_1,\ldots,e_n)$ be a filtered basis of the space $S$ relative to a valuation $v$. Consider the sequence of subspaces {introduced in Proposition~\ref{prop:filtered_basis}} \[ S_1\subset S_2\subset\cdots \subset S_n=S \] where $S_i$ denotes the subspace of $S$ generated by $e_1,\ldots ,e_i$. We will refer to this sequence of spaces as the \emph{filtration of $S$ relative to $v$}. Since dimensions of spaces are unchanged by multiplication by a constant element, we may assume $e_1=1$ and $S_1=K$. It will be useful to consider the lattice of subspaces of $S^2$ consisting of the products of subspaces $S_iS_j$ and ordered by inclusion, as represented on Figure~\ref{fig:subspaces}. We will consider directed edges between $S_iS_j$ and $S_iS_{j+1}$ and between $S_iS_j$ and $S_{i+1}S_{j}$, and label both edges by a weight defined as the codimension of $S_iS_j$ inside $S_iS_{j+1}$ and $S_{i+1}S_{j}$ respectively. We will make several times the argument that the sum of weights on two directed paths that lead from the same initial vertex to the same terminal vertex must be the same because they both equal the codimension of the initial subspace inside the terminal subspace. Notice also that all weights must be positive because the valuation set of an initial subspace must be strictly smaller than the valuation set of the corresponding terminal subspace: indeed, $e_ie_{j+1}$ is an element of minimal valuation of $S_iS_{j+1}$ that cannot belong to $S_iS_j$ because the minimum of $v(S_iS_j)$ is attained by $e_ie_j$, and similarly for $S_{i+1}S_j$. \begin{figure}[!h] \centering \begin{tikzpicture}[scale=0.8] \node[name=S11] at (4,4) {$K=S_1^2$}; \node[name=S12] at (6,4) {$S_{1}S_{2}$}; \node[name=S13] at (8,4) {$S_1S_3$}; \node[name=S14] at (10,4) {$S_1S_4$}; \node[name=S15] at (12,4) {$S_1S_5$}; \node[name=S22] at (6,6) {$S_2^2$}; \node[name=S23] at (8,6) {$S_2S_3$}; \node[name=S24] at (10,6) {$S_2S_4$}; \node[name=S25] at (12,6) {$S_2S_5$}; \node[name=S33] at (8,8) {$S_3^2$}; \node[name=S34] at (10,8) {$S_3S_4$}; \node[name=S35] at (12,8) {$S_3S_5$}; \node[name=S44] at (10,10) {$S_4^2$}; \node[name=S45] at (12,10) {$S_4S_5$}; \node[name=S55] at (12,12) {$S_5^2$}; \draw[->] (S11) -- (S12) edge (S13) (S13) edge (S14) (S14) edge (S15) (S15) edge (S25) (S25) edge (S35) (S35) edge (S45) (S45) edge (S55); \draw[->] (S22) -- (S23) edge (S24) (S24) edge (S25); \draw[->] (S33)--(S34) edge (S35); \draw[->] (S14) to (S24) edge (S34) (S34) edge (S44) (S44) edge (S45); \draw[->] (S12) edge (S22); \draw[->] (S13) -- (S23) edge (S33); \end{tikzpicture} \caption{the lattice of subspaces}\label{fig:subspaces} \end{figure} The following lemma states that when two edges that fall into the same terminal vertex both have weight $1$, then the initial vertices correspond to the same subspace. \begin{lemm}\label{lem:codim1} Suppose the spaces $S_iS_{j+1}$ and $S_{i+1}S_j$ both have codimension~$1$ inside $S_{i+1}S_{j+1}$, then $S_iS_{j+1}= S_{i+1}S_j$. \end{lemm} \begin{proof} Let $U=\{s\in S_{i+1}S_{j+1}, v(s)>\min v(S_{i+1}S_{j+1})\}$. We have that $U\subsetneqq S_{i+1}S_{j+1}$ and $U$ is a subspace containing both $S_iS_{j+1}$ and $S_{i+1}S_j$ which must therefore all have the same dimension and be equal. \end{proof} \subsection{The structure of \texorpdfstring{$S$}{S} when \texorpdfstring{$\gamma=0$}{gamma=0}}\label{sec:Vosper} Like in the previous subsection we assume that $e_1=1$, and we moreover set $x=e_2$. \begin{lemm}\label{lem:vosper} Suppose all directed edges lying on any path from $S_1$ to $S_iS_j$, $2\leq i$, have weight~$1$. Then for every $k$, $2\leq k\leq j$, the space $S_k$ is generated by $1,x,x^2,\ldots,x^{k-1}$. \end{lemm} \begin{proof} Proceed by induction on $k$. Suppose the result is proved for $k$ and prove it for $k+1\leq j$. By applying Lemma~\ref{lem:codim1} to $S_1S_{k+1}$ and $S_2S_k$ inside $S_2S_{k+1}$, we obtain $S_{k+1}=\langle 1,x\rangle S_k$ meaning that $S_{k+1}$ is generated by $(1,x,x^2,\ldots,x^{k})$. \end{proof} As an immediate corollary we obtain the following theorem, which is proved in~\cite{bszVosper} in more generality. Its proof illustrates the usefulness of the subspace lattice described above. \begin{theo}\label{thm:genus0} Let $K$ be an algebraically closed field, and let $S$ be a finite-dimensional $K$-vector space lying in a field extension $F$ of $K$. If $\dim S^2=2\dim S-1$ then $S$ has a basis in geometric progression, i.e. of the form $(a,ax,ax^2,\ldots,ax^{n-1})$. \end{theo} \begin{proof} Replacing $S$ by $e_1^{-1}S$ reduces to the case $e_1=1$. Because the codimension of $K$ in $S^2$ is $2\dim S-2$ and is equal to the length of any path from $K$ to $S^2$ in the lattice, we have that every edge must be of weight $1$. The result therefore follows from Lemma~\ref{lem:vosper}. \end{proof} We now turn to Riemann--Roch spaces that provide more spaces of low combinatorial genus~$\gamma$. \section{Divisors, Riemann--Roch spaces, and characterising spaces with combinatorial genus \texorpdfstring{$\gamma=1$}{gamma=1}}\label{sec:divisors} \subsection{Divisors and Riemann--Roch spaces on function fields}\label{subsec:divisors} We quickly recall some basic notions on the theory of the function fields in one variable (or equivalently of algebraic curves). For further details, we refer the reader to~\cite{Stichtenoth} or to~\cite{Fulton} for a more geometric point of view. In the present subsection, in order to introduce some notions that will also be useful in the more general setting of Section~\ref{sec:perfect}, we do not assume that $K$ is algebraically closed. Let $F$ be a function field over $K$ such that $K$ is algebraically closed in $F$. Following~\cite[Chapter~I]{Stichtenoth}, let us call a \emph{place} $P$ of $F$ the maximal ideal of a valuation ring. Valuations, valuation rings, places are interchangeable notions in the sense that any one unambiguously defines the others. Informally, a place captures the concept of ``point'' of the associated algebraic curve. For a place $P$ we denote by $v_P$ the (unique) associated discrete valuation. The \emph{degree} $\deg P$ of a place $P$ is the dimension over $K$ of its residue field $\OO/P$. It is always finite and equal to $1$ when $K$ is algebraically closed. A \emph{divisor on} $F$ is an element of the free abelian group generated by the places of $F$. Thus it is a formal $\Z$--linear combination of places. Given a function $f \in F^{\times}$, the divisor of $f$ is defined as \[ (f):=\sum_{P \textrm{ place of } F} v_P(f)P. \] The group of divisors is partially ordered as follows: given a divisor $G= g_1 P_1 + \cdots + g_m P_m$, we have $G\geq0$ if $g_1, \dots, g_m\geq0$. Next $G\geq H$ if $G-H\geq0$. The \emph{degree} of the divisor $G$ is defined as \[ \deg G= g_1\deg P_1 + \cdots +g_m\deg P_m. \] Given a divisor $D$ of $F$, the Riemann--Roch space $L(D)$ is defined as \[ L(D):=\{ f\in F~\|~(f) + D\geq0\} \cup \{0\}. \] The dimension of this space is given by the famous Riemann--Roch theorem~\cite[Theorem~1.5.15]{Stichtenoth}. In particular it satisfies: \begin{equation} \text{If } \deg D>2g-2 \text{ then }\dim L(D)=\deg(D)+1-g \end{equation} where $g$ denotes the \emph{genus} of the field $F$ (see~\cite[Definition~1.4.15]{Stichtenoth} for a definition). Two divisors $D$, $D'$ are said to be \emph{linearly equivalent} which we denote by $D \sim D'$ if $D'= D+(f)$ for some function $f \in F^\times$. Such an equivalence induces an isomorphism between the Riemann--Roch spaces which is explicit: \[ \map{L(D')}{L(D)}{s}{fs.} \] In short $L(D)= f \cdot L(D')$. The following well-known result due to Mumford gives an explicit formula for the product of Riemann--Roch spaces. \begin{theo}[{\cite[Theorem~6]{Mumford}}]\label{thm:mumford} Let $D$, $D'$ be two divisors of a function field $F$ of genus $g$ {over an algebraically closed field $K$}. Suppose that $\deg D\geq2g$ and $\deg D'\geq2g+1$. Then \[ L(D)L(D')= L(D+D'). \] \end{theo} In particular, combining the Riemann--Roch theorem with Theorem~\ref{thm:mumford}, one has that in a function field of genus $g$, for any divisor $D$ of degree larger than $2g+1$, the space $L(D)$ has combinatorial genus $\gamma=g$. This has in particular motivated Definition~\ref{def:gamma}. Finally recall that, {over an algebraically closed field $K$}, a function field $F$ has genus~$0$ if and only if it is a purely transcendental extension $F=K(x)$ of $K$. In such an extension, the space generated by the functions $1,x,x^2,\ldots,x^n$ is equal to the Riemann--Roch space $L(nP_\infty)$ where $P_\infty$ is the place at infinity. We remark that the statement of Theorem~\ref{thm:genus0} is equivalent to saying that a space $S$ has combinatorial genus $\gamma=0$ if and only if it has genus $0$ and is equal to a Riemann--Roch space $L(D)=aL(nP_\infty)$ for a divisor $D=nP_\infty-(a)$ and a function~$a$. \subsection{Statement of the main theorem}\label{sec:Vosper+1} Until the end of Section~\ref{sec:genus0}, the base field $K$ is supposed to be algebraically closed. Our main purpose is to classify spaces over $K$ with combinatorial genus $1$. That is to say, given a finitely generated field $F$ over $K$ we want to understand the structure of $K$--spaces $S \subseteq F$ such that $\dim S^2=2 \dim S$. As remarked at the end of Section~\ref{sec:freiman}, we know from Theorem~\ref{thm:freiman_field} that the transcendence degree of $S$ must be equal to $1$, so that, assuming without loss of generality $1\in S$, $F$ is a function field (in one variable). With the case $\gamma=1$ in mind, we recall for future reference its additive analogue: \begin{prop}\label{prop:A+A=2A} A subset $A$ of the integers, $\|A\|\geq4$, is such that $\|A+A\|=2\|A\|$ if and only if it is of the form $A=a+\{0,2d,3d,\ldots,(n-1)d,nd\}$ for some {integer $a$ and some} non-zero $d$: in other words, writing $A$ as an increasing sequence, it is an arithmetic progression with a missing element after the first position (positive $d$) or before the last position (negative $d$). \end{prop} Indeed, Freiman's $3k-4$ Theorem applied to the case $\|A+A\|=2\|A\|$ gives that $A$ is an arithmetic progression with a single missing element, which is then easily seen to be necessarily at an extreme end of the progression. Proposition~\ref{prop:A+A=2A} is also true in the integers modulo a prime $p$, provided $\|A+A\|\leq p-2$, see~\cite{hr00} (and is therefore necessarily true in $\Z$). To generate a space $S$ such that $\gamma=1$, Proposition~\ref{prop:A+A=2A} suggests naturally to take a basis of the form $x^a, a\in A$, where $A$ is such that $\|A+A\|=2\|A\|$. Such a space is a subspace of codimension~$1$ inside a space with a basis in geometric progression, i.e. inside a Riemann--Roch space of genus $0$. Alternatively, Theorem~\ref{thm:mumford} tells us that Riemann--Roch spaces of genus $1$ will also give us spaces with combinatorial genus equal to $1$. Our main result states, broadly speaking, that the two constructions above cover all possible cases: \begin{theo}\label{thm:main} Let $K$ be an algebraically closed field and $F$ be a function field over $K$. Let $S \subseteq F$, $1\in S$, be a space of finite dimension $n\geq4$ and combinatorial genus $\gamma=1$. Then $S$ has genus $0$ or $1$. Moreover, \begin{itemize} \item if $S$ has genus $1$ then $S=L(D)$ for $D$ a divisor of degree $n$, \item if $S$ has genus $0$, then $S$ is a subspace of codimension~$1$ inside a space $L(D)$ for $D$ a divisor of degree $n$. \end{itemize} \end{theo} We remark that in the genus $g=0$ case, all subspaces of codimension~$1$ inside an $L(D)$ space do not necessarily have combinatorial genus $\gamma$ equal to $1$. { For instance the space $S=\langle 1, x, x^3, x^4 \rangle$ has codimension~$1$ in a Riemann Roch space of a field of genus $0$, while it has combinatorial genus $2$.} We postpone to Section~\ref{sec:genus0} the precise characterisation of such subspaces which is slightly more involved than in the additive case given by Proposition~\ref{prop:A+A=2A}. \section{Proof of Theorem~\ref{thm:main}}\label{sec:proof_main} \subsection{Overview} Since the proof of the theorem is somewhat lengthy, we give an outline. As we have argued before, we may always assume that $1\in S$, and that $F=K(S)$. We start by fixing an arbitrary place $P$ and an associated $P$-filtered basis which, possibly after replacing $S$ by a multiplicative translate $s^{-1}S$, is of the form \[ e_1=1,e_2=x,e_3=y,\ldots, e_n \] with valuations in decreasing order $v_P(1)=0>v_P(x)>v_P(y)>\cdots >v_P(e_n)$. Next we define (Section~\ref{sec:divisor}) the divisor $D_U$ of a space $U$ to be the smallest divisor such that the Riemann--Roch space {$L(D_U)$} contains $U$. Our strategy will be to study closely the chain of divisors $D_{S_i}$ for the filtration $(S_i)$ of $S$ relative to $P$. Our goal will be to show that $S_i$ is either equal to $L(D_{S_i})$ or of codimension~$1$ inside $L(D_{S_i})$, for all $i\geq2$. We will consider closely the lattice of subspaces introduced in Section~\ref{sec:lattice} and exploit the fact that most of its edges are of weight $1$. A crucial intermediate result will be Lemma~\ref{lem:D_Si} which will tell us that the divisor increments $D_{S_{i+1}}-D_{S_i}$ must all be equal to $D_{S_3}-D_{S_2}$, except possibly for one index $i$, that we call the $P$-index of $S$, which is the unique index $i$ for which $\dim S_iS_{i+1}>\dim S_i^2+1$. Sections~\ref{sec:separation} and~\ref{sec:Pindex} build up material leading up to Section~\ref{sec:changing} which derives Lemma~\ref{lem:D_Si}. Section~\ref{sec:genus} considers next the algebraic equations satisfied by $x$ and $y$. We will show that $F=K(S)=K(x,y)$ and that $F$ must be of genus $g\leq1$. We then turn to determining the sequence $(D_{S_i})$ exactly. Lemma~\ref{lem:D_Si} tells us that when the $P$-index equals $2$, the divisors $D_{S_2}$ and $D_{S_3}$ determine the whole sequence. In Section~\ref{sec:Pindex=2} we show that in this case we must have $D_{S_2}=P+Q$ and $D_{S_3}=2P+Q$ for some place $Q$ (possibly equal to $P$), so that the whole sequence of divisors must take the form $0,P+Q,2P+Q,3P+Q,\ldots,(n-1)P+Q$. Section~\ref{sec:Pindex>2} deals with the remaining case, for which it is shown that the sequence of divisors must be of the form $0,P,2P,\ldots,(n-2)P,(n-1)P+Q$. \subsection{Minimum valuations, the divisor of a space}\label{sec:divisor} The following lemma is straightforward: \begin{lemm}\label{lem:sum_min_val} Let $U,V$ be two finite dimensional $K$--spaces in $F$. Let $v$ be a valuation on $F$. Then, $\min v(UV)=\min v(U)+ \min v(V)$. \end{lemm} Note that $\min v(U)=0$ for all valuations $v$ on $F$ but finitely many of them. This justifies the following: \begin{defi}\label{def:DU} We denote by $D_U$ the divisor \[ D_U:=\sum_{P\textrm{ place of }F} -\min v_P(U)P. \] This is the smallest divisor $D$ such that $U \subseteq L(D)$. \end{defi} \subsection{Separation}\label{sec:separation} \begin{defi}[Separation] Given a finite dimensional $K$-space $U \subset F$ and two distinct places $P_1$ and $P_2$, one says that $U$ \emph{separates} $P_1$ and $P_2$ if there exists $f_1, f_2 \in U$ such that \begin{enumerate} \item $v_{P_i} (f_i)=\min v_{P_i}(U)$ for $i \in \{1,2\}$; \item for $i \neq j \in \{1,2\}$, $v_{P_i}(f_j) > \min v_{P_i}(U)$. \end{enumerate} \end{defi} Given a $K$-space $U \subset F$ and a place $P$, let $U_P:=\{ u \in U~\|~v_P(u) > \min v_P(U)\}$. Such a space has codimension~$1$ in $U$ and the notion of separation of two distinct places can be reformulated as follows. \begin{lemm}\label{lem:U_pU_Q} The space $U$ separates two distinct places $P, Q$ if and only if $U_P \neq U_Q$. \end{lemm} A first example of spaces having a good property of separation are Riemann--Roch spaces. The following statement is classical, we provide a proof for the sake of self-containedness. \begin{lemm}\label{lem:L(D)sep} Let $F$ be a function field of genus $g$ and let $D$ be a divisor of $F$ such that $\deg D > 2g$. Then the space $L(D)$ separates any two places $P$ and $Q$. \end{lemm} \begin{proof} Since $\deg (D) > 2g$, we have as a consequence of the Riemann--Roch Theorem \begin{align} \dim L(D-Q) &= \dim L(D)-1\\ \dim L(D-P) &= \dim L(D)-1\\ \dim L(D-P-Q) &= \dim L(D)-2. \end{align} Indeed, all the considered divisors have degree greater than $2g-2$. If we set $U= L(D)$ we get $U_P \neq U_Q$ and conclude using Lemma~\ref{lem:U_pU_Q}. \end{proof} The next lemma deals with separation in products of spaces. \begin{lemm}\label{lem:sep_products} Let $U, V \subseteq F$ be two $K$-spaces and $P, Q$ two places of $F$. Then, $UV$ separates $P$ and $Q$ if and only if $U$ or $V$ separates $P$ and $Q$. \end{lemm} \begin{proof} Let us suppose first that $U$ separates $P$ and $Q$. Let $a \in U$ be such that $v_P(a)=\min v_P(U)$ and $v_Q(a) > \min v_Q(U)$. Let $b \in V$ be such that $v_P(b)=\min v_P(V)$. We have $ab \in (UV)_Q \setminus (UV)_P$, hence $UV$ separates $P$ and $Q$. Conversely, suppose that neither $U$ nor $V$ separates $P$ and $Q$. Let $u \in U$ and $v\in V$ be such that \[ U= U_P \oplus Ku \qquad \textrm{and} \qquad V= V_P \oplus Kv. \] Then, \[ UV=(U_P V_P + uV_P + U_P v) + Kuv. \] Clearly $(U_P V_P + uV_P + U_P v) \subseteq {(UV)}_P$ and since $(U_P V_P + uV_P + U_P v)$ has codimension at most $1$ in $UV$ we conclude that \[ (U_P V_P + uV_P + U_P v)={(UV)}_P. \] By assumption, we have $U_P= U_Q$ and $V_P= V_Q$ and hence \[ {(UV)}_P= U_Q V_Q + u V_Q + U_Q v={(UV)}_Q \] so $UV$ does not separate $P$ and $Q$ either. This concludes the proof. \end{proof} \subsection{The lattice of subspaces and the \texorpdfstring{$P$}{P}-index of a space}\label{sec:Pindex} For the remainder of Section~\ref{sec:proof_main}, $P$ is a fixed arbitrary place of $F=K(S)$. We choose a filtered basis $(e_1, \ldots, e_n)$ where, having replaced $S$ by $e_1^{-1}S$ if necessary, we have set $e_1=1$. We consider the filtration $S_1 \subset S_2\subset \cdots \subset S_n= S$ associated to $P$, together with the lattice of subspaces $S_iS_j$ introduced in Section~\ref{sec:lattice} and illustrated in Figure~\ref{fig:subspaces}. Recall that the weight of an edge $V\rightarrow W$ is given by the codimension of $V$ in $W$. In the case $\dim S^2=2\dim S$ we have: \begin{lemm}\label{lem:weight2} All edges lying on a directed path from $S_1^2$ to $S_n^2= S^2$ have weight $1$ except for an edge which has weight $2$. \end{lemm} \begin{proof} The path has $2n-2$ edges, while $\dim S_1^2=1$ and $\dim S_n^2=\dim S^2=2n$, therefore the codimension of $S_1^2$ in $S_n^2$, which is also the sum of weights on the path, equals $2n-1$. Remembering that weights are at least $1$, the result follows. \end{proof} \begin{lemm}\label{lem:vertical} In the subspace lattice, every vertical edge from $S_iS_j$ to $S_{i+1}S_j$ has weight~$1$ for $i\geq2$. \end{lemm} \begin{proof} If not, then such an edge has weight $2$, which implies that every edge on the sublattice of directed paths from $S_1^2$ to $S_iS_j$ has weight $1$ by Lemma~\ref{lem:weight2}. But then, Lemma~\ref{lem:vosper} implies that $S_j$ has a basis in geometric progression, which in turn implies that $\dim S_j^2=2\dim S_j-1$, meaning that all edges on the sublattice of paths from $S_1^2$ to $S_j^2$ have weight $1$, a contradiction. \end{proof} \begin{figure}[h] \centering \begin{tikzpicture}[scale=0.8] \node[name=S22] at (4,4) {$S_2^2$}; \node[name=S23] at (6,4) {$S_2S_3$}; \node[name=S24] at (8,4) {$S_2S_4$}; \node[name=S25] at (10,4) {$S_2S_5$}; \node[name=S26] at (12,4) {$S_2S_6$}; \node[name=S33] at (6,6) {$S_3^2$}; \node[name=S34] at (8,6) {$S_3S_4$}; \node[name=S35] at (10,6) {$S_3S_5$}; \node[name=S36] at (12,6) {$S_3S_6$}; \node[name=S44] at (8,8) {$S_4^2$}; \node[name=S45] at (10,8) {$S_4S_5$}; \node[name=S46] at (12,8) {$S_4S_6$}; \node[name=S55] at (10,10) {$S_5^2$}; \node[name=S56] at (12,10) {$S_5S_6$}; \node[name=S66] at (12,12) {$S_6^2$}; \draw (S22) --node[above]{$1$} (S23)--node[above]{$1$}(S24)--node[above]{$2$}(S25)--node[above]{$1$}(S26)--node[left]{$1$}(S36)--node[left]{$1$}(S46)--node[left]{$1$}(S56)--node[left]{$1$}(S66); \draw (S33)--node[above]{$1$}(S34)--node[above]{$2$}(S35)--node[above]{$1$}(S36); \draw (S44)--node[above]{$2$}(S45)--node[above]{$1$}(S46); \draw (S25)--node[left]{$1$}(S35)--node[left]{$1$}(S45)--node[left]{$1$}(S55)--node[above]{$1$}(S56); \draw (S23)--node[left]{$1$}(S33); \draw (S24)--node[left]{$1$}(S34)--node[left]{$1$}(S44); \end{tikzpicture} \caption{$n=6$ and $j_0=4$ for the $P$-index}\label{fig:Pindex} \end{figure} Since any path from $S_1^2$ to $S_n^2$ has exactly one edge of weight $2$ (Lemma~\ref{lem:weight2}), Lemma~\ref{lem:vertical} implies that all horizontal edges $S_iS_j \rightarrow S_iS_{j+1}$ of weight $2$ occur for a common index $j$, that we call the \emph{$P$--index} of the space $S$. Summarising: \goodbreak \begin{lemm}\label{lem:Pindex} There is an index $j_0$, called the \emph{$P$-index} of $S$, such that $\dim(S_{i}S_{j_0+1})-\dim(S_iS_{j_0})=2$ for every $i=2,\dots, j_0$. \end{lemm} The above statement is illustrated on Figure~\ref{fig:Pindex}. We will see later that there are only two possible values for the $P$-index, namely $j_0=2$ and $j_0=n-1$. \subsection{Changing the valuation}\label{sec:changing} A single valuation $v_P$ may not be enough to describe sufficiently the spaces $S_i$, and it will be useful to involve alternative valuations. We now argue that some information obtained from a valuation $v_P$ may be ``transferred'' and hence provide some information with respect to another valuation $v_Q$. When all weights are equal to $1$ on the sublattice from $S_iS_j$ to $S_{i+1}S_{j+1}$, i.e. in the situation illustrated on Figure~\ref{fig:square}, \begin{figure}[h] \centering \begin{tikzpicture} \node[name=S00] at (0,0) {$S_iS_j$}; \node[name=S01] at (0,2) {$S_{i+1}S_{j}$}; \node[name=S10] at (2,0) {$S_{i}S_{j+1}$}; \node[name=S11] at (2,2) {$S_{i+1}S_{j+1}$}; \draw (S00) --node[above]{$1$} (S10) --node[left]{$1$} (S11) --node[above]{$1$} (S01)--node[left]{$1$} (S00); \end{tikzpicture} \caption{weights are equal to $1$}\label{fig:square} \end{figure} we have already observed (Lemma~\ref{lem:codim1}) that $S_{i}S_{j+1}=S_{i+1}S_{j}$. From this equality, we conclude that for any place $Q$, we have \[ v_Q(S_{i}S_{j+1})=v_Q(S_{i+1}S_{j}), \] and hence, thanks to Lemma~\ref{lem:sum_min_val}, \begin{equation}\label{eq:delta} -\min v_Q(S_{j+1})+\min v_Q(S_j)=-\min v_Q(S_{i+1})+\min v_Q(S_i). \end{equation} Applying~\eqref{eq:delta} when $i=2$ yields the following useful lemma. \begin{lemm}\label{lem:D_Si} For every $j\geq2$ that differs from the $P$-index $j_0$ of $S$, we have $D_{S_{j+1}}-D_{S_j}=D_{S_3}-D_{S_2}$. \end{lemm} We now turn to determining the genus of $F$. \subsection{The genus of the ambient field}\label{sec:genus} We prove first that $F=K(S)$ is in fact generated by the subspace $S_3$. \begin{lemm}\label{lem:dimSiSi+1} We have $F= K(S_3)$. \end{lemm} \begin{proof} For any $i\geq1$, we have \[ S_{i-1} S_i= S_{i-1}^2 + S_{i-1} e_i. \] Lemma~\ref{lem:weight2} asserts $\dim (S_iS_{i-1}) - \dim S_{i-1}^2\leq2$. Moreover, if $i\geq4$, $\dim S_{i-1}\geq3$ and hence the intersection $S_{i-1}^2 \cap S_{i-1}e_i$ is non-zero. Consequently, $e_i \in K(S_{i-1})$. Therefore $F=K(S_n)=K(S_{n-1})=\cdots=K(S_3)$. \end{proof} Remembering that $e_1=1$, and that we use the notation $x=e_2$ and $y=e_3$, Lemma~\ref{lem:dimSiSi+1} says that $F=K(x,y)$. Our next goal will be to determine the genus of $F$ and for this, we will identify an equation of lowest degree satisfied by $x$ and $y$: its degree will determine the genus of $F$. \begin{prop}\label{prop:genus} The field $F$ has genus less than or equal to $1$. \end{prop} \begin{proof} Depending on the value of the $P$--index being greater than $2$ or equal to $2$, we have either $\dim S_2 S_3=4$ or $\dim S_2 S_3=5$. Moreover, $S_2S_3$ is generated by $(1,x,x^2,xy,y)$. If $\dim S_2 S_3=4$ then we get a linear relation between $1,x,x^2,xy,y$ which immediately shows that $y\in K(x)$ and consequently that $F=K(x)$ and has genus $0$. We note that we have found an irreducible quadratic relation between $x$ and $y$, meaning that $F$ is the function field of a plane irreducible conic. If $\dim S_2 S_3=5$, then $1,x,x^2,xy,y$ are linearly independent over $K$; the subspace $S_3^2$, which is generated by $(1, x, y, x^2, x y, y^2)$ and has dimension~$6$, does also not produce an algebraic relation between $x$ and $y$. We need to go to $S_3S_4$, which is of dimension~$7$ and is generated by $(1, x, y, e_4, x^2, x y, x e_4, y^2, y e_4)$. It entails the existence of two independent relations \begin{align} e_4 L_1(x,y)&= Q_1(x, y) \label{eq:relation1}\\ e_4 L_2(x,y)&= Q_2(x, y) \label{eq:relation2} \end{align} where $L_1, L_2$ are linear polynomials and $Q_1, Q_2$ are quadratic polynomials. Moreover, the linear polynomials $L_1, L_2$ are nonzero since $\dim S_3^2=6$ and hence, there is no quadratic polynomial vanishing on $x, y$. By eliminating $e_4$ we get \begin{equation} L_1(x, y) Q_2 (x, y)= L_2(x, y) Q_1(x, y). \end{equation} The polynomial $L_1 Q_2 - L_2 Q_1$ is nonzero because the relations~\eqref{eq:relation1} and~\eqref{eq:relation2} are independent. This polynomial has degree at most $3$ and, since $\dim S_3^2=6$, there is no quadratic relation relating $e_1, x, y$, which asserts that the degree is exactly $3$. Therefore, the genus of $F$ is either $0$ (if the curve of equation $L_1 Q_2 - L_2 Q_1$ has a singularity) or $1$, as a consequence of Bézout's Theorem~\cite{Fulton}. \end{proof} \begin{enonce}[remark]{Summary} Writing $S_2=\langle 1,x\rangle$ and $S_3=\langle 1,x,y \rangle$, we may distinguish three cases. \begin{enumerate} \item\label{item:conic} $\dim S_2S_3=4$. In this situation, $F=K(x)$ and there is an irreducible quadratic polynomial $Q$ such that $Q(x,y)=0$. \item\label{item:sing_cubic} $\dim S_2S_3=5$ and there is a cubic relation \[ L_1(x,y) Q_2(x,y) - L_2(x,y) Q_1(x,y)=0 \] such that the corresponding projective plane curve is singular. \item\label{item:smooth_cubic} $\dim S_2S_3=5$ and there is a cubic relation \[ L_1(x,y) Q_2(x,y) - L_2(x,y) Q_1(x,y)=0 \] such that the corresponding projective plane curve is smooth. \end{enumerate} Cases~\eqref{item:conic} and~\eqref{item:sing_cubic} correspond to the genus $0$ case. Case~\eqref{item:smooth_cubic} correspond to the genus $1$ case. \end{enonce} In order to finish the proof of Theorem~\ref{thm:main}, it remains to compute the divisor $D_S$, as defined in~\ref{def:DU}. For this, we will first determine $D_{S_2}$ and $D_{S_3}$, and then, iteratively compute $D_{S_i}$ for $i\leq n$. \subsection{The \texorpdfstring{$P$}{P}-index is equal to \texorpdfstring{$2$}{2}}\label{sec:Pindex=2} In this subsection, we treat the case of the $P$-index being equal to $2$, which amounts to $\dim S_2S_3=5$. We have already proved that $x$ and $y$ satisfy an equation of degree~$3$; in the next lemma we show that moreover this equation has a specific form. \begin{lemm}\label{lem:deg2} The field $F= K(x,y)$ has degree~$2$ over $K(x)$ and the equation satisfied by $x$ and $y$ is of the form \begin{equation}\label{eq:G} y^2+B(x)y+C(x)=0 \end{equation} where $\deg B\leq2$ and $\deg C\leq3$. \end{lemm} \begin{proof} The field $F$ is generated by $x$ and $y$ and the proof of Proposition~\ref{prop:genus} has shown that there is a relation $G(x,y)=0$ of degree~$3$. Suppose that $G(x,y)$ contains a term in $y^3$ and write $G(x,y)$ as \begin{equation} G(x, y)= y^3 + A(x)y^2 + B(x)y + C(x)=0 \end{equation} where $\deg A\leq1$, $\deg B\leq2$ and $\deg C\leq3$. By construction, we have $v_P(y^3)<v_P(xy^2)<v_P(x^2y)<v_P(x^3)$ so $v_P(y^3)<v_P(A(x)y^2+B(x)y+C(x))$ which is in contradiction with $G(x,y)=0$. So the equation has the form $A(x)y^2 + B(x)y + C(x)=0$. With a similar reasoning we can see that moreover $A(x)$ must be a constant. It remains to rule out the case when $A(x)=0$, which would mean that $y\in K(x)$ and $F=K(x)$. Let us assume we are in this case and reach a contradiction. Because $v_P(x)<0$, $P=P_\infty$ is the place at infinity of $K(x)$ and $v_P(x)=-1$. In particular $D_{S_2}=L(P)$. Regarding $y$, we know that $v_P(y)<v_P(x)$ so the only possibility is $v_P(y)=-2$ because of the structure of $v_P(S)$ which contains $\{0,-1\}$: indeed, recall from Proposition~\ref{prop:A+A=2A} that it can have a missing element only after its first or before its last value and since $n\geq4$ the value before the smallest value of $v_P(S)$ cannot be $v_P(y)$. According to Lemma~\ref{lem:L(D)sep}, $S_2$ separates $P$ and any other place $Q\neq P$; according to Lemma~\ref{lem:sep_products}, so does $S_2S_4$. But $S_2S_4=S_3^2$ from Lemma~\ref{lem:codim1} which entails that also $S_3$ separates $P$ and $Q$. So $y$ cannot have a pole at $Q$, which leaves the only possibility $y=D(x)$ {for some polynomial $D$ with} $\deg(D)=2$. But this situation is not compatible with the condition that $\dim S_2S_3=5$. \end{proof} \begin{prop} When $\dim S_2S_3=5$, there is a place $Q$, possibly equal to $P$, such that, for all $i=2,\ldots,n$, \[ D_{S_i}=(i-1)P+Q. \] \end{prop} \begin{proof} We first focus on determining the divisors of $S_2$ and $S_3$. Because $v_P(x)<0$, the place $P$ is above the place at infinity of $K(x)$, that we will denote $P_\infty$. Since $K(x,y)$ has degree~$2$ over $K(x)$ by Lemma~\ref{lem:deg2}, we have from~\cite[Chapter~3]{Stichtenoth} that $P_{\infty}$ decomposes in $F=K(x,y)$ either as $2P$ (the ramified case) or as $P+Q$ where $Q\neq P$ (the split case). For any other place $R\notin\{P, Q\}$, the valuation $v_R(x)$ is non negative, and we have therefore $D_{S_2}=2P$ in the ramified case and $D_{S_2}=P+Q$ in the split case. We now focus on determining $D_{S_3}$. From~\eqref{eq:G} the valuation $v_R(y)$ can only be non negative for any place $R \notin\{P, Q\}$, so we are left with determining the valuation at $P$ and $Q$ of $y$. We now view $K(x,y)$ as an algebraic extension of $K(y)$ instead of an extension of $K(x)$. We remark that $P$, respectively $P$ and $Q$ in the split case, are also the places above the place at infinity of $K(y)$. So, since $[K(x,y):K(y)]\leq3$, we also know from~\cite[Chapter~3]{Stichtenoth} that $v_P(y)\geq-3$, and, in the split case, that $v_P(y)+v_Q(y)\geq-3$. Taking account of this, we see that in the ramified case $2P$ we necessarily have $v_P(x)=-2$ and $v_P(y)=-3$, and so, $D_{S_2}=2P$ and $D_{S_3}=3P$. In the split case $P+Q$, i.e. $v_P(x)=v_Q(x)=-1$, we can conclude so far that $v_P(y)=-2$ or $-3$. But the case $v_P(y)=-3$ would create a forbidden hole in $v_P(S)$ that contains $\{v_P(1)=0,v_P(x)=-1\}$ (because not in first or last position). So the only possibility is $v_P(y)=-2$. Now since $v_P(y)+v_Q(y)\geq-3$ we must have $v_Q(y)\geq-1$. So $D_{S_2}=P+Q$ and $D_{S_3}=2P+Q$. Finally, to obtain $D_{S_i}=(i-1)P+Q$ for $i\geq4$ we apply Lemma~\ref{lem:D_Si}. \end{proof} In the case when $\dim S_2S_3=5$, the above proposition concludes the proof of Theorem~\ref{thm:main}. Indeed, in the case when $F$ is of genus $1$, Riemann--Roch theorem tells us that $S$ must coincide with the space $L((n-1)P+Q)$. In the genus $0$ case, $S$ is of codimension~$1$ inside $L((n-1)P+Q)$. \subsection{The \texorpdfstring{$P$}{P}-index is greater than \texorpdfstring{$2$}{2}, or the plane conic case}\label{sec:Pindex>2} If $S_2 S_3$ has dimension~$4$, then recall that $F=K(x)$ and that Lemma~\ref{lem:vosper} implies that $S_i$ is generated by $(1,x,\dots,x^{i-1})$ for every $i$, $2\leq i\leq k$, where $k$ is the $P$-index of $S$; in other words, in this range, $S_i=L((i-1)P)$ where $P=P_{\infty}$ is the place at infinity of $K(x)$. \begin{lemm}\label{lem:kP+Q} We have $D_{S_{k+1}}= kP+Q$ for some place $Q$ possibly equal to $P$. \end{lemm} \begin{proof} Let $z$ be such that $S_{k+1}=S_k+Kz$ with $z$ of minimum $P$-valuation in $S_{k+1}$. We already know that $v_P(S_{k+1})$ is either an arithmetic progression or an arithmetic progression with a missing element, in other words either $v_P(z)=-k$ or $v_P(z)=-(k+1)$. Consider first the case $v_P(z)=-(k+1)$. Consider the product $S_3S_{k+1}$ which must be of dimension $(k+1)+3$. The space $S_3$ is generated by $1,x,x^2$ and we have $v_P(S_3S_{k+1})\supset\{v_P(x^k), v_P(z), v_P(xz),v_P(x^2z)\}$ so that \[ v_P(S_3S_{k+1})=\{0,-1,-2,\ldots,-(k-1),-k,-(k+1),-(k+2),-(k+3)\}. \] Since $x^k=xx^{k-1}$ and $x^{k+1}=x^2x^{k-1}$ are contained in $S_3S_{k+1}$, we have that $S_3S_{k+1}$ contains the subspace generated by the geometric progression $1,x,x^2,\ldots,x^{k+1}$, which is equal to the subspace of $S_3S_{k+1}$ of functions of $P$-valuation $\geq-(k+1)$, because this must be a space of dimension $k+2=\dim S_3S_{k+1}-2$. Since $v_P(z)=-(k+1)$, the function $z$ must belong to the aforementioned subspace, meaning that $z$ is a polynomial in $x$ of degree $k+1$, in other words $S_{k+1}\subset L((k+1)P)$. Consider now the remaining case $v_P(z)=-k$. The set $v_P(S_{k+1})$ is now the arithmetic progression $\{0,-1,\ldots, -k\}$ and we have $D_{S_{k+1}}= kP+D$ for some positive divisor $D$. Consider again the product $S_3S_{k+1}$ and let $U$ be the subspace of those elements of $S_3S_{k+1}$ that have a valuation { at $P$} greater than the minimum, namely $-k-2=v_P(z)+v_P(x^2)$. We have that $U$ has codimension~$1$ in $S_3S_{k+1}$ (Proposition~\ref{prop:filtered_basis}) i.e., $\dim U=k+3$. Note also that $U$ contains $1,x,\ldots,x^{k+1}$, so that there exists $u\in U$ of positive $P$-valuation, such that $u,1,x,\ldots,x^{k+1}$ is a basis of~$U$. Now since $v_P(z)=-k$, we have $z\in U$ and \begin{equation}\label{eq:pole} z= P_{k}(x)+\lambda u, \quad \lambda\in K \end{equation} with $P_{k}(x)$ a polynomial in $x$ of degree at most $k$. Note that we must have $\lambda~\neq~0$ otherwise, since $v_P(z)=-k$, $z$ is a polynomial of degree $k$ in $x$ contradicting that $\dim S_3S_{k+1}=k+4$. The equality~\eqref{eq:pole} implies therefore that $\alpha\in K$ is a pole of $z$ if and only if it is a pole of $u$. For such a pole $\alpha$, we have $(x-\alpha)z\in U$ since $v_P((x-\alpha)z)=-(k+1)$, hence \[ (x-\alpha)z= Q_{k+1}(x) + \mu u, \quad \mu\in K \] for $Q_{k+1}(x)$ a polynomial in $x$ of degree at most $k+1$. This implies that $\mu=0$ otherwise the left hand side and the right hand side would not have the same $\alpha$-valuation. This proves that $z$ has a pole of order $1$ at $\alpha$ and simultaneously that $z$ cannot have a pole at $\beta$ for $\beta\neq \alpha$. Therefore $z$ has a single pole of order $1$ besides $P_\infty$. \end{proof} We conclude with the following statement. \begin{prop} The $P$--index $k$ of $S$ equals $n-1$. \end{prop} \begin{proof} In the case when $Q=P$ in Lemma~\ref{lem:kP+Q}, since the set of $P$-valuations can only be an arithmetic progression with a hole in the last position, we must have $k=n-1$. We may therefore suppose that $Q\neq P$. Suppose towards a contradiction that $k\leq n-2$. The space $S_k$ is a Riemann--Roch space. Hence, from Lemma~\ref{lem:L(D)sep}, $S_k$ separates $P$ with any place $Q\neq P$ of $F$. Therefore, from Lemma~\ref{lem:sep_products} so does $S_kS_{k+2}$. On the other hand $S_{k+1}$ does not separate $P$ and $Q$ and hence, again applying Lemma~\ref{lem:sep_products}, $S_{k+1}^2$ does not separate them either. This is a contradiction since, from Lemma~\ref{lem:D_Si}, $S_{k}S_{k+2}$ should be equal to $S_{k+1}^2$. \end{proof} As a conclusion, in this situation, $S$ is a subspace of codimension~$1$ of a Riemann--Roch space of the form $L((n-1)P+Q)$ where $Q$ is a place, possibly equal to $P$. \section{Further description of spaces with genus \texorpdfstring{$0$}{0} and combinatorial genus \texorpdfstring{$1$}{1}}\label{sec:genus0} Theorem~\ref{thm:main} gives a complete characterisation of spaces $S$ of genus $1$ with combinatorial genus $\gamma=1$ by saying that they are exactly Riemann--Roch spaces. However, in the case when the genus of the field $F$ is $0$, it only says that $\gamma=1$ implies that $S$ is of codimension~$1$ inside a Riemann--Roch space: but not all subspaces of codimension~$1$ inside an $L(D)$ space have combinatorial genus $1$, so this raises the question of exactly which subspaces have $\gamma=1$. The following theorem gives a precise answer. \begin{theo}\label{thm:g=0} Let $S$ be of genus $g=0$ and of combinatorial genus $\gamma=1$. Then, up to multiplication by a constant, $S$ has a basis of one of the following two types: \begin{enumerate} \item $1,t,t^2,\ldots,t^{n-2},(t+\alpha)t^{n-1}$, \item $1,(t+\alpha)t,(t+\alpha)t^2,\ldots, (t+\alpha)t^{n-2}, (t+\alpha)t^{n-1}$ \end{enumerate} for some function $t$ and some constant $\alpha\in K$. \end{theo} Before proving Theorem~\ref{thm:g=0} we introduce an intermediate result. The proof of Theorem~\ref{thm:main} has shown that $S$ (after replacing it by a suitable multiplicative translate $s^{-1}S$) is such that $1\in S$ and $S\subset L((n-1)P+Q)$ where $P$ is the initial arbitrary place of $F=K(S)$ and $Q$ is some place that may or may not be equal to $P$. The following proposition states that there always is a choice of $P$ for which we have $Q=P$. \begin{prop}\label{prop:goodP} There exists a place $P$ and a function $s\in S$ such that $s^{-1}S\subset L(nP)$. \end{prop} \begin{proof} We start with an arbitrary choice of $P$ so that we may suppose $1\in S$ and $S\subset L((n-1)P+Q)$ with $Q\neq P$. Since the action of $\mathrm{PGL}(2,K)$ on places is $3$-transitive, we may choose a function $t$ for which $F=K(t)$ and such that $P$ and $Q$, viewed over $K(t)$, are the place at infinity and the place at zero respectively. In other words $L((n-1)P+Q)$ is the space of Laurent polynomials of the form \begin{equation}\label{eq:laurent} f(t)=\frac {a_{-1}} t + a_0 + a_1 t + a_2 t^2 + \cdots + a_{n-1} t^{n-1}. \end{equation} Since $S$ has codimension~$1$ inside $L((n-1)P+Q)$, there exist coefficients $\lambda_{-1}$, $\lambda_0,\ldots,\lambda_{n-1}$ in $K$, such that $S$ consists of the space of functions~\eqref{eq:laurent} satisfying \begin{equation}\label{eq:lambda} \lambda_{-1}a_{-1}+\lambda_0a_0+\cdots + \lambda_{n-1}a_{n-1}=0. \end{equation} If $\lambda_{-1}=0$ then $\frac{1}{t}\in S$ so that $1\in tS$ and $tS\subset L(nP)$ and we are finished. Suppose therefore $\lambda_{-1}\neq 0$. We claim there exists $a\in K$ such that the function $(t-a)^n\in tS$. Indeed, expanding the expression $(t-a)^n$ as \[ (t-a)^n=a_{-1}+a_0t+\cdots +a_{n-1}t^n \] we see that the quantity $\lambda_{-1}a_{-1}+\cdots + \lambda_{n-1}a_{n-1}$ is a polynomial in $a$ of degree exactly $n$, which has roots in $K$ since $K$ is algebraically closed. For such an $a$ we get that~\eqref{eq:lambda} is satisfied. Now since $tS$ consists only of polynomials in $t$, equivalently in $t-a$, we have that the space $\frac 1{(t-a)^n}tS$ contains $1$ and is included in $L(nP_a)$ where $P_a$ is the place at $a$. \end{proof} \begin{proof}[Proof of Theorem~\ref{thm:g=0}] Applying Proposition~\ref{prop:goodP}, we may suppose $1\in S\subset L(nP)$ and, without loss of generality, that $P$ is the place at infinity over $K(t)$: in other words, $S$ consists of a space of polynomials, of degree at most $n$, and including constants. The space $S$ must contain a polynomial of degree $n$, otherwise, because $\dim S=n$, $S$ would be equal to the space $L((n-1)P)$ and we would have $\dim S^2=2\dim S-1$, contradicting $\gamma=1$. Since $S$ contains constants we have that the set of degrees $d(S)$ of the elements of $S$ is included in the arithmetic progression $\{0,1,\ldots,n\}$, and since we may find at most $2n$ different degrees in $S^2$, Proposition~\ref{prop:A+A=2A} implies that \begin{enumerate} \item either \ $d(S)=\{0,1,2,\ldots n-3,n-2,n\}$, \item $\mathrlap{\text{or}}$\phantom{either \ }$d(S)=\{0,2,3,\ldots n-2,n-1,n\}$. \end{enumerate} In case 1, we have that $S$ contains as a subspace the space of all polynomials of degree at most $n-2$, and also a polynomial of degree $n$. This gives the existence of the basis of type $(i)$ mentioned by the theorem. It remains to deal with case 2 for which there exists a basis of $S$ of the form \[ 1,p_2,p_3,\ldots,p_n \] where $p_i$ is a polynomial of degree $i$ in the variable $t$. Consider the sequence of subspaces \[ S_1=K\subset S_2\subset\cdots \subset S_n=S \] where $S_i= S_{i-1}+Kp_i$ for $i\geq2$. We shall prove by induction on $k$ that for $k=3,4,\ldots,n$, the space $S_k$ has, possibly after changing the variable $t$, a basis of the form $1,(t+\alpha)t,\ldots, (t+\alpha)t^{k-1}$, yielding the desired basis of $S$ for $k=n$. Write the Euclidean division of $p_3$ by $p_2$, \[ p_3=(t+a)p_2 + bt+c \] where we have set the leading coefficients of $p_2$ and $p_3$ equal to $1$. By replacing if needed be $p_2$ by $p_2+b$ and $p_3$ by $p_3+ab-c$ we see that we may suppose that $p_2$ divides $p_3$. Without loss of generality (change the variable $t$ to $t-\beta$, $\beta\in K$), we may suppose that one of the roots of $p_2$ is $0$, so that $p_2=(t+\alpha)t$ for some constant $\alpha$, and we have that $S_3$ has a basis of the required form, possibly after adding to $p_3$ a scalar multiple of $p_2$. Suppose now that $S_k$ has a basis of the required form, $3\leq k\leq n-1$, and consider $S_{k+1}=S_k+Kp_{k+1}$. Without loss of generality suppose $p_{k+1}$ has no constant term, i.e. is divisible by $t$ (replacing $p_{k+1}$ by $p_{k+1}+c$, $c\in K$, does not change the space $S_{k+1}$). Let $T_k$ be the subspace of $S^2$ consisting of all polynomials in $t$ of degree at most $k+1$. Now the set of degrees of $S^2$ is $0,2,3,\ldots,2n$, which implies that $T_k$ cannot be equal to the whole space of polynomials of degree at most $k+1$ so that $\dim T_k\leq k+1$. Notice also that $T_k$ contains \begin{equation}\label{eq:Sk} 1,(t+\alpha)t,(t+\alpha)t^2,\ldots,(t+\alpha)t^{k-1} \end{equation} which are all in $S_k$ by the induction hypothesis, and $T_k$ contains also \[ (t+\alpha)^2t^{k-1}=(t+\alpha)t \times (t+\alpha)t^{k-2}. \] Since $\dim T_k\leq k+1$, a basis of $T_k$ is therefore given by~\eqref{eq:Sk} together with $(t+\alpha)^2t^{k-1}$. Now $p_{k+1}\in T_k$, so that it decomposes over the above basis, and since $p_{k+1}$ has no constant term, we have just proved that it is a multiple of $(t+\alpha)t$, which shows the existence of a basis of $S_{k+1}$ of the required form. \end{proof} Theorem~\ref{thm:g=0} shows in particular that there always exists a valuation $v$, for which the set of valuations $v(S)$ of a space of genus $0$ and combinatorial genus $1$ is an arithmetic progression with a missing element (after the first or last position). In contrast, the set of valuations for an arbitrary $v$ will typically be an arithmetic progression. We now make the remark that when $g=1$ and $\gamma=1$, there also always exists a valuation $v$ for which $v(S)$ is an arithmetic progression with a missing element. Denote by $\sim$ the linear equivalence of divisors, and recall that $G \sim H$ means that $L(G)= fL(H)$ for some function $f$. \begin{lemm}\label{lem:one_point} Let $E$ be an elliptic curve and $G$ be a divisor on $E$ of degree $d$. Then, there exists a point $R$ of $E$ such that $G \sim dR$. \end{lemm} \begin{proof} Let $G= r_1 P_1 + \cdots + r_s P_s$. Denote by $\oplus$ the group law on the elliptic curve. Let $P= r_1P_1 \oplus \cdots \oplus r_s P_s$. From~\cite[Proposition~III.3.4]{Silverman}, we get $ G - dO \sim P-O $ where $O$ is the zero element of the group of points of $E$. Over an algebraically closed field the group of points of $E$ is divisible (see~\cite[Theorem~4.10$\MK$(a)]{Silverman}), hence there exists $R \in E$ such that $P= dR$. Therefore: \[ G-dO \sim d(R-O)\quad \Longrightarrow \quad G \sim dR.\qedhere \] \end{proof} \begin{rema} According to the proof, the point $R$ may not be unique since it can be replaced by the point $R \oplus T$ where $T$ is a $d$--torsion point. Thus, if $d$ is prime to the characteristic of $K$ there are $d^2$ possibilities for $R$. \end{rema} Consequently, $S$ is of the form $f L(nR)$ for some place $R$ and some nonzero function $f$. It is well--known that the sequence of valuations of a space $L(nR)$ is $\{0, -2, -3, \ldots, -n\}$, which can be easily derived from the Riemann--Roch Theorem. Multiplication by $f$ only translates the sequence of valuations. \section{{Function fields over non-algebraically closed fields}}\label{sec:perfect} In this section we generalise Theorems~\ref{thm:freiman_field}, \ref{thm:genus0} and~\ref{thm:main} to non-algebraically closed, perfect fields $K$. Recall that a field $K$ is called \emph{perfect} if all algebraic extensions of $K$ are separable. \begin{theo}\label{thm:freiman_perfect} Let $K$ be a perfect field and let $F \supseteq K$ be an extension field of $K$ such that $K$ is algebraically closed in $F$. Let $S$ be a $K$-vector subspace of $F$ of finite dimension and of transcendence degree $d$. Then \[ \dim S^2\geq(d+1)\dim S -d(d+1)/2. \] \end{theo} \begin{proof} Let $K'$ be an algebraic closure of $K$ and $F'=K'(S)$ be defined inside the algebraic closure of $F$. It holds that any $K$-linearly independent elements of $F$ are also $K'$-linearly independent in $F'$. (\cite[Proposition~III.6.1]{Stichtenoth}\footnote{The context of the proposition is that of functions fields of one variable, but its proof applies verbatim to arbitrary field extensions.}). Therefore $\dim_KS=\dim_{K'}K'S$ and $\dim_KS^2=\dim_{K'}K'S^2$, and the theorem is proved by arguing that the transcendence degree of $S$ is the same over $K'$ as over $K$, and that therefore \[ \dim_{K'}K'S^2\geq(d+1)\dim_{K'}K'S -d(d+1)/2 \] by applying Theorem~\ref{thm:freiman_field}. \end{proof} We remark that the above proof has only used that any finite extension of $K$ is generated by a single element, so that Theorem~\ref{thm:freiman_perfect} actually holds in this somewhat more general case. \begin{theo}\label{thm:perfect} Let $K$ be a perfect field, algebraically closed in an extension field $F$. Let $S \subseteq F$, $1\in S$, be a space of finite dimension $n$ and combinatorial genus $\gamma$. \begin{enumerate} \item \label{9.1} If $n\geq3$ and $\gamma=0$, then $S$ has genus $0$ and $S=L(D)$ for $D$ a divisor of degree $n-1$. \item \label{9.2} If $n\geq4$ and $\gamma=1$ then $S$ has genus $0$ or $1$. Moreover, \begin{enumerate} \item if $S$ has genus $1$ then $S=L(D)$ for $D$ a divisor of degree $n$, \item if $S$ has genus $0$, then $S$ is a subspace of codimension~$1$ inside a space $L(D)$ for $D$ a divisor of degree $n$. \end{enumerate} \end{enumerate} \end{theo} Before proving Theorem~\ref{thm:perfect}, let us remind the reader of some basic facts concerning algebraic extensions of function fields that we need to call upon. We refer the reader to~\cite[Chapter~III]{Stichtenoth} for more background. Let $F'/K'$ be an algebraic extension of $F/K$, meaning that $F'\supset F$ is an algebraic extension and that $K'\supset K$. Recall that if $P$ is a place of $F$ and $P'$ a place of $F'$ such that $P=F\cap P'$, $P$ is said to \emph{lie under} $P'$ and $P'$ to \emph{lie over} $P$. One writes $P'\|P$ to mean that $P'$ lies over $P$. For any place $P$ of $F$, there always exists at least a place $P'$ over $P$ (\cite[Proposition~III.1.7]{Stichtenoth}), and for any such $P$ and $P'$ there exists (\cite[Proposition~III.1.4]{Stichtenoth}) an integer $e=e(P'\|P)\geq1$ such that $v_{P'}(x)=e\cdot v_P(x)$ for any $x\in F$. The positive integer $e(P'\|P)$ is called the \emph{ramification index} of $P'$ over $P$. The \emph{conorm}, with respect to $F'/F$, of a place $P$ of $F$ is defined as the divisor: \[ Con_{F'/F}(P)=\sum_{P'\|P}e(P'\|P)P'. \] The conorm extends to divisors $D=\sum_P\alpha_PP$ of $F$ through the formula \[ Con_{F'/F}(D)=\sum_P\alpha_P Con_{F'/F}(P). \] \begin{proof}[Proof of Theorem~\ref{thm:perfect}] Without loss of generality assume $F=K(S)$. Let $K'$ be the algebraic closure of $K$ and let $F'=K'(S)$ be defined inside the algebraic closure of $F$. We note that such an extension $F'/F$ is unramified (\cite[Theorem~III.6.3$\MK$(a)]{Stichtenoth}), meaning that $e(P'\|P)=1$ for any place $P$ in $F$ and any $P'$ above it. As remarked at the end of the proof of Theorem~\ref{thm:freiman_perfect}, $K$-linearly independent elements of $F$ are also $K'$-linearly independent in $F'$, therefore $\dim_KS=\dim_{K'}K'S$ and $\dim_KS^2=\dim_{K'}(K'S)^2$, so that $K'S$ has combinatorial genus $\gamma$. Next, Theorems~\ref{thm:genus0} (case $\gamma=0$) and~\ref{thm:main} (case $\gamma=1$) apply to $K'S$ in the extension $F'/K'$. Recall (Definition~\ref{def:DU}) that \[ D_S=\sum_{P,\, \text{place of}\, F}-\min v_P(S)P \] is such that $L(D_S)$ is the Riemann--Roch space in $F$ of smallest dimension that contains~$S$. By~\cite[Theorem~III.6.3$\MK$(b)]{Stichtenoth}, $F/K$ and $F'/K'$ have the same genus $g$. It remains therefore only to prove that \begin{equation}\label{eq:dimL(D_S)} \dim_KL(D_S)=\dim_{K'}L(D_{K'S}). \end{equation} Let $P$ be any place in the support of $D_S$, For any place $P'$ above $P$ we have $v_{P'}(s)= e(P'\|P)v_P(s)=v_P(s)$ (since $F'/F$ is unramified), therefore $P'$ appears in the support of $D_{K'S}$. Furthermore, $v_{P'}(s)=v_P(s)$ for every $s\in S$, so that \[ \min_{s\in S}v_P(s)=\min_{s\in S}v_{P'}(s)=\min_{x\in K'S}v_{P'}(x) \] since any $K'$-linear combination of elements of $S$ has a $P'$-valuation at least equal to $\min_{s\in S}v_{P'}(s)$. Therefore, the coefficient in $D_{K'S}$ of every place $P'$ above $P$ equals exactly the coefficient of $P$ in $D_S$. Since any place $P'$ of $F'$ has a unique place $P$ lying under it in $F$, we deduce that we have \[ Con_{F'/F}(D_S)= D_{K'S} \] from which~\eqref{eq:dimL(D_S)} follows by~\cite[Theorem~III.6.3$\MK$(d)]{Stichtenoth}. \end{proof} We conclude by remarking that when $K$ is not algebraically closed, statement~\eqref{9.1} of Theorem~\ref{thm:perfect} is the correct generalisation of Theorem~\ref{thm:genus0}. Indeed, there exist spaces $S$ of combinatorial genus $0$ in extensions $F/K$, where $K$ is algebraically closed in $F$, and such that $S$ does not have a basis in geometric progression. One such example, given in~\cite{bszVosper}, is obtained by considering the field $F=\Q(x,y)$, where $\Q$ denotes the rational field, and $y$ is algebraic over $\Q(x)$ such that $y^2+x^2+1=0$. We have that $\Q$ is algebraically closed in $F$, and in the extension $F/\Q$, the space $S$ generated by $1,x,y$ has combinatorial genus $0$ but can be seen not to have a basis in geometric progression. The space $S$ is however equal to a Riemann--Roch space $L(P)$, where $P$ is a place of degree~$2$. When one extends the base field $\Q$ to the complex field $\C$, we have that $\C S$ has the basis $t^{-1},1,t$, where $t=x+iy$,$t^{-1}=-x+iy$. Hence $\C S= L(P_0+P_{\infty})$, where $P_0$ and $P_\infty$ are the places at $0$ and at $\infty$ in $\C F=\C(t)$, and are the two places that lie above $P$ in $\C F$. Finally, we remark that the argument spelt out in the proof of Theorem~\ref{thm:perfect} shows that if Conjecture~\ref{conj} holds, then it also holds for perfect base fields. \bibliographystyle{amsplain-ac} \bibliography{ALCO_Bachoc_50} \end{document}
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https://www.zentralblatt-math.org/matheduc/en/?id=28507&type=tex	zentralblatt-math.org	CC-MAIN-2019-51	text/plain	application/x-tex	crawl-data/CC-MAIN-2019-51/segments/1575540507109.28/warc/CC-MAIN-20191208072107-20191208100107-00409.warc.gz	935,018,377	1,467	\input zb-basic \input zb-matheduc \iteman{ZMATH 2010e.00563} \itemau{Johnson, Heather L.} \itemti{Investigating the fundamental theorem of calculus.} \itemso{Math. Teach. (Reston) 103, No. 6, 430-435 (2010).} \itemab Summary: The fundamental theorem of calculus, in its simplified complexity, connects differential and integral calculus. The power of the theorem comes not merely from recognizing it as a mathematical fact but from using it as a systematic tool. As a high school calculus teacher, the author developed and taught lessons on this fundamental theorem that were reasonably successful with students. However, she was dissatisfied with the level of her students' understanding of the theorem and reflected that they would need to understand that an integral with a variable upper limit is a function. In this article, the author shares how she was inspired to create a lesson on the fundamental theorem of calculus that drew on students' current understanding of definite integrals and allowed them to develop the understanding that an integral with a variable upper limit is a function. A student's response to the lesson on the fundamental theorem of calculus expands the lesson to include representing accumulated area as a function. (Contains 3 tables and 5 figures.) (ERIC) \itemrv{~} \itemcc{I54 I55} \itemut{calculus; upper secondary; graphing calculators; integrals; integral calculus; concept formation} \itemli{http://www.nctm.org/eresources/article\_summary.asp?URI=MT2010-02-430a&from=B} \end
https://vision.in.tum.de/?key=klodt_etal_2013gcpr&astex=1	tum.de	CC-MAIN-2020-34	application/x-latex	application/x-latex	crawl-data/CC-MAIN-2020-34/segments/1596439738950.31/warc/CC-MAIN-20200812225607-20200813015607-00521.warc.gz	556,777,400	1,380	\documentclass[11pt,a4paper]{article} \usepackage{ifthen} \newcommand{\aufdeutsch}{false} \usepackage{german} \usepackage{enumerate} \usepackage{epsfig} \usepackage{fancyhdr} \oddsidemargin 0cm \topmargin -0 cm \topskip 0mm \headsep 1cm \headheight 0mm \textwidth 160 mm \parindent 0mm \parskip 1 ex \textheight 23cm \pagestyle{fancy} \lhead{\Large \bf Key: Klodt_etal_2013gcpr} \rhead{\Large \bf List of Publications} \renewcommand{\headrulewidth}{1pt} \begin{document} \tabcolsep 0.5cm \begin{center} \end{center} \tabcolsep 0.4cm \Large {\bf Conference and Workshop Papers}\\[-8mm] \tabcolsep 0.4cm \begin{center} \begin{enumerate}[{[C}1{]}] \normalsize \normalsize \item \parbox[t]{150mm}{ \rm M. Klodt, J. Sturm and D. Cremers,\\ {\bf Scale-Aware Object Tracking with Convex Shape Constraints on RGB-D Images,}\\ {\em{German Conference on Pattern Recognition (GCPR)}},\ Saarbr\"ucken, Germany,\ September\ 2013.} \end{enumerate} \end{center} \end{document}
http://gbg-nolte.de/seminarfach/texvorlage-facharbeit.tex	gbg-nolte.de	CC-MAIN-2020-10	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2020-10/segments/1581875143646.38/warc/CC-MAIN-20200218085715-20200218115715-00232.warc.gz	65,232,240	1,446	\documentclass[12pt,a4paper]{report} \usepackage{german,a4} \usepackage{epsf} \pagestyle{headings} \usepackage[cp1250]{inputenc} \usepackage{graphicx} \setlength{\headsep}{1.5cm} \setlength{\parskip}{1.5ex plus0.5ex minus0.5ex} \renewcommand{\baselinestretch}{1.25} \setlength{\topmargin}{0pt} \setlength{\headheight}{0pt} \setlength{\topskip}{0pt} \setlength{\textheight}{230mm} \setlength{\textwidth}{155mm} \setlength{\oddsidemargin}{10mm} \setlength{\footskip}{10mm} \setlength{\parindent}{0pt} \author{\textbf{Horst}} \title{\textbf{Mein Physikunterricht}} \date{\textbf{23.12.2015}} \begin{document} \frenchspacing \maketitle \tableofcontents \chapter{Einleitung} \label{Einleitung} Ich liebe Facharbeiten. \chapter{Grundlagen} \label{Grundlagen} \section{Der Stromkreis} \label{Stromkreis} Der ist einfach.\footnote{\cite{Gerthsen}, S.24} \subsection{Strom, Spannung und Widerstand} \label{IUR} Ich weiß sehr viel darüber. Wie in \ref{Stromkreis} genannt, ... \begin{appendix} \chapter{Skizze 1}\label{Skizze1} \end{appendix} \begin{thebibliography}{99} \bibitem[Gerthsen, Physik]{Gerthsen} Helmut Vogel.~~\textsl{Gerthsen Physik}. ~~Springer-Verlag, Berlin-Heidelberg-New York 1997, 19. Auflage \end{thebibliography} \newpage \thispagestyle{empty} Ich versichere, dass ich die Arbeit selbstständig angefertigt, keine anderen als die angegebenen Hilfsmittel benutzt und die Stellen, welche im Wortlaut oder im wesentlichen Inhalt anderen Werken entnommen wurden, mit genauer Angabe der Quelle kenntlich gemacht habe. Seelze, 24.12.2015 \vspace{2cm} ................................................................. \hspace{2cm} Pappnase \end{document}
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Counter-essentialism supposedly proves that the victim is eternally innocent, so victims’ actions and reactions are forever beyond reproach; all good Christians know that suffering is ennobling.” \forcelinebreak — Essentialism and the Problem of Identity Politics} \end{quote} \section{A Note on Call-Out Culture By Asam Ahmad} Call-out culture refers to the tendency among progressives, radicals, activists, and community organizers to publicly name instances or patterns of oppressive behaviour and language use by others. People can be called out for statements and actions that are sexist, racist, ableist, and the list goes on. Because call-outs tend to be public, they can enable a particularly armchair and academic brand of activism: one in which the act of calling out is seen as an end in itself. What makes call-out culture so toxic is not necessarily its frequency so much as the nature and performance of the call-out itself. Especially in online venues like Twitter and Facebook, calling someone out isn’t just a private interaction between two individuals: it’s a public performance where people can demonstrate their wit or how pure their politics are. Indeed, sometimes it can feel like the performance itself is more significant than the content of the call- out. This is why “calling in” has been proposed as an alternative to calling out: calling in means speaking privately with an individual who has done some wrong, in order to address the behaviour without making a spectacle of the address itself. In the context of call-out culture, it is easy to forget that the individual we are calling out is a human being, and that different human beings in different social locations will be receptive to different strategies for learning and growing. For instance, most call-outs I have witnessed immediately render anyone who has committed a perceived wrong as an outsider to the community. One action becomes a reason to pass judgment on someone’s entire being, as if there is no difference between a community member or friend and a random stranger walking down the street (who is of course also someone’s friend). Call-out culture can end up mirroring what the prison industrial complex teaches us about crime and punishment: to banish and dispose of individuals rather than to engage with them as people with complicated stories and histories. It isn’t an exaggeration to say that there is a mild totalitarian undercurrent not just in call-out culture but also in how progressive communities police and define the bounds of who’s in and who’s out. More often than not, this boundary is constructed through the use of appropriate language and terminology – a language and terminology that are forever shifting and almost impossible to keep up with. In such a context, it is impossible not to fail at least some of the time. And what happens when someone has mastered proficiency in languages of accountability and then learned to justify all of their actions by falling back on that language? How do we hold people to account who are experts at using anti-oppressive language to justify oppressive behaviour? We don’t have a word to describe this kind of perverse exercise of power, despite the fact that it occurs on an almost daily basis in progressive circles. Perhaps we could call it Anti-Oppressiveness. Humour often plays a role in call-out culture and by drawing attention to this I am not saying that wit has no place in undermining oppression; humour can be one of the most useful tools available to oppressed people. But when people are reduced to their identities of privilege (as white, cisgender, male, etc.) and mocked as such, it means we’re treating each other as if our individual social locations stand in for the total systems those parts of our identities represent. Individuals become synonymous with systems of oppression, and this can turn systemic analysis into moral judgment. Too often, when it comes to being called out, narrow definitions of a person’s identity count for everything. “But when people are reduced to their identities of privilege (as white, cisgender, male, etc.) and mocked as such, it means we’re treating each other as if our individual social locations stand in for the total systems those parts of our identities represent. Individuals become synonymous with systems of oppression, and this can turn systemic analysis into moral judgment.” No matter the wrong we are naming, there are ways to call people out that do not reduce individuals to agents of social advantage. There are ways of calling people out that are compassionate and creative, and that recognize the whole individual instead of viewing them simply as representations of the systems from which they benefit. Paying attention to these other contexts will mean refusing to unleash all of our very real trauma onto the psyches of those we imagine to only represent the systems that oppress us. Given the nature of online social networks, call-outs are not going away any time soon. But reminding ourselves of what a call-out is meant to accomplish will go a long way toward creating the kinds of substantial, material changes in people’s behaviour – and in community dynamics – that we envision and need. Asam Ahmad is a Toronto-based writer who still has a hard time trusting words. He coordinates the It Gets Fatter Project, a body positivity group started by fat queer people of colour. \section{Questioning Rape by Anonymous} \subsection{Coming To Terms} How do you begin to say, “I think we’ve been going about this all wrong?” How do you get out of a dead-end without going in reverse? It seems like in the last fifteen years, rape has gone from being an issue that was only talked about by feminists and downplayed in other radical communities, to one of the most commonly addressed forms of oppression. Part of this change might be owed to the hard work of feminist and queer activists, another part to the spread of anarchism, with its heavy emphasis on both class and gender politics, and another part to the antiglobalization movement, which brought together many previously separated single issues. Despite all the changes in fifteen years, its just as common to hear the sentiment that rape is still tacitly permitted in radical communities or that the issues of gender and patriarchy are minimized, even though in most activist or anarchist conferences and distros I know about, rape culture and patriarchy have been among the most talked about topics, and it wasn’t just talk. In the communities I have been a part of there have been cases of accused rapists or abusers being kicked out and survivors being supported, along with plenty of feminist activities, events, and actions. All the same, every year I meet more people who have stories of communities torn apart by accusations of rape or abuse, both by the shock and trauma of the original harm, and then by the way people have responded and positioned themselves. One option is to blame a passive majority that toe the line, giving lip service to the new politically correct doctrine, without living up to their ideals. In some cases I think that is exactly what happened. But even when there is full community support, it still often goes wrong. After years of thinking about this problem, learning about other people’s experiences, and witnessing accountability processes from the margins and from the center, I strongly believe that the model we have for understanding and responding to rape is deeply flawed. For a long time I have heard criticisms of this model, but on the one hand I never found a detailed explanation of these criticisms and on the other I was trained to assume that anyone criticizing the model was an apologist for rape, going on the defensive because their own patriarchal attitudes were being called out. After personally meeting a number of critical people who were themselves longtime feminists and survivors, I started to seriously question my assumptions. Since then, I have come to the conclusion that the way we understand and deal with rape is all wrong and it often causes more harm than good. But many of the features of the current model were sensible responses to the Left that didn’t give a damn about rape and patriarchy. Maybe the biggest fault of the model, and the activists who developed it, is that even though they rejected the more obvious patriarchal attitudes of the traditional Left, they unconsciously included a mentality of puritanism and law and order that patriarchal society trains us in. I don’t want to go back to a complicit silence on these issues. For that reason, I want to balance every criticism I make of the current model with suggestion for a better way to understand and deal with rape. \subsection{My Experience} When I was in a mutually abusive relationship, one in which both of us were doing things we should not have done, without being directly aware of it, that resulted in causing serious psychological harm to the other person, I learned some interesting things about the label of “survivor.” It represents a power that is at odds with the process of healing. If I was called out for abuse, I became a morally contemptible person. But if I were also a survivor, I suddenly deserved sympathy and support. None of this depended on the facts of the situation, on how we actually hurt each other. In fact, no one else knew of the details, and even the two of us could not agree on them. The only thing that mattered was to make an accusation. And as the activist model quickly taught us, it was not enough to say, “You hurt me.” We had to name a specific crime. “Abuse.” “Assault.” “Rape.” A name from a very specific list of names that enjoy a special power. Not unlike a criminal code. I did not want to create an excuse for how I hurt someone I loved. I wanted to understand how I was able to hurt that person without being aware of it at the time. But I had to turn my pain and anger with the other person into accusations according to a specific language, or I would become a pariah and undergo a much greater harm than the self-destruction of this one relationship. The fact that I come from an abusive family could also win me additional points. Everyone, even those who do not admit it, know that within this system having suffered abuse in your past grants you a sort of legitimacy, even an excuse for harming someone else. But I don’t want an excuse. I want to get better, and I want to live without perpetuating patriarchy. I sure as hell don’t want to talk about painful stories from my past with people who are not unconditionally sympathetic towards me, as the only way to win their sympathy and become a human in their eyes. As for the other person, I don’t know what was going on in their head, but I do know that they were able to deny ever harming me, violating my consent, violating my autonomy, and lying to me, by making the accusation of abuse. The label of “survivor” protected them from accountability. It also enabled them to make demands of me, all of which I met, even though some of those demands were harmful to me and other people. Because I had not chosen to make my accusation publicly, I had much less power to protect myself in this situation. And as for the so-called community, those who were good friends supported me. Some of them questioned me and made sure I was going through a process of self-criticism. Those who were not friends or who held grudges against me tried to exclude me, including one person who had previously been called out for abuse. In other words, the accusation of abuse was used as an opportunity for power plays within our so-called community. For all its claims about giving importance to feelings, the activist model is coded with total apathy. The only way to get the ball of community accountability rolling is to accuse someone of committing a specific crime. The role of our most trusted friends in questioning our responses, our impulses, and even our own experiences is invaluable. This form of questioning is in fact one of the most precious things that friendship offers. No one is infallible and we can only learn and grow by being questioned. A good friend is one who can question your behavior in a difficult time without ever withdrawing their support for you. The idea that “the survivor is always right” creates individualistic expectations for the healing process. A survivor as much as a perpetrator needs to be in charge of their own healing process, but those who support them cannot be muted and expected to help them fulfill their every wish. This is a obvious in the case of someone who has harmed someone else it should also be clear in the case of someone who has been harmed. We need each other to heal. But the others in a healing process cannot be muted bodies. They must be communicative and critical bodies. \subsection{Perp\Slash{}Survivor} The term “perpetrator” should set off alarm bells right away. The current model uses not only the vocabulary but also the grammar of the criminal justice system, which is a patriarchal institution through and through. This makes perfect sense: law and order is one of the most deeply rooted elements of the American psyche, and more immediately, many feminist activists have one foot in radical communities and another foot in NGOs (Non-Governmental Organizations). The lack of a critique of these NGOs only makes it more certain that they will train us in institutional modes of thinking. The current method is not only repulsive for its puritanism and its similarity to the Christian notions of the elect and the damned; it is also a contradiction of queer, feminist, and anarchist understandings of patriarchy. If everyone or most people are capable of causing harm, being abusive, or even of raping someone (according to the activist definition which can include not recognizing lack of consent, unlike the traditional definition which focuses on violent rape), then it makes no sense to morally stigmatize those people as though they were especially bad or dangerous. The point we are trying to make is not that the relatively few people who are called out for abuse or even for rape are especially evil, but that the entire culture supports such power dynamics, to the extent that these forms of harm are common. By taking a self righteous, “tough on crime” stance, everyone else can make themselves seem like the good guys. But there can’t be good guys without bad guys. This is the same patriarchal narrative of villain, victim, and savior, though in the latter role, instead of the boyfriend or police officer, we now have the community. The term “survivor,” on the other hand, continues to recreate the victimization of the standard term, “victim,” that it was designed to replace. One reason for calling someone a “survivor” is to focus on their process of overcoming the rape, even though it defines them perpetually in relation to it. The other reason is to spread awareness of how many thousands of people, predominately women, queer, and trans people, are injured or killed every year by patriarchal violence. This is an important point to make. However, given the way that rape has been redefined in activist circles, and the extension of the term “survivor” to people who suffer any form of abuse, the vast majority of things that constitute rape or abuse do not have the slightest possibility of ending someone’s life. This term blurs very different forms of violence. \subsection{Judging Harm} Hopefully, the reader is thinking that an action does not need to be potentially lethal to constitute a very real form of harm. I absolutely agree. But if that’s the case, why do we need to make it sound like it does in order to take it seriously? Why connect all forms of harm to life-threatening harm instead of communicating that all forms of harm are serious? As for these crimes, their definitions have changed considerably, but they still remain categories of criminality that must meet the requirements of a certain definition to justify a certain punishment. The activist model has been most radical by removing the figure of the judge and allowing the person harmed to judge for themselves. However, the judge role has not been abolished, simply transferred to the survivor, and secondarily to the people who manage the accountability process. The act of judging still takes place, because we are still dealing with punishment for a crime, even if it is never called that. The patriarchal definition of rape has been abandoned in favor of a new understanding that defines rape as sex without consent, with whole workshops and pamphlets dedicated to the question of consent. Consent must be affirmative rather than the absence of a negative, it is cancelled by intoxication, intimidation, or persistence, it should be verbal and explicit between people who don’t know each other as well, and it can be withdrawn at any time. The experience of a survivor can never be questioned, or to put it another way an accusation of rape is always true. A similar formulation that sums up this definition is, “assault is when I feel assaulted.” \subsection{Distinguishing Rape and Abuse} I don’t want to distinguish rape from other forms of harm without talking about how to address all instances of harm appropriately. One solution that does not require us to judge which form of harm is more important, but also does not pretend they are all the same, would have two parts. The first part is to finally acknowledge the importance of feelings, by taking action when someone says “I have been hurt,” and not waiting until someone makes an accusation of a specific crime, such as abuse or rape. Because we are responding to the fact of harm and not the violation of an unwritten law, we do not need to look for someone to blame. The important thing is that someone is hurting, and they need support. Only if they discover that they cannot get better unless they go through some form of mediation with the other person or unless they gain space and distance from them, does that other person need to be brought into it. The other person does not need to be stigmatized, and the power plays involved in the labels of perpetrator and survivor are avoided. The second part changes the emphasis from defining violations of consent to focusing on how to prevent them from happening again. Every act of harm can be looked at with the following question in mind: “What would have been necessary to prevent this from happening.” This question needs to be asked by the person who was harmed, by their social circle, and if possible by the person who caused the harm. The social circle is most likely to be able to answer this question when the harm relates to long-term relationships or shared social spaces. They might realize that if they had been more attentive or better prepared they would have seen the signs of an abusive relationship, expressed their concern, and offered help. Or they might realize that, in a concert hall they commonly use, there are a number of things they can all do to make it clear that groping and harassing is not acceptable. But in some situations they can only offer help after the fact. They cannot be in every bedroom or on every dark street to prevent forms of gender violence or intimate violence that happen there. In the case of the person who caused the harm, the biggest factor is whether they are emotionally present to ask themselves this question. If they can ask, “what could I have done to not have hurt this person,” they have taken the most important step to identifying their own patriarchal conditioning, and to healing from unresolved past trauma if that’s an issue. If they are emotionally present to the harm they have caused, they deserve support. Those closest to the person they hurt may rightfully be angry and not want anything to do with them, but there should be other people wiling to play this role. The person they have hurt deserves distance, if they want it, but except in extreme cases it does no good to stigmatize or expel them in a permanent way. If they can ask themselves this question honestly, and especially if their peers can question them in this process, they may discover that they have done nothing wrong, or that they could not have known their actions would have been harmful. Sometimes, relationships simply hurt, and it is not necessary to find someone to blame, though this is often the tendency, justified or not. The fact that some relationships are extremely hurtful but also totally innocent is another reason why it is dangerous to lump all forms of harm together, presupposing them all to be the result of an act of abuse for which someone is responsible. If their friends are both critical and sympathetic, they are most likely to be able to recognize when they did something wrong, and together with their friends, they are the ones in the best position to know how to change their behavior so they don’t cause similar harm in the future. If their friends have good contact with the person who was hurt (or that person’s friends), they are more likely to take the situation seriously and not let the person who caused the harm off the hook with a band-aid solution. This new definition is a response to the patriarchal definition, which excuses the most common forms of rape (rape by acquaintances, rape of someone unable to give consent, rape in which someone does not clearly say “no”). It is a response to a patriarchal culture that was always making excuses for rape or blaming the victim. The old definition and the old culture are abhorrent. But the new definition and the practice around it do not work. We need to change these without going back to the patriarchal norm. In fact, we haven’t fully left the patriarchal norm behind us. Saying “assault is when I feel assaulted” is only a new way to determine when the crime of assault has been committed, keeping the focus on the transgression of the assaulter, then we still have the mentality of the criminal justice system, but without the concept of justice or balance. At the other extreme, there are people who act inexcusably and are totally unable to admit it. Simply put, if someone hurts another person and they are not emotionally present in the aftermath, simply put, it is impossible to take their feelings into consideration. You can’t save someone who doesn’t want help. In such a case, the person hurt and their social circle need to do what is best for themselves, both to heal and to protect themselves from a person they have no guarantee will treat them well in the future. Maybe they will decide to shame that person, frighten them, beat them up, or kick them out of town. Although kicking them out of town brings the greatest peace of mind, it should be thought of as a last resort, because it passes off the problem on the next community where the expelled person goes. Because it is a relatively easy measure it is also easy to use disproportionately. Rather than finding a solution that avoids future conflict, it is better to seek a conflictive solution. This also forces people to face the consequences of their own righteous anger which can be a learning process. Finally, the most important question comes from the person who was hurt. The victimistic mentality of our culture, along with the expectation that everyone is out to blame the victim, make it politically incorrect to insist the person who has been hurt ask themselves, “what would have made it possible to avoid this?” but \forcelinebreak such an attitude is necessary to overcoming the victim mentality and feeling empowered again. It is helpful for everyone who lives in a patriarchal world where we will probably encounter more people who try to harm us. Its not about blaming ourselves for what happened, but about getting stronger and more able to defend ourselves in the future. I know that some zealous defenders of the present model will make the accusation that I am blaming the victim, so I want to say this again: it’s about preventing future rapes and abuse, not blaming ourselves if we have been raped or abused. The current model basically suggests that people play the role of victims and wait for society or the community to save them. Many of us think this is bullshit. Talking with friends of mine who have been raped and looking back at my own history of being abused, I know that we grew stronger in certain ways, and this is because we took responsibility for our own health and safety. In some cases, the person who was hurt will find that if they had recognized certain patterns of dependence or jealousy, if they had had more self-esteem, or they had asserted themselves, they could have avoided being harmed. Unless they insist on retaining a puritan morality this is not to say that it was their fault. It is a simple recognizing of how they need to grow in order to be safer and stronger in a dangerous world. This method focuses not on blame, but on making things better. \subsection{The Most Extreme Form of Harm} Sometimes, however, the person will come to the honest conclusion, “there was nothing I could have done (except staying home \Slash{} having a gun \Slash{} having a bodyguard).” This answer marks the most extreme form of harm. Someone has suffered a form of violence that they could not have avoided because of the lengths the aggressor went to in order to override their will. Even shouting “No!” would not have been enough. It is a form of harm that cannot be prevented at an individual level and therefore it will continue to be reproduced until there is a profound social revolution, if that ever happens. If we have to define rape, it seems more consistent with a radical analysis of patriarchy to define rape as sex against someone’s will. Because will is what we want taken into the realm of action, this idea of rape does not make the potential victim dependent on the good behavior of the potential rapist. It is our own responsibility to depress our will. Focusing on expressing and enacting our will directly strengthens ourselves as individuals and our struggles against rape and all other forms of domination. If rape is all sex without affirmative consent, then it is the potential rapist, and not the potential victim, who retains the power over the sexual encounter. They have the responsibility to make sure the other person gives consent. If it is the sole responsibility of one person to receive consent from another person, then we are saying that person is more powerful then the other, without proposing how to change those power dynamics. Additionally, if a rape can happen accidentally, simply because this responsible person, the one expected to play the part of the perfect gentleman, is inattentive or insensitive, or drunk, or oblivious to things like body language that can negate verbal consent, or from another culture with a different body language, then we’re not necessarily dealing with a generalized relationship of social power, because not everyone who rapes under this definition believes they have a right to the other person’s body. Rape needs to be understood as a very specific form of harm. We can’t encourage the naive ideal of a harm-free world. People will always hurt each other, and it is impossible to learn how not to hurt others without also making mistakes. As far as harm goes, we need to be more understanding than judgemental. But we can and must encourage the ideal of a world without rape, because rape is the result of a patriarchal society teaching its members that men and other more powerful people have a right to the bodies of women and other less powerful people. Without this social idea, there is no rape. What’s more, rape culture, understood in this way, lies at least partially at the heart of slavery, property, and work, at the roots of the State, capitalism, and authority. This is a dividing line between one kind of violence and all the other forms of abuse. It’s not to say that the other forms of harm are less serious or less important. It is a recognition that the other forms of harm can be dealt with using less extreme measures. A person or group of people who would leave someone no escape can only be dealt with through exclusion and violence. Then it becomes a matter of pure self-defense. In all the other cases, there is a possibility for mutual growth and healing. \subsection{Questioning Rape} Sympathetic or supportive questioning can play a key role in responses to abuse. If we accept rape as a more extreme form of violence that the person could not have reasonably avoided, they need the unquestioning support and love of their friends. We need to educate ourselves how systematically patriarchy has silenced thosewho talk about being raped through suspicion, disbelief, or counter accusations. But we also need to be aware that there have been a small number of cases in which accusations of rape have not been true. No liberating practice should ever require us to surrender our own critical judgement and demand that we follow a course of action we are not allowed to question. Being falsely accused of rape or being accused in a non-transparent way is a heavily traumatizing experience. It is a far less common occurrence than valid accusations of rape that the accused person denies, but we should never have to opt for one kind of harm in order to avoid another. If it is true that rapists exist in our circles, it is also true that pathological liars exist in our circles. There has been at least one city where such a person made a rape accusation to discredit another activist. People who care about fighting patriarchy will not suspect someone of being a pathological liar every time they are unsure about a rape accusation. If you are close to someone for long enough, you will inevitably find out if they are a fundamentally dishonest person (or if they are like the rest of us, sometimes truthful, sometimes less so). Therefore, someone’s close acquaintances, if they care about the struggle against rape culture, will never accuse them of lying if they say they’ve been raped. But often accusations spread by rumors and reach people who do not personally know the accuser and the accused. The culture of anonymous communication through rumors and the internet often create a harmful situation in which it is impossible to talk about accountability or about the truth of what happened in a distant situation. Anarchists and other activists also have many enemies who have proven themselves capable of atrocities in the course of repression. A fake rape accusation is nothing to them. A police infiltrator in Canada used the story of being a survivor of an abusive relationship to avoid questions about her past and win the trust of anarchists she would later set up for prison sentences.\footnote{http:\Slash{}\Slash{}anarchistnews.org\Slash{}node\Slash{}19486,http:\Slash{}\Slash{}www.crimethinc.com\Slash{}blog\Slash{}2011\Slash{}11\Slash{}24\Slash{}g20-conspiracy-case-the-inside-story\Slash{}} Elsewhere, a member of an authoritarian socialist group made an accusation against several rival anarchists, one of whom, it turned out, was not even in town on the night in question. Some false accusations of rape are totally innocent. Sometimes a person begins to relive a previous traumatic experience while in a physically intimate space with another person, and it is not always easy or possible to distinguish between the one experience and the other. A person can begin to relive a rape while they are having consensual sex. It is definitely not the one person’s fault for having a normal reaction to trauma, but it is also not necessarily the other person’s fault that the trauma was triggered. A mutual and dynamic definition of consent as active communication instead of passive negation would help reduce triggers being mislabeled as rape. If potential triggers are discussed before the sexual exchange and the responsibility for communicating needs and desires around disassociation is in the hands of the person who disassociated then consent is part of an active sexual practice instead of just being an imperfect safety net. If someone checks out during sex, and they know they check out during sex, it is their responsibility to explain what that looks like and what they would like the other person to do when it happens. We live in a society where many people are assaulted, raped or have traumatic experiences at some point in their lives. Triggers are different for everyone. The expectation that ones partner should always be attuned enough to know when one is disassociating, within a societal context that does not teach us about the effects of rape, much less their intimate emotive and psychological consequences — is unrealistic. Consent is empowering as an active tool, it should not be approached as a static obligation. Still, the fact remains that not all rape accusation can be categorized as miscommunication, some are in fact malicious. There is a difficult contradiction between the fact that patriarchy covers up rape, and the fact that there will be some false, unjustified, or even malicious rape accusations in activist communities. The best option is not to go with statistical probability and treat every accusation as valid, because a false accusation can tear apart an entire community make people apathetic or skeptical towards future accountability processes. It is far better to educate ourselves, to be aware of the prevalence of rape, to recognize common patterns of abusive behavior, to learn how to respond in a sensitive and supportive way, and also to recognize that there are some exceptions to the rules, and many more situations that are complex and defy definition. The typical proposal for responding to rape, the community accountability process, is based on a transparent lie. There are no activist communities, only the desire for communities, or the convenient fiction of communities. A community is a material web that binds people together, for better and for worse, in interdependence. If its members move away every couple years because the next pace seems cooler, it is not a community. If it is easier to kick someone out than to go through a difficult series of conversations with them, it is not a community. Among the societies that had real communities, exile was the most extreme sanction possible, tantamount to killing them. On many levels, losing the community and all the relationships it involved was the same as dying. Let’s not kid ourselves: we don’t have communities. In many accountability processes, the so-called community has done as much harm, or acted as selfishly, as the perpetrator. Giving such a fictitious, self- interested group the power and authority of judge, jury, and executioner is a recipe for disaster. What we have are groups of friends and circles of acquaintances. We should not expect to be able to deal with rape or abuse in a way that does not generate conflict between or among these different groups and circles. There will probably be no consensus, but we should not think of conflict as a bad thing. Every rape is different, every person is different, and every situation will require a different solution. By trying to come up with a constant mechanism for dealing with rape, we are thinking like the criminal justice system. It is better to admit that we have no catch-all answer to such a difficult problem. We only have our own desire to make things better, aided by the knowledge we share. The point is not to build up a structure that becomes perfect and unquestionable, but to build up experience that allows us to remain flexible but effective. \subsection{Conclusion} The many failings in the current model have burned out one generation after another in just a few short years, setting the stage for the next generation of zealous activists to take their ideals to the extreme, denouncing anyone who questions them as apologists, and unaware how many times this same dynamic has played out before because the very model functions to expel the unorthodox, making it impossible to learn from mistakes. One such mistake has been the reproduction of a concept similar to the penal sentence of the criminal justice system. If the people in charge of the accountability process decide that someone must be expelled, or forced to go to counseling, or whatever else, everyone in the so-called community is forced to recognize that decision. Those who are not are accused of supporting rape culture. A judge has a police force to back up his decision. The accountability process has to use accusations and emotional blackmail. But the entire premise that everyone has to agree on the resolution is flawed. The two or more people directly involved in the problem may likely have different needs, even if they are both sincerely focused on their own healing. The friends of the person who has been hurt might be disgusted, and they might decide to beat the other person up. Other people in the broader social circle might feel a critical sympathy with the person who hurt someone else, and decide to support them. Both of these impulses are correct. Getting beaten up as a result of your actions, and receiving support, simply demonstrate the complex reactions we generate. This is the real world, and facing its complexity can help us heal. The impulse of the activist model is to expel the perpetrator, or to force them to go through a specific process. Either of these paths rest on the assumption that the community mechanism holds absolute right, and they both require that everyone complies with the decision and recognize its legitimacy. This is authoritarianism. This is the criminal justice system, recreated. This is patriarchy, still alive in our hearts. What we need is a new set of compass points, and no new models. We need to identify and overcome the mentalities of puritanism and law and order. We need to recognize the complexity of individuals and of interpersonal relationships. To avoid a formulaic morality, we need to avoid the formula of labels and mass categories. Rather than speaking of rapists, perpetrators, and survivors, we need to talk abut specific acts and specific limitations, recognizing that everyone changes, and that most people are capable of hurting and being hurt, and also of growing, healing, and learning how to not hurt people, or not be victimized, in the future. We also need to make the critical distinction between the forms of harm that can be avoided as we get smarter and stronger, and the kinds that require a collective self-defense. The suggestions I have made offer no easy answers, and no perfect categories. They demand flexibility, compassion, intelligence, bravery, and patience. How could we expect to confront patriarchy with anything less? \subsection{Epilogue} Half a dozen lessons I might never learn, not until them troubles come around\dots{}\footnote{Gillian Welch. “Only One and Only.” Revival, Alamo Sounds, 1996.} First off, this zine was meant to be descriptive not prescriptive, although I own the suggestions I’ve laid out and continue to hold to them. The hope was that the zine would encourage contextual, thoughtful and critical responses to rape and abuse. It should be possible within anarchist circles to have critical reflection about the use of essentialist categories without being accused of being a rape apologist. We are all holding on so tight to these labels and I think it is apparent that they are not working for us. The zine was meant to parse out what wasn’t working about our ever-expanding definition of rape and assault. It was an attempt to call the innate judicial reasoning behind accountability processes into question. It was meant as a critique of innocence and guilt, not an attack on people who identify as survivors. \textbf{“When we rely on appeals to innocence, we foreclose a form of resistance that is outside the limits of law, and instead ally ourselves with the State \dots{}When people identify with their victimization, we need to critically consider whether it is being used as a tactical maneuver to construct themselves as innocent and exert power without being questioned. That does not mean delegitimizing the claims made by survivors— but rather, rejecting the framework of innocence, examining each situation closely, and being conscientious of the multiple power struggles at play in different conflicts.”\footnote{Wang, Jackie. “Against Innocence: Race, Gender, and the Politics of Safety.” LIES: A Journal of Materialist Feminism Volume 1, 2012, pg 162.}} Giving voice to the “multiple power struggles” at play is an uncomfortable process. Many people have offered feedback that they did not like the zine because it perpetuates the myth that abuse is a dynamic between two people and that feels like blaming the victim. It was never my intention to downplay the pain of abuse. I do, however, think that abuse is participatory and that it is useful to understand it as such in order to heal. My criticism of an essentialist understanding of victim or survivor is twofold: first, not everyone uses those categories with honesty or transparency, and second, even when they do, I am not sure that these identities really help you heal. Personally, I don’t find it helpful to think of myself as a victim or survivor. I realize that the identity of survivor was meant to address the focus on passivity that occurs with the term victim, but in practice I think the two terms are not always well delineated and the same associations and assumptions often accrue. These identities make me the subject, the passive receiver, of another’s violence or abuse. In that reading of the situation, the power to end the cycle lies firmly with the active party, the “abuser.” That is a balance of power that I am uncomfortable with. In order to not feel completely helpless it has been necessary for me to honestly reflect on the parts that I played in unhealthy dynamics and violent situations because those are the things that I have the ability to change. I started writing about accountability because I was grappling with why I felt so angry that I was supposed to identify myself as the right kind of victim in order to get support. It made me angry because I did not want to continue to be defined in relation to someone who had taken so much from me. I could not continue that relationship; in order to put myself back together I needed to cut all ties. I also could not wait for the person who harmed me to redress their ways before I began to heal. It wasn’t realistic. I would have waited forever. Think of what your body does when you cut yourself. Along with blood clotting and the immune response, your body builds a network of collagen to isolate the wound site. This allows white blood cells to clean up the area without spreading the infection. Continuing to define yourself by the pain that others have caused you creates dehiscence and keeps the wound open. Accountability is so tied up in adjudication and external affirmations, or condemnations, that it can be very hard to modulate and process shifting feelings as you go through different stages of healing. Being someone’s rape victim or survivor of abuse is not emotionally healthy. Every time a scar starts to form some part of the community process requires you to reference back to the initial pain as if it were new, and the scab gets ripped off. This can lead to chronic inflammation that can go systemic and eventually poison other relationships in your life. Community processes that offer support based on victimization lend themselves to focusing and fixating on painful experiences. I have been raped. I was in an abusive relationship, and when I left I was stalked. Those experiences disrupted my life for a long time. I did not deserve to be treated that way, but I was not a passive participant. Being honest about participatory abuse is not the same as self-recrimination, and analyzing unhealthy dynamics is not a form of self- blame—it’s a form of self-reflection. I have a hard time understanding why people are so offended at the idea that abuse is participatory because it was the epiphany that I was also responsible for my terrible caustic relationship that allowed me to leave. I stayed in a damaging relationship for so much longer than I should have, even after I realized it was abusive, under the absurd delusion that we were going to “end cycles of violence” together. We weren’t ending any fucking cycles, we were continuing them. Until I rediscovered my agency I was totally paralyzed. How could I ever feel safe if nothing I had done contributed to the abuse? What could I change about the way I loved? Did I just need to implicitly know if people had that tendency in them? How do you pick “undamaged” lovers? How could I ever fall in love, and more importantly break up with anyone again, without being afraid? Different choices along the way could have kept things from getting so fucking crazy at the end, and it is both naïve and dangerous to pretend otherwise. Acknowledging that doesn’t mean I deserved to be mistreated or stalked; but it does mean that because I understand the bad choices I made, I can make better ones in the future. I realize the rejection of victim or survivor identity is harder to stomach when it comes to violent sexual assault, but even with rape one can go through a process of critical reflection. This, of course, does not absolve the assaulter from responsibility. No one deserves to be sexually assaulted or is ever to blame for being raped. We must differentiate blame from self-reflection. In order to move on with my life and regain the ability to work and travel alone it has helped me to focus on the things I have concrete control over. It has been useful to takestock of what kind of situations I put myself in, who I trust, what kind of contingency plans I make and what weapons I am actually comfortable using. Will being proactive about these kinds of considerations keep me from all future harm? Probably not—it’s a fucked up world out there. Will these considerations give me a more grounded sense of control and remind me of my own power to deal with and affect the course of potential violence? Yes, I think so. This of course brings us to the issue of retaliatory violence and the zine being criticized for “glorifying violence.” I think Stokely Carmichael got the heart of why we must be wary of moral narratives about violence: \textbf{“The way the oppressor tries to stop the oppressed from using violence as a means to attain liberation is to raise ethical or moral questions about violence. I want to state emphatically here that violence in any society is neither moral nor is it ethical. It neither right, nor is it wrong. It is just simply a question of who has the power to legalize violence.”\footnote{Carmichael, Stokely. Stokely Speaks: Black Power Back to Pan-Africanism. New York: Random House, 1972.}} I don’t have an absolute moral or ethical justifier for retaliatory violence, because one should never work in tactical absolutes. No solution or approach will be appropriate all the time. All I can do is clarify in what context retaliatory violence makes sense to me. I think people who are violently physically assaulted should be able to beat their rapist. However it is essential to understand karmic\Slash{}proportional retribution. I don’t think retaliatory violence is appropriate for situations that were not physically violent. Responding to physical violence with physical violence is understandable but responding to gray area miscommunications of consent with physical violence is manipulative and unnecessary. I also do not think it is appropriate to ask others to enact violence if you cannot bring yourself to participate. If you can’t do it yourself (with help), then you need to pick a different kind of revenge. The point is catharsis, isn’t it? A beating will send a direct message, but nothing can really communicate the experience of rape— only the anger and despair that come afterward. Violence should be approached with humility and as a final resort. It is worth noting that it may not make you feel better, it may make you feel worse—it’s hard to know beforehand. Revenge is intimate, and not always healthy. Protracted campaigns of shame and intimidation continue to tie you emotionally and psychologically to the person who hurt you. At some point the best revenge is separating yourself in the ways you can and trying to live a happy life. This doesn’t mean you have to forgive to heal. I hold to my bitterness because it keeps me safe, but because I do not expect others to join me in that hatred it has been easier, with the passage of time, to let some of the pain recede. To those who feel I gave up on transformative justice too soon, perhaps I did. I think if I lived in a different kind of community I would have more faith in transformative justice. I have heard that these models have worked in other kinds of communities. Within the anarchist scenes of North America however, I just don’t see the cohesion, gentleness or longevity required for transformative processes to work. People are too transient. I am not an optimist at a structural level. It’s not something I am particularly proud of so perhaps I shouldn’t be suggesting others accept my dismal assessment of anarchist “community.” Really the discourse of transformative justice is hard for me to take at face value because the person I was in an abusive relationship with was very adept at using that kind of language in a manipulative manner, while the person who raped me had absolutely no point of reference for anything so radical. “Breaking cycles of abuse” is an enticing and lofty goal but sometimes I fear that all it means is that we put tons of time and energy into pieces of shit who will never address their socialization. At what point is it just not your fucking problem anymore? This of course gets to the heart of most people’s problem with the zine. It was criticized for not offering a productive solution. I admit, I don’t have one; there is no one solution. A tendency towards myopic essentialism got us into this mess, a fancy rewriting of the survivor\Slash{}perpetrator dualism with slightly more nuance sure as hell isn’t going to get us out. We should be discussing what consent really means. We have done a good job of defining healthy sex as an active yes—and not just the absence of no, but is that really a standard we practice and how do we hold people to it? If consent is a continual process what expectations do we have about how no gets communicated? Intimacy is complicated and we are all damaged in our own way. Who is responsible for identifying when yes becomes no? I would like to propose that we are responsible not only for obtaining a yes from our lovers before proceeding and keeping those lines of communication open but, more importantly, we are responsible for vocalizing our own yes or no. We need to redefine healthy consent as communicating our sexual needs in a proactive manner. If that doesn’t happen we should be able to say, “you didn’t notice I was dissociating, can we talk about PTSD and trauma?” That conversation seems more productive to me than, “you raped me because you didn’t notice I checked out, even though I didn’t say no.” It needs to be okay to make mistakes and we need a language for hurt that doesn’t default to the worst kind of hurt ever. Hyperbolic language leads to a ranking of pain. Does everything need to be called assault or rape before we help our friends work through it? We need an intermediary language, something between “that was perfectly communicated every step of the way,” and “you assaulted me.” At a spiritual level it is important to ask why couldn’t I vocalize my needs? What kinds of conversations, or partners, do I need in order to do that? We should not expect our lovers to read our minds. We need to make contingency plans. Healthy sex should involve telling your lovers what you want them to do when you check out. We are all responsible for our own happiness, pleasure and safety —these things are too important to outsource. As for getting through the dark days, the only concrete advice I can give about sorting through the pain of assault or abuse is don’t turn to a larger community for support—turn to your friends, your chosen family and a therapist (if you believe in them). Don’t expect that people who were not already close to you will understand the situation or be able to respond or empathize in a way that feels good to you. They probably won’t. Get as far away from the person who hurt you as humanly possible and don’t take on their fucking process. Settle into the isolation and pain, because it’s going to be with you for a long time. Understand your part in the experience not because you deserved it, or because you were to blame for it, but understand your part so you can play a different, healthier, role in the future. Ultimately, I think I have come back to a state of relative homeostasis again because I took the time to consider what parts of the abuse and rape were mine to carry and which ones weren’t. The process has been slow and painful. I think I began to heal when I stopped caring so much when, or if, it happened. I made my peace with being broken, and as I accepted the damage the scars slowly keratinized. I no longer care if the people who hurt me have become less caustic, because I am not responsible for them. I also don’t care if people who are not close to me understand what happened. Accountability processes are much too tied into social currency, reputation and propriety. I will not be held hostage to the theoretical dictates of a false anarchist “community.” I try and hold myself accountable to the community of people I have real ties to—those I parent, work and struggle with. Beyond that circle I have found the idea of accountability doesn’t hold up well under strain. It’s not that I don’t believe in accountability—I do, just with a little “a.” **It should be noted that the substitution of “survivor” for “victim” does not entail any actual critique of victimhood, or how victimhood embodies a patriarchal and legalistic role. Those who wish to end patriarchy should feel no affinity with the victim-mentality. It is important to distinguish a political critique of victimhood from a lack of support for victims. It is understandable that we sometimes fall back on victimhood, a socially recognized powerlessness, because it is one of the only identifiable ways to access support, and taking a different route requires more intention and energy than most people can muster during a vulnerable period in their lives. We should have compassionfor the people who, lacking other clear options, fall into the role of victim while acknowledging that it is time to create alternative narratives. \section{Excommunicate Me from the Church of Social Justice by Frances Lee} There is a particularly aggressive strand of social justice activism weaving in and out of my Seattle community that has troubled me, silenced my loved ones, and turned away potential allies. I believe in justice. I believe in liberation. I believe it is our duty to obliterate white supremacy, anti-blackness, cisheteropatriarchy, ableism, capitalism, and imperialism. And I also believe there should be openness around the tactics we use and ways our commitments are manifested over time. Beliefs and actions are too often conflated with each other, yet questioning the latter should not renege the former. As a Cultural Studies scholar, I am interested in the ways that culture does the work of power. What then, is the culture of activism, and in what ways are activists restrained by it? To be clear, I’m only one person who is trying to figure things out, and I’m open to revisions and learning. But as someone who has spent the last decade recovering from a forced conversion to evangelical Christianity, I’m seeing a disturbing parallel between religion and activism in the presence of dogma: \subsection{1. Seeking purity} There is an underlying current of fear in my activist communities, and it is separate from the daily fear of police brutality, eviction, discrimination, and street harassment. It is the fear of appearing impure. Social death follows when being labeled a “bad” activist or simply “problematic” enough times. I’ve had countless hushed conversations with friends about this anxiety, and how it has led us to refrain from participation in activist events, conversations, and spaces because we feel inadequately radical. I actually don’t prefer to call myself an activist, because I don’t fit the traditional mold of the public figure marching in the streets and interrupting business as usual. When I was a Christian, all I could think about was being good, showing goodness, and proving to my parents and my spiritual leaders that I was on the right path to God. All the while, I believed I would never be good enough, so I had to strain for the rest of my life towards an impossible destination of perfection. I feel compelled to do the same things as an activist a decade later. I self-police what I say in activist spaces. I stopped commenting on social media with questions or pushback on leftist opinions for fear of being called out. I am always ready to apologize for anything I do that a community member deems wrong, oppressive, or inappropriate- no questions asked. The amount of energy I spend demonstrating purity in order to stay in the good graces of fast-moving activist community is enormous. Activists are some of the judgiest people I’ve ever met, myself included. There’s so much wrongdoing in the world that we work to expose. And yet, grace and forgiveness are hard to come by in these circles. At times, I have found myself performing activism more than doing activism. I’m exhausted, and I’m not even doing the real work I am committed to do. It is a terrible thing to be afraid of my own community members, and know they’re probably just as afraid of me. Ultimately, the quest for political purity is a treacherous distraction for well-intentioned activists. \subsection{2. Reproducing colonialist logics} Postcolonialist black Caribbean philosopher Frantz Fanon in his 1961 book Wretched of the Earth writes about the volatile relationship between the colonizer and the colonized, and the conditions of decolonization. In it, he sharply warns the colonized against reproducing and maintaining the oppressive systems of colonization by replacing those at top by those previously at the bottom after a successful revolution. As a QTPOC (queer, trans person of color), I have experienced discrimination and rejection due to who I am. I have sought out QTPOC-only spaces to heal, find others like me, and celebrate our differences. Those spaces and relationships have saved me from despair time and time again. And yet, I reject QTPOC supremacy, the idea that QTPOCs or any other marginalized groups deserve to dominate society. The experiences of oppression do not grant supremacy, in the same way that being a powerful colonizer does not. Justice will never look like supremacy. I wish for a new societal order that does not revolve around relations of power and domination. \subsection{3. Preaching\Slash{}Punishments} Telling people what to do and how to live out their lives is endemic to dogmatic religion and activism. It’s not that my comrades are the bosses of me, but that dogmatic activism creates an environment that encourages people to tell other people what to do. This is especially prominent on Facebook. Scrolling through my news feed sometimes feels Iike sliding into a pew to be blasted by a fragmented, frenzied sermon. I know that much of the media posted there means to discipline me to be a better activist and community member. But when dictates aren’t followed, a common procedure of punishment ensues. Punishments for saying\Slash{}doing\Slash{}believing the wrong thing include shaming, scolding, calling out, isolating, or eviscerating someone’s social standing. Discipline and punishment has been used for all of history to control and destroy people. Why is it being used in movements meant to liberate all of us? We all have made serious mistakes and hurt other people, intentionally or not. We get a chance to learn from them when those around us respond with kindness and patience. Where is our humility when examining the mistakes of others? Why do we position ourselves as morally superior to the un-woke? Who of us came into the world fully awake? \subsection{4. Sacred texts} There are also some online publications of dogmatic activism that could be considered sacred texts. For example, the intersectional site Everyday Feminism receives millions of views a month. It features more than 40 talented writers who pen essays on a wide range of anti-oppression topics, zeroing in on ones that haven’t yet broached larger activist conversations online. When Everyday Feminism articles are shared among my friends, I feel both grateful that the conversation is sparking and also very belittled. Nearly all of their articles follow a standard structure: an instructive title, list of problematic or suggested behaviors, and a final statement of hard opinion. The titles, the educational tone, and the prescriptive checklists contribute to creating the idea that there is only one way to think about and do activism. And it’s a swiftly moving target that is always just out of reach. In trying to liberate readers from the legitimately oppressive structures, I worry that sites like Everyday Feminism are replacing them with equally restrictive orthodoxy on the other end of the political spectrum. At this year’s Allied Media Conference, BLM co-founder Alicia Garza gave an explosive speech to a theatre full of brilliant and passionate organizers. She urged us to set aside our distrust and critique of newer activists and accept that they will hurt and disappoint us. Don’t shut them out because their politics are outdated or they don’t wield the same language. If we are interested in building the mass movements needed to destroy mass oppression, our movements must include people not like us, people with whom we will never fully agree, and people with whom we have conflict. That’s a much higher calling than railing at people from a distance and labeling them as wrong. Ultimately, according to Garza, building a movement is about restoring humanity to all of us, even to those of us who have been inhumane. Movements are where people are called to be transformed in service of liberation of themselves and others. I want to spend less time antagonizing and more time crafting alternative futures where we don’t have to fight each other for resources and care. For an introvert like me, that may look like shifting my activism towards small scale projects and recognizing personal relationships as locations of mutual transformation. It might mean carefully choosing whether I want to be part of public disruptions or protests, and giving myself full permission to refrain at times. It may mean drawing attention to the ways in which other people outside of movements have been living out activism, even if no one has ever called it that. It might mean checking in with myself about how I have let my heart grow hard. It may mean admitting that speaking my truth isn’t justification for being mean. It might mean directly dealing with my religious hangups so that I can come to a place where the resonant aspects of theology or spirituality become part of my toolkit. It means cultivating long-term relationships with those outside my (not that) safe and exclusive community, understanding I will learn so much from them. It means ceasing to “other” people and leave them behind. It means honoring their humanity, in spite of their hurtful political beliefs and violent actions. It means seeing them as individuals, not ideologies or systems. It means acknowledging their agency to act justly. It means inviting them to be with us in love, and pushing through repeated rejection. Otherwise, I’m not sure how I can sustain this work for the rest of my life. \begin{quote} \textbf{“Here is the problem with using this (accountability process) model for emotional abuse: its an unhealthy dynamic between two people. So who gets to call it? Who gets to wield that power in the community? (And lets all be honest that there is power in calling someone to an accountability process.) People in unhealthy relationships need a way to get out of them without it getting turned into a community judgment against whomever was unlucky enough to not realize a bad dynamic or call it abuse first. These processes frequently exacerbate mutually unhealthy power plays between hurt parties. People are encouraged to pick sides and yet no direct conflict brings these kinds of entanglements to any kind of resolve. I am sick of accountability and its lack of transparency. I am sick of triangulating. I am sick of hiding power exchange. I am sick of hope. I have been raped. I have been an unfair manipulator of power in some of my intimate relationships. I have had sexual exchanges that were a learning curve for better consent. I have the potential in me to be both survivor and perp — abused and abuser — as we all do.” \forcelinebreak — Safety is an Illusion: Reflections on Accountability} \end{quote} % begin final page \clearpage % if we are on an odd page, add another one, otherwise when imposing % the page would be odd on an even one. \ifthispageodd{\strut\thispagestyle{empty}\clearpage}{} % new page for the colophon \thispagestyle{empty} \begin{center} The Anarchist Library (Mirror) \smallskip Anti-Copyright \bigskip \includegraphics[width=0.25\textwidth]{logo-yu.pdf} \bigskip \end{center} \strut \vfill \begin{center} Various authors Setting Fire to the Church of Social Justice 3 Critiques of Identity Politics, Call-Out Culture \& Other Models of Statist Thinking 14\textsuperscript{th} September 2017 \bigskip Retrieved on 14\textsuperscript{th} January 2022 from \href{https://warzonedistro.noblogs.org/files/2017/12/Setting-Fire-to-the-Church-of-Social-Justice.pdf}{warzonedistro.noblogs.org\Slash{}files\Slash{}2017\Slash{}12\Slash{}Setting-Fire-to-the-Church-of-Social-Justice.pdf} \bigskip \textbf{usa.anarchistlibraries.net} \end{center} % end final page with colophon \end{document} % No format ID passed.
http://ofap.ulstu.ru/resources/1412/two_certificate.tex?association=resources&parent_scaffold=fremantle%2Fguest%2Fresource_types&resource_type_id=26	ulstu.ru	CC-MAIN-2022-05	text/x-tex	text/x-matlab	crawl-data/CC-MAIN-2022-05/segments/1642320303385.49/warc/CC-MAIN-20220121131830-20220121161830-00160.warc.gz	44,379,239	2,646	%% LaTeX2e-файл %% Создано движком Фримантл (https://gitlab.com/korobkov/fremantle) %% в 2022-01-21T17:52:23+04:00 %% Фримантл — Свободный движок репозитория электронных ресурсов %% Copyright © 2009—2018 Лаборатория «Автоматизированные системы» [email protected], УлГТУ %% %% Фримантл is free software: you can redistribute it and/or modify %% it under the terms of the GNU Affero General Public License as published by %% the Free Software Foundation, either version 3 of the License, or %% (at your option) any later version. %% %% Фримантл is distributed in the hope that it will be useful, %% but WITHOUT ANY WARRANTY; without even the implied warranty of %% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the %% GNU Affero General Public License for more details. %% %% You should have received a copy of the GNU Affero General Public License %% along with Фримантл. If not, see <https://www.gnu.org/licenses/>. \documentclass[a4paper,fontsize=18pt]{scrartcl} \usepackage[landscape,left=2cm,right=2cm,top=1cm,bottom=1.5cm,bindingoffset=0cm]{geometry} \usepackage{graphicx, polyglossia, pst-barcode, tabu, wallpaper} \setmainfont{Liberation Serif} \setmonofont{Liberation Mono} \setsansfont{Liberation Sans} \defaultfontfeatures{Scale=MatchLowercase, Mapping=tex-text} \setdefaultlanguage[spelling=modern]{russian} \setotherlanguage{english} \graphicspath{{/srv/http/ofap/releases/20180921145927/app/assets/images/fremantle/two_certificate/}} \CenterWallPaper{1.00}{border.png} \begin{document} \begin{hyphenrules}{nohyphenation} \begin{center} \thispagestyle{empty} {\Large ОФАП УОЦ НИТ} \bigskip\bigskip \begin{tabu}{ b{5cm} >{\centering}b{19cm} } \includegraphics [height=4.5cm]{logo.png} & Ульяновский государственный технический университет Ульяновский областной центр новых информационных технологий Областной фонд алгоритмов и программ \bigskip {\Huge \textit{Свидетельство №\,1412}} \bigskip о регистрации программно-информационного продукта \end{tabu} \bigskip \begin{tabu}{ b{5cm} >{\raggedright \itshape}p{19cm} }\hline \\ Наименование: & \textbf{Изучение светодиодного индикатора АЛС318} \\ Тип: & Методические указания \\ URI: & \textbf{http://ofap.ulstu.ru/1412} \\ Авторы: & Докторова Елена Анатольевна, Докторов Александр Евгеньевич -- Кафедра «Измерительно-вычислительные комплексы» (УлГТУ/ФИСТ) \\ Дата регистрации: & 07 апреля 2015 г. \\ \end{tabu} \vfill \begin{tabu} to 24cm { b{2cm} l X >{\itshape}l } & Директор Ульяновского областного центра НИТ & & \textit{К.В.\,Святов} \\ \psbarcode{2015-04-07 http://ofap.ulstu.ru/1412}{format=compact layers=4}{azteccode} \rowfont{\small} & Администратор базы данных ОФАП & & \textit{Ю.А.\,Лапшов} \\ \end{tabu} \end{center} \end{hyphenrules} \clearpage \end{document}
https://docs.qore.org/qore-0.9.14/lang/latex/release_notes.tex	qore.org	CC-MAIN-2021-31	application/octet-stream	application/x-tex	crawl-data/CC-MAIN-2021-31/segments/1627046153491.18/warc/CC-MAIN-20210727202227-20210727232227-00102.warc.gz	230,231,595	120,253	\hypertarget{release_notes_qore_0914}{}\doxysection{Qore 0.\+9.\+14}\label{release_notes_qore_0914} \begin{DoxyParagraph}{Release Summary} Bugfix release; see below for more information \end{DoxyParagraph} \hypertarget{release_notes_qore_0914_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0914_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}} module updates\+: \begin{DoxyItemize} \item fixed a bug where pseudocolumn references were used ambiguously in joins (\href{https://github.com/qorelanguage/qore/issues/4214}{\texttt{ issue 4214}}) \item fixed a bug where pseudocolumn names were quoted in queries leading to errors (\href{https://github.com/qorelanguage/qore/issues/4210}{\texttt{ issue 4210}}) \item added an exception when {\ttfamily offset} or {\ttfamily limit} are used with {\ttfamily forupdate} (\href{https://github.com/qorelanguage/qore/issues/4206}{\texttt{ issue 4206}}) \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module updates\+: \begin{DoxyItemize} \item fixed a bug where pseudocolumn references were used ambiguously in joins (\href{https://github.com/qorelanguage/qore/issues/4214}{\texttt{ issue 4214}}) \end{DoxyItemize} \item \href{../../modules/Swagger/html/index.html}{\texttt{ Swagger}} module updates\+: \begin{DoxyItemize} \item fixed a bug where unknown string format types were not ignored but instead caused an exception to be thrown (\href{https://github.com/qorelanguage/qore/issues/4203}{\texttt{ issue 4203}}) \end{DoxyItemize} \item \href{../../modules/Util/html/index.html}{\texttt{ Util}} module updates\+: \begin{DoxyItemize} \item fixed a bug in {\ttfamily parse\+\_\+memory\+\_\+size()} with numbers larger than {\ttfamily 9} (\href{https://github.com/qorelanguage/qore/issues/4198}{\texttt{ issue 4198}}) \end{DoxyItemize} \item fixed module path handling on Windows to respect the {\ttfamily \textquotesingle{}};\textquotesingle{} separator as well as the {\ttfamily \textquotesingle{}}\+:\textquotesingle{} character (\href{https://github.com/qorelanguage/qore/issues/4154}{\texttt{ issue 4154}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0913}{}\doxysection{Qore 0.\+9.\+13}\label{release_notes_qore_0913} \begin{DoxyParagraph}{Release Summary} Bugfix release; see below for more information \end{DoxyParagraph} \hypertarget{release_notes_qore_0913_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0913_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module updates\+: \begin{DoxyItemize} \item fixed a bug handling the {\ttfamily struct} key in mappers (\href{https://github.com/qorelanguage/qore/issues/4189}{\texttt{ issue 4189}}) \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_0912}{}\doxysection{Qore 0.\+9.\+12}\label{release_notes_qore_0912} \begin{DoxyParagraph}{Release Summary} Bugfix release; see below for more information \end{DoxyParagraph} \hypertarget{release_notes_qore_0912_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0912_bug_fixes} \begin{DoxyItemize} \item fixes in modules \begin{DoxyItemize} \item \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} \begin{DoxyItemize} \item fixed a bug handling {\ttfamily 100-\/continue} requests when no handler is matched (\href{https://github.com/qorelanguage/qore/issues/4155}{\texttt{ issue 4155}}) \end{DoxyItemize} \end{DoxyItemize} \item fixed module path handling on Windows to respect the {\ttfamily \textquotesingle{}};\textquotesingle{} separator (\href{https://github.com/qorelanguage/qore/issues/4154}{\texttt{ issue 4154}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0911}{}\doxysection{Qore 0.\+9.\+11}\label{release_notes_qore_0911} \begin{DoxyParagraph}{Release Summary} Bugfix release; see below for more information \end{DoxyParagraph} \hypertarget{release_notes_qore_0911_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0911_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} \begin{DoxyItemize} \item updated read and write data providers to provide verbose option support (\href{https://github.com/qorelanguage/qore/issues/4139}{\texttt{ issue 4139}}) \item implemented support for the missing {\ttfamily bool} and {\ttfamily $\ast$bool} types (\href{https://github.com/qorelanguage/qore/issues/4118}{\texttt{ issue 4118}}) \end{DoxyItemize} \item \href{../../modules/DataProvider/html/index.html}{\texttt{ Data\+Provider}} \begin{DoxyItemize} \item fixed an issue where it was not possible for pipeline to flush any pending data or to perform reset or purge operations when pipeline processing is complete; for this the {\ttfamily \mbox{\hyperlink{group__string__functions_ga56e62bf88b3fa54aa9aa75508d5d6c05}{Abstract\+Data\+Processor\+::flush()}}} and {\ttfamily Abstract\+Data\+Processor\+::flush\+Impl()} methods were implemented (\href{https://github.com/qorelanguage/qore/issues/4107}{\texttt{ issue 4107}}) \end{DoxyItemize} \item \href{../../modules/FixedLengthUtil/html/index.html}{\texttt{ Fixed\+Length\+Util}} \begin{DoxyItemize} \item updated read and write data providers to provide verbose option support (\href{https://github.com/qorelanguage/qore/issues/4139}{\texttt{ issue 4139}}) \end{DoxyItemize} \item \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} \begin{DoxyItemize} \item fixed a bug shutting down dedicated socket I/O handlers (\href{https://github.com/qorelanguage/qore/issues/4130}{\texttt{ issue 4130}}) \item fixed a bug where invalid H\+T\+TP responses were send with error messages and chunked transfer encoding (\href{https://github.com/qorelanguage/qore/issues/4124}{\texttt{ issue 4124}}) \item fixed a bug where H\+T\+TP stream handlers could not also implement protocol switching (\href{https://github.com/qorelanguage/qore/issues/4111}{\texttt{ issue 4111}}) \end{DoxyItemize} \item \href{../../modules/HttpServerUtil/html/index.html}{\texttt{ Http\+Server\+Util}} \begin{DoxyItemize} \item fixed a bug where it was not possible to include C\+O\+RS headers or any context-\/sensitive information in a 401 response (\href{https://github.com/qorelanguage/qore/issues/4136}{\texttt{ issue 4136}}) \item fixed a bug where H\+T\+TP stream handlers could not also implement protocol switching (\href{https://github.com/qorelanguage/qore/issues/4111}{\texttt{ issue 4111}}) \item fixed a bug handling responses to streaming requests with {\ttfamily H\+E\+AD} requests with a {\ttfamily Transfer-\/\+Encoding\+: chunked} response (\href{https://github.com/qorelanguage/qore/issues/4109}{\texttt{ issue 4109}}) \end{DoxyItemize} \item \href{../../modules/ServiceNowRestDataProvider/html/index.html}{\texttt{ Service\+Now\+Rest\+Data\+Provider}} \begin{DoxyItemize} \item fixed a type error in Data\+Provider A\+PI support (\href{https://github.com/qorelanguage/qore/issues/4104}{\texttt{ issue 4104}}) \end{DoxyItemize} \item fixed support for 64-\/bit\+A\+RM C\+P\+Us; added stack guard support (\href{https://github.com/qorelanguage/qore/issues/3965}{\texttt{ issue 3965}}) \item fixed a bug handling types in assignments with complex hashes (\href{https://github.com/qorelanguage/qore/issues/4133}{\texttt{ issue 4133}}) \item fixed a bug in the \mbox{\hyperlink{operators_remove}{remove}} operator when used with a slice of a hash or an object; hash keys for nonexistent values were returned in a manner inconsistnent with the hash slice operator when not used with the \mbox{\hyperlink{operators_remove}{remove}} operator (\href{https://github.com/qorelanguage/qore/issues/4122}{\texttt{ issue 4122}}) \item fixed a bug in the \mbox{\hyperlink{operators_cast}{cast$<$$>$}} operator; invalid exceptions were raised during parsing for values that could still inherit the target class; the check must only be made at runtime (\href{https://github.com/qorelanguage/qore/issues/4113}{\texttt{ issue 4113}}) \item fixed a bug in the \mbox{\hyperlink{operators_instanceof}{instanceof}} operator; invalid exceptions were raised during parsing for values that could still inherit the target class; the check must only be made at runtime (\href{https://github.com/qorelanguage/qore/issues/4112}{\texttt{ issue 4112}}) \item fixed a bug where it was not possible to poll for I/O on more than one \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} at a time; for this the \mbox{\hyperlink{class_qore_1_1_socket_aa3efaf66dd7fcaf2b631d161e9bc8e4a}{Socket\+::poll()}} static method was implemented (\href{https://github.com/qorelanguage/qore/issues/4069}{\texttt{ issue 4069}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0910}{}\doxysection{Qore 0.\+9.\+10}\label{release_notes_qore_0910} \begin{DoxyParagraph}{Release Summary} Bugfix release; see below for more information \end{DoxyParagraph} \hypertarget{release_notes_qore_0910_new_modules}{}\doxysubsection{New Modules in Qore}\label{release_notes_qore_0910_new_modules} \begin{DoxyItemize} \item \href{../../modules/ServiceNowRestClient/html/index.html}{\texttt{ Service\+Now\+Rest\+Client}}\+: provides A\+P\+Is for communicating with the Service\+Now R\+E\+ST A\+PI \item \href{../../modules/ServiceNowRestDataProvider/html/index.html}{\texttt{ Service\+Now\+Rest\+Data\+Provider}}\+: Provides a \href{../../modules/DataProvider/html/index.html}{\texttt{ data provider}} A\+PI for the Service\+Now R\+E\+ST A\+PI \end{DoxyItemize}\hypertarget{release_notes_qore_0910_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0910_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/WebUtil/html/index.html}{\texttt{ Web\+Util}} module updates\+: \begin{DoxyItemize} \item fixed a bug serving files did not work in server contexts with multiple threads (\href{https://github.com/qorelanguage/qore/issues/4096}{\texttt{ issue 4096}}) \end{DoxyItemize} \item fixed an invalid assert in class handling in complex hierarchies (\href{https://github.com/qorelanguage/qore/issues/4094}{\texttt{ issue 4094}}) \end{DoxyItemize}\hypertarget{release_notes_qore_099}{}\doxysection{Qore 0.\+9.\+9}\label{release_notes_qore_099} \begin{DoxyParagraph}{Release Summary} Bugfix release; see below for more information \end{DoxyParagraph} \hypertarget{release_notes_qore_099_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_099_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module updates\+: \begin{DoxyItemize} \item additional fixes to R\+E\+ST path handling with schema validators with a base path (\href{https://github.com/qorelanguage/qore/issues/4059}{\texttt{ issue 4059}}) \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_098}{}\doxysection{Qore 0.\+9.\+8}\label{release_notes_qore_098} \begin{DoxyParagraph}{Release Summary} Bugfix release; see below for more information \end{DoxyParagraph} \hypertarget{release_notes_qore_098_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_098_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module updates\+: \begin{DoxyItemize} \item fixed a bug where C\+SV iteration would fail if a quoted field had a line break in it (\href{https://github.com/qorelanguage/qore/issues/4079}{\texttt{ issue 4079}}) \end{DoxyItemize} \item \href{../../modules/WebSocketClient/html/index.html}{\texttt{ Web\+Socket\+Client}} module updates\+: \begin{DoxyItemize} \item fixed handling Web\+Socket message fragmentation (\href{https://github.com/qorelanguage/qore/issues/4073}{\texttt{ issue 4073}}) \end{DoxyItemize} \item \href{../../modules/WebSocketHandler/html/index.html}{\texttt{ Web\+Socket\+Handler}} module updates\+: \begin{DoxyItemize} \item fixed a bug handling closing server-\/side web sockets on demand (\href{https://github.com/qorelanguage/qore/issues/4075}{\texttt{ issue 4075}}) \item fixed a bug where I/O could not be flushed before closing the socket (\href{https://github.com/qorelanguage/qore/issues/4074}{\texttt{ issue 4074}}) \item fixed handling Web\+Socket message fragmentation (\href{https://github.com/qorelanguage/qore/issues/4073}{\texttt{ issue 4073}}) \end{DoxyItemize} \item \href{../../modules/WebSocketUtil/html/index.html}{\texttt{ Web\+Socket\+Util}} module updates\+: \begin{DoxyItemize} \item fixed handling Web\+Socket message fragmentation (\href{https://github.com/qorelanguage/qore/issues/4073}{\texttt{ issue 4073}}) \end{DoxyItemize} \item fixed type errors with the \mbox{\hyperlink{operators_map}{Map Operator (map)}} when used as a functional operator (\href{https://github.com/qorelanguage/qore/issues/4085}{\texttt{ issue 4085}}) \item added \mbox{\hyperlink{class_qore_1_1_abstract_line_iterator_ad29d146dd1dd3b9b248ff92e1b6bce3b}{Abstract\+Line\+Iterator\+::get\+Split\+Line()}} to allow quoted fields with line breaks to be iterated in \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} (\href{https://github.com/qorelanguage/qore/issues/4079}{\texttt{ issue 4079}}) \item fixed a crash in \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}} methods with negative timeout values in debug builds (\href{https://github.com/qorelanguage/qore/issues/4077}{\texttt{ issue 4077}}) \end{DoxyItemize}\hypertarget{release_notes_qore_097}{}\doxysection{Qore 0.\+9.\+7}\label{release_notes_qore_097} \begin{DoxyParagraph}{Release Summary} Bugfix release; see below for more information \end{DoxyParagraph} \hypertarget{release_notes_qore_097_notes}{}\doxysubsection{Release Notes}\label{release_notes_qore_097_notes} Note that when a R\+E\+ST validator is present in a R\+E\+ST connection, any U\+RI path in the connection U\+RL is ignored; to change the base path specified by a R\+E\+ST validator, use the {\itshape swagger\+\_\+base\+\_\+path} connection option.\hypertarget{release_notes_qore_097_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_097_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/DataProvider/html/index.html}{\texttt{ Data\+Provider}} module updates\+: \begin{DoxyItemize} \item fixed type-\/handling bugs handling data provider options (\href{https://github.com/qorelanguage/qore/issues/4062}{\texttt{ issue 4062}}) \end{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module updates\+: \begin{DoxyItemize} \item fixed a bug where the base path in the Swagger schema was ignored; note that when a R\+E\+ST validator is present, any U\+RI path in the connection U\+RL is ignored; to change the base path specified by a R\+E\+ST validator, use the {\itshape swagger\+\_\+base\+\_\+path} connection option (\href{https://github.com/qorelanguage/qore/issues/4059}{\texttt{ issue 4059}}) \end{DoxyItemize} \item \href{../../modules/Swagger/html/index.html}{\texttt{ Swagger}} module updates\+: \begin{DoxyItemize} \item fixed a type error in {\ttfamily Swagger\+::get\+Base\+Path()} for the case when the base path is not set (\href{https://github.com/qorelanguage/qore/issues/4064}{\texttt{ issue 4064}}) \end{DoxyItemize} \item \href{../../modules/WebSocketHandler/html/index.html}{\texttt{ Web\+Socket\+Handler}} module updates\+: \begin{DoxyItemize} \item fixed a bug handling the case when a connection object is deleted in a callback method (\href{https://github.com/qorelanguage/qore/issues/4063}{\texttt{ issue 4063}}) \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_096}{}\doxysection{Qore 0.\+9.\+6}\label{release_notes_qore_096} \begin{DoxyNote}{Note} From Qore 0.\+9.\+6 onwards, Qore releases will use \href{https://semver.org/}{\texttt{ semantic versioning}}. \end{DoxyNote} \begin{DoxyParagraph}{Release Summary} Bugfix release; see below for more information \end{DoxyParagraph} \hypertarget{release_notes_qore_096_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_096_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/DataProvider/html/index.html}{\texttt{ Data\+Provider}} module updates\+: \begin{DoxyItemize} \item fixed invalid default return values for {\ttfamily Abstract\+Data\+Processor} methods (\href{https://github.com/qorelanguage/qore/issues/4043}{\texttt{ issue 4043}}) \end{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module updates\+: \begin{DoxyItemize} \item added the {\itshape swagger\+\_\+base\+\_\+path} option to R\+E\+ST clients and connections to allow for Swagger schemas to have their base path overridden (\href{https://github.com/qorelanguage/qore/issues/4059}{\texttt{ issue 4059}}) \end{DoxyItemize} \item \href{../../modules/SwaggerDataProvider/html/index.html}{\texttt{ Swagger\+Data\+Provider}} module updates\+: \begin{DoxyItemize} \item fixed a bug where the base path in the Swagger schema was ignored (\href{https://github.com/qorelanguage/qore/issues/4059}{\texttt{ issue 4059}}) \end{DoxyItemize} \item fixed a problem with lazy resolution of static class variables that could lead to incorrect runtime execution (\href{https://github.com/qorelanguage/qore/issues/4045}{\texttt{ issue 4045}}) \item fixed a symbol conflict with the {\ttfamily \mbox{\hyperlink{group__threading__functions_ga95ed8e572309b44b3f5b49673238c3e6}{gettid()}}} C++ function; use {\ttfamily q\+\_\+gettid()} instead to avoid potential symbol conflicts that can result in a crash (\href{https://github.com/qorelanguage/qore/issues/4046}{\texttt{ issue 4046}}) \item fixed a bug handling the class context in closures created with the \mbox{\hyperlink{operators_background}{background operator}} when created in the context of a subclass of the method called (\href{https://github.com/qorelanguage/qore/issues/4051}{\texttt{ issue 4051}}) \item fixed a bug that could cause a crash destroying thread-\/local vars when threads terminate (\href{https://github.com/qorelanguage/qore/issues/4053}{\texttt{ issue 4053}}) \item fixed a race condition that could cause a crash when deleting closure-\/local variable data while holding a lock (\href{https://github.com/qorelanguage/qore/issues/4055}{\texttt{ issue 4055}}) \end{DoxyItemize}\hypertarget{release_notes_qore_095}{}\doxysection{Qore 0.\+9.\+5}\label{release_notes_qore_095} \begin{DoxyParagraph}{Release Summary} Bugfix release with minor new features; including full A\+RM C\+PU support; see below for more information \end{DoxyParagraph} \hypertarget{release_notes_qore_095_compatibility}{}\doxysubsection{Fixes That Can Affect Backwards-\/\+Compatibility}\label{release_notes_qore_095_compatibility} \begin{DoxyItemize} \item The \href{../../modules/ConnectionProvider/html/index.html}{\texttt{ Connection\+Provider}} module was updated with support for verbose option reporting and a connection cache; support for the deprecated constructor was removed from {\ttfamily Http\+Connection}, Http\+Based\+Connection, as well as from other connection classes \item The \mbox{\hyperlink{namespace_qore_a834e1f95eb108bd6e4d564daecd68eda}{mkdir()}} function was modified to provide consistent behavior and a consistent return value with and without the {\itshape parents} argument; this function never throws an exception now, and always returns either {\ttfamily 0} (meaning no error occurred) or {\ttfamily 1} (meaning an error occurred) and no longer returns the number of directories created when {\itshape parents} = \mbox{\hyperlink{basic_data_types_True}{True}}. Use \mbox{\hyperlink{class_qore_1_1_dir_a9e9f05c88ac58cdbf027f8f4d8bcdc40}{Dir\+::create()}} to get the number of directories created as in previous versions of Qore; \begin{DoxySeeAlso}{See also} \mbox{\hyperlink{namespace_qore_a93887c395ed9044e39a25046ab27f7b3}{Qore\+::mkdir\+\_\+ex()}} \end{DoxySeeAlso} \item Fixed broken \mbox{\hyperlink{group__list__functions_gaad3b9056f1b0dfef032d130c7500f517}{range()}} and \mbox{\hyperlink{group__range__functions_gad5b4d3ad3f6c36d2e714bc6ed757a507}{xrange()}} where the upper limit of the range was included in the result for maximum compatibility with other languages. To get the old behavior, use the \mbox{\hyperlink{parse_directives_broken-range}{\%broken-\/range}} parse directive. \item Floating-\/point values are always converted to strings with a decimal point; in previous releases of Qore, round floating-\/point values were converted to strings without any decimal point; i.\+e. {\ttfamily 1.\+0} will now be converted to {\ttfamily \char`\"{}1.\+0\char`\"{}} (in previous releases of Qore, it would be converted to simply {\ttfamily \char`\"{}1\char`\"{}}) \end{DoxyItemize}\hypertarget{release_notes_qore_095_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_095_new_features} \begin{DoxyItemize} \item \href{../../modules/CdsRestClient/html/index.html}{\texttt{ Cds\+Rest\+Client}} \begin{DoxyItemize} \item new module providing A\+P\+Is for communicating with the Microsoft Common Data Service R\+E\+ST A\+PI \end{DoxyItemize} \item \href{../../modules/CdsRestDataProvider/html/index.html}{\texttt{ Cds\+Rest\+Data\+Provider}} \begin{DoxyItemize} \item new module providing a \href{../../modules/DataProvider/html/index.html}{\texttt{ data provider}} A\+PI for the Microsoft Common Data Service R\+E\+ST A\+PI \end{DoxyItemize} \item \href{../../modules/ConnectionProvider/html/index.html}{\texttt{ Connection\+Provider}} \begin{DoxyItemize} \item added support for verbose connection option reporting \item added a connection cache \item all connection classes updated to support verbose option reporting \end{DoxyItemize} \item \href{../../modules/DataProvider/html/index.html}{\texttt{ Data\+Provider}} module updates\+: \begin{DoxyItemize} \item added new Qore base types to the data type hierarchy \item implemented the following classes\+: \begin{DoxyItemize} \item {\ttfamily Abstract\+Data\+Processor} \item {\ttfamily Data\+Provider\+Bulk\+Record\+Iterator} \item {\ttfamily Data\+Provider\+Pipeline} ~\newline (\href{https://github.com/qorelanguage/qore/issues/3876}{\texttt{ issue 3876}}) \end{DoxyItemize} \item added the {\ttfamily D\+U\+P\+L\+I\+C\+A\+T\+E-\/\+R\+E\+C\+O\+RD} exception documentation for {\ttfamily Abstract\+Data\+Provider\+::create\+Record()} \item updated to allow data provider type attributes to appear as children in the type hierarchy (\href{https://github.com/qorelanguage/qore/issues/4015}{\texttt{ issue 4015}}) \end{DoxyItemize} \item \href{../../modules/FsUtil/html/index.html}{\texttt{ Fs\+Util}} module updates\+: \begin{DoxyItemize} \item added \mbox{\hyperlink{class_qore_1_1_dir}{Dir}} as a parent class of {\ttfamily Tmp\+Dir} (\href{https://github.com/qorelanguage/qore/issues/3945}{\texttt{ issue 3945}}) \end{DoxyItemize} \item \href{../../modules/reflection/html/index.html}{\texttt{ reflection}} module updates\+: \begin{DoxyItemize} \item added {\ttfamily Abstract\+Constant\+::get\+Module\+Name()} \item added {\ttfamily Abstract\+Reflection\+Function\+::get\+Code\+Flags()} \item added {\ttfamily Abstract\+Reflection\+Function\+::get\+Code\+Flag\+List()} \item added {\ttfamily Abstract\+Reflection\+Function\+::get\+Domain()} \item added {\ttfamily Abstract\+Reflection\+Function\+::get\+Domain\+String\+List()} \item added {\ttfamily Abstract\+Reflection\+Function\+::get\+Module\+Name()} \item added {\ttfamily Namespace\+::get\+Module\+Name()} \item added {\ttfamily Typed\+Hash\+::do\+Cast()} \end{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} \begin{DoxyItemize} \item added the {\ttfamily no\+\_\+charset} option to options (\href{https://github.com/qorelanguage/qore/issues/3328}{\texttt{ issue 3328}}) \end{DoxyItemize} \item \href{../../modules/RestSchemaValidator/html/index.html}{\texttt{ Rest\+Schema\+Validator}} \begin{DoxyItemize} \item added the {\ttfamily no\+\_\+charset} option to options (\href{https://github.com/qorelanguage/qore/issues/3328}{\texttt{ issue 3328}}) \end{DoxyItemize} \item \href{../../modules/Schema/html/index.html}{\texttt{ Schema}} module updates\+: \begin{DoxyItemize} \item allow schema operations to be executed with no output (verbose $<$ 0) (\href{https://github.com/qorelanguage/qore/issues/3996}{\texttt{ issue 3996}}) \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module updates\+: \begin{DoxyItemize} \item new {\ttfamily Abstract\+Table} methods returning a hash with info about the operation as well as the S\+QL and any bind arguments used \end{DoxyItemize} \item \href{../../modules/Util/html/index.html}{\texttt{ Util}} module updates\+: \begin{DoxyItemize} \item added the {\ttfamily parse\+\_\+memory\+\_\+size()} function (\href{https://github.com/qorelanguage/qore/issues/4004}{\texttt{ issue 4004}}) \end{DoxyItemize} \item New data type\+: \begin{DoxyItemize} \item \mbox{\hyperlink{data_type_declarations_softbinary_type}{softbinary}} \end{DoxyItemize} \item New methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_acfc588c5d6f57c8a04a0f14819c90128}{H\+T\+T\+P\+Client\+::add\+Default\+Headers()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_af114b3a0915063dfd94b6cdd38fae9e7}{H\+T\+T\+P\+Client\+::get\+Default\+Headers()}} \item \mbox{\hyperlink{class_qore_1_1_program_a7f13a387f3c4eeae169d88e0cc932caf}{Program\+::call\+Static\+Method()}} \item \mbox{\hyperlink{class_qore_1_1_program_a18173d853d29fcd28cd2851cc33ce15e}{Program\+::call\+Static\+Method\+Args()}} \end{DoxyItemize} \item New functions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__math__functions_ga129fcfa5d3eb69023df68ab6d5ee0a08}{compare()}} compares floating-\/point and arbitrary-\/precision numeric values with a given epsilon \item \mbox{\hyperlink{group__threading__functions_gaa97833f603fb51b23fe0bb6c22b7f95f}{get\+\_\+stack\+\_\+size()}} now works on Darwin / mac\+OS \item \mbox{\hyperlink{namespace_qore_a93887c395ed9044e39a25046ab27f7b3}{mkdir\+\_\+ex()}} \end{DoxyItemize} \item Added stack guard support for A\+RM processors (\href{https://github.com/qorelanguage/qore/issues/3965}{\texttt{ issue 3965}}) \end{DoxyItemize}\hypertarget{release_notes_qore_095_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_095_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/DataProvider/html/index.html}{\texttt{ Data\+Provider}} module updates\+: \begin{DoxyItemize} \item fixed a bug where {\ttfamily Hash\+Data\+Type} would not enforce fields or field types when checking for type and value compatibility (\href{https://github.com/qorelanguage/qore/issues/4037}{\texttt{ issue 4037}}) \end{DoxyItemize} \item \href{../../modules/FreetdsSqlUtil/html/index.html}{\texttt{ Freetds\+Sql\+Util}} module updates\+: \begin{DoxyItemize} \item fixed a bug generating literal date/time values for S\+QL queries (\href{https://github.com/qorelanguage/qore/issues/3948}{\texttt{ issue 3948}}) \end{DoxyItemize} \item \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module updates\+: \begin{DoxyItemize} \item fixed a bug where the H\+T\+TP server would not always stop the \mbox{\hyperlink{class_qore_1_1_thread_1_1_thread_pool}{Thread\+Pool}} which caused process shutdowns to hang (\href{https://github.com/qorelanguage/qore/issues/3999}{\texttt{ issue 3999}}) \item fixed a bug where the {\ttfamily Expect} header was not supported and where binary message bodies were read as strings (\href{https://github.com/qorelanguage/qore/issues/4035}{\texttt{ issue 4035}}) \end{DoxyItemize} \item \href{../../modules/MysqlSqlUtil/html/index.html}{\texttt{ Mysql\+Sql\+Util}} module updates\+: \begin{DoxyItemize} \item fixed a bug generating literal date/time values for S\+QL queries (\href{https://github.com/qorelanguage/qore/issues/3948}{\texttt{ issue 3948}}) \end{DoxyItemize} \item \href{../../modules/PgsqlSqlUtil/html/index.html}{\texttt{ Pgsql\+Sql\+Util}} module updates\+: \begin{DoxyItemize} \item implemented atomic merge / upsert support (\href{https://github.com/qorelanguage/qore/issues/3963}{\texttt{ issue 3963}}) \item fixed a bug generating literal date/time values for S\+QL queries (\href{https://github.com/qorelanguage/qore/issues/3948}{\texttt{ issue 3948}}) \end{DoxyItemize} \item \href{../../modules/Qdx/html/index.html}{\texttt{ Qdx}} module updates\+: \begin{DoxyItemize} \item fixed a bug where Qore-\/language post processing fixes were applied to non-\/Qore docs (\href{https://github.com/qorelanguage/qore/issues/3985}{\texttt{ issue 3985}}) \end{DoxyItemize} \item \href{../../modules/QUnit/html/index.html}{\texttt{ Q\+Unit}} module updates\+: \begin{DoxyItemize} \item updated to allow tests to be run with argument handling from languages that do not support lvalue references (\href{https://github.com/qorelanguage/qore/issues/3934}{\texttt{ issue 3934}}) \end{DoxyItemize} \item fixed a bug in \mbox{\hyperlink{group__list__functions_gaad3b9056f1b0dfef032d130c7500f517}{range()}} and \mbox{\hyperlink{group__range__functions_gad5b4d3ad3f6c36d2e714bc6ed757a507}{xrange()}} where the upper limit of the range was included in the result (\href{https://github.com/qorelanguage/qore/issues/4031}{\texttt{ issue 4031}}) \item fixed a bug in exception handling with external language modules where stack trace elements were added in reverse order (\href{https://github.com/qorelanguage/qore/issues/4030}{\texttt{ issue 4030}}) \item fixed a bug in \mbox{\hyperlink{namespace_qore_a834e1f95eb108bd6e4d564daecd68eda}{Qore\+::mkdir()}} with {\ttfamily parents} = \mbox{\hyperlink{basic_data_types_True}{True}} (\href{https://github.com/qorelanguage/qore/issues/3992}{\texttt{ issue 3992}}) \item fixed a bug where complex formatting output with \mbox{\hyperlink{group__string__functions_ga7a74be141f814ef286046c367b21091c}{sprintf()}} and related dunctions would have {\ttfamily \char`\"{}.\char`\"{}} separators instead of {\ttfamily \char`\"{},\char`\"{}} separators when floating-\/point values were included in the output (\href{https://github.com/qorelanguage/qore/issues/3947}{\texttt{ issue 3947}}) \item fixed a bug handling embedded nulls in U\+T\+F-\/8 strings (\href{https://github.com/qorelanguage/qore/issues/2942}{\texttt{ issue 2942}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0947}{}\doxysection{Qore 0.\+9.\+4.\+7}\label{release_notes_qore_0947} \begin{DoxyParagraph}{Release Summary} \end{DoxyParagraph} Bugfix release; see details below\hypertarget{release_notes_qore_0947_bug_fixesd}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0947_bug_fixesd} \begin{DoxyItemize} \item fixed a bug in the return type of \mbox{\hyperlink{class_qore_1_1_dir_a53181a09db1ea32f65bb6c6b50f4692d}{Dir\+::statvfs()}} (\href{https://github.com/qorelanguage/qore/issues/3989}{\texttt{ issue 3989}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0946}{}\doxysection{Qore 0.\+9.\+4.\+6}\label{release_notes_qore_0946} \begin{DoxyParagraph}{Release Summary} \end{DoxyParagraph} Bugfix release; see details below\hypertarget{release_notes_qore_0946_bug_fixesd}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0946_bug_fixesd} \begin{DoxyItemize} \item \href{../../modules/Swagger/html/index.html}{\texttt{ Swagger}} module updates\+: \begin{DoxyItemize} \item fixed a bug supporting number formats (\href{https://github.com/qorelanguage/qore/issues/3979}{\texttt{ issue 3979}}) \end{DoxyItemize} \item fixed a bug maintaining the socket encoding for outgoing messages in \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client}{H\+T\+T\+P\+Client}} objects (\href{https://github.com/qorelanguage/qore/issues/3978}{\texttt{ issue 3978}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0945}{}\doxysection{Qore 0.\+9.\+4.\+5}\label{release_notes_qore_0945} \begin{DoxyParagraph}{Release Summary} \end{DoxyParagraph} Bugfix release; see details below\hypertarget{release_notes_qore_0945_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_0945_new_features} \begin{DoxyItemize} \item \href{../../modules/DataProvider/html/index.html}{\texttt{ Data\+Provider}} module updates\+: \begin{DoxyItemize} \item added a thread callback for background queue threads (\href{https://github.com/qorelanguage/qore/issues/3927}{\texttt{ issue 3927}}) \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_0945_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0945_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module updates\+: \begin{DoxyItemize} \item fixed a bug handling external runtime keys with bulk input for keys that do not require the current input value (\href{https://github.com/qorelanguage/qore/issues/3931}{\texttt{ issue 3931}}) \end{DoxyItemize} \item fixed a race condition in closure-\/bound variable reference handling that could result in a runtime crash (\href{https://github.com/qorelanguage/qore/issues/3939}{\texttt{ issue 3939}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0944}{}\doxysection{Qore 0.\+9.\+4.\+4}\label{release_notes_qore_0944} \begin{DoxyParagraph}{Release Summary} \end{DoxyParagraph} Bugfix release; see details below\hypertarget{release_notes_qore_0944_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_0944_new_features} \begin{DoxyItemize} \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module updates\+: \begin{DoxyItemize} \item added support for mapper context in mapper field key handlers (\href{https://github.com/qorelanguage/qore/issues/3893}{\texttt{ issue 3893}}) \item added support for nested mappers and the {\ttfamily submappers} option (\href{https://github.com/qorelanguage/qore/issues/3414}{\texttt{ issue 3414}}) \item implemented the {\ttfamily output\+\_\+create\+\_\+ignore\+\_\+duplicates} option \end{DoxyItemize} \item added support for freestanding expression evaluation\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_expression}{Expression}} class \item \mbox{\hyperlink{class_qore_1_1_program_a370c2c5429950cce89297e7e944f0f55}{Program\+::get\+Expression()}} method \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_0944_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0944_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module updates\+: \begin{DoxyItemize} \item fixed {\ttfamily Fixed\+Length\+Write\+Data\+Provider} to return the record created with the {\ttfamily create\+Record()} call (\href{https://github.com/qorelanguage/qore/issues/3914}{\texttt{ issue 3914}}) \end{DoxyItemize} \item \href{../../modules/DataProvider/html/index.html}{\texttt{ Data\+Provider}} module updates\+: \begin{DoxyItemize} \item added the {\ttfamily D\+U\+P\+L\+I\+C\+A\+T\+E-\/\+R\+E\+C\+O\+RD} exception documentation for {\ttfamily Abstract\+Data\+Provider\+::create\+Record()} \end{DoxyItemize} \item \href{../../modules/FixedLengthUtil/html/index.html}{\texttt{ Fixed\+Length\+Util}} module updates\+: \begin{DoxyItemize} \item fixed {\ttfamily Csv\+Write\+Data\+Provider} to return the record created with the {\ttfamily create\+Record()} call (\href{https://github.com/qorelanguage/qore/issues/3914}{\texttt{ issue 3914}}) \end{DoxyItemize} \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module updates\+: \begin{DoxyItemize} \item fixed a bug where mapper output data was not logged in case of an error in an output provider (\href{https://github.com/qorelanguage/qore/issues/3909}{\texttt{ issue 3909}}) \item updated mapper key handler calling convertion + docs (\href{https://github.com/qorelanguage/qore/issues/3894}{\texttt{ issue 3894}}) \item fixed {\ttfamily Mapper\+::map\+Auto()} to return \mbox{\hyperlink{basic_data_types_NOTHING}{N\+O\+T\+H\+I\+NG}} with no input (\href{https://github.com/qorelanguage/qore/issues/3872}{\texttt{ issue 3872}}) \end{DoxyItemize} \item \href{../../modules/SalesforceRestDataProvider/html/index.html}{\texttt{ Salesforce\+Rest\+Data\+Provider}} module updates\+: \begin{DoxyItemize} \item fixed a bug deleting records with no matches (\href{https://github.com/qorelanguage/qore/issues/3921}{\texttt{ issue 3921}}) \item fixed serializing {\ttfamily D\+A\+TE} fields (\href{https://github.com/qorelanguage/qore/issues/3908}{\texttt{ issue 3908}}) \end{DoxyItemize} \item fixed a bug in class copy methods with {\ttfamily private\+:internal} members (\href{https://github.com/qorelanguage/qore/issues/3901}{\texttt{ issue 3901}}) \item fixed bugs running {\ttfamily qdbg} (\href{https://github.com/qorelanguage/qore/issues/3900}{\texttt{ issue 3900}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0943}{}\doxysection{Qore 0.\+9.\+4.\+3}\label{release_notes_qore_0943} \begin{DoxyParagraph}{Release Summary} \end{DoxyParagraph} Bugfix release; see details below\hypertarget{release_notes_qore_0943_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_0943_new_features} \begin{DoxyItemize} \item \href{../../modules/DataProvider/html/index.html}{\texttt{ Data\+Provider}} module updates\+: \begin{DoxyItemize} \item added new classes\+: \begin{DoxyItemize} \item {\ttfamily Abstract\+Data\+Processor} \item {\ttfamily Data\+Provider\+Bulk\+Record\+Iterator} \item {\ttfamily Data\+Provider\+Pipeline} \end{DoxyItemize}(\href{https://github.com/qorelanguage/qore/issues/3876}{\texttt{ issue 3876}}) \end{DoxyItemize} \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module updates\+: \begin{DoxyItemize} \item added the Mapper\+::map\+Auto() method and the {\ttfamily disable\+\_\+bulk} option (\href{https://github.com/qorelanguage/qore/issues/3872}{\texttt{ issue 3872}}) \item {\ttfamily Mapper} now inherits {\ttfamily Data\+Provider\+::\+Abstract\+Data\+Provider\+Record\+Processor} (\href{https://github.com/qorelanguage/qore/issues/3876}{\texttt{ issue 3876}}) \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_0943_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0943_bug_fixes} \begin{DoxyItemize} \item fixed a bug in the \mbox{\hyperlink{class_qore_1_1_thread_1_1_thread_pool}{Thread\+Pool}} class where queued tasks were discarded without being executed when \mbox{\hyperlink{class_qore_1_1_thread_1_1_thread_pool_a7dcb42215303978ddee052d32dca8bb1}{Thread\+Pool\+::stop\+Wait()}} was called (\href{https://github.com/qorelanguage/qore/issues/3897}{\texttt{ issue 3897}}) \item fixed a bug determining method signature compatibility with variants of the \mbox{\hyperlink{data_type_declarations_softlist_type}{softlist}} type (\href{https://github.com/qorelanguage/qore/issues/3887}{\texttt{ issue 3887}}) \item fixed a parse-\/time type error taking a slice of a hashdecl value (\href{https://github.com/qorelanguage/qore/issues/3882}{\texttt{ issue 3882}}) \item fixed H\+T\+TP responses with no message body and no {\ttfamily Transfer-\/\+Encoding} header to include a {\ttfamily Content-\/\+Length\+: 0} header to correctly support \href{http://tools.ietf.org/html/rfc2616\#section-4.4}{\texttt{ R\+F\+C-\/2616}} (\href{https://github.com/qorelanguage/qore/issues/3879}{\texttt{ issue 3879}}) \item fixed a crash in handling reference arguments in call references in mixed class contexts (\href{https://github.com/qorelanguage/qore/issues/3869}{\texttt{ issue 3869}}) \item fixed a memory leak in the code that manages remote client certificates in the \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} class (\href{https://github.com/qorelanguage/qore/issues/3865}{\texttt{ issue 3865}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0942}{}\doxysection{Qore 0.\+9.\+4.\+2}\label{release_notes_qore_0942} \begin{DoxyParagraph}{Release Summary} \end{DoxyParagraph} Bugfix release; see details below\hypertarget{release_notes_qore_0942_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_0942_new_features} \begin{DoxyItemize} \item new user modules\+: \begin{DoxyItemize} \item \href{../../modules/BillwerkRestClient/html/index.html}{\texttt{ Billwerk\+Rest\+Client}} \begin{DoxyItemize} \item added this new module providing A\+P\+Is for communicating with \href{http://www.billwerk.com}{\texttt{ billwerk.\+com}}\textquotesingle{}s R\+E\+ST A\+PI \end{DoxyItemize} \end{DoxyItemize} \item \href{../../modules/DataProvider/html/index.html}{\texttt{ Data\+Provider}} module updates\+: \begin{DoxyItemize} \item implemented callbacks to allow for dynamic elements of request-\/response data providers (such as U\+RI paths) to be resolved at runtime (\href{https://github.com/qorelanguage/qore/issues/3838}{\texttt{ issue 3838}}) \item {\ttfamily Abstract\+Data\+Provider\+Type} and {\ttfamily Abstract\+Data\+Field} classes made serializable (\href{https://github.com/qorelanguage/qore/issues/3809}{\texttt{ issue 3809}}) \item implemented the {\ttfamily Data\+Provider\+Type\+Cache} class to encapsulate reusable type caching logic (\href{https://github.com/qorelanguage/qore/issues/3810}{\texttt{ issue 3810}}) \end{DoxyItemize} \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module updates\+: \begin{DoxyItemize} \item added the {\ttfamily ignore\+\_\+missing\+\_\+input} mapper option (\href{https://github.com/qorelanguage/qore/issues/3837}{\texttt{ issue 3837}}) \item added support for the {\ttfamily use\+\_\+input\+\_\+record} output field mapping key (\href{https://github.com/qorelanguage/qore/issues/3823}{\texttt{ issue 3823}}) \end{DoxyItemize} \item \href{../../modules/MapperUtil/html/index.html}{\texttt{ Mapper\+Util}} module updates\+: \begin{DoxyItemize} \item added support for the {\ttfamily use\+\_\+input\+\_\+record} output field mapping key (\href{https://github.com/qorelanguage/qore/issues/3823}{\texttt{ issue 3823}}) \end{DoxyItemize} \item \href{../../modules/reflection/html/index.html}{\texttt{ reflection}} module updates\+: \begin{DoxyItemize} \item {\ttfamily Type} class made serializable (\href{https://github.com/qorelanguage/qore/issues/3810}{\texttt{ issue 3810}}) \end{DoxyItemize} \item new methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a5a665637cd08310c5c4296d0e88a4bb7}{H\+T\+T\+P\+Client\+::get\+Assumed\+Encoding()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_aee4d57e5a86611578ef85c7cd2246092}{H\+T\+T\+P\+Client\+::set\+Assumed\+Encoding()}} \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_0942_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0942_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/DataProvider/html/index.html}{\texttt{ Data\+Provider}} module\+: \begin{DoxyItemize} \item fixed {\ttfamily Abstract\+Data\+Provider\+Type\+::get()} to return the correct type with all string arguments (\href{https://github.com/qorelanguage/qore/issues/3829}{\texttt{ issue 3829}}) \end{DoxyItemize} \item \href{../../modules/DataProvider/html/index.html}{\texttt{ Q\+Unit}} module\+: \begin{DoxyItemize} \item allow Q\+Unit to be used from other languages like Java (\href{https://github.com/qorelanguage/qore/issues/3857}{\texttt{ issue 3857}}) \end{DoxyItemize} \item \href{../../modules/SmtpClient/html/index.html}{\texttt{ Smtp\+Client}} module\+: \begin{DoxyItemize} \item fixed type errors sending mails (\href{https://github.com/qorelanguage/qore/issues/3813}{\texttt{ issue 3813}}) \end{DoxyItemize} \item \href{../../modules/SwaggerDataProvider/html/index.html}{\texttt{ Swagger\+Data\+Provider}} module\+: \begin{DoxyItemize} \item fixed support empty responses (\href{https://github.com/qorelanguage/qore/issues/3801}{\texttt{ issue 3801}}) \end{DoxyItemize} \item \href{../../modules/Swagger/html/index.html}{\texttt{ Swagger}} module\+: \begin{DoxyItemize} \item fixed {\ttfamily date-\/time} value handling (\href{https://github.com/qorelanguage/qore/issues/3847}{\texttt{ issue 3847}}) \item fixed a bug where sibling elements to a {\ttfamily \char`\"{}\$ref\char`\"{}} were not ignored (see \href{https://swagger.io/docs/specification/using-ref}{\texttt{ https\+://swagger.\+io/docs/specification/using-\/ref}}) (\href{https://github.com/qorelanguage/qore/issues/3843}{\texttt{ issue 3843}}) \item fixed support for query parameters of type object (\href{https://github.com/qorelanguage/qore/issues/3799}{\texttt{ issue 3799}}) \end{DoxyItemize} \item \href{../../modules/Util/html/index.html}{\texttt{ Util}} module\+: \begin{DoxyItemize} \item fixed bugs in {\ttfamily E\+V\+AL=} expressions in parse\+\_\+to\+\_\+qore\+\_\+value() where expressions that evaluated to integer 0 or floating-\/point values were returned as \mbox{\hyperlink{basic_data_types_NOTHING}{N\+O\+T\+H\+I\+NG}} (\href{https://github.com/qorelanguage/qore/issues/3851}{\texttt{ issue 3851}}) \end{DoxyItemize} \item fixed a bug where spurious {\ttfamily D\+U\+P\+L\+I\+C\+A\+T\+E-\/\+S\+I\+G\+N\+A\+T\+U\+RE} parse errors were raised with signatures that referred to classes that differed only in their namespace paths (\href{https://github.com/qorelanguage/qore/issues/3861}{\texttt{ issue 3861}}) \item fixed the {\ttfamily Type} object for {\ttfamily \char`\"{}$\ast$hash$<$auto$>$\char`\"{}} to return the correct name (\href{https://github.com/qorelanguage/qore/issues/3826}{\texttt{ issue 3826}}) \item added additional accept and returns keys for base type that accept and return integers; now they return both {\ttfamily int} and {\ttfamily integer} to ensure that they match for logic that does standard comparisons with {\ttfamily \char`\"{}integer\char`\"{}} (\href{https://github.com/qorelanguage/qore/issues/3854}{\texttt{ issue 3854}}) \item fixed certificate verification; openssl will now use default CA certs when \mbox{\hyperlink{class_qore_1_1_socket_aa530d889c522a410e7e5e5163204d1db}{Socket\+::accept\+All\+Certificates(False)}} is set when \mbox{\hyperlink{group__ssl__mode__constants_gae29e3d0203f536c5bf5c0cb225c73c1a}{S\+S\+L\+\_\+\+V\+E\+R\+I\+F\+Y\+\_\+\+P\+E\+ER}} or similar is used with \mbox{\hyperlink{class_qore_1_1_socket_aaafb6b597a1e5b3372d88ea53ea4cbac}{Socket\+::set\+Ssl\+Verify\+Mode()}} (\href{https://github.com/qorelanguage/qore/issues/3818}{\texttt{ issue 3818}}) \item fixed hostname verification in X.\+508 certificate verification (\href{https://github.com/qorelanguage/qore/issues/3808}{\texttt{ issue 3808}}) \item fixed patch version to appear in the Qore version (\href{https://github.com/qorelanguage/qore/issues/3797}{\texttt{ issue 3797}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0941}{}\doxysection{Qore 0.\+9.\+4.\+1}\label{release_notes_qore_0941} \begin{DoxyParagraph}{Release Summary} \end{DoxyParagraph} Bugfix release; see details below\hypertarget{release_notes_qore_0941_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_0941_new_features} \begin{DoxyItemize} \item New \href{../../modules/FileLocationHandler/html/index.html}{\texttt{ File\+Location\+Handler}} module\+: provides an A\+PI for retrieving file data based on a U\+R\+L-\/like location string \end{DoxyItemize}\hypertarget{release_notes_qore_0941_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0941_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/DataProvider/html/index.html}{\texttt{ Data\+Provider}} module\+: \begin{DoxyItemize} \item allow type paths to resolved to internal fields in {\ttfamily Data\+Provider\+::get\+Type()} and {\ttfamily Data\+Provider\+::get\+Type\+Ex()} (\href{https://github.com/qorelanguage/qore/issues/3791}{\texttt{ issue 3791}}) \end{DoxyItemize} \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module\+: \begin{DoxyItemize} \item added the Mapper\+::set\+Nullable\+Output() method and the {\ttfamily output\+\_\+nullable} option (\href{https://github.com/qorelanguage/qore/issues/3788}{\texttt{ issue 3788}}) \end{DoxyItemize} \item \href{../../modules/Swagger/html/index.html}{\texttt{ Swagger}} module\+: \begin{DoxyItemize} \item added support for the {\ttfamily x-\/nullable} attribute to allow for nullable values (\href{https://github.com/qorelanguage/qore/issues/3785}{\texttt{ issue 3785}}) \item fixed support for types with no type declaration (\href{https://github.com/qorelanguage/qore/issues/3775}{\texttt{ issue 3775}}) \end{DoxyItemize} \item \href{../../modules/SwaggerDataProvider/html/index.html}{\texttt{ Swagger\+Data\+Provider}} module\+: \begin{DoxyItemize} \item fixed support for requests that do not require a request hash (\href{https://github.com/qorelanguage/qore/issues/3784}{\texttt{ issue 3784}}) \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_094}{}\doxysection{Qore 0.\+9.\+4}\label{release_notes_qore_094} \begin{DoxyParagraph}{Release Summary} The main new feature in this release is the \href{../../modules/DataProvider/html/index.html}{\texttt{ Data\+Provider}} A\+PI, which provides a generic A\+PI for introspecting and manipulating data in any format and over any protocol. Qore 0.\+9.\+4 also contains many usability and consistency fixes as well. \end{DoxyParagraph} \hypertarget{release_notes_qore_094_compatibility}{}\doxysubsection{Fixes That Can Affect Backwards-\/\+Compatibility}\label{release_notes_qore_094_compatibility} \begin{DoxyItemize} \item \href{../../modules/RestHandler/html/index.html}{\texttt{ Rest\+Handler}} module\+: renamed {\ttfamily Rest\+Handler\+::get\+Possible\+Sub\+Classes()} to {\ttfamily Rest\+Handler\+::do\+Get\+Possible\+Sub\+Classes()} in order to avoid a collision with a R\+E\+ST method name (\href{https://github.com/qorelanguage/qore/issues/3614}{\texttt{ issue 3614}}) \item fixed broken \mbox{\hyperlink{operators_cast}{cast$<$$>$}} operator handling; in previous releases, \mbox{\hyperlink{operators_cast}{cast$<$$>$}} would accept and return \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} without raising an error with type specifications that did not accept or return \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}}. To get the old behavior, use the \mbox{\hyperlink{parse_directives_broken-cast}{\%broken-\/cast}} parse directive. \item disallowed the use of the deprecated {\ttfamily returns} keyword by default. To get the old behavior, use the \mbox{\hyperlink{parse_directives_allow-returns}{\%allow-\/returns}} parse directive. \item classes inheriting {\ttfamily Abstract\+Connection} must be serializable; the {\ttfamily Abstract\+Connection\+::get\+Constructor\+Info()} and {\ttfamily Abstract\+Connection\+::get\+Constructor\+Info\+Impl()} methods have been removed and are ignored in child classes \item the following are now reserved words in \mbox{\hyperlink{namespace_qore}{Qore}} to prohibit them from being redefined\+: \begin{DoxyItemize} \item \mbox{\hyperlink{basic_data_types_NULL}{N\+U\+LL}} \item \mbox{\hyperlink{basic_data_types_NOTHING}{N\+O\+T\+H\+I\+NG}} \item \mbox{\hyperlink{basic_data_types_True}{True}} \item \mbox{\hyperlink{basic_data_types_False}{False}} \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_094_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_094_new_features} \begin{DoxyItemize} \item \href{../../modules/ConnectionProvider/html/index.html}{\texttt{ Connection\+Provider}} module\+: \begin{DoxyItemize} \item implemented support for serializing connections (\href{https://github.com/qorelanguage/qore/issues/3696}{\texttt{ issue 3696}}) \end{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module\+: \begin{DoxyItemize} \item adds \href{../../modules/DataProvider/html/index.html}{\texttt{ data provider}} A\+PI support \end{DoxyItemize} \item \href{../../modules/DataProvider/html/index.html}{\texttt{ Data\+Provider}} module\+: \begin{DoxyItemize} \item supports arbitrary data inputs and outputs with introspection and strong type support \end{DoxyItemize} \item \href{../../modules/DbDataProvider/html/index.html}{\texttt{ Db\+Data\+Provider}} module\+: \begin{DoxyItemize} \item adds a data provider A\+PI for databases \end{DoxyItemize} \item \href{../../modules/FixedLengthUtil/html/index.html}{\texttt{ Fixed\+Length\+Util}} module\+: \begin{DoxyItemize} \item adds \href{../../modules/DataProvider/html/index.html}{\texttt{ data provider}} A\+PI support \end{DoxyItemize} \item \href{../../modules/FtpPoller/html/index.html}{\texttt{ Ftp\+Poller}} module\+: \begin{DoxyItemize} \item added this new module to support polling files from a remote directory with the F\+TP protocol \end{DoxyItemize} \item \href{../../modules/FtpPollerUtil/html/index.html}{\texttt{ Ftp\+Poller\+Util}} module\+: \begin{DoxyItemize} \item added this new module to provide definitions for the \href{../../modules/FtpPoller/html/index.html}{\texttt{ Ftp\+Poller}} module \end{DoxyItemize} \item \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module\+: \begin{DoxyItemize} \item added support for sending chunked replies from an \mbox{\hyperlink{class_qore_1_1_input_stream}{Input\+Stream}} \end{DoxyItemize} \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module\+: \begin{DoxyItemize} \item adds \href{../../modules/DataProvider/html/index.html}{\texttt{ data provider}} A\+PI support \end{DoxyItemize} \item \href{../../modules/SalesforceRestDataProvider/html/index.html}{\texttt{ Salesforce\+Rest\+Data\+Provider}} module\+: \begin{DoxyItemize} \item adds a data provider A\+PI for Salesforce R\+E\+ST connections \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}}\+: \begin{DoxyItemize} \item adds infrastructure support for the \href{../../modules/DataProvider/html/index.html}{\texttt{ data provider}} module \item implemented the {\ttfamily op\+\_\+in\+\_\+select()} function for where\+\_\+clauses \end{DoxyItemize} \item \href{../../modules/SwaggerDataProvider/html/index.html}{\texttt{ Swagger\+Data\+Provider}} module\+: \begin{DoxyItemize} \item adds a data provider A\+PI for Swagger / Open\+A\+PI schemas \end{DoxyItemize} \item support for Unicode character matching in regular expressions\+: \begin{DoxyItemize} \item the {\ttfamily {\ttfamily /u}} option in \mbox{\hyperlink{qore_regex_qore_regex_options}{Qore Regular Expression Operator Options}} \item the \mbox{\hyperlink{group__regex__constants_ga21b62f0275713de5c68a338bc9102f11}{R\+E\+\_\+\+Unicode}} constant \item the {\ttfamily \char`\"{}\%w\char`\"{}} string format code that uses character widths with field widths (ex\+: {\ttfamily \char`\"{}\%5w\char`\"{}} specifies a field 5 characters wide; see \mbox{\hyperlink{group__string__functions_format_specification}{String Format Specification}} for more information) \end{DoxyItemize} \item new constants\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__event__constants_ga093cec6d88a60023236594cac4d5b19c}{E\+V\+E\+N\+T\+\_\+\+H\+T\+T\+P\+\_\+\+C\+H\+U\+N\+K\+E\+D\+\_\+\+D\+A\+T\+A\+\_\+\+R\+E\+AD}} \item \mbox{\hyperlink{group__event__constants_ga5ee5ae9464e8c883fb037cfe08631b47}{E\+V\+E\+N\+T\+\_\+\+H\+T\+T\+P\+\_\+\+C\+H\+U\+N\+K\+E\+D\+\_\+\+D\+A\+T\+A\+\_\+\+S\+E\+NT}} \item \mbox{\hyperlink{group__event__constants_ga6d61f2f6079e62adc313fb3bf4c0c414}{E\+V\+E\+N\+T\+\_\+\+H\+T\+T\+P\+\_\+\+C\+H\+U\+N\+K\+E\+D\+\_\+\+F\+O\+O\+T\+E\+R\+S\+\_\+\+S\+E\+NT}} \item \mbox{\hyperlink{group__event__constants_gac180096573633537266011b54a4eb7c2}{E\+V\+E\+N\+T\+\_\+\+H\+T\+T\+P\+\_\+\+H\+E\+A\+D\+E\+R\+S\+\_\+\+R\+E\+AD}} \item \mbox{\hyperlink{group__event__constants_ga895ad2bb875777a11a0a7613494ab791}{E\+V\+E\+N\+T\+\_\+\+S\+O\+C\+K\+E\+T\+\_\+\+D\+A\+T\+A\+\_\+\+R\+E\+AD}} \item \mbox{\hyperlink{group__event__constants_gaf1b9c3c3f5dd24192e021b178fabccb9}{E\+V\+E\+N\+T\+\_\+\+S\+O\+C\+K\+E\+T\+\_\+\+D\+A\+T\+A\+\_\+\+S\+E\+NT}} \item \mbox{\hyperlink{group__type__code__constants_ga87b893b75b8d54179ca75bb34539ccec}{N\+T\+\_\+\+A\+LL}} \item \mbox{\hyperlink{group__regex__constants_ga21b62f0275713de5c68a338bc9102f11}{R\+E\+\_\+\+Unicode}} \item \mbox{\hyperlink{group__parse__options_ga740012ab51f05f39efc31eab365138e8}{P\+O\+\_\+\+A\+L\+L\+O\+W\+\_\+\+R\+E\+T\+U\+R\+NS}} \item \mbox{\hyperlink{group__parse__options_gaad25cc6a2b8ede564839d12622d90398}{P\+O\+\_\+\+B\+R\+O\+K\+E\+N\+\_\+\+C\+A\+ST}} \item \mbox{\hyperlink{group__parse__options_ga6faa558bfb68cd290e785653e24525de}{P\+O\+\_\+\+S\+T\+R\+I\+C\+T\+\_\+\+T\+Y\+P\+ES}} \end{DoxyItemize} \item new pseudo-\/methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8objectzzz9_a1d67fa79b6676b3dcb9eaf088bbb2d4e}{Qore\+::zzz8objectzzz9\+::get\+Call\+Reference()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a2bed0246b3ce9aebf17d5d2ee29d51f3}{Qore\+::zzz8stringzzz9\+::width()}} \end{DoxyItemize} \item pseudo-\/methods now run in the same class context as the caller \item new functions \begin{DoxyItemize} \item \mbox{\hyperlink{group__string__functions_ga3fcd81fc200908f483d2dc90f8431930}{Qore\+::char\+\_\+width()}} \item \mbox{\hyperlink{group__misc__functions_ga6b730c0585f1fe62929d6877c32ee0c7}{Qore\+::get\+\_\+call\+\_\+reference()}} \end{DoxyItemize} \item new methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_ftp_client_a39423f304cf2777d89ba866dc3de5181}{Ftp\+Client\+::send\+Control\+Message()}} \item \mbox{\hyperlink{class_qore_1_1_program_aea73d2c2b293387b51fbb5de782b7a7c}{Program\+::get\+Call\+Reference()}} \end{DoxyItemize} \item updated methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_input_stream_afa843e81a854eeb13f215a76da80cea4}{Binary\+Input\+Stream\+::constructor()}} accepts strings as well as binary values \item \mbox{\hyperlink{class_qore_1_1_ftp_client_a8e7b3685bc3ac840bf64896f7d1868c3}{Ftp\+Client\+::set\+Control\+Event\+Queue()}}\+: added the {\itshape arg} and {\itshape with\+\_\+data} options \item \mbox{\hyperlink{class_qore_1_1_ftp_client_a653ffafc1bd4b8da05f9ce18cc7fe854}{Ftp\+Client\+::set\+Data\+Event\+Queue()}}\+: added the {\itshape arg} and {\itshape with\+\_\+data} options \item \mbox{\hyperlink{class_qore_1_1_ftp_client_a105c9076a7dd0e0cd58b0a562545cb77}{Ftp\+Client\+::set\+Event\+Queue()}}\+: added the {\itshape arg} and {\itshape with\+\_\+data} options \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_af48e59604f6e7da844c79ac958b45f6a}{H\+T\+T\+P\+Client\+::set\+Event\+Queue()}}\+: added the {\itshape arg} and {\itshape with\+\_\+data} options \item \mbox{\hyperlink{class_qore_1_1_program_a300ffe0abd0b09cc39feb637a9bab9ba}{Program\+::load\+Apply\+To\+User\+Module()}}\+: added the {\itshape reexport} argument \item \mbox{\hyperlink{class_qore_1_1_program_ae5534c8443a553834b352b7d62a78ca3}{Program\+::load\+Apply\+To\+User\+Module\+Warn()}}\+: added the {\itshape reexport} argument \item \mbox{\hyperlink{class_qore_1_1_read_only_file_a44207327eadce535f46cbfcba1bff28a}{Read\+Only\+File\+::set\+Event\+Queue()}}\+: added the {\itshape arg} and {\itshape with\+\_\+data} options \item \mbox{\hyperlink{class_qore_1_1_socket_ad1259b25b8b8533d042a1f7bc29894b1}{Socket\+::set\+Event\+Queue()}}\+: added the {\itshape arg} and {\itshape with\+\_\+data} options \end{DoxyItemize} \item new parse options\+: \begin{DoxyItemize} \item \mbox{\hyperlink{parse_directives_allow-returns}{\%allow-\/returns}} \item \mbox{\hyperlink{parse_directives_broken-cast}{\%broken-\/cast}} \item \mbox{\hyperlink{parse_directives_loose-types}{\%loose-\/types}} \item \mbox{\hyperlink{parse_directives_strict-types}{\%strict-\/types}} \end{DoxyItemize} \item \href{../../modules/reflection/html/index.html}{\texttt{ reflection}} module updates\+: \begin{DoxyItemize} \item added {\ttfamily Type\+::is\+Assignable\+From()} methods \item added a working {\ttfamily Type\+::constructor()} method \item added {\ttfamily Type\+::get\+Accept\+Type\+Hash()} \item added {\ttfamily Type\+::get\+Base\+Type()} \item added {\ttfamily Type\+::get\+Base\+Type\+Code()} \item added {\ttfamily Type\+::get\+Element\+Type()} \item added {\ttfamily Type\+::get\+Return\+Type\+Hash()} \item added {\ttfamily Type\+::get\+Typed\+Hash()} \item added {\ttfamily Type\+::has\+Type()} \item added {\ttfamily Type\+::is\+Compatible()} \item added {\ttfamily Type\+::is\+Or\+Nothing\+Type()} \item added {\ttfamily Type\+::is\+Typed\+Hash()} \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_094_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_094_bug_fixes} \begin{DoxyItemize} \item fixes in modules\+: \begin{DoxyItemize} \item \href{../../modules/HttpServerUtil/html/index.html}{\texttt{ Http\+Server\+Util}} and \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}}\+: \begin{DoxyItemize} \item fixed the version number reported by the server \end{DoxyItemize} \item \href{../../modules/MysqlSqlUtil/html/index.html}{\texttt{ Mysql\+Sql\+Util}}\+: \begin{DoxyItemize} \item fixed a bug where the table collation could not be specified (\href{https://github.com/qorelanguage/qore/issues/3752}{\texttt{ issue 3752}}) \item fixed quoting reserved words with backticks (\href{https://github.com/qorelanguage/qore/issues/3750}{\texttt{ issue 3750}}) \end{DoxyItemize} \item \href{../../modules/Swagger/html/index.html}{\texttt{ Swagger}}\+: \begin{DoxyItemize} \item fixed support for additional Y\+A\+ML M\+I\+ME types (\href{https://github.com/qorelanguage/qore/issues/3699}{\texttt{ issue 3699}}) \item fixed a bug resolving out of order definitions (\href{https://github.com/qorelanguage/qore/issues/3694}{\texttt{ issue 3694}}) \item fixed a bug handling {\ttfamily form\+Data} elements (\href{https://github.com/qorelanguage/qore/issues/3692}{\texttt{ issue 3692}}) \end{DoxyItemize} \end{DoxyItemize} \item the default exception handler now shows the exception {\ttfamily \char`\"{}arg\char`\"{}} key exceptions in builtin code if present (\href{https://github.com/qorelanguage/qore/issues/3768}{\texttt{ issue 3768}}) \item fixed reporting the exception location when exceptions occur in builtin code (\href{https://github.com/qorelanguage/qore/issues/3742}{\texttt{ issue 3742}}) \item fixed type handling in list and hash evaluation with complex types that can only be determined at runtime (\href{https://github.com/qorelanguage/qore/issues/3740}{\texttt{ issue 3740}}) \item fixed setting the time zone region in date/time values to not include the system-\/specific zoneinfo path prefix in order to allow for deserialization of date/time values on different systems (\href{https://github.com/qorelanguage/qore/issues/3736}{\texttt{ issue 3736}}) \item fixed a crash in parse error handling for recursive constant parse hash resolution cases (\href{https://github.com/qorelanguage/qore/issues/3708}{\texttt{ issue 3708}}) \item fixed a bug retrieving H\+T\+TP message bodies with servers that do not send a {\ttfamily Content-\/\+Length} header but close the connection (\href{https://github.com/qorelanguage/qore/issues/3691}{\texttt{ issue 3691}}) \item fixed inconsistent handling of the \mbox{\hyperlink{operators_plus_equals_operator}{+= operator}} with \mbox{\hyperlink{data_type_declarations_list_or_nothing_type}{$\ast$list$<$...$>$}} types with element types (\href{https://github.com/qorelanguage/qore/issues/3586}{\texttt{ issue 3586}}) \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a34c43c49f859529054ef495eb395e6bb}{Qore\+::zzz8stringzzz9\+::split(string, string, bool)}} and \mbox{\hyperlink{group__string__functions_gad3db83c0fd5df500b0cc9d2ddb0e7d85}{Qore\+::split(string, string, string, bool)}} now properly handle double quote characters as an alternative way to include quotes in fields (\href{https://github.com/qorelanguage/qore/issues/3550}{\texttt{ issue 3550}}) \item the \mbox{\hyperlink{operators_cast}{cast$<$$>$}} operator can now cast directly to \char`\"{}or nothing\char`\"{} types\+: ex\+: \begin{DoxyCode}{0} \DoxyCodeLine{list<int> l = cast<list<int>>(getList()); } \end{DoxyCode} (\href{https://github.com/qorelanguage/qore/issues/3331}{\texttt{ issue 3331}}) \item fixed detecting invalid input in \mbox{\hyperlink{group__date__and__time__functions_gaa990826f93b4f22f786fcfe431c4886d}{date(string, string)}} (\href{https://github.com/qorelanguage/qore/issues/3239}{\texttt{ issue 3239}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0933}{}\doxysection{Qore 0.\+9.\+3.\+3}\label{release_notes_qore_0933} \begin{DoxyParagraph}{Release Summary} \end{DoxyParagraph} Bugfix release; see details below\hypertarget{release_notes_qore_0933_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0933_bug_fixes} \begin{DoxyItemize} \item fixed a bug where a crash would result when calling \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_a34834d2da5e1e8f13949810e76a6e1cd}{Datasource\+::get\+Option()}} when the connection was closed (\href{https://github.com/qorelanguage/qore/issues/3754}{\texttt{ issue 3754}}) \item \href{../../modules/MysqlSqlUtil/html/index.html}{\texttt{ Mysql\+Sql\+Util}} module fix\+: updated to work also with newer versions of My\+S\+QL / Maria\+DB that support sequences (\href{https://github.com/qorelanguage/qore/issues/3747}{\texttt{ issue 3747}}) \item fixed a bug where the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource}{Datasource}} class would not always remove the transaction thread resource when rolling back transactions (\href{https://github.com/qorelanguage/qore/issues/3745}{\texttt{ issue 3745}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0932}{}\doxysection{Qore 0.\+9.\+3.\+2}\label{release_notes_qore_0932} \begin{DoxyParagraph}{Release Summary} \end{DoxyParagraph} Bugfix release; see details below\hypertarget{release_notes_qore_0932_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_0932_new_features} \begin{DoxyItemize} \item the \href{../../modules/Sap4HanaRestClient/html/index.html}{\texttt{ Sap4\+Hana\+Rest\+Client}} module was added (\href{https://github.com/qorelanguage/qore/issues/3600}{\texttt{ issue 3600}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0932_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0932_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/RestHandler/html/index.html}{\texttt{ Rest\+Handler}}\+: fixed a bug handling exceptions in R\+E\+ST methods with unserializable exception data (\href{https://github.com/qorelanguage/qore/issues/3667}{\texttt{ issue 3667}}) \item fixed a bug in hashdecl member initialization in constants (\href{https://github.com/qorelanguage/qore/issues/3654}{\texttt{ issue 3654}}) \item fixed a bug in type handling that could cause a runtime crash (\href{https://github.com/qorelanguage/qore/issues/3644}{\texttt{ issue 3644}}) \item \href{../../modules/MysqlSqlUtil/html/index.html}{\texttt{ Mysql\+Sql\+Util}}\+: fixed a bug where the sequence table name was not respected in {\ttfamily Mysql\+Database\+::get\+Next\+Sequence\+Value\+Impl()} (\href{https://github.com/qorelanguage/qore/issues/3641}{\texttt{ issue 3641}}) \item \href{../../modules/Schema/html/index.html}{\texttt{ Schema}}\+: fixed a bug where too little information was passed to post schema alignment code (\href{https://github.com/qorelanguage/qore/issues/3640}{\texttt{ issue 3640}}) \item fixed a bug where in-\/object calls to implicit {\ttfamily copy()} methods would result in a core dump (\href{https://github.com/qorelanguage/qore/issues/3637}{\texttt{ issue 3637}}) \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module\+: fixed a bug where list values could not be passed as a value in non-\/bulk mode (\href{https://github.com/qorelanguage/qore/issues/3611}{\texttt{ issue 3611}}) \item fixed an error with runtime method call resolution with {\bfseries{{\ttfamily private\+:internal}}} methods (\href{https://github.com/qorelanguage/qore/issues/3596}{\texttt{ issue 3596}}) \item \href{../../modules/PgsqlSqlUtil/html/index.html}{\texttt{ Pgsql\+Sql\+Util}} module\+: fixed compatibility with Postgre\+S\+QL 12 (\href{https://github.com/qorelanguage/qore/issues/3589}{\texttt{ issue 3589}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0931}{}\doxysection{Qore 0.\+9.\+3.\+1}\label{release_notes_qore_0931} \begin{DoxyParagraph}{Release Summary} \end{DoxyParagraph} Bugfix release; see details below\hypertarget{release_notes_qore_0931_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0931_bug_fixes} \begin{DoxyItemize} \item fixed a critical error handling thread resources where if an exception was thrown handling thread resources, user thread resource handlers queued afterwards were not executed (\href{https://github.com/qorelanguage/qore/issues/3571}{\texttt{ issue 3571}}) \item fixed a crash handling recursive user module dependencies with directory-\/based (split) user modules (\href{https://github.com/qorelanguage/qore/issues/3570}{\texttt{ issue 3570}}) \item fixed an error handling aborted chunked H\+T\+TP transfers that can result in a long timeout stalling the I/O thread (\href{https://github.com/qorelanguage/qore/issues/3564}{\texttt{ issue 3564}}) \item added library option constants and functions to allow the T\+LS v1.\+3 protocol to be disabled when the library is initialized or at runtime (\href{https://github.com/qorelanguage/qore/issues/3561}{\texttt{ issue 3561}}) \item fixed a bug where different connections on the same \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} object could not be identified; code that relied on \mbox{\hyperlink{class_qore_1_1_socket_a287387be61ed857ad44f9fa79ad4292c}{Socket\+::get\+Socket()}} is unreliable as the same descriptor can be reassigned (\href{https://github.com/qorelanguage/qore/issues/3558}{\texttt{ issue 3558}}) \item fixed a core dump in \mbox{\hyperlink{class_qore_1_1_file_line_iterator_a06a105043332a4c4ff52a3c2d3bcc163}{File\+Line\+Iterator\+::get\+File\+Name()}} (\href{https://github.com/qorelanguage/qore/issues/3555}{\texttt{ issue 3555}}) \item fixed a race condition in thread resource cleanups where a spurious exception could be raised (\href{https://github.com/qorelanguage/qore/issues/3551}{\texttt{ issue 3551}}) \item \href{../../modules/RestSchemaValidator/html/index.html}{\texttt{ Rest\+Schema\+Validator}}\+: fixed a bug where R\+E\+ST serialization errors in server responses were ignored and a {\ttfamily 200 OK} response was sent instead (\href{https://github.com/qorelanguage/qore/issues/3547}{\texttt{ issue 3547}}) \item fixed a bug where false positive parse-\/time matches with a complex list or hash type could be made with incompatible types (\href{https://github.com/qorelanguage/qore/issues/3546}{\texttt{ issue 3546}}) \item \href{../../modules/astparser/html/index.html}{\texttt{ astparser}} module\+: \begin{DoxyItemize} \item fixed memory leaks in astparser module (\href{https://github.com/qorelanguage/qore/issues/3344}{\texttt{ issue 3344}}) \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_093}{}\doxysection{Qore 0.\+9.\+3}\label{release_notes_qore_093} \begin{DoxyParagraph}{Release Summary} \end{DoxyParagraph} Bugfix release; see details below\hypertarget{release_notes_qore_093_compatibility}{}\doxysubsection{Fixes That Can Affect Backwards-\/\+Compatibility}\label{release_notes_qore_093_compatibility} Complex type fixes in this release have the effect that complex type declarations are not exactly equal to the base types without a complex type restrictions, and also abstract argument type matching with concrete implementations has been loosened to accept nearly identical matches, so that for example an abstract method may declare a parameter with a {\ttfamily hash$<$auto$>$} type which may be implemented by a concrete method with type {\ttfamily hash}.\hypertarget{release_notes_qore_093_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_093_new_features} \begin{DoxyItemize} \item the \href{../../modules/ConnectionProvider/html/index.html}{\texttt{ Connection\+Provider}} module was updated to support connection tags (\href{https://github.com/qorelanguage/qore/issues/3486}{\texttt{ issue 3486}}) \item updated the \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client}{H\+T\+T\+P\+Client}} class to support the following new constructor options\+: \begin{DoxyItemize} \item {\ttfamily encoding\+\_\+passthru} \item {\ttfamily error\+\_\+passthru} \item {\ttfamily redirect\+\_\+passthru} as well as the {\ttfamily \char`\"{}response-\/headers-\/raw\char`\"{}} output info key, plus the following methods\+: \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a00ba9d3416ca2c73444ab2b585a3e53f}{H\+T\+T\+P\+Client\+::get\+Host\+Header\+Value()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a022d5d67e51ad2d2742e8f43f02f5dce}{H\+T\+T\+P\+Client\+::get\+Encoding\+Passthru()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a50b0c1fe246fe6f0d2a61bcf7f304cac}{H\+T\+T\+P\+Client\+::set\+Encoding\+Passthru()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a6cdbac64375086f309b6d2737721814a}{H\+T\+T\+P\+Client\+::get\+Error\+Passthru()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a178a903d388dbf76e78df59c3fc8cfc8}{H\+T\+T\+P\+Client\+::set\+Error\+Passthru()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_ae0c812e5462014718091864a8d9ad07c}{H\+T\+T\+P\+Client\+::get\+Redirect\+Passthru()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_aef3874b2cf110ccc2e15ce0f79071962}{H\+T\+T\+P\+Client\+::set\+Redirect\+Passthru()}} \end{DoxyItemize}(\href{https://github.com/qorelanguage/qore/issues/3472}{\texttt{ issue 3472}}) \item added the following methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_get_opt_a54a3b13b00dd1a95f525f03409bca8ee}{Get\+Opt\+::parse(hash$<$auto$>$, reference$<$list$<$string$>$$>$)}} \item \mbox{\hyperlink{class_qore_1_1_get_opt_a0623e1c6ad888a7b1ecba22cf9da1db9}{Get\+Opt\+::parse\+Ex(hash$<$auto$>$, reference$<$list$<$string$>$$>$)}} \item \mbox{\hyperlink{class_qore_1_1_get_opt_ac7c14bec422068688736aac2557e427b}{Get\+Opt\+::parse\+Exit(hash$<$auto$>$, reference$<$list$<$string$>$$>$)}} \item \mbox{\hyperlink{class_qore_1_1_socket_a71487cf967828b884ba41ad30ff4bda1}{Socket\+::get\+Remote\+Certificate()}} \end{DoxyItemize} \item added the following new functions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__type__conversion__functions_ga538c7c66624fd35b37a74108be62a04e}{auto\+\_\+cast()}} \item \mbox{\hyperlink{group__hmac__functions_gaefc09e78e7bccccf7bc3629e4e86c9e2}{digest()}} \item \mbox{\hyperlink{group__hmac__functions_ga227c4f084f2cffee4c466989d68a1fe3}{get\+\_\+digests()}} \item \mbox{\hyperlink{group__hmac__functions_gaf88021aec5a7048984b0a0e5ce21733d}{hmac()}} \end{DoxyItemize} \item added the following new constants\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__digest__algorithms_ga08088b7c0d1162c80782a6dbd8fa05a7}{Digest\+Map}} \item \mbox{\hyperlink{group__digest__algorithms_ga5ae4457b5e78d3913a5f1c9c0c3db66c}{C\+R\+Y\+P\+T\+O\+\_\+\+D\+I\+G\+E\+S\+T\+\_\+\+M\+D2}} \item \mbox{\hyperlink{group__digest__algorithms_gaa7373cfba42ce06748fea2455e63e70a}{C\+R\+Y\+P\+T\+O\+\_\+\+D\+I\+G\+E\+S\+T\+\_\+\+M\+D4}} \item \mbox{\hyperlink{group__digest__algorithms_gaf41b0d17486bbcc917ec447540cf8785}{C\+R\+Y\+P\+T\+O\+\_\+\+D\+I\+G\+E\+S\+T\+\_\+\+M\+D5}} \item \mbox{\hyperlink{group__digest__algorithms_gaf0156e70f3e7dc7edf5804ef32b455f4}{C\+R\+Y\+P\+T\+O\+\_\+\+D\+I\+G\+E\+S\+T\+\_\+\+S\+HA}} \item \mbox{\hyperlink{group__digest__algorithms_ga4860ea19cda90914fe06346d12db9564}{C\+R\+Y\+P\+T\+O\+\_\+\+D\+I\+G\+E\+S\+T\+\_\+\+S\+H\+A1}} \item \mbox{\hyperlink{group__digest__algorithms_ga1be49f7eeacfce675bc0551f89248789}{C\+R\+Y\+P\+T\+O\+\_\+\+D\+I\+G\+E\+S\+T\+\_\+\+S\+H\+A224}} \item \mbox{\hyperlink{group__digest__algorithms_ga9b747da4eed94175c0844cc3a2cea4aa}{C\+R\+Y\+P\+T\+O\+\_\+\+D\+I\+G\+E\+S\+T\+\_\+\+S\+H\+A256}} \item \mbox{\hyperlink{group__digest__algorithms_ga06fb50eb1917c154217dfa19f56cb258}{C\+R\+Y\+P\+T\+O\+\_\+\+D\+I\+G\+E\+S\+T\+\_\+\+S\+H\+A384}} \item \mbox{\hyperlink{group__digest__algorithms_ga6ed1d1807fe333274bd5781f8f6923bc}{C\+R\+Y\+P\+T\+O\+\_\+\+D\+I\+G\+E\+S\+T\+\_\+\+S\+H\+A512}} \item \mbox{\hyperlink{group__digest__algorithms_ga84e4167bc334d99becf32a4c9297ef8b}{C\+R\+Y\+P\+T\+O\+\_\+\+D\+I\+G\+E\+S\+T\+\_\+\+D\+SS}} \item \mbox{\hyperlink{group__digest__algorithms_gad9807282c7a2d251c33ab3fa8e4cbcee}{C\+R\+Y\+P\+T\+O\+\_\+\+D\+I\+G\+E\+S\+T\+\_\+\+D\+S\+S1}} \item \mbox{\hyperlink{group__digest__algorithms_ga96568e3ff1e16cf6fe1c924c3a5af70b}{C\+R\+Y\+P\+T\+O\+\_\+\+D\+I\+G\+E\+S\+T\+\_\+\+M\+D\+C2}} \item \mbox{\hyperlink{group__digest__algorithms_ga9658d092ce4ee79653f45292dc47964f}{C\+R\+Y\+P\+T\+O\+\_\+\+D\+I\+G\+E\+S\+T\+\_\+\+R\+I\+P\+E\+M\+D160}} \end{DoxyItemize} \item added the \mbox{\hyperlink{struct_qore_1_1_url_info}{Qore\+::\+Url\+Info}} hash as the return type to\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__misc__functions_ga54e6ccaa8fdaa3213ae5550aa66629c9}{parse\+\_\+url()}} \item \mbox{\hyperlink{group__misc__functions_gae1961be84af7e6bc5553049bf978f922}{parse\+U\+RL()}} \end{DoxyItemize} \item added the {\itshape module\+\_\+visibility} parameter to \mbox{\hyperlink{class_qore_1_1_program_abf634534cb29157d05aab5ff3ffd6bea}{Program\+::import\+Class()}} and the \mbox{\hyperlink{group__import__visibility__constants}{Import Visibility Constants}} as possible argument values \item added the {\itshape max\+\_\+file\+\_\+len} param to \mbox{\hyperlink{class_qore_1_1_read_only_file_a41a3763d813c0b7d41eec553819e1354}{Read\+Only\+File\+::read\+Text\+File()}} and \mbox{\hyperlink{class_qore_1_1_read_only_file_a149f83530ad4d521af205a711253662c}{Read\+Only\+File\+::read\+Binary\+File()}} (\href{https://github.com/qorelanguage/qore/issues/3525}{\texttt{ issue 3525}}) \item added \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a825e0531419ae8abce66288e9d5ea4b1}{Qore\+::zzz8stringzzz9\+::to\+Binary()}} \item added the \href{../../modules/AwsRestClient/html/index.html}{\texttt{ Aws\+Rest\+Client}} module \item the \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module was updated to enable remote certificates to be retrieved in listeners and handlers by default; added new A\+PI entry points for listeners and handlers with more flexible and saner parameters, deprecated old complex methods (\href{https://github.com/qorelanguage/qore/issues/3512}{\texttt{ issue 3512}}) \item the \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module now supports the {\ttfamily \char`\"{}runtime\+\_\+keys\char`\"{}} option for adding support for new field keys to existing classes (\href{https://github.com/qorelanguage/qore/issues/3535}{\texttt{ issue 3535}}) \item the \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module now supports {\ttfamily \char`\"{}hash\char`\"{}} and {\ttfamily \char`\"{}any\char`\"{}} types for output fields (\href{https://github.com/qorelanguage/qore/issues/3453}{\texttt{ issue 3453}}) \item the \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module now supports dot notation in output fields for the \char`\"{}hash\char`\"{} output type (\href{https://github.com/qorelanguage/qore/issues/3413}{\texttt{ issue 3413}}) \item the \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module was updated so that {\ttfamily Rest\+Connection} objects now support the {\ttfamily \char`\"{}headers\char`\"{}} option (\href{https://github.com/qorelanguage/qore/issues/3455}{\texttt{ issue 3455}}) \item {\ttfamily qdbg-\/vsc-\/adapter} supports the V\+S\+Code Debug Protocol (\href{https://github.com/qorelanguage/qore/issues/3392}{\texttt{ issue 3392}}) \end{DoxyItemize}\hypertarget{release_notes_qore_093_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_093_bug_fixes} \begin{DoxyItemize} \item fixed bugs in handling object members assigned to references (\href{https://github.com/qorelanguage/qore/issues/3523}{\texttt{ issue 3523}}) \item fixed bugs in thread-\/local variable handling and Program destruction (\href{https://github.com/qorelanguage/qore/issues/3521}{\texttt{ issue 3521}}) \item fixed a bug where a crash would result when serializing imported typed hashes (\href{https://github.com/qorelanguage/qore/issues/3518}{\texttt{ issue 3518}}) \item fixed a bug where attempting to serialize a weak references to a serializable object would result in an exception (\href{https://github.com/qorelanguage/qore/issues/3515}{\texttt{ issue 3515}}) \item fixed a bug where new \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} connections were left in place when calls to \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a04c351f440ddfdbe79f9b4ef26608e6f}{Datasource\+Pool\+::begin\+Transaction()}} would fail with an exception (\href{https://github.com/qorelanguage/qore/issues/3509}{\texttt{ issue 3509}}) \item fixed bugs importing user modules with an injected A\+PI in an existing \mbox{\hyperlink{class_qore_1_1_program}{Program}} container (\href{https://github.com/qorelanguage/qore/issues/3504}{\texttt{ issue 3504}}) \item fixed a memory leak in \mbox{\hyperlink{class_qore_1_1_serializable_aa2aa4a161c1857ef601bb31ea186a443}{Serializable\+::deserialize(string)}} \item fixed a memory leak (crash in debug mode) related to \mbox{\hyperlink{container_data_types_garbage_collection}{deterministic garbage collection}} (\href{https://github.com/qorelanguage/qore/issues/3481}{\texttt{ issue 3481}}) \item fixed a bug where H\+T\+TP redirect messages with a simple path and not a full U\+RL were not processed correctly (\href{https://github.com/qorelanguage/qore/issues/3475}{\texttt{ issue 3475}}) \item fixed a bug where H\+T\+TP connections with U\+N\+IX domain sockets were sending an incorrect {\ttfamily Host\+:} header without U\+RL encoding (\href{https://github.com/qorelanguage/qore/issues/3474}{\texttt{ issue 3474}}) \item fixed bugs affecting injection and \mbox{\hyperlink{class_qore_1_1_program}{Program}} A\+PI management (\href{https://github.com/qorelanguage/qore/issues/3461}{\texttt{ issue 3461}}) \item fixed a bug where a {\ttfamily \textquotesingle{}/\textquotesingle{}} character in an H\+T\+TP username would cause a U\+RL to be parsed incorrectly (\href{https://github.com/qorelanguage/qore/issues/3457}{\texttt{ issue 3457}}) \item added optional flags to the following methods to allow them to open file streams in nonblocking mode to handle opening named pipes independently of the writer without blocking\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_input_stream_afa843e81a854eeb13f215a76da80cea4}{File\+Input\+Stream\+::constructor()}} \item \mbox{\hyperlink{class_qore_1_1_file_line_iterator_abf669d5c3e7bbfa809b22c930ea237d8}{File\+Line\+Iterator\+::constructor()}} \end{DoxyItemize}(\href{https://github.com/qorelanguage/qore/issues/3451}{\texttt{ issue 3451}}) \item fixed a bug compiling with openssl with the M\+D\+C2 algorithm disabled (\href{https://github.com/qorelanguage/qore/issues/3443}{\texttt{ issue 3443}}) \item fixed a confusing error message with runtime overload type errors where complex type information was missing (\href{https://github.com/qorelanguage/qore/issues/3441}{\texttt{ issue 3441}}) \item fixed parse-\/time error handling complex types in hashes (\href{https://github.com/qorelanguage/qore/issues/3438}{\texttt{ issue 3438}}) \item fixed many type errors with complex types (\href{https://github.com/qorelanguage/qore/issues/3429}{\texttt{ issue 3429}}) \item fixed inconsistent behavior of references with pseudo-\/methods (\href{https://github.com/qorelanguage/qore/issues/3417}{\texttt{ issue 3417}}) \item fixed bugs in the return types of \mbox{\hyperlink{group__string__functions_ga9f8c21f961daa29578dcfd596f5871ff}{Qore\+::regex\+\_\+extract()}} and \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_aeaf99b23a4de2db748a1fe0bbc3811f5}{Qore\+::zzz8stringzzz9\+::regex\+Extract()}} (\href{https://github.com/qorelanguage/qore/issues/3416}{\texttt{ issue 3416}}) \item fixed documentation links between dependent modules (\href{https://github.com/qorelanguage/qore/issues/3406}{\texttt{ issue 3406}}) \item fixed a bug where an lvalue with a complex type accepted incompatible assignments from values without complex types if the base type was the same; this fix also ensures that complex type declarations with {\ttfamily auto} are not treated as identical to the base type without any complex type restrictions, in addition abstract type matching was loosened to accept near matches with parameter types so that ab stract method with a parameter type of {\ttfamily hash$<$auto$>$} can be implemented with a concrete method with a {\ttfamily hash} parameter type, for example. (\href{https://github.com/qorelanguage/qore/issues/3404}{\texttt{ issue 3404}}) \item fixed a bug where a crash could result when deserializing invalid integer data (\href{https://github.com/qorelanguage/qore/issues/3395}{\texttt{ issue 3395}}) \item fixed a parse type error in initialization using return value of abstract method (\href{https://github.com/qorelanguage/qore/issues/3387}{\texttt{ issue 3387}}) \item fixed a bug where sort functions were incorrectly sorting strings with different lengths (\href{https://github.com/qorelanguage/qore/issues/3378}{\texttt{ issue 3378}}) \item fixed a member initialization bug with imported classes (\href{https://github.com/qorelanguage/qore/issues/3368}{\texttt{ issue 3368}}) \item \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module\+: \begin{DoxyItemize} \item shut down dedicated socket conenctions last in order to allow for effective keep-\/alive implementations with Web\+Socket for example (\href{https://github.com/qorelanguage/qore/issues/3488}{\texttt{ issue 3488}}) \item fixed a bug where disconnected connections could cause unhandled exceptions to be output in the connection thread (\href{https://github.com/qorelanguage/qore/issues/3415}{\texttt{ issue 3415}}) \item fixed certificate and key errors for H\+T\+T\+PS listeners to generate user-\/friendly exceptions (\href{https://github.com/qorelanguage/qore/issues/3397}{\texttt{ issue 3397}}) \end{DoxyItemize} \item \href{../../modules/Logger/html/index.html}{\texttt{ Logger}} module\+: \begin{DoxyItemize} \item added {\ttfamily Logger\+::log\+Args()} (\href{https://github.com/qorelanguage/qore/issues/3492}{\texttt{ issue 3492}}) \end{DoxyItemize} \item \href{../../modules/Mime/html/index.html}{\texttt{ Mime}} module\+: \begin{DoxyItemize} \item fixed bugs parsing binary data in multipart messages (\href{https://github.com/qorelanguage/qore/issues/2936}{\texttt{ issue 2936}}) \end{DoxyItemize} \item \href{../../modules/PgsqlSqlUtil/html/index.html}{\texttt{ Pgsql\+Sql\+Util}} module\+: \begin{DoxyItemize} \item fixed comparison of triggers with column restrictions with table alignment (\href{https://github.com/qorelanguage/qore/issues/3466}{\texttt{ issue 3466}}) \end{DoxyItemize} \item \href{../../modules/Pop3Client/html/index.html}{\texttt{ Pop3\+Client}} module\+: \begin{DoxyItemize} \item fixed the timeout value for upgrading the S\+SL connection in {\ttfamily Pop3\+Client} (\href{https://github.com/qorelanguage/qore/issues/3388}{\texttt{ issue 3388}}) \end{DoxyItemize} \item \href{../../modules/QUnit/html/index.html}{\texttt{ Q\+Unit}} module\+: \begin{DoxyItemize} \item allow binary modules to be subjected to dependency injections (\href{https://github.com/qorelanguage/qore/issues/3382}{\texttt{ issue 3382}}) \end{DoxyItemize} \item \href{../../modules/RestHandler/html/index.html}{\texttt{ Rest\+Handler}} module\+: \begin{DoxyItemize} \item fixed Rest\+Handler losing internal exception info when response was considered invalid by schema validator (\href{https://github.com/qorelanguage/qore/issues/3435}{\texttt{ issue 3435}}) \item fixed Rest\+Handler incorrectly handling Accept header of incoming requests (\href{https://github.com/qorelanguage/qore/issues/3426}{\texttt{ issue 3426}}) \item added debug logging for R\+E\+ST schema validation errors (\href{https://github.com/qorelanguage/qore/issues/3410}{\texttt{ issue 3410}}) \end{DoxyItemize} \item \href{../../modules/RestSchemaValidator/html/index.html}{\texttt{ Rest\+Schema\+Validator}} module\+: \begin{DoxyItemize} \item fixed {\ttfamily Null\+Rest\+Schema\+Validator} not respecting set Content-\/\+Type header from Rest\+Class (\href{https://github.com/qorelanguage/qore/issues/3427}{\texttt{ issue 3427}}) \end{DoxyItemize} \item \href{../../modules/SmtpClient/html/index.html}{\texttt{ Smtp\+Client}} module\+: \begin{DoxyItemize} \item fixed the timeout value for upgrading to S\+SL connection in {\ttfamily Smtp\+Client} (\href{https://github.com/qorelanguage/qore/issues/3381}{\texttt{ issue 3381}}) \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module\+: \begin{DoxyItemize} \item fixed quoting of reserved words in column names in table alignment (\href{https://github.com/qorelanguage/qore/issues/3400}{\texttt{ issue 3400}}) \item implemented the {\ttfamily Abstract\+Database\+::get\+Physical\+Size()} method (\href{https://github.com/qorelanguage/qore/issues/3385}{\texttt{ issue 3385}}) \end{DoxyItemize} \item \href{../../modules/Util/html/index.html}{\texttt{ Util}} module\+: \begin{DoxyItemize} \item fixed a bug parsing nested lists in {\ttfamily parse\+\_\+to\+\_\+qore\+\_\+value()} (\href{https://github.com/qorelanguage/qore/issues/3483}{\texttt{ issue 3483}}) \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_092}{}\doxysection{Qore 0.\+9.\+2}\label{release_notes_qore_092} \begin{DoxyParagraph}{Release Summary} \end{DoxyParagraph} Bugfix release; see details below\hypertarget{release_notes_qore_092_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_092_new_features} \begin{DoxyItemize} \item {\ttfamily qdbg-\/remote} supports an option to provide H\+T\+TP headers for Web\+Socket connections (\href{https://github.com/qorelanguage/qore/issues/3350}{\texttt{ issue 3350}}) \end{DoxyItemize}\hypertarget{release_notes_qore_092_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_092_bug_fixes} \begin{DoxyItemize} \item implemented support for deserializing data from a binary string (\href{https://github.com/qorelanguage/qore/issues/3357}{\texttt{ issue 3357}}) \item fixed a bug with class initialization that could sometimes result in members of parent classes not being initialized when objects were constructed (\href{https://github.com/qorelanguage/qore/issues/3355}{\texttt{ issue 3355}}) \item fixed a bug in the \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module that could lead to a deadlock when D\+ML methods are used with a datasource pool with connection contention (\href{https://github.com/qorelanguage/qore/issues/3352}{\texttt{ issue 3352}}) \end{DoxyItemize}\hypertarget{release_notes_qore_091}{}\doxysection{Qore 0.\+9.\+1}\label{release_notes_qore_091} \begin{DoxyParagraph}{Release Summary} \end{DoxyParagraph} Bugfix release; see details below\hypertarget{release_notes_qore_091_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_091_new_features} \begin{DoxyItemize} \item the serialization protocol has been updated to version 1.\+1; it still reads both binary-\/ and data-\/serialized data from v1.\+0 \item added the \mbox{\hyperlink{struct_qore_1_1_list_serialization_info}{List\+Serialization\+Info}} hashdecl to support serializing and deserializing lists with complex type information \item new user modules\+: \begin{DoxyItemize} \item \href{../../modules/ZeyosRestClient/html/index.html}{\texttt{ Zeyos\+Rest\+Client}} \begin{DoxyItemize} \item added this new module providing A\+P\+Is for communicating with \href{http://www.zeyos.com}{\texttt{ Zeyos.\+com}}\textquotesingle{}s R\+E\+ST A\+PI \end{DoxyItemize} \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_091_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_091_bug_fixes} \begin{DoxyItemize} \item fixed a bug where the Salesforce rest connection returns \textquotesingle{}rest\textquotesingle{} type instead of \textquotesingle{}sfrests\textquotesingle{} (\href{https://github.com/qorelanguage/qore/issues/3346}{\texttt{ issue 3346}}) \item fixed a bug where an invalid parse exception would be raised with an assignment of a global variable to another global variable with the same name in a different namespace (\href{https://github.com/qorelanguage/qore/issues/3337}{\texttt{ issue 3337}}) \item implemented support for serializing and deserializing complex type information in lists and hashes (\href{https://github.com/qorelanguage/qore/issues/3318}{\texttt{ issue 3318}}) \item fixed bugs handling unassigned lvalues with complex type declarations with the \mbox{\hyperlink{operators_push}{push}} and \mbox{\hyperlink{operators_unshift}{unshift}} operators (\href{https://github.com/qorelanguage/qore/issues/3317}{\texttt{ issue 3317}}) \item fixed a memory leak in copy constructor execution in complex class hierarchies (\href{https://github.com/qorelanguage/qore/issues/3312}{\texttt{ issue 3312}}) \item implemented support for automatically initializing the {\ttfamily Qore} library from Java when dynamically loaded from the J\+VM; additionally in this case the \href{https://github.com/qorelanguage/module-jni}{\texttt{ jni}} module is loaded automatically immediately after the {\ttfamily Qore} library is initialized (\href{https://github.com/qorelanguage/qore/issues/3310}{\texttt{ issue 3310}}) \item implemented support for performing binary searches in binary data by adding the following new pseudo-\/methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8binaryzzz9_a4bcd3dd7e317d56d4bb5135a58c47fb1}{Qore\+::zzz8binaryzzz9\+::find(data, softint)}} \item \mbox{\hyperlink{class_qore_1_1zzz8binaryzzz9_a689c2d2bacc24aa2e286245269888729}{Qore\+::zzz8binaryzzz9\+::rfind(data, softint)}} \end{DoxyItemize}(\href{https://github.com/qorelanguage/qore/issues/3300}{\texttt{ issue 3300}}) \item \href{../../modules/Util/html/index.html}{\texttt{ Util}} module fixes\+: \begin{DoxyItemize} \item fixed a bug in {\ttfamily get\+\_\+exception\+\_\+string()} with Java exceptions (\href{https://github.com/qorelanguage/qore/issues/3304}{\texttt{ issue 3304}}) \end{DoxyItemize} \item \href{../../modules/QUnit/html/index.html}{\texttt{ Q\+Unit}} module fixes\+: \begin{DoxyItemize} \item fixed a bug where tests could not be nested (\href{https://github.com/qorelanguage/qore/issues/3306}{\texttt{ issue 3306}}) \end{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}}\+: \begin{DoxyItemize} \item fixed a bug with charset in the Rest\+Client module (\href{https://github.com/qorelanguage/qore/issues/3328}{\texttt{ issue 3328}}) \item fixed default option handling in R\+E\+ST connections including timeout handling (\href{https://github.com/qorelanguage/qore/issues/3321}{\texttt{ issue 3321}}) \end{DoxyItemize} \item \href{../../modules/SalesforceRestClient/html/index.html}{\texttt{ Salesforce\+Rest\+Client}}\+: \begin{DoxyItemize} \item fixed default option handling in R\+E\+ST connections including timeout handling (\href{https://github.com/qorelanguage/qore/issues/3321}{\texttt{ issue 3321}}) \end{DoxyItemize} \item \href{../../modules/SewioRestClient/html/index.html}{\texttt{ Sewio\+Rest\+Client}}\+: \begin{DoxyItemize} \item fixed default option handling in R\+E\+ST connections including timeout handling (\href{https://github.com/qorelanguage/qore/issues/3321}{\texttt{ issue 3321}}) \end{DoxyItemize} \item \href{../../modules/WebUtil/html/index.html}{\texttt{ Web\+Util}}\+: \begin{DoxyItemize} \item fixed a bug when Static\+Template\+Manager does not respect constructor\textquotesingle{}s parse options in templates (\href{https://github.com/qorelanguage/qore/issues/3334}{\texttt{ issue 3334}} \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_09}{}\doxysection{Qore 0.\+9}\label{release_notes_qore_09} \begin{DoxyParagraph}{Release Summary} This is a major release of Qore with large portions of code subject to extensive optimizations leading to large memory and performance improvements along with more control of \mbox{\hyperlink{class_qore_1_1_program}{Program}} logic containers, multithreading, and a \href{../../modules/reflection/html/index.html}{\texttt{ reflection A\+PI}}. This release breaks binary compatibility with older versions of Qore as well, requiring binary modules to support the new A\+PI and A\+BI. \end{DoxyParagraph} \hypertarget{release_notes_qore_09_compatibility}{}\doxysubsection{Changes That Can Affect Backwards-\/\+Compatibility}\label{release_notes_qore_09_compatibility} \begin{DoxyItemize} \item \mbox{\hyperlink{namespace_qore}{Qore}} classes and functions are now immutable once created; any attempt to add a new user variant to an existing function or method or to add new declarations to an existing class will result in a parse error. \item \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects now only support a single complete parse action (\mbox{\hyperlink{class_qore_1_1_program_ad59f1b6ce7adaa693086e1b858cbe896}{Program\+::parse()}} or \mbox{\hyperlink{class_qore_1_1_program_a789d84e0f40137ad3b38064378b50e1b}{Program\+::parse\+Commit()}}); subsequent attempts to parse code into the same Program object will fail with an exception. If parsing fails due to a parse exception, the \mbox{\hyperlink{class_qore_1_1_program}{Program}} object is generally no longer usable and must be recreated to be used. \item \mbox{\hyperlink{class_qore_1_1_program_acc27af9225963f20947e0045186ecfb7}{Program\+::parse\+Rollback()}} is now deprecated; this action removes all user code and most builtin code from the \mbox{\hyperlink{class_qore_1_1_program}{Program}} object; delete the object instead of using this method \item the \mbox{\hyperlink{qore_classes_transient}{transient}} keyword has been introduced to support control over \mbox{\hyperlink{class_qore_1_1_serializable}{object serialization}}; see also \mbox{\hyperlink{parse_directives_no-transient}{\%no-\/transient}} \end{DoxyItemize}\hypertarget{release_notes_qore_09_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_09_new_features} \begin{DoxyItemize} \item Up to 70\% reduced memory usage in Qore programs through\+: \begin{DoxyItemize} \item Extensive memory optimizations \item Changing the default thread stack size from 8 MB to 512 KB (\href{https://github.com/qorelanguage/qore/issues/2701}{\texttt{ issue 2701}}) \item Eliminating heap-\/allocated, atomic-\/reference-\/counted integer and floating-\/point values resulted in reduced memory usage as well as faster runtime execution \end{DoxyItemize} \item \href{../../modules/reflection/html/index.html}{\texttt{ Reflection A\+PI}} \item \mbox{\hyperlink{class_qore_1_1_serializable}{Data and object serialization}} support\+: \begin{DoxyItemize} \item All data types except \mbox{\hyperlink{expressions_closure}{closures}}, \mbox{\hyperlink{expressions_call_reference}{call references}}, \mbox{\hyperlink{lvalue_references}{references}}, and non-\/serializable objects can be serializeed \item All objects from classes inheriting \mbox{\hyperlink{class_qore_1_1_serializable}{Serializable}} can be serialized \item Class members declared with the \mbox{\hyperlink{qore_classes_transient}{transient}} keyword (new in this release) will not be serialized but instead will get their default values when deserialized \item Classes can define their own local serialization and deserialization logic by defining the \mbox{\hyperlink{class_qore_1_1_serializable_ae2a384d8d7fc0a628609f1907ea32b07}{serialize\+Members()}} and \mbox{\hyperlink{class_qore_1_1_serializable_a7d59dd31c2e7f9a06eafb995db5b1381}{deserialize\+Members()}} methods, respectively \item The following builtin classes support serialization\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource}{Datasource}} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} \item \mbox{\hyperlink{class_qore_1_1_s_s_l_certificate}{S\+S\+L\+Certificate}} \item \mbox{\hyperlink{class_qore_1_1_s_s_l_private_key}{S\+S\+L\+Private\+Key}} \item \mbox{\hyperlink{class_qore_1_1_time_zone}{Time\+Zone}} \end{DoxyItemize} \end{DoxyItemize} \item New classes\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_abstract_s_q_l_statement}{Abstract\+S\+Q\+L\+Statement}}\+: has been added as the parent class defining an abstract A\+PI for \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} \item \mbox{\hyperlink{class_qore_1_1_serializable}{Serializable}}\+: a new class supporting data and object serialization \item \mbox{\hyperlink{class_qore_1_1_stream_base}{Stream\+Base}}\+: a base class for stream classes allowing for a controlled handoff of a stream to another thread \end{DoxyItemize} \item Added support for importing a split user module represented as directory (\href{https://github.com/qorelanguage/qore/issues/2562}{\texttt{ issue 2562}}) \item New and updated methods in existing classes\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_abstract_datasource_afdf23f69850ebb8e0c337ade7fcb793d}{Abstract\+Datasource\+::get\+S\+Q\+L\+Statement()}} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_a39ef1a8bff15788d039672359c28772e}{Datasource\+::get\+S\+Q\+L\+Statement()}} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_af59598025506fa7079b734018a89decf}{Datasource\+Pool\+::get\+S\+Q\+L\+Statement()}} \item \mbox{\hyperlink{class_qore_1_1_file_a8ce1cf401892b56a61bbb16754366079}{File\+::redirect()}} \item \mbox{\hyperlink{class_qore_1_1_ftp_client_a288bbef821ce9641b0175a2052680001}{Ftp\+Client\+::get\+Network\+Family()}} \item \mbox{\hyperlink{class_qore_1_1_ftp_client_a1ced03072c695abf25df4d419b64dfa0}{Ftp\+Client\+::set\+Network\+Family()}} \item \mbox{\hyperlink{class_qore_1_1_ftp_client_ab07b745d71fb0d9be7860fd41c9450c8}{Ftp\+Client\+::get\+Control\+Peer\+Info()}} \item \mbox{\hyperlink{class_qore_1_1_ftp_client_aa9bd9f5c986f891fa1e2021d426c0969}{Ftp\+Client\+::get\+Control\+Socket\+Info()}} \item \mbox{\hyperlink{class_qore_1_1_ftp_client_a4655d94c5f3a25d14098b65c21755d31}{Ftp\+Client\+::get\+Data\+Peer\+Info()}} \item \mbox{\hyperlink{class_qore_1_1_ftp_client_a9c91cf56b957986b28ae36db98466d0b}{Ftp\+Client\+::get\+Data\+Socket\+Info()}} \item \mbox{\hyperlink{class_qore_1_1_program_aee25b65b811efa96f8d3690c0d19314e}{Program\+::get\+Parse\+Option\+String\+List()}} \item \mbox{\hyperlink{class_qore_1_1_program_afe6fc6b4013b8e2ff209ac9dad421487}{Program\+::issue\+Module\+Cmd()}} \item \mbox{\hyperlink{class_qore_1_1_program_a2f83d6257c25cc5ae867d9d461019996}{Program\+::load\+Apply\+To\+Private\+User\+Module()}} \item \mbox{\hyperlink{class_qore_1_1_program_ae15ccde47d36af187a972a6468bafc2a}{Program\+::load\+Apply\+To\+Private\+User\+Module\+Warn()}} \item \mbox{\hyperlink{class_qore_1_1_program_a300ffe0abd0b09cc39feb637a9bab9ba}{Program\+::load\+Apply\+To\+User\+Module()}} \item \mbox{\hyperlink{class_qore_1_1_program_ae5534c8443a553834b352b7d62a78ca3}{Program\+::load\+Apply\+To\+User\+Module\+Warn()}} \item \mbox{\hyperlink{class_qore_1_1_program_a9bc54a95f735cdc10bfb52e5166259b2}{Program\+::load\+Module()}} \item \mbox{\hyperlink{class_qore_1_1_program_a08a74eec43638d3132b99de1479c0a27}{Program\+::load\+Module\+Warn()}} \item \mbox{\hyperlink{class_qore_1_1_program_a88ead6a191a58736b49e794f3220869f}{Program\+::load\+User\+Module\+With\+Program()}} \item \mbox{\hyperlink{class_qore_1_1_program_a1675c1af5ba3d423af82dbc026c0202f}{Program\+::load\+User\+Module\+With\+Program\+Warn()}} \item \mbox{\hyperlink{class_qore_1_1_program_ad59f1b6ce7adaa693086e1b858cbe896}{Program\+::parse()}} \item \mbox{\hyperlink{class_qore_1_1_program_ac943bad226fcf69ce5007b101828f8c1}{Program\+::parse\+Pending()}} \item \mbox{\hyperlink{class_qore_1_1_s_s_l_certificate_aba1f8b7876a1c6630f8c474a713daa2e}{S\+S\+L\+Certificate\+::copy()}} \item \mbox{\hyperlink{class_qore_1_1_s_s_l_certificate_adc018f372e971b43a44d678b96c222ca}{S\+S\+L\+Certificate\+::get\+D\+ER()}} \item \mbox{\hyperlink{class_qore_1_1_s_s_l_private_key_abc635ed38e5d73865bbc356267b6d26e}{S\+S\+L\+Private\+Key\+::copy()}} \item \mbox{\hyperlink{class_qore_1_1_s_s_l_private_key_af6efb915453871f442bed6554a30b156}{S\+S\+L\+Private\+Key\+::get\+D\+ER()}} \item \mbox{\hyperlink{class_qore_1_1_stream_reader_aacf2ab395e40fcc8c05dfc42cc82c5f2}{Stream\+Reader\+::get\+Input\+Stream()}} \item \mbox{\hyperlink{class_qore_1_1_stream_writer_a43a64e7d6774c777071fff39245477d6}{Stream\+Writer\+::get\+Output\+Stream()}} \item \mbox{\hyperlink{class_qore_1_1_thread_1_1_counter_a7c098cd52caeff8f5ff18dddff2eeeb5}{Counter\+::inc()}} \end{DoxyItemize} \item New functions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__object__functions_ga46a72b2a2a84282c5125b6fd7a2e6b23}{call\+\_\+static\+\_\+method()}} \item \mbox{\hyperlink{group__object__functions_gaf3059a3551575f93e04f2f58ae0ab4c4}{call\+\_\+static\+\_\+method\+\_\+args()}} \item \mbox{\hyperlink{group__threading__functions_ga82d1b72e32a368be71b3b91462cbe0da}{get\+\_\+default\+\_\+thread\+\_\+stack\+\_\+size()}} \item \mbox{\hyperlink{group__misc__functions_ga26bb5a87af0e8be0e661a590fb722c83}{get\+\_\+module\+\_\+option()}} \item \mbox{\hyperlink{namespace_qore_a9c666f750378638e71530ced628538a3}{get\+\_\+netif\+\_\+list()}} \item \mbox{\hyperlink{group__threading__functions_gaa97833f603fb51b23fe0bb6c22b7f95f}{get\+\_\+stack\+\_\+size()}} \item \mbox{\hyperlink{group__threading__functions_ga79f9cd8de9606cae29c29e3b08d234f0}{get\+\_\+thread\+\_\+name()}} \item \mbox{\hyperlink{group__misc__functions_ga24b04239fa5f45bd1c3d430dfab49019}{load\+\_\+module\+\_\+warn()}} \item \mbox{\hyperlink{group__threading__functions_gadbd86685c49fd7b4960b8b21e05cb2f0}{set\+\_\+default\+\_\+thread\+\_\+stack\+\_\+size()}} \item \mbox{\hyperlink{group__misc__functions_ga9034376bb44beb761d76156600b537f8}{set\+\_\+module\+\_\+option()}} \item \mbox{\hyperlink{group__threading__functions_ga321040a3e764383dd68c50d496436e87}{set\+\_\+thread\+\_\+name()}} \end{DoxyItemize} \item Updated functions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__misc__functions_gaaa60e9a984c59e662b2e7cac84a3899d}{get\+\_\+ex\+\_\+pos()}}\+: {\ttfamily lang} info was added to the result string if available \item \mbox{\hyperlink{group__misc__functions_gaf0922a51e6c5471b02a947cb0cb008ba}{load\+\_\+module()\+: added an optional {\ttfamily warning\+\_\+mask} parameter}} \end{DoxyItemize} \item New modules\+: \begin{DoxyItemize} \item \href{../../modules/FsUtil/html/index.html}{\texttt{ Fs\+Util}} \item \href{../../modules/Logger/html/index.html}{\texttt{ Logger}} \item \href{../../modules/reflection/html/index.html}{\texttt{ reflection}} \end{DoxyItemize} \item New and updated hashdecls\+: \begin{DoxyItemize} \item \mbox{\hyperlink{struct_qore_1_1_net_if_info}{Net\+If\+Info}}\+: new \mbox{\hyperlink{hashdecl}{hashdecl}} for the \mbox{\hyperlink{namespace_qore_a9c666f750378638e71530ced628538a3}{get\+\_\+netif\+\_\+list()}} function \item \mbox{\hyperlink{struct_qore_1_1_call_stack_info}{Call\+Stack\+Info}}\+: updated with new members\+: \begin{DoxyItemize} \item {\ttfamily lang} \item {\ttfamily programid} \item {\ttfamily statementid} \end{DoxyItemize} \item \mbox{\hyperlink{struct_qore_1_1_exception_info}{Exception\+Info}}\+: updated with a new member\+: \begin{DoxyItemize} \item {\ttfamily lang} \end{DoxyItemize} \end{DoxyItemize} \item New constants\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_ga5e61e3651bfad227600a9cf7120fb727}{Domain\+Code\+Map}} \item \mbox{\hyperlink{group__parse__options_ga2c80f990c3c3ad952018ee6cdddbfa9c}{Domain\+String\+Map}} \item \mbox{\hyperlink{group__option__constants_ga39b9cdc4df2f0b13b08ce661b3f31d6b}{H\+A\+V\+E\+\_\+\+G\+E\+T\+\_\+\+N\+E\+T\+I\+F\+\_\+\+L\+I\+ST}} \item \mbox{\hyperlink{group__option__constants_gae9654317eddd561ad25dbdf76959a60e}{H\+A\+V\+E\+\_\+\+G\+E\+T\+\_\+\+S\+T\+A\+C\+K\+\_\+\+S\+I\+ZE}} \item \mbox{\hyperlink{group__option__constants_ga3e3b196e3ae7f8b26e890ce36c120901}{H\+A\+V\+E\+\_\+\+M\+A\+N\+A\+G\+E\+\_\+\+S\+T\+A\+CK}} \item \mbox{\hyperlink{group__option__constants_ga5c7b490cc1b6c8749d42067ee4baa7b2}{H\+A\+V\+E\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+N\+A\+ME}} \item \mbox{\hyperlink{group__parse__options_ga46fa5284de5681ab4c8e8cb842f35fff}{P\+O\+\_\+\+B\+R\+O\+K\+E\+N\+\_\+\+S\+P\+R\+I\+N\+TF}} \item \mbox{\hyperlink{group__parse__options_ga454fabf3a392b8fec9ee587e97a2d8e8}{P\+O\+\_\+\+N\+O\+\_\+\+R\+E\+F\+L\+E\+C\+T\+I\+ON}} \item \mbox{\hyperlink{group__parse__options_ga4d9e69dc24ed1eed0ea11f4947cceca2}{P\+O\+\_\+\+N\+O\+\_\+\+T\+R\+A\+N\+S\+I\+E\+NT}} \item \mbox{\hyperlink{group__functional__domain__constants}{Functional Domain Constants}} \end{DoxyItemize} \item New \mbox{\hyperlink{group__date__and__time__functions_date_formatting}{date formatting}} codes for \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_aeff0dd69a9ef8f228b54ba5543b2e3c6}{Qore\+::zzz8datezzz9\+::format()}} and \mbox{\hyperlink{group__date__and__time__functions_gad5572fcb49964bfe3005e144da579361}{format\+\_\+date()}}\+: \begin{DoxyItemize} \item {\ttfamily \char`\"{}\+Dn\char`\"{}} and {\ttfamily \char`\"{}\+D\+N\char`\"{}}\+: the ordinal day number in the year \item {\ttfamily \char`\"{}\+I\char`\"{}}\+: I\+S\+O-\/8601 week string \item {\ttfamily \char`\"{}\+Id\char`\"{}} and {\ttfamily \char`\"{}\+I\+D\char`\"{}}\+: \href{http://en.wikipedia.org/wiki/ISO_week_date}{\texttt{ I\+S\+O-\/8601 week}} day number \item {\ttfamily \char`\"{}\+I\+F\char`\"{}}\+: the value in \href{https://en.wikipedia.org/wiki/ISO_8601}{\texttt{ I\+S\+O-\/8601}} format for both \mbox{\hyperlink{basic_data_types_relative_dates}{relative}} (ex\+: {\ttfamily \char`\"{}\+P2\+Y1\+M3\+D\+T5\+H7\+M9.\+002\+S\char`\"{}}) and \mbox{\hyperlink{basic_data_types_absolute_dates}{absolute}} dates (ex\+: {\ttfamily \char`\"{}2018-\/03-\/23\+T10\+:43\+:12.\+067628+01\+:00\char`\"{}}) \item {\ttfamily \char`\"{}\+Iw\char`\"{}} and {\ttfamily \char`\"{}\+I\+W\char`\"{}}\+: \href{http://en.wikipedia.org/wiki/ISO_week_date}{\texttt{ I\+S\+O-\/8601 week}} number \item {\ttfamily \char`\"{}\+Iy\char`\"{}} and {\ttfamily \char`\"{}\+I\+Y\char`\"{}}\+: \href{http://en.wikipedia.org/wiki/ISO_week_date}{\texttt{ I\+S\+O-\/8601 week}} year \end{DoxyItemize} \item New parse directives\+: \begin{DoxyItemize} \item \mbox{\hyperlink{parse_directives_broken-sprintf}{\%broken-\/sprintf}} \item \mbox{\hyperlink{parse_directives_correct-sprintf}{\%correct-\/sprintf}} \item \mbox{\hyperlink{parse_directives_no-reflection}{\%no-\/reflection}} \item \mbox{\hyperlink{parse_directives_no-transient}{\%no-\/transient}} \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_program_ad59f1b6ce7adaa693086e1b858cbe896}{Program\+::parse()}} and \mbox{\hyperlink{class_qore_1_1_program_ac943bad226fcf69ce5007b101828f8c1}{Program\+::parse\+Pending()}} updates\+: the {\itshape format\+\_\+label} parameter is obsolete/ignored (\href{https://github.com/qorelanguage/qore/issues/2903}{\texttt{ issue 2903}}) \item Module updates \begin{DoxyItemize} \item \href{../../modules/reflection/html/index.html}{\texttt{ reflection}}\+: a new binary module providing a reflection A\+PI to Qore \item \href{../../modules/ConnectionProvider/html/index.html}{\texttt{ Connection\+Provider}} module changes\+: \begin{DoxyItemize} \item The {\ttfamily Abstract\+Connection\+::get\+Constructor\+Info()} method (and supporting declarations) was added to allow connections to be created dynamically, potentially in another process from a network call (\href{https://github.com/qorelanguage/qore/issues/2628}{\texttt{ issue 2628}}) \item The {\ttfamily Abstract\+Connection} has new public flag {\ttfamily enabled}. Also constructors are updated. (\href{https://github.com/qorelanguage/qore/issues/3001}{\texttt{ issue 3001}}) \item The {\ttfamily Abstract\+Connection} has new constructors, old ones are obsolete. Custom U\+R\+L/\+U\+RI parsing is possible (\href{https://github.com/qorelanguage/qore/issues/3162}{\texttt{ issue 3162}}) \end{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module updates\+: \begin{DoxyItemize} \item Added public methods {\ttfamily Abstract\+Csv\+Iterator\+::get\+Raw\+Line()} and {\ttfamily Abstract\+Csv\+Iterator\+::get\+Raw\+Line\+Values()} (\href{https://github.com/qorelanguage/qore/issues/2739}{\texttt{ issue 2739}}) \end{DoxyItemize} \item \href{../../modules/FreetdsSqlUtil/html/index.html}{\texttt{ Freetds\+Sql\+Util}} module changes\+: \begin{DoxyItemize} \item Added support for serializing and deserializing {\ttfamily Abstract\+Table} objects (\href{https://github.com/qorelanguage/qore/issues/2663}{\texttt{ issue 2663}}) \end{DoxyItemize} \item \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module changes\+: \begin{DoxyItemize} \item added the {\ttfamily \char`\"{}header-\/info\char`\"{}} hash to the context argument when calling handlers (\href{https://github.com/qorelanguage/qore/issues/3260}{\texttt{ issue 3260}}) \item Added support for adding new H\+T\+TP methods to the server with the {\ttfamily Http\+Server\+::add\+Http\+Method()} method (\href{https://github.com/qorelanguage/qore/issues/2805}{\texttt{ issue 2805}}) \end{DoxyItemize} \item \href{../../modules/Mime/html/index.html}{\texttt{ Mime}} module changes\+: \begin{DoxyItemize} \item allow the default type for unknown extensions to be overridden in {\ttfamily get\+\_\+mime\+\_\+type\+\_\+from\+\_\+ext()} (\href{https://github.com/qorelanguage/qore/issues/3260}{\texttt{ issue 3260}}) \end{DoxyItemize} \item \href{../../modules/MysqlSqlUtil/html/index.html}{\texttt{ Mysql\+Sql\+Util}} module changes\+: \begin{DoxyItemize} \item Added support for serializing and deserializing {\ttfamily Abstract\+Table} objects (\href{https://github.com/qorelanguage/qore/issues/2663}{\texttt{ issue 2663}}) \end{DoxyItemize} \item \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}} module changes\+: \begin{DoxyItemize} \item Implemented a check for allowed types when is the A\+U\+T\+O\+\_\+\+I\+N\+C\+R\+E\+M\+E\+NT flag used (\href{https://github.com/qorelanguage/qore/issues/2978}{\texttt{ issue 2978}}) \item Added support for serializing and deserializing {\ttfamily Abstract\+Table} objects (\href{https://github.com/qorelanguage/qore/issues/2663}{\texttt{ issue 2663}}) \end{DoxyItemize} \item \href{../../modules/PgsqlSqlUtil/html/index.html}{\texttt{ Pgsql\+Sql\+Util}} module changes\+: \begin{DoxyItemize} \item Added support for serializing and deserializing {\ttfamily Abstract\+Table} objects (\href{https://github.com/qorelanguage/qore/issues/2663}{\texttt{ issue 2663}}) \end{DoxyItemize} \item \href{../../modules/QUnit/html/index.html}{\texttt{ Q\+Unit}} module changes\+: \begin{DoxyItemize} \item updated {\ttfamily Test\+::test\+Skip()} to use the reason argument a format string with \mbox{\hyperlink{group__string__functions_gab2494031a30dc02d9f6696435a8c4485}{vsprintf()}} (\href{https://github.com/qorelanguage/qore/issues/3172}{\texttt{ issue 3172}}) \end{DoxyItemize} \item \href{../../modules/RestHandler/html/index.html}{\texttt{ Rest\+Handler}} module changes\+: \begin{DoxyItemize} \item added the {\ttfamily Rest\+Handler\+::return\+Rest\+Exception()} method that allows subclasses to determine how exceptions are handled (\href{https://github.com/qorelanguage/qore/issues/3235}{\texttt{ issue 3235}}) \item Updated to support alternative U\+RI paths for actions so that an \char`\"{}action=xxx\char`\"{} argument is not needed; instead the action can be added to the end of the U\+RI path so that {\ttfamily \char`\"{}\+P\+U\+T path/xxx\char`\"{}} can be used instead of {\ttfamily \char`\"{}\+P\+U\+T path?action=xxx\char`\"{}} (\href{https://github.com/qorelanguage/qore/issues/2994}{\texttt{ issue 2994}}) \end{DoxyItemize} \item \href{../../modules/RestSchemaValidator/html/index.html}{\texttt{ Rest\+Schema\+Validator}} module changes\+: \begin{DoxyItemize} \item Updated the default validator to try all serialization methods if multiple methods are available and one fails (\href{https://github.com/qorelanguage/qore/issues/2831}{\texttt{ issue 2831}}) \end{DoxyItemize} \item \href{../../modules/Schema/html/index.html}{\texttt{ Schema}} module changes\+: \begin{DoxyItemize} \item improved logging output when aligning schemas (\href{https://github.com/qorelanguage/qore/issues/3114}{\texttt{ issue 3114}}) \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module changes\+: \begin{DoxyItemize} \item Deprecated {\ttfamily Abstract\+Table\+::get\+Row\+Iterator()} for {\ttfamily Abstract\+Table\+::get\+Statement()} (\href{https://github.com/qorelanguage/qore/issues/2326}{\texttt{ issue 2326}}) \item Updated the module to use the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_abstract_s_q_l_statement}{Abstract\+S\+Q\+L\+Statement}} class instead of the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} (\href{https://github.com/qorelanguage/qore/issues/2326}{\texttt{ issue 2326}}) \item Added support for serializing and deserializing {\ttfamily Abstract\+Table} objects (\href{https://github.com/qorelanguage/qore/issues/2663}{\texttt{ issue 2663}}) \end{DoxyItemize} \item \href{../../modules/Swagger/html/index.html}{\texttt{ Swagger}}\+: \begin{DoxyItemize} \item Swagger module does not accept multipart/form-\/data content-\/type and also does not work with list and hash parameters (\href{https://github.com/qorelanguage/qore/issues/2932}{\texttt{ issue 2932}}) \end{DoxyItemize} \item \href{../../modules/Util/html/index.html}{\texttt{ Util}} module updates\+: \begin{DoxyItemize} \item Added public function {\ttfamily parse\+\_\+ranges()} (\href{https://github.com/qorelanguage/qore/issues/2438}{\texttt{ issue 2438}}) \item Added public function {\ttfamily check\+\_\+ip\+\_\+address()} (\href{https://github.com/qorelanguage/qore/issues/2483}{\texttt{ issue 2483}}) \item Updated {\ttfamily parse\+\_\+to\+\_\+qore\+\_\+value()} to support single-\/element lists and hashes with curly brackets including empty hashes (\href{https://github.com/qorelanguage/qore/issues/3138}{\texttt{ issue 3138}}) \item updated {\ttfamily get\+\_\+exception\+\_\+string()} to show the {\ttfamily lang} value (\href{https://github.com/qorelanguage/qore/issues/3182}{\texttt{ issue 3182}}) \end{DoxyItemize} \item \href{../../modules/WebSocketHandler/html/index.html}{\texttt{ Web\+Socket\+Handler}}\+: \begin{DoxyItemize} \item added stopping connection from server side via {\ttfamily Web\+Socket\+Connection\+::stop()}, {\ttfamily Web\+Socket\+Handler\+::stop\+One()} and {\ttfamily Web\+Socket\+Client} handling of the {\ttfamily W\+S\+C\+C\+\_\+\+Going\+Away} event \end{DoxyItemize} \item \href{../../modules/WebUtil/html/index.html}{\texttt{ Web\+Util}} module changes\+: \begin{DoxyItemize} \item updated to allow more control over file serving (\href{https://github.com/qorelanguage/qore/issues/3260}{\texttt{ issue 3260}}) \end{DoxyItemize} \end{DoxyItemize} \item \mbox{\hyperlink{basic_data_types_relative_dates}{Relative date}} changes \begin{DoxyItemize} \item Fractional seconds are accepted in the \mbox{\hyperlink{basic_data_types_single_reldates}{Single Relative Time Format}} \item Fractional date components are accepted in the \mbox{\hyperlink{basic_data_types_short_reldates}{Short Relative Time Format}} based on \href{https://en.wikipedia.org/wiki/ISO_8601\#Durations}{\texttt{ I\+S\+O-\/8601 durations}} \end{DoxyItemize} \item Improved debugging support\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_program_control_ada1ff792e44ca555e6c4f5d77c411153}{Program\+Control\+::get\+Statement\+Id\+Info()}} provides breakpoint info \item Command to resolve statement \item Interrupt notification provides call stack info \item {\ttfamily \char`\"{}\+Run to statement\char`\"{}} implementation \item \href{../../modules/DebugHandler/html/index.html}{\texttt{ Debug\+Handler}} reimplemented to support multiple websocket handlers \item Programs are not interrupted in bootstrap code \item Command line utils display source line code when interrupted \end{DoxyItemize} \item Runtime thread stack traces are available in all builds and the \mbox{\hyperlink{group__option__constants_ga5d3b3ad72dbc870686836888c5cb92e0}{H\+A\+V\+E\+\_\+\+R\+U\+N\+T\+I\+M\+E\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+S\+T\+A\+C\+K\+\_\+\+T\+R\+A\+CE}} constant is always {\ttfamily True}. Furthermore, the Qore library has been extended to support stack tracing when embedding or integrating code in other programming languages at runtime \end{DoxyItemize}\hypertarget{release_notes_qore_09_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_09_bug_fixes} \begin{DoxyItemize} \item fixed a bug in \mbox{\hyperlink{group__misc__functions_ga54e6ccaa8fdaa3213ae5550aa66629c9}{parse\+\_\+url()}} with single-\/character hostnames with a port number (\href{https://github.com/qorelanguage/qore/issues/3287}{\texttt{ issue 3287}}) \item fixed a minor bug handling error info in exception handling in the \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module (\href{https://github.com/qorelanguage/qore/issues/3280}{\texttt{ issue 3280}}) \item fixed a crash in acquiring a new connection with datasource options (\href{https://github.com/qorelanguage/qore/issues/3262}{\texttt{ issue 3262}}) \item fixed a bug reporting the source location for runtime type errors related to missing return statements (\href{https://github.com/qorelanguage/qore/issues/3255}{\texttt{ issue 3255}}) \item fixed bugs where \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_a7713f26c809821a7942a60e27f924742}{Datasource\+::get\+Config\+String()}} and \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_a8291b3c3010a8c0d1522afeaa3411a02}{Datasource\+::get\+Config\+Hash()}} would require a connection to the server, making it impossible to check option before connecting (\href{https://github.com/qorelanguage/qore/issues/3247}{\texttt{ issue 3247}}) \item fixed a bug with \mbox{\hyperlink{operators_weak_assignment_operator}{weak references}} in some assignment expressions (\href{https://github.com/qorelanguage/qore/issues/3202}{\texttt{ issue 3202}}) \item fixed bugs in \mbox{\hyperlink{group__string__functions_ga7a74be141f814ef286046c367b21091c}{sprintf()}}, \mbox{\hyperlink{group__string__functions_gab2494031a30dc02d9f6696435a8c4485}{vsprintf()}}, and all variants where \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} was not treated the same as no value (\href{https://github.com/qorelanguage/qore/issues/3184}{\texttt{ issue 3184}}) \item worked around a potential C\+OW bug in {\ttfamily std\+::string} in G\+NU libdstdc++ 6+ (\href{https://github.com/qorelanguage/qore/issues/3179}{\texttt{ issue 3179}}) \item fixed a bug with simple additional and subtraction with mixed \mbox{\hyperlink{data_type_declarations_timeout_type}{timeout}} and \mbox{\hyperlink{data_type_declarations_date_type}{date}} values; updated docs that arithmetic operations with timeout values are not recommended and can return unexpected values in some situations (\href{https://github.com/qorelanguage/qore/issues/3157}{\texttt{ issue 3157}}) \item fixed a bug in deterministic garbage collection where \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}} objects were not scanned and therefore cycles due to \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}} elements would cause a memory and reference leak (\href{https://github.com/qorelanguage/qore/issues/3101}{\texttt{ issue 3101}}) \item fixed a bug where call references did not set the execution context with builtin functions and therefore calls to builtin functions in modules (such as {\ttfamily jni}) with per-\/program private data would fail (\href{https://github.com/qorelanguage/qore/issues/3024}{\texttt{ issue 3024}}) \item fixed a bug where rvalue references with complex subtypes could get modified during an assignment (\href{https://github.com/qorelanguage/qore/issues/2891}{\texttt{ issue 2891}}) \item Fixed a bug where class members could be initialized multiple times in a class with multiple inheritance where the same class is inherited multiple times in the hierarchy (\href{https://github.com/qorelanguage/qore/issues/2741}{\texttt{ issue 2741}}) \item Fixed bugs handling \mbox{\hyperlink{qore_classes_abstract}{abstract}} methods in complex hierarchies with multiple inheritance (\href{https://github.com/qorelanguage/qore/issues/2741}{\texttt{ issue 2741}}) \item Fixed bugs handling object scope in \mbox{\hyperlink{operators_background}{background}} expressions (\href{https://github.com/qorelanguage/qore/issues/2653}{\texttt{ issue 2653}}) \item Fixed a bug\+: \mbox{\hyperlink{group__type__conversion__functions_ga97015b71e0a9f1118be166fc6465e48e}{hash(list$<$auto$>$)}} where l has an odd number of elements never returns (\href{https://github.com/qorelanguage/qore/issues/2860}{\texttt{ issue 2860}}) \item Fixed a bug where no error is issued when an expression does not have meaning as a top-\/level statement (\href{https://github.com/qorelanguage/qore/issues/2826}{\texttt{ issue 2826}}), and also where such expression is an argument to the \mbox{\hyperlink{operators_background}{background}} operator (\href{https://github.com/qorelanguage/qore/issues/2747}{\texttt{ issue 2747}}) \item Fixed a bug where the parser does not recognize that a return value of a function call is not ignored if it is an object and its method is immediately called (\href{https://github.com/qorelanguage/qore/issues/2863}{\texttt{ issue 2863}}), \item Fixed a bug where {\ttfamily public} and {\ttfamily private} members of classes inherited with {\ttfamily private\+:internal} inheritance were not initialized when objects were created (\href{https://github.com/qorelanguage/qore/issues/2970}{\texttt{ issue 2970}}), \item Module fixes\+: \begin{DoxyItemize} \item \href{../../modules/QUnit/html/index.html}{\texttt{ Q\+Unit}}\+: \begin{DoxyItemize} \item fixed error reporting with type errors with number values (\href{https://github.com/qorelanguage/qore/issues/2984}{\texttt{ issue 2984}}) \end{DoxyItemize} \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_08139}{}\doxysection{Qore 0.\+8.\+13.\+9}\label{release_notes_qore_08139} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08139_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08139_bug_fixes} \begin{DoxyItemize} \item fixed a bug handling start and end arguments in \mbox{\hyperlink{group__string__functions_ga757f5b4682cb6787e7e186ddcc2b2b56}{replace()}} that would cause a crash (\href{https://github.com/qorelanguage/qore/issues/3345}{\texttt{ issue 3345}}) \item fixed a bug handling invalid DB driver options in datasource creation that could lead to a crash with some drivers (\href{https://github.com/qorelanguage/qore/issues/3243}{\texttt{ issue 3243}}) \item fixed a memory error in internal list handling that could lead to memory corruption and crashes (\href{https://github.com/qorelanguage/qore/issues/3206}{\texttt{ issue 3206}}) \item fixed calls to Dir\+::list$\ast$() methods which failed whenever there was a symlink with a non-\/existent target in a directory (\href{https://github.com/qorelanguage/qore/issues/3192}{\texttt{ issue 3192}}) \item fixed a bug handling illegal abstract method definitions of special class methods (\href{https://github.com/qorelanguage/qore/issues/3126}{\texttt{ issue 3126}}) \item fixed handling {\ttfamily 304 Not Modified} responses in the \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client}{H\+T\+T\+P\+Client}} class (\href{https://github.com/qorelanguage/qore/issues/3116}{\texttt{ issue 3116}}) \item fixed a crashing bug in the \mbox{\hyperlink{class_qore_1_1_transform}{Transform}} class when used with encryption algorithms (\href{https://github.com/qorelanguage/qore/issues/3111}{\texttt{ issue 3111}}) \item fixed a crash with multiple hash keys when parsing the \mbox{\hyperlink{operators_hmap}{hash map operator}} (\href{https://github.com/qorelanguage/qore/issues/3108}{\texttt{ issue 3108}}) \item module fixes\+: \begin{DoxyItemize} \item \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}}\+: \begin{DoxyItemize} \item fixed responses that cannot have a message body (ex\+: {\ttfamily H\+E\+AD} requests and others) (\href{https://github.com/qorelanguage/qore/issues/3116}{\texttt{ issue 3116}}) \end{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}}\+: \begin{DoxyItemize} \item fixed default option handling in R\+E\+ST connections including timeout handling (\href{https://github.com/qorelanguage/qore/issues/3321}{\texttt{ issue 3321}}) \end{DoxyItemize} \item \href{../../modules/SalesforceRestClient/html/index.html}{\texttt{ Salesforce\+Rest\+Client}}\+: \begin{DoxyItemize} \item fixed default option handling in R\+E\+ST connections including timeout handling (\href{https://github.com/qorelanguage/qore/issues/3321}{\texttt{ issue 3321}}) \end{DoxyItemize} \item \href{../../modules/SewioRestClient/html/index.html}{\texttt{ Sewio\+Rest\+Client}}\+: \begin{DoxyItemize} \item fixed default option handling in R\+E\+ST connections including timeout handling (\href{https://github.com/qorelanguage/qore/issues/3321}{\texttt{ issue 3321}}) \end{DoxyItemize} \item \href{../../modules/WebSocketClient/html/index.html}{\texttt{ Web\+Socket\+Client}}\+: \begin{DoxyItemize} \item added missing exception handling in the connection close callback (\href{https://github.com/qorelanguage/qore/issues/3225}{\texttt{ issue 3225}}) \end{DoxyItemize} \item \href{../../modules/WebSocketHandler/html/index.html}{\texttt{ Web\+Socket\+Handler}}\+: \begin{DoxyItemize} \item added missing exception handling to connection registration code (\href{https://github.com/qorelanguage/qore/issues/3215}{\texttt{ issue 3215}}) \end{DoxyItemize} \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_08138}{}\doxysection{Qore 0.\+8.\+13.\+8}\label{release_notes_qore_08138} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08138_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08138_bug_fixes} \begin{DoxyItemize} \item fixed a bug where \mbox{\hyperlink{group__io__constants_ga44ab38fe66ed7aa87731a2de976017c6}{Qore\+::stdout}}, \mbox{\hyperlink{group__io__constants_ga0cfa7aea34f3c921036623600e42b21f}{Qore\+::stdin}}, \mbox{\hyperlink{group__io__constants_ga697e4968984d273562f14bfed155b4a8}{Qore\+::stderr}}, \mbox{\hyperlink{group__io__constants_gad35de1bb3d368f94ca75b1a4e165f361}{Qore\+::stdout\+\_\+stream}}, \mbox{\hyperlink{group__io__constants_gae2e16a518aa5a69148ad5b218ae91109}{Qore\+::stdin\+\_\+stream}}, and \mbox{\hyperlink{group__io__constants_gae762f18fd8b6318f15f8aaf1d18c595e}{Qore\+::stderr\+\_\+stream}}, would perform automatic C\+R\+LF -\/$>$ LF translations on Windows (\href{https://github.com/qorelanguage/qore/issues/3061}{\texttt{ issue 3061}}) \item fixed a bug in secure socket T\+LS communication making it impossible to talk to servers that require \href{https://en.wikipedia.org/wiki/Server_Name_Indication}{\texttt{ S\+NI}} (\href{https://github.com/qorelanguage/qore/issues/3053}{\texttt{ issue 3053}}) \item fixed a deadlock in \mbox{\hyperlink{class_qore_1_1_ftp_client_a835c52e32ee089773d48574f297e7965}{Ftp\+Client\+::put()}} with zero-\/length files (\href{https://github.com/qorelanguage/qore/issues/3038}{\texttt{ issue 3038}}) \item fixed an error respecting the I/O timeout in \mbox{\hyperlink{class_qore_1_1_ftp_client_a835c52e32ee089773d48574f297e7965}{Ftp\+Client\+::put()}} with \mbox{\hyperlink{class_qore_1_1_input_stream}{Input\+Stream}} argugments (\href{https://github.com/qorelanguage/qore/issues/3032}{\texttt{ issue 3032}}) \item fixed an error where \mbox{\hyperlink{class_qore_1_1_ftp_client}{Ftp\+Client}} {\ttfamily P\+O\+RT} operations would not time out (\href{https://github.com/qorelanguage/qore/issues/3031}{\texttt{ issue 3031}}) \end{DoxyItemize}\hypertarget{release_notes_qore_08137}{}\doxysection{Qore 0.\+8.\+13.\+7}\label{release_notes_qore_08137} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08137_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08137_bug_fixes} \begin{DoxyItemize} \item module fixes\+: \begin{DoxyItemize} \item \href{../../modules/ConnectionProvider/html/index.html}{\texttt{ Connection\+Provider}}\+: \begin{DoxyItemize} \item removed unnecessary serialization from Abstract\+Connection\+::get() (\href{https://github.com/qorelanguage/qore/issues/2880}{\texttt{ issue 2880}}) \end{DoxyItemize} \item \href{../../modules/PgsqlSqlUtil/html/index.html}{\texttt{ Pgsql\+Sql\+Util}} \begin{DoxyItemize} \item fixed schema alignment when there are functions to be dropped (\href{https://github.com/qorelanguage/qore/issues/2963}{\texttt{ issue 2963}}) \end{DoxyItemize} \end{DoxyItemize} \item fixed a race condition in \mbox{\hyperlink{class_qore_1_1_thread_1_1_thread_pool}{Thread\+Pool}} destruction that could cause a crash (\href{https://github.com/qorelanguage/qore/issues/2906}{\texttt{ issue 2906}}) \item fixed a hard to reproduce bug with internal runtime type matching that sometimes caused invalid runtime exceptions to be raised with base class constructors (\href{https://github.com/qorelanguage/qore/issues/2928}{\texttt{ issue 2928}}) \item fixed an error handling attach errors to \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects from foreign threads after the program has been deleted (\href{https://github.com/qorelanguage/qore/issues/2950}{\texttt{ issue 2950}}) \item fixed a bug that would cause a crash if an unknown {\ttfamily \char`\"{}\+Content-\/\+Encoding\char`\"{}} value were received by the \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client}{H\+T\+T\+P\+Client}} class (\href{https://github.com/qorelanguage/qore/issues/2953}{\texttt{ issue 2953}}) \item fixed a memory leak with binary objects in certain operations such as when reading a file into a binary object (\href{https://github.com/qorelanguage/qore/issues/2982}{\texttt{ issue 2982}}) \end{DoxyItemize}\hypertarget{release_notes_qore_08136}{}\doxysection{Qore 0.\+8.\+13.\+6}\label{release_notes_qore_08136} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08136_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08136_bug_fixes} \begin{DoxyItemize} \item fixed a deadlock in lvalue handling with complex object operations in multithreaded contexts (\href{https://github.com/qorelanguage/qore/issues/2889}{\texttt{ issue 2889}}) \item fixed type errors with complex hashes in \mbox{\hyperlink{class_qore_1_1zzz8hashzzz9_aa0a89864ecb2f16870af201163a6e3a7}{Qore\+::zzz8hashzzz9\+::values()}} and \mbox{\hyperlink{group__misc__functions_gaf5d769ebf4e89f22c223f36beacf5000}{hash\+\_\+values()}} (\href{https://github.com/qorelanguage/qore/issues/2877}{\texttt{ issue 2877}}) \item fixed an error handling complex types with the \mbox{\hyperlink{operators_plus_equals_operator}{+=}} operator (\href{https://github.com/qorelanguage/qore/issues/2869}{\texttt{ issue 2869}}) \item fixed a memory leak in \mbox{\hyperlink{class_qore_1_1_tree_map_a4bfaf979430e7cac9c265101f0d057dd}{Tree\+Map\+::put()}} (\href{https://github.com/qorelanguage/qore/issues/2840}{\texttt{ issue 2840}}) \item fixed a crashing bug in {\ttfamily qpp} (used in building \mbox{\hyperlink{namespace_qore}{Qore}} from source) (\href{https://github.com/qorelanguage/qore/issues/2838}{\texttt{ issue 2838}}) \item fixed a crashing bug in \mbox{\hyperlink{class_qore_1_1_socket_a39eb3993cde9b9e0096412d1edbc3a57}{Socket\+::accept()}} handling (\href{https://github.com/qorelanguage/qore/issues/2835}{\texttt{ issue 2835}}) \item fixed a cosmetic bug in module load error messages to provide the context of the module where the error is found in cases where it was missing (\href{https://github.com/qorelanguage/qore/issues/2834}{\texttt{ issue 2834}}) \item module fixes\+: \begin{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}}\+: \begin{DoxyItemize} \item schema alignment fails when user accidentally creates table schema with strings instead of hashes (\href{https://github.com/qorelanguage/qore/issues/2761}{\texttt{ issue 2358}}) \end{DoxyItemize} \item \href{../../modules/Swagger/html/index.html}{\texttt{ Swagger}}\+: \begin{DoxyItemize} \item Swagger module does not use text/plain Content-\/\+Type for simple string responses (\href{https://github.com/qorelanguage/qore/issues/2893}{\texttt{ issue 2893}}) \item Swagger module does not check response body if response schema is missing in Swaggerfile (\href{https://github.com/qorelanguage/qore/issues/2894}{\texttt{ issue 2894}}) \end{DoxyItemize} \item \href{../../modules/WebSocketClient/html/index.html}{\texttt{ Web\+Socket\+Client}}\+: \begin{DoxyItemize} \item allowed the handling of {\ttfamily P\+I\+NG} messages to be customized (\href{https://github.com/qorelanguage/qore/issues/2887}{\texttt{ issue 2887}}) \end{DoxyItemize} \item \href{../../modules/WebSocketHandler/html/index.html}{\texttt{ Web\+Socket\+Handler}}\+: \begin{DoxyItemize} \item added support for heartbeat messages (\href{https://github.com/qorelanguage/qore/issues/2887}{\texttt{ issue 2887}}) \end{DoxyItemize} \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_08135}{}\doxysection{Qore 0.\+8.\+13.\+5}\label{release_notes_qore_08135} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08135_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08135_bug_fixes} \begin{DoxyItemize} \item fixed a bug where user modules with global variables could not be loaded into \mbox{\hyperlink{class_qore_1_1_program}{Program}} containers where \mbox{\hyperlink{group__parse__options_ga00fcb14e17ebe9073cc0b768c276cf64}{P\+O\+\_\+\+N\+O\+\_\+\+G\+L\+O\+B\+A\+L\+\_\+\+V\+A\+RS}} was set (\href{https://github.com/qorelanguage/qore/issues/2807}{\texttt{ issue 2807}}) \item fixed a deadlock with \mbox{\hyperlink{class_qore_1_1_thread_1_1_r_w_lock}{R\+W\+Lock}} and \mbox{\hyperlink{class_qore_1_1_thread_1_1_condition}{Condition}} objects when the read lock is held recursively (\href{https://github.com/qorelanguage/qore/issues/2817}{\texttt{ issue 2817}}) \item module fixes\+: \begin{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}}\+: \begin{DoxyItemize} \item implemented the {\ttfamily number\+\_\+format} option to allow numbers with alternative decimal separators to be parsed and generated (\href{https://github.com/qorelanguage/qore/issues/2806}{\texttt{ issue 2806}}) \end{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}}\+: \begin{DoxyItemize} \item added support for R\+E\+ST requests with binary message bodies; added the {\ttfamily \char`\"{}bin\char`\"{}} serialization method (\href{https://github.com/qorelanguage/qore/issues/2816}{\texttt{ issue 2816}}) \end{DoxyItemize} \item \href{../../modules/RestSchemaValidator/html/index.html}{\texttt{ Rest\+Schema\+Validator}}\+: \begin{DoxyItemize} \item fixed the null validator to handle binary message bodies; fixed issues with {\ttfamily \char`\"{}text\char`\"{}} serialization with binary message bodies (\href{https://github.com/qorelanguage/qore/issues/2816}{\texttt{ issue 2816}}) \end{DoxyItemize} \item \href{../../modules/Mime/html/index.html}{\texttt{ Mime}}\+: \begin{DoxyItemize} \item fixed a bug in {\ttfamily mime\+\_\+parse\+\_\+form\+\_\+urlencoded\+\_\+string()} where repeated elements would be overwriteen by subsequent keys with the same name (\href{https://github.com/qorelanguage/qore/issues/2761}{\texttt{ issue 2761}}) \end{DoxyItemize} \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_08134}{}\doxysection{Qore 0.\+8.\+13.\+4}\label{release_notes_qore_08134} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08134_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08134_bug_fixes} \begin{DoxyItemize} \item fixed a bug where hashes and lists with subtype \mbox{\hyperlink{data_type_declarations_auto_type}{auto}} were not created correctly with implicit initialization causing excess type stripping which could lead to performance issues with large data structures (\href{https://github.com/qorelanguage/qore/issues/2767}{\texttt{ issue 2767}}) \item implemented a new optional D\+BI statement method to allow for statement execution only for describing the result set to solve performance issues when describing statements with large data sets (\href{https://github.com/qorelanguage/qore/issues/2773}{\texttt{ issue 2773}}) \item fixed a performance bug by eliminating overzealous and unnecessary internal type stripping (\href{https://github.com/qorelanguage/qore/issues/2791}{\texttt{ issue 2791}}) \item module fixes\+: \begin{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}}\+: \begin{DoxyItemize} \item implemented the {\ttfamily csvutil\+\_\+set\+\_\+global\+\_\+compat\+\_\+force\+\_\+empty\+\_\+string()} function and the {\ttfamily compat\+\_\+force\+\_\+empty\+\_\+string} C\+SV parsing option to force {\ttfamily \char`\"{}$\ast$string\char`\"{}} fields with no value to return an empty string when parsing rather than \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} for backwards compatibility with very early versions of Csv\+Util (\href{https://github.com/qorelanguage/qore/issues/2476}{\texttt{ issue 2476}}) \end{DoxyItemize} \item \href{../../modules/Mime/html/index.html}{\texttt{ Mime}}\+: \begin{DoxyItemize} \item mime\+\_\+parse\+\_\+form\+\_\+urlencoded\+\_\+string raies a parse exception when there is no value for a key (\href{https://github.com/qorelanguage/qore/issues/2760}{\texttt{ issue 2760}}) \end{DoxyItemize} \item \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}} module changes \begin{DoxyItemize} \item synonym resolving can fail with duplicated object name (\href{https://github.com/qorelanguage/qore/issues/2758}{\texttt{ issue 758}}) \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}}\+: \begin{DoxyItemize} \item implemented the {\ttfamily Abstract\+Table\+::get\+Row\+Iterator\+No\+Exec()} method (\href{https://github.com/qorelanguage/qore/issues/2773}{\texttt{ issue 2773}}) \end{DoxyItemize} \item \href{../../modules/TableMapper/html/index.html}{\texttt{ Table\+Mapper}}\+: \begin{DoxyItemize} \item updated to use the new S\+QL statement D\+BI method for efficient execution of queries only for describing result sets with outbound mappers to solve performance problems related to mappers that have statements with large data sets (\href{https://github.com/qorelanguage/qore/issues/2773}{\texttt{ issue 2773}}) \item fixed {\ttfamily Raw\+Sql\+Statement\+Outbound\+Mapper} to be usable without subclassing (\href{https://github.com/qorelanguage/qore/issues/2775}{\texttt{ issue 2775}}) \end{DoxyItemize} \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_08133}{}\doxysection{Qore 0.\+8.\+13.\+3}\label{release_notes_qore_08133} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08133_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_08133_new_features} \begin{DoxyItemize} \item improved debugging support\+: \begin{DoxyItemize} \item added support for a \href{https://code.visualstudio.com/}{\texttt{ Visual Studio Code}} debug adapter for Qore \item the debugger can now retrieve sources when running from a remote debug server \item debugger options can now be set from command line (verbosity etc.) \item the {\ttfamily on\+Attach()} event is now executed synchronously when the program thread context starts \item the {\ttfamily on\+Detach()} event is executed properly when program thread contexts terminate \item the {\ttfamily on\+Step()} now provides the {\ttfamily breakpoint\+Id} value if available \item the {\ttfamily on\+Exit()} event was added for greater control over code execution in the debugger \item the {\ttfamily on\+Exception()} event was improved \item server commands now support {\ttfamily frameid} as a parameter \item added the following methods to support retrieving source code in the debugger\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_program_control_aba9d573eccbad75e63fd188b07c2e413}{Program\+Control\+::get\+Source\+File\+Names()}} \item \mbox{\hyperlink{class_qore_1_1_program_control_afcd1bd3d3337759f9a1d66d647da533d}{Program\+Control\+::get\+Source\+Labels()}} \end{DoxyItemize} \end{DoxyItemize} \item new module\+: \begin{DoxyItemize} \item \href{../../modules/DebugLinenoiseCmdLine/html/index.html}{\texttt{ Debu\+Linenoise\+Cmd\+Line}} \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_08133_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08133_bug_fixes} \begin{DoxyItemize} \item module fixes\+: \begin{DoxyItemize} \item \href{../../modules/QUnit/html/index.html}{\texttt{ Q\+Unit}}\+: \begin{DoxyItemize} \item improved output in assertion failures for strings with special whitespace and for multi-\/line data structures (\href{https://github.com/qorelanguage/qore/issues/2680}{\texttt{ issue 2680}}) \end{DoxyItemize} \item \href{../../modules/WebUtil/html/index.html}{\texttt{ Web\+Util}}\+: \begin{DoxyItemize} \item made it possible for File\+Handler subclasses to add headers to response (\href{https://github.com/qorelanguage/qore/issues/2686}{\texttt{ issue 2686}}) \end{DoxyItemize} \end{DoxyItemize} \item \href{../../modules/HttpServerUtil/html/index.html}{\texttt{ Http\+Server\+Util}}\+: \begin{DoxyItemize} \item improved H\+T\+TP log masking to mask fewer false positives when attempting to mask sensitive data (\href{https://github.com/qorelanguage/qore/issues/2621}{\texttt{ issue 2621}}) \end{DoxyItemize} \item fixed a crashing bug initializing constants with recursive references to code (\href{https://github.com/qorelanguage/qore/issues/3027}{\texttt{ issue 3027}}) \item fixed a crashing bug in the \mbox{\hyperlink{operators_plus_equals_operator}{+= operator}} with objects and hashes when \mbox{\hyperlink{parse_directives_require-types}{\%require-\/types}} is not in force (\href{https://github.com/qorelanguage/qore/issues/2634}{\texttt{ issue 2634}}) \item fixed a crashing bug in the \mbox{\hyperlink{operators_background}{background operator}} with non-\/constant hash expressions with local variable references (\href{https://github.com/qorelanguage/qore/issues/2637}{\texttt{ issue 2637}}) \item worked around an Oracle bug in materialized view creation in the \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}} module where when the schema user is missing the {\ttfamily C\+R\+E\+A\+TE M\+A\+T\+E\+R\+I\+A\+L\+I\+Z\+ED V\+I\+EW} grant the table backing the view is created but the materialized view itself is not created causing future creation actions to fail (\href{https://github.com/qorelanguage/qore/issues/2643}{\texttt{ issue 2643}}) \item implemented support for an optional error-\/handling method in S\+QL callbacks in the \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module to allow Sql\+Util to recover from error scenarios in schema creation/alignment (\href{https://github.com/qorelanguage/qore/issues/2643}{\texttt{ issue 2643}}) \item fixed a design bug where an empty list {\ttfamily ()} and an empty hash {\ttfamily \{\}} could not be assigned to complex types, leading to excess typing and casting for simple operations (\href{https://github.com/qorelanguage/qore/issues/2647}{\texttt{ issue 2647}}) \item fixed a bug in the \mbox{\hyperlink{operators_map}{map operator}} with complex types and empty list expressions (\href{https://github.com/qorelanguage/qore/issues/2651}{\texttt{ issue 2651}}) \item fixed a bug where implicitly-\/declared values of complex \char`\"{}or nothing\char`\"{} types would not be declared with the correct runtime type information (\href{https://github.com/qorelanguage/qore/issues/2652}{\texttt{ issue 2652}}) \item fixed a bug affecting class initialization with out of order initialization (\href{https://github.com/qorelanguage/qore/issues/2657}{\texttt{ issue 2657}}) \item implemented support for the more concise declaration of immediate typed hash values (\href{https://github.com/qorelanguage/qore/issues/2675}{\texttt{ issue 2675}}) \item fixed a bug where a crash would result when evaluating certain expressions in the \mbox{\hyperlink{operators_background}{brackground operator}} due to a memory error (\href{https://github.com/qorelanguage/qore/issues/2679}{\texttt{ issue 2679}}) \item fixed \mbox{\hyperlink{group__date__and__time__functions_date_formatting}{date formatting}} output with the {\ttfamily Z} placeholder to always output the U\+TC offset as documented (\href{https://github.com/qorelanguage/qore/issues/2684}{\texttt{ issue 2684}}) \item fixed program thread context to return frames properly (\href{https://github.com/qorelanguage/qore/issues/2674}{\texttt{ issue 2674}}) \item fixed an internal memory bug that could cause unallocated memory to be read when creating objects (\href{https://github.com/qorelanguage/qore/issues/2712}{\texttt{ issue 2712}}) \item fixed a memory issue with typed hashes that could lead to a runtime creash (\href{https://github.com/qorelanguage/qore/issues/2725}{\texttt{ issue 2725}}) \end{DoxyItemize}\hypertarget{release_notes_qore_08132}{}\doxysection{Qore 0.\+8.\+13.\+2}\label{release_notes_qore_08132} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08132_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_08132_new_features} \begin{DoxyItemize} \item {\ttfamily \char`\"{}thread list\char`\"{}}, {\ttfamily \char`\"{}backtrace all\char`\"{}} commands implemented for the debugger (\href{https://github.com/qorelanguage/qore/issues/2608}{\texttt{ issue 2608}}) \item \href{../../modules/QUnit/html/index.html}{\texttt{ Q\+Unit}}\+: overloaded the {\ttfamily test\+Assertion\+Value()} method to support auto/number/float and more verbose output when a difference in number/float values is found (\href{https://github.com/qorelanguage/qore/issues/2556}{\texttt{ issue 2556}}) \item qdbg-\/remote supports Connection\+Provider connections (\href{https://github.com/qorelanguage/qore/issues/2613}{\texttt{ issue 2613}}) \item new method\+: \mbox{\hyperlink{class_qore_1_1_breakpoint_a68760cc4fde41e64496725927e873bcf}{Breakpoint\+::get\+Program()}} \end{DoxyItemize}\hypertarget{release_notes_qore_08132_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08132_bug_fixes} \begin{DoxyItemize} \item module fixes\+: \begin{DoxyItemize} \item \href{../../modules/DebugCmdLine/html/index.html}{\texttt{ Debug\+Cmd\+Line}}\+: \begin{DoxyItemize} \item improved breakpoint usability (\href{https://github.com/qorelanguage/qore/issues/2604}{\texttt{ issue 2604}}) \item fixed a bug parsing call signatures when setting breakpoints (\href{https://github.com/qorelanguage/qore/issues/2601}{\texttt{ issue 2601}}) \end{DoxyItemize} \item \href{../../modules/DebugProgramControl/html/index.html}{\texttt{ Debug\+Program\+Control}}\+: \begin{DoxyItemize} \item improved breakpoint usability (\href{https://github.com/qorelanguage/qore/issues/2604}{\texttt{ issue 2604}}) \item fixed a bug providing the program\+Id context (\href{https://github.com/qorelanguage/qore/issues/2603}{\texttt{ issue 2603}}) \end{DoxyItemize} \item \href{../../modules/QUnit/html/index.html}{\texttt{ Q\+Unit}}\+: \begin{DoxyItemize} \item improved error location reporting by providing all stack location information up until the Q\+Unit call to cover the case when multiple code layers are used such as one or more test modules (\href{https://github.com/qorelanguage/qore/issues/1720}{\texttt{ issue 1720}}) \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}}\+: \begin{DoxyItemize} \item implemented support for literal values in column operators taking column arguments with {\ttfamily cop\+\_\+value()} (\href{https://github.com/qorelanguage/qore/issues/2555}{\texttt{ issue 2555}}) \end{DoxyItemize} \item \href{../../modules/WebSocketClient/html/index.html}{\texttt{ Web\+Socket\+Client}}\+: \begin{DoxyItemize} \item added {\ttfamily Web\+Socket\+Client\+::pong()} to allow unsolicited {\ttfamily P\+O\+NG} messages to be sent (\href{https://github.com/qorelanguage/qore/issues/2566}{\texttt{ issue 2566}}) \end{DoxyItemize} \item \href{../../modules/WebSocketHandler/html/index.html}{\texttt{ Web\+Socket\+Handler}}\+: \begin{DoxyItemize} \item fixed a bug where unsolicited {\ttfamily P\+O\+NG} messages caused the connection to be prematurely closed (\href{https://github.com/qorelanguage/qore/issues/2566}{\texttt{ issue 2566}}) \end{DoxyItemize} \end{DoxyItemize} \item fixed a bug with implicit initialization of typed hashes; this is now illegal and a {\ttfamily H\+A\+S\+H\+D\+E\+C\+L-\/\+I\+M\+P\+L\+I\+C\+I\+T-\/\+C\+O\+N\+S\+T\+R\+U\+C\+T\+I\+O\+N-\/\+E\+R\+R\+OR} exception is raised in such cases (\href{https://github.com/qorelanguage/qore/issues/2491}{\texttt{ issue 2491}}) \item fixed a bug with \mbox{\hyperlink{class_qore_1_1_thread_1_1_condition}{Condition}} variable handling on mac\+OS High Sierra due to an internal undocumented A\+PI change (\href{https://github.com/qorelanguage/qore/issues/2576}{\texttt{ issue 2576}}) \item fixed a memory error with the \mbox{\hyperlink{operators_plus_equals_operator}{+= operator}} and uninitialized date/time values (\href{https://github.com/qorelanguage/qore/issues/2591}{\texttt{ issue 2591}}) \item fixed a bug in the remote debugger {\ttfamily qdbg-\/remote} where {\ttfamily wss\+://} schemes were not accepted (\href{https://github.com/qorelanguage/qore/issues/2596}{\texttt{ issue 2596}}) \item fixed a bug in an error message in \mbox{\hyperlink{class_qore_1_1_program_control_abeb009c4ccc44659d90584bff3e8ff4b}{Program\+Control\+::find\+Function\+Statement\+Id()}} (\href{https://github.com/qorelanguage/qore/issues/2600}{\texttt{ issue 2600}}) \item fixed a crash when \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a7d57e49bdde9c6fa2d67013f3fb0a4c8}{H\+T\+T\+P\+Client\+::set\+Default\+Path()}} was called with no argument (\href{https://github.com/qorelanguage/qore/issues/2610}{\texttt{ issue 2610}}) \item fixed a bug in debugger when program is not set (\href{https://github.com/qorelanguage/qore/issues/2603}{\texttt{ issue 2603}}) \end{DoxyItemize}\hypertarget{release_notes_qore_08131}{}\doxysection{Qore 0.\+8.\+13.\+1}\label{release_notes_qore_08131} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08131_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_08131_new_features} \begin{DoxyItemize} \item the {\ttfamily sqlutil} script has been updated with the {\ttfamily --select} option to allow dumped table rows to be filtered (\href{https://github.com/qorelanguage/qore/issues/2509}{\texttt{ issue 2509}}) \end{DoxyItemize}\hypertarget{release_notes_qore_08131_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08131_bug_fixes} \begin{DoxyItemize} \item fixes in modules\+: \begin{DoxyItemize} \item {\ttfamily astparser} module fixes\+: \begin{DoxyItemize} \item fixed memory leaks in {\ttfamily Ast\+Parser\+::parse\+File()} and {\ttfamily Ast\+Parser\+::parse\+String()} methods (\href{https://github.com/qorelanguage/qore/issues/2261}{\texttt{ issue 2261}}) \item fixed incorrect flex code regarding parse options leading to segfaults (\href{https://github.com/qorelanguage/qore/issues/2262}{\texttt{ issue 2262}}) \end{DoxyItemize} \item \href{../../modules/DebugCmdLine/html/index.html}{\texttt{ Debug\+Cmd\+Line}} module fixes\+: \begin{DoxyItemize} \item fixed value setting to process all remaining arguments on the command line (\href{https://github.com/qorelanguage/qore/issues/2294}{\texttt{ issue 2294}}) \end{DoxyItemize} \item \href{../../modules/DebugCmdLine/html/index.html}{\texttt{ Debug\+Cmd\+Line}} module fixes\+: \begin{DoxyItemize} \item the debugger should report ambiguous partial matches as an error (\href{https://github.com/qorelanguage/qore/issues/2292}{\texttt{ issue 2292}}) \end{DoxyItemize} \item \href{../../modules/MailMessage/html/index.html}{\texttt{ Mail\+Message}} module fixes\+: \begin{DoxyItemize} \item fixed {\ttfamily Message\+::add\+Body()} with no body present (issue \href{https://github.com/qorelanguage/qore/issues/2360}{\texttt{ issue 2360}}) \end{DoxyItemize} \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module fixes\+: \begin{DoxyItemize} \item fixed a bug in the {\ttfamily S\+T\+R\+I\+N\+G-\/\+T\+O\+O-\/\+L\+O\+NG} exception (\href{https://github.com/qorelanguage/qore/issues/2495}{\texttt{ issue 2405}}) \end{DoxyItemize} \item \href{../../modules/PgsqlSqlUtil/html/index.html}{\texttt{ Pgsql\+Sql\+Util}} module fixes\+: \begin{DoxyItemize} \item fixed a bug where default column values were compared incorrectly leading to false positives when comparing and aligning DB schemas (\href{https://github.com/qorelanguage/qore/issues/2527}{\texttt{ issue 2527}}) \end{DoxyItemize} \item \href{../../modules/Qdx/html/index.html}{\texttt{ Qdx}} module fixes\+: \begin{DoxyItemize} \item fixed a bug in documentation post-\/processing for \mbox{\hyperlink{hashdecl}{hashdecl}} declarations (\href{https://github.com/qorelanguage/qore/issues/2298}{\texttt{ issue 2298}}) \end{DoxyItemize} \item \href{../../modules/QUnit/html/index.html}{\texttt{ Q\+Unit}} fixes\+: \begin{DoxyItemize} \item added missing comparison methods (\href{https://github.com/qorelanguage/qore/issues/1588}{\texttt{ issue 1588}})\+: \begin{DoxyItemize} \item {\ttfamily Test\+::assert\+Regex()} \item {\ttfamily Test\+::assert\+N\+Regex()} \item {\ttfamily Test\+::assert\+Neq()} \item {\ttfamily Test\+::assert\+Neq\+Soft()} \item {\ttfamily Test\+::assert\+Gt()} \item {\ttfamily Test\+::assert\+Gt\+Soft()} \item {\ttfamily Test\+::assert\+Ge()} \item {\ttfamily Test\+::assert\+Ge\+Soft()} \item {\ttfamily Test\+::assert\+Lt()} \item {\ttfamily Test\+::assert\+Lt\+Soft()} \item {\ttfamily Test\+::assert\+Le()} \item {\ttfamily Test\+::assert\+Le\+Soft()} \item {\ttfamily Test\+::assert\+Nothing()} \end{DoxyItemize} \end{DoxyItemize} \item \href{../../modules/RestHandler/html/index.html}{\texttt{ Rest\+Handler}} module fixes\+: \begin{DoxyItemize} \item updated to return a 400 Bad Request error when R\+E\+ST schema validation fails on messages received \href{https://github.com/qorelanguage/qore/issues/2344}{\texttt{ issue 2344}}) \item updated to return a 400 Bad Request error when there are string encoding errors with messages received (\href{https://github.com/qorelanguage/qore/issues/2398}{\texttt{ issue 2398}}) \item updated to return a 404 Not Found error when R\+E\+ST subclass does not exist (\href{https://github.com/qorelanguage/qore/issues/2405}{\texttt{ issue 2405}}) \item updated to return a 400 Bad Request error when E\+N\+C\+O\+D\+I\+N\+G-\/\+C\+O\+N\+V\+E\+R\+S\+I\+O\+N-\/\+E\+R\+R\+OR occurs during request parsing (\href{https://github.com/qorelanguage/qore/issues/2543}{\texttt{ issue 2543}}) \end{DoxyItemize} \item \href{../../modules/RestSchemaValidator/html/index.html}{\texttt{ Rest\+Schema\+Validator}} module fixes\+: \begin{DoxyItemize} \item updated docs for {\ttfamily Abstract\+Rest\+Schema\+Validator\+::parse\+Request()} to reflect how validation exceptions should be raised for proper error reporting (\href{https://github.com/qorelanguage/qore/issues/2344}{\texttt{ issue 2344}}) \item fixed handling of messages with non-\/object (i.\+e. non-\/hash) bodies (\href{https://github.com/qorelanguage/qore/issues/2366}{\texttt{ issue 2366}}) \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module changes \begin{DoxyItemize} \item implemented support for custom column operators (\href{https://github.com/qorelanguage/qore/issues/2314}{\texttt{ issue 2314}}) \end{DoxyItemize} \item \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}} module changes \begin{DoxyItemize} \item implemented support for chained synonyms (\href{https://github.com/qorelanguage/qore/issues/2408}{\texttt{ issue 2408}}) \item allow to use D\+B\+A\+\_\+$\ast$ views instead of A\+L\+L\+\_\+$\ast$ if possible (\href{https://github.com/qorelanguage/qore/issues/2418}{\texttt{ issue 2418}}) \end{DoxyItemize} \item \href{../../modules/Swagger/html/index.html}{\texttt{ Swagger}} module fixes\+: \begin{DoxyItemize} \item fixed handling of string type date and date-\/time formats (\href{https://github.com/qorelanguage/qore/issues/2341}{\texttt{ issue 2341}}) \item fixed example value for binary type (\href{https://github.com/qorelanguage/qore/issues/2342}{\texttt{ issue 2342}}) \item fixed serialization of date/time values (\href{https://github.com/qorelanguage/qore/issues/2349}{\texttt{ issue 2349}}) \item updated to return a 400 Bad Request error when R\+E\+ST schema validation fails on messages received \href{https://github.com/qorelanguage/qore/issues/2344}{\texttt{ issue 2344}}) \item fixed handling of non-\/string enum types (\href{https://github.com/qorelanguage/qore/issues/2364}{\texttt{ issue 2364}}) \item fixed confusing error messages with invalid parameter types (\href{https://github.com/qorelanguage/qore/issues/2365}{\texttt{ issue 2365}}) \item fixed handling of messages with non-\/object (i.\+e. non-\/hash) bodies (\href{https://github.com/qorelanguage/qore/issues/2366}{\texttt{ issue 2366}}) \item fixed handling of optional parameters (\href{https://github.com/qorelanguage/qore/issues/2369}{\texttt{ issue 2369}}) \item fixed handling of non-\/string query parameters (\href{https://github.com/qorelanguage/qore/issues/2388}{\texttt{ issue 2388}}) \item fixed a bug where string value constraints were only enforced in requests but not responses (\href{https://github.com/qorelanguage/qore/issues/2396}{\texttt{ issue 2396}}) \item fixed a bug where invalid date, binary, and byte values would cause a {\ttfamily 500 Internal Server Error} response to be returned instead of a {\ttfamily 400 Bad Request} error (\href{https://github.com/qorelanguage/qore/issues/2397}{\texttt{ issue 2397}}) \item fixed a bug where date values were formatted incorrectly in Swagger responses (\href{https://github.com/qorelanguage/qore/issues/2409}{\texttt{ issue 2409}}) \item fixed a bug which made it impossible to send data with other content/mime types than json, yamlrpc, Form\+Url\+Encoded or Multipart\+Form\+Data (\href{https://github.com/qorelanguage/qore/issues/2497}{\texttt{ issue 2497}}) \item fixed handling of string/binary values (\href{https://github.com/qorelanguage/qore/issues/2505}{\texttt{ issue 2505}}) \item fixed a bug where consumes property of operations was sometimes ignored (\href{https://github.com/qorelanguage/qore/issues/2507}{\texttt{ issue 2507}}) \item fixed parsing of responses without Content-\/\+Type header (\href{https://github.com/qorelanguage/qore/issues/2517}{\texttt{ issue 2517}}) \item fixed path matching for paths not beginning with a slash (\href{https://github.com/qorelanguage/qore/issues/2516}{\texttt{ issue 2516}}) \end{DoxyItemize} \item \href{../../modules/TableMapper/html/index.html}{\texttt{ Table\+Mapper}} module fixes\+: \begin{DoxyItemize} \item fixed issues where where description fields of input and output records for automatically-\/generated options did not reflect column comments and could not be overridden with user input (\href{https://github.com/qorelanguage/qore/issues/2520}{\texttt{ issue 2520}}) \end{DoxyItemize} \end{DoxyItemize} \item fixed bugs affecting debugging matching function/method variants and finding statements with special methods and with complex types (\href{https://github.com/qorelanguage/qore/issues/1865}{\texttt{ issue 1865}}) \item fixed a bug in {\ttfamily qpp} generating hashdecl code in a specific namespace (\href{https://github.com/qorelanguage/qore/issues/2255}{\texttt{ issue 2255}}) \item fixed an error in a \mbox{\hyperlink{hashdecl}{hashdecl}} documentation example (\href{https://github.com/qorelanguage/qore/issues/2299}{\texttt{ issue 2299}}) \item made C++ A\+P\+Is for complex types for modules public (\href{https://github.com/qorelanguage/qore/issues/2271}{\texttt{ issue 2271}}) \item fixed inconsistencies in the behavior of the \mbox{\hyperlink{operators_range_operator}{range operator (..)}} and the \mbox{\hyperlink{operators_list_element_operator}{square brackets operator \mbox{[}\mbox{]}}} with lists and ranges between immediate evaluation and lazy functional evaluation and aligned the behavior of the operators among supported data types with the \mbox{\hyperlink{operators_remove}{remove}} and \mbox{\hyperlink{operators_delete}{delete}} operators (\href{https://github.com/qorelanguage/qore/issues/2260}{\texttt{ issue 2260}}) \item fixed a bug handling statement indices with parse errors (\href{https://github.com/qorelanguage/qore/issues/2312}{\texttt{ issue 2312}}) \item fixed too-\/agressive class hierachy checks that disallowed legal hierarchies where the same base class appears more than once in the hierarchy (\href{https://github.com/qorelanguage/qore/issues/2317}{\texttt{ issue 2317}}) \item fixed a crashing bug in the background operator when the object in context goes out of scope with the thread and an exception is thrown (\href{https://github.com/qorelanguage/qore/issues/2319}{\texttt{ issue 2319}}) \item fixed sending duplicate headers when header hash keys differ only in case; headers that differ only in case will be overwritten by the last header in the hash with a matching name with a case-\/insensitive search (\href{https://github.com/qorelanguage/qore/issues/2340}{\texttt{ issue 2340}}) \item fixed {\ttfamily q\+\_\+absolute\+\_\+path\+\_\+windows} to correctly recognize relative Windows paths beginning with a drive letter (\href{https://github.com/qorelanguage/qore/issues/2377}{\texttt{ issue 2377}}) \item fixed a bug in {\ttfamily {\bfseries{private\+:internal}}} in method execution within a class hierarchy in some cases (\href{https://github.com/qorelanguage/qore/issues/2380}{\texttt{ issue 2380}}) \item fixed an obscure bug handling runtime errors in code calls with a variant matched at parse time where a runtime exception could occur (\href{https://github.com/qorelanguage/qore/issues/2392}{\texttt{ issue 2392}}) \item improved breakpoints (enabled by default), extended help texts, load/save debug history and session (\href{https://github.com/qorelanguage/qore/issues/2401}{\texttt{ issue 2401}}) \item fixed a bug in an error message regarding binary module signal assignments (\href{https://github.com/qorelanguage/qore/issues/2439}{\texttt{ issue 2439}}) \item added C++ functions to allow binary modules to allocate and deallocate multiple signals atomically (\href{https://github.com/qorelanguage/qore/issues/2440}{\texttt{ issue 2440}}) \item eliminated a warning in a header file when building with g++ 7+ (\href{https://github.com/qorelanguage/qore/issues/2449}{\texttt{ issue 2449}}) \item implemented a fix in {\ttfamily qdbg} to resume any blocked threads before exiting to ensure a clean and correct shutdown of the debugger; fixes a problem when the process ould freeze on {\ttfamily quit} (\href{https://github.com/qorelanguage/qore/issues/2472}{\texttt{ issue 2472}}) \item fixed bugs in Windows builds (\href{https://github.com/qorelanguage/qore/issues/2529}{\texttt{ issue 2529}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0813}{}\doxysection{Qore 0.\+8.\+13}\label{release_notes_qore_0813} \begin{DoxyParagraph}{Release Summary} Major new features and bug fixes including input and output stream support and sigificant new functionality including several new modules. \end{DoxyParagraph} \hypertarget{release_notes_qore_0813_compatibility}{}\doxysubsection{Changes That Can Affect Backwards-\/\+Compatibility}\label{release_notes_qore_0813_compatibility} \begin{DoxyItemize} \item fixed broken \mbox{\hyperlink{statements_continue}{continue}} and \mbox{\hyperlink{statements_break}{break}} statements that were accepted anywhere in the source and behaved like a \mbox{\hyperlink{statements_return}{return}} statement; now such statements outside a loop context will result in a parse exception; to get the old behavior, use \mbox{\hyperlink{parse_directives_broken-loop-statement}{\%broken-\/loop-\/statement}} in your source code \item fixed broken \mbox{\hyperlink{data_type_declarations_reference_type}{reference}} and \mbox{\hyperlink{data_type_declarations_reference_or_nothing_type}{$\ast$reference}} type restrictions which had no effect prior to this release; to get the old behavior, use \mbox{\hyperlink{parse_directives_broken-references}{\%broken-\/references}} in your source code \item the random number generator is always seeded with a random number when the \mbox{\hyperlink{namespace_qore}{Qore}} library is initialized; to get a predictable sequence from \mbox{\hyperlink{namespace_qore_a6ed36f08f41864dfe007504e8b4ff5c3}{rand()}}, you must explicitly seed the random number generator by calling \mbox{\hyperlink{namespace_qore_aeb017e3b5ea8ff39e270e844f280e32b}{srand()}} with a predefined seed number \item the \mbox{\hyperlink{threading_synchronized}{synchronized}} keyword now operates differently depending on the context; {\ttfamily {\bfseries{synchronized}}} functions have a global reentrant lock associated with the function (as in previous versions of Qore), whereas now {\ttfamily {\bfseries{synchronized}}} normal class methods share a reentrant lock associated with the object, while {\ttfamily {\bfseries{synchronized}}} static class methods share a reentrant lock associated with the class itself. This aligns Qore\textquotesingle{}s \mbox{\hyperlink{threading_synchronized}{synchronized}} behavior with that of Java and {\ttfamily \mbox{[}Method\+Impl(Method\+Impl\+Options.\+Synchronized)\mbox{]}} .N\+E\+T/\+C\+LR (\href{https://github.com/qorelanguage/qore/issues/894}{\texttt{ issue 894}}). \item classes may not have the name {\ttfamily \char`\"{}auto\char`\"{}} due to the introduction of this identifier as a special type name \item a new keyword \mbox{\hyperlink{hashdecl}{hashdecl}} has been introduced to support type-\/safe hash declarations \end{DoxyItemize}\hypertarget{release_notes_qore_0813_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_0813_new_features} \begin{DoxyItemize} \item complex type support \begin{DoxyItemize} \item \mbox{\hyperlink{hashdecl}{type safe hashes}} (\mbox{\hyperlink{data_type_declarations_hash_hashdecl_type}{Type-\/\+Safe Hash Type}}); ex\+: \begin{DoxyCode}{0} \DoxyCodeLine{hash<MyInfo> = get\_info(); } \end{DoxyCode} \item new system types\+: \begin{DoxyItemize} \item \mbox{\hyperlink{struct_qore_1_1_call_stack_info}{Call\+Stack\+Info}} \item \mbox{\hyperlink{struct_qore_1_1_date_time_info}{Date\+Time\+Info}} \item \mbox{\hyperlink{struct_qore_1_1_dir_stat_info}{Dir\+Stat\+Info}} \item \mbox{\hyperlink{struct_qore_1_1_exception_info}{Exception\+Info}} \item \mbox{\hyperlink{struct_qore_1_1_filesystem_info}{Filesystem\+Info}} \item \mbox{\hyperlink{struct_qore_1_1_iso_week_info}{Iso\+Week\+Info}} \item \mbox{\hyperlink{struct_qore_1_1_stat_info}{Stat\+Info}} \end{DoxyItemize} \item \mbox{\hyperlink{data_type_declarations_hash_complex_type}{hash with type-\/safe values}}; ex\+: \begin{DoxyCode}{0} \DoxyCodeLine{hash<string, int> h = (\textcolor{stringliteral}{"str"}: 1); } \end{DoxyCode} \item \mbox{\hyperlink{data_type_declarations_list_complex_type}{list with type-\/safe values}}; ex\+: \begin{DoxyCode}{0} \DoxyCodeLine{list<int> l = (1); } \end{DoxyCode} \item \mbox{\hyperlink{data_type_declarations_reference_complex_type}{reference with type-\/safe lvalues}}; ex\+: \begin{DoxyCode}{0} \DoxyCodeLine{int i = 1; reference<int> r = $\backslash$i; } \end{DoxyCode} \item \mbox{\hyperlink{data_type_declarations_auto_type}{auto}} (allows any value including complex types to be assigned without losing complex type information); ex\+: \begin{DoxyCode}{0} \DoxyCodeLine{auto l = (1, 2); } \end{DoxyCode} \item improved \mbox{\hyperlink{operators_new}{new}}, \mbox{\hyperlink{operators_cast}{cast$<$$>$}}, and \mbox{\hyperlink{operators_instanceof}{instanceof}} operators \item the \mbox{\hyperlink{operators_instanceof}{instanceof}} operator now works with any type; ex\+: \begin{DoxyCode}{0} \DoxyCodeLine{bool b = v instanceof hash<string, int>; } \end{DoxyCode} \item note that complex type information is lost when assigning to an lvalue with a compatible but more generic type or by assigning to an untyped lvalue; this was necessary to allow complex types to be introduced in Qore without breaking backwards compatibility. \end{DoxyItemize} \item support for input and output streams for the efficient piecewise processing of small or large amounts of data with a low memory overhead \begin{DoxyItemize} \item includes the following classes\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_binary_input_stream}{Binary\+Input\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_binary_output_stream}{Binary\+Output\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_buffered_stream_reader}{Buffered\+Stream\+Reader}} \item \mbox{\hyperlink{class_qore_1_1_encoding_conversion_input_stream}{Encoding\+Conversion\+Input\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_encoding_conversion_output_stream}{Encoding\+Conversion\+Output\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_file_input_stream}{File\+Input\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_file_output_stream}{File\+Output\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_input_stream}{Input\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_input_stream_line_iterator}{Input\+Stream\+Line\+Iterator}} \item \mbox{\hyperlink{class_qore_1_1_output_stream}{Output\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_pipe_input_stream}{Pipe\+Input\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_pipe_output_stream}{Pipe\+Output\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_stream_pipe}{Stream\+Pipe}} \item \mbox{\hyperlink{class_qore_1_1_stream_reader}{Stream\+Reader}} \item \mbox{\hyperlink{class_qore_1_1_stream_writer}{Stream\+Writer}} \item \mbox{\hyperlink{class_qore_1_1_string_input_stream}{String\+Input\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_string_output_stream}{String\+Output\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_transform}{Transform}} \item \mbox{\hyperlink{class_qore_1_1_transform_input_stream}{Transform\+Input\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_transform_output_stream}{Transform\+Output\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_stdout_output_stream}{Stdout\+Output\+Stream}} \item \mbox{\hyperlink{class_qore_1_1_stderr_output_stream}{Stderr\+Output\+Stream}} \end{DoxyItemize} \item Three constants were introduced for accessing standard input/output using streams A\+PI\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__io__constants_gae2e16a518aa5a69148ad5b218ae91109}{stdin\+\_\+stream}} \item \mbox{\hyperlink{group__io__constants_gad35de1bb3d368f94ca75b1a4e165f361}{stdout\+\_\+stream}} \item \mbox{\hyperlink{group__io__constants_gae762f18fd8b6318f15f8aaf1d18c595e}{stderr\+\_\+stream}} \end{DoxyItemize} \item Additionally, stream support has been added to the following functions and methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_ftp_client_a835c52e32ee089773d48574f297e7965}{Qore\+::\+Ftp\+Client\+::put()}} \item \mbox{\hyperlink{class_qore_1_1_ftp_client_a2b06a66db173df6bac61b1af48c7a11c}{Qore\+::\+Ftp\+Client\+::get()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a5f2689469e270c7a5ea8f5fb024889a3}{Qore\+::\+H\+T\+T\+P\+Client\+::send()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a2b7084887db1c7b65744504feae95727}{Qore\+::\+H\+T\+T\+P\+Client\+::send\+Chunked()}} \item \mbox{\hyperlink{class_qore_1_1_socket_af9d1cff50c37b6a92b6ce60357f3593c}{Qore\+::\+Socket\+::send\+H\+T\+T\+P\+Chunked\+Body\+From\+Input\+Stream()}} \item \mbox{\hyperlink{class_qore_1_1_socket_ade1db5c9f051718cac1a1bdecb9e897e}{Qore\+::\+Socket\+::read\+H\+T\+T\+P\+Chunked\+Body\+To\+Output\+Stream()}} \end{DoxyItemize} \item Stream support was also added to the following user modules\+: \begin{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} \item \href{../../modules/FixedLengthUtil/html/index.html}{\texttt{ Fixed\+Length\+Util}} \end{DoxyItemize} \end{DoxyItemize} \item support for \mbox{\hyperlink{operators_op_functional}{lazy functional evaluation}} of functional operators (including nested lazy evaluation) for much more efficient processing of iterated expressions; affects\+: \begin{DoxyItemize} \item \mbox{\hyperlink{operators_map}{map}}\+: supports lazy evaluation of itself and also of the iterator expression \item \mbox{\hyperlink{operators_select}{select}}\+: supports lazy evaluation of itself and also of the iterator expression \item \mbox{\hyperlink{operators_keys}{keys}}\+: supports lazy evaluation of itself \item \mbox{\hyperlink{operators_foldl}{foldl}}\+: supports lazy evaluation of the iterator expression \item \mbox{\hyperlink{operators_foldr}{foldlr}}\+: supports lazy evaluation of the iterator expression \item \mbox{\hyperlink{statements_foreach}{foreach}}\+: supports lazy evaluation of the iterator expression \item \mbox{\hyperlink{operators_range_operator}{.. (range operator)}}\+: supports lazy evaluation of itself \item \mbox{\hyperlink{operators_list_element_operator}{\mbox{[}n,m,...\mbox{]} (list, string, or binary dereference with multiple indices))}}\+: supports lazy evaluation of itself \end{DoxyItemize} \item support for list, string, and binary slices with offsets and ranges\+: \begin{DoxyItemize} \item \mbox{\hyperlink{container_data_types_list_slicing}{list slices}} \item \mbox{\hyperlink{basic_data_types_string_slicing}{string slices}} \item \mbox{\hyperlink{basic_data_types_binary_slicing}{binary slices}} \item new \mbox{\hyperlink{operators_range_operator}{.. range operator}} \item updated \mbox{\hyperlink{operators_list_element_operator}{\mbox{[}\mbox{]} operator}} \end{DoxyItemize} \item enhanced cryptographic support including support for \href{https://en.wikipedia.org/wiki/Advanced_Encryption_Standard}{\texttt{ A\+ES}} with Additional Authenticated Data and \href{https://en.wikipedia.org/wiki/Message_authentication_code}{\texttt{ Message Authentication Code (M\+AC)}} support \begin{DoxyItemize} \item The following new A\+PI functions were added\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__hmac__functions_gad159aa97f0f07e827e74b4b9a12b92ca}{Qore\+::decrypt\+\_\+to\+\_\+binary()}} \item \mbox{\hyperlink{group__hmac__functions_ga94bc9698c368c32987d7207096806df1}{Qore\+::decrypt\+\_\+to\+\_\+string()}} \item \mbox{\hyperlink{group__hmac__functions_ga7141b56ffa6c5a4f8c9c58f788f33780}{Qore\+::encrypt()}} \item \mbox{\hyperlink{group__hmac__functions_ga23662a1e7f11f483a6e841da96389197}{Qore\+::get\+\_\+crypto\+\_\+info()}} \item \mbox{\hyperlink{group__hmac__functions_ga913932d6120f9ea1e3918168fb204976}{Qore\+::get\+\_\+decryptor()}} \item \mbox{\hyperlink{group__hmac__functions_ga6e67ba0396d70cd012f7c46c7562b81f}{Qore\+::get\+\_\+encryptor()}} \end{DoxyItemize} \item The following constants were added to support the new generic cryptographic A\+P\+Is\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__crypto__transformations_ga73689cc7289473ce0061551c392120bf}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+A\+E\+S\+\_\+128}} \item \mbox{\hyperlink{group__crypto__transformations_ga022dfeaa3c3e4ee34f0cb55ba1129125}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+A\+E\+S\+\_\+192}} \item \mbox{\hyperlink{group__crypto__transformations_ga5a725d566fde3fdf16cf967f24396d4f}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+A\+E\+S\+\_\+256}} \item \mbox{\hyperlink{group__crypto__transformations_ga537286d57ff4a0326f427e8d513cbfb0}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+B\+L\+O\+W\+F\+I\+SH}} \item \mbox{\hyperlink{group__crypto__transformations_ga422366c05ce16fb7bd4891e96eab6e8e}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+B\+L\+O\+W\+F\+I\+S\+H\+\_\+\+C\+FB}} \item \mbox{\hyperlink{group__crypto__transformations_ga2a5dfd4cdf80d6da8c2a9447ed0c4d13}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+B\+L\+O\+W\+F\+I\+S\+H\+\_\+\+O\+FB}} \item \mbox{\hyperlink{group__crypto__transformations_gab6dd39c61668eed9ee863a86c0536023}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+C\+A\+S\+T5}} \item \mbox{\hyperlink{group__crypto__transformations_ga5d4040b319f9c4bd307e4df9ed426676}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+C\+A\+S\+T5\+\_\+\+C\+FB}} \item \mbox{\hyperlink{group__crypto__transformations_gab4eced22515cb6dd7c6a28e436534a0d}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+C\+A\+S\+T5\+\_\+\+O\+FB}} \item \mbox{\hyperlink{group__crypto__transformations_gab2509ba7b5427976e71ed4441b96cb39}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+D\+ES}} \item \mbox{\hyperlink{group__crypto__transformations_ga4271e36093c0a96caf2a189dcf703f86}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+D\+E\+S\+\_\+\+C\+FB}} \item \mbox{\hyperlink{group__crypto__transformations_gab9ae17ec1fae8d177132b6abbe94dfb4}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+D\+E\+S\+\_\+\+O\+FB}} \item \mbox{\hyperlink{group__crypto__transformations_gae1d1fcde9e41fb04b5f1ecca97a69824}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+D\+E\+S\+\_\+\+E\+DE}} \item \mbox{\hyperlink{group__crypto__transformations_ga48839b104df4562c36fc787f7c262c56}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+D\+E\+S\+\_\+\+E\+D\+E\+\_\+\+C\+FB}} \item \mbox{\hyperlink{group__crypto__transformations_ga68234e274ee028b255e2af4417577b71}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+D\+E\+S\+\_\+\+E\+D\+E\+\_\+\+O\+FB}} \item \mbox{\hyperlink{group__crypto__transformations_ga056d23c2aaeeb75f37d4e7e515db5a6d}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+D\+E\+S\+\_\+\+E\+D\+E3}} \item \mbox{\hyperlink{group__crypto__transformations_gacadc7af0b9f9bf99c24f2045847544d8}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+D\+E\+S\+\_\+\+E\+D\+E3\+\_\+\+C\+FB}} \item \mbox{\hyperlink{group__crypto__transformations_gac2f3e064d44a1d71316036d2dd47fb3d}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+D\+E\+S\+\_\+\+E\+D\+E3\+\_\+\+O\+FB}} \item \mbox{\hyperlink{group__crypto__transformations_ga87d409efe9ca4136e594c9d7f054c7d5}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+D\+E\+SX}} \item \mbox{\hyperlink{group__crypto__transformations_ga5c88760095c4fd3d4306e69362d9e462}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+R\+C2}} \item \mbox{\hyperlink{group__crypto__transformations_ga7c32cf736fcb8a6580b7807a61e97c74}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+R\+C2\+\_\+\+C\+FB}} \item \mbox{\hyperlink{group__crypto__transformations_ga267f3f2ee291872b9e829ccce4c101f9}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+R\+C2\+\_\+\+O\+FB}} \item \mbox{\hyperlink{group__crypto__transformations_ga99a646fac8a832add2cff0a957680289}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+R\+C4}} \item \mbox{\hyperlink{group__crypto__transformations_gae9bcc35cfb5dc20aaf28434c852ee0ef}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+R\+C5}} \item \mbox{\hyperlink{group__crypto__transformations_ga9d66718f85fb96613009043d7ba9e391}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+R\+C5\+\_\+\+C\+FB}} \item \mbox{\hyperlink{group__crypto__transformations_gad93f79055d46a93781a138ca839f2b1b}{Qore\+::\+C\+R\+Y\+P\+T\+O\+\_\+\+A\+L\+G\+\_\+\+R\+C5\+\_\+\+O\+FB}} \end{DoxyItemize} \end{DoxyItemize} \item support for binding output placeholder buffers for \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_resultset_output_binding}{result sets}} that return an \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} object\+: \begin{DoxyItemize} \item new D\+BI capability constant \mbox{\hyperlink{group__dbi__capabilities_ga91b90789d24991b1eebce9c11491f015}{D\+B\+I\+\_\+\+C\+A\+P\+\_\+\+H\+A\+S\+\_\+\+R\+E\+S\+U\+L\+T\+S\+E\+T\+\_\+\+O\+U\+T\+P\+UT}} \item new placeholder buffer specification constant \mbox{\hyperlink{group__sql__constants_ga9d23a1d69fcb188296a231a36c6b6da2}{R\+E\+S\+U\+L\+T\+S\+ET}} \end{DoxyItemize} \item new debugging support (note that A\+P\+Is are subject to change until the next major release)\+: \begin{DoxyItemize} \item new classes\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_breakpoint}{Breakpoint}} \item \mbox{\hyperlink{class_qore_1_1_debug_program}{Debug\+Program}} \item \mbox{\hyperlink{class_qore_1_1_program_control}{Program\+Control}} \end{DoxyItemize} \item new modules\+: \begin{DoxyItemize} \item \href{../../modules/DebugCmdLine/html/index.html}{\texttt{ Debug\+Cmd\+Line}} \item \href{../../modules/DebugHandler/html/index.html}{\texttt{ Debug\+Handler}} \item \href{../../modules/DebugProgramControl/html/index.html}{\texttt{ Debug\+Program\+Control}} \item \href{../../modules/DebugUtil/html/index.html}{\texttt{ Debug\+Util}} \end{DoxyItemize} \item new parse directives\+: \begin{DoxyItemize} \item \mbox{\hyperlink{parse_directives_allow-debugger}{\%allow-\/debugger}}\+: allows running debug commands \item \mbox{\hyperlink{parse_directives_no-debugging}{\%no-\/debugging}}\+: forbids debugging of the current \mbox{\hyperlink{class_qore_1_1_program}{Program}} object \end{DoxyItemize} \end{DoxyItemize} \item new user modules\+: \begin{DoxyItemize} \item \href{../../modules/DebugCmdLine/html/index.html}{\texttt{ Debug\+Cmd\+Line}} \item \href{../../modules/DebugHandler/html/index.html}{\texttt{ Debug\+Handler}} \item \href{../../modules/DebugProgramControl/html/index.html}{\texttt{ Debug\+Program\+Control}} \item \href{../../modules/DebugUtil/html/index.html}{\texttt{ Debug\+Util}} \item \href{../../modules/ConnectionProvider/html/index.html}{\texttt{ Connection\+Provider}} \item \href{../../modules/DatasourceProvider/html/index.html}{\texttt{ Datasource\+Provider}} \item \href{../../modules/Qdx/html/index.html}{\texttt{ Qdx}} \item \href{../../modules/SewioRestClient/html/index.html}{\texttt{ Sewio\+Rest\+Client}} \item \href{../../modules/SewioWebSocketClient/html/index.html}{\texttt{ Sewio\+Web\+Socket\+Client}} \item \href{../../modules/Swagger/html/index.html}{\texttt{ Swagger}} \item \href{../../modules/TextWrap/html/index.html}{\texttt{ Text\+Wrap}} \end{DoxyItemize} \item new access modifiers\+: {\ttfamily {\bfseries{private\+:internal}}} (providing strong encapsulation of the following declaration(s)) and {\ttfamily {\bfseries{private\+:hierarchy}}} (which is equivalent to {\ttfamily {\bfseries{private}}}; \href{https://github.com/qorelanguage/qore/issues/1197}{\texttt{ issue 1197}}) \item new parse options and directives\+: \begin{DoxyItemize} \item \mbox{\hyperlink{parse_directives_allow-debugger}{\%allow-\/debugger}}\+: allows running debug commands \item \mbox{\hyperlink{parse_directives_no-debugging}{\%no-\/debugging}}\+: forbids debugging of the current \mbox{\hyperlink{class_qore_1_1_program}{Program}} object \item \mbox{\hyperlink{parse_directives_allow-weak-references}{\%allow-\/weak-\/references}}\+: allows the use of the \mbox{\hyperlink{operators_weak_assignment_operator}{weak assignment operator (\+:=)}} \item \mbox{\hyperlink{parse_directives_broken-loop-statement}{\%broken-\/loop-\/statement}}\+: allows \mbox{\hyperlink{statements_continue}{continue}} and \mbox{\hyperlink{statements_break}{break}} statements to be accepted anywhere in the source and behave like a \mbox{\hyperlink{statements_return}{return}} statement \item \mbox{\hyperlink{parse_directives_broken-references}{\%broken-\/references}}\+: allows \mbox{\hyperlink{data_type_declarations_reference_type}{reference}} and \mbox{\hyperlink{data_type_declarations_reference_or_nothing_type}{$\ast$reference}} type restrictions to accept any type contrary to the documented design and intention of these type restrictions \item \mbox{\hyperlink{parse_directives_correct-loop-statement}{\%correct-\/loop-\/statement}}\+: to revert the effect of \mbox{\hyperlink{parse_directives_broken-loop-statement}{\%broken-\/loop-\/statement}} \item \mbox{\hyperlink{parse_directives_correct-references}{\%correct-\/references}}\+: to revert the effect of \mbox{\hyperlink{parse_directives_broken-references}{\%broken-\/references}} \item \mbox{\hyperlink{parse_directives_no-uncontrolled-apis}{\%no-\/uncontrolled-\/apis}}\+: disallow access to uncontrolled A\+P\+Is such as external language bindings or direct generic system call A\+P\+Is that could bypass Qore\textquotesingle{}s sandboxing controls \item \mbox{\hyperlink{parse_directives_strong-encapsulation}{\%strong-\/encapsulation}}\+: disallows out of line class and namespace declarations \item \mbox{\hyperlink{parse_directives_try-reexport-module}{\%try-\/reexport-\/module}}\+: conditionally loads a module in a \mbox{\hyperlink{qore_modules_user_modules}{user module}} and allows for that module to be reexported as well \end{DoxyItemize} \item new constants\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__dbi__capabilities_ga91b90789d24991b1eebce9c11491f015}{D\+B\+I\+\_\+\+C\+A\+P\+\_\+\+H\+A\+S\+\_\+\+R\+E\+S\+U\+L\+T\+S\+E\+T\+\_\+\+O\+U\+T\+P\+UT}}\+: D\+BI capability for drivers that support returning an \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} object for a \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_resultset_output_binding}{result set}} when bound with the \mbox{\hyperlink{group__sql__constants_ga9d23a1d69fcb188296a231a36c6b6da2}{R\+E\+S\+U\+L\+T\+S\+ET}} placeholder specification \item \mbox{\hyperlink{group__system__and__build__constants_ga92a67b51fbd91b3f09ccb8fd84fd8975}{Path\+Sep}}\+: defines the platform-\/specific path separator character \item \mbox{\hyperlink{group__parse__options_gad0d38cd46f08bf4210d4010204269cc9}{P\+O\+\_\+\+A\+L\+L\+O\+W\+\_\+\+D\+E\+B\+U\+G\+G\+ER}}\+: allows running debugger commands \item \mbox{\hyperlink{group__parse__options_ga36ecb26e0659608fc8d35bf9c9a3b5b2}{P\+O\+\_\+\+N\+O\+\_\+\+D\+E\+B\+U\+G\+G\+I\+NG}}\+: disallows debugging of the \mbox{\hyperlink{class_qore_1_1_program}{Program}} \item \mbox{\hyperlink{group__parse__options_ga7cbf296853bb3a9d7cd1cf3a3e9556a5}{P\+O\+\_\+\+A\+L\+L\+O\+W\+\_\+\+W\+E\+A\+K\+\_\+\+R\+E\+F\+E\+R\+E\+N\+C\+ES}}\+: allows the use of the \mbox{\hyperlink{operators_weak_assignment_operator}{weak assignment operator (\+:=)}} \item \mbox{\hyperlink{group__parse__options_ga80bef77e62dead678bbb426794f5f337}{P\+O\+\_\+\+B\+R\+O\+K\+E\+N\+\_\+\+L\+O\+O\+P\+\_\+\+S\+T\+A\+T\+E\+M\+E\+NT}}\+: allows \mbox{\hyperlink{statements_continue}{continue}} and \mbox{\hyperlink{statements_break}{break}} statements to be accepted anywhere in the source and behave like a \mbox{\hyperlink{statements_return}{return}} statement \item \mbox{\hyperlink{group__parse__options_ga889aa80f8ab33266c165478b5fe3c279}{P\+O\+\_\+\+B\+R\+O\+K\+E\+N\+\_\+\+R\+E\+F\+E\+R\+E\+N\+C\+ES}}\+: reverts \mbox{\hyperlink{data_type_declarations_reference_type}{reference}} and \mbox{\hyperlink{data_type_declarations_reference_or_nothing_type}{$\ast$reference}} type restrictions to pre-\/Qore-\/0.\+8.\+13 behavior where they would have no effect \item \mbox{\hyperlink{group__parse__options_ga88a927479c495b99209a6397ef67c240}{P\+O\+\_\+\+N\+O\+\_\+\+U\+N\+C\+O\+N\+T\+R\+O\+L\+L\+E\+D\+\_\+\+A\+P\+IS}}\+: disallow access to uncontrolled A\+P\+Is such as external language bindings or direct generic system call A\+P\+Is that could bypass Qore\textquotesingle{}s sandboxing controls; note that this parse option was also added to \mbox{\hyperlink{group__parse__options_gabcd4198285f25da13a5883006f06a2b7}{P\+O\+\_\+\+N\+O\+\_\+\+IO}} and \mbox{\hyperlink{group__parse__options_ga10aefe54a313d86a87fedc46820ffb02}{P\+O\+\_\+\+N\+O\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+A\+C\+C\+E\+SS}} \item \mbox{\hyperlink{group__parse__options_gaa8259d8e3b4c908f9d09c6987c8c6167}{P\+O\+\_\+\+S\+T\+R\+O\+N\+G\+\_\+\+E\+N\+C\+A\+P\+S\+U\+L\+A\+T\+I\+ON}}\+: disallows out of line class and namespace declarations \item \mbox{\hyperlink{group__sql__constants_ga9d23a1d69fcb188296a231a36c6b6da2}{R\+E\+S\+U\+L\+T\+S\+ET}}\+: specifies that an \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} object should be returned from a \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_resultset_output_binding}{result set}} output variable in an S\+QL query \item \mbox{\hyperlink{group__ssl__mode__constants_ga3e03ac75e51a9f4e994518fc3fc69ab7}{S\+S\+L\+\_\+\+V\+E\+R\+I\+F\+Y\+\_\+\+N\+O\+NE}}\+: \mbox{\hyperlink{class_qore_1_1_socket_aaafb6b597a1e5b3372d88ea53ea4cbac}{Socket\+::set\+Ssl\+Verify\+Mode()}} option\+: do not verify peer certificates \item \mbox{\hyperlink{group__ssl__mode__constants_gae29e3d0203f536c5bf5c0cb225c73c1a}{S\+S\+L\+\_\+\+V\+E\+R\+I\+F\+Y\+\_\+\+P\+E\+ER}}\+: \mbox{\hyperlink{class_qore_1_1_socket_aaafb6b597a1e5b3372d88ea53ea4cbac}{Socket\+::set\+Ssl\+Verify\+Mode()}} option\+: verify peer certificates \item \mbox{\hyperlink{group__ssl__mode__constants_ga7053aa1b8d954e00530f632c502c91d2}{S\+S\+L\+\_\+\+V\+E\+R\+I\+F\+Y\+\_\+\+F\+A\+I\+L\+\_\+\+I\+F\+\_\+\+N\+O\+\_\+\+P\+E\+E\+R\+\_\+\+C\+E\+RT}}\+: \mbox{\hyperlink{class_qore_1_1_socket_aaafb6b597a1e5b3372d88ea53ea4cbac}{Socket\+::set\+Ssl\+Verify\+Mode()}} option\+: fail if the client does not provide a certificate (server mode only) \item \mbox{\hyperlink{group__ssl__mode__constants_ga70bdb100f9ffb3564dfc38505740a0cb}{S\+S\+L\+\_\+\+V\+E\+R\+I\+F\+Y\+\_\+\+C\+L\+I\+E\+N\+T\+\_\+\+O\+N\+CE}}\+: \mbox{\hyperlink{class_qore_1_1_socket_aaafb6b597a1e5b3372d88ea53ea4cbac}{Socket\+::set\+Ssl\+Verify\+Mode()}} option\+: only require the client to send a certificate once (server mode only) \item \mbox{\hyperlink{group__parse__options_gac5bb2159e3353d40072d974c057882b4}{Qore\+::\+Parse\+Option\+Cmd\+Code\+Map}} \item \mbox{\hyperlink{group__parse__options_gaa932d004bc88438547cdfc4e217461e5}{Qore\+::\+Parse\+Option\+Cmd\+String\+Map}} \item see new cryptographic constants listed above \end{DoxyItemize} \item implemented additional parse-\/time checks for many \mbox{\hyperlink{operators}{operators}} to provide feedback for invalid operations detected at parse time \item implemented the \mbox{\hyperlink{operators_weak_assignment_operator}{weak assignment operator (\+:=)}} (only available with \mbox{\hyperlink{parse_directives_allow-weak-references}{\%allow-\/weak-\/references}}) \item implemented the \mbox{\hyperlink{operators_range_operator}{range operator (..)}} \item implemented support for list expressions inside the \mbox{\hyperlink{operators_list_element_operator}{dereference operator (\mbox{[}\mbox{]})}} \item new methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_program_ae9ed01da361e88222eb447491e4cf91e}{Qore\+::\+Program\+::get\+All\+Defines()}} \item \mbox{\hyperlink{class_qore_1_1_program_af850abe615e1fac34dae8e4fc9efc1f2}{Qore\+::\+Program\+::get\+Global\+Vars()}} \item \mbox{\hyperlink{class_qore_1_1_program_a029c9dbdbdc3dc13e685f7d101e5829e}{Qore\+::\+Program\+::import\+Hash\+Decl()}} \item \mbox{\hyperlink{class_qore_1_1_program_a4aef71f37e505dbe84be95b0a2848cba}{Qore\+::\+Program\+::import\+System\+Hash\+Decls()}} \item \mbox{\hyperlink{class_qore_1_1_program_a8be97bfcd125d83a9415c843694734ac}{Qore\+::\+Program\+::set\+Global\+Var\+Value()}} \item \mbox{\hyperlink{class_qore_1_1_program_a6fda138e987e698d3c5b11294d21bcdb}{Qore\+::\+Program\+::set\+Thread\+Init()}} \item \mbox{\hyperlink{class_qore_1_1_program_a5435e046150b69d97f215c0f6b192ce0}{Qore\+::\+Program\+::get\+Thread\+List()}} \item \mbox{\hyperlink{class_qore_1_1_socket_aa530d889c522a410e7e5e5163204d1db}{Qore\+::\+Socket\+::accept\+All\+Certificates()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a1338b37101ef0b82a6dde62b5369f5b9}{Qore\+::\+Socket\+::get\+Accept\+All\+Certificates()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a749e2b7f8882b0e6fcc058886134daf5}{Qore\+::\+Socket\+::get\+Ssl\+Verify\+Mode()}} \item \mbox{\hyperlink{class_qore_1_1_socket_aaafb6b597a1e5b3372d88ea53ea4cbac}{Qore\+::\+Socket\+::set\+Ssl\+Verify\+Mode()}} \end{DoxyItemize} \item updated methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_thread_1_1_counter_a31f5a01212067685e54de06ae29a9984}{Counter\+::dec()}}\+: now returns the current value of the counter \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a1966daad73f8cd30da527e16618eb768}{Qore\+::\+H\+T\+T\+P\+Client\+::constructor()}} updates \begin{DoxyItemize} \item Added support for the following options\+: \begin{DoxyItemize} \item {\ttfamily ssl\+\_\+cert\+\_\+path\+:} allows an X.\+509 client certificate to be set in the constructor \item {\ttfamily ssl\+\_\+key\+\_\+path\+:} allows a private key for an X.\+509 client certificate to be set in the constructor \item {\ttfamily ssl\+\_\+key\+\_\+password\+:} allows a password-\/protected private key to be used wih an X.\+509 client certificate \item {\ttfamily ssl\+\_\+verify\+\_\+cert\+:} enforces server certificate validation with H\+T\+T\+PS connections \end{DoxyItemize} \item Additionally, the H\+T\+T\+P\+Client class now understands the {\ttfamily P\+A\+T\+CH} method (\href{https://tools.ietf.org/html/rfc5789}{\texttt{ R\+FC 5789}}) \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_range_iterator_acdcab14b075fb022dfd4a221c3ddf1ab}{Qore\+::\+Range\+Iterator\+::constructor(int)}} was updated; the second argument was removed to avoid ambiguity with the other overloaded constructor \item \mbox{\hyperlink{class_qore_1_1_tree_map_a53a50c34b01c6a0a4829f58243191175}{Tree\+Map\+::get()}}\+: added a new optional argument to return the unmatched part of the search string \item the following read-\/only static methods were moved from the \mbox{\hyperlink{class_qore_1_1_file}{File}} class to the \mbox{\hyperlink{class_qore_1_1_read_only_file}{Read\+Only\+File}} class\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_read_only_file_a1de2cddec975057ca61f3c5621256833}{Read\+Only\+File\+::hstat()}} \item \mbox{\hyperlink{class_qore_1_1_read_only_file_aa0e7a9d95c754b065ed043810bd32b33}{Read\+Only\+File\+::hlstat()}} \item \mbox{\hyperlink{class_qore_1_1_read_only_file_a62ad0f18f4c04543040b67f0e522bc46}{Read\+Only\+File\+::lstat()}} \item \mbox{\hyperlink{class_qore_1_1_read_only_file_a0cf734a177ff5efd3efb2366dddd8c33}{Read\+Only\+File\+::stat()}} \item \mbox{\hyperlink{class_qore_1_1_read_only_file_ade31b4901849ae29223e11d0cae6e464}{Read\+Only\+File\+::statvfs()}} \end{DoxyItemize} \end{DoxyItemize} \item new pseudo-\/methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8intzzz9_a52e3a4df1cf57a32686d651666a9643a}{Qore\+::zzz8intzzz9\+::format(int, string, string)}} \item \mbox{\hyperlink{class_qore_1_1zzz8floatzzz9_a0a1ed20b3cbe9a7d99681b2ee1b4802b}{Qore\+::zzz8floatzzz9\+::format(int, string, string)}} \item \mbox{\hyperlink{class_qore_1_1zzz8numberzzz9_a31013414002c3808718a217d8d488f7b}{Qore\+::zzz8numberzzz9\+::format(int, string, string)}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_ae5fc7b01d0469fc2a015a0f6f3b0ae26}{Qore\+::zzz8stringzzz9\+::to\+Int(int)}} \item \mbox{\hyperlink{class_qore_1_1zzz8intzzz9_a1a7c8f41ba26bec22c1a0f485d90a48a}{Qore\+::zzz8intzzz9\+::to\+Base(int)}} \item \mbox{\hyperlink{class_qore_1_1zzz8numberzzz9_ae6d52cb434c6eef372ef064852038f8a}{Qore\+::zzz8numberzzz9\+::to\+Base(int)}} \item \mbox{\hyperlink{class_qore_1_1zzz8floatzzz9_a138a6d9c7f0c10546c96a875bc29d242}{Qore\+::zzz8floatzzz9\+::to\+Base(int)}} \item \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_a3ef4fe2f9389f29e7c53e2cfc4217a97}{Qore\+::zzz8valuezzz9\+::complex\+Type()}} \item \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_a74179a71cd4d02fd8367d469df86edfc}{Qore\+::zzz8valuezzz9\+::full\+Type()}} \end{DoxyItemize} \item new functions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__hmac__functions_gad159aa97f0f07e827e74b4b9a12b92ca}{Qore\+::decrypt\+\_\+to\+\_\+binary()}} \item \mbox{\hyperlink{group__hmac__functions_ga94bc9698c368c32987d7207096806df1}{Qore\+::decrypt\+\_\+to\+\_\+string()}} \item \mbox{\hyperlink{group__hmac__functions_ga7141b56ffa6c5a4f8c9c58f788f33780}{Qore\+::encrypt()}} \item \mbox{\hyperlink{group__compresssion__functions_gabdbd68fb7146a0fe2c5c4bb13d481cb8}{Qore\+::get\+\_\+compressor()}} \item \mbox{\hyperlink{group__hmac__functions_ga23662a1e7f11f483a6e841da96389197}{Qore\+::get\+\_\+crypto\+\_\+info()}} \item \mbox{\hyperlink{group__compresssion__functions_ga1590535ac15c91dee832b9ffae8fa69f}{Qore\+::get\+\_\+decompressor()}} \item \mbox{\hyperlink{group__hmac__functions_ga913932d6120f9ea1e3918168fb204976}{Qore\+::get\+\_\+decryptor()}} \item \mbox{\hyperlink{group__hmac__functions_ga6e67ba0396d70cd012f7c46c7562b81f}{Qore\+::get\+\_\+encryptor()}} \item \mbox{\hyperlink{group__misc__functions_ga35f238f6343017d7e4736cd2c3007752}{Qore\+::get\+\_\+global\+\_\+vars()}} \item \mbox{\hyperlink{group__misc__functions_gac3c60c8fa6766bc3e6809468acca8465}{Qore\+::get\+\_\+local\+\_\+vars()}} \item \mbox{\hyperlink{group__hmac__functions_gaa5fd7a2cd931d0390368d54865602c20}{Qore\+::get\+\_\+random\+\_\+bytes()}} \item \mbox{\hyperlink{group__threading__functions_gaff3b8af236d59870ff5c6a36c17c4907}{Qore\+::get\+\_\+thread\+\_\+call\+\_\+stack()}} \item \mbox{\hyperlink{group__string__functions_gac63ded32a4a0217e954935848210808e}{Qore\+::parse\+\_\+int()}} \item \mbox{\hyperlink{group__misc__functions_gaea05595c0ea4cf4affef51c323c7eed1}{Qore\+::set\+\_\+global\+\_\+var\+\_\+value()}} \item \mbox{\hyperlink{group__misc__functions_ga20e0c1f20a6afc4b02dbd9862996d57a}{Qore\+::set\+\_\+local\+\_\+var\+\_\+value()}} \end{DoxyItemize} \item updated functions/methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_thread_1_1_counter_a31f5a01212067685e54de06ae29a9984}{Counter\+::dec()}}\+: now returns the current value of the counter \item \mbox{\hyperlink{group__threading__functions_ga23d27aeac0640b070f964f2eb9f1cc8a}{Qore\+::thread\+\_\+yield()}} \end{DoxyItemize} \item updated functions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__math__functions_gab5e499c271ead1e1dfb44cec71a9254e}{ceil()}}\+: now allows the precision to be specified \item \mbox{\hyperlink{group__math__functions_gaef0b0eaa3ff1b0535cc4059e3afbdfb5}{floor()}}\+: now allows the precision to be specified \item \mbox{\hyperlink{group__type__conversion__functions_ga0231dbb472dd230310af7c7c34f56e92}{hash()}}\+: now returns an untyped hash stripped of any key type information \item \mbox{\hyperlink{namespace_qore_a834e1f95eb108bd6e4d564daecd68eda}{mkdir()}}\+: now allows parent directories to be created in the same call \item \mbox{\hyperlink{group__math__functions_ga99beb41177f06433ce9dda9fcfd07ec7}{round()}}\+: now allows the precision to be specified \item \mbox{\hyperlink{group__threading__functions_gae83c32576b59a1ecfa906d9b3c3af557}{set\+\_\+thread\+\_\+init()}}\+: now allows for thread init code to be removed \item \mbox{\hyperlink{group__range__functions_ga85798861f6ac3dc0adafaa8db337d8e5}{Qore\+::xrange(int)}} was updated; the second argument was removed to avoid ambiguity with the other overloaded variant \end{DoxyItemize} \item module updates\+: \begin{DoxyItemize} \item \href{../../modules/BulkSqlUtil/html/index.html}{\texttt{ Bulk\+Sql\+Util}} module updates\+: \begin{DoxyItemize} \item added complex type support \item added the {\ttfamily Abstract\+Bulk\+Operation\+::size()} method \item implemented analytic/window functions\+: new functions \mbox{[}\href{https://github.com/qorelanguage/qore/issues/2203}{\texttt{ issue 2202}}\mbox{]} \item implemented analytic/window functions\+: cop\+\_\+over full support including O\+R\+D\+ER BY \mbox{[}\href{https://github.com/qorelanguage/qore/issues/2203}{\texttt{ issue 2203}}\mbox{]} \end{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module updates\+: \begin{DoxyItemize} \item added support for streams \end{DoxyItemize} \item \href{../../modules/FixedLengthUtil/html/index.html}{\texttt{ Fixed\+Length\+Util}} module updates\+: \begin{DoxyItemize} \item added support for streams \item added {\ttfamily Fixed\+Length\+File\+Iterator\+::get\+File\+Name()} (\href{https://github.com/qorelanguage/qore/issues/1164}{\texttt{ issue 1164}}) \item added field as well as global option \char`\"{}truncate\char`\"{} (\href{https://github.com/qorelanguage/qore/issues/1841}{\texttt{ issue 1841}}) \item added field as well as global option \char`\"{}tab2space\char`\"{} (\href{https://github.com/qorelanguage/qore/issues/1866}{\texttt{ issue 1866}}) \end{DoxyItemize} \item \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module updates\+: \begin{DoxyItemize} \item added a minimal substring of string bodies received to the log message when logging H\+T\+TP requests \end{DoxyItemize} \item \href{../../modules/HttpServerUtil/html/index.html}{\texttt{ Http\+Server\+Util}} module updates\+: \begin{DoxyItemize} \item the {\ttfamily parse\+\_\+uri\+\_\+query()} function was moved to the \href{../../modules/Util/html/index.html}{\texttt{ Util}} module \end{DoxyItemize} \item \href{../../modules/Mime/html/index.html}{\texttt{ Mime}} module updates\+: \begin{DoxyItemize} \item added complex type support \item added the following constants\+: \begin{DoxyItemize} \item {\ttfamily Mime\+Type\+Multipart\+Form\+Data} \item {\ttfamily Mime\+Type\+Multipart\+Related} \item {\ttfamily Mime\+Type\+Multipart\+Mixed} \end{DoxyItemize} \item added the following methods\+: \begin{DoxyItemize} \item {\ttfamily Multipart\+Message\+::get\+Boundary()} \item {\ttfamily Multipart\+Message\+::serialize\+Body()} \item {\ttfamily Multipart\+Message\+::size()} \end{DoxyItemize} \item fixed a bug parsing multipart messages where unnecessary characters were searched (\href{https://github.com/qorelanguage/qore/issues/2099}{\texttt{ issue 2099}}) \end{DoxyItemize} \item \href{../../modules/Pop3Client/html/index.html}{\texttt{ Pop3\+Client}} module updates\+: \begin{DoxyItemize} \item added the {\ttfamily Pop3\+Connection} class to support the \href{../../ConnectionProvider/html/index.html}{\texttt{ Connection\+Provider}} module \end{DoxyItemize} \item \href{../../modules/Qorize/html/index.html}{\texttt{ Qorize}} module updates\+: \begin{DoxyItemize} \item {\ttfamily qorize\+\_\+named()} added support for objects \end{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module updates\+: \begin{DoxyItemize} \item added the {\ttfamily Rest\+Connection} class to support the \href{../../ConnectionProvider/html/index.html}{\texttt{ Connection\+Provider}} module \item support for the {\ttfamily text/plain} {\ttfamily Content-\/\+Type} \end{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module updates\+: \begin{DoxyItemize} \item added support for runtime R\+E\+ST A\+PI validation against a R\+E\+ST schema using the \href{../../modules/RestSchemaValidator/html/index.html}{\texttt{ Rest\+Schema\+Validator}} module \item added support for Swagger 2.\+0 R\+E\+ST A\+PI validation and {\ttfamily \char`\"{}swagger\char`\"{}} options using the \href{../../modules/Swagger/html/index.html}{\texttt{ Swagger}} module in the {\ttfamily Rest\+Client} and {\ttfamily Rest\+Connection} classes \end{DoxyItemize} \item \href{../../modules/RestHandler/html/index.html}{\texttt{ Rest\+Handler}} module updates\+: \begin{DoxyItemize} \item added an A\+PI to allow R\+E\+ST calls to be made internally (\href{https://github.com/qorelanguage/qore/issues/1899}{\texttt{ issue 1899}}) \item added support for runtime R\+E\+ST A\+PI validation against a R\+E\+ST schema using the \href{../../modules/RestSchemaValidator/html/index.html}{\texttt{ Rest\+Schema\+Validator}} module \end{DoxyItemize} \item \href{../../modules/RestSchemaValidator/html/index.html}{\texttt{ Rest\+Schema\+Validator}} module\+: \begin{DoxyItemize} \item added this new module providing a \href{https://en.wikipedia.org/wiki/Representational_state_transfer}{\texttt{ R\+E\+ST}} schema validation A\+PI \end{DoxyItemize} \item \href{../../modules/SalesforceRestClient/html/index.html}{\texttt{ Salesforce\+Rest\+Client}} module updates\+: \begin{DoxyItemize} \item added the {\ttfamily Salesforc\+Rest\+Connection} class to support the \href{../../ConnectionProvider/html/index.html}{\texttt{ Connection\+Provider}} module \end{DoxyItemize} \item \href{../../modules/Schema/html/index.html}{\texttt{ Schema}} module updates\+: \begin{DoxyItemize} \item added the {\ttfamily c\+\_\+blob()} and {\ttfamily c\+\_\+clob()} functions (\href{https://github.com/qorelanguage/qore/issues/1851}{\texttt{ issue 1851}}) \end{DoxyItemize} \item \href{../../modules/SewioRestClient/html/index.html}{\texttt{ Sewio\+Rest\+Client}} module\+: \begin{DoxyItemize} \item added this new module providing A\+P\+Is for communicating with \href{http://www.sewio.net}{\texttt{ Sewio.\+net}}\textquotesingle{}s R\+T\+LS Studio R\+E\+ST A\+PI \end{DoxyItemize} \item \href{../../modules/SewioWebSocketClient/html/index.html}{\texttt{ Sewio\+Web\+Socket\+Client}} module\+: \begin{DoxyItemize} \item added this new module providing A\+P\+Is for communicating with \href{http://www.sewio.net}{\texttt{ Sewio.\+net}}\textquotesingle{}s R\+T\+LS Studio Web\+Socket A\+PI \end{DoxyItemize} \item \href{../../modules/SmtpClient/html/index.html}{\texttt{ Smtp\+Client}} module updates\+: \begin{DoxyItemize} \item added the {\ttfamily Smtp\+Connection} class to support the \href{../../ConnectionProvider/html/index.html}{\texttt{ Connection\+Provider}} module \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module updates\+: \begin{DoxyItemize} \item implemented the {\ttfamily cop\+\_\+trunc\+\_\+date()} function (\href{https://github.com/qorelanguage/qore/issues/2032}{\texttt{ issue 2032}}) \end{DoxyItemize} \item \href{../../modules/Swagger/html/index.html}{\texttt{ Swagger}} module added\+: \begin{DoxyItemize} \item added this new module providing a \href{https://swagger.io/}{\texttt{ Swagger 2.\+0 R\+E\+ST A\+PI validation A\+PI}} to Qore \end{DoxyItemize} \item \href{../../modules/TableMapper/html/index.html}{\texttt{ Table\+Mapper}} module updates\+: \begin{DoxyItemize} \item added support for upserts in {\ttfamily Inbound\+Table\+Mapper} (\href{https://github.com/qorelanguage/qore/issues/1067}{\texttt{ issue 1067}}) \item added {\ttfamily Inbound\+Table\+Mapper\+::queue\+Data(list)} \end{DoxyItemize} \item \href{../../modules/TelnetClient/html/index.html}{\texttt{ Telnet\+Client}} module updates\+: \begin{DoxyItemize} \item added the {\ttfamily Telnet\+Connection} class to support the \href{../../ConnectionProvider/html/index.html}{\texttt{ Connection\+Provider}} module \item added support for U\+R\+Ls in the constructor() \item added the {\ttfamily Telnet\+Client\+::get\+Target()} method \end{DoxyItemize} \item \href{../../modules/Util/html/index.html}{\texttt{ Util}} module updates\+: \begin{DoxyItemize} \item the {\ttfamily parse\+\_\+uri\+\_\+query()} function was moved here from the \href{../../modules/HttpServerUtil/html/index.html}{\texttt{ Http\+Server\+Util}} module \item {\ttfamily parse\+\_\+uri\+\_\+query()} now handles repeated query arguments as a list \item added public function {\ttfamily flatten()} \item added public function {\ttfamily uniq()} \end{DoxyItemize} \item \href{../../modules/WebSocketClient/html/index.html}{\texttt{ Web\+Socket\+Client}} module updates\+: \begin{DoxyItemize} \item added the {\ttfamily Web\+Socket\+Connection\+Object} class to support the \href{../../ConnectionProvider/html/index.html}{\texttt{ Connection\+Provider}} module \item updated for complex types \item fixed a bug where the event loop thread would immediately terminate after a reconnection (\href{https://github.com/qorelanguage/qore/issues/2061}{\texttt{ issue 2061}}) \item improved client logging \item fixed a bug where the {\ttfamily Web\+Socket\+Client} class did not validate the {\ttfamily Sec-\/\+Web\+Socket-\/\+Accept} response header according to R\+F\+C6455 (\href{https://github.com/qorelanguage/qore/issues/2062}{\texttt{ issue 2062}}) \end{DoxyItemize} \item \href{../../modules/WebSocketUtil/html/index.html}{\texttt{ Web\+Socket\+Util}} module updates\+: \begin{DoxyItemize} \item added the {\ttfamily ws\+\_\+get\+\_\+response\+\_\+key()} function \end{DoxyItemize} \end{DoxyItemize} \item the following classes can be used from binary modules\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_file}{File}} \item \mbox{\hyperlink{class_qore_1_1_read_only_file}{Read\+Only\+File}} \end{DoxyItemize} \item updated the build to require a \href{https://en.wikipedia.org/wiki/C\%2B\%2B11}{\texttt{ C++11}} compiler or better to build Qore (\href{https://github.com/qorelanguage/qore/issues/994}{\texttt{ issue 994}}) \item a relative time stamp is now logged in trace and debug output \end{DoxyItemize}\hypertarget{release_notes_qore_0813_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0813_bug_fixes} \begin{DoxyItemize} \item fixed a bug causing \mbox{\hyperlink{class_qore_1_1_abstract_quantified_bidirectional_iterator}{Abstract\+Quantified\+Bidirectional\+Iterator}} not being available (\href{https://github.com/qorelanguage/qore/issues/968}{\texttt{ issue 968}}) \item \href{../../modules/BulkSqlUtil/html/index.html}{\texttt{ Bulk\+Sql\+Util}} module fixes\+: \begin{DoxyItemize} \item fixed the module to work properly even with DB drivers that do not support parameter array binding (\href{https://github.com/qorelanguage/qore/issues/1154}{\texttt{ issue 1154}}) \end{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module fixes\+: \begin{DoxyItemize} \item fixed a bug in an error message validating input data (\href{https://github.com/qorelanguage/qore/issues/1062}{\texttt{ issue 1062}}) \item added an exception when detected headers do not match the {\itshape fields} option (\href{https://github.com/qorelanguage/qore/issues/2179}{\texttt{ issue 2179}}) \end{DoxyItemize} \item \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module fixes\+: \begin{DoxyItemize} \item added logic to attempt to mask passwords in log messages (\href{https://github.com/qorelanguage/qore/issues/1086}{\texttt{ issue 1086}}) \end{DoxyItemize} \item \href{../../modules/HttpServerUtil/html/index.html}{\texttt{ Http\+Server\+Util}} module fixes\+: \begin{DoxyItemize} \item fixed a bug where the {\itshape msg} arg to {\ttfamily Abstract\+Authenticator\+::do401()} was ignored (\href{https://github.com/qorelanguage/qore/issues/1047}{\texttt{ issue 1047}}) \end{DoxyItemize} \item \href{../../modules/RestHandler/html/index.html}{\texttt{ Rest\+Handler}} module fixes\+: \begin{DoxyItemize} \item added logic to allow sensitive data to be masked in log messages (\href{https://github.com/qorelanguage/qore/issues/1086}{\texttt{ issue 1086}}) \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module fixes\+: \begin{DoxyItemize} \item fixed a bug in update and upsert statement generation when the given data does not have enough columns to use the unique index found, an error message is generated that contains all the columns names instead of just the column names required by the index (\href{https://github.com/qorelanguage/qore/issues/1013}{\texttt{ issue 1013}}) \end{DoxyItemize} \item \href{../../modules/WebSocketClient/html/index.html}{\texttt{ Web\+Socket\+Client}} module fixes\+: \begin{DoxyItemize} \item fixed a thread lock starvation race condition (\href{https://github.com/qorelanguage/qore/issues/2130}{\texttt{ issue 2130}}) \end{DoxyItemize} \item {\ttfamily U\+T\+F-\/16} fixes\+: \begin{DoxyItemize} \item fixed a bug comparing strings in {\ttfamily U\+T\+F-\/16} encodings (\href{https://github.com/qorelanguage/qore/issues/1579}{\texttt{ issue 1579}}) \item fixed \mbox{\hyperlink{group__string__functions_gafe621446ada382d5b086a1d2a20934c9}{Qore\+::substr()}} and \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_ab5ad54b1fe38b46ee071e55563d9d245}{Qore\+::zzz8stringzzz9\+::substr()}} with strings in {\ttfamily U\+T\+F-\/16} encodings (\href{https://github.com/qorelanguage/qore/issues/1586}{\texttt{ issue 1586}}) \item fixed \mbox{\hyperlink{group__string__functions_gae8d314e819a299d46d181696600d4293}{Qore\+::trim()}}, \mbox{\hyperlink{group__string__functions_gaa3c396510f9d106aee5161cbb144e163}{Qore\+::ltrim()}}, \mbox{\hyperlink{group__string__functions_ga25264bfb9950ac66862db9b4a32eeee8}{Qore\+::rtrim()}} and the \mbox{\hyperlink{operators_trim}{trim}} operator with strings with {\ttfamily U\+T\+F-\/16} encodings (\href{https://github.com/qorelanguage/qore/issues/1775}{\texttt{ issue 1775}}) \end{DoxyItemize} \item fixed a bug where \mbox{\hyperlink{statements_break}{break}} and \mbox{\hyperlink{statements_continue}{continue}} statements were accepted outside of loops (\href{https://github.com/qorelanguage/qore/issues/976}{\texttt{ issue 976}}) \item fixed a bug compiling on Solaris S\+P\+A\+RC with g++ where {\ttfamily M\+P\+F\+R\+\_\+\+D\+E\+C\+L\+\_\+\+I\+N\+I\+T()} is compiled incorrectly with -\/O1 or greater (\href{https://github.com/qorelanguage/qore/issues/958}{\texttt{ issue 958}}) \item fixed a bug causing an infinite loop in decompression functions (\href{https://github.com/qorelanguage/qore/issues/966}{\texttt{ issue 966}}) \item fixed an issue where an internal C++ A\+PI (Qore\+Program\+::parse\+Cmd\+Line\+Defines()) performed a needless copy of a data structure (\href{https://github.com/qorelanguage/qore/issues/1099}{\texttt{ issue 1099}}) \item fixed a stack corruption bug with asynchronous I/O on U\+N\+IX systems with \mbox{\hyperlink{class_qore_1_1_read_only_file}{Read\+Only\+File}} methods (\href{https://github.com/qorelanguage/qore/issues/1106}{\texttt{ issue 1106}}) \item fixed bugs with inconsistent conversions of \mbox{\hyperlink{data_type_declarations_int_type}{int}}, \mbox{\hyperlink{data_type_declarations_float_type}{float}}, and \mbox{\hyperlink{data_type_declarations_bool_type}{boolean}} values to date/time values, now they are all converted uniformly to \mbox{\hyperlink{basic_data_types_relative_dates}{relative date/time values}} (\href{https://github.com/qorelanguage/qore/issues/1156}{\texttt{ issue 1156}}) \item fixed a bug where \mbox{\hyperlink{namespace_qore}{Qore}} allowed code to be declared both public and private without a warning (\href{https://github.com/qorelanguage/qore/issues/1187}{\texttt{ issue 1187}}) \item fixed a bug where the \mbox{\hyperlink{operators_instanceof}{instanceof}} operator would return \mbox{\hyperlink{basic_data_types_True}{True}} with objects that did not publically inherit the given class or where the given class is not accessible (\href{https://github.com/qorelanguage/qore/issues/1191}{\texttt{ issue 1191}}) \item fixed a bug in qpp support of the \textquotesingle{}final\textquotesingle{} class flag (\href{https://github.com/qorelanguage/qore/issues/1222}{\texttt{ issue 1222}}) \item fixed a bug where the \mbox{\hyperlink{operators_plus_operator}{+ operator}} provided access to private members from outside the class (\href{https://github.com/qorelanguage/qore/issues/1209}{\texttt{ issue 1209}}) \item fixed a bug where different \mbox{\hyperlink{overloading}{overloaded}} method variant resolution rules were used at parse time (best match in hierarchy) and runtime (best match in first matching class) in a class hierarchy (\href{https://github.com/qorelanguage/qore/issues/1229}{\texttt{ issue 1229}}) \item fixed a bug where exceptions in base class constructor calls did not reflect the actual source location (\href{https://github.com/qorelanguage/qore/issues/1230}{\texttt{ issue 1230}}) \item fixed a bug where runtime function/method variant matching was incorrectly biased towards default matches for missing arguments (\href{https://github.com/qorelanguage/qore/issues/1231}{\texttt{ issue 1231}}) \item fixed bugs where calls to \mbox{\hyperlink{class_qore_1_1_socket_ad471f7399655c3fb211c72b55ca568d9}{Socket\+::upgrade\+Client\+To\+S\+SL()}} and \mbox{\hyperlink{class_qore_1_1_socket_a83385d31d5b112409424269f025de5ea}{Socket\+::upgrade\+Server\+To\+S\+SL()}} were ignored with no exception thrown if the socket was not connected (\href{https://github.com/qorelanguage/qore/issues/1258}{\texttt{ issue 1258}}) \item fixed a bug where a closure created in an object scope could not be called if the object had been deleted, even if the closure did not refer to the object (\href{https://github.com/qorelanguage/qore/issues/1303}{\texttt{ issue 1303}}) \item fixed a bug where \mbox{\hyperlink{group__string__functions_gab1aedfc4b3b7aed6dffead7e46c72b07}{ord()}} would return negative numbers for bytes with the high bit set with compilers where {\ttfamily char} is the same as {\ttfamily signed char} (\href{https://github.com/qorelanguage/qore/issues/1385}{\texttt{ issue 1385}}) \item fixed a bug where \mbox{\hyperlink{group__type__conversion__functions_gaedc7dfca9a2bab4770135bb01a34b63c}{int(number)}} returned rounded value instead of the integer part (while \mbox{\hyperlink{group__type__conversion__functions_gaedc7dfca9a2bab4770135bb01a34b63c}{int(float)}} behaved correctly; also cf. initializing a softint value from a number vs. from a float) (\href{https://github.com/qorelanguage/qore/issues/1463}{\texttt{ issue 1463}}) \item \mbox{\hyperlink{class_qore_1_1_read_only_file_ac4475042a820d3d303b1b67f3921e728}{File\+::read()}} now uses character semantics for the length argument (\href{https://github.com/qorelanguage/qore/issues/1548}{\texttt{ issue 1548}}) \item fixed a bug with strongly-\/typed lvalue assignments with classes created in different \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects (\href{https://github.com/qorelanguage/qore/issues/1551}{\texttt{ issue 1551}}) \item fixed a bug where an A\+S\+C\+II string and the same string in a different encoding and with diacritics could incorrectly be marked as equal (\href{https://github.com/qorelanguage/qore/issues/1579}{\texttt{ issue 1579}}) \item fixed bugs in \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client}{H\+T\+T\+P\+Client}} methods where string message bodies were not converted to the object\textquotesingle{}s \mbox{\hyperlink{character_encoding}{character encoding}} before transmission (\href{https://github.com/qorelanguage/qore/issues/1813}{\texttt{ issue 1813}}) \item fixed a bug in the \mbox{\hyperlink{data_type_declarations_reference_type}{reference}} and \mbox{\hyperlink{data_type_declarations_reference_or_nothing_type}{$\ast$reference}} assignment restrictions; previously any value was accepted, now only references are accepted as the initial assignment values (\href{https://github.com/qorelanguage/qore/issues/1819}{\texttt{ issue 1819}}) \item fixed a bug in handling the {\ttfamily Sql\+Util\+::\+B\+L\+OB} type in the \href{../../modules/FreetdsSqlUtil/html/index.html}{\texttt{ Freetds\+Sql\+Util}} module (\href{https://github.com/qorelanguage/qore/issues/1852}{\texttt{ issue 1852}}) \item fixed a bug in overloaded call variant matching where missing arguments were counted towards the match (\href{https://github.com/qorelanguage/qore/issues/1897}{\texttt{ issue 1897}}) \item fixed many bugs where parse-\/time errors could be reported at an incorrect source location; parse-\/time error location reporting has been completely overhauled and reimplemented for correctness (\href{https://github.com/qorelanguage/qore/issues/1930}{\texttt{ issue 1930}}) \item fixed a bug where code signatures would accept parameter variables without {\ttfamily \char`\"{}\$\char`\"{}} signs even when \mbox{\hyperlink{parse_directives_allow-bare-refs}{\%allow-\/bare-\/refs}} was not in effect (\href{https://github.com/qorelanguage/qore/issues/1941}{\texttt{ issue 1941}}) \item fixed memory leaks in the scanner related to E\+OF conditions (\href{https://github.com/qorelanguage/qore/issues/1976}{\texttt{ issue 1976}}) \item rewrote Qore functions \mbox{\hyperlink{namespace_qore_aa4ca4c902bdebd8b368fb2ae00bf76b2}{Qore\+::gethostbyname()}}, \mbox{\hyperlink{namespace_qore_a1e221d6e6ab07e4ea90b63f4ab888d47}{Qore\+::gethostbyname\+\_\+long()}} and \mbox{\hyperlink{namespace_qore_abf75d8247386c90c83583f6cd6909e1b}{Qore\+::gethostbyaddr()}} to use standard C functions {\ttfamily getaddrinfo(3)} and {\ttfamily getnameinfo(3)} internally instead of the deprecated {\ttfamily gethostbyname(3)} and {\ttfamily gethostbyaddr(3)} (\href{https://github.com/qorelanguage/qore/issues/1952}{\texttt{ issue 1952}}) \item fixed cmake builds on Darwin (\href{https://github.com/qorelanguage/qore/issues/1980}{\texttt{ issue 1980}}) \item fixed a bug where immediate date-\/time values were not marked with their type at parse time (\href{https://github.com/qorelanguage/qore/issues/2001}{\texttt{ issue 2001}}) \item fixed a bug where the \mbox{\hyperlink{data_type_declarations_data_or_nothing_type}{$\ast$data}} type restriction would allow all types to be assigned at runtime (\href{https://github.com/qorelanguage/qore/issues/2002}{\texttt{ issue 2002}}) \item \mbox{\hyperlink{class_qore_1_1_range_iterator_acdcab14b075fb022dfd4a221c3ddf1ab}{Qore\+::\+Range\+Iterator\+::constructor(int)}} and \mbox{\hyperlink{group__range__functions_ga85798861f6ac3dc0adafaa8db337d8e5}{Qore\+::xrange(int)}} were updated; the second arguments were removed to avoid ambiguity with the other overloaded variants (\href{https://github.com/qorelanguage/qore/issues/2016}{\texttt{ issue 2016}}) \item fixed a bug where \mbox{\hyperlink{group__string__functions_ga757f5b4682cb6787e7e186ddcc2b2b56}{Qore\+::replace()}} could get in an infinite loop with arguments with embededed nulls (\href{https://github.com/qorelanguage/qore/issues/2098}{\texttt{ issue 2098}}) \item fixed a bug in regular expression extraction where an infinite loop could occur (\href{https://github.com/qorelanguage/qore/issues/2083}{\texttt{ issue 2083}}) \item fixed a bug where a call reference to an object method that crosses \mbox{\hyperlink{class_qore_1_1_program}{Program}} boundaries could result in a core dump when called due to an error managing thread-\/local data (\href{https://github.com/qorelanguage/qore/issues/2145}{\texttt{ issue 2145}}) \item fixed crashes in scanner due to E\+OF in comments (\href{https://github.com/qorelanguage/qore/issues/2175}{\texttt{ issue 2175}}) \end{DoxyItemize}\hypertarget{release_notes_qore_081212}{}\doxysection{Qore 0.\+8.\+12.\+12}\label{release_notes_qore_081212} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_081212_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_081212_new_features} \begin{DoxyItemize} \item added the \mbox{\hyperlink{group__option__constants_gafdc62dff75931ccafe0a105e62bb1d05}{H\+A\+V\+E\+\_\+\+D\+SS}} constant to indicate if the outdated \mbox{\hyperlink{group__digest__functions_gab75d2872586f27999e85b7ed990f6dad}{D\+S\+S()}}, \mbox{\hyperlink{group__digest__functions_ga418f6b8eb4acc61b72a3a600d418a1b6}{D\+S\+S1()}}, \mbox{\hyperlink{group__digest__functions_ga20bcfd88e83ae5c08af1d4ef5b6a10c7}{D\+S\+S\+\_\+bin()}}, \mbox{\hyperlink{group__digest__functions_gad7149067899176a4910c1aff7f8c3157}{D\+S\+S1\+\_\+bin()}}, D\+S\+S\+\_\+\+H\+M\+A\+C(), and D\+S\+S1\+\_\+\+H\+M\+A\+C() functions are available in the opnessl library used to compile Qore \end{DoxyItemize}\hypertarget{release_notes_qore_081212_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_081212_bug_fixes} \begin{DoxyItemize} \item fixed a bug handling {\ttfamily argv} in base class constructor execution (\href{https://github.com/qorelanguage/qore/issues/2030}{\texttt{ issue 2030}}) \item fixed a bug handling the connection status in the \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client}{H\+T\+T\+P\+Client}} class (\href{https://github.com/qorelanguage/qore/issues/2058}{\texttt{ issue 2058}}) \item fixed building with openssl 1.\+1+ (\href{https://github.com/qorelanguage/qore/issues/2135}{\texttt{ issue 2135}}) \item fixed binding more than one wilcard port on a specific address in the \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module (\href{https://github.com/qorelanguage/qore/issues/2155}{\texttt{ issue 2155}}) \item fixed a bug in \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} with column aliases that are reserved words (\href{https://github.com/qorelanguage/qore/issues/2163}{\texttt{ issue 2163}}) \item fixed a memory bug in the \mbox{\hyperlink{operators_splice}{splice}} operator with a binary operand (\href{https://github.com/qorelanguage/qore/issues/2303}{\texttt{ issue 2303}}) \item fixed a bug where calling any \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} method in another thread with an active connection from a \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} causes a crash (\href{https://github.com/qorelanguage/qore/issues/2334}{\texttt{ issue 2334}}) \item fixed a bug in \href{../../modules/RestHandler/html/index.html}{\texttt{ Rest\+Handler}} regarding inconsistent handling of U\+RI parameter arguments; the {\ttfamily \char`\"{}action\char`\"{}} key was only removed from the {\ttfamily ah} hash when there were no other arguments, introducing an inconsistency in argument handling in R\+E\+ST services (\href{https://github.com/qorelanguage/qore/issues/2479}{\texttt{ issue 2479}}) \item fixed a bug where {\ttfamily E\+N\+C\+O\+D\+I\+N\+G-\/\+C\+O\+N\+V\+E\+R\+S\+I\+O\+N-\/\+E\+R\+R\+OR} exceptions were not thrown with newer G\+NU iconv libraries with an A\+PI change (\href{https://github.com/qorelanguage/qore/issues/2500}{\texttt{ issue 2500}}) \end{DoxyItemize}\hypertarget{release_notes_qore_081211}{}\doxysection{Qore 0.\+8.\+12.\+11}\label{release_notes_qore_081211} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_081211_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_081211_new_features} \begin{DoxyItemize} \item \href{https://github.com/qorelanguage/qore/issues/1947}{\texttt{ issue 1947}} added \mbox{\hyperlink{warnings_warning-broken-logic-precedence}{broken-\/logic-\/precedence}} warning. \end{DoxyItemize}\hypertarget{release_notes_qore_081211_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_081211_bug_fixes} \begin{DoxyItemize} \item fixed documentation regarding escaping of characters in strings and added a parse exception in case of trying to escape octal values in range 400-\/777 (\href{https://github.com/qorelanguage/qore/issues/50}{\texttt{ issue 50}}) \item fixed a crashing bug where \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_a7713f26c809821a7942a60e27f924742}{Datasource\+::get\+Config\+String()}} was called without a connection, also could crash in an implicit internal call to this method with the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} class when connections were lost and the warning callback should be called (\href{https://github.com/qorelanguage/qore/issues/1992}{\texttt{ issue 1992}}) \item fixed a bug where \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_a8291b3c3010a8c0d1522afeaa3411a02}{Datasource\+::get\+Config\+Hash()}} returned different values depending on if the object was connected or not (\href{https://github.com/qorelanguage/qore/issues/1994}{\texttt{ issue 1994}}) \end{DoxyItemize}\hypertarget{release_notes_qore_081210}{}\doxysection{Qore 0.\+8.\+12.\+10}\label{release_notes_qore_081210} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_081210_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_081210_bug_fixes} \begin{DoxyItemize} \item module fixes\+: \begin{DoxyItemize} \item \href{../../modules/FixedLengthUtil/html/index.html}{\texttt{ Fixed\+Length\+Util}}\+: \begin{DoxyItemize} \item fixes and improvements to errors and exceptions (\href{https://github.com/qorelanguage/qore/issues/1828}{\texttt{ issue 1828}}) \end{DoxyItemize} \item \href{../../modules/HttpServerUtil/html/index.html}{\texttt{ Http\+Server\+Util}}\+: \begin{DoxyItemize} \item eliminated excess logging of all H\+T\+TP chunks sent and received (\href{https://github.com/qorelanguage/qore/issues/1832}{\texttt{ issue 1832}}) \end{DoxyItemize} \item \href{../../modules/PgsqlSqlUtil/html/index.html}{\texttt{ Pgsql\+Sql\+Util}}\+: \begin{DoxyItemize} \item fixed a bug in setting a {\ttfamily comment} for a table column (\href{https://github.com/qorelanguage/qore/issues/1886}{\texttt{ issue 1886}}) \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}}\+: \begin{DoxyItemize} \item fixed a bug in the {\ttfamily offset} query hash argument in S\+QL operation methods (\href{https://github.com/qorelanguage/qore/issues/1880}{\texttt{ issue 1880}}) \item fixed a bug that prohibited only columns from the main query to be selected when joins are used (\href{https://github.com/qorelanguage/qore/issues/1909}{\texttt{ issue 1909}}) \end{DoxyItemize} \item \href{../../modules/TableMapper/html/index.html}{\texttt{ Table\+Mapper}}\+: \begin{DoxyItemize} \item fixed a bug in flush messages in the {\ttfamily Inbound\+Table\+Mapper} class (\href{https://github.com/qorelanguage/qore/issues/1849}{\texttt{ issue 1849}}) \end{DoxyItemize} \end{DoxyItemize} \item fixed a bug that could cause spurious parse-\/time exceptions to be thrown when matching call variants with multiple return types for the same callable object (\href{https://github.com/qorelanguage/qore/issues/1928}{\texttt{ issue 1928}}) \item fixed the process return code in the output reference in \mbox{\hyperlink{group__misc__functions_gaee11d366f841cd34c9aa6ac8c7c49577}{backquote()}} on Unix/\+Linux platforms (\href{https://github.com/qorelanguage/qore/issues/1884}{\texttt{ issue 1884}}) \item fixed a bug where connections were not immediately released back to the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} in case of an {\ttfamily S\+Q\+L\+S\+T\+A\+T\+E\+M\+E\+N\+T-\/\+E\+R\+R\+OR} exception (\href{https://github.com/qorelanguage/qore/issues/1836}{\texttt{ issue 1836}}) \item eliminated a spurious exception in the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} class in case of a \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} timeout (\href{https://github.com/qorelanguage/qore/issues/1832}{\texttt{ issue 1832}}) \item fixed a crash when the incorrect type was passed to a parameter declared \mbox{\hyperlink{data_type_declarations_reference_or_nothing_type}{$\ast$reference}} (\href{https://github.com/qorelanguage/qore/issues/1815}{\texttt{ issue 1815}}) \item fixed a crash when the Qore library exits caused by an error in handling module dependencies with injected modules (\href{https://github.com/qorelanguage/qore/issues/1805}{\texttt{ issue 1805}}) \item fixed segfault crashes caused by calling object methods with null pointers (\href{https://github.com/qorelanguage/qore/issues/1791}{\texttt{ issue 1791}}) \item added internal A\+PI support to make it easier for D\+BI drivers to handle lost connections and to allow D\+BI drivers that must close all open handles before a connection is closed (such as the oracle driver); due to this change, \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} objects based on a \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} are closed automatically whenever the datasource is returned to the pool (\href{https://github.com/qorelanguage/qore/issues/1250}{\texttt{ issue 1250}}) \item implemented new parse options to revert the effect of parse options that affect code safety (\href{https://github.com/qorelanguage/qore/issues/1895}{\texttt{ issue 1895}})\+: \begin{DoxyItemize} \item \mbox{\hyperlink{parse_directives_correct-list-parsing}{\%correct-\/list-\/parsing}} \item \mbox{\hyperlink{parse_directives_correct-logic-precedence}{\%correct-\/logic-\/precedence}} \item \mbox{\hyperlink{parse_directives_correct-int-assignments}{\%correct-\/int-\/assignments}} \item \mbox{\hyperlink{parse_directives_correct-operators}{\%correct-\/operators}} \item \mbox{\hyperlink{parse_directives_loose-args}{\%loose-\/args}} \end{DoxyItemize} \item fixed parse locations of strings and regexes (\href{https://github.com/qorelanguage/qore/issues/1905}{\texttt{ issue 1905}}) \end{DoxyItemize}\hypertarget{release_notes_qore_08129}{}\doxysection{Qore 0.\+8.\+12.\+9}\label{release_notes_qore_08129} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08129_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08129_bug_fixes} \begin{DoxyItemize} \item fixed a memory leak where references participate in recursive references (\href{https://github.com/qorelanguage/qore/issues/1774}{\texttt{ issue 1774}}) \item fixed a build issue with clang++ (\href{https://github.com/qorelanguage/qore/issues/1768}{\texttt{ issue 1768}}) \item fixed a memory leak in the \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}} copy constructor when the \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}} was used in other objects (such as an event queue, etc; \href{https://github.com/qorelanguage/qore/issues/1749}{\texttt{ issue 1749}}) \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module fixes\+: \begin{DoxyItemize} \item fixed bugs handling the {\ttfamily allow\+\_\+dot} and {\ttfamily allow\+\_\+output\+\_\+dot} options (\href{https://github.com/qorelanguage/qore/issues/1690}{\texttt{ issue 1690}}) \item fixed {\ttfamily Table\+Mapper} bugs introduced in \mbox{\hyperlink{namespace_qore}{Qore}} 0.\+8.\+12.\+7 (\href{https://github.com/qorelanguage/qore/issues/1754}{\texttt{ issue 1754}}) \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_08128}{}\doxysection{Qore 0.\+8.\+12.\+8}\label{release_notes_qore_08128} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08128_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08128_bug_fixes} \begin{DoxyItemize} \item fixed a memory leak in \mbox{\hyperlink{parse_directives_try-module}{\%try-\/module}} error handling (\href{https://github.com/qorelanguage/qore/issues/1690}{\texttt{ issue 1690}}) \item fixed a bug in \mbox{\hyperlink{group__string__functions_ga49c6b104180fd40bb21d164773df1f4b}{trunc\+\_\+str()}} when the string has an invalid multi-\/byte character at the end of the string and the string is exactly the byte width requested (\href{https://github.com/qorelanguage/qore/issues/1693}{\texttt{ issue 1693}}) \item fixed a bug where \mbox{\hyperlink{class_qore_1_1_read_only_file_ab6946821b81fc2b9b4f07ef27ebacd45}{Read\+Only\+File\+::getchar()}} did not respect character semantics as documented (\href{https://github.com/qorelanguage/qore/issues/1547}{\texttt{ issue 1547}}) \item \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}} module fixes\+: \begin{DoxyItemize} \item fixed a bug in {\ttfamily character\+\_\+semantics} for standalone column (\href{https://github.com/qorelanguage/qore/issues/1688}{\texttt{ issue 1688}}) \end{DoxyItemize} \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module fixes\+: \begin{DoxyItemize} \item fixed a bug in handling \char`\"{}list mode\char`\"{} data such as submitted by {\ttfamily Inbound\+Table\+Mapper\+::queue\+Data()} (\href{https://github.com/qorelanguage/qore/issues/1736}{\texttt{ issue 1736}}, bug introduced in \mbox{\hyperlink{namespace_qore}{Qore}} 0.\+8.\+12.\+7 with the fix for \href{https://github.com/qorelanguage/qore/issues/1626}{\texttt{ issue 1626}}) \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module fixes\+: \begin{DoxyItemize} \item fixed schema alignment skipping column with name \char`\"{}driver\char`\"{} (\href{https://github.com/qorelanguage/qore/issues/1684}{\texttt{ issue 1684}}) \item fixed sqlutil schema management\+: functional indexes are rejected without () in name (\href{https://github.com/qorelanguage/qore/issues/1610}{\texttt{ issue 1610}}) \end{DoxyItemize} \item \href{../../modules/TableMapper/html/index.html}{\texttt{ Table\+Mapper}} module fixes\+: \begin{DoxyItemize} \item fixed a bug in handling \char`\"{}list mode\char`\"{} data with optimized inserts (\href{https://github.com/qorelanguage/qore/issues/1736}{\texttt{ issue 1736}}, bug introduced in \mbox{\hyperlink{namespace_qore}{Qore}} 0.\+8.\+12.\+7 with the fix for \href{https://github.com/qorelanguage/qore/issues/1626}{\texttt{ issue 1626}}) \end{DoxyItemize} \item \href{../../modules/WebSocketClient/html/index.html}{\texttt{ Web\+Socket\+Client}} module fixes\+: \begin{DoxyItemize} \item added timeout values to \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} and \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client}{H\+T\+T\+P\+Client}} calls (\href{https://github.com/qorelanguage/qore/issues/1725}{\texttt{ issue 1725}}) \end{DoxyItemize} \item \href{../../modules/WebSocketHandler/html/index.html}{\texttt{ Web\+Socket\+Handler}} module fixes\+: \begin{DoxyItemize} \item added timeout values to \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} calls (\href{https://github.com/qorelanguage/qore/issues/1725}{\texttt{ issue 1725}}) \end{DoxyItemize} \item \href{../../modules/WebSocketUtil/html/index.html}{\texttt{ Web\+Socket\+Util}} module fixes\+: \begin{DoxyItemize} \item added timeout values to \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} calls (\href{https://github.com/qorelanguage/qore/issues/1725}{\texttt{ issue 1725}}) \end{DoxyItemize} \item fixed a bug where a type conversion error in an lvalue assignment could generate a confusing unrelated runtime exception (\href{https://github.com/qorelanguage/qore/issues/1697}{\texttt{ issue 1697}}) \item fixed a bug where invalid characters in the port specification in a U\+RL were ignored (\href{https://github.com/qorelanguage/qore/issues/1728}{\texttt{ issue 1728}}) \item fixed a bug with S\+SL socket communication the remote closing the connection during a send operation could cause the current thread to go into an infinite loop consuming 100\% C\+PU (\href{https://github.com/qorelanguage/qore/issues/1729}{\texttt{ issue 1729}}) \item fixed a bug in the \mbox{\hyperlink{class_qore_1_1_hash_list_iterator}{Hash\+List\+Iterator}} class iterating hashes with a mix of lists and single values such as used by bulk D\+ML binds; now the single values will appear as the current value for all list elements as per the original design instead of throwing a runtime exception (\href{https://github.com/qorelanguage/qore/issues/1738}{\texttt{ issue 1738}}) \end{DoxyItemize}\hypertarget{release_notes_qore_08127}{}\doxysection{Qore 0.\+8.\+12.\+7}\label{release_notes_qore_08127} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08127_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08127_bug_fixes} \begin{DoxyItemize} \item fixed bug in internal string generation with {\ttfamily size\+\_\+t} arguments that could cause invalid data to be output or crashes on 32-\/bit platforms (\href{https://github.com/qorelanguage/qore/issues/1640}{\texttt{ issue 1640}}) \item fixed a runtime memory leak and invalid runtime behavior with undetected recursive lvalue references (\href{https://github.com/qorelanguage/qore/issues/1617}{\texttt{ issue 1617}}) \item improved \mbox{\hyperlink{container_data_types_garbage_collection}{prompt collection}} performance with large graphs of objects by eliminating additional unnecessary graph scans, resulting in further large performance improvements in the garbage collector (\href{https://github.com/qorelanguage/qore/issues/1363}{\texttt{ issue 1363}}) \item improved {\ttfamily Inbound\+Table\+Mapper\+::queue\+Data()} performance (in the \href{../../modules/TableMapper/html/index.html}{\texttt{ Table\+Mapper}} module) when used with data in hash of lists format to use bulk D\+ML in input and output without internal data conversions (\href{https://github.com/qorelanguage/qore/issues/1626}{\texttt{ issue 1626}}) \item \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}} module fixes\+: \begin{DoxyItemize} \item worked around {\ttfamily O\+R\+A-\/22165} from {\ttfamily op\+\_\+in()} caused by Oracle\textquotesingle{}s limit on number of collection elements (\href{https://github.com/qorelanguage/qore/issues/1660}{\texttt{ issue 1660}}) \item fixed a bug in the {\itshape force} option (i.\+e. cascade) for dropping types (\href{https://github.com/qorelanguage/qore/issues/1683}{\texttt{ issue 1683}}) \end{DoxyItemize} \item improved \mbox{\hyperlink{parse_directives_try-module}{\%try-\/module}} error reporting and documentation (\href{https://github.com/qorelanguage/qore/issues/1648}{\texttt{ issue 1648}}) \end{DoxyItemize}\hypertarget{release_notes_qore_08126}{}\doxysection{Qore 0.\+8.\+12.\+6}\label{release_notes_qore_08126} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08126_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08126_bug_fixes} \begin{DoxyItemize} \item fixed a bug in \mbox{\hyperlink{group__misc__functions_ga54e6ccaa8fdaa3213ae5550aa66629c9}{Qore\+::parse\+\_\+url()}} parsing single-\/character hostnames (\href{https://github.com/qorelanguage/qore/issues/1524}{\texttt{ issue 1524}}) \item fixed a bug where \mbox{\hyperlink{group__parse__options_ga32ca9503dd181920af97c058d9bd1164}{P\+O\+\_\+\+L\+O\+C\+K\+D\+O\+WN}} was not set when parsing {\ttfamily init} and {\ttfamily del} attributes in \mbox{\hyperlink{qore_modules_user_modules}{user module}} headers (\href{https://github.com/qorelanguage/qore/issues/1535}{\texttt{ issue 1535}}) \item fixed a bug parsing exception catch block parameter errors (in debug builds only; \href{https://github.com/qorelanguage/qore/issues/1558}{\texttt{ issue 1558}}) \item fixed a bug dereferencing \mbox{\hyperlink{basic_data_types_binary}{binary values}} with the \mbox{\hyperlink{operators_list_element_operator}{\mbox{[}\mbox{]} operator}}; the behavior now corresponds to the documentation (\href{https://github.com/qorelanguage/qore/issues/1566}{\texttt{ issue 1566}}) \item fixed a bug that would result in a crash if a method were declared both {\ttfamily static} and {\ttfamily abstract} (\href{https://github.com/qorelanguage/qore/issues/1590}{\texttt{ issue 1590}}) \item fixed performance issues with the \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module (and by extension the \href{../../modules/TableMapper/html/index.html}{\texttt{ Table\+Mapper}} module) for mappers with many identity (i.\+e. 1\+:1) and constant mappings (\href{https://github.com/qorelanguage/qore/issues/1620}{\texttt{ issue 1620}}) \item fixed a bug in the {\ttfamily Bulk\+Insert\+Operation} class in the \href{../../modules/BulkSqlUtil/html/index.html}{\texttt{ Bulk\+Sql\+Util}} module where inserts would fail or silently insert invalid data in the second or later blocks when constant hashes were used (\href{https://github.com/qorelanguage/qore/issues/1625}{\texttt{ issue 1625}}) \end{DoxyItemize}\hypertarget{release_notes_qore_08125}{}\doxysection{Qore 0.\+8.\+12.\+5}\label{release_notes_qore_08125} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08125_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_08125_new_features} \begin{DoxyItemize} \item added the \href{../../modules/SalesforceRestClient/html/index.html}{\texttt{ Salesforce\+Rest\+Client}} module for communicating with Salesforce.\+com using the R\+E\+ST A\+P\+Is \item module \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} \begin{DoxyItemize} \item has support for native default values in tables (\href{https://github.com/qorelanguage/qore/issues/1428}{\texttt{ issue 1428}}) \item has support for Oracle named types (eg. spatial types) for Schema.\+qm and Schema\+Reverse.\+qm. (\href{https://github.com/qorelanguage/qore/issues/1465}{\texttt{ issue 1465}}) \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_08125_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08125_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/Mime/html/index.html}{\texttt{ Mime}} module\+: \begin{DoxyItemize} \item added support for U\+RL form-\/encoded messages (\href{https://github.com/qorelanguage/qore/issues/1436}{\texttt{ issue 1436}} \end{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module\+: \begin{DoxyItemize} \item added support for U\+RL form-\/encoded messages (\href{https://github.com/qorelanguage/qore/issues/1436}{\texttt{ issue 1436}} \item added support for the {\ttfamily \char`\"{}rawxml\char`\"{}} message body encoding (\href{https://github.com/qorelanguage/qore/issues/1437}{\texttt{ issue 1437}} \end{DoxyItemize} \item fixed handling of invalid compressed data in the following functions (\href{https://github.com/qorelanguage/qore/issues/1432}{\texttt{ issue 1432}})\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__compresssion__functions_gae3d26c1886e243d300d5d7ca1686ba9e}{Qore\+::gunzip\+\_\+to\+\_\+binary()}} \item \mbox{\hyperlink{group__compresssion__functions_ga5684efdbe38373331255d4984ef13c9d}{Qore\+::gunzip\+\_\+to\+\_\+string()}} \item \mbox{\hyperlink{group__compresssion__functions_gad1fe94d17de0489667c6909b88c01d43}{Qore\+::uncompress\+\_\+to\+\_\+binary()}} \item \mbox{\hyperlink{group__compresssion__functions_ga873701e40ef6eb9831c9cf66fc8cd981}{Qore\+::uncompress\+\_\+to\+\_\+string()}} \end{DoxyItemize} \item fixed {\ttfamily @inf@} on Windows (\href{https://github.com/qorelanguage/qore/issues/1442}{\texttt{ issue 1442}}) \item fixed \mbox{\hyperlink{group__misc__functions_ga54e6ccaa8fdaa3213ae5550aa66629c9}{Qore\+::parse\+\_\+url()}} with single-\/character usernames (\href{https://github.com/qorelanguage/qore/issues/1455}{\texttt{ issue 1455}}) \item corrected the error message with S\+SL reads when the server closes the connection prematurely (\href{https://github.com/qorelanguage/qore/issues/1488}{\texttt{ issue 1488}}) \item fixed the {\ttfamily Host} header in H\+T\+TP requests to not include the port if the port is the default port for the scheme because it causes some servers to reject the request (\href{https://github.com/qorelanguage/qore/issues/1489}{\texttt{ issue 1489}}) \end{DoxyItemize}\hypertarget{release_notes_qore_08124}{}\doxysection{Qore 0.\+8.\+12.\+4}\label{release_notes_qore_08124} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08124_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08124_bug_fixes} \begin{DoxyItemize} \item fixed a reference bug in the \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}} class introduced in the last release (\href{https://github.com/qorelanguage/qore/issues/1309}{\texttt{ issue 1309}}) \item fixed a bug where database types could not be correctly aligned if they had dependencies (\href{https://github.com/qorelanguage/qore/issues/1314}{\texttt{ issue 1314}}); entailed updates in the following modules\+: \begin{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} \item \href{../../modules/FreetdsSqlUtil/html/index.html}{\texttt{ Freetds\+Sql\+Util}} \item \href{../../modules/MysqlSqlUtil/html/index.html}{\texttt{ Mysql\+Sql\+Util}} \item \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}} \item \href{../../modules/PgsqlSqlUtil/html/index.html}{\texttt{ Pgsql\+Sql\+Util}} \item \href{../../modules/Schema/html/index.html}{\texttt{ Schema}} \end{DoxyItemize} \item fixed a bug in \mbox{\hyperlink{group__string__functions_ga49c6b104180fd40bb21d164773df1f4b}{trunc\+\_\+str()}} where an infinite loop could be triggered with certain arguments and multi-\/byte character encodings (\href{https://github.com/qorelanguage/qore/issues/1327}{\texttt{ issue 1327}}) \item improved \mbox{\hyperlink{container_data_types_garbage_collection}{prompt collection}} performance with larger graphs of objects by eliminating unnecessary graph scans made during object method calls (\href{https://github.com/qorelanguage/qore/issues/1363}{\texttt{ issue 1363}}) \item fixed bugs in \mbox{\hyperlink{group__date__and__time__functions_ga835071f44cebd259e52045a822009cac}{date(string)}} and \mbox{\hyperlink{group__date__and__time__functions_gaa990826f93b4f22f786fcfe431c4886d}{date(string, string)}} where invalid input data was ignored and invalid dates were returned (\href{https://github.com/qorelanguage/qore/issues/1369}{\texttt{ issue 1369}}) \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module\+: \begin{DoxyItemize} \item fixed a bug in {\ttfamily Abstract\+Csv\+Iterator\+::identify\+Type\+Impl()} generating an error message (\href{https://github.com/qorelanguage/qore/issues/1355}{\texttt{ issue 1355}}) \end{DoxyItemize} \item \href{../../modules/MailMessage/html/index.html}{\texttt{ Mail\+Message}} module\+: \begin{DoxyItemize} \item fixed a bug using the default encoding in {\ttfamily Message\+::attach()} (issue \href{https://github.com/qorelanguage/qore/issues/1352}{\texttt{ issue 1352}}) \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module\+: \begin{DoxyItemize} \item fixed the ignored character\+\_\+semantics column option in schema alignmed (\href{https://github.com/qorelanguage/qore/issues/1379}{\texttt{ issue 1379}}) \item implemented the {\ttfamily cop\+\_\+length()} column function (\href{https://github.com/qorelanguage/qore/issues/1395}{\texttt{ issue 1395}}) \end{DoxyItemize} \item \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}} module\+: \begin{DoxyItemize} \item Oracle\+Package attribute body\+\_\+src is now public to access package bodies \end{DoxyItemize} \item \href{../../modules/Qorize/html/index.html}{\texttt{ Qorize}} module\+: \begin{DoxyItemize} \item Qorize module\+: new qorize\+\_\+val() set of functions; qorize\+\_\+named() introduced; qorize tests \end{DoxyItemize} \item \href{../../modules/TableMapper/html/index.html}{\texttt{ Table\+Mapper}} module\+: \begin{DoxyItemize} \item fixed runtime option propagation to {\ttfamily Table\+Mapper\+::\+Sql\+Statement\+Mapper\+Iterator} from {\ttfamily Table\+Mapper\+::\+Abstract\+Sql\+Statement\+Outbound\+Mapper\+::iterator()} (\href{https://github.com/qorelanguage/qore/issues/1418}{\texttt{ issue 1418}}) \item fixed Sql\+Statement\+Mapper\+Iterator\+::get\+Count() (\href{https://github.com/qorelanguage/qore/issues/1417}{\texttt{ issue 1417}}) \item added the following methods\+: \begin{DoxyItemize} \item {\ttfamily Table\+Mapper\+::\+Abstract\+Sql\+Statement\+Outbound\+Mapper\+::get\+Row\+Iterator()} \item {\ttfamily Table\+Mapper\+::\+Inbound\+Table\+Mapper\+::iterator()} \item {\ttfamily Table\+Mapper\+::\+Inbound\+Table\+Mapper\+Iterator\+::get\+Runtime()} \item {\ttfamily Table\+Mapper\+::\+Inbound\+Table\+Mapper\+Iterator\+::replace\+Runtime()} \item {\ttfamily Table\+Mapper\+::\+Inbound\+Table\+Mapper\+Iterator\+::set\+Runtime()} \item {\ttfamily Table\+Mapper\+::\+Sql\+Statement\+Mapper\+Iterator\+::get\+Runtime()} \item {\ttfamily Table\+Mapper\+::\+Sql\+Statement\+Mapper\+Iterator\+::replace\+Runtime()} \item {\ttfamily Table\+Mapper\+::\+Sql\+Statement\+Mapper\+Iterator\+::set\+Runtime()} \end{DoxyItemize} \end{DoxyItemize} \item \href{../../modules/QUnit/html/index.html}{\texttt{ Q\+Unit}} module\+: \begin{DoxyItemize} \item fixed showing the assertion location when there are test modules on top of Q\+Unit (\href{https://github.com/qorelanguage/qore/issues/1046}{\texttt{ issue 1046}}) \end{DoxyItemize} \item fixed inconsistency between list splice operator and splice function (\href{https://github.com/qorelanguage/qore/issues/1380}{\texttt{ issue 1380}}) \end{DoxyItemize}\hypertarget{release_notes_qore_08123}{}\doxysection{Qore 0.\+8.\+12.\+3}\label{release_notes_qore_08123} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08123_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08123_bug_fixes} \begin{DoxyItemize} \item fixed the documentation (and DB modules) where \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement_ab889448c79985fc26e41b7e2086308df}{S\+Q\+L\+Statement\+::fetch\+Columns()}} was inconsistent; now it will return a empty hash when no more rows are available to fetch (\href{https://github.com/qorelanguage/qore/issues/1241}{\texttt{ issue 1241}}) \item added I/O timeout support to the \mbox{\hyperlink{class_qore_1_1_ftp_client}{Ftp\+Client}} class (\href{https://github.com/qorelanguage/qore/issues/1252}{\texttt{ issue 1252}}) \item fixed bugs in \mbox{\hyperlink{class_qore_1_1_socket_adba4badd712c161df1b2da87e528ecb8}{Socket\+::recv()}} and \mbox{\hyperlink{class_qore_1_1_socket_aa255d1dcfbddb208e80684eebecc800d}{Socket\+::recv\+Binary()}} with {\ttfamily size = 0} where \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} could be returned which is invalid according to the methods\textquotesingle{} declared return types (\href{https://github.com/qorelanguage/qore/issues/1260}{\texttt{ issue 1260}}) \item fixed a bug where \mbox{\hyperlink{class_qore_1_1_ftp_client_a2b06a66db173df6bac61b1af48c7a11c}{Ftp\+Client\+:get()}} would fail with an exception when retrieving an empty file (\href{https://github.com/qorelanguage/qore/issues/1255}{\texttt{ issue 1255}}) \item fixed a bug where executing a call reference to a deleted object method would cause a crash (\href{https://github.com/qorelanguage/qore/issues/1268}{\texttt{ issue 1268}}) \item fixed a bug where \mbox{\hyperlink{namespace_qore}{Qore}} would allow methods to be called on already deleted objects under certain conditions (\href{https://github.com/qorelanguage/qore/issues/1270}{\texttt{ issue 1270}}) \item fixed a bug where calling \mbox{\hyperlink{namespace_qore_a3ec32747f455642fd9ce503094a5cc85}{exit()}} in a multithreaded program could result in a segmentation fault (\href{https://github.com/qorelanguage/qore/issues/1215}{\texttt{ issue 1215}}) \item fixed a bug where \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server\+::add\+Listener()}} could not accept a bind on port 0 to mean any random port (\href{https://github.com/qorelanguage/qore/issues/1284}{\texttt{ issue 1284}}) \item fixed a race condition in \mbox{\hyperlink{container_data_types_garbage_collection}{prompt collection}} that could lead to a crash (\href{https://github.com/qorelanguage/qore/issues/1084}{\texttt{ issue 1084}}) \item fixed a bug clearing \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} event queues when the \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} goes out of scope that could lead to a crash (\href{https://github.com/qorelanguage/qore/issues/1292}{\texttt{ issue 1292}}) \item fixed a bug with \mbox{\hyperlink{class_qore_1_1_ftp_client_a49a2e47cde50ae8bbcbca8721199dd16}{Ftp\+Client\+::set\+Warning\+Queue()}} that could cause a crash (\href{https://github.com/qorelanguage/qore/issues/1293}{\texttt{ issue 1293}}) \item fixed a bug where \mbox{\hyperlink{class_qore_1_1_ftp_client_a50427e074d3f14757491ad26295d7e6b}{Qore\+::\+Ftp\+Client\+::pwd()}} returned invalid directory names (\href{https://github.com/qorelanguage/qore/issues/1295}{\texttt{ issue 1295}}) \end{DoxyItemize}\hypertarget{release_notes_qore_08122}{}\doxysection{Qore 0.\+8.\+12.\+2}\label{release_notes_qore_08122} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08122_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08122_bug_fixes} \begin{DoxyItemize} \item fixed bugs in handling websocket close status codes in the \href{../../modules/WebSocketUtil/html/index.html}{\texttt{ Web\+Socket\+Util}}, \href{../../modules/WebSocketClient/html/index.html}{\texttt{ Web\+Socket\+Client}}, and \href{../../modules/WebSocketHandler/html/index.html}{\texttt{ Web\+Socket\+Handler}} modules (\href{https://github.com/qorelanguage/qore/issues/1216}{\texttt{ issue 1216}}) \item fixed a crashing bug with recursive class initialization (\href{https://github.com/qorelanguage/qore/issues/2023}{\texttt{ issue 2023}}) \end{DoxyItemize}\hypertarget{release_notes_qore_08121}{}\doxysection{Qore 0.\+8.\+12.\+1}\label{release_notes_qore_08121} \begin{DoxyParagraph}{Release Summary} Bugfix release; see details below \end{DoxyParagraph} \hypertarget{release_notes_qore_08121_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_08121_bug_fixes} \begin{DoxyItemize} \item \href{../../modules/TableMapper/html/index.html}{\texttt{ Table\+Mapper}} module fixes\+: \begin{DoxyItemize} \item fixed a bug with the {\ttfamily Sql\+Statement\+Outbound\+Mapper\+::iterator()} method; corrected the iterator object return value which was causing {\ttfamily Abstract\+Mapper\+Iterator\+::map\+Bulk()} to fail (\href{https://github.com/qorelanguage/qore/issues/979}{\texttt{ issue 979}}) \item fixed a bug with {\ttfamily Sql\+Statement\+Outbound\+Mapper}; it would throw an error if the required {\ttfamily \char`\"{}table\char`\"{}} or {\ttfamily \char`\"{}sh\char`\"{}} options were used and only worked with subclasses that declared these options (\href{https://github.com/qorelanguage/qore/issues/981}{\texttt{ issue 981}}) \item fixed a bug where {\ttfamily Abstract\+Sql\+Statement\+Outbound\+Mapper\+::iterator()} failed to use options when creating the new {\ttfamily Mapper} object (\href{https://github.com/qorelanguage/qore/issues/1088}{\texttt{ issue 1088}}) \end{DoxyItemize} \item fixed a bug where optional arguments were not handled correctly in some rare cases (\href{https://github.com/qorelanguage/qore/issues/974}{\texttt{ issue 974}}) \item fixed a bug causing a crash when \mbox{\hyperlink{group__misc__functions_ga0160c0c4cbe7180d70048577e4e40bcc}{parse\+\_\+base64\+\_\+string\+\_\+to\+\_\+string()}} was called with an empty string (\href{https://github.com/qorelanguage/qore/issues/996}{\texttt{ issue 996}}) \item fixed a bug resolving base class method calls during parse initialization (\href{https://github.com/qorelanguage/qore/issues/1075}{\texttt{ issue 1075}}) \item fixed thread memory handling bug with some operator expressions and the \mbox{\hyperlink{operators_background}{background operator}} (\href{https://github.com/qorelanguage/qore/issues/1096}{\texttt{ issue 1096}}) \item fixed a race condition in the prompt collection of closure-\/bound local variables in the \mbox{\hyperlink{container_data_types_garbage_collection}{garbage collector}} (\href{https://github.com/qorelanguage/qore/issues/1103}{\texttt{ issue 1103}}) \item fixed a bug where \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client}{H\+T\+T\+P\+Client}} class method variants such as \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_ac4b1dbf34a656d23a89e719a8dadac38}{H\+T\+T\+P\+Client\+::get()}} without a callback would fail to return the message body when the server sent a reply with chunked transfer encoding (\href{https://github.com/qorelanguage/qore/issues/1117}{\texttt{ issue 1117}}) \item fixed a bug in Csv\+Util where backward compatibility was broken for single-\/row-\/type format (\href{https://github.com/qorelanguage/qore/issues/1124}{\texttt{ issue 1124}}) \item fixed bugs where declared public functions were missing from the library A\+BI (\href{https://github.com/qorelanguage/qore/issues/1126}{\texttt{ issue 1126}}) \item fixed bugs where \mbox{\hyperlink{group__string__functions_ga33bb08516773ed10def16bb42d6b8159}{Qore\+::format\+\_\+number()}} and \mbox{\hyperlink{class_qore_1_1zzz8floatzzz9_a456f92c6ee27c0c772223745f918bcbc}{Qore\+::zzz8floatzzz9\+::format()}} gave incorrect results when rounding to the significant decimals given in the format string (\href{https://github.com/qorelanguage/qore/issues/1149}{\texttt{ issue 1149}}) \item fixed a bug referencing {\ttfamily self} in base class constructor arguments (\href{https://github.com/qorelanguage/qore/issues/1169}{\texttt{ issue 1169}}) \item fixed a bug where the incorrect class destructor was called in the openldap module (\href{https://github.com/qorelanguage/qore/issues/1174}{\texttt{ issue 1174}}) \item fixed a bug where declaring a {\ttfamily copy()} method as \mbox{\hyperlink{threading_synchronized}{synchronized}} would result in a crash when the method was called (\href{https://github.com/qorelanguage/qore/issues/1188}{\texttt{ issue 1188}}) \item fixed bugs in \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a4b2cac04c91fb14fcb5a79469550b820}{Qore\+::zzz8stringzzz9\+::get\+Encoded()}} and \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a07b89a849ef94f060e0fcf2c040fd296}{Qore\+::zzz8stringzzz9\+::get\+Decoded()}} regarding \mbox{\hyperlink{group___string_concat_encoding_gadb85427aabfa0641ebfd5ac5186e5d9e}{C\+E\+\_\+\+X\+ML}} and \mbox{\hyperlink{group___string_concat_encoding_gaa1fefe1dab38a1b1b4a32d84e34fa3f4}{C\+E\+\_\+\+N\+O\+N\+A\+S\+C\+II}} (\href{https://github.com/qorelanguage/qore/issues/1193}{\texttt{ issue 1193}}) \item fixed bugs where \mbox{\hyperlink{group__object__functions_ga733217c233efed0557e133a6cc45189f}{Qore\+::call\+\_\+object\+\_\+method()}} and \mbox{\hyperlink{group__object__functions_ga3f3c875b6632a9b028a5d63be30bec14}{Qore\+::call\+\_\+object\+\_\+method\+\_\+args()}} allowed private methods to be called from outside the class (\href{https://github.com/qorelanguage/qore/issues/1194}{\texttt{ issue 1194}}) \item fixed a bug where \mbox{\hyperlink{deprecated}{Deprecated List}} methods were being internally registered as \mbox{\hyperlink{code_flags_RUNTIME_NOOP}{R\+U\+N\+T\+I\+M\+E\+\_\+\+N\+O\+OP}} (\href{https://github.com/qorelanguage/qore/issues/1197}{\texttt{ issue 1197}}) \item fixed bugs where the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource}{Datasource}} class would open a connection to the server in the constructor before options were set and where a server connection was required to call \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_a34834d2da5e1e8f13949810e76a6e1cd}{Datasource\+::get\+Option()}} or \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_ad64b2409e602054d6e29257442b8601e}{Datasource\+::set\+Option()}} (\href{https://github.com/qorelanguage/qore/issues/1201}{\texttt{ issue 1201}}) \item fixed memory errors in the \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}} class where spurious exceptions could be raised (\href{https://github.com/qorelanguage/qore/issues/1202}{\texttt{ issue 1202}}) \item fixed a memory leak with static class member initializers (\href{https://github.com/qorelanguage/qore/issues/1206}{\texttt{ issue 1206}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0812}{}\doxysection{Qore 0.\+8.\+12}\label{release_notes_qore_0812} \begin{DoxyParagraph}{Release Summary} Major new release with major new features and bug fixes as well as packaging fixes\+: \begin{DoxyItemize} \item added support for \mbox{\hyperlink{container_data_types_garbage_collection}{deterministic garbage collection}} \item standardized function naming convention \item new functions, methods, constants, operators, and user modules \item greatly improved support on Windows \end{DoxyItemize} \end{DoxyParagraph} \hypertarget{release_notes_qore_0812_compatibility}{}\doxysubsection{Changes That Can Affect Backwards-\/\+Compatibility}\label{release_notes_qore_0812_compatibility} \begin{DoxyItemize} \item fixed broken list parsing; in previous releases, Qore\textquotesingle{}s parser re-\/wrote lists without parentheses used as top-\/level statements with certain assignment operators (\mbox{\hyperlink{operators_assignment_operator}{=}}, \mbox{\hyperlink{operators_plus_equals_operator}{+=}}, \mbox{\hyperlink{operators_minus_equals_operator}{-\/=}}, \mbox{\hyperlink{operators_multiply_equals_operator}{$\ast$=}}, and \mbox{\hyperlink{operators_divide_equals_operator}{/=}}, but not with others) so that statements like {\ttfamily list l = 1, 2, 3;} were valid assignments. Due to operator precedence, such statements should normally be interpreted as {\ttfamily (list l = 1), 2, 3;}, which is not a valid expression. Not only were the rules applied with only some assignment operators, but such lists were only rewritten if used as top-\/level statements, therefore the rules were applied inconsistenctly depending on where the expression was located in the parse tree. As of Qore 0.\+8.\+12, these inconsistencies have been eliminated by default from Qore; all lists are processed according to the precedence rules defined in \mbox{\hyperlink{operators}{Operators}}. This could break old code that relied on the old, broken behavior. To get the old behavior, use the \mbox{\hyperlink{parse_directives_broken-list-parsing}{\%broken-\/list-\/parsing}} parse directive. \item fixed broken \mbox{\hyperlink{data_type_declarations_int_type}{int}} and \mbox{\hyperlink{data_type_declarations_softint_type}{softint}} assignments; previously runtime type errors with these type restrictions were ignored and all values were silently converted to integers for the assignment, now runtime type errors are thrown according to the original design. Parse errors are detected as before. This could break old code that relied on the old, broken behavior. To get the old behavior, use the \mbox{\hyperlink{parse_directives_broken-int-assignments}{\%broken-\/int-\/assignments}} parse directive. \item fixed broken multi-\/character operator parsing; the Qore parser has been updated to no longer accept multi-\/character operators with whitespace between the chacters making up the operator; it is believed that this was never used and simply caused the parser to be needlessly complicated and caused Qore to be less compatible with other languages. To get the old behavior, use the \mbox{\hyperlink{parse_directives_broken-operators}{\%broken-\/operators}} parse directive. \item the \mbox{\hyperlink{operators_push}{push}}, \mbox{\hyperlink{operators_unshift}{unshift}}, \mbox{\hyperlink{operators_pop}{pop}} and \mbox{\hyperlink{operators_shift}{shift}} operators now throw an exception when their first operand is not a list and \mbox{\hyperlink{parse_directives_strict-args}{\%strict-\/args}} is in effect \end{DoxyItemize}\hypertarget{release_notes_qore_0812_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_0812_new_features} \begin{DoxyItemize} \item Added the \mbox{\hyperlink{operators_value_coalescing_operator}{Value Coalescing Operator (?$\ast$)}} which checks first argument if it evaluates to \mbox{\hyperlink{basic_data_types_False}{False}} with \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_a3a66486cee14aa073cf90fbed5a23edd}{Qore\+::zzz8valuezzz9\+::val()}} and if so assigns the second argument. The operator can be further chained; for example\+: \begin{DoxyCode}{0} \DoxyCodeLine{expr1 ?* expr2 ?* expr3 } \end{DoxyCode} \item Added the \mbox{\hyperlink{operators_null_coalescing_operator}{Null Coalescing Operator (??)}} which checks the first operand for \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} or \mbox{\hyperlink{basic_data_types_null}{N\+U\+LL}}; if true returns the second argument. The operator can be further chained, in which case the first operand with a value is returned; ex\+: \begin{DoxyCode}{0} \DoxyCodeLine{expr1 ?? expr2 ?? expr3 } \end{DoxyCode} \item Qore identifiers can now begin with an underscore character {\ttfamily \char`\"{}\+\_\+\char`\"{}}; the following is now a valid (with \mbox{\hyperlink{parse_directives_new-style}{\%new-\/style}})\+: \begin{DoxyCode}{0} \DoxyCodeLine{int \_var = 1;} \end{DoxyCode} \item hash enhancements\+: \begin{DoxyItemize} \item new syntax for an expression giving an empty hash\+: {\ttfamily \{\}}; for example\+: \begin{DoxyCode}{0} \DoxyCodeLine{hash h = \{\};} \end{DoxyCode} \item new literal hash support\+: hashes can now be given as literal values as follows\+: \begin{DoxyCode}{0} \DoxyCodeLine{(<key\_expr>: <val\_expr>, [...]) } \end{DoxyCode} For example\+: \begin{DoxyCode}{0} \DoxyCodeLine{\textcolor{keywordflow}{return} (get\_key(): get\_value()); } \end{DoxyCode} in the past the keys in literal hashes had to be either a string or a constant; now any valid Qore expression can be used to generate the hash keys at runtime \item new hash syntax; hash elements can now be enclosed by curly brackets as well as regular parentheses; the version with curly brackets when used with the \mbox{\hyperlink{operators_hmap}{map}} operator results in the hash version of the map operator being used \item Added new \mbox{\hyperlink{operators_hmap}{hash version of the map}} operator to build a hash from a list or iterator expression; ex\+: \begin{DoxyCode}{0} \DoxyCodeLine{hash h = map \{\$1, h2.\$1\}, i; } \end{DoxyCode} \end{DoxyItemize} \item implemented support for loading user modules in a pre-\/defined \mbox{\hyperlink{class_qore_1_1_program}{Program}} object (that can have a custom A\+PI) in the following new functions and methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__misc__functions_ga59d94b7cc4dfcc6e39030097458b8afe}{load\+\_\+user\+\_\+module\+\_\+with\+\_\+program()}} \item \mbox{\hyperlink{class_qore_1_1_program_a2f83d6257c25cc5ae867d9d461019996}{Program\+::load\+Apply\+To\+Private\+User\+Module()}} \item \mbox{\hyperlink{class_qore_1_1_program_a300ffe0abd0b09cc39feb637a9bab9ba}{Program\+::load\+Apply\+To\+User\+Module()}} \item \mbox{\hyperlink{class_qore_1_1_program_a88ead6a191a58736b49e794f3220869f}{Program\+::load\+User\+Module\+With\+Program()}} \end{DoxyItemize} \item implemented support for code / dependency injections in \mbox{\hyperlink{class_qore_1_1_program}{Program}} containers with the following changes\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_program_abf634534cb29157d05aab5ff3ffd6bea}{Qore\+::\+Program\+::import\+Class()}} now accepts optional arguments that allow the imported version of the class to live in another namespace and have another name and an argument that allows the imported version of the class to remain even if it overlaps with an imported system or user class from a module \item \mbox{\hyperlink{class_qore_1_1_program_a9a2e3da4029c50643169cbb72e57f494}{Qore\+::\+Program\+::import\+Function()}} now accepts an optional argument that allows the imported version of the function to remain even if it overlaps with an imported system or user function from a module \item the new parse option \mbox{\hyperlink{group__parse__options_ga1c78ca9bda4b8f5b2ad669c48fe0368d}{Qore\+::\+P\+O\+\_\+\+A\+L\+L\+O\+W\+\_\+\+I\+N\+J\+E\+C\+T\+I\+ON}} must be set on the \mbox{\hyperlink{class_qore_1_1_program}{Program}} object in order to use code / dependency injection parameters in the above methods \item \mbox{\hyperlink{class_qore_1_1_program}{Program}} changes\+: \begin{DoxyItemize} \item Once the object has an injected A\+PI set up, the system A\+PI can be imported (possibly already overridden with injected code) with the following new methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_program_a8abea6fe89712e9b4f84c7f7b0420151}{Qore\+::\+Program\+::import\+System\+Api()}} \item \mbox{\hyperlink{class_qore_1_1_program_ad512b5c0b491823d186e0de7cf8d87d4}{Qore\+::\+Program\+::import\+System\+Classes()}} \item \mbox{\hyperlink{class_qore_1_1_program_a2942f186ac759fb7a71cbb9ec0ffb72a}{Qore\+::\+Program\+::import\+System\+Constants()}} \item \mbox{\hyperlink{class_qore_1_1_program_adc115cc0b1c0f196ed0d764eb33c4009}{Qore\+::\+Program\+::import\+System\+Functions()}} \end{DoxyItemize} \item Additionally user modules can be loaded with overridden injected code with the following new functions / methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__misc__functions_ga59d94b7cc4dfcc6e39030097458b8afe}{load\+\_\+user\+\_\+module\+\_\+with\+\_\+program()}} \item \mbox{\hyperlink{class_qore_1_1_program_a2f83d6257c25cc5ae867d9d461019996}{Program\+::load\+Apply\+To\+Private\+User\+Module()}} \item \mbox{\hyperlink{class_qore_1_1_program_a300ffe0abd0b09cc39feb637a9bab9ba}{Program\+::load\+Apply\+To\+User\+Module()}} \item \mbox{\hyperlink{class_qore_1_1_program_a88ead6a191a58736b49e794f3220869f}{Program\+::load\+User\+Module\+With\+Program()}} \end{DoxyItemize} \item Furthermore the following function can be used to reload injected modules with the non-\/injected version\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__misc__functions_ga84fcab69e514fd31cefe8de51bbe8acd}{reload\+\_\+module()}} \end{DoxyItemize} \end{DoxyItemize} \end{DoxyItemize} \item implemented support for user-\/defined thread-\/resource management, allowing Qore code to safely manage resources associated to a particular thread\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_thread_1_1_abstract_thread_resource}{Qore\+::\+Thread\+::\+Abstract\+Thread\+Resource}} \item \mbox{\hyperlink{group__threading__functions_gadc994316e54fdf50111018de9bd15dc6}{Qore\+::remove\+\_\+thread\+\_\+resource()}} \item \mbox{\hyperlink{group__threading__functions_ga1a1fbc371cfc8885ed78e4bff25d35b1}{Qore\+::set\+\_\+thread\+\_\+resource()}} \end{DoxyItemize} \item new constants\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__system__and__build__constants_ga6cebae5097d4414ca8c6da4be8cf9922}{Qore\+::\+Dir\+Sep}} \item \mbox{\hyperlink{group__system__and__build__constants_ga003f84c29bc6d145ea7ab890cadc5b41}{Qore\+::\+Platform}} \item \mbox{\hyperlink{group__parse__options_gacb154a5a9c64065609d22c5fb62b0d04}{Qore\+::\+Parse\+Option\+Code\+Map}} \item \mbox{\hyperlink{group__parse__options_gad7a1c95d88d0f59ecc3e9985b904dd4a}{Qore\+::\+Parse\+Option\+String\+Map}} \item \mbox{\hyperlink{group__parse__options_ga0d64d3a06cb049d7a50bdeaefb236245}{Qore\+::\+P\+O\+\_\+\+B\+R\+O\+K\+E\+N\+\_\+\+L\+I\+S\+T\+\_\+\+P\+A\+R\+S\+I\+NG}} \item \mbox{\hyperlink{group__parse__options_ga83f83114a31c6c0367370557650f4ae2}{Qore\+::\+P\+O\+\_\+\+B\+R\+O\+K\+E\+N\+\_\+\+L\+O\+G\+I\+C\+\_\+\+P\+R\+E\+C\+E\+D\+E\+N\+CE}} \item \mbox{\hyperlink{group__parse__options_ga6647f2e40ae673ba85d42f9df6199472}{Qore\+::\+P\+O\+\_\+\+B\+R\+O\+K\+E\+N\+\_\+\+O\+P\+E\+R\+A\+T\+O\+RS}} \item \mbox{\hyperlink{group__parse__options_gaec5488ae61db4b43af0e89ddc532e379}{Qore\+::\+P\+O\+\_\+\+N\+O\+\_\+\+I\+N\+H\+E\+R\+I\+T\+\_\+\+S\+Y\+S\+T\+E\+M\+\_\+\+C\+O\+N\+S\+T\+A\+N\+TS}} \item \mbox{\hyperlink{group__parse__options_gaea230eb2f3d02cb456ed8838b805960f}{Qore\+::\+P\+O\+\_\+\+N\+O\+\_\+\+I\+N\+H\+E\+R\+I\+T\+\_\+\+U\+S\+E\+R\+\_\+\+C\+O\+N\+S\+T\+A\+N\+TS}} \item \mbox{\hyperlink{group__parse__options_ga922d0591649ab5fcfa6d6ca3df24a48a}{Qore\+::\+P\+O\+\_\+\+N\+O\+\_\+\+A\+PI}} \item \mbox{\hyperlink{group__parse__options_ga0b4be620288f71a4b591608c931082d0}{Qore\+::\+P\+O\+\_\+\+N\+O\+\_\+\+S\+Y\+S\+T\+E\+M\+\_\+\+A\+PI}} \item \mbox{\hyperlink{group__parse__options_ga58354296ab988435714ebba1fffd59ae}{Qore\+::\+P\+O\+\_\+\+N\+O\+\_\+\+U\+S\+E\+R\+\_\+\+A\+PI}} \item \mbox{\hyperlink{group__dbi__capabilities_ga87128ed8eccc517cb36ceb5f27ceaa53}{Qore\+::S\+QL\+::D\+B\+I\+\_\+\+C\+A\+P\+\_\+\+H\+A\+S\+\_\+\+A\+R\+R\+A\+Y\+\_\+\+B\+I\+ND}} \item \mbox{\hyperlink{group___string_concat_encoding}{String Concatenation Encoding Codes}} \item \mbox{\hyperlink{group___string_concat_decoding}{String Concatenation Decoding Codes}} \end{DoxyItemize} \item new classes\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_data_line_iterator}{Qore\+::\+Data\+Line\+Iterator}} \item \mbox{\hyperlink{class_qore_1_1_thread_1_1_abstract_thread_resource}{Qore\+::\+Thread\+::\+Abstract\+Thread\+Resource}} \end{DoxyItemize} \item other new methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a6b84d1a73d81d05158087517ae31bdfe}{Qore\+::\+S\+Q\+L\+::\+Datasource\+Pool\+::get\+Capabilities()}} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a2689d495aa3dc819c2e928dc86ea9357}{Qore\+::\+S\+Q\+L\+::\+Datasource\+Pool\+::get\+Capability\+List()}} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement_a50d360812380f793b0b0ab7f0b181792}{Qore\+::\+S\+Q\+L\+::\+S\+Q\+L\+Statement\+::current\+Thread\+In\+Transaction()}} \item \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue_ab55ff73e8143bf963aa2ce62b93d7c7f}{Qore\+::\+Thread\+::\+Queue\+::set\+Error()}} \item \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue_a49732032b1eeda812640acbaf35cc884}{Qore\+::\+Thread\+::\+Queue\+::clear\+Error()}} \end{DoxyItemize} \item updated methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_serializable_a7bbf6cf2d7ac53a80e8023790c540c5f}{Time\+Zone\+::constructor()}}\+: now accepts a path to the zoneinfo file if the \mbox{\hyperlink{group__parse__options_ga5e466ed886222f0b57b0a399b455be71}{Qore\+::\+P\+O\+\_\+\+N\+O\+\_\+\+F\+I\+L\+E\+S\+Y\+S\+T\+EM}} sandboxing restrictions is not set \end{DoxyItemize} \item the {\ttfamily S\+O\+C\+K\+E\+T-\/\+T\+H\+R\+O\+U\+G\+H\+P\+U\+T-\/\+W\+A\+R\+N\+I\+NG} event is no longer raised on the warning queue if the transfer size is less than 1024 bytes; this affects\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_ftp_client_a49a2e47cde50ae8bbcbca8721199dd16}{Qore\+::\+Ftp\+Client\+::set\+Warning\+Queue()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_ae2aafddbf5be67012e3b57f846c4105e}{Qore\+::\+H\+T\+T\+P\+Client\+::set\+Warning\+Queue()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a4c3b78b845de5f48434e527755dec18a}{Qore\+::\+Socket\+::set\+Warning\+Queue()}} \end{DoxyItemize} \item new functions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__object__functions_ga6a929dc065cfb0b20639ac815be9cad3}{Qore\+::create\+\_\+object()}} \item \mbox{\hyperlink{group__object__functions_ga6eaee4a61dd7e3f58de1dab76154397f}{Qore\+::create\+\_\+object\+\_\+args()}} \item \mbox{\hyperlink{group__misc__functions_gafd6a2b1500aca8b73c112b723695af4f}{Qore\+::decode\+\_\+uri\+\_\+request()}} \item \mbox{\hyperlink{group__misc__functions_gad0bbcfc5357d459cb538e57e85c1971e}{Qore\+::encode\+\_\+uri\+\_\+request()}} \item \mbox{\hyperlink{group__date__and__time__functions_gac96ed9dc0e5436a5f77c7fbeb5c5842e}{Qore\+::get\+\_\+duration\+\_\+seconds\+\_\+f()}} \item \mbox{\hyperlink{namespace_qore_a9b6def5a046c853cb4a108d5438e6767}{Qore\+::getgroups()}} \item \mbox{\hyperlink{group__user__and__group__functions_ga6be17484ff802389da795f831a549e4e}{Qore\+::getusername()}} \item \mbox{\hyperlink{group__string__functions_gaa3c396510f9d106aee5161cbb144e163}{Qore\+::ltrim()}} \item \mbox{\hyperlink{group__string__functions_gad09a541dcd0e0f42a0447c92a7a60d36}{Qore\+::parse\+\_\+float()}} \item \mbox{\hyperlink{group__string__functions_ga0024906d05096f7f8c1130396dde53c7}{Qore\+::parse\+\_\+number()}} \item \mbox{\hyperlink{namespace_qore_a59c7b40bb68308943c26473b3536594d}{Qore\+::realpath()}} \item \mbox{\hyperlink{group__string__functions_ga25264bfb9950ac66862db9b4a32eeee8}{Qore\+::rtrim()}} \item \mbox{\hyperlink{group__misc__functions_ga51444e624e7ba2b2ecfb45dd49e6db42}{Qore\+::set\+\_\+return\+\_\+value()}} \item \mbox{\hyperlink{namespace_qore_aac8ec21015bc2dc8970cad98a1c6586c}{Qore\+::setgroups()}} \item \mbox{\hyperlink{group__threading__functions_gadc994316e54fdf50111018de9bd15dc6}{Qore\+::remove\+\_\+thread\+\_\+resource()}} \item \mbox{\hyperlink{group__threading__functions_ga1a1fbc371cfc8885ed78e4bff25d35b1}{Qore\+::set\+\_\+thread\+\_\+resource()}} \end{DoxyItemize} \item updated functions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__string__functions_ga774b6d0f9d5835de7d7362400aa2cdd1}{Qore\+::parse\+\_\+boolean()}} \item \mbox{\hyperlink{group__type__conversion__functions_gacf16b4126b795f4b6933ef3425cadae3}{Qore\+::string()}} \item \mbox{\hyperlink{group__string__functions_gaabfb10141a51d31ef100d9fd3a02252e}{Qore\+::strmul()}} \end{DoxyItemize} \item new pseudo-\/methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_ae0566a68783890f894213258833b0b37}{Qore\+::zzz8datezzz9\+::day\+Number()}} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_a776388307af89346ac4456a09d8fb22d}{Qore\+::zzz8datezzz9\+::day\+Of\+Week()}} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_a51af864148656e9fe7dd6e9bc1aba1df}{Qore\+::zzz8datezzz9\+::duration\+Seconds\+Float()}} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_ad38a12c3b55fab4825bbb7d6125df1e5}{Qore\+::zzz8datezzz9\+::iso\+Day\+Of\+Week()}} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_ada1be7d54d1a218ed90b7ee9cdb5130a}{Qore\+::zzz8datezzz9\+::iso\+Week\+Hash()}} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_aa03daafa0fe01dfa0abf447d8ca135fd}{Qore\+::zzz8datezzz9\+::iso\+Week\+String()}} \item \mbox{\hyperlink{class_qore_1_1zzz8objectzzz9_a0702bbe59ecc54c7eed8c16550a010ed}{Qore\+::zzz8objectzzz9\+::unique\+Hash()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a07b89a849ef94f060e0fcf2c040fd296}{Qore\+::zzz8stringzzz9\+::get\+Decoded()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a4b2cac04c91fb14fcb5a79469550b820}{Qore\+::zzz8stringzzz9\+::get\+Encoded()}} \end{DoxyItemize} \item the following functions were moved from the \href{../../modules/Util/html/index.html}{\texttt{ Util}} module to Qore\+: \begin{DoxyItemize} \item \mbox{\hyperlink{namespace_qore_a59a85037788f39c5269f0aadbb499f90}{Qore\+::absolute\+\_\+path()}} \item \mbox{\hyperlink{namespace_qore_a77456f40ff1734bb6d5692e6dbb9e8eb}{Qore\+::absolute\+\_\+path\+\_\+windows()}} \item \mbox{\hyperlink{namespace_qore_ac13e5f3c1a03fbb5e6c60213a595795f}{Qore\+::absolute\+\_\+path\+\_\+unix()}} \end{DoxyItemize} \item camel-\/case functions were deprecated in this release \begin{DoxyItemize} \item the following functions were deprecated\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__object__functions_ga22ceceed9c9da64694045ef7a32409c4}{Qore\+::call\+Object\+Method()}}\+: deprecated for \mbox{\hyperlink{group__object__functions_ga733217c233efed0557e133a6cc45189f}{Qore\+::call\+\_\+object\+\_\+method()}} \item \mbox{\hyperlink{group__object__functions_ga1aa450b9391a7e36b01caf570d458ab5}{Qore\+::call\+Object\+Method\+Args()}}\+: deprecated for \mbox{\hyperlink{group__object__functions_ga3f3c875b6632a9b028a5d63be30bec14}{Qore\+::call\+\_\+object\+\_\+method\+\_\+args()}} \item \mbox{\hyperlink{group__misc__functions_ga83615e15094fca9ffe868ee0d80cd002}{Qore\+::exists\+Function()}}\+: deprecated for \mbox{\hyperlink{group__misc__functions_ga3a1dcf3c8f3908896ca2aabfcc41010c}{Qore\+::exists\+\_\+function()}} \item \mbox{\hyperlink{group__misc__functions_ga5ae2be041abe7d02be8a2ccc67c0032f}{Qore\+::function\+Type()}}\+: deprecated for \mbox{\hyperlink{group__misc__functions_ga23f1e7651ff70e32e9ba7c28907b1306}{Qore\+::function\+\_\+type()}} \item \mbox{\hyperlink{group__threading__functions_ga52baa4131379e22e307ae742ffbe3ee1}{Qore\+::get\+All\+Thread\+Call\+Stacks()}}\+: deprecated for \mbox{\hyperlink{group__threading__functions_gae4d42c6ab7b7fc7d9a9cb1be139f6773}{Qore\+::get\+\_\+all\+\_\+thread\+\_\+call\+\_\+stacks()}} \item \mbox{\hyperlink{group__misc__functions_ga46b9c2df48897cb68e765cb6d66728ac}{Qore\+::get\+Class\+Name()}}\+: deprecated for \mbox{\hyperlink{group__misc__functions_gaa9a0d3f277ef8cbdc99fe146dd3db49b}{Qore\+::get\+\_\+class\+\_\+name()}} \item \mbox{\hyperlink{group__date__and__time__functions_ga86f47ab9a928a2c8aff8cbac9b5f3518}{Qore\+::get\+Date\+From\+I\+S\+O\+Week()}}\+: deprecated for \mbox{\hyperlink{group__date__and__time__functions_ga1401d634f3bcbec80d64f75cdd9d4921}{Qore\+::get\+\_\+date\+\_\+from\+\_\+iso\+\_\+week()}} \item \mbox{\hyperlink{group__date__and__time__functions_ga08d26e9c0ed9635a1ee1158ee4bf24a5}{Qore\+::get\+Day\+Number()}}\+: deprecated for \mbox{\hyperlink{group__date__and__time__functions_gaec9d8c1ba3a39869904f27e8c0706589}{Qore\+::get\+\_\+day\+\_\+number()}} \item \mbox{\hyperlink{group__date__and__time__functions_ga5719e06bb6919c3cc370f99910f78277}{Qore\+::get\+Day\+Of\+Week()}}\+: deprecated for \mbox{\hyperlink{group__date__and__time__functions_gaa546956fb71d56f18c903aff1f3fc01a}{Qore\+::get\+\_\+day\+\_\+of\+\_\+week()}} \item \mbox{\hyperlink{group__old__dbi__functions_ga330acb764484b16529d4f25960c45fa8}{Qore\+::\+S\+Q\+L\+::get\+D\+B\+I\+Driver\+Capabilities()}}\+: deprecated for \mbox{\hyperlink{group__old__dbi__functions_ga40597983f24f3b0edc06149246d1cbe2}{Qore\+::\+S\+Q\+L\+::dbi\+\_\+get\+\_\+driver\+\_\+capabilities()}} \item \mbox{\hyperlink{group__old__dbi__functions_ga7854c258d52bc1aa47faad90ac5b8e6b}{Qore\+::\+S\+Q\+L\+::get\+D\+B\+I\+Driver\+Capability\+List()}}\+: deprecated for \mbox{\hyperlink{group__old__dbi__functions_ga2c836575bb7327e5ef81df5dff4799ff}{Qore\+::\+S\+Q\+L\+::dbi\+\_\+get\+\_\+driver\+\_\+capability\+\_\+list()}} \item \mbox{\hyperlink{group__old__dbi__functions_ga20fdc611dd5a56fce211b3106578840c}{Qore\+::\+S\+Q\+L\+::get\+D\+B\+I\+Driver\+List()}}\+: deprecated for \mbox{\hyperlink{group__old__dbi__functions_gae91b14606e0b3d0ca9155a911ec06a5c}{Qore\+::\+S\+Q\+L\+::dbi\+\_\+get\+\_\+driver\+\_\+list()}} \item \mbox{\hyperlink{group__misc__functions_ga82a9721ba77a2a344b0e356d45c5a37f}{Qore\+::get\+Feature\+List()}}\+: deprecated for \mbox{\hyperlink{group__misc__functions_ga86de08439e084c19460ae57d3d6269e5}{Qore\+::get\+\_\+feature\+\_\+list()}} \item \mbox{\hyperlink{group__date__and__time__functions_ga92ef075d0aa1945a11580a864bc7f4cb}{Qore\+::get\+I\+S\+O\+Day\+Of\+Week()}}\+: deprecated for \mbox{\hyperlink{group__date__and__time__functions_ga64bfe13c03c1b2746bfb5c80f5279e2a}{Qore\+::get\+\_\+iso\+\_\+day\+\_\+of\+\_\+week()}} \item \mbox{\hyperlink{group__date__and__time__functions_ga62eb1df91fe17207d865565e52fa1e19}{Qore\+::get\+I\+S\+O\+Week\+Hash()}}\+: deprecated for \mbox{\hyperlink{group__date__and__time__functions_ga2e891572705fb44c6d881bfeb48e8b8e}{Qore\+::get\+\_\+iso\+\_\+week\+\_\+hash()}} \item \mbox{\hyperlink{group__date__and__time__functions_ga04331a3a415abfaaa228c4253a04859b}{Qore\+::get\+I\+S\+O\+Week\+String()}}\+: deprecated for \mbox{\hyperlink{group__date__and__time__functions_gadfb87ebf695f7e037efb64367cdb6626}{Qore\+::get\+\_\+iso\+\_\+week\+\_\+string()}} \item \mbox{\hyperlink{group__object__functions_ga88b51a14acbe008f2e60fca211b98a50}{Qore\+::get\+Method\+List()}}\+: deprecated for \mbox{\hyperlink{group__object__functions_gaaf374f86d44e428d57a23caee48374af}{Qore\+::get\+\_\+method\+\_\+list()}} \item \mbox{\hyperlink{group__misc__functions_ga34248adafed4b00da2a526f8f23017cf}{Qore\+::get\+Module\+Hash()}}\+: deprecated for \mbox{\hyperlink{group__misc__functions_gab64b871ddf6f09568d4a0798c0ca755a}{Qore\+::get\+\_\+module\+\_\+hash()}} \item \mbox{\hyperlink{group__misc__functions_ga82506074037fe39372ea4f44e2582a75}{Qore\+::get\+Module\+List()}}\+: deprecated for \mbox{\hyperlink{group__misc__functions_ga18cc840553c5850216308dbefa9d5a78}{Qore\+::get\+\_\+module\+\_\+list()}} \item \mbox{\hyperlink{group__misc__functions_ga302de285f031c3dd4b059df3494bd21c}{Qore\+::make\+Base64\+String()}}\+: deprecated for \mbox{\hyperlink{group__misc__functions_ga8de429a31ac854f93c8c66e14baaaf66}{Qore\+::make\+\_\+base64\+\_\+string()}} \item \mbox{\hyperlink{group__misc__functions_gae4ca24e1000d327df636f75c7bf4f00c}{Qore\+::make\+Hex\+String()}}\+: deprecated for \mbox{\hyperlink{group__misc__functions_gae7be18717b0ed9010c48166a437c35b4}{Qore\+::make\+\_\+hex\+\_\+string()}} \item \mbox{\hyperlink{group__misc__functions_ga1e6e24f780713c4d10cb9b98fa45cd35}{Qore\+::parse\+Base64\+String()}}\+: deprecated for \mbox{\hyperlink{group__misc__functions_ga34c9bccc1d1e61d6a8a8988ceb4a8a6c}{Qore\+::parse\+\_\+base64\+\_\+string()}} \item \mbox{\hyperlink{group__misc__functions_ga1f1a63790a7c60a3a61c5d1569fe4e4c}{Qore\+::parse\+Base64\+String\+To\+String()}}\+: deprecated for \mbox{\hyperlink{group__misc__functions_ga0160c0c4cbe7180d70048577e4e40bcc}{Qore\+::parse\+\_\+base64\+\_\+string\+\_\+to\+\_\+string()}} \item \mbox{\hyperlink{group__old__dbi__functions_gab8f5a597374024a8c78e767dbfcafc15}{Qore\+::\+S\+Q\+L\+::parse\+Datasource()}}\+: deprecated for \mbox{\hyperlink{group__old__dbi__functions_ga6c3dab42570887656fc05f5a22eb370a}{Qore\+::\+S\+Q\+L\+::parse\+\_\+datasource()}} \item \mbox{\hyperlink{group__misc__functions_ga74fed7603d2176dd5d433d3fae02ad9f}{Qore\+::parse\+Hex\+String()}}\+: deprecated for \mbox{\hyperlink{group__misc__functions_gaedf4a2c140fa284c9e09a68b743763b3}{Qore\+::parse\+\_\+hex\+\_\+string()}} \item \mbox{\hyperlink{group__list__functions_gad9e205ca0a43f52a1388611b54521c19}{Qore\+::sort\+Descending()}}\+: deprecated for \mbox{\hyperlink{group__list__functions_ga0149391f4fb2c97dd4ad2080f9240753}{Qore\+::sort\+\_\+descending()}} \item \mbox{\hyperlink{group__list__functions_gacd07eea87f385a0bb8764a9fa5b47075}{Qore\+::sort\+Descending\+Stable()}}\+: deprecated for \mbox{\hyperlink{group__list__functions_ga59bf2466a7bd64db585ad1b2b5f7ae7d}{Qore\+::sort\+\_\+descending\+\_\+stable()}} \item \mbox{\hyperlink{group__list__functions_ga6202469e6119631474b685952cefe11f}{Qore\+::sort\+Stable()}}\+: deprecated for \mbox{\hyperlink{group__list__functions_gad03629b1133f3a6b47a2f33792801dbf}{Qore\+::sort\+\_\+stable()}} \item \mbox{\hyperlink{group__threading__functions_ga401f0e787e79f2e4851d60b9223bb8d2}{Qore\+::throw\+Thread\+Resource\+Exceptions()}}\+: deprecated for \mbox{\hyperlink{group__threading__functions_ga421dca39ccb55b191d5d09fd98c2075a}{Qore\+::throw\+\_\+thread\+\_\+resource\+\_\+exceptions()}} \end{DoxyItemize} \item Functions deprecated in this release will remain for the forseeable future for backwards-\/compatibility \end{DoxyItemize} \item Added support for reexporting imported definitions in user module with the new {\ttfamily \%requires(reexport)} form of the \mbox{\hyperlink{parse_directives_requires}{\%requires}} parse directive. \item \mbox{\hyperlink{group__range__functions_gad5b4d3ad3f6c36d2e714bc6ed757a507}{Qore\+::xrange()}} and \mbox{\hyperlink{class_qore_1_1_range_iterator}{Qore\+::\+Range\+Iterator}} updates\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__range__functions_gad5b4d3ad3f6c36d2e714bc6ed757a507}{Qore\+::xrange()}} and \mbox{\hyperlink{class_qore_1_1_range_iterator_ae1659e4a23b185f2cf371b015d806088}{Qore\+::\+Range\+Iterator\+::constructor()}} and \mbox{\hyperlink{class_qore_1_1zzz8listzzz9_a4483a03f84971f0f3e64dace2de2f737}{Qore\+::zzz8listzzz9\+::range\+Iterator()}} updated to take an optional value to return in the \mbox{\hyperlink{class_qore_1_1_range_iterator_a96d2eb508ede8cc4a26141ccf94acecc}{Qore\+::\+Range\+Iterator\+::get\+Value()}} method \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_ftp_client}{Qore\+::\+Ftp\+Client}} updates\+: \begin{DoxyItemize} \item added \mbox{\hyperlink{class_qore_1_1_ftp_client_abe7fe74d0bf2ea11fdedc5f0c67af5dc}{Qore\+::\+Ftp\+Client\+::get\+Mode()}} \end{DoxyItemize} \item Performance improvements\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_hash_pair_iterator}{Qore\+::\+Hash\+Pair\+Iterator}} and \mbox{\hyperlink{class_qore_1_1_object_pair_iterator}{Qore\+::\+Object\+Pair\+Iterator}} objects (returned by \mbox{\hyperlink{class_qore_1_1zzz8hashzzz9_aae2e67b218a51791103c21866df5217b}{Qore\+::zzz8hashzzz9\+::pair\+Iterator()}} and \mbox{\hyperlink{class_qore_1_1zzz8objectzzz9_a7d6df627d80aa7f74c7e895fb352c837}{Qore\+::zzz8objectzzz9\+::pair\+Iterator()}}, respectively and the associated reverse iterators) have had their performance improved by approximately 70\% by reusing the hash iterator object when possible \end{DoxyItemize} \item module directory handling changed \begin{DoxyItemize} \item user modules are now stored in prefix/share/qore-\/modules/version \item prefix/share/qore-\/modules is also added to the module path \item version-\/specific module directories are added first, then the \char`\"{}generic\char`\"{} directories \end{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module updates\+: \begin{DoxyItemize} \item new {\ttfamily \char`\"{}tolwr\char`\"{}} option in structured text parsing classes \item {\ttfamily Abstract\+Csv\+Writer} will set {\ttfamily \char`\"{}headers\char`\"{}} from the {\ttfamily \char`\"{}fields\char`\"{}} option if {\ttfamily \char`\"{}headers\char`\"{}} are not explicitly set \item added write() methods returning the generated strings to the {\ttfamily Csv\+String\+Writer} class for A\+PI compatibility with the corresponding Fixed\+Length\+Data\+Writer methods \item implemented support for \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} as an iterator source for {\ttfamily Abstract\+Csv\+Writer\+::write()} \item {\ttfamily quote\+\_\+escape} option implemented in {\ttfamily Abstract\+Csv\+Writer} \item implemented the {\ttfamily \char`\"{}datamap\char`\"{}} and {\ttfamily \char`\"{}info\+\_\+log\char`\"{}} options for C\+SV generation \item implemented alternative options with underscores instead of dashes for all constructors \item extended multi-\/type support, record type rules and default value in field specification \item implemented multi-\/type record support in {\ttfamily Abstract\+Csv\+Writer} and {\ttfamily Abstract\+Csv\+Iterator} using {\ttfamily resolve\+\_\+type} and {\ttfamily headers} options \end{DoxyItemize} \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module updates\+: \begin{DoxyItemize} \item implemented the {\ttfamily \char`\"{}constant\char`\"{}} field tag, allowing a constant value for an output field to be specified directly in the mapper hash \item implemented the {\ttfamily \char`\"{}default\char`\"{}} field tag, giving a default value if no input value is specified \item implemented the global {\ttfamily \char`\"{}date\+\_\+format\char`\"{}} mapper option \item implemented support for structured output fields with dot notation in the output field name \item implemented per-\/field and global {\ttfamily \char`\"{}number\+\_\+format\char`\"{}} mapper options \item changed the behavior of the {\ttfamily \char`\"{}number\char`\"{}} field type\+: now leaves numeric values in their original type, converts all other types to a number \item removed the deprecated {\ttfamily \char`\"{}crec\char`\"{}} option \item implemented the {\ttfamily \char`\"{}input\char`\"{}} option with input record validation \item implemented the {\ttfamily \char`\"{}output\char`\"{}} option with output record validation \item implemented the {\ttfamily \char`\"{}info\+\_\+log\char`\"{}} option and removed the {\ttfamily \char`\"{}trunc\char`\"{}} option \item implemented the {\ttfamily \char`\"{}runtime\char`\"{}} field tag \item implemented the {\ttfamily \char`\"{}index\char`\"{}} field tag \item improved the Mapper\+::map\+All() method by adding support for hashes of lists to better support input from bulk D\+ML (\mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement_ab889448c79985fc26e41b7e2086308df}{S\+Q\+L\+Statement\+::fetch\+Columns()}}) \end{DoxyItemize} \item \href{../../modules/TableMapper/html/index.html}{\texttt{ Table\+Mapper}} module updates\+: \begin{DoxyItemize} \item added table name and datasource description to error messages \item implemented more efficient support for inserts from a sequence for databases supporting the {\ttfamily \char`\"{}returning\char`\"{}} clause in insert statements; now such inserts are made in a single round trip instead of n + 1 where n is the number of sequences in the insert \item implemented an optimized insert approach assuming stable input data \item implemented the following new options\+: \begin{DoxyItemize} \item {\ttfamily unstable\+\_\+input\+:} to accommodate unstable input data and disable the insert optimization (default\+: False) \item {\ttfamily insert\+\_\+block\+:} for DB drivers supporting bulk D\+ML, the number of rows inserted at once (default\+: 500, only used when {\ttfamily unstable\+\_\+input} is False) and bulk inserts are supported in the table object \end{DoxyItemize} \item added methods for bulk / batch inserts for db drivers supporting bulk D\+ML (ex\+: Oracle) \item updated to \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} changes\+: use table description to define output record for the \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module \item added the Abstract\+Sql\+Statement\+Outbound\+Mapper class \item added the Inbound\+Identity\+Table\+Mapper class \item added the Sql\+Statement\+Mapper\+Iterator class \item added the Sql\+Statement\+Outbound\+Mapper class \end{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module updates\+: \begin{DoxyItemize} \item implemented Rest\+Client\+::add\+Default\+Headers() \item implemented Rest\+Client\+::get\+Default\+Headers() \item implemented Rest\+Client\+::get\+Send\+Encoding() \item implemented Rest\+Client\+::set\+Content\+Encoding() \item when possible, R\+E\+ST bodies are decoded and stored in the {\itshape info} output argument when the H\+T\+TP server returns a status code $<$ 100 or $>$= 300 to allow for error-\/handling in the client \end{DoxyItemize} \item \href{../../modules/RestHandler/html/index.html}{\texttt{ Rest\+Handler}} module updates\+: \begin{DoxyItemize} \item implemented support for notifying persistent connections when the connection is terminated while a persistent connection is in place \item the Abstract\+Rest\+Stream\+Request\+Handler class is now the base abstract class for R\+E\+ST stream request handlers \end{DoxyItemize} \item \href{../../modules/WebUtil/html/index.html}{\texttt{ Web\+Util}} module updates\+: \begin{DoxyItemize} \item updated File\+Handler\+::handle\+Request() to allow for chunked sends \end{DoxyItemize} \item \href{../../modules/BulkSqlUtil/html/index.html}{\texttt{ Bulk\+Sql\+Util}} module\+: \begin{DoxyItemize} \item added this new module providing A\+P\+Is supporting bulk D\+ML with \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} with supported drivers \end{DoxyItemize} \item \href{../../modules/FilePoller/html/index.html}{\texttt{ File\+Poller}} module\+: \begin{DoxyItemize} \item added this new module to support polling files in directories on the filesystem \end{DoxyItemize} \item \href{../../modules/FixedLengthUtil/html/index.html}{\texttt{ Fixed\+Length\+Util}} module\+: \begin{DoxyItemize} \item added this new module for handling fixed length line data \end{DoxyItemize} \item \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module updates\+: \begin{DoxyItemize} \item \href{../../modules/HttpServerUtil/html/index.html}{\texttt{ Http\+Server\+Util}} module split from the \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module containing supporting definitions for handler classes and other code interfacing with the \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module \item added the Permissive\+Authenticator class \item translate {\ttfamily \char`\"{}+\char`\"{}} (plus) to {\ttfamily \char`\"{} \char`\"{}} (space) in the query portion of U\+R\+Is in parse\+\_\+uri\+\_\+query() \item implemented support for notifying persistent connections when the connection is terminated while a persistent connection is in place \item new methods implemented in Http\+Server\+: \begin{DoxyItemize} \item Http\+Server\+::get\+Listener\+Log\+Options() \item Http\+Server\+::get\+Listener\+Log\+Options\+I\+D() \item Http\+Server\+::set\+Listener\+Log\+Options() \item Http\+Server\+::set\+Listener\+Log\+Options\+I\+D() \item Http\+Server\+::add\+Listeners() (new variant taking a hash of S\+SL info) \item Http\+Server\+::listener\+Started() (to allow for reporting when listeners are actually running since they are started asynchronously) \end{DoxyItemize} \item improved performance matching request U\+R\+Is to handlers \item added the {\ttfamily \char`\"{}ssl\char`\"{}} key to the listener socket info hash \item implemented support for notifying persistent connections when the connection is terminated while a persistent connection is in place \item removed the unused Abstract\+Stream\+Request\+Handler class \item fixed parse\+\_\+uri\+\_\+query() to always return {\itshape params} as a hash (\href{https://github.com/qorelanguage/qore/issues/569}{\texttt{ issue 569}}) \item added {\ttfamily root\+\_\+path} to the context hash if the path was matched by a U\+RL path prefix (\href{https://github.com/qorelanguage/qore/issues/570}{\texttt{ issue 570}}) \item implemented support for configurable stream handler timeout values (\href{https://github.com/qorelanguage/qore/issues/719}{\texttt{ issue 719}}) \end{DoxyItemize} \item \href{../../modules/Schema/html/index.html}{\texttt{ Schema}} module updates\+: \begin{DoxyItemize} \item added the following public functions to make column definitions easier\+: \begin{DoxyItemize} \item c\+\_\+char() \item c\+\_\+date() \item c\+\_\+int() \item c\+\_\+number() \item c\+\_\+timestamp() \item c\+\_\+varchar() \end{DoxyItemize} \end{DoxyItemize} \item added option \mbox{\hyperlink{group__option__constants_ga8315f695323cb4e3a69f51c85f23cce8}{H\+A\+V\+E\+\_\+\+D\+E\+T\+E\+R\+M\+I\+N\+I\+S\+T\+I\+C\+\_\+\+GC}} for Qore builds where deterministic garbage collection is enabled \item \mbox{\hyperlink{class_qore_1_1_program}{Program}} class enhancements\+: \begin{DoxyItemize} \item the \mbox{\hyperlink{class_qore_1_1_program}{Program}} class now creates \mbox{\hyperlink{conditional_parsing}{parse defines}} for parse options so that conditional code can be implemented depending on the sandboxing configuration of the program container \item the \mbox{\hyperlink{class_qore_1_1_program_abf634534cb29157d05aab5ff3ffd6bea}{Qore\+::\+Program\+::import\+Class()}} method now accepts an optional {\itshape new\+\_\+name} argument to allow for importing classes with a different name and namespace path \end{DoxyItemize} \item added a timeout parameter to the following \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_socket_ad471f7399655c3fb211c72b55ca568d9}{Qore\+::\+Socket\+::upgrade\+Client\+To\+S\+S\+L()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a83385d31d5b112409424269f025de5ea}{Qore\+::\+Socket\+::upgrade\+Server\+To\+S\+S\+L()}} \end{DoxyItemize} \item added zoneinfo -\/$>$ Windows time zone translation code on Windows to support standard U\+N\+IX (zoneinfo) time zone names on Windows; time zone information is still taken from the Windows registry but region names are reported using the standard zoneinfo names \item \mbox{\hyperlink{class_qore_1_1_file_line_iterator}{Qore\+::\+File\+Line\+Iterator}} updates\+: \begin{DoxyItemize} \item added \mbox{\hyperlink{class_qore_1_1_file_line_iterator_afd0b7665ba69bba57fa903410680773f}{Qore\+::\+File\+Line\+Iterator\+::hstat()}} and \mbox{\hyperlink{class_qore_1_1_file_line_iterator_ac2f0e659a278d44a1acab92e7ecbff6e}{Qore\+::\+File\+Line\+Iterator\+::stat()}} \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module updates\+: \begin{DoxyItemize} \item implemented insert option support and support for the {\ttfamily \char`\"{}returning\char`\"{}} clause in supported drivers to avoid server round trips \item implemented the Abstract\+Table\+::get\+Desc() method and improved exception description messages \item implemented support for late table resoluton in join arguments to enable joins from serialized parameters \item improved error messages for common errors such as join errors \item implemented support for D\+BA management actions \item implemented support for driver-\/dependent pseudocolumns \item implemented per-\/column support for the {\ttfamily \char`\"{}desc\char`\"{}} keyword in orderby expressions \item implemented the {\ttfamily \char`\"{}wop\+\_\+or()\char`\"{}} function to allow complex S\+QL expressions to be generated with {\ttfamily \char`\"{}or\char`\"{}} as well as {\ttfamily \char`\"{}and\char`\"{}} \item implemented the {\ttfamily \char`\"{}cop\+\_\+cast()\char`\"{}} operator for converting \mbox{[}column\mbox{]} value into another datatype \item implemented the {\ttfamily \char`\"{}cop\+\_\+sum()\char`\"{}} aggregate operator for returning sum of column values \item implemented update operators {\ttfamily \char`\"{}uop\+\_\+plus()\char`\"{}}, {\ttfamily \char`\"{}uop\+\_\+minus()\char`\"{}}, {\ttfamily \char`\"{}uop\+\_\+multiply()\char`\"{}}, {\ttfamily \char`\"{}uop\+\_\+divide()\char`\"{}} \item implemented Abstract\+Table\+::get\+Bulk\+Upsert\+Closure() to better support bulk S\+QL merge operations \item removed all A\+P\+Is that handle implicit transactions; A\+P\+Is must commit transactions explicitly \item {\itshape orderby} and {\itshape groupby} select options now take positive integers as column identifiers \item column aliases (defined with cop\+\_\+as()) can now be used in the where hash argument and in join criteria \item column operator functions can be used in the where clause and in join conditions (\href{https://github.com/qorelanguage/qore/issues/529}{\texttt{ issue 529}}) \item implemented the {\ttfamily \char`\"{}cop\+\_\+coalesce()\char`\"{}} column operation function to support the {\ttfamily \char`\"{}\+C\+O\+A\+L\+E\+S\+C\+E\char`\"{}} operator in queries (\href{https://github.com/qorelanguage/qore/issues/671}{\texttt{ issue 671}}) \item implemented {\ttfamily cop\+\_\+substr()} and {\ttfamily uop\+\_\+substr()} operators (\href{https://github.com/qorelanguage/qore/issues/801}{\texttt{ issue 801}}) \item implemented {\ttfamily op\+\_\+substr()} where operator (\href{https://github.com/qorelanguage/qore/issues/883}{\texttt{ issue 883}}) \item implemented the {\ttfamily \char`\"{}omit\+\_\+update\char`\"{}} upsert option for asymmetrical upserts (updates only update a subset of the columns inserted) (\href{https://github.com/qorelanguage/qore/issues/791}{\texttt{ issue 791}}) \item implemented the {\ttfamily \char`\"{}\+Upsert\+Update\+Only\char`\"{}} upsert option (\href{https://github.com/qorelanguage/qore/issues/793}{\texttt{ issue 793}}) \end{DoxyItemize} \item \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}} module updates\+: \begin{DoxyItemize} \item implemented support for views for D\+ML in the Oracle\+Table class \item implemented support for Oracle pseudocolumns in queries \item return lists from Oracle\textquotesingle{}s data dictionary ordered \item implemented Abstract\+Table\+::empty\+Strings\+As\+Null() \end{DoxyItemize} \item \href{../../modules/PgsqlSqlUtil/html/index.html}{\texttt{ Pgsql\+Sql\+Util}} module updates\+: \begin{DoxyItemize} \item added support for the following datatypes and aliases\+: {\ttfamily bool}, {\ttfamily float}, {\ttfamily int}, {\ttfamily timetz}, {\ttfamily timestamptz}, {\ttfamily varbit} \item added support for listing Postgre\+S\+QL types and materialized views (\href{https://github.com/qorelanguage/qore/issues/699}{\texttt{ issue 699}}) \end{DoxyItemize} \item \href{../../modules/MysqlSqlUtil/html/index.html}{\texttt{ Mysql\+Sql\+Util}} module updates\+: \begin{DoxyItemize} \item added support for the following datatypes\+: {\ttfamily binary}, {\ttfamily varbinary} \end{DoxyItemize} \item \href{../../modules/Util/html/index.html}{\texttt{ Util}} module updates\+: \begin{DoxyItemize} \item added public function {\ttfamily glob\+\_\+to\+\_\+regex()} \item added public functions {\ttfamily lpad()} and {\ttfamily rpad()} \item added public function {\ttfamily ordinal()} \item added public function {\ttfamily plural()} \item added public function {\ttfamily regex\+\_\+escape()} \item added public function {\ttfamily zip()} \item {\ttfamily parse\+\_\+to\+\_\+qore\+\_\+value()} now respects parentheses when parsing lists and hashes (\href{https://github.com/qorelanguage/qore/issues/846}{\texttt{ issue 846}}) \end{DoxyItemize} \item added initial support for U\+T\+F-\/16 character encoding; note that U\+T\+F-\/16 is not backwards-\/compatible with A\+S\+C\+II and therefore not supported universally in Qore; it\textquotesingle{}s recommended to convert these strings to U\+T\+F-\/8 in Qore; do not use U\+T\+F-\/16 as the default character encoding in Qore; currently U\+T\+F-\/16 data can be parsed using the following classes that convert the data to U\+T\+F-\/8\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_data_line_iterator}{Qore\+::\+Data\+Line\+Iterator}} \item \mbox{\hyperlink{class_qore_1_1_file_line_iterator}{Qore\+::\+File\+Line\+Iterator}} \end{DoxyItemize} \item removed support for the C++ {\ttfamily Q\+D\+B\+I\+\_\+\+M\+E\+T\+H\+O\+D\+\_\+\+A\+B\+O\+R\+T\+\_\+\+T\+R\+A\+N\+S\+A\+C\+T\+I\+O\+N\+\_\+\+S\+T\+A\+RT} D\+BI method; transactions are always assumed to be in progress even if an exec call throws an exception in the first statement in a new transaction; this is necessary to handle bulk D\+ML where a single statement can partially succeed and partially fail; the A\+BI remains unchanged; drivers that set this D\+BI method will no longer have it called because it\textquotesingle{}s not necessary; in the upcoming A\+P\+I/\+A\+BI change this C++ D\+BI method will be removed entirely \item added support for \mbox{\hyperlink{operators_unary_plus_operator}{unary plus}} \item added support for empty private blocks in classes \item added support for \mbox{\hyperlink{namespace_qore_addd77c64341dc7694cfd3ba51c7becac}{Qore\+::statvfs()}} on Windows (simulated from {\ttfamily Get\+Disk\+Free\+Space\+Ex()} \href{https://github.com/qorelanguage/qore/issues/618}{\texttt{ issue 618}}) \item assignment of a variable to itself is now illegal (\href{https://github.com/qorelanguage/qore/issues/526}{\texttt{ issue 526}}) \item extended qpp to support the \textquotesingle{}final\textquotesingle{} class flag (\href{https://github.com/qorelanguage/qore/issues/876}{\texttt{ issue 876}}) \item extended qpp to support private members (\href{https://github.com/qorelanguage/qore/issues/924}{\texttt{ issue 924}}) \item added \mbox{\hyperlink{class_qore_1_1zzz8floatzzz9_aea0691501b3c4e0325034bd7a77f83fb}{Qore\+::zzz8floatzzz9\+::infp()}} and \mbox{\hyperlink{class_qore_1_1zzz8floatzzz9_af592f928a4c796aeb82be290b7973f91}{Qore\+::zzz8floatzzz9\+::nanp()}} predicates to \mbox{\hyperlink{data_type_declarations_float_type}{float}} (\href{https://github.com/qorelanguage/qore/issues/909}{\texttt{ issue 909}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0812_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0812_bug_fixes} \begin{DoxyItemize} \item fixed format of octal constant -\/ there was an error if a string contained octal constant that is shorter than 3 digit \item \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module fixes\+: \begin{DoxyItemize} \item fixed a bug setting the response encoding in Http\+Server\+::set\+Reply\+Headers() where the Socket encoding was not set properly and therefore the encoding in the Content-\/\+Type in the response header did not necessarily match the encoding of the response \item fixed a socket / connection performance problem with H\+T\+T\+PS listeners where the S\+SL connection was being negotiated inline with the accept instead of in the connection thread, thereby blocking new connections from being accepted \item fixed bugs where U\+RI strings were improperly encoded and decoded (also fixed in the \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module) \item fixed a bug in the \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module where chunked sends were not received and decoded properly in all cases for handlers that did not explicitly handle chunked messages \item fixed a bug in Http\+Server\+::add\+Listener() with an integer argument; a U\+N\+IX socket was opened instead of a wildcard listener on the given port \item fixed typos causing bugs in H\+T\+TP error logging (\href{https://github.com/qorelanguage/qore/issues/308}{\texttt{ issue 308}}) \item fixed a bug formatting I\+Pv6 host addresses in the return value to {\ttfamily Http\+Server\+::http\+\_\+get\+\_\+url\+\_\+from\+\_\+bind()} (\href{https://github.com/qorelanguage/qore/issues/821}{\texttt{ issue 821}}) \end{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module fixes\+: \begin{DoxyItemize} \item fixed bugs where U\+RI strings were improperly encoded and decoded (also fixed in the \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module) \item fixed a bug where U\+RI paths were sent as relative paths instead of absolute paths \item fixed issues where multiple leading {\ttfamily \char`\"{}/\char`\"{}} chars were sometimes present in the request U\+RI path \item fixed an issue where a trailing {\ttfamily \char`\"{}/\char`\"{}} char was sometimes added to the request U\+RI path (\href{https://github.com/qorelanguage/qore/issues/899}{\texttt{ issue 899}}) \end{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module fixes\+: \begin{DoxyItemize} \item fixed a bug where the {\ttfamily \char`\"{}format\char`\"{}} field option was not usable with fields assigned type {\ttfamily \char`\"{}$\ast$date\char`\"{}} \item fixed the default field type as \char`\"{}$\ast$string\char`\"{} (from \char`\"{}string\char`\"{}) to avoid parsing and outputting empty strings for missing input data \end{DoxyItemize} \item \href{../../modules/Schema/html/index.html}{\texttt{ Schema}} module fixes\+: \begin{DoxyItemize} \item Abstract\+Schema\+::combine\+Options() fails when an option variable contains \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} instead of a valid hash \item fixed a bug with {\itshape \char`\"{}insert-\/only reference data\char`\"{}} with the verbose option; the upsert strategy was changed to {\ttfamily Upsert\+Select\+First} which means that insert-\/only reference data could also be updated \item fixed a bug where it was not possible to provide Database options when creating schemas (\href{https://github.com/qorelanguage/qore/issues/501}{\texttt{ issue 501}}) \end{DoxyItemize} \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} module fixes\+: \begin{DoxyItemize} \item moved field length checks after all transformations have been applied \item fixed bugs in the {\ttfamily \char`\"{}timezone\char`\"{}} and {\ttfamily \char`\"{}input\+\_\+timezone\char`\"{}} options, documented those options \item fixed a bug where {\ttfamily \char`\"{}constant\char`\"{}} field tags assigned to a value that evaluated to boolean \mbox{\hyperlink{basic_data_types_False}{False}} were not recognized (\href{https://github.com/qorelanguage/qore/issues/610}{\texttt{ issue 610}}) \end{DoxyItemize} \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module fixes\+: \begin{DoxyItemize} \item fixed a bug with queries using a {\itshape desc} argument with the {\itshape orderby} query option with multiple sort columns; the {\ttfamily \char`\"{}desc\char`\"{}} string was added only to the last column but should have been added to all columns \item fixed a bug where foreign key constraints with supporting indexes were not tracked and therefore schema alignment on D\+Bs that automatically create indexes for foreign key constraints would fail \item fixed a bug where driver-\/specific objects were not included when dropping a schema \item fixed a bug in subquery handling where bind-\/by-\/value arguments from the subquery were lost \item fixed a bug in the partition by/over operator where column names as given in the query argument hash were not properly recognized \item fixed a bug in schema alignment; when aligning a schema and an index supporting a PK constraint is introduced in the new schema, the alignment would fail when a constraint is attempted to be disabled that doesn\textquotesingle{}t exist \item fixed a bug generating select statements for tables accessed through a synonym when used with join clauses; previously inconsistent schema prefixes could be used which could cause errors parsing the S\+QL statements generated \item fixed a bug where the Abstract\+Table lock was held while executing S\+QL to determine the upsert strategy to use with Upsert\+Auto \item fixed a bug where complex bind values as hashes (such as used by the pgsql and oracle drivers) were rejected by Sql\+Util (\href{https://github.com/qorelanguage/qore/issues/494}{\texttt{ issue 494}}) when updating \item fixed a bug where wildcard columns in join tables were not working (\href{https://github.com/qorelanguage/qore/issues/499}{\texttt{ issue 499}}) \item fixed a bug in {\ttfamily \char`\"{}op\+\_\+in()\char`\"{}} where invalid S\+QL was generated with an argument of 0 (\href{https://github.com/qorelanguage/qore/issues/500}{\texttt{ issue 500}}) \item fixed bugs in {\ttfamily cop\+\_\+seq()} and {\ttfamily cop\+\_\+seq\+\_\+currval()} (\href{https://github.com/qorelanguage/qore/issues/624}{\texttt{ issue 624}}) \item fixed a bug in {\ttfamily join\+\_\+inner()} where the {\itshape cond} argument was ignored (\href{https://github.com/qorelanguage/qore/issues/645}{\texttt{ issue 645}}) \item fixed {\ttfamily \char`\"{}uop\+\_\+lower()\char`\"{}} and {\ttfamily \char`\"{}uop\+\_\+upper()\char`\"{}} operators to allow nesting (\href{https://github.com/qorelanguage/qore/issues/657}{\texttt{ issue 657}}) \item fixed a bug where Sql\+Util was generating invalid S\+QL for some D\+Bs where a wilcard was used with explicit column names (\href{https://github.com/qorelanguage/qore/issues/708}{\texttt{ issue 708}}) \item fixed a bug where updating an index without any source constraints caused an invalid exception to be raised (\href{https://github.com/qorelanguage/qore/issues/768}{\texttt{ issue 768}}) \item fixed a bug in {\ttfamily Abstract\+Table\+::update()} with sequence operators (\href{https://github.com/qorelanguage/qore/issues/942}{\texttt{ issue 942}}) \end{DoxyItemize} \item \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}} module fixes\+: \begin{DoxyItemize} \item fixed a bug where column names that are reserved words were not quoted in generated S\+QL \item fixed bugs in {\ttfamily cop\+\_\+seq()} and {\ttfamily cop\+\_\+seq\+\_\+currval()} (\href{https://github.com/qorelanguage/qore/issues/624}{\texttt{ issue 624}}) \end{DoxyItemize} \item \href{../../modules/PgsqlSqlUtil/html/index.html}{\texttt{ Pgsql\+Sql\+Util}} module fixes\+: \begin{DoxyItemize} \item fixed a bug in Pgsql\+Table\+::try\+Insert\+Impl(); added an explicit {\ttfamily \char`\"{}begin\char`\"{}} call to make the savepoint work with Postgre\+S\+QL 9.\+3+ servers \item fixed a bug retrieving foreign constraints; columns were not guaranteed to be returned in declaration order \item fixed a bug handling tablespaces in unique constraints \item fixed a bug handling {\ttfamily \char`\"{}time\char`\"{}} columns; they were being issued as {\ttfamily \char`\"{}time6\char`\"{}} instead of \char`\"{}time(6)\char`\"{} (\href{https://github.com/qorelanguage/qore/issues/385}{\texttt{ issue 385}}) \item fixed support for the following datatypes and aliases\+: {\ttfamily \char`\"{}bit\char`\"{}}, {\ttfamily \char`\"{}bit varying\char`\"{}}, {\ttfamily \char`\"{}char\char`\"{}}, {\ttfamily \char`\"{}character\char`\"{}}, {\ttfamily \char`\"{}character varying\char`\"{}}, {\ttfamily \char`\"{}char varying\char`\"{}}, {\ttfamily \char`\"{}oid\char`\"{}}, {\ttfamily \char`\"{}varchar\char`\"{}} \item fixed bugs in {\ttfamily cop\+\_\+seq()} and {\ttfamily cop\+\_\+seq\+\_\+currval()} (\href{https://github.com/qorelanguage/qore/issues/624}{\texttt{ issue 624}}) \end{DoxyItemize} \item \href{../../modules/MysqlSqlUtil/html/index.html}{\texttt{ Mysql\+Sql\+Util}} module fixes\+: \begin{DoxyItemize} \item corrected support for the {\ttfamily varbinary} type (\href{https://github.com/qorelanguage/qore/issues/403}{\texttt{ issue 403}}) \item corrected support for the {\ttfamily binary} type (\href{https://github.com/qorelanguage/qore/issues/524}{\texttt{ issue 524}}) \item {\ttfamily schema} member incorrectly set by \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_abstract_datasource_aea226bb7ae548363ae25a4f1e306b34a}{Abstract\+Datasource\+::get\+User\+Name()}} instead of \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_abstract_datasource_a1e0d642801b1ce96fea0553ae4def964}{Abstract\+Datasource\+::get\+D\+B\+Name()}} (\href{https://github.com/qorelanguage/qore/pull/519}{\texttt{ issue 519}}) \end{DoxyItemize} \item \href{../../modules/WebUtil/html/index.html}{\texttt{ Web\+Util}} module fixes\+: \begin{DoxyItemize} \item fixed a bug where template programs with \mbox{\hyperlink{group__parse__options_gaa980dd723754782db7b8be9abe77615a}{Qore\+::\+P\+O\+\_\+\+A\+L\+L\+O\+W\+\_\+\+B\+A\+R\+E\+\_\+\+R\+E\+FS}} set did not work \item fixed a bug serving index files in {\ttfamily File\+Handler\+::try\+Serve\+Request()} where index files could be incorrectly served with a {\ttfamily \char`\"{}204 No Content\char`\"{}} response (\href{https://github.com/qorelanguage/qore/issues/616}{\texttt{ issue 616}}) \end{DoxyItemize} \item \href{../../modules/WebSocketHandler/html/index.html}{\texttt{ Web\+Socket\+Handler}} module fixes\+: \begin{DoxyItemize} \item fixed a bug where the connection object was deleted when the connection closes which could cause excess exceptions in multithreaded server code \item added the Web\+Socket\+Connection\+::connection\+Closed() method to be called when the connection is closed \end{DoxyItemize} \item \href{../../modules/WebSocketClient/html/index.html}{\texttt{ Web\+Socket\+Client}} module updates\+: \begin{DoxyItemize} \item updated module to version 1.\+3 \item ignore {\ttfamily S\+O\+C\+K\+E\+T-\/\+N\+O\+T-\/\+O\+P\+EN} errors when closing (server already closed the connection) \end{DoxyItemize} \item \href{../../modules/RestHandler/html/index.html}{\texttt{ Rest\+Handler}} module fixes\+: \begin{DoxyItemize} \item fold all possible arguments in the R\+E\+ST request body into the argument hash so that complex R\+E\+ST requests can be made with clear U\+RI strings \item fixed a bug where an error calling an internal nonexistent method would be reported with an incorrect error message \item send errors are now reported in the {\ttfamily Abstract\+Rest\+Stream\+Request\+Handler} object so they can be properly logged (\href{https://github.com/qorelanguage/qore/issues/734}{\texttt{ issue 734}}) \item unknown R\+E\+ST class errors with the base class are now reported consistently like all other such errors (\href{https://github.com/qorelanguage/qore/issues/859}{\texttt{ issue 859}}) \item fixed an issue where request U\+RI paths with multiple consecutive {\ttfamily \char`\"{}/\char`\"{}} chars were handled incorrectly (\href{https://github.com/qorelanguage/qore/issues/900}{\texttt{ issue 900}}) \end{DoxyItemize} \item \href{../../modules/Util/html/index.html}{\texttt{ Util}} module fixes\+: \begin{DoxyItemize} \item fixed {\ttfamily normalize\+\_\+dir\+\_\+windows()} handling of U\+NC paths (\href{https://github.com/qorelanguage/qore/issues/813}{\texttt{ issue 813}}) \end{DoxyItemize} \item fixed a memory error in error-\/handling with type errors when parsing user module headers that could cause a crash \item fixed a memory leak in \mbox{\hyperlink{class_qore_1_1_socket_a4c3b78b845de5f48434e527755dec18a}{Socket\+::set\+Warning\+Queue()}}\+: when a callback argument is used, the argument can be leaked when the \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} is destroyed \item fixed a bug where the \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client}{H\+T\+T\+P\+Client}} class did not send the X.\+509 certificate and private key when making a client S\+SL connection \item fixed a bug in the \mbox{\hyperlink{class_qore_1_1_thread_1_1_thread_pool}{Thread\+Pool}} class where an error in shutdown handling could cause a crash in rare conditions when \mbox{\hyperlink{class_qore_1_1_thread_1_1_thread_pool}{Thread\+Pool}} methods are called while the pool is shutting down \item fixed a crashing bug initializing some lvalues with type restrictions; affected static class variables at least \item fixed a bug where a class calling an overridden method in a base class constructor that referred to a member that should have been initialized in the subclass would be executed before the subclass\textquotesingle{}s members were initialized causing the method call to fail \item fixed a memory leak in classes with multiple inheritance and base classes that are inherited multiple times with member initialization \item fixed a bug in the \mbox{\hyperlink{parse_directives_include}{\%include}} and \mbox{\hyperlink{parse_directives_append-module-path}{\%append-\/module-\/path}} parse directives where relative paths were not calculated from the script\textquotesingle{}s directory but instead were calculated from the current working directory, causing such paths to fail \item fixed a bug in \mbox{\hyperlink{group__misc__functions_gaa0c7ff8f74f88213fdcee6fd6082b16d}{Qore\+::get\+\_\+qore\+\_\+library\+\_\+info()}} that could cause a crash due to treating the {\itshape Build} attribute as a string when it was an integer \item fixed a bug in the \mbox{\hyperlink{operators_divide_equals_operator}{divide-\/equals (/=) operator}} where an exception was not thrown when an operand of zero with arbitrary-\/precision numeric arguments is used \item fixed a bug where the connection mode would be reset for every connection in the \mbox{\hyperlink{class_qore_1_1_ftp_client}{Qore\+::\+Ftp\+Client}} class \item fixed a bug in the \mbox{\hyperlink{class_qore_1_1_ftp_client}{Qore\+::\+Ftp\+Client}} class where connection problems in the data channel when executing certain F\+TP commands could cause a crash due to missing error checking \item fixed a bug in \mbox{\hyperlink{namespace_qore}{Qore}}\textquotesingle{}s internal strcasestr() function on platforms that do not support this function (ex\+: Solaris) that could result in a crash \item fixed a bug in \mbox{\hyperlink{namespace_qore}{Qore}} where string data formatted with {\ttfamily \%n}, {\ttfamily \%N}, or {\ttfamily \%y} could be added to another string with a different character encoding without any automatic conversions, therefore resulting in an improperly-\/encoded string \item fixed a crash when parsing when parsing function, method, or closure arguments when either of the \mbox{\hyperlink{warnings_duplicate-local-vars}{duplicate-\/local-\/vars}} or \mbox{\hyperlink{warnings_duplicate-block-vars}{duplicate-\/block-\/vars}} warnings are set due to an error handling thread-\/local variable info in parse initialization \item fixed a bug where code with mixed coding styles (old and new) could result in invalid parse errors when parsing base class constructor calls to a base class defined in another coding style \item fixed a bug where an H\+T\+TP response with an unknown {\ttfamily Content-\/\+Encoding} header would cause a crash \item fixed a memory error with receiving H\+T\+TP chunked data with receive callbacks where the buffer object was reset with reference counts $>$ 1 \item fixed a bug in the \mbox{\hyperlink{class_qore_1_1_ftp_client}{Ftp\+Client}} class where socket errors would not cause the connection to be closed automatically and therefore further use of the object required a manual disconnect even though the object supports transparent auto-\/reconnection \item fixed a bug where conversions from float to number would introduce inaccuracy in the arbitrary-\/precision number; ex\+: {\ttfamily 737.\+38.\+to\+Number() -\/$>$ 737.\+3799999999999954525264911353588104248} \item fixed a bug where \mbox{\hyperlink{parse_directives_requires}{\%requires}} would fail loading a user module inside a \mbox{\hyperlink{parse_directives_try-module}{\%try-\/module}} block \item fixed a bug in \mbox{\hyperlink{class_qore_1_1_program_abf634534cb29157d05aab5ff3ffd6bea}{Qore\+::\+Program\+::import\+Class()}} where the import would fail if a namespace-\/justified class name was given and any element of the namespace path didn\textquotesingle{}t already exist in the target whereas the same import would succeed if the namespace were omitted in the call \item fixed bugs in \mbox{\hyperlink{class_qore_1_1_program_abf634534cb29157d05aab5ff3ffd6bea}{Qore\+::\+Program\+::import\+Class()}}, \mbox{\hyperlink{class_qore_1_1_program_a9a2e3da4029c50643169cbb72e57f494}{Qore\+::\+Program\+::import\+Function()}}, and \mbox{\hyperlink{class_qore_1_1_program_a5db34046e2722a8519642ad98f412ed3}{Qore\+::\+Program\+::import\+Global\+Variable()}} when namespace-\/justified arguments were given, in this case when namespaces were created in the target, the internal root namespace index was not updated so the imported objects could not be found with namespace-\/justified references until the root indexes were updated \item fixed a bug in the \mbox{\hyperlink{parse_directives_requires}{\%requires}} directive where relative paths were not calculated from the script\textquotesingle{}s directory but rather from the current working directory \item fixed various bugs in path handling on Windows in the following areas\+: \begin{DoxyItemize} \item \mbox{\hyperlink{namespace_qore_a2552ac9c7f40c474e3b311b6178d7909}{Qore\+::basename()}} \item \mbox{\hyperlink{group__misc__functions_ga4730f5a695996be26efbfa9760417b1b}{Qore\+::get\+\_\+script\+\_\+dir()}} \item \mbox{\hyperlink{group__misc__functions_ga3ebc5d7d350677395e4b89686ca335b4}{Qore\+::get\+\_\+script\+\_\+path()}} \item \mbox{\hyperlink{group__misc__functions_gade1f45f4d12597822362d920c84695a5}{Qore\+::get\+\_\+script\+\_\+name()}} \item \mbox{\hyperlink{class_qore_1_1_dir}{Qore\+::\+Dir}} \item module importing and include file handling \end{DoxyItemize} \item fixed a bug in parsing constant value assignment expressions where such expressions could use or instantiate classes with uncommitted changes and therefore a crash could result \item fixed a bug in user module initialization and destruction where call references were not accepted, contrary to the documentation and design goals \item fixed a bug in \mbox{\hyperlink{class_qore_1_1_socket_adb234af8e02eee33b15a55f0ad37f690}{Qore\+::\+Socket\+::accept\+S\+S\+L()}} and \mbox{\hyperlink{class_qore_1_1_socket_a3d64c129d67687ab0e00b96b495059c5}{Qore\+::\+Socket\+::connect\+S\+S\+L()}} where the timeout argument was not respected for S\+SL protocol negotation by implementing non-\/blocking I/O support for the internal S\+SL calls for upgrading the socket connection \item fixed a memory leak in exception handling in the \mbox{\hyperlink{class_qore_1_1_ftp_client_a835c52e32ee089773d48574f297e7965}{Qore\+::\+Ftp\+Client\+::put()}} method (thanks to nros) \item fixed a memory error in string handling in the \mbox{\hyperlink{class_qore_1_1_ftp_client}{Qore\+::\+Ftp\+Client}} class\textquotesingle{}s F\+TP response handling code \item fixed a bug in aligning table data in the sqlutil example program \item fixed a bug when loading modules by a path argument; if the module is already loaded, then do not throw an exception \item adjusted the stack guard buffer for x86\+\_\+64 from 20K -\/$>$ 32K which solved some rare crashes related to stack exhaustion (ex\+: make check works consistently now on x86\+\_\+64 Linux) \item fixed a bug handling H\+T\+TP send callbacks that returned zero-\/length strings and binary objects which would cause invalid chunked data to be sent violating the H\+T\+TP protocol \item fixed a bug in the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a953480807dbdafae0808a6c47014c0d6}{Datasource\+Pool\+::get\+Server\+Version()}} method where the connection to the server was not guaranteed to be in place before the call, in case of connection errors in the pool a crash could result \item fixed a crash in \mbox{\hyperlink{class_qore_1_1_file_line_iterator_a00df8c3068548371230467c0cbca0169}{Qore\+::\+File\+Line\+Iterator\+::copy()}} when no {\itshape eol} attribute is set \item fixed a bug importing invalid user modules with no module declaration \item fixed bugs in \mbox{\hyperlink{class_qore_1_1_socket_a39eb3993cde9b9e0096412d1edbc3a57}{Qore\+::\+Socket\+::accept()}} and \mbox{\hyperlink{class_qore_1_1_socket_adb234af8e02eee33b15a55f0ad37f690}{Qore\+::\+Socket\+::accept\+S\+S\+L()}} where the S\+SL configuration was not copied to the new \mbox{\hyperlink{class_qore_1_1_socket}{Qore\+::\+Socket}} \item fixed some object encapsulation violation bugs where access to methods of a privately-\/inherited class was allowed from a subclass in certain situations \item fixed inconsistent object encapsulation enforcement with method references; if a reference to a method is created inside the class, then when executed the call inherits the access rights at the time of creation \item fixed inconsistent thread gating for code data structures in \mbox{\hyperlink{class_qore_1_1_program}{Program}} containers that could have theoretically lead to crashes in \mbox{\hyperlink{class_qore_1_1_program}{Program}} containers that parse code while threads are running \item fixed a bug in \mbox{\hyperlink{class_qore_1_1_program_a9a2e3da4029c50643169cbb72e57f494}{Qore\+::\+Program\+::import\+Function()}} with function names with a namespace path \item fixed a bug in closure calls when a closure is called from within a closure and referes to closure-\/bound locally variables in the internal closure call which would previously result in a crash \item fixed a parse-\/time memory leak in call reference calls when the callable object is resolved from a class constant \item fixed a bug in maintaining the conditional compilation status when parsing \mbox{\hyperlink{parse_directives_include}{\%include}} directives and \mbox{\hyperlink{parse_directives_requires}{\%requires}} directives with user modules \item fixed an obscure bug when a thread terminates in a \mbox{\hyperlink{class_qore_1_1_program}{Program}} object after the Program container itself has already been deleted where the termination would hang while waiting for the Program\textquotesingle{}s thread count to reach zero while the last thread doing the waiting also held the last thread reference \item fixed a bug where incompatible class definitions were not verified at parse time which could cause a crash in debug builds and unpredictable behavior in non-\/debug builds \item fixed a race condition in finalizing thread-\/local data in \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects during Program destruction that could lead to a runtime crash \item fixed a crash when user modules have recursive dependencies \item fixed a bug with \mbox{\hyperlink{parse_directives_push-parse-options}{\%push-\/parse-\/options}} when used multiple times in the same file; now multiple appearances of this parse directive are ignored \item fixed a bug initializing static class variables in the parse commit phase where a crash could result due to an error in managing parse commit dependencies \item fixed \mbox{\hyperlink{namespace_qore_a1f94b219bfc67a292a80cafcd2416ee5}{Qore\+::is\+\_\+writable()}}\+: \begin{DoxyItemize} \item on Windows when used with a directory \item on U\+N\+IX to return a value for the current permissions the program is running under \end{DoxyItemize} \item fixed a bug in \mbox{\hyperlink{group__string__functions_ga9f8c21f961daa29578dcfd596f5871ff}{Qore\+::regex\+\_\+extract()}} and in the \mbox{\hyperlink{operators_regex_extract_operator}{Regular Expression Pattern Extraction Operator}} where the result buffer was not resized when it was too small, limiting regular expressions to nine subpatterns; the maximum has been raised to between 90 and 100 before an exception is raised (since the subpattern buffer is allocated on the stack, we need to enforce a limit) \item fixed a bug with the \mbox{\hyperlink{operators_cast}{cast$<$$>$() operator where compatible classes were not recognized at runtime that would otherwise be recognized correctly without the cast}} \item fixed the return type in \mbox{\hyperlink{namespace_qore_a891ce19bfbec289e7ef2a1e20d44ba4a}{Qore\+::getcwd()}} to \mbox{\hyperlink{data_type_declarations_string_or_nothing_type}{$\ast$string}} \item fixed a bug in the \mbox{\hyperlink{statements_return}{return statement}} where the runtime return type was used at parse time which did not work when parsing embedded code \item fixed a bug validating return values in method evaluation that could lead to a qore crash \item fixed a bug in the \mbox{\hyperlink{parse_directives_requires}{\%requires}} directive when applied to builtin features where code to manage user module dependencies was inappropriately applied \item fixed a bug nesting 3 levels or more of parse conditionals (\mbox{\hyperlink{parse_directives_ifdef}{\%ifdef}} and \mbox{\hyperlink{parse_directives_ifndef}{\%ifndef}}) where the conditional parse state could be lost (and an assertion was made in debug mode) \item fixed a bug where ==, $>$, and $<$ operators applied type precedence incorrectly when applying optimizations at parse time in relation to arbitrary-\/precision numeric values \item fixed a static memory leak in the parser handling out of line method declarations \item fixed a bug in handling socket disconnection errors in S\+SL operations where the S\+SL helper object was deleted and then used causing a crash \item fixed a bug where \mbox{\hyperlink{deprecated}{Deprecated List}} and \mbox{\hyperlink{warnings_return-value-ignored}{return-\/value-\/ignored}} warnings were reported at the incorrect source location \item fixed a bug in \mbox{\hyperlink{group__threading__functions_gae83c32576b59a1ecfa906d9b3c3af557}{Qore\+::set\+\_\+thread\+\_\+init()}} where thread initialization did not occur when foreign threads attached to a \mbox{\hyperlink{class_qore_1_1_program}{Qore\+::\+Program}} object with thread initialization set \item fixed a bug in call references and objects by replacing string references to the containing Program object with weak references which solved a recursive reference / memory leak issue \item fixed a memory leak when a thread init call reference was used with \mbox{\hyperlink{class_qore_1_1_program}{Qore\+::\+Program}} objects \item fixed bugs in \mbox{\hyperlink{namespace_qore}{Qore}} S\+SL socket handling when the remote connection is disconnected while performing an S\+SL upgrade (client or server) that could cause a crash \item fixed a bug where the sending an invalid H\+T\+TP header to the \mbox{\hyperlink{class_qore_1_1_socket_a3e3d6f1bda0a9b6aaf92c5859c94a01d}{Qore\+::\+Socket\+::send\+H\+T\+T\+P\+Response()}} method could cause a crash \item fixed bugs in \mbox{\hyperlink{namespace_qore_ab480d27a192337309e6497158df8e54c}{system()}}\+: \begin{DoxyItemize} \item the shell was not being used to execute commands with commands where shell meta-\/characters were not found with a manual search which caused such commands to fail; additionally {\ttfamily \&} (ampersand) characters were not recognized as shell meta-\/characters \item fixed problems with signal handling in child processes on U\+N\+I\+Xes\+: \mbox{\hyperlink{namespace_qore_ab480d27a192337309e6497158df8e54c}{system()}} now always performs a {\ttfamily fork(2)}, enables all signals, and calls {\ttfamily execl(\char`\"{}/bin/sh\char`\"{}, \char`\"{}sh\char`\"{}, \char`\"{}-\/c\char`\"{}, }{\itshape command}{\ttfamily , 0)} in the child process (on U\+N\+IX systems; on Windows, system(3) is used directly as before) \end{DoxyItemize} \item fixed a race condition in the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} class when opening new datasources after a connection error in the first datasource which could cause a crash. Now the first datasource is no longer a \char`\"{}special\char`\"{} datasource used for configuration information; configuration information is contained in a separate object which serves as an internal Datasource factory \item fixed a problem where {\ttfamily S\+I\+G\+C\+H\+LD} was blocked by default which caused deadlocks when spawning child processes that in turn waited on grandchild processes -\/ now Qore no longer blocks {\ttfamily S\+I\+G\+C\+H\+LD} on U\+N\+IX platforms \item fixed a bug in Binary\+Node\+::clear() where the internal pointer was freed but not set to 0 leading to a subsequent crash when the object is destroyed; affected H\+T\+T\+P\+Client chunked reads of binary data when used with a callback \item fixed a bug where the runtime exception location could be reported in the wrong location \item fixed a bug where the bzip2 library can request a buffer size that could not be handled by the bzip2 library which is not handled by qore and causes a crash while decompressing certain input \item fixed a bug handling closure-\/bound local variables when closures are created in the background operator expression that caused a core dump \item fixed the precedence of the \mbox{\hyperlink{operators_assignment_operator}{assignment operator (=)}}; now the precedence of this operator is the same as the other assignment operators (\mbox{\hyperlink{operators_plus_equals_operator}{+=}}, \mbox{\hyperlink{operators_minus_equals_operator}{-\/=}}, \mbox{\hyperlink{operators_multiply_equals_operator}{$\ast$=}}, and \mbox{\hyperlink{operators_divide_equals_operator}{/=}}, etc); this does not break any code, but does align Qore with other programming languages (such as C, among others) and allows for expressions such as \begin{DoxyCode}{0} \DoxyCodeLine{a = b += 2} \end{DoxyCode} to be correctly parsed \item fixed a parse-\/time bug in the \mbox{\hyperlink{operators_trim}{trim operator}} where the operator\textquotesingle{}s return type was incorrectly returned as \mbox{\hyperlink{data_type_declarations_int_type}{int}} instead of the type of the lvalue \item fixed a bug initializing object members with a closure that refers to {\itshape self} \item fixed bugs in the documentation and return types of\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_read_only_file_a149f83530ad4d521af205a711253662c}{Qore\+::\+Read\+Only\+File\+::read\+Binary\+File()}} \item \mbox{\hyperlink{class_qore_1_1_read_only_file_a41a3763d813c0b7d41eec553819e1354}{Qore\+::\+Read\+Only\+File\+::read\+Text\+File()}} \end{DoxyItemize} \item fixed a bug in \mbox{\hyperlink{class_qore_1_1_get_opt_a1e0267d9c8fe2785cfce2b115d77802e}{Qore\+::\+Get\+Opt\+::parse(softlist$<$auto$>$)}}, \mbox{\hyperlink{class_qore_1_1_get_opt_a2977199c93490409e08ad702f0691817}{Qore\+::\+Get\+Opt\+::parse2(softlist$<$auto$>$)}}, and \mbox{\hyperlink{class_qore_1_1_get_opt_a1e35348c2a154a13ec09cd591b80b23d}{Qore\+::\+Get\+Opt\+::parse3(softlist$<$auto$>$)}} where call-\/by-\/value and copy-\/on-\/write semantics were not enforced and a shared list argument could be modified \item fixed a bug in zoneinfo file parsing where invalid bands with no U\+TC offset changes against the previous band could cause invalid date/time values to be displayed by \mbox{\hyperlink{namespace_qore}{Qore}} for dates on the invalid transition \item fixed a bug where imported global variables (\mbox{\hyperlink{class_qore_1_1_program_a5db34046e2722a8519642ad98f412ed3}{Qore\+::\+Program\+::import\+Global\+Variable()}}) were added to the pending global variable list and therefore were removed if a parse exception occurred, hwoever the namespace indexes remained, which could lead to unexpected problems at runtime including a crash. Additionally the pending global variable list was not checked which could lead to a memory leak if the a single global variable name is pending, imported, and then committed to the \mbox{\hyperlink{class_qore_1_1_program}{Program}} object. \item fixed memory errors managing program feature lists in the Char\+Ptr\+List class by copying string memory instead of using sometimes temporary values in the list \item fixed minor bugs with directive parsing, mostly related to error reporting \item fixed bugs in relative date arithmetic where operands were swapped with the \mbox{\hyperlink{operators_minus_operator}{-\/ operator}} if the first operand was a \mbox{\hyperlink{basic_data_types_relative_dates}{relative date/time value}}, additionally an operation with the \mbox{\hyperlink{operators_minus_operator}{-\/ operator}} where the first operand is a \mbox{\hyperlink{basic_data_types_relative_dates}{relative date}} and the second operand is a \mbox{\hyperlink{basic_data_types_absolute_dates}{absolute date}} is now calculated using the \mbox{\hyperlink{basic_data_types_absolute_dates}{absolute date}}\textquotesingle{}s epoch offset (offset in seconds and microseconds from {\ttfamily 1970-\/01-\/01Z}), and a \mbox{\hyperlink{basic_data_types_relative_dates}{relative date/time value}} is produced \item fixed a bug normalizing the result of date arithmetic between hour and minute components of \mbox{\hyperlink{basic_data_types_relative_dates}{relative date/time value}} \item fixed a bug where time components of absolute date/time values before the U\+N\+IX epoch were returned with invalid values \item fixed a bug where the \mbox{\hyperlink{parse_directives_exec-class}{\%exec-\/class}} directive did not check for classes with unimplemented abstract variants \item fixed a bug where the \mbox{\hyperlink{operators_push}{push}} and \mbox{\hyperlink{operators_unshift}{unshift}} operators applied to a variable declared as softlist did not use the default value \item fixed a bug where calls to \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a59c32a1cb1c23f5616a57c7b349521ef}{Qore\+::\+H\+T\+T\+P\+Client\+::set\+Connect\+Timeout()}} had no effect (\href{https://github.com/qorelanguage/qore/issues/323}{\texttt{ issue 323}}) \item fixed several bugs with logical comparison operators and arbitrary-\/precision numeric values (\href{https://github.com/qorelanguage/qore/issues/330}{\texttt{ issue 330}}) \item fixed a bug where \mbox{\hyperlink{class_qore_1_1_hash_list_iterator}{Qore\+::\+Hash\+List\+Iterator}} (and therefore \mbox{\hyperlink{class_qore_1_1zzz8hashzzz9_aab3d2e6e69d212dbe05de43136f14367}{Qore\+::zzz8hashzzz9\+::context\+Iterator()}}) would not iterate a simple hash with non-\/list values once but would instead silently ignore the hash (\href{https://github.com/qorelanguage/qore/issues/336}{\texttt{ issue 336}}) \item fixed a bug where a warning was not always issued when square brackets were used on unsuitable types (\href{https://github.com/qorelanguage/qore/issues/184}{\texttt{ issue 184}}), internally ported the square bracket operator to the C++ Qore\+Operator\+Node hierarchy \item fixed a bug handling return type information for method and pseudo-\/method calls; uninitialized memory could be used which could cause a runtime crash (\href{https://github.com/qorelanguage/qore/issues/364}{\texttt{ issue 364}}) \item corrected the name of the \mbox{\hyperlink{operators_modulo_operator}{modulo operator}} (was incorrectly referred to as the \char`\"{}modula\char`\"{} operator earlier\+: \href{}{\texttt{ issue 389}}) \item fixed a bug handling identifiers in parentheses used to dereference hashes or objects; the identifer is not resolved properly whereas previoulsy it was incorrectly interpreted as a string literal (\href{https://github.com/qorelanguage/qore/issues/416}{\texttt{ issue 416}}) \item fixed a bug with handling local variables in const initializers (\href{https://github.com/qorelanguage/qore/issues/421}{\texttt{ issue 421}}) \item fixed a bug where {\ttfamily select(2)} was called after {\ttfamily E\+I\+N\+TR} without reinitializing the descriptor array argument (\href{https://github.com/qorelanguage/qore/issues/435}{\texttt{ issue 435}}) \item fixed a crashing bug on all platforms where select(2) was being called with socket descriptor values $>$ {\ttfamily F\+D\+\_\+\+S\+E\+T\+S\+I\+ZE} (\href{https://github.com/qorelanguage/qore/issues/436}{\texttt{ issue 436}}) \item fixed inconsistencies \mbox{\hyperlink{basic_data_types_reldate_comparisons}{comparing relative date/time values}} (\href{https://github.com/qorelanguage/qore/issues/437}{\texttt{ issue 437}}) \item fixed a bug where \mbox{\hyperlink{statements_on_exit}{on\+\_\+exit Statements}} and \mbox{\hyperlink{statements_on_error}{on\+\_\+error Statements}} statements were not being executed if an exception was raised in an earlier-\/executed \mbox{\hyperlink{statements_on_exit}{on\+\_\+exit Statements}}, \mbox{\hyperlink{statements_on_error}{on\+\_\+error Statements}}, or \mbox{\hyperlink{statements_on_success}{on\+\_\+success Statements}} statement (\href{https://github.com/qorelanguage/qore/issues/380}{\texttt{ issue 380}}) \item fixed a bug where \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_ac4b1dbf34a656d23a89e719a8dadac38}{Qore\+::\+H\+T\+T\+P\+Client\+::get()}} and \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_ac3e1328f5f008a181ad066e5a3a73229}{Qore\+::\+H\+T\+T\+P\+Client\+::post()}} would try to retrieve a message body even if {\ttfamily Content-\/\+Length\+: 0} was returned (or if no {\ttfamily Content-\/\+Length} header was returned at all) which would result in a deadlock until the server would close the connection (\href{https://github.com/qorelanguage/qore/issues/434}{\texttt{ issue 434}}) \item fixed a bug where regular expression substitution would go into an infinite loop when used with an empty pattern and the global flag (\mbox{\hyperlink{group__regex__constants_gaea655c36090c9f1e6bb24cb8de998a04}{Qore\+::\+R\+E\+\_\+\+Global}}, \href{https://github.com/qorelanguage/qore/issues/329}{\texttt{ issue 329}}) \item fixed a bug with connection handling in the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} class; an exception is now thrown if a \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} object tries to execute its prepared S\+QL on a connection other than the original connection used to prepare the statement (\href{https://github.com/qorelanguage/qore/issues/465}{\texttt{ issue 465}}) \item fixed a bug where \mbox{\hyperlink{namespace_qore_a0255009acc4b2cb332fd3f9d2aae7c05}{Qore\+::is\+\_\+executable()}} would return N\+O\+T\+H\+I\+NG instead of False (as per documentation) when called with non-\/existent path as it\textquotesingle{}s parameter (\href{https://github.com/qorelanguage/qore/issues/470}{\texttt{ issue 470}}) \item fixed precedence of logical and bitwise \mbox{\hyperlink{operators}{Operators}} (\href{https://github.com/qorelanguage/qore/issues/481}{\texttt{ issue 481}}) \item fixed a bug where nested lists were not parsed correctly in some cases (\href{https://github.com/qorelanguage/qore/issues/320}{\texttt{ issue 320}}) \item fixed a bug where the type of catch parameter was ignored (\href{https://github.com/qorelanguage/qore/issues/28}{\texttt{ issue 28}}) \item fixed a bug where namespace hierarchies were not indexed during parse time when added to already-\/committed namespaces which lead to symbol resolution errors for valid code (\href{https://github.com/qorelanguage/qore/issues/538}{\texttt{ issue 538}}) \item fixed a bug where a \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} operation attempted in another thread while a callback operation on the same socket was in progress would result in a confusing error message (\href{https://github.com/qorelanguage/qore/issues/530}{\texttt{ issue 530}}) \item fixed a bug where local variable declarations in class member initialization expressions caused a crash (\href{https://github.com/qorelanguage/qore/issues/574}{\texttt{ issue 574}}) \item fixed a bug where H\+T\+TP data in H\+T\+TP socket events was modified even though it was shared which caused data consistency problems and crashes in the worst case (\href{https://github.com/qorelanguage/qore/issues/576}{\texttt{ issue 576}}) \item fixed a bug where the \`{}+=\`{} operator handled N\+O\+T\+H\+I\+NG values incorrectly (\href{https://github.com/qorelanguage/qore/issues/582}{\texttt{ issue 582}}) \item fixed a bug where a non-\/numeric define specified on the command line could cause a crash (\href{https://github.com/qorelanguage/qore/issues/583}{\texttt{ issue 583}}) \item fixed a bug where the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement_a1cc37a8464e3c8a6e50b08d366d3d629}{Qore\+::\+S\+Q\+L\+::\+S\+Q\+L\+Statement\+::describe()}} method would not grab the transation lock even when statements were implicitly executed (\href{https://github.com/qorelanguage/qore/issues/591}{\texttt{ issue 591}}) \item fixed the order of initialization of class members (\href{https://github.com/qorelanguage/qore/issues/42}{\texttt{ issue 42}}) \item fixed a bug in \mbox{\hyperlink{class_qore_1_1_time_zone_a177b96464e04cdc717cd6adc51f83371}{Qore\+::\+Time\+Zone\+::date(string)}} where the date returned was in the current contextual time zone and not that of the object (\href{https://github.com/qorelanguage/qore/issues/584}{\texttt{ issue 584}}) \item fixed a bug parsing windows paths in U\+R\+Ls with \mbox{\hyperlink{group__misc__functions_ga54e6ccaa8fdaa3213ae5550aa66629c9}{Qore\+::parse\+\_\+url()}} (\href{https://github.com/qorelanguage/qore/issues/618}{\texttt{ issue 618}}) \item fixed a bug in \mbox{\hyperlink{class_qore_1_1_time_zone_ab77972801cee2c9d116a9631dfd631d9}{Qore\+::\+Time\+Zone\+::constructor(string)}} on Windows when used with an absolute path (\href{https://github.com/qorelanguage/qore/issues/626}{\texttt{ issue 626}}) \item fixed an I/\+O-\/handling bug in the \mbox{\hyperlink{class_qore_1_1_read_only_file}{Qore\+::\+Read\+Only\+File}} and \mbox{\hyperlink{class_qore_1_1_file}{Qore\+::\+File}} classes where I/O errors in read operations were silently ignored (\href{https://github.com/qorelanguage/qore/issues/627}{\texttt{ issue 627}}) \item fixed bugs in \mbox{\hyperlink{class_qore_1_1_read_only_file_a41a3763d813c0b7d41eec553819e1354}{Qore\+::\+Read\+Only\+File\+::read\+Text\+File()}} and \mbox{\hyperlink{class_qore_1_1_read_only_file_a149f83530ad4d521af205a711253662c}{Qore\+::\+Read\+Only\+File\+::read\+Binary\+File()}} would return \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} instead of an empty object when reading empty files; now empty objects are returned in these cases (\href{https://github.com/qorelanguage/qore/issues/508}{\texttt{ issue 508}}) \item fixed a bug in $\ast$printf() outputs on Windows with scientific notation with floating-\/point values (\href{https://github.com/qorelanguage/qore/issues/631}{\texttt{ issue 621}}) \item fixed a bug where the precision of numbers during arithmetic operations was not adjusted correctly (\href{https://github.com/qorelanguage/qore/issues/630}{\texttt{ issue 630}}, \href{https://github.com/qorelanguage/qore/issues/908}{\texttt{ issue 908}}) \item fixed a bug where the type of subtraction of two numbers was inferred as N\+O\+T\+H\+I\+NG during parsing (\href{https://github.com/qorelanguage/qore/issues/636}{\texttt{ issue 636}}) \item fixed a bug on Windows with \mbox{\hyperlink{class_qore_1_1_dir_a9e9f05c88ac58cdbf027f8f4d8bcdc40}{Qore\+::\+Dir\+::create()}} (\href{https://github.com/qorelanguage/qore/issues/643}{\texttt{ issue 643}}) \item fixed a bug where C\+R\+LF line endings were not handled correctly by the exec-\/class parse directive (\href{https://github.com/qorelanguage/qore/issues/653}{\texttt{ issue 653}}) \item fixed a bug on Windows where \mbox{\hyperlink{namespace_qore_a23f46efaa2b9f2288f7ccd6bdcaa654f}{Qore\+::glob()}} would return paths beginning with {\ttfamily \char`\"{}.\char`\"{}} by default (\href{https://github.com/qorelanguage/qore/issues/660}{\texttt{ issue 660}}) \item fixed a bug on Windows where \mbox{\hyperlink{namespace_qore_a23f46efaa2b9f2288f7ccd6bdcaa654f}{Qore\+::glob()}} would fail on {\ttfamily \char`\"{}\textbackslash{}$\ast$\char`\"{}} or {\ttfamily xxx} \char`\"{}/$<$i$>$$<$/i$>$$\ast$\char`\"{} (\href{https://github.com/qorelanguage/qore/issues/664}{\texttt{ issue 664}}) \item fixed a bug on Windows where \mbox{\hyperlink{namespace_qore_a23f46efaa2b9f2288f7ccd6bdcaa654f}{Qore\+::glob()}} would not return paths in sorted order by default (\href{https://github.com/qorelanguage/qore/issues/665}{\texttt{ issue 665}}) \item fixed a bug on Windows where the \mbox{\hyperlink{class_qore_1_1_dir}{Qore\+::\+Dir}} class would incorrectly normalize U\+NC paths by stripping the leading backslash (\href{https://github.com/qorelanguage/qore/issues/666}{\texttt{ issue 666}}) \item fixed a bug where the \mbox{\hyperlink{data_type_declarations_int_type}{int}} type restriction would accept any data type at runtime instead of throwing a {\ttfamily R\+U\+N\+T\+I\+M\+E-\/\+T\+Y\+P\+E-\/\+E\+R\+R\+OR} exception (\href{https://github.com/qorelanguage/qore/issues/683}{\texttt{ issue 683}}) \item fixed bugs reporting the current method context with certain \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client}{H\+T\+T\+P\+Client}} methods that would report the \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} class instead (\href{https://github.com/qorelanguage/qore/issues/689}{\texttt{ issue 689}}) \item fixed a bug handling aborted H\+T\+TP chunked transfers; now any data available for reading on a socket when a chunked transfer is aborted is read instead of having a {\ttfamily S\+O\+C\+K\+E\+T-\/\+S\+E\+N\+D-\/\+E\+R\+R\+OR} thrown when the remote end closes the socket during the transfer (\href{https://github.com/qorelanguage/qore/issues/691}{\texttt{ issue 691}}) \item fixed a bug with socket handling where S\+SL send failures did not cause an exception to be thrown in all cases (\href{https://github.com/qorelanguage/qore/issues/732}{\texttt{ issue 732}}) \item fixed a bug on Windows where \mbox{\hyperlink{namespace_qore_a23f46efaa2b9f2288f7ccd6bdcaa654f}{Qore\+::glob()}} returned files matched without the leading path component (\href{https://github.com/qorelanguage/qore/issues/761}{\texttt{ issue 761}}) \item fixed a bug with socket connection refused handling on Windows where connections were waiting until the timeout instead of returning an error immediately (\href{https://github.com/qorelanguage/qore/issues/763}{\texttt{ issue 763}}) \item fixed a bug where it was not possible to escape an escape character before a {\ttfamily \textquotesingle{}\$\textquotesingle{}} character in a regular expression substitution target string (\href{https://github.com/qorelanguage/qore/issues/777}{\texttt{ issue 777}}) \item fixed a bug where object member references were treated as expressions returning a constant value which could cause a crash when used in an expression used to initialize a constant value at parse time (\href{https://github.com/qorelanguage/qore/issues/817}{\texttt{ issue 817}}) \item fixed a bug parsing I\+Pv6 localhost ({\ttfamily \char`\"{}\+::\char`\"{}}) with \mbox{\hyperlink{group__misc__functions_ga54e6ccaa8fdaa3213ae5550aa66629c9}{Qore\+::parse\+\_\+url()}} (\href{https://github.com/qorelanguage/qore/issues/822}{\texttt{ issue 822}}) \item fixed a bug in Windows timezone handling caused by erroneous region names (\href{https://github.com/qorelanguage/qore/issues/824}{\texttt{ issue 824}}) \item fixed an internal memory-\/handling bug that caused a crash when cleaning up the qore library on Free\+B\+SD with clang++ and possibly other platforms (\href{https://github.com/qorelanguage/qore/issues/839}{\texttt{ issue 839}}) \item fixed a bug where {\ttfamily C\+A\+L\+L-\/\+W\+I\+T\+H-\/\+T\+Y\+P\+E-\/\+E\+R\+R\+OR} exceptions were thrown based on the parse options in the caller instead of in the target when calling across a \mbox{\hyperlink{class_qore_1_1_program}{Program}} barrier (\href{https://github.com/qorelanguage/qore/issues/841}{\texttt{ issue 841}}) \item fixed a bug where \mbox{\hyperlink{namespace_qore_a1f94b219bfc67a292a80cafcd2416ee5}{Qore\+::is\+\_\+writable()}} and \mbox{\hyperlink{namespace_qore_af04a8a04f9130664f938cf7dc10dbaed}{Qore\+::is\+\_\+readable()}} could return an incorrect value in some cases (\href{https://github.com/qorelanguage/qore/issues/852}{\texttt{ issue 852}}) \item fixed a bug where \mbox{\hyperlink{group__string__functions_ga33bb08516773ed10def16bb42d6b8159}{Qore\+::format\+\_\+number()}} would return an invalid string when the number of decimals to be returned was 0 (\href{https://github.com/qorelanguage/qore/issues/851}{\texttt{ issue 851}}) \item fixed a bug where the \mbox{\hyperlink{operators_delete}{delete}} and \mbox{\hyperlink{operators_remove}{remove}} operators would incorrectly create hash keys when attempting to delete inside complex hash structures with non-\/existent keys (\href{https://github.com/qorelanguage/qore/issues/855}{\texttt{ issue 855}}) \item fixed a bug where duplicate global variable declarations caused a crash (\href{https://github.com/qorelanguage/qore/issues/891}{\texttt{ issue 891}}) \item fixed a memory leak in \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} initialization when the minimum connections cannot be established (\href{https://github.com/qorelanguage/qore/issues/994}{\texttt{ issue 994}}) \item fixed handling of NaN values in logical operators (\href{https://github.com/qorelanguage/qore/issues/915}{\texttt{ issue 915}}) \item fixed sort\+\_\+descending\+\_\+stable so that it keeps (instead of reversing) the original order of items that compare equal (\href{https://github.com/qorelanguage/qore/issues/940}{\texttt{ issue 940}}) \item fixed a bug in {\ttfamily copy()} method argument parsing; compatible type declarations were not accepted (\href{https://github.com/qorelanguage/qore/issues/946}{\texttt{ issue 946}}) \end{DoxyItemize}\hypertarget{release_notes_qore_0811}{}\doxysection{Qore 0.\+8.\+11}\label{release_notes_qore_0811} \begin{DoxyParagraph}{Release Summary} Minor bugfix release for U\+N\+IX, major bugfixes for Windows \end{DoxyParagraph} \hypertarget{release_notes_qore_0811_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_0811_new_features} \begin{DoxyItemize} \item added the \mbox{\hyperlink{group__network__address__family__constants_ga70894a206b70fd3973f0d4dad1322a02}{Qore\+::\+A\+F\+Map}} and \mbox{\hyperlink{group__network__address__family__constants_gafda5d0bb6a1cac9536eb682ae75c4b5c}{Qore\+::\+A\+F\+Str\+Map}} constants \item \href{../../modules/WebUtil/html/index.html}{\texttt{ Web\+Util}} updates\+: \begin{DoxyItemize} \item added logic to the default file serving code to determine if the file is a binary or text file from the M\+I\+ME type \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_aca21bac933b892a3cb27e77a50d9461a}{H\+T\+T\+P\+Client\+::send\+With\+Send\+Callback()}} and \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_aca21bac933b892a3cb27e77a50d9461a}{H\+T\+T\+P\+Client\+::send\+With\+Send\+Callback()}} updated such that if a response is received while the chunked send operation is still in progress, an error is assumed, the send operation is aborted, and the response header is read immediately \end{DoxyItemize}\hypertarget{release_notes_qore_0811_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0811_bug_fixes} \begin{DoxyItemize} \item Windows fixes\+: \begin{DoxyItemize} \item fixed Time\+Zone copying to use the standard name instead of the display name so that the info can be found in the registry \item \href{../../modules/Util/html/index.html}{\texttt{ Util}} module fixes\+: \begin{DoxyItemize} \item fixed get\+\_\+random\+\_\+string() on Windows \item fixed absolute\+\_\+path\+\_\+windows() \end{DoxyItemize} \item \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module fixes\+: \begin{DoxyItemize} \item when binding a wildcard address with \mbox{\hyperlink{group__network__address__family__constants_gac4f81abe9d374562b41117c51950fb80}{A\+F\+\_\+\+U\+N\+S\+P\+EC}} on Windows with Http\+Server\+::add\+Listeners() and both I\+Pv6 and I\+Pv4 addresses are returned, bind both addresses since Windows doesn\textquotesingle{}t direct the I\+Pv4 requests to the wildcard-\/bound I\+Pv6 listener \end{DoxyItemize} \item fixed file reading by always opening in binary mode \item added support for the W\+S\+A\+E\+C\+O\+N\+N\+A\+B\+O\+R\+T\+ED socket error \item replaced Mime\+::\+Multi\+Part\+Message\+::get\+Random\+String() with Util\+::get\+\_\+random\+\_\+string() to make it work on Windows \end{DoxyItemize} \item fixed a bug in the D\+BI layer where calling \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement_a1cc37a8464e3c8a6e50b08d366d3d629}{S\+Q\+L\+Statement\+::describe()}} would crash when called with an older module that did not implement this method \item other fixes in the \href{../../modules/Util/html/index.html}{\texttt{ Util}} module (in addition to the Windows-\/specific fixes above)\+: \begin{DoxyItemize} \item fixed parse\+\_\+to\+\_\+qore\+\_\+value() with hashes with a comma in the first key name \item read from /dev/urandom instead of /dev/random since reads from the latter can block for long periods to fill the entropy pool \end{DoxyItemize} \item do not start signal thread after a fork() if signal handling is enabled, pthread\+\_\+create() is not async-\/signal safe (on Free\+B\+SD at least this reliably causes segfaults) \end{DoxyItemize}\hypertarget{release_notes_qore_0810}{}\doxysection{Qore 0.\+8.\+10}\label{release_notes_qore_0810} \begin{DoxyParagraph}{Release Summary} Major release with many many bugfixes and new features such as much improved H\+T\+TP and R\+E\+ST support (ex\+: chunked transfer support + new client and server classes for R\+E\+ST support for chunked transfers and data streaming), improved DB support (ex\+: new \href{../../modules/Schema/html/index.html}{\texttt{ Schema}} module, \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} improvements), and much more. \end{DoxyParagraph} \hypertarget{release_notes_qore_0810_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_0810_new_features} \begin{DoxyItemize} \item better H\+T\+TP support; support for chunked sends and receives for streaming data over H\+T\+TP and other improvements\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_aca21bac933b892a3cb27e77a50d9461a}{H\+T\+T\+P\+Client\+::send\+With\+Send\+Callback()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a38aeb117b3923c90cf6a1a6e6e05b239}{H\+T\+T\+P\+Client\+::send\+With\+Recv\+Callback()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a9f59809a0a95796b7533b32cf614f527}{H\+T\+T\+P\+Client\+::send\+With\+Callbacks()}} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a2e3bd5ea66d056b0a3f69b4d0e86964e}{H\+T\+T\+P\+Client\+::set\+Persistent()}} \item \mbox{\hyperlink{class_qore_1_1_socket_aa3c8f41a0879b440a999db5c55663d30}{Socket\+::read\+H\+T\+T\+P\+Chunked\+Body\+Binary\+With\+Callback()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a97ffc465250c06c5b4fbc512bd17ee64}{Socket\+::read\+H\+T\+T\+P\+Chunked\+Body\+With\+Callback()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a2bea5bfd918980fafa1d152edd59cfd5}{Socket\+::send\+H\+T\+T\+P\+Message\+With\+Callback()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a43ee02b46ffe20bc219a65c72944386f}{Socket\+::send\+H\+T\+T\+P\+Response\+With\+Callback()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a16039558967b42619176a9609bce5399}{Socket\+::pending\+Http\+Chunked\+Body()}} \end{DoxyItemize} \item added a minimum body size threshold for compression to \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module updates\+: \begin{DoxyItemize} \item configurable content encoding for send request message bodies is now supported (ie optional compression) \end{DoxyItemize} \item new user modules\+: \begin{DoxyItemize} \item \href{../../modules/Schema/html/index.html}{\texttt{ Schema}}\+: for D\+B-\/independent schema management \end{DoxyItemize} \item new public C++ socket performance instrumentation A\+PI \item new functions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{namespace_qore_ab6595c1e20c2e84bea8a17544ec35a7f}{Qore\+::close\+\_\+all\+\_\+fd()}} \end{DoxyItemize} \item new constants\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__error__constants_ga921039c89f6e5c4a48564de6bed1d360}{E\+S\+R\+CH}}\+: search error \end{DoxyItemize} \item \mbox{\hyperlink{group__misc__functions_ga34248adafed4b00da2a526f8f23017cf}{get\+Module\+Hash()}} and \mbox{\hyperlink{group__misc__functions_ga82506074037fe39372ea4f44e2582a75}{get\+Module\+List()}} no longer return the {\ttfamily \char`\"{}filename\char`\"{}} key when run in a \mbox{\hyperlink{class_qore_1_1_program}{Program}} context with \mbox{\hyperlink{group__parse__options_ga213aab826b55076c29ffeecebbaea237}{Qore\+::\+P\+O\+\_\+\+N\+O\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+I\+N\+FO}} set \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} updates\+: \begin{DoxyItemize} \item added insert operator support; for example, for inserting with values from sequences \item added new upsert constant maps \item added static Sql\+Util\+::\+Abstract\+Sql\+Util\+Base\+::get\+Datasource\+Desc() method \item added new Table\+::insert\+From\+Select$\ast$() variants taking Table arguments \item added Sql\+Util\+::\+Table\+::check\+Existence() method \item added support for the {\ttfamily \char`\"{}forupdate\char`\"{}} select option \end{DoxyItemize} \item \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}} updates\+: \begin{DoxyItemize} \item fixed selects with \char`\"{}limit\char`\"{} but no \char`\"{}offset\char`\"{} \item convert date/time values to timestamps with microseconds resolution instead of dates with second resolution when dynamically inserting values as strings in S\+QL (binding by value not affected) \end{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module updates\+: \begin{DoxyItemize} \item added the {\ttfamily \char`\"{}write-\/headers\char`\"{}} option to {\ttfamily Abstract\+Csv\+Writer} and subclasses to enable headers to be suppressed \item added the {\ttfamily \char`\"{}optimal-\/quotes\char`\"{}} option to {\ttfamily Abstract\+Csv\+Writer} and subclasses to enable more efficient csv output (now the default) \end{DoxyItemize} \item added \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_abstract_datasource_a2760e15dfe892c6f37f4f9cab6e86379}{Abstract\+Datasource\+::current\+Thread\+In\+Transaction()}} which is reimplemented as \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_a5661e26369193015c195166e52c6d121}{Datasource\+::current\+Thread\+In\+Transaction()}} and \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_ac983fd7cd64d2de924113b8cb540ca11}{Datasource\+Pool\+::current\+Thread\+In\+Transaction()}}; the base class method throws an exception when called; it was not added as an abstract method in order to not break existing subclasses of Abstract\+Datasource \item enhanced module license support \begin{DoxyItemize} \item module license strings may now be specified in binary and user modules \item \mbox{\hyperlink{group__misc__functions_ga34248adafed4b00da2a526f8f23017cf}{Qore\+::get\+Module\+Hash()}} and \mbox{\hyperlink{group__misc__functions_ga82506074037fe39372ea4f44e2582a75}{Qore\+::get\+Module\+List()}} now report license information for each module \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_0810_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0810_bug_fixes} \begin{DoxyItemize} \item fixed an issue with class constant parse initialization where invalid recursive class constant definition parse exceptions could be raised and in some cases also crashes could result \item \href{../../modules/SmtpClient/html/index.html}{\texttt{ Smtp\+Client}} module\+: fixed missing username and missing password errors \item fixed a bug where a qore switch statement with no case conditions and only a default label would erroneously never have it\textquotesingle{}s default code executed \item fixed a reference leak related to exception handling with invalid arguments with \mbox{\hyperlink{class_qore_1_1_socket_a4c3b78b845de5f48434e527755dec18a}{Qore\+::\+Socket\+::set\+Warning\+Queue()}} and \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_ae2aafddbf5be67012e3b57f846c4105e}{Qore\+::\+H\+T\+T\+P\+Client\+::set\+Warning\+Queue()}} \item fixed several bugs where the parse location could be reported incorrectly for type errors regarding in-\/object variable references \item fixed a bug where an error could result with \mbox{\hyperlink{class_qore_1_1_thread_1_1_condition_a8f29b21d4146f40315e25d3bbf840196}{Condition\+::wait()}} with timeouts $>$ 2147483648ms \item fixed bugs handling \char`\"{}bigint\char`\"{} and \char`\"{}double precision\char`\"{} column types with schema alignments with the \href{../../modules/PgsqlSqlUtil/html/index.html}{\texttt{ Pgsql\+Sql\+Util}} module \item fixed a bug handling parse initialization of constant values requiring run-\/time evaluation after other parse exceptions have been raised that could cause a parse-\/time crash \item fixed a bug where qore could crash on exit with certain openssl versions by calling E\+R\+R\+\_\+remove\+\_\+state(0) in the main thread\textquotesingle{}s cleanup function \item fixed a bug where qore could crash on exit due to user module destruction not taking into consideration user module dependencies \item fixed a bug in schema management in \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} where excessively verbose column aliases were used that caused errors when automatically updating columns with existing rows and new default values and non-\/null contraints with Postgre\+S\+QL databases \item fixed a bug where a call reference to an abstract object method returned from an abstract class could be executed even though it must have been instantiated by a concrete subclass \item fixed a bug where a valid call reference to a private object method was created within the class, then in some cases an object protection exception was raised when the call reference was called outside the class \item fixed a bug in the \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module when the yaml binary module is not available \item fixed programmatic select queries with \char`\"{}limit\char`\"{} but no \char`\"{}offset\char`\"{} in \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}} \item fixed a bug in \mbox{\hyperlink{class_qore_1_1_program_a9a2e3da4029c50643169cbb72e57f494}{Qore\+::\+Program\+::import\+Function()}} where only the committed function list was checked when importing functions with a specific target namespace path \item fixed a bug in \mbox{\hyperlink{class_qore_1_1_program_abf634534cb29157d05aab5ff3ffd6bea}{Qore\+::\+Program\+::import\+Class()}} where only the committed class list was checked when importing functions with a specific target namespace path \item fixed a bug when parsing subnamespaces into a parent namespace where the subnamespace already exists (either in the committed list or in the pending list) \item fixed a memory and reference leak caused by recursive references when closures encapsulating an object\textquotesingle{}s scope are assigned to or accessible from members of the object by making references to the object from within a closure encapsulating the object\textquotesingle{}s state weak references instead of strong references \item fixed schema information classes when the \char`\"{}string-\/numbers\char`\"{} driver option is enabled \item fixed crashing bugs in \mbox{\hyperlink{group__threading__functions_ga1bf3fa656c5e803e9453a5ed84fd556c}{Qore\+::get\+\_\+thread\+\_\+data()}} in certain use cases \item fixed a bug in \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} where select and row iterator operations could fail with certain select hash arguments without a {\ttfamily \char`\"{}columns\char`\"{}} entry but where column names were otherwise required \item fixed a bug in H\+T\+TP response parsing where case-\/signficant comparisons where being made with certain critical header values \item fixed a bug handling thread cancellation with the \mbox{\hyperlink{class_qore_1_1_thread_1_1_thread_pool}{Thread\+Pool}} class \item fixed several race conditions and potential deadlocks in \mbox{\hyperlink{class_qore_1_1_thread_1_1_thread_pool}{Thread\+Pool}} destruction with active threads in the pool \end{DoxyItemize}\hypertarget{release_notes_qore_089}{}\doxysection{Qore 0.\+8.\+9}\label{release_notes_qore_089} \begin{DoxyParagraph}{Release Summary} Major release with many new features and also many bugfixes. \end{DoxyParagraph} \hypertarget{release_notes_qore_089_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_089_new_features} \begin{DoxyItemize} \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module updates\+: \begin{DoxyItemize} \item new classes\+: \begin{DoxyItemize} \item {\ttfamily Csv\+Abstract\+Iterator\+:} base abstract iterator class for iterating line-\/based C\+SV data \item {\ttfamily Csv\+Data\+Iterator\+:} iterator class allowing for C\+SV string data to be processed line by line on a record basis \item {\ttfamily Abstract\+Csv\+Writer\+:} a base class for new C\+SV writer implementations \item {\ttfamily Csv\+File\+Writer\+:} C\+SV file writer class \item {\ttfamily Csv\+String\+Writer\+:} C\+SV in memory writer class \end{DoxyItemize} \item implemented support for allowing subclasses of Csv\+File\+Iterator to implement support for other custom types \item no need to set {\ttfamily \char`\"{}headers\char`\"{}} in the constructor if {\ttfamily \char`\"{}fields\char`\"{}} are set; headers are assumed to be the field labels in the same order \end{DoxyItemize} \item added the \mbox{\hyperlink{group__misc__functions_ga639fba8c278c69ac4d4190ca1db19235}{Qore\+::encode\+\_\+url()}} function with \href{http://tools.ietf.org/html/rfc3986\#section-2.1}{\texttt{ R\+FC 3986 section 2.\+1}} compliance \item \mbox{\hyperlink{group__misc__functions_ga51b949c2d20900fdc2e1b8e46988d2b1}{Qore\+::decode\+\_\+url()}} function updated to decode U\+T\+F-\/8 encoded characters according to \href{http://tools.ietf.org/html/rfc3986\#section-2.1}{\texttt{ R\+FC 3986 section 2.\+1}} \item added get\+\_\+byte\+\_\+size() and get\+\_\+marketing\+\_\+byte\+\_\+size() to the \href{../../modules/Util/html/index.html}{\texttt{ Util}} module \item the error message now includes the module path used for the search when a module cannot be found in the module path \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} enhancements\+: \begin{DoxyItemize} \item new method\+: \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_ae3f91bf804ee55f47169b8ae9669ad40}{Datasource\+Pool\+::clear\+Warning\+Callback()}} \item new method\+: \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a8793cfc4c27420eda345f8a8d0224d6d}{Datasource\+Pool\+::set\+Warning\+Callback()}} \item new method\+: \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a8247564b5f796c196f6532603c27d244}{Datasource\+Pool\+::get\+Usage\+Info()}} \item new method\+: \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a2347794ada3fa9c629e705b7d1e6ee56}{Datasource\+Pool\+::set\+Error\+Timeout()}} \item new method\+: \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a4043aba7b45cce75a8962f38ac9c4249}{Datasource\+Pool\+::get\+Error\+Timeout()}} \item new method\+: \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a358c35bb971eccbdcf917b9c5e3bed19}{Datasource\+Pool\+::set\+Event\+Queue()}} \item new method\+: \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_ad10f884015b96adea7182c970ac6e1e3}{Datasource\+Pool\+::clear\+Event\+Queue()}} \item the new methods allow for monitoring \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} objects for pool contention issues (in case the pool needs to be resized), for throwing an exception if a connection is not acquired within the error timeout period (new default\+: 2 minutes), and for D\+BI drivers to raise warnings on an event queue that can be monitored in a separate thread \item additionally connection acquisition statistics are tracked and returned in \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a8247564b5f796c196f6532603c27d244}{Datasource\+Pool\+::get\+Usage\+Info()}} (total requests, hits, maximum wait time) \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource}{Datasource}} enhancements\+: \begin{DoxyItemize} \item new method\+: \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_ad4953ced1fde3271c67b0dc838756ebf}{Datasource\+::set\+Event\+Queue()}} \item new method\+: \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_ac9a78046de816a73c17ced8195e6e2eb}{Datasource\+::clear\+Event\+Queue()}} \item the new methods allow for D\+BI drivers to raise warnings on an event queue that can be monitored in a separate thread \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} enhancements\+: \begin{DoxyItemize} \item new method\+: \mbox{\hyperlink{class_qore_1_1_socket_a4c3b78b845de5f48434e527755dec18a}{Socket\+::set\+Warning\+Queue()}} \item new method\+: \mbox{\hyperlink{class_qore_1_1_socket_a9879dc24c43dbc9784386e36f1c2425b}{Socket\+::clear\+Warning\+Queue()}} \item new method\+: \mbox{\hyperlink{class_qore_1_1_socket_a2f5986d840537423b8ec72a62c1e5db1}{Socket\+::get\+Usage\+Info()}} \item new method\+: \mbox{\hyperlink{class_qore_1_1_socket_aa11d890255025ccbbf02ff26724b282c}{Socket\+::clear\+Stats()}} \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_ftp_client}{Ftp\+Client}} enhancements\+: \begin{DoxyItemize} \item new method\+: \mbox{\hyperlink{class_qore_1_1_ftp_client_a49a2e47cde50ae8bbcbca8721199dd16}{Ftp\+Client\+::set\+Warning\+Queue()}} \item new method\+: \mbox{\hyperlink{class_qore_1_1_ftp_client_a3c4ed4f609453368ba483ead948d8cf9}{Ftp\+Client\+::clear\+Warning\+Queue()}} \item new method\+: \mbox{\hyperlink{class_qore_1_1_ftp_client_a8734c1ff4459851cbc320443d3b921e6}{Ftp\+Client\+::get\+Usage\+Info()}} \item new method\+: \mbox{\hyperlink{class_qore_1_1_ftp_client_a1732a34fe1f8349fc05ef113b3c5af08}{Ftp\+Client\+::clear\+Stats()}} \end{DoxyItemize} \item \href{../../modules/SmtpClient/html/index.html}{\texttt{ Smtp\+Client}} module updates\+: \begin{DoxyItemize} \item optimized connection and login code; H\+E\+L\+O/\+E\+H\+LO and authorization are performed when connecting only, not before each email \item added support for socket performance instrumentation and warning events \end{DoxyItemize} \item \href{../../modules/Pop3Client/html/index.html}{\texttt{ Pop3\+Client}} module updates\+: \begin{DoxyItemize} \item added support for socket performance instrumentation and warning events \end{DoxyItemize} \item \href{../../modules/TelnetClient/html/index.html}{\texttt{ Telnet\+Client}} module updates\+: \begin{DoxyItemize} \item added support for socket performance instrumentation and warning events \end{DoxyItemize} \item \href{../../modules/WebSocketClient/html/index.html}{\texttt{ Web\+Socket\+Client}} module updates\+: \begin{DoxyItemize} \item added support for socket performance instrumentation and warning events \end{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module updates\+: \begin{DoxyItemize} \item use the new \mbox{\hyperlink{group__misc__functions_ga639fba8c278c69ac4d4190ca1db19235}{Qore\+::encode\+\_\+url()}} function to encode U\+RL paths to ensure that valid requests are sent when spaces, percent characters, and non-\/ascii characters are used in the U\+RL path \item set the character encoding in the {\ttfamily Content-\/\+Type} request header when sending strings \item set the {\ttfamily Accept} header correctly in requests (previously only indicated yaml ({\ttfamily \char`\"{}text/x-\/yaml\char`\"{}}) as an acceptible response encoding) \end{DoxyItemize} \item \href{../../modules/RestHandler/html/index.html}{\texttt{ Rest\+Handler}} module updates\+: \begin{DoxyItemize} \item added support for the {\ttfamily O\+P\+T\+I\+O\+NS} method \item return a 400 {\ttfamily \char`\"{}\+Bad Request\char`\"{}} error if an unsupported H\+T\+TP method is used in a R\+E\+ST Call \end{DoxyItemize} \item added new {\ttfamily Upsert\+Insert\+Only} upsert strategy to \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} \item new pseudo-\/methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_aefcaa86868b4993dd5b0f91fa7b5c1ad}{Qore\+::zzz8valuezzz9\+::sizep()}}\+: returns \mbox{\hyperlink{basic_data_types_True}{True}} if the type can return a non-\/zero size (\mbox{\hyperlink{basic_data_types_True}{True}} for containers including \mbox{\hyperlink{basic_data_types_binary}{binary objects}} and \mbox{\hyperlink{basic_data_types_string}{strings}}, \mbox{\hyperlink{basic_data_types_False}{False}} for everything else) \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_ab5a4673da652f758677d729e40c1e415}{Qore\+::zzz8stringzzz9\+::get\+Line()}}\+: finds lines in a string buffer \end{DoxyItemize} \item \href{../../modules/Mime/html/index.html}{\texttt{ Mime}} module updates\+: \begin{DoxyItemize} \item added mime type for W\+S\+DL files ({\ttfamily \char`\"{}application/wsdl+xml\char`\"{}}) \item added mappings for {\ttfamily \char`\"{}xls\char`\"{}} and {\ttfamily \char`\"{}xlst\char`\"{}} extensions to Mime\+Type\+Xml \end{DoxyItemize} \item added new modules\+: \begin{DoxyItemize} \item \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}}\+: data mapping module \item \href{../../modules/TableMapper/html/index.html}{\texttt{ Table\+Mapper}}\+: data mapping module using \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} and \href{../../modules/Mapper/html/index.html}{\texttt{ Mapper}} to map to an S\+QL table target \item \href{../../modules/FreetdsSqlUtil/html/index.html}{\texttt{ Freetds\+Sql\+Util}}\+: provides back-\/end support for MS S\+QL Server and Sybase databases with \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} using the \href{https://github.com/qorelanguage/module-sybase}{\texttt{ freetds module}} \end{DoxyItemize} \item the \mbox{\hyperlink{parse_directives_include}{\%include}} parse directive now supports environment variable substitution at the beginning of the file path \end{DoxyItemize}\hypertarget{release_notes_qore_089_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_089_bug_fixes} \begin{DoxyItemize} \item fixed a crashing bug handling access to members as default values of normal method arguments (\href{https://github.com/qorelanguage/qore/issues/3240}{\texttt{ issue 3240}}) \item fixed a bug in the \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}} module where the {\ttfamily \char`\"{}response-\/code\char`\"{}} key of the info output hash could be missing in some cases (\href{https://github.com/qorelanguage/qore/issues/3237}{\texttt{ issue 3237}}) \item fixed bugs handling object-\/local access in member initialization (\href{https://github.com/qorelanguage/qore/issues/3193}{\texttt{ issue 3193}}) \item fixed a crashing bug when H\+T\+TP messages with duplicate {\ttfamily Connection}, {\ttfamily Content-\/\+Encoding}, {\ttfamily Transfer-\/\+Encoding}, {\ttfamily Location}, or {\ttfamily Content-\/\+Type} headers are received \item fixed a bug parsing octal character constants in the lexer when octal digits followed the octal constant (ex\+: {\ttfamily \char`\"{}\textbackslash{}0441\char`\"{}} where the {\ttfamily \char`\"{}1\char`\"{}} would cause an error) \item allow escaping \char`\"{}\$\char`\"{} character in regular expression substitution target strings, previously it was impossible to output a literal \char`\"{}\$\char`\"{} + a digit, since this would be interpreted as a numbered input pattern expression \item fixed a bug in the \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a9a9b553de7854b86ca978a8d10c3c9dd}{H\+T\+T\+P\+Client\+::get\+U\+RL()}} and \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a3018d4114a87d90d914a0ed62e924e83}{H\+T\+T\+P\+Client\+::get\+Proxy\+U\+RL()}} methods where the U\+RL\textquotesingle{}s path was not given with a leading \char`\"{}/\char`\"{} character \item \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module fixes\+: \begin{DoxyItemize} \item fixed {\ttfamily \char`\"{}date\char`\"{}} field handling with empty input (now maps to 1970-\/01-\/01) \item fixed Csv\+Data\+Iterator\+::next() when header\+\_\+lines $>$ 0 and working with empty input data \end{DoxyItemize} \item added support for compiling on O\+SX Mavericks \item fixed an infinitely recursive call in Table\+::del() in \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} \item fixed a bug in v$\ast$printf() where {\ttfamily \textquotesingle{}\%\textquotesingle{}} was not handled correctly in all cases \item fixed bugs in \mbox{\hyperlink{group__date__and__time__functions_ga5ecb2657b5cc84fc2f16ae1a4cc3fae7}{microseconds}} and \mbox{\hyperlink{group__date__and__time__functions_gac8e561799a9f873502e161695670c06d}{milliseconds()}} with large arguments \item fixed a bug where a call to a call reference to a static method across a program boundary with local variables as arguments would cause a crash due to improper setting of the program context before the arguments are evaluated \item fixed a bug in \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_a196d09ba7c9e3cb9e6a228593152b5fd}{Datasource\+::copy()}} method where implicitly-\/set options were not carried over into the new object \item fixed a bug in the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} class where implicitly-\/opened connections would not be guaranteed to have the same server time zone setting as the initial connections (for example, could cause problems with server timezone settings if running in a program context with a different local time zone attribute) \item fixed bugs in \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} generating \char`\"{}create table\char`\"{} and \char`\"{}align table\char`\"{} S\+QL with D\+Bs where unique indexes automatically create unique constraints (ex\+: My\+S\+QL) \item fixed a bug in lchown() where chown() was used interally instead of lchown() \item fixed a bug in \href{../../modules/PgsqlSqlUtil/html/index.html}{\texttt{ Pgsql\+Sql\+Util}} retrieving sequence values with Database\+::get\+Next\+Sequence\+Value() \item fixed an off-\/by-\/one memory bug in \mbox{\hyperlink{group__date__and__time__functions_gaa990826f93b4f22f786fcfe431c4886d}{Qore\+::date(string, string)}} parsing a 4-\/digit date mask \item fixed memory leaks in class member and class static variable management \item fixed memory leaks when an entire class has to be rolled back due to parse errors and the class has pending static variables \item fixed memory leaks in constant handling with values containing call references \item fixed a memory leak in constant destruction with parse rollbacks when the constant value was N\+U\+LL \item fixed an error in the rounding heuristic for arbitrary-\/precision numeric values that could produce invalid results (ex\+: 34.\+9n $\ast$ 100 = 34902n) \item enforce \mbox{\hyperlink{group__parse__options_ga5e466ed886222f0b57b0a399b455be71}{P\+O\+\_\+\+N\+O\+\_\+\+F\+I\+L\+E\+S\+Y\+S\+T\+EM}} with the \mbox{\hyperlink{parse_directives_include}{\%include}} directive \item fixed a bug managing object private data in complex inheritance cases where the same class may be inherited with virtual private data and also real private data \item fixed a bug in socket timeout handling with select() errors \item fixed a memory leak in handling abstract methods when multiple abstract methods with the same name but different signatures were declared in a class \end{DoxyItemize}\hypertarget{release_notes_qore_088}{}\doxysection{Qore 0.\+8.\+8}\label{release_notes_qore_088} \begin{DoxyParagraph}{Release Summary} Major new features and bug fixes with a particular focus on enhanced H\+T\+TP capabilities and enhanced database processing \end{DoxyParagraph} \hypertarget{release_notes_qore_088_compatibility}{}\doxysubsection{Changes That Can Affect Backwards-\/\+Compatibility}\label{release_notes_qore_088_compatibility} \begin{DoxyItemize} \item Fixed method resolution order; it\textquotesingle{}s now possible to call pseudo-\/methods directly on classes that implement \mbox{\hyperlink{qore_classes_methodGate_methods}{method\+Gate() methods}} \item Added the following abstract methods to \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_abstract_datasource}{Abstract\+Datasource}}\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_abstract_datasource_a3929e6477e0d9da8155c0b0bf0d236cf}{Abstract\+Datasource\+::get\+Config\+Hash()}} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_abstract_datasource_a79772d8676975c1ab23710bc91d666ae}{Abstract\+Datasource\+::get\+Config\+String()}} \end{DoxyItemize} \item \char`\"{}hard\char`\"{} string comparisons now perform encoding conversions if necessary (however as usual different data types cause the comparison to fail) \end{DoxyItemize}\hypertarget{release_notes_qore_088_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_088_new_features} \begin{DoxyItemize} \item new \mbox{\hyperlink{qore_modules_user_modules}{user modules}} delivered with Qore\+: \begin{DoxyItemize} \item \href{../../modules/RestClient/html/index.html}{\texttt{ Rest\+Client}}\+: Provides a simple A\+PI for communicating with H\+T\+TP servers implementing \href{http://en.wikipedia.org/wiki/Representational_state_transfer}{\texttt{ R\+E\+ST}} services \item \href{../../modules/RestHandler/html/index.html}{\texttt{ Rest\+Handler}}\+: Provides an easy to use interface to the \mbox{\hyperlink{namespace_qore}{Qore}} \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module for implementing server-\/side \href{http://en.wikipedia.org/wiki/Representational_state_transfer}{\texttt{ R\+E\+ST}} services \item \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}}\+: Provides a high-\/level D\+B-\/independent A\+PI for working with database objects \begin{DoxyItemize} \item \href{../../modules/MysqlSqlUtil/html/index.html}{\texttt{ Mysql\+Sql\+Util}}\+: Provides a high-\/level D\+B-\/independent A\+PI for working with My\+S\+QL database objects; loaded automatically by the \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module when working with My\+S\+QL databases \item \href{../../modules/OracleSqlUtil/html/index.html}{\texttt{ Oracle\+Sql\+Util}}\+: Provides a high-\/level D\+B-\/independent A\+PI for working with Oracle database objects; loaded automatically by the \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module when working with Oracle databases \item \href{../../modules/PgsqlSqlUtil/html/index.html}{\texttt{ Pgsql\+Sql\+Util}}\+: Provides a high-\/level D\+B-\/independent A\+PI for working with Postgre\+S\+QL database objects; loaded automatically by the \href{../../modules/SqlUtil/html/index.html}{\texttt{ Sql\+Util}} module when working with Postgre\+S\+QL databases \end{DoxyItemize} \item \href{../../modules/Util/html/index.html}{\texttt{ Util}}\+: Provides a some miscellaneous generally useful routines \item \href{../../modules/WebSocketClient/html/index.html}{\texttt{ Web\+Socket\+Client}}\+: Provides a client A\+PI for connecting to Web\+Socket servers \item \href{../../modules/WebSocketHandler/html/index.html}{\texttt{ Web\+Socket\+Handler}}\+: Provides an interface to the \mbox{\hyperlink{namespace_qore}{Qore}} \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module for implementing server-\/side Web\+Socket services \item \href{../../modules/WebSocketUtil/html/index.html}{\texttt{ Web\+Socket\+Util}}\+: Provides common client and server code for implementing Web\+Socket protocol services in Qore \item \href{../../modules/WebUtil/html/index.html}{\texttt{ Web\+Util}}\+: Provides server support for implementing complex web services including serving resources with mixed text and Qore code that are automatically rendered on demand \end{DoxyItemize} \item improvements in existing \mbox{\hyperlink{qore_modules_user_modules}{user modules}}\+: \begin{DoxyItemize} \item much improved \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module, better performance, much better R\+FC compliance, more flexibility \item new C\+SV generation class in \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} \item much better message serialization and email attachment handling in the \href{../../modules/SmtpClient/html/index.html}{\texttt{ Smtp\+Client}} and \href{../../modules/MailMessage/html/index.html}{\texttt{ Mail\+Message}} modules \end{DoxyItemize} \item there is a new \mbox{\hyperlink{class_qore_1_1_thread_1_1_thread_pool}{Thread\+Pool}} class for implementing thread pools that automatically upscale and downscale within user-\/defined limits depending on the load placed on them \item it\textquotesingle{}s possible to inherit concrete versions of abstract method variants from a parent class that does not define the abstract method, meaning that concrete variants of an abstract method do not have to be implemented in a direct subclass of the class declaring the abstract method~\newline this makes using abstract base classes much easier in complex hierarchies using multiple inheritance; now common code can be separated into a single class and inherited by child classes sharing the common implementation \item major \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} read performance increase by implementing internal read buffering (up to 10x faster socket read performance for certain operations, particularly with H\+T\+TP methods) \item improved Unicode / U\+T\+F-\/8 support \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_ae2329c573986ede4a54e70e9ccef30e2}{Qore\+::zzz8stringzzz9\+::lwr()}}, \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a0b5c301c6742fccb8645968845b00fc1}{Qore\+::zzz8stringzzz9\+::upr()}}, \mbox{\hyperlink{group__string__functions_ga69274a2dc60bef5acb7a8adad8b96b8b}{Qore\+::tolower(string)}}, and \mbox{\hyperlink{group__string__functions_ga55350788372fc736eee9c0102ec82215}{Qore\+::toupper(string)}} now operate on a very wide range of non-\/\+A\+S\+C\+II characters, including Latin, Cyrillic, Greek, Armenian, Georgian, etc characters whereas they were previously limited to working on A\+S\+C\+II characters \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a227ef4978fde1a808f14bc7ead59eb2e}{Qore\+::zzz8stringzzz9\+::unaccent()}} was added which removes accents from strings using a Unicode lookup map from a very wide range of accented Unicode characters to unaccented characters \end{DoxyItemize} \item new \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource}{Datasource}} and \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_a8291b3c3010a8c0d1522afeaa3411a02}{Qore\+::\+S\+Q\+L\+::\+Datasource\+::get\+Config\+Hash()}} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_a7713f26c809821a7942a60e27f924742}{Qore\+::\+S\+Q\+L\+::\+Datasource\+::get\+Config\+String()}} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a3bb2405fb47462198f771428226c12d7}{Qore\+::\+S\+Q\+L\+::\+Datasource\+Pool\+::get\+Config\+Hash()}} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a1eddfff5b95e355b5608554975984307}{Qore\+::\+S\+Q\+L\+::\+Datasource\+Pool\+::get\+Config\+String()}} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a5dd026e94aff8eedf8820db9e83a2e56}{Qore\+::\+S\+Q\+L\+::\+Datasource\+Pool\+::copy()}} \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client}{H\+T\+T\+P\+Client}} changes\+: \begin{DoxyItemize} \item the \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client}{H\+T\+T\+P\+Client}} class is now a subclass of \mbox{\hyperlink{class_qore_1_1_socket}{Socket}}, so all \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} methods can be called on \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client}{H\+T\+T\+P\+Client}} objects, making it easier to implement protocols based on H\+T\+TP \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a2917c58f43d176b49075d6db1c517ea5}{Qore\+::\+H\+T\+T\+P\+Client\+::get\+Default\+Path()}}\+: added \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a7d57e49bdde9c6fa2d67013f3fb0a4c8}{Qore\+::\+H\+T\+T\+P\+Client\+::set\+Default\+Path()}}\+: added \item \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a9a9b553de7854b86ca978a8d10c3c9dd}{Qore\+::\+H\+T\+T\+P\+Client\+::get\+U\+R\+L()}}\+: changed\+: now returns \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} if no U\+RL is set instead of an invalid U\+RL \end{DoxyItemize} \item new functions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__object__functions_ga87ca75da87ef4242a4b1ce3a9e5d188b}{call\+\_\+pseudo\+\_\+args()}} \item \mbox{\hyperlink{group__string__functions_ga8b90bec06c9dabd6d54fff51684f9da6}{substr(binary, softint)}} \item \mbox{\hyperlink{group__string__functions_gaf00ab0e1f2c880e0da287c102aca9873}{substr(binary, softint, softint)}} \end{DoxyItemize} \item new pseudo methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8binaryzzz9_a5b99353f309cc3cdfd0fe7227d99eee5}{Qore\+::zzz8binaryzzz9\+::substr(softint)}} \item \mbox{\hyperlink{class_qore_1_1zzz8binaryzzz9_a87459df5b2a455d190644ae47a468791}{Qore\+::zzz8binaryzzz9\+::substr(softint, softint)}} \item \mbox{\hyperlink{class_qore_1_1zzz8binaryzzz9_ab30735fae927ea3be3e3a710574ff486}{Qore\+::zzz8binaryzzz9\+::to\+Base64()}} \item \mbox{\hyperlink{class_qore_1_1zzz8binaryzzz9_ada0665f689a4787b2697c1ff399b7cac}{Qore\+::zzz8binaryzzz9\+::to\+Hex()}} \item \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_a073b50bf1e4e7b646da0d7a6db6180a8}{Qore\+::zzz8binaryzzz9\+::to\+String()}} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_a61fbd9f6e28a6af34d666ecb7b0bdad2}{Qore\+::zzz8datezzz9\+::get\+Epoch\+Seconds()}} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_ac7dff505bad9f169f79215cdd3f368dc}{Qore\+::zzz8datezzz9\+::get\+Epoch\+Seconds\+Local\+Time()}} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_a1ec48e2108e1b70a2ef9ff85c672e161}{Qore\+::zzz8datezzz9\+::info()}} \item \mbox{\hyperlink{class_qore_1_1zzz8floatzzz9_a2adeb1fcae50106e1a3ed4506d5b12ea}{Qore\+::zzz8floatzzz9\+::abs()}} \item Qore\+::zzz8hashzzz9\+::compare\+Keys(hash) \item \mbox{\hyperlink{class_qore_1_1zzz8intzzz9_a2853596aba431a8e4ad3e3e7e2417c37}{Qore\+::zzz8intzzz9\+::abs()}} \item \mbox{\hyperlink{class_qore_1_1zzz8intzzz9_a97747fdeeebc700bdf6c101f34d59d82}{Qore\+::zzz8intzzz9\+::encode\+Lsb(int)}} \item \mbox{\hyperlink{class_qore_1_1zzz8intzzz9_a5b9876a1b6173efa7ae157ce1680871a}{Qore\+::zzz8intzzz9\+::encode\+Msb(int)}} \item \mbox{\hyperlink{class_qore_1_1zzz8intzzz9_ac442a991ff2423860f44768b9e961918}{Qore\+::zzz8intzzz9\+::to\+Unicode()}} \item \mbox{\hyperlink{class_qore_1_1zzz8numberzzz9_a638c34b8465f9a9ce773c25e4a263cd9}{Qore\+::zzz8numberzzz9\+::abs()}} \item \mbox{\hyperlink{class_qore_1_1zzz8objectzzz9_a53db2b90a03e13947b32a34bfddf553b}{Qore\+::zzz8objectzzz9\+::has\+Callable\+Method()}} \item \mbox{\hyperlink{class_qore_1_1zzz8objectzzz9_a21ad831080f7d554f84c849e92e918d0}{Qore\+::zzz8objectzzz9\+::has\+Callable\+Normal\+Method()}} \item \mbox{\hyperlink{class_qore_1_1zzz8objectzzz9_a53b9a99bec7d7372eddd523303c5f1e3}{Qore\+::zzz8objectzzz9\+::has\+Callable\+Static\+Method()}} \item \mbox{\hyperlink{class_qore_1_1zzz8listzzz9_a4483a03f84971f0f3e64dace2de2f737}{Qore\+::zzz8listzzz9\+::range\+Iterator()}} \item \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9_a146f90597d71a88584a23c93806c9bb7}{Qore\+::zzz8nothingzzz9\+::range\+Iterator()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_aabf1bb32b32060ffc6a68164157d86aa}{Qore\+::zzz8stringzzz9\+::compare\+Partial()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_ac677323f97c583af45f7f77984462e3d}{Qore\+::zzz8stringzzz9\+::get\+Unicode()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a215bc851affd3a2a57b80cefc484f139}{Qore\+::zzz8stringzzz9\+::equal\+Partial()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a87b81daaffa46700be92e0596578b200}{Qore\+::zzz8stringzzz9\+::equal\+Partial\+Path()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a13b13f9681a94272d0e16371d2f22d90}{Qore\+::zzz8stringzzz9\+::to\+Base64()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_af4a4f62237f079383098441132967527}{Qore\+::zzz8stringzzz9\+::to\+Hex()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a227ef4978fde1a808f14bc7ead59eb2e}{Qore\+::zzz8stringzzz9\+::unaccent()}} \item \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_ad4bcbe12f38c710e0e7e67a68ab0512f}{Qore\+::zzz8valuezzz9\+::to\+Number()}} \end{DoxyItemize} \item other new methods and method changes\+: \begin{DoxyItemize} \item added new static methods in the \mbox{\hyperlink{class_qore_1_1_read_only_file}{Read\+Only\+File}} class making it easier to read entire files in one call\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_read_only_file_a41a3763d813c0b7d41eec553819e1354}{Qore\+::\+Read\+Only\+File\+::read\+Text\+File()}} \item \mbox{\hyperlink{class_qore_1_1_read_only_file_a149f83530ad4d521af205a711253662c}{Qore\+::\+Read\+Only\+File\+::read\+Binary\+File()}} \end{DoxyItemize} \item changes to catch usage errors with the \mbox{\hyperlink{class_qore_1_1_thread_1_1_counter}{Counter}} class\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_thread_1_1_counter_a99a25b2f06f40edd2535b43ede25ef5a}{Qore\+::\+Thread\+::\+Counter\+::constructor()}} will throw an exception if called with an argument $<$ 0 \item \mbox{\hyperlink{class_qore_1_1_thread_1_1_counter_a31f5a01212067685e54de06ae29a9984}{Qore\+::\+Thread\+::\+Counter\+::dec()}} will now throw an exception if called when the Counter is already at 0 \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue_adbc347a8bc17d1a9aec0dceec5b06cdb}{Qore\+::\+Thread\+::\+Queue\+::empty()}}\+: new method \item \mbox{\hyperlink{class_qore_1_1_socket_a430d67ff882a9733d02ff1fa745ca159}{Qore\+::\+Socket\+::listen()}}\+: now has a new {\itshape backlog} parameter; the default backlog queue size was changed from 5 to 20 \item \mbox{\hyperlink{class_qore_1_1_socket_aa7bd4b05c84b9ce41078abd86ba6c223}{Qore\+::\+Socket\+::get\+Peer\+Info()}} and \mbox{\hyperlink{class_qore_1_1_socket_a36d7bde2fa763acc9a84673a6193e48b}{Qore\+::\+Socket\+::get\+Socket\+Info()}}\+: now takes an optional argument to avoid name lookups \item \mbox{\hyperlink{class_qore_1_1_socket_ac3e0f0383c3337783a49ff85d8805bad}{Qore\+::\+Socket\+::read\+H\+T\+T\+P\+Header\+String()}}\+: new method \item \mbox{\hyperlink{class_qore_1_1_dir}{Qore\+::\+Dir}}\+: all list$\ast$() methods now take an optional parameter to return a list of file status value hashes plus {\ttfamily \char`\"{}name\char`\"{}} and optionally {\ttfamily \char`\"{}link\char`\"{}} keys for symbolic links; additionally symbolic links are now followed and files and directories are differentiated based on their targets when processing symbolic links \end{DoxyItemize} \item function changes \begin{DoxyItemize} \item added optional {\itshape start} and {\itshape end} parameters to the \mbox{\hyperlink{group__string__functions_ga757f5b4682cb6787e7e186ddcc2b2b56}{replace()}} function \end{DoxyItemize} \item all \mbox{\hyperlink{data_type_declarations}{data type declarations}} that optionally accept \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} also now accept \mbox{\hyperlink{basic_data_types_null}{N\+U\+LL}} and map \mbox{\hyperlink{basic_data_types_null}{N\+U\+LL}} to \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}}; this makes direct assignments from values derived from S\+QL queries much easier \item added an optional reference to an integer to the \mbox{\hyperlink{group__misc__functions_gaee11d366f841cd34c9aa6ac8c7c49577}{Qore\+::backquote()}} function to return the return code of the program executed \item \mbox{\hyperlink{expressions_implicit_index}{implicit index}} references now work in the \mbox{\hyperlink{operators_map}{map}} and \mbox{\hyperlink{operators_select}{select}} operators with lists and iterators \item the \mbox{\hyperlink{operators_regex_extract_operator}{Regular Expression Pattern Extraction Operator}} now accepts an optional {\ttfamily g} specifier to extract all occurrences of the pattern(s) in a string; also \mbox{\hyperlink{group__string__functions_ga9f8c21f961daa29578dcfd596f5871ff}{regex\+\_\+extract()}} and \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_aeaf99b23a4de2db748a1fe0bbc3811f5}{Qore\+::zzz8stringzzz9\+::regex\+Extract(string, int)}} now accept \mbox{\hyperlink{group__regex__constants_gaea655c36090c9f1e6bb24cb8de998a04}{Qore\+::\+R\+E\+\_\+\+Global}} to extract all occurrences of the pattern(s) in a string \item the \mbox{\hyperlink{operators_splice}{splice}} and \mbox{\hyperlink{operators_extract}{extract}} operators were extended to work on \mbox{\hyperlink{basic_data_types_binary}{binary objects}} as well as lists and strings \item printing out binary values with the {\ttfamily \char`\"{}\%y\char`\"{}} \mbox{\hyperlink{group__string__functions_string_formatting}{format specifier}} now produces Y\+A\+M\+L-\/like output for the binary value \item added path name to error messages in \mbox{\hyperlink{class_qore_1_1_dir}{Dir}} class exception strings \end{DoxyItemize}\hypertarget{release_notes_qore_088_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_088_bug_fixes} \begin{DoxyItemize} \item fixed a bug where the ?\+: operator could thrown spurious exceptions when parsing because it would return the type of the initial boolean expression as the return type of the operator \item fixed a bug where classes with unimplemented inherited abstract variants would sometimes cause runtime exceptions to be thrown when instantiated but should have instead been caught at parse time \item fixed a parser bug where out-\/of-\/line class method definitions could not be defined in a namespace block \item fixed a bug parsing arguments in parse\+\_\+uri\+\_\+query() in the \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module \item fixed several bugs where parse exceptions could show the wrong source location\+: \begin{DoxyItemize} \item with type errors in function calls \item when resolving global variables \item in base class constructor arguments \item for empty blocks with a missing return statement \item when validating types used with the return statement (also associated warnings) \item in methods calls \item in hash value expressions \item with redeclaring local variable return types \item in local variable object instantiations \end{DoxyItemize} \item really fixed the bug thought to be fixed in 0.\+8.\+7 \char`\"{}where S\+S\+L errors would cause the affected thread to go into a infinite loop using 100\% C\+P\+U\char`\"{} -\/ this turned out to be easily reproducible on all platforms; when the S\+SL connection was shut down cleanly by the remote end before a response message was returned, an infinite loop would result \item fixed a bug where it was impossible to output a single \textquotesingle{}\textbackslash{}\textquotesingle{} character in regex substitution expressions; \textquotesingle{}\textbackslash{}\textquotesingle{} was taken as an escape character, and \textquotesingle{}\textbackslash{}\textbackslash{}\textquotesingle{} was output literally, now \textquotesingle{}\textbackslash{}\textbackslash{}\textquotesingle{} is output as \textquotesingle{}\textbackslash{}\textquotesingle{} \item fixed a bug where a parse-\/time crash would occur when calling the copy() method for a class that does not implement an explicit copy() method \item fixed a bug where arguments passed to a copy method were ignored; now an exception is thrown \item fixed a bug where public members and static variables of privately-\/inherited classes were incorrectly treated as public attributes of the child class \item fixed a bug where slices could be made of objects from outside the class including private members \item fixed a bug where \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement_af7fe60e95959cc5eb6cf0046adcb9ec6}{member\+Gate() methods}} were not being respected when taking a slice of an object \item fixed bugs in the integer Socket\+::recv$\ast$() methods where a {\ttfamily S\+O\+C\+K\+E\+T-\/\+C\+L\+O\+S\+ED} exception was not thrown when the remote end closed the connection \item fixed a bug related to out-\/of-\/order parse initialization for functions and methods which resulted in the wrong return type being returned for a method with more than 1 variant where the variant could not be matched at parse time \item fixed a bug where a non-\/variable-\/reference member of an \char`\"{}our\char`\"{} variable declaration list would cause a crash due to passing the incorrect argument in \mbox{\hyperlink{group__string__functions_ga7a74be141f814ef286046c367b21091c}{sprintf()}} \item fixed sandboxing / protection errors with inherited code; subclasses inheriting code from a parent class with different parse options would cause the child parse options to be used when running the parent class code which caused errors; now parse options are enforced properly on the block level \item fixed the \mbox{\hyperlink{class_qore_1_1_range_iterator}{Range\+Iterator}} class; it was still abstract due to a missing \mbox{\hyperlink{class_qore_1_1_range_iterator_ad235b23928683ba0929d97f6d6401bb9}{Qore\+::\+Range\+Iterator\+::valid()}} method \item fixed a bug where the wrong error was being returned after a connection reset (remote connection close) in sockets with integer recv$\ast$() methods which could in some cases lead to an infinite loop \item fixed a bug where private members of a common base class were not accessible by objects of subclasses sharing the common base class \item fixed many bugs in \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} and updated the module version to 1.\+1 \item initialize static openssl crypto locks for multi-\/threaded openssl library access; without this crashes can result (for example in error queue management) \item fixed a bug where \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a9a9b553de7854b86ca978a8d10c3c9dd}{Qore\+::\+H\+T\+T\+P\+Client\+::get\+U\+R\+L()}} returned an invalid U\+RL when no U\+RL was set; now it returns \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} in this case \item fixed a bug managing feature/module lists in inherited \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects; user modules were listed in the child \mbox{\hyperlink{class_qore_1_1_program}{Program}} object even though user module code is not imported in child \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects \item fixed a bug where an invalid guard condition in critical lvalue storage code can cause unreferenced data to be returned while in a lock which can cause a crash in a multithreaded program \item fixed a bug where references were not being written to the output variable if an exception was active when the code block exited \item fixed a bug setting the precision for arbitrary-\/precision numbers with large exponents (like \char`\"{}1e100n\char`\"{}) \item implemented more strict adherence to \href{http://tools.ietf.org/html/rfc2616}{\texttt{ R\+FC 2616}} (H\+T\+TP 1.\+1) regarding message-\/body handling in requests and response message generation and parsing \item fixed a bug with \mbox{\hyperlink{class_qore_1_1_thread_1_1_condition_a8f29b21d4146f40315e25d3bbf840196}{Condition\+::wait()}} on Darwin with negative timeout values where a short timeout was used instead of an indefinite wait \item fixed bugs in the \href{../../modules/SmtpClient/html/index.html}{\texttt{ Smtp\+Client}} and \href{../../modules/MailMessage/html/index.html}{\texttt{ Mail\+Message}} modules where mail messages were being serialized incorrectly if there were no attachments (there was no possibility to set the content transfer encoding) and also where it was not possible to set the content-\/type for the message body when it was sent as a part of a multipart message \item fixed bugs handling arguments declared as type \mbox{\hyperlink{data_type_declarations_reference_or_nothing_type}{$\ast$reference}} (reference or nothing) \item fixed bugs in executing code accross \mbox{\hyperlink{class_qore_1_1_program}{Program}} object barriers with reference arguments \item fixed a bug with the switch statement where character encoding differences would cause strings to mismatch even if they were otherwise identical; now hard comparisons with strings allow for implicit automatic temporary character encoding conversions for the comparison \item fixed a bug where qore failed to set the time zone region correctly when set from /etc/localtime and this file is a relative symlink rather than absolute \item fixed a bug where \mbox{\hyperlink{group__string__functions_gafe621446ada382d5b086a1d2a20934c9}{substr()}} and \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_ab5ad54b1fe38b46ee071e55563d9d245}{Qore\+::zzz8stringzzz9\+::substr()}} were returning \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} if the arguments could not be satisifed contrary to the documentation and the declared return type, now an empty string is returned in those cases \item fixed bugs rounding number values between 10 and -\/10 (non-\/inclusive) for display, fixed bugs rounding number value regarding digits after the decimal point for display with \mbox{\hyperlink{group__number__formatting__constants_ga69cc628e70f6f1c4c9ba4997ac09e5b8}{Qore\+::\+N\+F\+\_\+\+Scientific}} \item fixed a bug in the \mbox{\hyperlink{class_qore_1_1_dir}{Qore\+::\+Dir}} class where it was not possible to chdir to the root directory {\ttfamily \char`\"{}/\char`\"{}} \item fixed a bug where recursive references were allowed and memory leaks would occur due to recursive references; these are now caught at runtime and a {\ttfamily R\+E\+F\+E\+R\+E\+N\+C\+E-\/\+E\+R\+R\+OR} exception is thrown \item fixed a configure bug with bison $>$= 3 \item fixed a bug in the \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module when automatically uncompressing supported content-\/encodings to set the resulting string\textquotesingle{}s character encoding correctly \item fixed a bug in the \mbox{\hyperlink{operators_instanceof}{instanceof}} operator when working with objects and classes created from different source \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects \item fixed a bug in $\ast$printf() formatting with floating-\/point and number values where no digits were displayed right of the decimal point unless a specific number of digits was specified in the format string \item fixed the return type of \mbox{\hyperlink{class_qore_1_1zzz8boolzzz9_ab1dbc0ed03411f54af90e04a8172a56a}{Qore\+::zzz8boolzzz9\+::type\+Code()}}; was returning a boolean instead of \mbox{\hyperlink{group__type__code__constants_ga2d3c90a766ca129ff13d243a27b41c90}{Qore\+::\+N\+T\+\_\+\+B\+O\+O\+L\+E\+AN}} \item fixed a bug there \mbox{\hyperlink{basic_data_types_null}{N\+U\+LL}} was evaluated as \mbox{\hyperlink{basic_data_types_True}{True}} in a boolean context rather than \mbox{\hyperlink{basic_data_types_False}{False}} \item fixed a bug where \mbox{\hyperlink{class_qore_1_1_socket_aa255d1dcfbddb208e80684eebecc800d}{Qore\+::\+Socket\+::recv\+Binary()}} would ignore the first data read \item fixed starting listeners on U\+N\+IX domain sockets on Soalris in the \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module \item fixed a bug where number(\char`\"{}\char`\"{}) was being converted to @NaN@n \item fixed return type of \mbox{\hyperlink{class_qore_1_1_h_t_t_p_client_a1d0fef0b049abca0d26c931c5e8f020b}{H\+T\+T\+P\+Client\+::get\+Connection\+Path()}} \item fixed several bugs with logical comparison operators and arbitrary-\/precision numeric values where arbitrary-\/precision numeric values were not being prioritized as numeric values and also in some cases were being first converted to doubles and then operated on \item fixed a bug in the socket code where the socket close condition was not flagged with S\+SL connections when writes failed due to the remote end closing the connection; an error would only be raised on the following socket operation \item fixed a mismatched delete/malloc error with time zone initialization and the localtime file \end{DoxyItemize}\hypertarget{release_notes_qore_087}{}\doxysection{Qore 0.\+8.\+7}\label{release_notes_qore_087} \begin{DoxyParagraph}{Release Summary} Code embedding improvements \end{DoxyParagraph} \hypertarget{release_notes_qore_087_compatibility}{}\doxysubsection{Changes That Can Affect Backwards-\/\+Compatibility}\label{release_notes_qore_087_compatibility} \begin{DoxyParagraph}{Fixes for Code Inheritance in Program Objects} The following changes are meant to sanitize code inheritance in child \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects to fix long-\/standing design bugs in code encapsulation by addressing the lack of fine-\/grained control over symbol visibility in inherited code. \begin{DoxyItemize} \item \mbox{\hyperlink{qore_modules_mod_public}{public}}\+: The \mbox{\hyperlink{qore_modules_mod_public}{public}} keyword\textquotesingle{}s usage in modules has now been expanded to provide the same functionality generically in \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects; if \mbox{\hyperlink{qore_classes}{classes}}, \mbox{\hyperlink{constants}{constants}}, \mbox{\hyperlink{qore_namespaces}{namespaces}}, \mbox{\hyperlink{qore_functions}{functions}}, or \mbox{\hyperlink{variables_global_variables}{global variables}} are defined with the \mbox{\hyperlink{qore_modules_mod_public}{public}} keyword, then these symbols will be inherited into child \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects as long as no \mbox{\hyperlink{group__parse__options}{parse options}} prohibit it.~\newline ~\newline This change was made to give programmers complete control over which symbols are inherited in child \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects, whereas because prior to this change, the control was very course.~\newline ~\newline \item the default behavior of Qore regarding inherting global variables and functions with user variants was changed to be consistent with namespaces, classes, and constants; that is; public symbols are inherited by default.~\newline ~\newline The following constants were renamed\+: \begin{DoxyItemize} \item {\ttfamily P\+O\+\_\+\+I\+N\+H\+E\+R\+I\+T\+\_\+\+U\+S\+E\+R\+\_\+\+F\+U\+N\+C\+\_\+\+V\+A\+R\+I\+A\+N\+TS} is now\+: \mbox{\hyperlink{group__parse__options_ga972fcd1745cc3f4efb6cb2a6e53cd832}{P\+O\+\_\+\+N\+O\+\_\+\+I\+N\+H\+E\+R\+I\+T\+\_\+\+U\+S\+E\+R\+\_\+\+F\+U\+N\+C\+\_\+\+V\+A\+R\+I\+A\+N\+TS}} \item {\ttfamily P\+O\+\_\+\+I\+N\+H\+E\+R\+I\+T\+\_\+\+G\+L\+O\+B\+A\+L\+\_\+\+V\+A\+RS} is now\+: \mbox{\hyperlink{group__parse__options_ga7cd01bb8ba1560c7893cd9655894c550}{P\+O\+\_\+\+N\+O\+\_\+\+I\+N\+H\+E\+R\+I\+T\+\_\+\+G\+L\+O\+B\+A\+L\+\_\+\+V\+A\+RS}}~\newline ~\newline This change was made to fix a long-\/standing design problem with symbol inheritance and make the implementation consistent.~\newline ~\newline \end{DoxyItemize} \item builtin symbols are no longer inherited from user modules; only independent user symbols; the main change is that if a user module adds new user methods to a builtin class or new user variants to a builtin function, these changes are no longer imported into target \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects. \end{DoxyItemize} \end{DoxyParagraph} \begin{DoxyParagraph}{File Method Changes} The following methods were updated to throw exceptions on all errors rather than a return code for I/O errors in order to avoid hard to debug conditions due to ignoring I/O errors by forgetting to check the return value on the following methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_file_aa0124826c6cc0c6cfa2a81a4612d4844}{Qore\+::\+File\+::f\+\_\+printf()}} \item \mbox{\hyperlink{class_qore_1_1_file_a04172f5443b2e559269849bf7e653219}{Qore\+::\+File\+::f\+\_\+vprintf()}} \item \mbox{\hyperlink{class_qore_1_1_file_a96b440e3903aa9099cc312ea8c649beb}{Qore\+::\+File\+::print()}} \item \mbox{\hyperlink{class_qore_1_1_file_a7fb81ceed3597d9424e9bbd5dd2e55c0}{Qore\+::\+File\+::printf()}} \item \mbox{\hyperlink{class_qore_1_1_file_a8e508aabefedf9fa70c42d0e5fab5959}{Qore\+::\+File\+::vprintf()}} \item \mbox{\hyperlink{class_qore_1_1_file_acd30e6f14435bae0393b1ed52bec502d}{Qore\+::\+File\+::write()}} \item \mbox{\hyperlink{class_qore_1_1_file_ad4f67c2a247f4b7fb9c6e26b51106aba}{Qore\+::\+File\+::writei1()}} \item \mbox{\hyperlink{class_qore_1_1_file_adcf79ce346b63b85ff517580fd96d0b0}{Qore\+::\+File\+::writei2()}} \item \mbox{\hyperlink{class_qore_1_1_file_a82dee19cad26e011ba1a0970d42b2130}{Qore\+::\+File\+::writei4()}} \item \mbox{\hyperlink{class_qore_1_1_file_a9de545742fe95945677bb3049a1900fc}{Qore\+::\+File\+::writei8()}} \item \mbox{\hyperlink{class_qore_1_1_file_a9004f5ff77ea368263121c33f95c87c5}{Qore\+::\+File\+::writei2\+L\+S\+B()}} \item \mbox{\hyperlink{class_qore_1_1_file_a6788f0f1bd5b015dd726a6b2d06077bf}{Qore\+::\+File\+::writei4\+L\+S\+B()}} \item \mbox{\hyperlink{class_qore_1_1_file_aab6932b3995a5b0963e41ef41bdd0b36}{Qore\+::\+File\+::writei8\+L\+S\+B()}} \end{DoxyItemize}Note that the above changes will hopefully only minimally impact backwards-\/compatibilty since the change is in error handling, and additionally each of the above methods could also throw an exception if called when the object was not open. \end{DoxyParagraph} \hypertarget{release_notes_qore_087_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_087_new_features} \begin{DoxyItemize} \item new methods offering code encapsulation enhancements \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_program_a9bc54a95f735cdc10bfb52e5166259b2}{Program\+::load\+Module()}}\+: allows modules to be loaded in a \mbox{\hyperlink{class_qore_1_1_program}{Program}} object directly \item \mbox{\hyperlink{class_qore_1_1_program_abf634534cb29157d05aab5ff3ffd6bea}{Program\+::import\+Class()}}\+: allows classes to be individually imported in \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects \end{DoxyItemize} \item new pseudo-\/methods in \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9}{Qore\+::zzz8nothingzzz9}} to allow for \mbox{\hyperlink{class_qore_1_1zzz8hashzzz9}{Qore\+::zzz8hashzzz9}} pseudo-\/methods to be safely used with \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9_a213d95ffb43f1439a5ba987a9efc9b87}{Qore\+::zzz8nothingzzz9\+::first\+Key()}} \item \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9_a0ce252bde5f2a79322def0893f78b23c}{Qore\+::zzz8nothingzzz9\+::first\+Value()}} \item \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9_a6b7ecd3769d24f276a237ac46359ade6}{Qore\+::zzz8nothingzzz9\+::has\+Key()}} \item \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9_a36021f943bc18e23b8712f8f57256b20}{Qore\+::zzz8nothingzzz9\+::has\+Key\+Value()}} \item \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9_a7045f452f423bd60001c19db3b576c58}{Qore\+::zzz8nothingzzz9\+::keys()}} \item \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9_ae44acd5f4f9e6710b8078bb5464c8f6f}{Qore\+::zzz8nothingzzz9\+::last\+Key()}} \item \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9_a86e91aa90079372efdb645987883ca08}{Qore\+::zzz8nothingzzz9\+::last\+Value()}} \item \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9_a26377a1d6c390e6f9242590c1b6cb977}{Qore\+::zzz8nothingzzz9\+::values()}} \end{DoxyItemize} \item other new pseudo-\/methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_aef0e1961cbf4e1f2b53b789d0727681f}{Qore\+::zzz8datezzz9\+::duration\+Seconds()}} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_a0a1bf587b81314cbc5cbabd4cc618476}{Qore\+::zzz8datezzz9\+::duration\+Milliseconds()}} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_afd98bf51bd4870ddc8469e0bc19f2b9c}{Qore\+::zzz8datezzz9\+::duration\+Microseconds()}} \end{DoxyItemize} \item removed most restrictions on embedded logic in user modules; user module \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects are subject to the same restrictions as the parent \mbox{\hyperlink{class_qore_1_1_program}{Program}} object (if any) \item added the \mbox{\hyperlink{group__misc__functions_ga6b1422bc842cbf53cf2bb53ef9322209}{get\+\_\+parse\+\_\+options()}} function so that parse options in the current \mbox{\hyperlink{class_qore_1_1_program}{Program}} can be determined at runtime \item added the \mbox{\hyperlink{group__misc__functions_gaaa60e9a984c59e662b2e7cac84a3899d}{get\+\_\+ex\+\_\+pos()}} function to help with formatting exception locations where the {\ttfamily source} and {\ttfamily offset} information is present \item new methods and method variants\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_socket_aa7bd4b05c84b9ce41078abd86ba6c223}{Qore\+::\+H\+T\+T\+P\+Client\+::get\+Peer\+Info()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a36d7bde2fa763acc9a84673a6193e48b}{Qore\+::\+H\+T\+T\+P\+Client\+::get\+Socket\+Info()}} \item \mbox{\hyperlink{class_qore_1_1_file_a0a9d380a83dc9e70f143c8ad1f85c7b4}{Qore\+::\+File\+::get\+Terminal\+Attributes()}} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_afb6307ab9be490fa5d770519bca9447c}{Qore\+::\+S\+Q\+L\+::\+Datasource\+::transaction\+Tid()}} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_a5661e26369193015c195166e52c6d121}{Qore\+::\+S\+Q\+L\+::\+Datasource\+::current\+Thread\+In\+Transaction()}} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_ac983fd7cd64d2de924113b8cb540ca11}{Qore\+::\+S\+Q\+L\+::\+Datasource\+Pool\+::current\+Thread\+In\+Transaction()}} \end{DoxyItemize} \item new location tags {\ttfamily \char`\"{}source\char`\"{}} and {\ttfamily \char`\"{}offset\char`\"{}} added for parse and runtime exceptions to allow for error-\/reporting to display information about files where sections of a source file are parsed; this allows both the label and line offset in the label and the file name and absolute file line position to be reported in exception information \begin{DoxyItemize} \item new parameters added to the following methods and function to accommodate the new location information\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_program_ad59f1b6ce7adaa693086e1b858cbe896}{Program\+::parse()}} \item \mbox{\hyperlink{class_qore_1_1_program_ac943bad226fcf69ce5007b101828f8c1}{Program\+::parse\+Pending()}} \item \mbox{\hyperlink{group__misc__functions_ga11da5fd06dcfa57a48a5381268a52086}{parse()}} \end{DoxyItemize} \item see \mbox{\hyperlink{struct_qore_1_1_exception_info}{Exception Hash}} and \mbox{\hyperlink{struct_qore_1_1_call_stack_info}{Call Stacks}} for new keys in exception and call stack information hashes \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_aeff0dd69a9ef8f228b54ba5543b2e3c6}{Qore\+::zzz8datezzz9\+::format()}} now accepts {\ttfamily \char`\"{}us\char`\"{}} for microseconds (see \mbox{\hyperlink{group__date__and__time__functions_date_formatting}{Date Formatting Codes}}) \item \href{../../modules/SmtpClient/html/index.html}{\texttt{ Smtp\+Client}} module improvements\+: \begin{DoxyItemize} \item added automatic recognition and support of the {\ttfamily \char`\"{}\+S\+T\+A\+R\+T\+T\+L\+S\char`\"{}} command when connecting to an E\+S\+M\+TP server; this way the class will automatically upgrade the connection to a secure T\+L\+S/\+S\+SL connection if the server supports it \item added support for S\+M\+TP server schemes in the U\+RL in the constructor (ex\+: {\ttfamily \char`\"{}esmtptls\+://user@password\+:smtp.\+example.\+com\char`\"{}}) \item added support for the deprecated (but still in use) {\ttfamily \char`\"{}smtps\char`\"{}} scheme with a default port of 465 \item when throwing an exception when a Message cannot be sent because it is incomplete, the reason for the error is also included in the exception (previously the exception message was generic making problems with the Message object harder to debug) \end{DoxyItemize} \item C++ A\+PI Enhancements \begin{DoxyItemize} \item added C++ A\+P\+Is to allow for Qore \mbox{\hyperlink{class_qore_1_1_file}{File}} and \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}} object arguments to be used by modules \item added C++ A\+P\+Is for controlling openssl initialization and cleanup by the qore library \item extended qpp to allow for parsing relative dates in qpp code for assignments/default argument values \item made it possible to call the C++ function Qore\+Function\+::find\+Variant() from threads where there is no current Qore\+Program object (such as from a thread created by foreign code) \item added A\+P\+Is to allow foreign threads to be registered/deregistered as Qore threads (for example, to allow Qore code to be called in a callback in a foreign thread created by a library linked with a Qore binary module) \item added A\+P\+Is to allow for T\+ID reservations to allow (for example) for a callback that is executed in the same foreign thread to always have the same T\+ID \item the old Datasource\+::exec\+Raw() function with the {\itshape args} parameter was deprecated since args was ignored anyway, a new Datasource\+::exec\+Raw() function was added that has no args parammeter \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_087_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_087_bug_fixes} \begin{DoxyItemize} \item fixed a runtime class matching bug when identical user classes were created in different \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects, the match could fail at runtime because the wrong A\+P\+Is were being used \item fixed a crashing bug in the \mbox{\hyperlink{operators_map}{map}} operator with a select expression when used with an \mbox{\hyperlink{class_qore_1_1_abstract_iterator}{Abstract\+Iterator}} object for the list operand \item fixed a bug where the generation of internal strings for abstract method signatures tries to resolve class names that are declared out of order, which incorrectly resulted in a parse exception; the fix is to use the class name in the signature before class resolution; the class is resolved in the second stage of parsing (symbol resolution) anyway, if it can\textquotesingle{}t be resolved then the changes to the \mbox{\hyperlink{class_qore_1_1_program}{Program}} are rolled back anyway \item a potential deadlock was fixed when calling \mbox{\hyperlink{namespace_qore_a3ec32747f455642fd9ce503094a5cc85}{exit()}} while background threads were running; it was possible for a thread to be canceled while holding a \mbox{\hyperlink{class_qore_1_1_thread_1_1_mutex}{Mutex}} (for example) and then for another thread to deadlock trying to acquire the \mbox{\hyperlink{class_qore_1_1_thread_1_1_mutex}{Mutex}} and therefore for the process to deadlock because pthread\+\_\+mutex\+\_\+lock() is not a cancellation point. The solution was to cancel all threads first, then wait half a second, then call exit() \item fixed a bug where global variables were being evaluated with strict mathematical boolean evaluation even when \mbox{\hyperlink{parse_directives_perl-bool-eval}{\%perl-\/bool-\/eval}} was enabled (which is the default) \item fixed bug in \mbox{\hyperlink{group__misc__functions_ga1e6e24f780713c4d10cb9b98fa45cd35}{Qore\+::parse\+Base64\+String()}} and \mbox{\hyperlink{group__misc__functions_ga1f1a63790a7c60a3a61c5d1569fe4e4c}{Qore\+::parse\+Base64\+String\+To\+String()}} when called with an empty string argument; in this case uninitialized memory was returned \item fixed runtime dynamic memory leaks in the \mbox{\hyperlink{operators_select}{Select From List Operator (select)}} and \mbox{\hyperlink{operators_map}{Map Operator (map)}} operators when used with iterators \item do thread-\/specific cleanup in the main thread when cleaning up/shutting down the qore library \item added additional openssl cleanup code for thread-\/local data and when cleaning up the qore library \item fixed a bug matching function/method variants at runtime \item fixed a race condition deleting global dynamic handlers in the \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module \item fixed a bug where declaring an abstract method with parameters and then declaring a concrete reimplementation of the method in a child class with no parameters caused a parse-\/time crash \item fixed a bug where trying to dynamically call a function that does not exist results in a deadlock due to an error where a mutex is not unlocked \item fixed a bug in the \mbox{\hyperlink{class_qore_1_1_socket_adf437ed165c08a1d166756ebe7b5ed4d}{Qore\+::\+Socket\+::send\+H\+T\+T\+P\+Message()}} and \mbox{\hyperlink{class_qore_1_1_socket_a3e3d6f1bda0a9b6aaf92c5859c94a01d}{Qore\+::\+Socket\+::send\+H\+T\+T\+P\+Response()}} methods regarding the timeout parameter \item fixed a bug in an socket S\+SL error message where the method name was printed from non-\/string memory (used wrong ptr for the {\ttfamily \%s} format argument) \item fixed some major crashing bugs related to reference handling; a global variable assigned a reference to a reference to a local variable would cause a crash \item \mbox{\hyperlink{data_type_declarations_reference_type}{reference}} and \mbox{\hyperlink{data_type_declarations_reference_or_nothing_type}{$\ast$reference}} type fixes\+: an error in \mbox{\hyperlink{data_type_declarations_reference_type}{reference}} type handling allowed non-\/reference values to be passed to builtin code expecing references which caused a crash; the \mbox{\hyperlink{data_type_declarations_reference_type}{reference}} and \mbox{\hyperlink{data_type_declarations_reference_or_nothing_type}{$\ast$reference}} types would accept any value type \item attempted to fix a non-\/reproducible bug seen on rhel5 in the \mbox{\hyperlink{class_qore_1_1_socket}{Socket class}} where S\+SL errors would cause the affected thread to go into a infinite loop using 100\% C\+PU \end{DoxyItemize}\hypertarget{release_notes_qore_0862}{}\doxysection{Qore 0.\+8.\+6.\+2}\label{release_notes_qore_0862} \begin{DoxyParagraph}{Release Summary} Iterator improvements and design fixes \end{DoxyParagraph} \hypertarget{release_notes_qore_0862_compatibility}{}\doxysubsection{Changes That Can Affect Backwards-\/\+Compatibility}\label{release_notes_qore_0862_compatibility} \begin{DoxyParagraph}{Fixes for Iterator Class Design Bugs} Iterators, particular regarding the \mbox{\hyperlink{operators_map}{map}} and \mbox{\hyperlink{operators_select}{select}} operators, were implemented in a confusing and inconsistent way; even the qore documentation was incorrect, and examples were given incorrectly. The following changes will break functionality using the badly-\/implemented behavior of iterators before, but since the fix comes fairly soon after the introduction, hopefully this change will not cause too many problems with existing code. All users polled about the iterator changes in this release saw them as positive and desired changes to the language. \begin{DoxyItemize} \item the \mbox{\hyperlink{operators_map}{map}} and \mbox{\hyperlink{operators_select}{select}} operators\textquotesingle{} behavior was changed when used with an \mbox{\hyperlink{class_qore_1_1_abstract_iterator}{Abstract\+Iterator}} object for the list operand; now the implied argument is the result of \mbox{\hyperlink{class_qore_1_1_abstract_iterator_a1f7b94aa7237f59c4f959f4d33333d9a}{Abstract\+Iterator\+::get\+Value()}} instead of the iterator object itself. This addresses a confusing design choice in the original iterator integration with the \mbox{\hyperlink{operators_map}{map}} and \mbox{\hyperlink{operators_select}{select}} operators \item the second boolean argument was removed from the \mbox{\hyperlink{class_qore_1_1_hash_iterator_a842d257239bb77f2989960dbe1ddabc9}{Qore\+::\+Hash\+Iterator\+::constructor}}(hash$<$auto$>$) \char`\"{}\+Hash\+Iterator\+::constructor(hash<auto>)\char`\"{} and \mbox{\hyperlink{class_qore_1_1_hash_reverse_iterator_aefb96e7e14db92d4e94f690e25965a86}{Qore\+::\+Hash\+Reverse\+Iterator\+::constructor}}(hash$<$auto$>$) \char`\"{}\+Hash\+Reverse\+Iterator\+::constructor(hash)\char`\"{} methods; use the new \mbox{\hyperlink{class_qore_1_1_hash_pair_iterator}{Hash\+Pair\+Iterator}} and \mbox{\hyperlink{class_qore_1_1_object_pair_iterator}{Object\+Pair\+Iterator}} classes instead (\mbox{\hyperlink{class_qore_1_1zzz8hashzzz9_aae2e67b218a51791103c21866df5217b}{Qore\+::zzz8hashzzz9\+::pair\+Iterator()}} and \mbox{\hyperlink{class_qore_1_1zzz8objectzzz9_a7d6df627d80aa7f74c7e895fb352c837}{Qore\+::zzz8objectzzz9\+::pair\+Iterator()}}) \item the single boolean argument was removed from \mbox{\hyperlink{class_qore_1_1zzz8hashzzz9_ad9c31b0d467e2a1496f57e3feff505ee}{Qore\+::zzz8hashzzz9\+::iterator()}} and \mbox{\hyperlink{class_qore_1_1zzz8objectzzz9_a7f5a44cdfd0b417a750deafa46980ce8}{Qore\+::zzz8objectzzz9\+::iterator()}}; use \mbox{\hyperlink{class_qore_1_1zzz8hashzzz9_aae2e67b218a51791103c21866df5217b}{Qore\+::zzz8hashzzz9\+::pair\+Iterator()}} and \mbox{\hyperlink{class_qore_1_1zzz8objectzzz9_a7d6df627d80aa7f74c7e895fb352c837}{Qore\+::zzz8objectzzz9\+::pair\+Iterator()}} instead to get the old behavior \end{DoxyItemize} \end{DoxyParagraph} \hypertarget{release_notes_qore_0862_changes}{}\doxysubsection{Changes in Qore}\label{release_notes_qore_0862_changes} \begin{DoxyItemize} \item new iterator classes\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_hash_key_iterator}{Hash\+Key\+Iterator}} \item \mbox{\hyperlink{class_qore_1_1_hash_key_reverse_iterator}{Hash\+Key\+Reverse\+Iterator}} \item \mbox{\hyperlink{class_qore_1_1_hash_pair_iterator}{Hash\+Pair\+Iterator}} \item \mbox{\hyperlink{class_qore_1_1_hash_pair_reverse_iterator}{Hash\+Pair\+Reverse\+Iterator}} \item \mbox{\hyperlink{class_qore_1_1_object_key_iterator}{Object\+Key\+Iterator}} \item \mbox{\hyperlink{class_qore_1_1_object_key_reverse_iterator}{Object\+Key\+Reverse\+Iterator}} \item \mbox{\hyperlink{class_qore_1_1_object_pair_iterator}{Object\+Pair\+Iterator}} \item \mbox{\hyperlink{class_qore_1_1_object_pair_reverse_iterator}{Object\+Pair\+Reverse\+Iterator}} \end{DoxyItemize} \item new pseudo-\/methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8hashzzz9_a4dde09aa84522bbd942d9339c0315ed5}{Qore\+::zzz8hashzzz9\+::key\+Iterator()}} \item \mbox{\hyperlink{class_qore_1_1zzz8hashzzz9_aae2e67b218a51791103c21866df5217b}{Qore\+::zzz8hashzzz9\+::pair\+Iterator()}} \item \mbox{\hyperlink{class_qore_1_1zzz8hashzzz9_aab3d2e6e69d212dbe05de43136f14367}{Qore\+::zzz8hashzzz9\+::context\+Iterator()}} \item \mbox{\hyperlink{class_qore_1_1zzz8objectzzz9_a473b74b10e5acd871ae6cc996e7427a6}{Qore\+::zzz8objectzzz9\+::key\+Iterator()}} \item \mbox{\hyperlink{class_qore_1_1zzz8objectzzz9_a7d6df627d80aa7f74c7e895fb352c837}{Qore\+::zzz8objectzzz9\+::pair\+Iterator()}} \item \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9_a63b832e2f9eb516106c180a52f3cf2fe}{Qore\+::zzz8nothingzzz9\+::key\+Iterator()}} \item \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9_afd1c98eb4d569e29284f0d777306be2a}{Qore\+::zzz8nothingzzz9\+::pair\+Iterator()}} \item \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9_a017185afed46950e373ebfdd2267bb88}{Qore\+::zzz8nothingzzz9\+::context\+Iterator()}} \end{DoxyItemize} \item the internal C++ Qore\+Program\+Helper object has been updated to wait until all background threads in the Qore library have executed before taking the \mbox{\hyperlink{class_qore_1_1_program}{Program}} object out of scope; this allows for callbacks and other code that might be needed by background threads started in user modules (for example) to stay valid until the threads in the user modules also have terminated. Note that this does not affect the case when using \mbox{\hyperlink{parse_directives_exec-class}{\%exec-\/class}} and an application program object goes out of scope with background threads in user modules having non-\/static method call references as callbacks to the application program; see \mbox{\hyperlink{qore_modules_user_module_program_scope}{Program Scope in Object-\/\+Oriented Programs Using User Modules Providing Their Own Threads}} for more information on this topic. \end{DoxyItemize}\hypertarget{release_notes_qore_0861}{}\doxysection{Qore 0.\+8.\+6.\+1}\label{release_notes_qore_0861} \begin{DoxyParagraph}{Release Summary} Major bug fixes and minor new features \end{DoxyParagraph} \hypertarget{release_notes_qore_0861_changes}{}\doxysubsection{Changes in Qore}\label{release_notes_qore_0861_changes} \begin{DoxyItemize} \item updated the \mbox{\hyperlink{parse_directives_try-module}{\%try-\/module}} parse directive to support a variant without an exception variable for usage in \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects where \mbox{\hyperlink{group__parse__options_ga3a99f2973e97f3986630d8204d7b91fd}{Qore\+::\+P\+O\+\_\+\+N\+O\+\_\+\+T\+O\+P\+\_\+\+L\+E\+V\+E\+L\+\_\+\+S\+T\+A\+T\+E\+M\+E\+N\+TS}} is set \item added code to raise an \mbox{\hyperlink{warnings_invalid-operation}{invalid-\/operation}} warning with the \mbox{\hyperlink{operators_elements}{elements operator}} when called with a type that can never return a value with this operator \item updated the \mbox{\hyperlink{class_qore_1_1_file}{File}} class\textquotesingle{}s internal buffer size from 4KB to 16KB which greatly improves read performance \item added new public A\+P\+Is for the Qore\+Number\+Node class to allow for proper de/serialization in external modules \item \href{../../modules/Pop3Client/html/index.html}{\texttt{ Pop3\+Client}} module\+: \begin{DoxyItemize} \item added the Pop3\+Client\+::log\+Password() methods and masked password by default in the debug log \item updated module to v1.\+1 \end{DoxyItemize} \item \href{../../modules/Mime/html/index.html}{\texttt{ Mime}} module\+: \begin{DoxyItemize} \item declared the Multi\+Part\+Message\+::get\+Msg\+And\+Headers() method abstract as originally intended \item added Multi\+Part\+Message\+::parse\+Body() static method \item updated module to v1.\+3 \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_0861_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0861_bug_fixes} \begin{DoxyItemize} \item fixed crashing bugs due to the lack of proper lvalue checks with the expression for the background operator with operators using lvalues with local variables \item fixed rounding of arbitrary-\/precision numeric values for display purposes when the last significant digit is just to the right of the decimal point (ex\+: was displaying 10.\+2 as \char`\"{}11.\char`\"{} for example) \item fixed a race condition in static destruction of the library when a background thread calls exit() that could cause a segfault on exit \item fixed a static memory leak in Program objects when constants contain code references to functions or static methods \item fixed a bug parsing user modules; the Program context was not set properly which could lead to a crash when parsing user modules loaded from the command-\/line or to incorrect parse options when loaded from user Program code \item fixed a bug where the \mbox{\hyperlink{warnings_invalid-operation}{invalid-\/operation}} warning with the \mbox{\hyperlink{operators_keys}{keys operator}} was not being triggered in common cases that should have triggered the warning \item \href{../../modules/MailMessage/html/index.html}{\texttt{ Mail\+Message}} module\+: \begin{DoxyItemize} \item fixed recognizing mime messages with additional text after the version number (ex\+: {\ttfamily \char`\"{}\+Mime-\/\+Version\+: 1.\+0 (\+Mac O\+S X Mail 6.\+2 \textbackslash{}(1499\textbackslash{}))\char`\"{}}) \item fixed a bug setting the content-\/type of message parts (this fix is now in the \href{../../modules/Mime/html/index.html}{\texttt{ Mime}} in the Multi\+Part\+Message\+::get\+Msg\+And\+Headers() method \item fixed multipart message parsing by using Multi\+Part\+Message\+::parse\+Body() in the \href{../../modules/Mime/html/index.html}{\texttt{ Mime}} module; now also parts with subparts are parsed correctly as well \item fixed a bug where the sender and from values were not being set properly when parsing email messages \item updated module to v1.\+0.\+3 \end{DoxyItemize} \end{DoxyItemize}\hypertarget{release_notes_qore_086}{}\doxysection{Qore 0.\+8.\+6}\label{release_notes_qore_086} \begin{DoxyParagraph}{Release Summary} Major new features and a few bug fixes \end{DoxyParagraph} \hypertarget{release_notes_qore_086_compatibility}{}\doxysubsection{Changes That Can Affect Backwards-\/\+Compatibility}\label{release_notes_qore_086_compatibility} \begin{DoxyParagraph}{Perl-\/\+Style Boolean Evaluation} Qore\textquotesingle{}s default boolean evaluation mode was changed from strict mathematical to a more intuitive perl-\/ (and Python-\/) like style. This change was implemented to address one of the oldest design bugs in Qore\+: strict mathematical boolean evaluation. See \mbox{\hyperlink{parse_directives_perl-bool-eval}{\%perl-\/bool-\/eval}} for a description of the new default boolean evaluation mode.~\newline ~\newline To get the old strict mathematical boolean evaluation, use the \mbox{\hyperlink{parse_directives_strict-bool-eval}{\%strict-\/bool-\/eval}} parse option.~\newline ~\newline An example of the change; now the following \mbox{\hyperlink{statements_if}{if statement}} block will be executed as the {\ttfamily {\bfseries{if}}} expression is now evaluated as \mbox{\hyperlink{basic_data_types_True}{True}}\+: \begin{DoxyCode}{0} \DoxyCodeLine{string str = \textcolor{stringliteral}{"hello"};} \DoxyCodeLine{\textcolor{keywordflow}{if} (str)} \DoxyCodeLine{ \mbox{\hyperlink{group__string__functions_ga32070517a9f8a70a32ef48f83a6f128e}{printf}}(\textcolor{stringliteral}{"Qore says hello$\backslash$n"});} \end{DoxyCode} Previously (i.\+e. with \mbox{\hyperlink{parse_directives_strict-bool-eval}{\%strict-\/bool-\/eval}}) the {\ttfamily {\bfseries{if}}} expression above would be evaluated as \mbox{\hyperlink{basic_data_types_False}{False}} because the string value was converted to an integer 0, however as of Qore 0.\+8.\+6 (with the default \mbox{\hyperlink{parse_directives_perl-bool-eval}{perl-\/bool-\/eval}}) it is \mbox{\hyperlink{basic_data_types_True}{True}} since the string is not empty; empty strings and string value {\ttfamily \char`\"{}0\char`\"{}} are evaluated as \mbox{\hyperlink{basic_data_types_False}{False}}.~\newline ~\newline Perhaps counterintuitively (and the reason this was changed to be the default in qore), the chance for regression errors in qore code is very small, because for all cases where the old logic could be applied (meaning excluding cases where the result was always \mbox{\hyperlink{basic_data_types_False}{False}} due to the data types or values being evaluated), the results are the same with the new logic, except for one case; the case where a string has more than one character and begins with a zero (ex\+: {\ttfamily \char`\"{}00\char`\"{}}). In this case, the old logic would always return \mbox{\hyperlink{basic_data_types_False}{False}}, because the value was first converted to an integer {\ttfamily 0}, whereas the new logic will return \mbox{\hyperlink{basic_data_types_True}{True}}. Note that in the case of a string with a single {\ttfamily \char`\"{}0\char`\"{}}, both the old and new boolean logic returns \mbox{\hyperlink{basic_data_types_False}{False}}.~\newline ~\newline Basically with this option set, qore\textquotesingle{}s boolean evaluation becomes like perl\textquotesingle{}s and Python\textquotesingle{}s, whereas any expression that has the following values is \mbox{\hyperlink{basic_data_types_False}{False}}\+: \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}}, \mbox{\hyperlink{basic_data_types_string}{string}} {\ttfamily \char`\"{}0\char`\"{}} and \mbox{\hyperlink{basic_data_types_string}{empty strings}}, \mbox{\hyperlink{basic_data_types_integer}{integer}}, \mbox{\hyperlink{basic_data_types_float}{float}}, and \mbox{\hyperlink{basic_data_types_number}{number}} {\ttfamily 0} (zero), \mbox{\hyperlink{basic_data_types_absolute_dates}{absolute date}} {\ttfamily 1970-\/01-\/01Z} (ie the start of the epoch with an offset of 0), \mbox{\hyperlink{basic_data_types_relative_dates}{relative date}} {\ttfamily 0s} (or any \mbox{\hyperlink{basic_data_types_relative_dates}{relative date}} with a 0 duration), \mbox{\hyperlink{basic_data_types_null}{N\+U\+LL}}, \mbox{\hyperlink{basic_data_types_binary}{empty binary objects}}, \mbox{\hyperlink{container_data_types_hash}{empty hashes}}, and \mbox{\hyperlink{container_data_types_list}{empty lists}}. All other values are \mbox{\hyperlink{basic_data_types_True}{True}}. \end{DoxyParagraph} \begin{DoxyNote}{Note} also affects the \mbox{\hyperlink{group__type__conversion__functions_ga22c89291d4105fcb558f49fe49aeae44}{boolean(any)}} function \end{DoxyNote} \begin{DoxyParagraph}{Changes in the Socket Class} The \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} class was enhanced to support timeouts with non-\/blocking I/O on all send operations; many Socket methods that send data were originally implemented to return an error code on error, however they would also throw exceptions if the socket were not open, so the error handling was inconsistent (exceptions versus return codes).~\newline ~\newline Additionally it was not possible to get error information at all for S\+SL errors if the socket was connected with S\+SL, which, according to Qore\textquotesingle{}s socket design, should be transparent for the programmer.~\newline ~\newline For these reasons the implementation was deemed inconsistent and unintuitive; the change was to add optional timeout parameters to all send methods and to allow the methods to throw exceptions (instead of simply returning -\/1 and not being able to determine the cause of the error in many cases).~\newline ~\newline The following methods were updated to accept optional timeout parameters and throw exceptions on all errors rather than a return code for I/O errors\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_socket_aa5937114e3c3339bf463303d4208ca86}{Qore\+::\+Socket\+::send()}} \item \mbox{\hyperlink{class_qore_1_1_socket_ada01381996dde5eb7dda1562f43fbda9}{Qore\+::\+Socket\+::send\+Binary()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a13a4582d75efdb29305b1b54bf66b31b}{Qore\+::\+Socket\+::sendi1()}} \item \mbox{\hyperlink{class_qore_1_1_socket_aaa62ba419d66dac29d8605c6dd5a7e68}{Qore\+::\+Socket\+::sendi2()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a88a630d0cda97256c4b01c1e8b71d6e3}{Qore\+::\+Socket\+::sendi4()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a8820f3ae73f1ce737aaf88b9cfb3c001}{Qore\+::\+Socket\+::sendi8()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a0139b7e63ce4d06edecdb96d64124511}{Qore\+::\+Socket\+::sendi2\+L\+S\+B()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a69c50668b38e98af23ab9fb07ce9adff}{Qore\+::\+Socket\+::sendi4\+L\+S\+B()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a142489a333f9444b7379ad5b2a365780}{Qore\+::\+Socket\+::sendi8\+L\+S\+B()}} \end{DoxyItemize} \end{DoxyParagraph} \begin{DoxyParagraph}{New Abstract Method in Abstract\+Iterator} The following abstract method was added\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_abstract_iterator_aee1def5d872b487b8917a166d9b263e8}{Qore\+::\+Abstract\+Iterator\+::valid()}} was added (with concrete implementations in all iterator classes derived from this base class delivered with Qore); this method tells if the object is currently pointing to a valid iterator.~\newline ~\newline For any user classes inherting \mbox{\hyperlink{class_qore_1_1_abstract_iterator}{Abstract\+Iterator}} directly (as opposed to another concrete iterator class in Qore, where the method has already been added), a concrete implementation of this method will have to be added as well or that class will become \mbox{\hyperlink{qore_classes_abstract}{abstract}} with this release of Qore. \end{DoxyItemize} \end{DoxyParagraph} \hypertarget{release_notes_qore_086_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_086_new_features} \begin{DoxyParagraph}{Arbitrary-\/\+Precision Numeric Support} Qore now uses the \href{http://www.mpfr.org/}{\texttt{ M\+P\+FR}} and \href{http://gmplib.org}{\texttt{ G\+MP}} libraries to provide arbitrary-\/precision numeric support. This type can be used for high-\/precision mathematics or for storing {\ttfamily N\+U\+M\+E\+R\+IC} (ie {\ttfamily D\+E\+C\+I\+M\+AL} or {\ttfamily N\+U\+M\+B\+ER}) column values when retrieved from databases by Qore D\+BI drivers that support the new capability \mbox{\hyperlink{group__dbi__capabilities_ga8394d1495944bf61d666de40489a038a}{D\+B\+I\+\_\+\+C\+A\+P\+\_\+\+H\+A\+S\+\_\+\+N\+U\+M\+B\+E\+R\+\_\+\+S\+U\+P\+P\+O\+RT}} (previously these values would be retrieved as Qore strings in order to avoid information loss).~\newline ~\newline For more information, see the new \mbox{\hyperlink{basic_data_types_number}{number}} type, \mbox{\hyperlink{data_type_declarations_number_type}{number}}, and \mbox{\hyperlink{class_qore_1_1zzz8numberzzz9}{Qore\+::zzz8numberzzz9}} \end{DoxyParagraph} \begin{DoxyParagraph}{New Csv\+Util Module} The \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module implements the Csv\+File\+Iterator class that allows for easy parsing of csv-\/like text files \end{DoxyParagraph} \begin{DoxyParagraph}{\%try-\/module Parse Directive to Handle Module Load Errors at Parse Time} The new \mbox{\hyperlink{parse_directives_try-module}{\%try-\/module}} parse directive allows for module load errors to be handled at parse time; ex\+: \begin{DoxyCode}{0} \DoxyCodeLine{\%\textcolor{keywordflow}{try}-\/module(\$ex) some-\/module > 1.0} \DoxyCodeLine{ \mbox{\hyperlink{group__string__functions_ga32070517a9f8a70a32ef48f83a6f128e}{printf}}(\textcolor{stringliteral}{"error loading module \%y: \%s: \%s$\backslash$n"}, ex.arg, ex.err, ex.desc);} \DoxyCodeLine{ exit(1);} \DoxyCodeLine{\%endtry} \end{DoxyCode} \end{DoxyParagraph} \begin{DoxyParagraph}{Abstract Class Hierarchy Improvement} As of this version of qore, concrete implementations of \mbox{\hyperlink{qore_classes_abstract}{abstract methods}} no longer have to have exactly the same return type as the abstract method; it is now sufficient that the return type in the concrete method meets a compatibility test with the return type of the abstract method in the parent class.~\newline ~\newline For example the following is now valid (and {\ttfamily My\+Concrete\+Class} is not abstract, whereas previously because the return types in the child class were not exact, {\ttfamily My\+Concrete\+Class} would be considered abstract by qore)\+: \begin{DoxyCode}{0} \DoxyCodeLine{\textcolor{keyword}{class }MyAbstractClass \{} \DoxyCodeLine{ abstract any doSomething();} \DoxyCodeLine{ abstract *string getString();} \DoxyCodeLine{\}} \DoxyCodeLine{} \DoxyCodeLine{\textcolor{keyword}{class }MyConcreteClass inherits MyAbstractClass \{} \DoxyCodeLine{ int doSomething() \{} \DoxyCodeLine{ \textcolor{keywordflow}{return} 1;} \DoxyCodeLine{ \}} \DoxyCodeLine{ string getString() \{} \DoxyCodeLine{ \textcolor{keywordflow}{return} \textcolor{stringliteral}{"hello"};} \DoxyCodeLine{ \}} \DoxyCodeLine{\}} \end{DoxyCode} \end{DoxyParagraph} \begin{DoxyParagraph}{D\+BI Improvements} Three new D\+BI capabilities were implemented, including a new option A\+PI as follows\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__dbi__capabilities_ga8394d1495944bf61d666de40489a038a}{D\+B\+I\+\_\+\+C\+A\+P\+\_\+\+H\+A\+S\+\_\+\+N\+U\+M\+B\+E\+R\+\_\+\+S\+U\+P\+P\+O\+RT}}\+: D\+BI drivers declaring this capability can accept \mbox{\hyperlink{basic_data_types_number}{number}} values and can also return \mbox{\hyperlink{basic_data_types_number}{number}} values, if a D\+BI driver does not declare this capability, then \mbox{\hyperlink{basic_data_types_number}{number}} values sent for binding by value are automatically converted to \mbox{\hyperlink{basic_data_types_float}{float}} values before being sent to the driver \item \mbox{\hyperlink{group__dbi__capabilities_ga428f8f4909b2737d03593d8808fe2227}{D\+B\+I\+\_\+\+C\+A\+P\+\_\+\+H\+A\+S\+\_\+\+O\+P\+T\+I\+O\+N\+\_\+\+S\+U\+P\+P\+O\+RT}}\+: this indicates that the driver supports the new option A\+PI, allowing options to be set on each connection. See the following for more information\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_serializable_a7bbf6cf2d7ac53a80e8023790c540c5f}{Datasource\+::constructor(hash)}}\+: now passes options to the D\+BI driver if the driver supports the option A\+PI \item \mbox{\hyperlink{class_qore_1_1_serializable_a7bbf6cf2d7ac53a80e8023790c540c5f}{Datasource\+::constructor(string)}}\+: (new in 0.\+8.\+6) passes options to the D\+BI driver if the driver supports the option A\+PI \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_a34834d2da5e1e8f13949810e76a6e1cd}{Datasource\+::get\+Option(string)}}\+: (new in 0.\+8.\+6) returns the value of the given option if the driver supports the option A\+PI \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_ac78f3f07aff86117dbe3808b5d2d7757}{Datasource\+::get\+Option\+Hash()}}\+: (new in 0.\+8.\+6) returns a hash of the current option values for the current connection if the driver supports the option A\+PI \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_ad64b2409e602054d6e29257442b8601e}{Datasource\+::set\+Option()}}\+: (new in 0.\+8.\+6) allows options to be changed after the object is created \item \mbox{\hyperlink{class_qore_1_1_serializable_a7bbf6cf2d7ac53a80e8023790c540c5f}{Datasource\+Pool\+::constructor(hash)}}\+: now passes options to the D\+BI driver if the driver supports the option A\+PI \item \mbox{\hyperlink{class_qore_1_1_serializable_a7bbf6cf2d7ac53a80e8023790c540c5f}{Datasource\+Pool\+::constructor(string)}}\+: (new in 0.\+8.\+6) passes options to the D\+BI driver if the driver supports the option A\+PI \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_abf16cc3f2c883bae4e0e6896e6ee2f69}{Datasource\+Pool\+::get\+Option(string)}}\+: (new in 0.\+8.\+6) returns the value of the given option if the driver supports the option A\+PI \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool_a7e229e19a615801165728ce76f88eb52}{Datasource\+Pool\+::get\+Option\+Hash()}}\+: (new in 0.\+8.\+6) returns a hash of the current option values for the current connection if the driver supports the option A\+PI \item \mbox{\hyperlink{group__old__dbi__functions_gafc8e6e00000f5c1a029f69d43dc66f82}{dbi\+\_\+get\+\_\+driver\+\_\+options(string)}}\+: (new in 0.\+8.\+6) returns a hash of driver option information without values \end{DoxyItemize} \item \mbox{\hyperlink{group__dbi__capabilities_ga9edf0826e734f77115fd8f1001cf4a9e}{D\+B\+I\+\_\+\+C\+A\+P\+\_\+\+S\+E\+R\+V\+E\+R\+\_\+\+T\+I\+M\+E\+\_\+\+Z\+O\+NE}}\+: indicates that the D\+BI driver will convert any bound date/time values to the server\textquotesingle{}s time zone before binding and also will tag date/time values retrieved from the server with the server\textquotesingle{}s time zone. This capability also implies that the driver supports the new {\ttfamily \char`\"{}timezone\char`\"{}} option. \end{DoxyItemize} \end{DoxyParagraph} \begin{DoxyParagraph}{Socket Improvements} The \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} class was updated to support non-\/blocking I/O on all send methods; the following methods were updated to accept optional timeout parameters\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_socket_ab98b2101a71b7660d6d2bad57988d0ef}{Qore\+::\+Socket\+::send2()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a681a441f39cea6a337902a90f4cc897f}{Qore\+::\+Socket\+::send\+Binary2()}} \item \mbox{\hyperlink{class_qore_1_1_socket_adf437ed165c08a1d166756ebe7b5ed4d}{Qore\+::\+Socket\+::send\+H\+T\+T\+P\+Message()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a3e3d6f1bda0a9b6aaf92c5859c94a01d}{Qore\+::\+Socket\+::send\+H\+T\+T\+P\+Response()}} \end{DoxyItemize}The following methods were enhanced to provide better error information when throwing exceptions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_socket_a9c362b07b1d06fce22bde3e6a888832d}{Qore\+::\+Socket\+::recvi1()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a4fba2fa5a88c8c9694c3557056116738}{Qore\+::\+Socket\+::recvi2()}} \item \mbox{\hyperlink{class_qore_1_1_socket_ac8ca3e12a7616dcad149754ffe8342ea}{Qore\+::\+Socket\+::recvi4()}} \item \mbox{\hyperlink{class_qore_1_1_socket_adc8295d79e2288b2e8c5143ac270d08c}{Qore\+::\+Socket\+::recvi8()}} \item \mbox{\hyperlink{class_qore_1_1_socket_ae243f8377cd00cf9be553a1cefc27b12}{Qore\+::\+Socket\+::recvi2\+L\+S\+B()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a6101e09f33fe75e8404c612177fff54c}{Qore\+::\+Socket\+::recvi4\+L\+S\+B()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a7d107840ba3dbac1bd621179a89b121a}{Qore\+::\+Socket\+::recvi8\+L\+S\+B()}} \item \mbox{\hyperlink{class_qore_1_1_socket_ab77e7118003c6ae4baac594ffd91d980}{Qore\+::\+Socket\+::recvu1()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a2866c8093c3cdd5216bf01c768054e7e}{Qore\+::\+Socket\+::recvu2()}} \item \mbox{\hyperlink{class_qore_1_1_socket_adbd053f544a6da11c74fa489ac1bbc14}{Qore\+::\+Socket\+::recvu4()}} \item \mbox{\hyperlink{class_qore_1_1_socket_aa1ea4a31ed5e4a0c1858bfd4e754eee0}{Qore\+::\+Socket\+::recvu2\+L\+S\+B()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a4cd9d50e0649da38ee3292e349f22b7a}{Qore\+::\+Socket\+::recvu4\+L\+S\+B()}} \end{DoxyItemize} \end{DoxyParagraph} \begin{DoxyParagraph}{Iterator Improvements} The following improvements were made in qore to support more flexible and ubiquitous iterators\+: \begin{DoxyItemize} \item new iterator classes\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_single_value_iterator}{Single\+Value\+Iterator}}\+: allows single values (or any value without an iterator class) to be iterated; this provides the basis for the return type for the new base \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_a16b7eeea1bb08b7c3faa69b2aa602fbb}{Qore\+::zzz8valuezzz9\+::iterator()}} method for non-\/container types \item \mbox{\hyperlink{class_qore_1_1_file_line_iterator}{File\+Line\+Iterator}}\+: allows files to be iterated line by line \item \mbox{\hyperlink{class_qore_1_1_object_iterator}{Object\+Iterator}}\+: a generic iterator for objects \item \mbox{\hyperlink{class_qore_1_1_object_reverse_iterator}{Object\+Reverse\+Iterator}}\+: a generic reverse iterator for objects \item \mbox{\hyperlink{class_qore_1_1_range_iterator}{Range\+Iterator}}\+: a numerical sequence generator (the basis for the return type for the new \mbox{\hyperlink{group__range__functions_gad5b4d3ad3f6c36d2e714bc6ed757a507}{xrange()}} function \end{DoxyItemize} \item new pseudo-\/methods were added to return iterator objects based on the value type\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_a16b7eeea1bb08b7c3faa69b2aa602fbb}{Qore\+::zzz8valuezzz9\+::iterator()}} \item \mbox{\hyperlink{class_qore_1_1zzz8hashzzz9_ad9c31b0d467e2a1496f57e3feff505ee}{Qore\+::zzz8hashzzz9\+::iterator()}} \item \mbox{\hyperlink{class_qore_1_1zzz8listzzz9_ac8e243d7957d6136a6c77d32f320bf24}{Qore\+::zzz8listzzz9\+::iterator()}} \item \mbox{\hyperlink{class_qore_1_1zzz8objectzzz9_a7f5a44cdfd0b417a750deafa46980ce8}{Qore\+::zzz8objectzzz9\+::iterator()}} \end{DoxyItemize}The base pseudo-\/method (\mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_a16b7eeea1bb08b7c3faa69b2aa602fbb}{Qore\+::zzz8valuezzz9\+::iterator()}}) ensures that any value can be iterated, and the type-\/specific methods ensure that the most suitable iterator for container types is returned for container values; values without an iterator class are iterated with the \mbox{\hyperlink{class_qore_1_1_single_value_iterator}{Single\+Value\+Iterator}} \item the \mbox{\hyperlink{class_qore_1_1_hash_iterator}{Hash\+Iterator}} and \mbox{\hyperlink{class_qore_1_1_hash_reverse_iterator}{Hash\+Reverse\+Iterator}} classes had an additional optional boolean argument added to their constructors; if \mbox{\hyperlink{basic_data_types_True}{True}}, then the \mbox{\hyperlink{class_qore_1_1_hash_iterator_ac476d576e747b685d4284fb02a5cf83e}{Hash\+Iterator\+::get\+Value()}} and \mbox{\hyperlink{class_qore_1_1_hash_iterator_ac476d576e747b685d4284fb02a5cf83e}{Hash\+Reverse\+Iterator\+::get\+Value()}} methods return a hash with the following keys\+: {\ttfamily \char`\"{}key\char`\"{}} and {\ttfamily \char`\"{}value\char`\"{}}, allowing for more convenient iteration with constructions that only use {\ttfamily get\+Value()} methods (such as the \mbox{\hyperlink{statements_foreach}{foreach statement}}); to accommodate this, two new methods were added to the \mbox{\hyperlink{class_qore_1_1_hash_iterator}{Hash\+Iterator}} base class\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_hash_iterator_a0d62ed2e642f1f9f0fc06cbd2d79b14b}{Qore\+::\+Hash\+Iterator\+::get\+Key\+Value()}} \item \mbox{\hyperlink{class_qore_1_1_hash_iterator_a1300d0cec84d5f08b89fdc3d18f1f229}{Qore\+::\+Hash\+Iterator\+::get\+Value\+Pair()}} \end{DoxyItemize} \item all iterator classes had copy methods added to them (ex\+: \mbox{\hyperlink{class_qore_1_1_hash_iterator_ae35efa6b6afd35bc56fdddd9d5622059}{Qore\+::\+Hash\+Iterator\+::copy()}}) \item new Python-\/inspired \mbox{\hyperlink{group__list__functions_gaad3b9056f1b0dfef032d130c7500f517}{range()}} and \mbox{\hyperlink{group__range__functions_gad5b4d3ad3f6c36d2e714bc6ed757a507}{xrange()}} functions (the latter returning a \mbox{\hyperlink{class_qore_1_1_range_iterator}{Range\+Iterator}} object to efficiently iterate large integral sequences or ranges \end{DoxyItemize} \end{DoxyParagraph} \begin{DoxyParagraph}{Text File Parsing Enhancements} The following improvements were made in qore to support more flexible file parsing\+: \begin{DoxyItemize} \item the \mbox{\hyperlink{class_qore_1_1_read_only_file}{Qore\+::\+Read\+Only\+File}} class was added as a parent class of \mbox{\hyperlink{class_qore_1_1_file}{Qore\+::\+File}} to allow for a more convenient A\+PI for reading files (the \mbox{\hyperlink{class_qore_1_1_file}{Qore\+::\+File}} class\textquotesingle{}s A\+PI remains the same as it publically inherits \mbox{\hyperlink{class_qore_1_1_read_only_file}{Qore\+::\+Read\+Only\+File}}) \item the \mbox{\hyperlink{class_qore_1_1_read_only_file_a3407127e38d2a2ffe3c473d02561f788}{Read\+Only\+File\+::read\+Line()}} method (formerlly a method of the \mbox{\hyperlink{class_qore_1_1_file}{Qore\+::\+File}} class) was enhanced to accept 2 optional arguments, allowing the end of line character(s) to be stripped from the line returned, and also to allow the end of line characters to be specified. If no end of line characters are specified, then the method automatically determines the end of line characters (can be {\ttfamily \char`\"{}\textbackslash{}n\char`\"{}}, {\ttfamily \char`\"{}\textbackslash{}r\char`\"{}}, or {\ttfamily \char`\"{}\textbackslash{}r\textbackslash{}n\char`\"{}}; the last one only if the underlying file is not a T\+TY in order to avoid stalling I/O on an interactive T\+TY) \item the \mbox{\hyperlink{group__file__stat__constants}{File Stat Constants}} were moved from the \mbox{\hyperlink{class_qore_1_1_file}{Qore\+::\+File}} class to the \mbox{\hyperlink{class_qore_1_1_read_only_file}{Qore\+::\+Read\+Only\+File}} class \item added a new \mbox{\hyperlink{class_qore_1_1_file_line_iterator}{File\+Line\+Iterator}} iterator class \item added a new optional parameter to \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a34c43c49f859529054ef495eb395e6bb}{Qore\+::zzz8stringzzz9\+::split(string, string, bool)}} and \mbox{\hyperlink{group__string__functions_gad3db83c0fd5df500b0cc9d2ddb0e7d85}{Qore\+::split(string, string, string, bool)}} to allow for automatic stripping unquoted fields of leading and trailing whitespace (the default is the old behavior; i.\+e. leave the whitespace as it is read) \item added a new \mbox{\hyperlink{class_qore_1_1_time_zone}{Time\+Zone}} method for parsing string dates in a specific \mbox{\hyperlink{class_qore_1_1_time_zone}{Time\+Zone}}\+: \mbox{\hyperlink{class_qore_1_1_time_zone_ab22bd3acfbfb1d7b7ce56f54c81897c7}{Qore\+::\+Time\+Zone\+::date(string, string)}} \item added a new function for parsing text as a boolean value\+: \mbox{\hyperlink{group__string__functions_ga774b6d0f9d5835de7d7362400aa2cdd1}{parse\+\_\+boolean()}} \item as mentioned above, the new \href{../../modules/CsvUtil/html/index.html}{\texttt{ Csv\+Util}} module was added, implementing the Csv\+File\+Iterator class that allows for easy parsing of csv-\/like text files \end{DoxyItemize} \end{DoxyParagraph} \begin{DoxyParagraph}{Other Improvements and Changes} \begin{DoxyItemize} \item the \mbox{\hyperlink{statements_foreach}{foreach statement}} now iterates objects derived from \mbox{\hyperlink{class_qore_1_1_abstract_iterator}{Abstract\+Iterator}} automatically \item added a \mbox{\hyperlink{group__option__constants_gaad0f8a0998b32e445a8708484acbd100}{H\+A\+V\+E\+\_\+\+S\+Y\+M\+L\+I\+NK}} constant for the symlink() function added in qore 0.\+8.\+5 \item added the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement_af7fe60e95959cc5eb6cf0046adcb9ec6}{S\+Q\+L\+Statement\+::member\+Gate()}} method so \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} objects can be dereferenced directly to a column value when iterated with \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement_a34dfdc4d3aa9d3c38817931986506fbd}{S\+Q\+L\+Statement\+::next()}}; also this method will throw exceptions when an unknown column name is used so that typos in column names can be caught (instead of being silently ignored producing hard to find bugs) \item implemented \mbox{\hyperlink{class_qore_1_1_serializable_a7bbf6cf2d7ac53a80e8023790c540c5f}{Datasource\+::constructor(string)}} and \mbox{\hyperlink{class_qore_1_1_serializable_a7bbf6cf2d7ac53a80e8023790c540c5f}{Datasource\+Pool\+::constructor(string)}} variants to allow for creating datasources from a string that can be parsed by \mbox{\hyperlink{group__old__dbi__functions_ga6c3dab42570887656fc05f5a22eb370a}{Qore\+::\+S\+Q\+L\+::parse\+\_\+datasource(string)}} \char`\"{}parse\+\_\+datasource(string)\char`\"{} \item added the following new D\+B\+I-\/related functions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__old__dbi__functions_gae91b14606e0b3d0ca9155a911ec06a5c}{dbi\+\_\+get\+\_\+driver\+\_\+list()}} \item \mbox{\hyperlink{group__old__dbi__functions_ga2c836575bb7327e5ef81df5dff4799ff}{dbi\+\_\+get\+\_\+driver\+\_\+capability\+\_\+list(string)}} \item \mbox{\hyperlink{group__old__dbi__functions_ga40597983f24f3b0edc06149246d1cbe2}{dbi\+\_\+get\+\_\+driver\+\_\+capabilities(string)}} \item \mbox{\hyperlink{group__old__dbi__functions_gafc8e6e00000f5c1a029f69d43dc66f82}{dbi\+\_\+get\+\_\+driver\+\_\+options(string)}} \item \mbox{\hyperlink{group__old__dbi__functions_ga6c3dab42570887656fc05f5a22eb370a}{parse\+\_\+datasource(string)}} \end{DoxyItemize} \item implemented support for {\ttfamily \char`\"{}\+A\char`\"{}} and {\ttfamily \char`\"{}a\char`\"{}}, (hexadecimal floating-\/point output) {\ttfamily \char`\"{}\+G\char`\"{}}, {\ttfamily \char`\"{}g\char`\"{}}, (compact floating-\/point output) {\ttfamily \char`\"{}\+F\char`\"{}}, (non-\/scientific floating-\/point output) and {\ttfamily \char`\"{}\+E\char`\"{}} and {\ttfamily \char`\"{}e\char`\"{}} (scientific/exponential floating-\/point output) format arguments for \mbox{\hyperlink{basic_data_types_float}{floats}} and \mbox{\hyperlink{basic_data_types_number}{numbers}} (new arbitrary-\/precision \mbox{\hyperlink{basic_data_types_number}{number type values}}); see \mbox{\hyperlink{group__string__functions_string_formatting}{String Formatting}} \item new pseudo-\/methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_a073b50bf1e4e7b646da0d7a6db6180a8}{Qore\+::zzz8valuezzz9\+::to\+String()}} \item \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_aed0897423af7ddcb1ade7df4c4a61364}{Qore\+::zzz8valuezzz9\+::to\+Int()}} \item \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_a11505ca76b6e168b1d143b3fc8d1ba60}{Qore\+::zzz8valuezzz9\+::to\+Float()}} \item \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_a671b4af222d6351eb969c2b1d710d463}{Qore\+::zzz8valuezzz9\+::to\+Bool()}} \item \mbox{\hyperlink{class_qore_1_1zzz8floatzzz9_a456f92c6ee27c0c772223745f918bcbc}{Qore\+::zzz8floatzzz9\+::format(string fmt)}} \item \mbox{\hyperlink{class_qore_1_1zzz8intzzz9_a4f4b203fef4e2ae785f838c98e5995be}{Qore\+::zzz8intzzz9\+::format(string fmt)}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a766250b7a8d910b7facce5bef7cfe855}{Qore\+::zzz8stringzzz9\+::is\+Data\+Ascii()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_ae568ad566fc87c944a64d6ce67dd3d16}{Qore\+::zzz8stringzzz9\+::is\+Data\+Printable\+Ascii()}} \item \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_a3bd7145235f0f4160b29e9ff1a925f4f}{Qore\+::zzz8valuezzz9\+::callp()}} \item \mbox{\hyperlink{class_qore_1_1zzz8callrefzzz9_a51595cfbda83bbed8fe486c744728c8b}{Qore\+::zzz8callrefzzz9\+::callp()}} \item \mbox{\hyperlink{class_qore_1_1zzz8intzzz9_aa7540bc9c4c5e8b3ba79e853c462c863}{Qore\+::zzz8intzzz9\+::sign()}} \item \mbox{\hyperlink{class_qore_1_1zzz8floatzzz9_ab12fc9ef4d1d45cbad74ac1558ec754e}{Qore\+::zzz8floatzzz9\+::sign()}} \end{DoxyItemize} \item the value of the \mbox{\hyperlink{group__sql__constants_ga8d5c7d08373364f4773f65e69063cd04}{N\+U\+M\+B\+ER}}, \mbox{\hyperlink{group__sql__constants_ga223c3ce9da5ccb29dd35eab11f161f9f}{N\+U\+M\+E\+R\+IC}}, and \mbox{\hyperlink{group__sql__constants_ga85bba3f8e978509f66f08011b264e9b0}{D\+E\+C\+I\+M\+AL}} \mbox{\hyperlink{group__sql__constants}{S\+QL Constants}} is now {\ttfamily \char`\"{}number\char`\"{}} instead of {\ttfamily \char`\"{}string\char`\"{}} (see also \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_sql_binding}{sql\+\_\+binding}}) \item new constants\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__math__constants_ga2326203043f44a1fe37ffebe35ab8513}{M\+\_\+\+P\+In}} \item \mbox{\hyperlink{group__math__constants_ga96d58fec2ca2cec95893872b16b84daa}{M\+A\+X\+I\+NT}} \item \mbox{\hyperlink{group__math__constants_gaba64488e1020a48909a9a33bb1f4e6ab}{M\+I\+N\+I\+NT}} \end{DoxyItemize} \item new functions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__list__functions_gaad3b9056f1b0dfef032d130c7500f517}{range()}} \item \mbox{\hyperlink{group__range__functions_gad5b4d3ad3f6c36d2e714bc6ed757a507}{xrange()}} \end{DoxyItemize} \item new methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_read_only_file_afd64015ff14cb58d2f2c365d36a9c85c}{Qore\+::\+Read\+Only\+File\+::is\+Tty()}} and \mbox{\hyperlink{class_qore_1_1_read_only_file_a9b323248355ff9dc2048ea913664e111}{Qore\+::\+Read\+Only\+File\+::get\+File\+Name()}} (the \mbox{\hyperlink{class_qore_1_1_read_only_file}{Qore\+::\+Read\+Only\+File}} class was added in qore 0.\+8.\+6 otherwise made up of methods formerly belonging to the \mbox{\hyperlink{class_qore_1_1_file}{Qore\+::\+File}} class) \end{DoxyItemize} \item added the \mbox{\hyperlink{parse_directives_append-module-path}{\%append-\/module-\/path}} parse directive \item \mbox{\hyperlink{qore_modules_user_modules}{user modules}} may now use \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects for embedded logic; any \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects created in a \mbox{\hyperlink{qore_modules_user_modules}{user module}} will have its parse options masked to be not less restrictive than the parse options in the current \mbox{\hyperlink{class_qore_1_1_program}{Program}}, and additionally parse options will be locked so that user module are not able to circumvent function restrictions imposed by parse options. \item updated docs to show functional restrictions tagged at the class level \end{DoxyItemize} \end{DoxyParagraph} \hypertarget{release_notes_qore_086_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_086_bug_fixes} \begin{DoxyItemize} \item fixed a bug in the \mbox{\hyperlink{operators_map}{map operator}} with a select expression when the list operand is \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}}; it was returning a list with one \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} element instead of \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} \item applied a patch by Reini Urban to allow for multi-\/arch builds on Debian \item fixed bugs calculating the byte offset for string searches in the c++ Qore\+String\+::index() and Qore\+String\+::rindex() functions when the offset is negative and the strings have a multi-\/byte character encoding (such as U\+T\+F-\/8) \item fixed a bug where calling an abstract method from a class where the abstract method is implemented was causing a parse error to be thrown \item fixed a bug where the wrong source code location was displayed when raising a parse exception in operator expression parse initialization for some operators \item fixed bugs in regexes in the Http\+Server\+::add\+Listeners() and Http\+Server\+::add\+Listeners\+With\+Handler() methods (\href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}} module version updated to 0.\+3.\+5) \item fixed bugs handling non-\/blocking reads in the \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} class; the timeout setting was only enforced for the first read; subsequent reads were made as blocking reads \item fixed a bug in the \mbox{\hyperlink{class_qore_1_1_socket}{Socket}} class when the S\+SL session requires renegotiation during non-\/blocking I/O \item \mbox{\hyperlink{class_qore_1_1_file_a3ebb12df5983eddf42394bce5033aa75}{File\+::constructor()}} now throws an exception if called with a tty target and \mbox{\hyperlink{parse_directives_no-terminal-io}{\%no-\/terminal-\/io}} is set \item fixed a bug in split with quote (\mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a34c43c49f859529054ef495eb395e6bb}{Qore\+::zzz8stringzzz9\+::split(string, string, bool)}} and \mbox{\hyperlink{group__string__functions_gad3db83c0fd5df500b0cc9d2ddb0e7d85}{Qore\+::split(string, string, string, bool)}}) if the separator pattern was not found and the single field was not quoted either \item fixed a bug handling nested \mbox{\hyperlink{parse_directives_ifdef}{\%ifdef}} and \mbox{\hyperlink{parse_directives_ifndef}{\%ifndef}} blocks with \mbox{\hyperlink{parse_directives_else}{\%else}} in the inside block \item fixed a crashing due to the failure to clear the \char`\"{}\+P\+F\+\_\+\+T\+O\+P\+\_\+\+L\+E\+V\+E\+L\char`\"{} flag when initializing statements, this could cause temporary variables in a statement to be marked as the start of the global thread-\/local variable list, and then after such variables are deleted, then a crash happens when trying to access the global thread-\/local variable list \item fixed a crashing bug at parse time merging function lists in namespaces declared multiple times \item fixed a bug in executing user module init() closures \item fixed a bug where the qore library could crash when destroying a Program object due to a race condition in removing signal handlers managed by the Program object; the Program calls the signal handler manager to remove the signals, but the signals can be removed concurrently to the request while the Program object is iterating the signal set (ie it is modified while being iterated), which causes a crash \item added code to detect when the same namespace is declared both with and without the \mbox{\hyperlink{qore_modules_mod_public}{public keyword}} when defining user modules which can result in entire namespaces being silently not exported (and can be difficult to debug); now a parse exception is thrown if this happens while parsing a user module \item added code tags to \mbox{\hyperlink{class_qore_1_1_file}{File}} methods without side effects \item made many minor documentation fixes \end{DoxyItemize}\hypertarget{release_notes_qore_0851}{}\doxysection{Qore 0.\+8.\+5.\+1}\label{release_notes_qore_0851} \begin{DoxyParagraph}{Release Summary} Bugfix release \end{DoxyParagraph} \hypertarget{release_notes_qore_0851_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_0851_bug_fixes} \begin{DoxyItemize} \item fixed a race condition accessing global and closure-\/bound thread-\/local variables in multithreaded contexts \item fixed a bug in transaction management with the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_datasource_pool}{Datasource\+Pool}} class when used with the \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} class \item fixed an error in the \href{../../modules/MailMessage/html/index.html}{\texttt{ Mail\+Message}} user module where mail headers requiring encoding were not encoded and those not requiring encoding were encoded with Q encoding \item fixed an error in the \href{../../modules/Mime/html/index.html}{\texttt{ Mime}} user module where {\ttfamily \char`\"{}\+\_\+\char`\"{}} characters in q-\/encoded headers were not encoded correctly \end{DoxyItemize} \DoxyHorRuler{0} \hypertarget{release_notes_qore_085}{}\doxysection{Qore 0.\+8.\+5}\label{release_notes_qore_085} \begin{DoxyParagraph}{Release Summary} Major new features and a few bug fixes \end{DoxyParagraph} \hypertarget{release_notes_qore_085_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_085_new_features} \begin{DoxyParagraph}{Abstract Methods and Interfaces} Qore now supports the {\bfseries{abstract}} keyword when declaring methods; an {\bfseries{abstract}} method has no implementation and must be implemented in child classes with the same signature for the child class to be instantiated.~\newline ~\newline Classes with {\bfseries{abstract}} methods define interfaces; a concrete implementation of the interface is a class that inherits the class with {\bfseries{abstract}} methods and implements all the {\bfseries{abstract}} methods.~\newline ~\newline Abstract methods are defined with the following syntax\+: \begin{DoxyCode}{0} \DoxyCodeLine{\textcolor{keyword}{class }MyAbstractInterface \{} \DoxyCodeLine{ abstract string doSomething(int param);} \DoxyCodeLine{ abstract bool checkSomething(string arg);} \DoxyCodeLine{\}} \end{DoxyCode} The following abstract classes now exist in Qore\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_abstract_datasource}{Abstract\+Datasource}} \item \mbox{\hyperlink{class_qore_1_1_abstract_iterator}{Abstract\+Iterator}} \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_abstract_quantified_iterator}{Abstract\+Quantified\+Iterator}} \item \mbox{\hyperlink{class_qore_1_1_abstract_bidirectional_iterator}{Abstract\+Bidirectional\+Iterator}} \item \mbox{\hyperlink{class_qore_1_1_abstract_quantified_bidirectional_iterator}{Abstract\+Quantified\+Bidirectional\+Iterator}} \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_thread_1_1_abstract_smart_lock}{Abstract\+Smart\+Lock}} (which was already present in Qore but now implements abstract methods) \end{DoxyItemize}The following new iterator classes have been added to Qore\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_hash_iterator}{Hash\+Iterator}} \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_hash_reverse_iterator}{Hash\+Reverse\+Iterator}} \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_hash_list_iterator}{Hash\+List\+Iterator}} \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_hash_list_reverse_iterator}{Hash\+List\+Reverse\+Iterator}} \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_list_hash_iterator}{List\+Hash\+Iterator}} \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_list_hash_reverse_iterator}{List\+Hash\+Reverse\+Iterator}} \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_list_iterator}{List\+Iterator}} \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_list_reverse_iterator}{List\+Reverse\+Iterator}} \end{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_s_q_l_1_1_s_q_l_statement}{S\+Q\+L\+Statement}} (which was already present in Qore but now implements the \mbox{\hyperlink{class_qore_1_1_abstract_iterator}{Abstract\+Iterator}} interface to allow query results to be iterated) \end{DoxyItemize}Classes inheriting \mbox{\hyperlink{class_qore_1_1_abstract_iterator}{Abstract\+Iterator}} have special support so that objects can be easily iterated in the following list operators\+: \begin{DoxyItemize} \item \mbox{\hyperlink{operators_map}{Map Operator (map)}} \item \mbox{\hyperlink{operators_foldr}{Fold Right Operator (foldr)}} and \mbox{\hyperlink{operators_foldl}{Fold Left Operator (foldl)}} \item \mbox{\hyperlink{operators_select}{Select From List Operator (select)}} \end{DoxyItemize} \end{DoxyParagraph} \begin{DoxyParagraph}{Universal References} All restrictions on references have been removed from Qore; references to local variables may now be passed to the \mbox{\hyperlink{operators_background}{background operator}} and passed as arguments to \mbox{\hyperlink{expressions_closure}{closures}}.~\newline ~\newline Basically when a reference is taken of a local variable that could result in the local variable being accessed in a multi-\/threaded context, the variable is treated as a closure-\/bound local variable in the sense that it\textquotesingle{}s lifetime is reference-\/counted, and all accesses are wrapped in a dedicated mutual-\/exclusion lock to ensure thread safety. \end{DoxyParagraph} \begin{DoxyParagraph}{Pop3\+Client Module} A \href{../../modules/Pop3Client/html/index.html}{\texttt{ Pop3\+Client}} module has been added providing an A\+PI for communicating with \href{http://en.wikipedia.org/wiki/Post_Office_Protocol}{\texttt{ P\+O\+P3}} servers and retrieving email messages.~\newline ~\newline The module uses functionality provided by the new \href{../../modules/MailMessage/html/index.html}{\texttt{ Mail\+Message}} module to represent email messages (and attachment data) downloaded from the server. \end{DoxyParagraph} \begin{DoxyParagraph}{Mail\+Message Module} The \href{../../modules/MailMessage/html/index.html}{\texttt{ Mail\+Message}} module provides common functionality to the \href{../../modules/Pop3Client/html/index.html}{\texttt{ Pop3\+Client}} and \href{../../modules/SmtpClient/html/index.html}{\texttt{ Smtp\+Client}} modules to represent email messages for receiving and sending, respectively. This module was created mostly from functionality removed from the \href{../../modules/SmtpClient/html/index.html}{\texttt{ Smtp\+Client}} and enhanced to provide support for reading email messages in the new \href{../../modules/Pop3Client/html/index.html}{\texttt{ Pop3\+Client}} module. \end{DoxyParagraph} \begin{DoxyParagraph}{Smtp\+Client Module Changes} The Message and Attachment classes were removed from the \href{../../modules/SmtpClient/html/index.html}{\texttt{ Smtp\+Client}} module to the \href{../../modules/MailMessage/html/index.html}{\texttt{ Mail\+Message}} module. Backwards-\/compatible definitions for the Message and Attachment classes are provided in the \href{../../modules/SmtpClient/html/index.html}{\texttt{ Smtp\+Client}} module to rexport the removed functionality for backwards compatibility. \end{DoxyParagraph} \begin{DoxyParagraph}{Other Minor Improvements and Changes} \begin{DoxyItemize} \item qpp updated to support abstract methods and multiple inheritance (+ other minor qpp enhancements) \item improved the {\ttfamily Q\+O\+R\+E\+A\+D\+D\+R\+I\+N\+F\+O-\/\+G\+E\+T\+I\+N\+F\+O-\/\+E\+R\+R\+OR} exception description by adding information about the arguments passed \item added a string argument to \mbox{\hyperlink{group__string__functions_gad77c02ae2ce2f5c321b98bb64a0e34c2}{char(softint, $\ast$string)}} to accept an output encoding \item added a \mbox{\hyperlink{group__type__conversion__functions_ga2de8717e92c5f97ccc6511f6062d6502}{int(string, int)}} variant to parse a string as a number and give the base \item added a new parameter to \mbox{\hyperlink{group__misc__functions_ga54e6ccaa8fdaa3213ae5550aa66629c9}{parse\+\_\+url()}} and \mbox{\hyperlink{group__misc__functions_gae1961be84af7e6bc5553049bf978f922}{parse\+U\+R\+L()}} to allow for any \mbox{[}\mbox{]} in the hostname to be included in the {\ttfamily \char`\"{}host\char`\"{}} output key for indicating that the \href{http://wikipedia.org/wiki/IPv6}{\texttt{ ipv6}} protocol be used \item added the following pseudo-\/methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_a6088d2158ce94d0d6c9159a628f79017}{Qore\+::zzz8valuezzz9\+::lsize()}} \item \mbox{\hyperlink{class_qore_1_1zzz8binaryzzz9_a7b9095703570b4cbbd90496367f47286}{Qore\+::zzz8binaryzzz9\+::split()}} \item \mbox{\hyperlink{class_qore_1_1zzz8binaryzzz9_a9eff25da172a81558e0bfab828bf9919}{Qore\+::zzz8binaryzzz9\+::to\+M\+D5()}} \item \mbox{\hyperlink{class_qore_1_1zzz8binaryzzz9_a3f9afb50f2f621c133f11330432561d6}{Qore\+::zzz8binaryzzz9\+::to\+S\+H\+A1()}} \item \mbox{\hyperlink{class_qore_1_1zzz8binaryzzz9_a40a67a7f4d31d72c67f65a71f98e9618}{Qore\+::zzz8binaryzzz9\+::to\+S\+H\+A224()}} \item \mbox{\hyperlink{class_qore_1_1zzz8binaryzzz9_a3fad715400f0b1901a24e727b887d169}{Qore\+::zzz8binaryzzz9\+::to\+S\+H\+A256()}} \item \mbox{\hyperlink{class_qore_1_1zzz8binaryzzz9_a7fa8629838806509270b0a5d48415611}{Qore\+::zzz8binaryzzz9\+::to\+S\+H\+A384()}} \item \mbox{\hyperlink{class_qore_1_1zzz8binaryzzz9_ab3a42f1beda2facfdbd32f465d9b8fe3}{Qore\+::zzz8binaryzzz9\+::to\+S\+H\+A512()}} \item \mbox{\hyperlink{class_qore_1_1zzz8datezzz9_a1946f38ad9528c2e80552b8e2bc39f62}{Qore\+::zzz8datezzz9\+::midnight()}} \item \mbox{\hyperlink{class_qore_1_1zzz8listzzz9_a7d460c5baf4290fac22d521d909e7f12}{Qore\+::zzz8listzzz9\+::first()}} \item \mbox{\hyperlink{class_qore_1_1zzz8listzzz9_a5cb7d0b52f91aca98030ec1926beb5c5}{Qore\+::zzz8listzzz9\+::join()}} \item \mbox{\hyperlink{class_qore_1_1zzz8listzzz9_a89cad7498a6102679b4d2a96d3eceef5}{Qore\+::zzz8listzzz9\+::last()}} \item \mbox{\hyperlink{class_qore_1_1zzz8listzzz9_a66451c32831c9ea7086d2b9fb62df31c}{Qore\+::zzz8listzzz9\+::lsize()}} \item \mbox{\hyperlink{class_qore_1_1zzz8nothingzzz9_a8070849ca746bcb7a7bc3b65b77aeb16}{Qore\+::zzz8nothingzzz9\+::lsize()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a4713c0132472cf5cf6599ad9517cdc5f}{Qore\+::zzz8stringzzz9\+::regex()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_aeaf99b23a4de2db748a1fe0bbc3811f5}{Qore\+::zzz8stringzzz9\+::regex\+Extract()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_afe181b134b4aff3851e3dcb02b9cf7c4}{Qore\+::zzz8stringzzz9\+::split()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_ab5ad54b1fe38b46ee071e55563d9d245}{Qore\+::zzz8stringzzz9\+::substr()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a2c63e2b65aafebf67928b88651d4cd39}{Qore\+::zzz8stringzzz9\+::to\+M\+D5()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a577cc1e9e6cb2f001c36f35a4cff4b74}{Qore\+::zzz8stringzzz9\+::to\+S\+H\+A1()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a3341bfb07348577260ece5244f958caf}{Qore\+::zzz8stringzzz9\+::to\+S\+H\+A224()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a11a362bbdba504966590d68bc6839350}{Qore\+::zzz8stringzzz9\+::to\+S\+H\+A256()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_ae572499e8fe84e24455806ba2556e5c5}{Qore\+::zzz8stringzzz9\+::to\+S\+H\+A384()}} \item \mbox{\hyperlink{class_qore_1_1zzz8stringzzz9_a0a8b0fd0c6dc97af23ad50be3125cb4d}{Qore\+::zzz8stringzzz9\+::to\+S\+H\+A512()}} \end{DoxyItemize} \item added the \href{http://code.google.com/p/xxhash/}{\texttt{ xxhash F\+A\+ST algorithm}} with unordered\+\_\+map to Qore on supported platforms resuling in nearly 2x haster hash lookups \item added the \mbox{\hyperlink{class_qore_1_1_read_only_file_a2744f4642700d0f273efbce43f709fb4}{Qore\+::\+File\+::is\+Open()}} method \item added the \mbox{\hyperlink{group__object__functions_ga94ac4c8106c0f948e95f3e445d7909ad}{Qore\+::call\+\_\+pseudo()}} function to explicitly call a pseudo method on a value \item added the \mbox{\hyperlink{namespace_qore_ae895213e0d9f207ab855e4546c791909}{Qore\+::symlink()}} function to create symbolic links \item added \mbox{\hyperlink{group__type__code__map__constants_ga2a480ee5f1ba574e58391be1b3a0eb24}{Qore\+::\+Type\+Code\+Map}} and \mbox{\hyperlink{group__type__code__map__constants_gabd2d01582297bf26346d7fd7e81163cd}{Qore\+::\+Type\+Name\+Map}} to lookup type codes from type names and vice versa \item added the following functions to allow the time zone to be set per thread\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__threading__functions_ga07fcdce92cacc7cea4b92504a737d7c2}{Qore\+::set\+\_\+thread\+\_\+tz()}} \item \mbox{\hyperlink{group__threading__functions_gad86831d8ae7b5b1d35e9bb14dc9f6325}{Qore\+::get\+\_\+thread\+\_\+tz()}} \end{DoxyItemize} \end{DoxyItemize} \end{DoxyParagraph} \hypertarget{release_notes_qore_085_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_085_bug_fixes} \begin{DoxyItemize} \item fixed \mbox{\hyperlink{group__date__and__time__functions_gad5572fcb49964bfe3005e144da579361}{format\+\_\+date()}} output for {\ttfamily \char`\"{}\+M\+O\+N\char`\"{}} and {\ttfamily \char`\"{}\+D\+A\+Y\char`\"{}}, etc \item fixed a memory leak in the parser related to parse exception handling with namespace members \item fixed an invalid assert() in module handling when an error occurs loading the module (only affected debug builds) \item tagged digest and crypto functions internally as \mbox{\hyperlink{code_flags_RET_VALUE_ONLY}{R\+E\+T\+\_\+\+V\+A\+L\+U\+E\+\_\+\+O\+N\+LY}} \item do not kill T\+ID 1 (the initial / main thread) when calling exit() in background threads as a crash can result with some 3rd party libraries that spawn their own threads on some platforms (observed on Darwin \& Solaris 10 at least) \item fixed a memory bug in the new builtin function A\+PI used by modules built with qpp \item fixed memory bugs in the type system where uninitialized type pointers could be used causing a crash \item fixed a memory bug in handling \char`\"{}or nothing\char`\"{} types where a non-\/null pointer would be assumed to be a pointer to the type, however it could actually be a pointer to the N\+O\+T\+H\+I\+NG object, the fix was to ensure that any N\+O\+T\+H\+I\+NG objects in argument lists would be substituted with a null pointer \item fixed a bug in parse-\/time variant matching where an argument with parse-\/time type \char`\"{}object\char`\"{} would be matched as a perfect match to any parameter with any class restriction; this would cause run-\/time type errors if another valid class was passed that matched another variant of the method or function \item fixed a build bug that caused qore to be built twice \end{DoxyItemize} \DoxyHorRuler{0} \hypertarget{release_notes_qore_084}{}\doxysection{Qore 0.\+8.\+4}\label{release_notes_qore_084} \begin{DoxyParagraph}{Release Summary} Major new features and changes that can affect backwards-\/compatibility, plus 40 bug fixes \end{DoxyParagraph} \hypertarget{release_notes_qore_084_compatibility}{}\doxysubsection{Changes That Can Affect Backwards-\/\+Compatibility}\label{release_notes_qore_084_compatibility} \begin{DoxyParagraph}{Namespace Changes} Qore\textquotesingle{}s internal namespace handling was nearly completely rewritten for Qore 0.\+8.\+4. This is because the old code was inefficient and applied namespaces inconsistently to \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects.~\newline ~\newline The main change that can cause backwards-\/compatibility issues is that now functions are full namespace members. If no namespace is explicitly given in a function definition, the function is a member of the unnamed root namespace.~\newline ~\newline Also the distinction between builtin and user functions was removed. Internally, there is only one kind of function object, which can contain both builtin and user function variants (overloaded variants of the same function with the same name but different arguments).~\newline ~\newline All Qore builtin functions were moved to the \mbox{\hyperlink{namespace_qore}{Qore}} namespace.~\newline ~\newline Other namespace changes\+: \begin{DoxyItemize} \item loading namespaces provided by builtin modules into a \mbox{\hyperlink{class_qore_1_1_program}{Program}} object is now an atomic operation that may fail, if, for example, objects have already been defined in the target \mbox{\hyperlink{class_qore_1_1_program}{Program}} with the same name as objects provided by the builtin module. Previously this could cause undefined behavior. \item namespace lookups are now truly breadth-\/first as documented; previously the algorithm was depth-\/first (contrary to the documentation) \item namespace lookups are now done (both at parse time and runtime) with the help of symbol lookup tables for fast lookups; tables are maintained for both committed and temporary uncomitted parse symbols; this leads to up to 3x faster parsing for Qore code \item global variables are also now full namespace members, however this does not cause problems with backwards-\/compatibility \end{DoxyItemize} \end{DoxyParagraph} \hypertarget{release_notes_qore_084_new_features}{}\doxysubsection{New Features in Qore}\label{release_notes_qore_084_new_features} \begin{DoxyParagraph}{User Modules} It is now possible to develop user modules in Qore; several user modules are now included in the Qore distribution, forming Qore-\/language components of Qore\textquotesingle{}s runtime library.~\newline ~\newline User modules delivered with Qore 0.\+8.\+4\+: \begin{DoxyItemize} \item \href{../../modules/HttpServer/html/index.html}{\texttt{ Http\+Server}}\+: a multi-\/threaded H\+T\+TP server implementation \item \href{../../modules/SmtpClient/html/index.html}{\texttt{ Smtp\+Client}}\+: an S\+M\+TP client library \item \href{../../modules/TelnetClient/html/index.html}{\texttt{ Telnet\+Client}}\+: a T\+E\+L\+N\+ET client implementation \item \href{../../modules/Mime/html/index.html}{\texttt{ Mime}}\+: a set of M\+I\+ME definitions and functions for manipulating M\+I\+ME data \end{DoxyItemize}There are also new example programs for the above modules in the examples/ directory.~\newline ~\newline User modules are subject to Qore\textquotesingle{}s functional restriction framework. \end{DoxyParagraph} \begin{DoxyParagraph}{Namespace Changes} As listed above\+:~\newline \begin{DoxyItemize} \item global variables and functions are now full namespace members \item all builtin functions are now in the \mbox{\hyperlink{namespace_qore}{Qore}} namespace \item real depth-\/first searches are used for namespace symbols \item symbols are resolved first in the current namespace when parsing declarations/code in a namespace \end{DoxyItemize} \end{DoxyParagraph} \begin{DoxyParagraph}{The final Keyword} Classes and methods can now be declared \char`\"{}final\char`\"{} to prevent subclassing or overriding in a subclass \end{DoxyParagraph} \begin{DoxyParagraph}{Pseudo Methods} Pseudo-\/methods are class methods that can be implemented on any value; they are also part of class hierarchy. The methods that can be executed on the value depend on the value\textquotesingle{}s type, and all \char`\"{}pseudo-\/classes\char`\"{} inherit methods from a common base class.~\newline ~\newline For example\+: \begin{DoxyCode}{0} \DoxyCodeLine{\textcolor{stringliteral}{"string"}.\mbox{\hyperlink{group__string__functions_gafc530772b929b2148ae2733569bada58}{strlen}}()} \DoxyCodeLine{<abf05da3>.size()} \DoxyCodeLine{500.typeCode()} \end{DoxyCode} Are examples of pseudo-\/methods on literal values.~\newline ~\newline Some expensive operations such as getting the first or last key (or value) of a hash are now cheap using pseudo-\/methods, for example\+: \begin{DoxyCode}{0} \DoxyCodeLine{hash.firstKey()} \DoxyCodeLine{hash.lastValue()} \end{DoxyCode} \end{DoxyParagraph} \begin{DoxyParagraph}{New Doxygen-\/\+Based Documentation} The Qore reference documentation is now generated by Doxygen, and is generated directly from the Qore sources. In fact, a new preprocessor known as \char`\"{}qpp\char`\"{} was developed for Qore 0.\+8.\+4 to facilitate and enforce doxygen documentation on Qore\textquotesingle{}s runtime library (as well as abstract the relatively complex A\+P\+Is used to bind C++ code to the Qore runtime library from the C++ programmer).~\newline ~\newline The documentation is more comprehensive, and corresponds much closer to the actual internal implementation since the documentation is now also contained in and directly generated from the internal C++ implementation of Qore.~\newline ~\newline For example, there is the \mbox{\hyperlink{class_qore_1_1zzz8valuezzz9_a3a66486cee14aa073cf90fbed5a23edd}{Qore\+::zzz8valuezzz9\+::val()}} method. This method is implemented in the base pseudo class and is reimplemented in other pseudo-\/classes for other runtime data types as necessary. This method returns \mbox{\hyperlink{basic_data_types_True}{True}} if the value has a value in the same sense as Perl\textquotesingle{}s boolean context evaluation. For example, if the value is a hash with no keys, it returns \mbox{\hyperlink{basic_data_types_False}{False}}; if it is a hash with keys, it returns \mbox{\hyperlink{basic_data_types_True}{True}}; if it is an empty string, it returns \mbox{\hyperlink{basic_data_types_False}{False}}; if it is a non-\/empty string, it returns \mbox{\hyperlink{basic_data_types_True}{True}}, etc. \end{DoxyParagraph} \begin{DoxyParagraph}{L\+Value Handling Changes} lvalue handling was rewritten as the old implementation was ugly and subject to deadlocks (in rare corner cases).~\newline ~\newline Furthermore, medium-\/term, an architectural goal of Qore is to store all ints, floats, and bools internally as the basic C++ type instead of using a class wrapper for each value, which needs dynamic allocation and destruction, which takes up more memory and negatively affects execution speed.~\newline ~\newline With Qore 0.\+8.\+4, all local and global variables are stored using optimized C++ types when declared with the appropriate type restrictions; for example\+: \begin{DoxyCode}{0} \DoxyCodeLine{int i0;} \DoxyCodeLine{our int i1;} \end{DoxyCode} These declares local and global variables that can only be assigned integer values; in Qore 0.\+8.\+4 the value internally will be stored as an \char`\"{}int64\char`\"{} value (and not a dynamically-\/allocated Qore\+Big\+Int\+Node object).~\newline ~\newline The same holds for\+: \begin{DoxyItemize} \item \mbox{\hyperlink{data_type_declarations_int_type}{int}} \item \mbox{\hyperlink{data_type_declarations_softint_type}{softint}} \item \mbox{\hyperlink{data_type_declarations_float_type}{float}} \item \mbox{\hyperlink{data_type_declarations_softfloat_type}{softfloat}} \item \mbox{\hyperlink{data_type_declarations_bool_type}{bool}} \item \mbox{\hyperlink{data_type_declarations_softbool_type}{softbool}} \end{DoxyItemize}Note that the optimized lvalue handling has not yet been applied to all lvalues, in particular non-\/static object members with declared types are not yet implemented with optimized storage; to do this requires a rewrite of Qore\textquotesingle{}s A\+PI and A\+BI (will happen in the next major release of Qore).~\newline ~\newline This change leads to improved integer and floating-\/point performance and a smaller runtime memory footprint. \end{DoxyParagraph} \begin{DoxyParagraph}{Runtime Optimizations} In addition to the up to 3x faster parsing (as decribed in the namespace changes above), Qore 0.\+8.\+4 contains many runtime optimizations designed to reduce the number of dynamic memory allocations performed at runtime.~\newline ~\newline The optimizations included in this version of Qore are only a half-\/measure compared to future changes that will necessitate a new binary Qore A\+PI. \end{DoxyParagraph} \begin{DoxyParagraph}{Per-\/\+Thread Initialization} the new \mbox{\hyperlink{group__threading__functions_gae83c32576b59a1ecfa906d9b3c3af557}{set\+\_\+thread\+\_\+init()}} function allows a call reference or closure to be set which will be automatically executed when new threads are started (or a new thread accesses a \mbox{\hyperlink{class_qore_1_1_program}{Program}} object) which can be used to transparently initialize thread-\/local data. \end{DoxyParagraph} \begin{DoxyParagraph}{More Control Over Thread Resource Exceptions} new functions\+: \begin{DoxyItemize} \item \mbox{\hyperlink{group__threading__functions_ga4e62409b8a1b414276d033267e7299e4}{throw\+\_\+thread\+\_\+resource\+\_\+exceptions\+\_\+to\+\_\+mark()}} \item \mbox{\hyperlink{group__threading__functions_gafa1c0f9e429a945b66fb261c7fa1b5bd}{mark\+\_\+thread\+\_\+resources()}} \end{DoxyItemize}Allow for only thread resouces created after a certain point to be processed (for example only thread resources left after some embedded code was called) \end{DoxyParagraph} \begin{DoxyParagraph}{New Socket Methods} new methods\+: \begin{DoxyItemize} \item \mbox{\hyperlink{class_qore_1_1_socket_ad471f7399655c3fb211c72b55ca568d9}{Qore\+::\+Socket\+::upgrade\+Client\+To\+S\+S\+L()}} \item \mbox{\hyperlink{class_qore_1_1_socket_a83385d31d5b112409424269f025de5ea}{Qore\+::\+Socket\+::upgrade\+Server\+To\+S\+S\+L()}} \end{DoxyItemize}Allow upgrading an already-\/existing socket connection to S\+SL \end{DoxyParagraph} \begin{DoxyParagraph}{Better Socket Error Messages} More information has been added to socket exceptions to provide better feedback when errors occur. \end{DoxyParagraph} \begin{DoxyParagraph}{New Socket Event Fields} \begin{DoxyItemize} \item added {\ttfamily \char`\"{}type\char`\"{}} and {\ttfamily \char`\"{}typename\char`\"{}} keys to the \mbox{\hyperlink{event_handling_EVENT_HOSTNAME_RESOLVED}{E\+V\+E\+N\+T\+\_\+\+H\+O\+S\+T\+N\+A\+M\+E\+\_\+\+R\+E\+S\+O\+L\+V\+ED}} event \item added {\ttfamily \char`\"{}type\char`\"{}}, {\ttfamily \char`\"{}typename\char`\"{}}, and {\ttfamily \char`\"{}address\char`\"{}} keys to the \mbox{\hyperlink{event_handling_EVENT_CONNECTING}{E\+V\+E\+N\+T\+\_\+\+C\+O\+N\+N\+E\+C\+T\+I\+NG}} event \end{DoxyItemize} \end{DoxyParagraph} \begin{DoxyParagraph}{Support For Blocking Writes in the Queue Class} \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}} objects can now be used as a blocking message channel (similar to a Go channel); if a maximum size is given to the \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}} constructor, then trying to write data to the \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}} when it is full will block until the \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}}\textquotesingle{}s size goes below the maximum size; optional timeout parameters have been added to \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}} methods that write to the \mbox{\hyperlink{class_qore_1_1_thread_1_1_queue}{Queue}}. \end{DoxyParagraph} \begin{DoxyParagraph}{New Queue\+::clear() Method} Does just what you think it does \+:) \end{DoxyParagraph} \begin{DoxyParagraph}{date(string, string) Improvement} added the possibility to specify microseconds when parsing dates against a mask with the \mbox{\hyperlink{group__date__and__time__functions_gaa80ee453b6a5653ac685d7e290c74e3f}{date()}} function \end{DoxyParagraph} \begin{DoxyParagraph}{New Support For ++ And -- Operators With Floating-\/\+Point Lvalues} previously this would either convert the lvalue to an int or throw an exception if the lvalue could not be converted to an int due to type restrictions \end{DoxyParagraph} \begin{DoxyParagraph}{Class Recognition/\+Compatibility Between Program Objects} The problem is that a user class created from the same source code in two different \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects would be recognized as a different class with parameter and variable type restrictions -\/ ie you could not declare a variable or parameter with a class type restrictions and assign it an object created from the same class source code but created in another \mbox{\hyperlink{class_qore_1_1_program}{Program}} object.~\newline ~\newline This problem is analogous to a similar problem with java in that classes built from the same source but from different classloaders are also recognized as different classes.~\newline ~\newline In Qore 0.\+8.\+4 a class signature is created of all public and private objects, and an S\+H\+A1 hash is maintained of the class signature, and if the class names and signatures match, then the classes are assumed to be identical, even if they have different internal class I\+Ds (because they were created in different \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects, for example). \end{DoxyParagraph} \begin{DoxyParagraph}{New Time\+Zone\+::date(string) Method} to support creating arbitrary dates in a given \mbox{\hyperlink{class_qore_1_1_time_zone}{Time\+Zone}} \end{DoxyParagraph} \begin{DoxyParagraph}{New Get\+Opt\+::parse3() method} This method will display any errors on \mbox{\hyperlink{group__io__constants_ga697e4968984d273562f14bfed155b4a8}{stderr}} and exit the program (which is the most typical way of handling command line errors anyway) \end{DoxyParagraph} \begin{DoxyParagraph}{+= Operator Optimization For object += hash} this operation is faster in this release \end{DoxyParagraph} \begin{DoxyParagraph}{New Parse Option P\+O\+\_\+\+N\+O\+\_\+\+M\+O\+D\+U\+L\+ES} Using this option disables module loading \end{DoxyParagraph} \begin{DoxyParagraph}{New Parse Option P\+O\+\_\+\+N\+O\+\_\+\+E\+M\+B\+E\+D\+D\+E\+D\+\_\+\+L\+O\+G\+IC} Using this option disables all dynamic parsing \end{DoxyParagraph} \begin{DoxyParagraph}{New Parse Directives} \begin{DoxyItemize} \item \mbox{\hyperlink{parse_directives_assume-global}{\%assume-\/global}}\+: the opposite of \mbox{\hyperlink{parse_directives_assume-local}{\%assume-\/local}} \item \mbox{\hyperlink{parse_directives_old-style}{\%old-\/style}}\+: the opposite of \mbox{\hyperlink{parse_directives_new-style}{\%new-\/style}} \item \mbox{\hyperlink{parse_directives_require-dollar}{\%require-\/dollar}}\+: the opposite of \mbox{\hyperlink{parse_directives_allow-bare-refs}{\%allow-\/bare-\/refs}} \item \mbox{\hyperlink{parse_directives_push-parse-options}{\%push-\/parse-\/options}}\+: allows parse options to be saved and restored when the current file is done parsing; very useful for include files \end{DoxyItemize} \end{DoxyParagraph} \begin{DoxyParagraph}{New Context Functions} \begin{DoxyItemize} \item \mbox{\hyperlink{group__context__functions_ga105b00b74b4fba117cbf3582d1ad7363}{cx\+\_\+value()}}\+: returns the value of the given key \item \mbox{\hyperlink{group__context__functions_gaf0dfc0d47bd06a2c1a6e76e3381f61eb}{cx\+\_\+first()}}\+: returns \mbox{\hyperlink{basic_data_types_True}{True}} if iterating the first row \item \mbox{\hyperlink{group__context__functions_gad5b21ea6273b824301e13be824205957}{cx\+\_\+last()}}\+: returns \mbox{\hyperlink{basic_data_types_True}{True}} if iterating the last row \item \mbox{\hyperlink{group__context__functions_gaf6605e041e703be65489058a15055ea7}{cx\+\_\+pos()}}\+: returns the current row number (starting from 0) \item \mbox{\hyperlink{group__context__functions_ga31bcc663a5fb7d93585a051c9b0ca694}{cx\+\_\+total()}}\+: returns the total number of rows in the set \end{DoxyItemize} \end{DoxyParagraph} \begin{DoxyParagraph}{S\+O\+C\+K\+E\+T-\/\+H\+T\+T\+P-\/\+E\+R\+R\+OR Exception Enhancement} The invalid header info received is reported in the exception\textquotesingle{}s {\ttfamily \char`\"{}arg\char`\"{}} key \end{DoxyParagraph} \begin{DoxyParagraph}{Improved Parse Error Messages} Improved some parse error messages dealing with namespace and class declaration errors \end{DoxyParagraph} \begin{DoxyParagraph}{Added N\+T\+\_\+\+C\+L\+O\+S\+U\+RE Constant} type code for runtime closure values \end{DoxyParagraph} \hypertarget{release_notes_qore_084_bug_fixes}{}\doxysubsection{Bug Fixes in Qore}\label{release_notes_qore_084_bug_fixes} \begin{DoxyItemize} \item fixed a race condition with \mbox{\hyperlink{class_qore_1_1_program}{Program}} objects when a signal handler is left active and the \mbox{\hyperlink{class_qore_1_1_program}{Program}} terminates \item fixed a bug in the \mbox{\hyperlink{class_qore_1_1_file}{File}} class where the encoding given in the constructor was ignored; if no encoding was given in the File\+::open$\ast$() method then the \mbox{\hyperlink{class_qore_1_1_file}{File}}\textquotesingle{}s encoding would always be set to the default encoding, now it\textquotesingle{}s set to the encoding given in the constructor (as documented) \item runtime checks have been implemented so that references to local variables cannot be passed to a closure; this would cause a runtime crash \item a fix has been made to the \mbox{\hyperlink{operators_delete}{delete}} and \mbox{\hyperlink{operators_remove}{remove}} operators; lists will not be extended when trying to remove/delete list elements that do not exist \item fixed some bugs showing the error location with bugs in the second stage of parsing (symbol resolution) \item apply type filters to blocks with a designated return type but no \mbox{\hyperlink{statements_return}{return statement}} \item fixed crashing bugs on some 32bit platforms where size\+\_\+t was assumed to be 64 bits \item fixed a crashing bug parsing invalid \mbox{\hyperlink{parse_directives_requires}{\%requires}} directives in the scanner \item fixed a bug in usleep() with relative date/time values (added a new usleep() variant to support this) \item fixed a typo in the command-\/line help for the qore binary with unknown parse options \item fixed \mbox{\hyperlink{group__option__constants_ga2b260e5d44de1d493adb8d97789f047f}{H\+A\+V\+E\+\_\+\+S\+I\+G\+N\+A\+L\+\_\+\+H\+A\+N\+D\+L\+I\+NG}} to be \mbox{\hyperlink{basic_data_types_False}{False}} if signal handling is disabled on platforms where signal handling is otherwise available \item fixed a scanner bug parsing out of line class definitions with a root-\/justified namespace path (ex\+: {\ttfamily \char`\"{}class \+::\+X\+::\+Class\+Name ...\char`\"{}}) \item merging code from binary modules at parse time and at runtime is now transaction-\/safe (before it would cause memory errors and/or a crash), now if errors are detected then an exception is raised and changes are not applied. \item fixed a crashing bug in the C++ A\+PI function Qore\+Hash\+Node\+::set\+Key\+Value() when the value is 0 and an exception occurs or is already active before the call is made \item fixed a bug in date parsing with a format string -\/ off by one with integer months -\/ added a regression test for this case \item fixed a memory error with the \mbox{\hyperlink{statements_rethrow}{rethrow statement}} in enclosing but nested try-\/catch blocks \item fixed a crashing bug where qore would try to instantiate a class for a type that did not represent a class (ex\+: {\ttfamily \char`\"{}int i();\char`\"{}}) \item fixed a memory leak in the \mbox{\hyperlink{data_type_declarations_softlist_type}{softlist}} and \mbox{\hyperlink{data_type_declarations_softlist_or_nothing_type}{$\ast$softlist}} type implementation \item make sure and raise a {\ttfamily S\+O\+C\+K\+E\+T-\/\+C\+L\+O\+S\+ED} error when reading a H\+T\+TP header if no data is received \item make sure and convert encodings with \mbox{\hyperlink{group__string__functions_gadaea9cfa0f698a6fb0650f70cf8d929e}{index()}} and \mbox{\hyperlink{group__string__functions_ga55663008aa59489b869e558b29c7c22d}{rindex()}} functions if the encodings don\textquotesingle{}t match \item build fix\+: only use a lib64 directory if the directory exists already \item raise a parse exception in the scanner if a numeric overflow occurs in literal integer values \item fixed a bug in \mbox{\hyperlink{class_qore_1_1_thread_1_1_abstract_smart_lock_afafe6ef19203993a7c5dd87e00068325}{Abstract\+Smart\+Lock\+::lock\+T\+ID()}} \item fixed a major crashing error in the C++ A\+PI function Qore\+String\+Node\+::create\+And\+Convert\+Encoding(); this function is used by the xml module when parsing X\+M\+L-\/\+R\+PC sent in a non-\/\+U\+T\+F-\/8 character encoding \item fixed \mbox{\hyperlink{class_qore_1_1_read_only_file_ab6946821b81fc2b9b4f07ef27ebacd45}{Qore\+::\+File\+::getchar()}} to always retrieve 1 character (even for multi-\/byte character encodings) \item fixed string evaluation in a boolean context to return \mbox{\hyperlink{basic_data_types_True}{True}} with floating-\/point numbers between -\/1.\+0 and 1.\+0 exclusive \item printf formatting fix\+: output Y\+A\+M\+L-\/style {\ttfamily \char`\"{}null\char`\"{}} for \mbox{\hyperlink{basic_data_types_nothing}{N\+O\+T\+H\+I\+NG}} with \%y \item scanner fix\+: accept {\ttfamily \char`\"{}\textbackslash{}r\char`\"{}} as whitespace to allow better parsing of sources with Windows E\+OL markers \item fixed parse-\/time type processing/checks for the keys, + and $\ast$ operators \item foreach statement fix\+: unconditionally evaluate the hash when iterating as otherwise it could change during iteration which could cause a crash \item fixed another parse-\/time variant matching bug where the variant-\/matching algorithm was too aggressive and excluded possible matches at parse time which could result in a false parse-\/time definitive match even though a better match could be available at runtime \item fixed a static memory leak when signal handlers are left registered when the qore library terminates \item fixed static memory leaks and 1 dynamic memory leak in \mbox{\hyperlink{group__string__functions_gaabfb10141a51d31ef100d9fd3a02252e}{strmul()}} \item fixed a crashing bug in handling recursive constant references \item fixed a bug in the C++ A\+PI function Hash\+Iterator\+::delete\+Key() when the node\textquotesingle{}s value is N\+U\+LL \item fixed time zone/\+D\+ST calculations for time zone regions with D\+ST with dates before the epoch but after the last D\+ST transition before the epoch \item fixed a memory error where invalid source expressions referenced in a regular expression substitution expression would cause a crash (ex\+:\begin{DoxyVerb}str =~ s/public (name)/$2/g \end{DoxyVerb} \item fixed a memory error in regular expression substitution where the unconverted string (if not given in U\+T\+F-\/8 encoding) was used when copying source expressions to the target string \item fixed a bug where a recursive class inheritance tree would cause a crash \item fixed a bug where a static class method could not access private members of the class \end{DoxyItemize}
https://theanarchistlibrary.org/library/sub-media-what-is-class.tex	theanarchistlibrary.org	CC-MAIN-2021-39	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2021-39/segments/1631780056892.13/warc/CC-MAIN-20210919160038-20210919190038-00281.warc.gz	609,706,979	5,723	\documentclass[DIV=12,% BCOR=10mm,% headinclude=false,% footinclude=false,% fontsize=11pt,% twoside,% paper=210mm:11in]% {scrartcl} \usepackage[noautomatic]{imakeidx} \usepackage{microtype} \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} \usepackage[shortlabels]{enumitem} \usepackage{tabularx} \usepackage[normalem]{ulem} \def\hsout{\bgroup \ULdepth=-.55ex \ULset} % https://tex.stackexchange.com/questions/22410/strikethrough-in-section-title % Unclear if \protect \hsout is needed. Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand{\forcelinebreak}{\strut\\{}} \newcommand{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand{\Slash}{\slash\hspace{0pt}} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} \usepackage{fontspec} \usepackage{polyglossia} \setmainlanguage{english} \setmainfont{LinLibertine_R.otf}[Script=Latin,% Ligatures=TeX,% Path=/usr/share/fonts/opentype/linux-libertine/,% BoldFont=LinLibertine_RB.otf,% BoldItalicFont=LinLibertine_RBI.otf,% ItalicFont=LinLibertine_RI.otf] \setmonofont{cmuntt.ttf}[Script=Latin,% Ligatures=TeX,% Scale=MatchLowercase,% Path=/usr/share/fonts/truetype/cmu/,% BoldFont=cmuntb.ttf,% BoldItalicFont=cmuntx.ttf,% ItalicFont=cmunit.ttf] \setsansfont{cmunss.ttf}[Script=Latin,% Ligatures=TeX,% Scale=MatchLowercase,% Path=/usr/share/fonts/truetype/cmu/,% BoldFont=cmunsx.ttf,% BoldItalicFont=cmunso.ttf,% ItalicFont=cmunsi.ttf] \newfontfamily\englishfont{LinLibertine_R.otf}[Script=Latin,% Ligatures=TeX,% Path=/usr/share/fonts/opentype/linux-libertine/,% BoldFont=LinLibertine_RB.otf,% BoldItalicFont=LinLibertine_RBI.otf,% ItalicFont=LinLibertine_RI.otf] \let\chapter\section % global style \pagestyle{plain} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand{\captionformat}{} \renewcommand{\figureformat}{} \renewcommand*{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} \deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} \frenchspacing % avoid vertical glue \raggedbottom % this will generate overfull boxes, so we need to set a tolerance % \pretolerance=1000 % pretolerance is what is accepted for a paragraph without % hyphenation, so it makes sense to be strict here and let the user % accept tweak the tolerance instead. \tolerance=200 % Additional tolerance for bad paragraphs only \setlength{\emergencystretch}{30pt} % (try to) forbid widows/orphans \clubpenalty=10000 \widowpenalty=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{What is Class?} \date{2016} \author{sub.media} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={What is Class?},% pdfauthor={sub.media},% pdfsubject={},% pdfkeywords={class; primer; video transcription; Breadtube}% } \begin{document} \thispagestyle{empty} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge What is Class?\par}}% \vskip 1em \vskip 2em {\usekomafont{author}{sub.media\par}}% \vskip 1.5em {\usekomafont{date}{2016\par}}% \end{center} \vskip 3em \par Class struggle, or the struggle within and against capitalism, is an intrinsic guiding force of anarchist theory and practice. Nonetheless, many enduring myths and misconceptions continue to cloud popular understanding of the social relationship that lies at the root of this conflict\dots{} namely, class itself. So\dots{} what is it, exactly? And what do anarchists have against it? Most people today primarily associate someone’s class with how much money they make. And while it's true that the size of a person's bank account is generally a good indication of their class position, this over-simplified definition tends to obscure the way that class actually operates, on both an individual and social level, while masking its inherently antagonistic nature. A more accurate way of defining class would be to say that it's a hierarchical social relationship characterized by exploitation, and anchored through an interconnected, state-based system of laws governing the ownership of property. Or to put it more simply\dots{} class is a way of organizing people according to who owns what. Of course, both hierarchy and exploitation have been around far longer than capitalism. From the priest-kings of Mesopotamia’s earliest city-states, to the Roman Empire and its gradual disintegration into Medieval feudalism, human civilizations have always been ruled by a small elite, who’ve ensured the highest concentration of wealth and prestige for themselves. The rise of capitalism displaced early feudal systems of social and economic control, such as the Divine Right of Kings in Europe, and the Mandate of Heaven in Imperial China, replacing these outdated superstitions with new, more sophisticated social myths based on the sanctity of private property and the unquestioned domination of the free market. Back in the mid 19th century, the famous socialist philosopher Karl Marx carried out an exhaustive exploration at how capitalism worked and the historical processes by which it had developed. Many prominent anarchists at the time, such as Mikhail Bakunin, bitterly disagreed with Marx and his followers on the question of revolutionary strategy, particularly the role of the state. Overall, however, they agreed with his description of capitalism as a system characterized by the emergence and spread of two mutually opposing classes. Those are: the working class - also known as the proletariat, and the capitalist class - also known as the bourgeoisie. Members of the capitalist class are defined by their ownership and control over capital, while members of the working class are defined by the fact that we don't own capital and are thus forced into exploitative relationships with capitalists in order to survive. Capitalists can be subdivided into three different categories based on the type of capital they own and how they generate profit. The first of these are industrial capitalists, who own and control the means of production - a fancy phrase to describe the tools and equipment necessary to produce commodities. In earlier stages of capitalism this usually referred to owners of factories and mines, but nowadays could refer to the owners and shareholders of a wide variety of businesses - anything from fast-food restaurants to software development companies. In other words, an industrial capitalist is your boss. They are someone who makes a profit by exploiting their workers. Second is landowners - capitalists who own land and real estate, and who make a profit by exploiting their tenants, or, as is increasingly common these days, through gentrification and other forms of real estate speculation and development. And finally, financial capitalists - who make a profit by loaning money at interest. This could be anyone from small pawnshops and payday loan centers, all the way up to the globe-spanning banks who loan money to other capitalists and even governments. The shift towards neoliberal capitalism beginning in the 1970s, saw financial capitalists massively expand their influence over the global economy. This expansion has allowed them to ramp up their direct exploitation of the working class through the introduction of new household debt instruments, such as personal credit cards, student loans and subprime mortgages. Over the years, the character of class exploitation has transformed as capitalism has evolved. In spite of this, many anti-capitalists still cling to narratives from an earlier era. Even today, the stereotypical image of a member of the working class tends to be the burly-chested, white factory worker of IWW lore - whereas the truth is that the majority of the global proletariat are female, and the overwhelming majority are of non-European descent. Yet even as capitalism has changed, the essential elements of the class relationship remain the same. It’s pretty well understood that the working class and capitalist classes have mutually opposing interests. The less our bosses pay us, and the more our landlords charge us rent, the more profit they make, and the poorer we get. What’s less understood, however, is that capitalist laws of universal competition and constant growth, create and shape internal divisions within each class. Capitalists within a certain industry are constantly competing with rivals over market share, which means that they must maintain a certain rate of profit, or risk going out of business. And capitalists from one industry sometimes have interests that run entirely contrary to those of another. High oil prices, for example, will lead to higher rates of profit for corporations like BP and ExxonMobil\dots{} but they can be devastating to capitalists in the manufacturing or transportation industries. While all members of the working class have a shared interest in ending capitalism, we are also often blinded by our own competing short-term interests. Not only do we have to compete with one another over the scraps capitalists give us to survive\dots{} but also, many of our jobs negatively impact the lives of other working-class people. And on a broader scale, the lower the wages paid to workers in the Global South, the cheaper the products on department store shelves. On top of that, our class is divided into hierarchies based on oppressive systems such as race and gender. Women, for instance, are often doubly exploited under capitalism in that we are expected to perform unpaid reproductive labour, such as cooking, cleaning and raising children, while simultaneously being paid less than our male counterparts at work. The role of the state is to manage the economy in a way that balances the interests of competing segments of the capitalist class, while protecting them all from the threat of working-class revolution. This is often achieved by playing up divisions within the working class based on nationalism, religious sectarianism, white supremacy and patriarchy. It is only by destroying these oppressive and divisive systems that our class can come together to wage a unified class war and begin to liberate ourselves from the shackles of this parasitic system of exploitation. We will only cease to be slaves when together, we seize everything. \bigskip % begin final page \clearpage % if we are on an odd page, add another one, otherwise when imposing % the page would be odd on an even one. \ifthispageodd{\strut\thispagestyle{empty}\clearpage}{} % new page for the colophon \thispagestyle{empty} \begin{center} The Anarchist Library \smallskip Anti-Copyright \bigskip \includegraphics[width=0.25\textwidth]{logo-en} \bigskip \end{center} \strut \vfill \begin{center} sub.media What is Class? 2016 \bigskip https:\Slash{}\Slash{}sub.media\Slash{}video\Slash{}what-is-class\Slash{} \bigskip \textbf{theanarchistlibrary.org} \end{center} % end final page with colophon \end{document} % No format ID passed.
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http://ofap.ulstu.ru/resources/1402/three_certificate.tex?association=resources&parent_scaffold=fremantle%2Fguest%2Fpeople&person_id=63	ulstu.ru	CC-MAIN-2020-24	text/x-tex	text/x-matlab	crawl-data/CC-MAIN-2020-24/segments/1590347426801.75/warc/CC-MAIN-20200602193431-20200602223431-00299.warc.gz	86,704,328	2,870	%% LaTeX2e-файл %% Создано движком Фримантл (https://gitlab.com/korobkov/fremantle) %% в 2020-06-03T00:26:08+04:00 %% Фримантл — Свободный движок репозитория электронных ресурсов %% Copyright © 2009—2018 Лаборатория «Автоматизированные системы» [email protected], УлГТУ %% %% Фримантл is free software: you can redistribute it and/or modify %% it under the terms of the GNU Affero General Public License as published by %% the Free Software Foundation, either version 3 of the License, or %% (at your option) any later version. %% %% Фримантл is distributed in the hope that it will be useful, %% but WITHOUT ANY WARRANTY; without even the implied warranty of %% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the %% GNU Affero General Public License for more details. %% %% You should have received a copy of the GNU Affero General Public License %% along with Фримантл. If not, see <https://www.gnu.org/licenses/>. \documentclass[a4paper,fontsize=18pt]{scrartcl} \providecommand{\chapterformat}{} \usepackage[landscape,left=2cm,right=2cm,top=1cm,bottom=1.5cm,bindingoffset=0cm]{geometry} \usepackage{graphicx, polyglossia, pst-barcode, tabu, wallpaper} \setmainfont{Liberation Serif} \setmonofont{Liberation Mono} \setsansfont{Liberation Sans} \defaultfontfeatures{Scale=MatchLowercase, Mapping=tex-text} \setdefaultlanguage[spelling=modern]{russian} \setotherlanguage{english} \graphicspath{{/srv/http/ofap/releases/20180921145927/app/assets/images/fremantle/three_certificate/}} \CenterWallPaper{1.00}{border.png} \begin{document} \begin{hyphenrules}{nohyphenation} \begin{center} \thispagestyle{empty} {\Large ОФАП УОЦ НИТ} \bigskip\bigskip \begin{tabu}{ b{5cm} >{\centering}b{19cm} } \includegraphics [height=4.5cm]{logo.png} & Ульяновский государственный технический университет Ульяновский областной центр новых информационных технологий Областной фонд алгоритмов и программ \bigskip {\Huge \textit{Свидетельство №\,1402}} \bigskip о регистрации программно-информационного продукта \end{tabu} \bigskip \begin{tabu}{ b{5cm} >{\raggedright \itshape}p{19cm} }\hline \\ Наименование: & \textbf{Разработка и исследование лабораторного стенда «Мостовые схемы с параметрическими преобразователями»} \\ Тип: & Научно-технический отчёт \\ URI: & \textbf{http://ofap.ulstu.ru/1402} \\ Авторы: & Вартанян Артур Сергеевич, Горбоконенко Вера Дмитриевна, Молотков Айрат Хасиатулович, Пляшев Андрей Валентинович -- Кафедра «Измерительно-вычислительные комплексы» (УлГТУ/ФИСТ) \\ Дата регистрации: & 07 апреля 2014 г. \\ \end{tabu} \vfill \begin{tabu} to 24cm { b{2cm} l X >{\itshape}l } & Проректор по научной работе УлГТУ & & \textit{Н.Г.\,Ярушкина} \\ & Директор Ульяновского областного центра НИТ & & \textit{К.В.\,Святов} \\ \psbarcode{2014-04-07 http://ofap.ulstu.ru/1402}{format=compact layers=4}{azteccode} \rowfont{\small} & Администратор базы данных ОФАП & & \textit{А.В.\,Коробков} \\ \end{tabu} \end{center} \end{hyphenrules} \clearpage \end{document}
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https://anarchistischebibliothek.org/library/kurze-reise-durch-das-soziale-gefangnis.tex	anarchistischebibliothek.org	CC-MAIN-2020-40	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2020-40/segments/1600400274441.60/warc/CC-MAIN-20200927085848-20200927115848-00231.warc.gz	252,739,052	13,879	\documentclass[DIV=12,% BCOR=0mm,% headinclude=false,% footinclude=false,open=any,% fontsize=11pt,% oneside,% paper=a4]% {scrbook} \usepackage{fontspec} \usepackage{polyglossia} \setmainfont{Linux Libertine O} % these are not used but prevents XeTeX to barf \setsansfont[Scale=MatchLowercase]{CMU Sans Serif} \setmonofont[Scale=MatchLowercase]{CMU Typewriter Text} \setmainlanguage{german} % global style \pagestyle{plain} \usepackage{microtype} % you need an updated texlive 2012, but harmless \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} % footnote handling \usepackage[fragile]{bigfoot} \usepackage{perpage} \DeclareNewFootnote{default} \DeclareNewFootnote{B} \MakeSorted{footnoteB} \renewcommand\thefootnoteB{(\arabic{footnoteB})} \deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~} % continuous numbering across the document. 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Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand{\captionformat}{} \renewcommand{\figureformat}{} \renewcommand{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand{\forcelinebreak}{\strut\\{}} \newcommand{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand{\Slash}{\slash\hspace{0pt}} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} % forbid widows/orphans \frenchspacing \sloppy \clubpenalty=10000 \widowpenalty=10000 % http://tex.stackexchange.com/questions/304802/how-not-to-hyphenate-the-last-word-of-a-paragraph \finalhyphendemerits=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{Kurze Reise durch das soziale Gefängnis} \date{Juli 2009} \author{} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={Kurze Reise durch das soziale Gefängnis},% pdfauthor={A Corps Perdu},% pdfsubject={},% pdfkeywords={Gefängnis; Abolitionismus; Zerstörung; Domestizierung}% } \begin{document} \begin{titlepage} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge Kurze Reise durch das soziale Gefängnis\par}}% \vskip 1em \vskip 2em \vskip 1.5em \vfill {\usekomafont{date}{Juli 2009\par}}% \end{center} \end{titlepage} \cleardoublepage \tableofcontents % start a new right-handed page \cleardoublepage \textbf{Ein menschliches Wesen während Monaten und Jahren auf ein paar wenigen Quadratmetern einsperren. Es kontrollieren, beobachten, erniedrigen und seiner Sinneserfahrungen berauben. Das Gefängnis ist unbestreitbar eine Form von Folter.} \textbf{Und doch, trotz der Abscheulichkeit der Folter, kann die Gesellschaft nicht ohne das Gefängnis. Um es besser auszudrücken, das Gefängnis ist nicht einfach eine Ausdünstung des Staates, die darauf abzielt «abweichende», nicht konforme, überflüssige oder unerwünschte Menschen zu unterdrücken und\Slash{}oder zu isolieren, es ist im Gegenteil ein organischer Bestandteil der Gesellschaft. Die Entwicklung der Dinge genau betrachtend, können wir behaupten, dass das Gefängnis keine Erweiterung der Gesellschaft ist, sondern die Gesellschaft eine Erweiterung des Gefängnisses. Anders gesagt: die ganze Gesellschaft ist ein Gefängnis, in welchem die Strafanstalten nur der offensichtlichste und brutalste Aspekt eines Systems darstellen, das uns alle zu Komplizen und Opfern, uns alle zu Eingeschlossenen macht.} \textbf{Dieser Text soll eine kurze Reise im Innern der «Trakte und Abteilungen» unserer Welt sein, eine Reise, die nicht beabsichtigt, das Subjekt zu erschöpfen, sondern die Verantwortlichkeiten hervorzuheben. Denn, wie schon öfters gesagt wurde: \emph{die Ungerechtigkeit hat einen Namen, ein Gesicht und eine Adresse}.} \section{Der Abolitionismus} Die Abschaffung des Gefängnisses ist absolut undenkbar ohne die Abschaffung, oder besser, die Zerstörung der gegenwärtigen sozialen Verhältnisse. Diejenigen, die noch immer die Ansicht verfechten, dass die Beseitigung der Folter innerhalb dieser Welt möglich ist, begehen also einen groben Fehler und leisten – auch wenn wir, in gewissen Fällen, ihre Aufrichtigkeit erkennen können – ein offen konservatives Werk. Das Argument, den staatlichen Gebrauch der Einsperrung zu beseitigen, da das Gefängnis \emph{nicht immer existierte} (tatsächlich ist es eine ziemlich neue Erfindung), führt im besten Fall zu nichts. Und im schlechtesten, wie es allzu oft passiert, führt es zur Formulierung von Thesen, die «den Abweichenden» durch alternative Zwangsmassnahmen wieder in die Gesellschaft integrieren wollen. Was in Wirklichkeit auf den Vorschlag hinausläuft, das Gefängnis durch eine erzwungene «Wiedereingliederung» des Individuums zu überwinden, indem man dieses in einen Prozess kultureller, moralischer und intellektueller Neubildung integriert. Mit anderen Worten, indem der freie Wille definitiv ausgemerzt wird. Was dies anbelangt, hat der moderne Staat schon einiges an Vorarbeit geleistet, und er hat es bestimmt nicht nötig, dass wir ihn mit der einen oder anderen Form von abolitionistischem Demokratismus unterstützen. Die Verliese, die Ledergürtel und die systematischen Leibesstrafen (alle ohne gänzlich verschwunden zu sein) haben den Platz subtileren Zwangsmethoden überlassen, deren Ziel, neben dem Freikaufen der Körper, auch die Zerstörung der Geister ist. Die Berufung auf die Psychiatrisierung der Abgeschotteten, die «Wiederintegrierung» durch soziale Arbeit, die Delegierung der Kontrolle an die Sozialhilfe und die technologischen Neuerungen wie die elektronische Fussfessel, sind alles Praktiken, die darauf abzielen, die Feindseligkeiten zu durchbrechen und «den Abweichenden» zu seinem eigenen Bullen zu machen. An diesen x-ten Zwangsmitteln der Macht sehen wir besser denn je, inwiefern die Mauern der Gefängnisse die ganze Gesellschaft umfassen. Wenn wir die Gefängnisse als eine Verallgemeinerung der Strafe auf industriell konzentrierter Ebene verstehen, sind sie der Ausdruck eines spezifischen politischen und ökonomischen Systems und daher nicht etwas unabwendbares. In dem Moment, wo dessen Entwicklung erfordert, die Strafe an neue politische und ökonomische Verhältnisse und Anforderungen anzupassen, wird die Herrschaft nicht zögern, das Gefängnis hinter sich zu lassen. Der Mensch hat sich in Wirklichkeit nicht von der Sklaverei, der Folter und dem Galgen befreit, vielmehr hat die Politik ihre Zwangs- und Strafmassnahmen an die (ideologischen und kommerziellen) Anforderungen der Produktion angepasst. Das Gefängnis, im Sinne von Mauern und Gitterstäben, taucht mit der industriellen Revolution auf, wandelt sich während diese vorbeizieht, und es ist durchaus denkbar, dass es in Zukunft wieder zurückgelassen und\Slash{}oder transformiert wird. Das alles bedeutet jedoch nicht, dass das Gefängnis, diesmal im Sinne einer Gesellschaft und politischen Notwendigkeit (der Einsperrung und Kontrolle), verschwinden wird. Wie sich hingegen im Verlauf der Geschichte gezeigt hat, neigen die Maschen des Zwangs dazu, sich selber in dem Masse zu verengen, wie die Erscheinung des «Zwangs» verschwommener und ungreifbarer wird. \section{Von der Zerstörung des Gefängnisses} Wenn wir also davon ausgehen, dass der Knast dieser Gesellschaft innewohnt, und dass sich das bestehende Herrschaftssystem momentan nicht von ihm trennen kann, scheint es offensichtlich, dass der Wille, die Gefängnisse zu zerstören, mit der Zerstörung der bestehenden sozialen Verhältnissen verbunden ist. In einem Wort: um gegen das Gefängnis zu sein, muss man unweigerlich auch Revolutionär sein. Diese Behauptung mag etwas platt und absolut wirken, doch eigentlich zeigt sie gut auf, was die Grenzen, oder besser, was die wichtigste Grenze der verschiedenen Kämpfe gegen die Gefängnisse ist. Menschen ohne revolutionäre Vision in einen Kampf gegen die Existenz von Gefängnissen verwickeln zu wollen, wäre wie zu denken, sie in eine Schlacht zu verwickeln, die die Beseitigung des Geldes voraussetzt. Es zeigt sich deutlich, dass man, um sich auf solche Ziele zu konzentrieren, den Teilkampf überwinden und zu einer Vision und Kritik der Totalität des Bestehenden gelangen muss. Die Arglosigkeit zahlreicher Kämpfe gegen das Gefängnis hat jedoch oft dazu geführt, diese Angelegenheit als etwas auf sich selbst stehendes zu behandeln, etwas der Herrschaft \emph{aufgesetztes} und nicht als einer ihrer Grundpfeiler. Das Problem ist, dass das Gefängnis weder eine Mülldeponie noch eine Autobahn ist, wo es denkbar wäre, dass sich eine Opposition \emph{innerhalb} der Herrschaft entwickelt. Die Anstrengungen sollten also nicht mehr darauf abzielen, die Leute auf etwas zu sensibilisieren, das entweder die revolutionäre Kritik oder die simple «solidarische» Unterstützung voraussetzt, sondern vielmehr darauf, die Tatsache vor Augen zu führen, dass das Gefängnis eine Angelegenheit aller ist, da es überall ist. In einem Wort, wir werden vor allem praktisch handeln müssen, um die Trennung zwischen dem Gefängnis, betrachtet als Mauern und Gitter und dem Gefängnis, betrachtet als Gesamtheit von Strukturen und Beziehungen, zu überwinden. Potentielle «Weggefährten», die wir unterwegs antreffen könnten, werden bestimmt nicht zu Revolutionären, indem sie sich unsere Predigt gegen die Knäste anhören, sie könnten aber vielleicht unsere Komplizen werden, als Gefangene in der Revolte gegen eine Gefängnisgesellschaft, die uns alle unterdrückt. \section{Von der Anschuldigung des Elends} Die gegenwärtigen ökonomischen Verhältnisse und die autoritäre Wende der Regierungen bewirken, dass \emph{alle} Armen potentiell das künftige Knast-«Vieh» darstellen. Der alte Spruch, der besagt: «\emph{du hast einen Fehler begangen, nun sollst du bezahlen}», auch wenn er in der Ideologie irgendwelcher begriffsstutziger Bürger noch präsent bleibt, wurde schon längst von den Fakten überholt: Es ist nicht mehr einfach die Wahl der Extra-legalität\footnote{Die Wahl den Rahmen von Legalität\Slash{}Illegalität hinter sich zu lassen.} oder der Illegalität die den \emph{Fehler} bestimmt, sondern schlicht und vorallem das Klassenverhältnis. Die legislativen Daumenschrauben, die sich täglich etwas tiefer in das Fleisch der Armen bohren, demonstrieren deutlich, dass es die Armut ist, die man anschuldigt und verfolgt, und nicht die Tat an sich. Im gleichen Masse, wie sich das Elend ausbreitet, werden immer mehr Handlungen in das Strafgesetzbuch eingetragen, so dass es selbst für den blindesten und optimistischsten der Ausgebeuteten ersichtlich wird, dass die Gefängnispforten früher oder später auch hinter ihm zuschlagen. In der modernen Gesellschaft ist die Figur des \emph{Kriminellen} dabei zu verschwinden, um jener des \emph{Schuldigen} Platz zu machen. Darum sind wir alle, als Bewohner der Gefängnisgesellschaft, auf austauschbare Weise dazu bestimmt, hinter den Stacheldrähten zu verfaulen: sei es nun in einer Strafanstalt, einem geschlossenen Zentrum oder einem Flüchtlingslager. Wenn man dieser Logik folgt, erscheint es auch nicht so paradox, dass angesichts der anwachsenden Gewalt, einem Symptom des weltweiten Bürgerkrieges, nicht so sehr die Gewalt an sich verfolgt wird (von dem Moment an, wo sie für den Status quo vielmehr das Lebenselexir darstellt, als eine Bedrohung), sondern eher die simple Tatsache zu \emph{existieren} und zu sein. Um es nocheinmal zu wiederholen, die Menschen werden bestraft, einge– und oft eliminiert – weil sie arm und\Slash{}oder für den Markt und das produktive Funktionieren überflüssig sind, und nicht weil sie tatsächlich durch extra-legales Handeln eine Bedrohung darstellen. Es ist also kein Zufall, dass der Alltag in den Gefängnissen, der Ausdruck der sozialen Beziehungen zwischen Gefangenen, zwischen Wärtern, zwischen Verwaltern und das Zusammenwirken all dessen, nicht so sehr auf der Kraft des Zwangs beruht, sondern vielmehr auf der Wiederzusammensetzung – in Miniatur und auf verschärftere Weise – der selben entfremdeten sozialen Beziehungen, die ausserhalb der Gitterstäbe gelebt werden. \section{Von der Reproduktion der Verhältnisse} Die Geistesschwäche der tapferen Verteidiger der «Menschenrechte» gründet in der Behauptung, dass die Einsperrung eine Verschlimmerung des Verhaltens von wieder freigelassenen Individuen bewirke. Das Sprichwort besagt, dass das Gefängnis eine Schule der Gewalt und der Verdummung menschlicher Wesen ist. Durch diese simplen Überlegungen, können wir deutlich erkennen, welcherart das morbide Band ist, das diese «guten Seelen» des Rechtes mit dem System unterhalten, das uns umgibt. Es ist nicht die Gewalt des Gefängnis, die in die Gesellschaft eindringt, sondern vielmehr das Gegenteil: Das hierarchische System, die Machtmissbräuche, der Machismus und die Unterwerfung, die in den Beziehungen zwischen den Gefangenen erlebt werden, sind die selben Beziehungen, die ein jeder von uns im Innern des sozialen Gefängnisses in sich trägt. Das Gefängnis reflektiert das, was \emph{draussen} ist, und nicht umgekehrt. Wenn die Ursachen der entfremdeten Beziehungen in dem Gefängnis gesucht werden müssen, dann ist dieses Gefängnis \emph{alles}, die Totalität des Bestehenden und der Wesen, die von der Einsperrung durchdrungen sind. \section{Von den moralischen und erzieherischen Gefängnissen} Wenn wir unter Gefängnis den Zwang von Körpern und Geistern, die Entfremdung von und durch sinnliche Erfahrungen, die auferlegte Hierarchie und die Pflicht zur Unterwerfung vor den Gesetzen (moralischen, juridischen und sittlichen) verstehen, wird offensichtlich, dass sich das Überleben, zu dem wir verurteilt sind, im Innern eines Gefängnisses abspielt, das kein \emph{ausserhalb} kennt. Schon von den jüngsten Jahren an büssen die «zivilisierten Menschen» ihre Strafe im Innern der Gefängnisgesellschaft ab und gewöhnen sich so an die Einschliessung als Norm. Die sogenannte Erziehung in den familiären und schulischen Strukturen ist nur der Anfang jener Lebenslänglichkeit, die uns abwechselnd zu Gefangenen und zu Wärtern der Reproduktion der Einsperrungs-Ideologie macht. Im Grunde basiert die passive Hinnahme der Situation des Gefangenen auf der Norm und der Ideologie: Von ganz klein an lernt das Individuum praktisch unmittelbar die Unterwerfung (ideologisch auch \emph{Respekt} genannt, obwohl er nicht im geringsten eine gegenseitige Basis impliziert) gegenüber der Autorität und den Hierarchien. Die Beziehung zum Vater, zu den Eltern, den Lehrern oder den Priestern kommt nicht «auf natürliche Weise» durch Wahl oder Willen zustande, sondern ist eine \emph{Verpflichtungssache}. Innerhalb solcher Beziehungen hat das Benehmen der Wärter keine Bedeutung – solange sie mit ihrer sozialen \emph{Rolle} betraut bleiben, können sie alles tun –, genausowenig wie die Sensibilität der Gefangenen: Die familiären und schulischen Autoritäten (oder jene der Gemeinschaft, in den seltenen Fällen, wo ihr Prinzip intakt geblieben ist) handeln für das Wohl des Gefangenen, für seine künftige Eingliederung, dafür, dass er keine «Fehler» begeht, und vor allem, um sich zu versichern, dass das kleine Individuum während dem Aufwachsen die selben Mechanismen reproduziert, auf denen die ganze Einschliessungs-Struktur basiert. An eben diesem Prinzip der «doppelten Bestrafung» kann man deutlich erkennen, wie die juridische Methode angewendet wird. Die Lehrkraft oder der Vater trifft mit dem betroffenen Subjekt nicht die geringste Vereinbarung, aber schreibt ihm Gesetze vor, die, falls sie übertreten werden, die Bestrafung des Individuums bewirken und nicht notwendigerweise die Sanktion der Übertretung. Wie für jeden Aspekt des sozialen Lebens, ist es der Mensch als Ganzes und in seiner Existenz, der bestraft wird, und nicht die Handlung an sich. Dieser Unterschied könnte als vernachlässigbar betrachtet werden angesichts dessen, dass die Bestrafung eines Aktes so oder so impliziert, dass die Person auf die eine oder andere Weise «anrührt» wird. Er wird dort jedoch fundamental, wo sich diese Begründung auf das idelogische Konstrukt einer Notwendigkeit zu bestrafen bezieht, auf die Schuldsprechung der Menschen in ihrem Wesen und nicht in ihrem Handeln. Die konzentrierte Organisation der schulischen Strukturen, aber immer mehr auch der Unterhaltung, sind bloss ein « Vorgeschmack », den uns die Gesellschaft offeriert, um die Geister und Gehirne zu domestizieren und sie an die stete Anwesenheit der Hühnerkäfige zu gewöhnen. In den Brutmaschinen der Passivität und der Entfremdung erlernen und verschlingen die Menschen eine zwiespältige und paradoxe «Persönlichkeit», bestehend aus einerseits dem Fakt, \emph{sich zu leben} wie eine Masse, und andererseits der hierarchischen Idee, sich über diese Masse zu stellen (aber immer als Bestadteil von dieser). Im Grunde liegt die Hoffnung darin, dass die Autorität eine gute Note erteilt, oder sogar Klassenbester zu werden, wenn möglich, indem man die Klasse erniedrigt, aber stets innerhalb der Klasse. Die Hauptsache ist also, sich niemals zu fragen, ob es richtig ist, dass uns jemand von einem irgendeinem Podium herab eine Note aufdrückt, eine Note, die immer weniger weder an unseren Verdienst, noch an ein spezifisches Verhalten gebunden ist, sondern schlicht an unser \emph{Beisammensein}: an den Fakt, Menschen in Gefängnissen zu sein. \section{Vom Gefängnis der Metropolen} Es genügt, irgendein während der letzten fünfzig Jahre erbautes Quartier zu beobachten, um sich der Art und Weise bewusst zu werden, mit welcher die Macht zu uns schaut. Es genügt insbesondere, die sogenannten Arbeiterviertel [frz.: quartier populaire] zu betrachten, diese Zellen worin die Armen konzentriert und eingeschlossen werden, um als erstes das Bild einer Haftanstalt im Kopf zu haben. Die aufeinanderfolgenden Regierungen haben die Armen stets präventiv für ihre soziale Stellung und ihr Gefährlichkeitspotential verurteilt. Die Aufeinanderfolge und Permanenz der «Volksaufstände» gegen die Arroganz der Mächtigen, getragen vom Traum von einem anderen Leben, haben die «Reaktion» dazu veranlasst, sich mit Mitteln zur Kontrolle und Eindämmung der Unzufriedenheit auf den Strassen auszurüsten. Eines dieser Mittel war die Entwicklung und Restrukturierung des Urbanismus. Wir könnten uns seitenweise über diese Sache auslassen und selbst dann würden wir nicht damit fertig, die beeindruckende Quantität konzipierter und konstruierter Monströsitäten aufzulisten, insbesondere jene der zweiten Hälfte des 20. Jahrhunderts. Angesichts der kürzlichen Unruhen in verschiedenen Städten der Welt verdient der am deutlichsten konzentrierte Aspekt des metropolitanen Monsters jedoch eine besondere Aufmerksamkeit. Die Architektur der Banlieues ist der Triumph der Entfremdung. Die Stadtteile sind Orte an denen die Untergebenen zusammengepfercht werden, bis sie in ihrer sozialen und individuellen Atomisierung krepieren, während die Wohnblöcke aus armiertem Beton überall mit der Obsession der Kontrolle aus dem Boden schiessen; ganz nach dem Bild dieser langen Korridore mit all den Gittern, die die Zugänge zu Orten der Reproduktion des Marktes und der Macht gegen potentiell gefährliche Menschen filtrieren. Sollten sich die Verbannten des «proletarischen Traumes» einmal auflehnen und gegen die Gitterstäbe schlagen, ja sogar ihre Zellen in Brand stecken, dann wird es mit einem solchen Dispositiv für den Aufseher umso leichter, diese Gänge ganz einfach abzuriegeln, indem er deren Ein- und Ausgänge kontrolliert, bevor von den Wachtürmen geschossen wird. Durch die Videoüberwachung ganzer Sektionen der Metropolen (mit Kameras an jeder Strassenecke), die permanenten Verbindungen zwischen den Aufsehern und die Datenverarbeitungsapperate, die Glasfaserkabel und das drahtlose Kommunikationssystem (die Kabel und Antennen sind überall im Gefängnis platziert), wird eine sehr schnelle Koordination unter den repressiven Kräften möglich. Die Architektur der Befriedung brachte einen qualitativen Sprung mit sich: zuvor sperrte man die Menschen ins Gefängnis, nachdem sie rebellierten, jetzt befinden sie sich bereits darin. Innerhalb eines solchen Kontexts passiert es allzu oft, dass die Revolten der Gefangenen selbst von der Einschliessung geprägt sind, und zwar indem der Angriff gegen einen Teilaspekt des Gefängnisses geführt wird, ohne seine Substanz anzutasten, oder indem sogar der Mythos und die Verteidigung des Gefängnisses einem Detail desselben gegenübergestellt wird. Was sonst bedeuten Phrasen wie «die Verteidigung des Quartiers», «mein Viertel», «keine Polizei in unseren Strassen», wenn nicht eine Aneignung der Einschliessungs-Ideologie? Wie kann man den Knast, der gegen uns konstruiert worden ist, als das « seine » bezeichnen? Die Viertel sind das Abbild der Einsperrung, zu der wir verurteilt sind, und der Verhältnisse, die uns auferlegt wurden. Als solche gehören sie zur Macht. Und von all dem, was zur Macht gehört, gibt es nichts zu retten. Damit wollen wir nicht sagen, dass die Wohnblöcke, in denen wir wohnen, in Brand gesteckt werden müssen, oder zumindest \emph{nicht sofort}. Doch wenn es gegenwärtig nur möglich ist, die Kontrolle zu zerschlagen, indem die falschen Zugehörigkeiten, die die Gefängnisideologie kreierte, aufgegeben werden und dies, um die tausenden Maschen des Kontrollgewebes wirklich zu sabotieren, dann werden wir von all dem nichts zu bewahren haben. \section{Von der Einsperrung der Geister} Wenn wir davon ausgehen, dass die Gesellschaft ein Gefängnis ist, dann ist das Gefängnis überall. Und in dem Überall gibt es kein Aussen. Schliesslich ist es uns schlicht nicht möglich auszubrechen, weil es keinen Ort gibt, wohin man gehen könnte. Diese Situation, die uns keinen einzigen «Notausgang» lässt, ist objektiv betrachtet untragbar, sie kreiert Bedrängnis, Schmerz und Verwirrung. Die Möglichkeit, einen Raum zu finden, wo man sich ein kleines Fleckchen partieller Freiheit errichten kann, ist mit dem Triumph der Entfremdung von und in den Beziehungen definitiv verloren gegangen. Die reelle Möglichkeit, die bestehenden Verhältnisse umzuwälzen, lässt auf sich warten und sowieso scheint es nur sehr wenige Leute zu interessieren. Ausgehend von dieser Feststellung braucht die Macht nicht mehr zu lügen und hat von einer Propaganda, nach welcher «dies die besteder möglichen Welten ist», zu einer anderen gewechselt, die besagt: «trotz alledem ist dies die einzigemögliche Welt». Indessen der Tatsache bewusst, dass immer mehr Betäubung nötig ist, um diese Existenz zu ertragen, bietet die Direktion der sozialen Strafanstalt ihren «Gästen» die einzig möglichen «Ausbrüche»: jene, die sich dem Geist \emph{annehmen}. Die Unterhaltung und die organisierte Ablenkung der Massen in den Stadien und während der « Ferien » betäubt bestimmt jeglichen Funken von selbstständigem Denken – indem man ihn in der künstlichen und obszönen Ekstase der festenden Meute erstickt –, aber scheinen nicht mehr ausreichend zu sein, um das Krebsgeschwür der Verurteilung zur Gefangenschaft zu stoppen. Seit mehreren Jahrzehnten und sich stetig weiterentwickelnd wird uns also, dank diversen psychoaktiven Substanzen, ein bisschen überall ein aufgesetzter geistiger Ausbruch angeboten. Allerlei Drogen verschiedenster Art, ob legal oder illegal, überfluten gegenwärtig diesen gigantischen Knast und während sie eine provisorische Flucht anbieten, errichten sie noch dazu ein neues Gefängnis innerhalb des Gefängnisses. In der russischen Babuschka der Einsperrung ist es dem Direktor endlich möglich, das letzte Stadium der Kontrolle zu erreichen und die Grundlagen für eine \emph{Gesellschaft des endlosen Wartens} zu entwerfen: Jene einer psychiatrisierten Welt. Eine Welt der Betäubung, wo das Unerträgliche erträglich, wo es \emph{lebbar} wird. Und wie immer in der Logik der Adaption, wenn irgendetwas lebbar wird, fühlen wir die Notwendigkeit nicht mehr, es zu verändern. Um die Gedanken unschädlich zu machen, brauchen sie also nicht mehr vernichtet oder mystifiziert zu werden: es reicht schlicht zu verhindern, dass sie entstehen, von ihrer « Geburt » bis zum Verlangen, selbst damit zu beginnen. Man kann sagen, dass der Ausbruch, den man uns \emph{vertickt}, die Abtreibung jeglichen \emph{Verstands} für die Freiheit ist. Er hat die selbe verabscheuenswürdige Funktion wie eine gute humanitäre Schwester in einem Lager, mit dem einzigen Unterschied, dass die Drogen (ob legal oder nicht) nicht einmal zum Verbinden der oberflächlichen Wunden dienen. Den Weg der Zerstörung des sozialen Gefängnisses angehen zu wollen und die permanente Konstruktion psychotischer Zwangsjacken für die Geister beiseite zu lassen, wäre wie den Staat abschaffen zu wollen, während man das Innenministerium verschont. In der modernen Welt ist es notwendiger denn je, die Verantwortlichkeiten des Zwangs neu zu definieren, um ganz klar zu sehen, was die Interessen jener sind (und folglich unsere Angriffsziele), die uns einsperren wollen – sowohl innerhalb als auch ausserhalb von uns selbst. Es wird Zeit, deutlich zu betonen, dass der Politiker, der Psychiater, der Bulle und der Drogenhändler auf gleiche Weise für unsere Unterdrückung verantwortlich sind. Und genauso, dass das Schicksal des Priesters, des «Bürgers» oder des Ideologen, der die Drogen als «befreiende Substanzen» verherrlicht (auch innerhalb der Szene), verbunden werden muss. \section{Von der Einsperrung der Körper} Der mangelhaften Rolle der Religion als delegierte Verwaltung des Lebens und des Todes, als Hoffnung (oder Toleranz) angesichts so vieler von den Menschen ertragener Übel und Missbräuche wird heute «endlich» durch eine neue weltliche Religion ausgeholfen: der Wissenschaftsgläubigkeit. In dieser Demokratie haben wir tatsächlich die Wahl: Unser Körper kann Gott gehören oder den Händen der Wissenschaft übergeben werden. Die Eingebildetsten können auch die beiden Aspekte versöhnen, indem sie ethisch ihre Seele Gott und ihren Körper den Wissenschaftlern übergeben. Die Entwicklung des Wissens ermöglichte im Namen des kollektiven Wohlbefindens in einen Grossteil des menschlichen Organismus einzudringen und die Kontrolle zu übernehmen. Gegenwärtig sind wir bei der genetischen Fichierung und Kartographierung angelangt. Hunderte neue Lombroso’s\footnote{Cesare Lombroso gilt als Begründer der kriminalanthropologisch ausgerichteten sogenannten \emph{Positiven Schule} der Kriminologie. Als selbst bezeichneter Rassist und Eugeniker sorgte er dafür, dass Kriminalität zunehmends unter naturwissenschaftlichen, biologischen und anthropologischen Aspekten betrachet wird.}, eingeschlossen in Laboratorien ein bisschen überall auf der Welt, träumen sogar davon, ihre Techniken zu verfeinern, um den geborenen Kriminellen zu entdecken, der in einem jeden von uns ruht. Diesmal nicht mit Hilfe von Hirnmessungen, sondern von Genen. In einer medikalisierten Gesellschaft, die einen Grossteil der Übel produziert und gleichzeitig das Monopol und die Kontrolle über ihre Gegenmittel besitzt, verfügen die Wissenschaftler über eine der grösst möglichen Mächte: Jene, das Leben zu erhalten. Es ist auch selbstverständlich, dass diese Betrachtungen nur ein Teil der Realität bleiben werden, solange die wichtigste Macht – wie im Fall der Religion – in der Tatsache liegt, angesichts eines gequälten Lebens, oder eher einer Art zu Überlebens, etwas Hoffnung einzuträufeln. Von ihrer Machtposition herab teilen sich die weiss behemdten Schakale dennoch bereits die Stücke unserer Körper auf und im Innern des Gefängnisses sind wir nun alle potentiell im Namen des Fortschritts zu opfernde Versuchskaninchen geworden. Uns selbst nicht gehörend, sind wir Instrumente und nicht Subjekte der Debatte. Die verschiedenen Heiligen Offizien und andere wissenschaftliche Kommissionen der Bioethik spielen sich gegenseitig den Ball zu, während sie uns vorschreiben wollen, wie wir zu leben haben, wie wir zu sterben haben, wem wir angehören und wie wir für uns zu sorgen haben. Im Namen Gottes, im Namen der Wissenschaft. In unserem Namen, niemals. Für all sie zählen wir nicht, da wir bloss Gefangene des Körpers sind, den sie uns verliehen haben. \section{Von der unmöglichen Flucht und der notwendigen Subversion} Wir haben ausführlich gesehen, dass es nirgends eine Möglichkeit gibt, dem sozialen Gefängnis zu entkommen, und dass sich dieses letztere über alle Aspekte des Bestehenden ausbreitet: Die einzige Möglichkeit, die noch bleibt, ist also die «Zerstörung der Inneneinrichtung». Durch die Subversion der sozialen Beziehungen können wir damit beginnen, jene Räume der Freiheit zu rekonstruieren, die man uns entsagt. Und um dahin zu gelangen, müssen wir uns der Hindernisse entledigen, die sich zwischen uns und unser Verlangen nach Emanzipation stellen. Stets dessen bewusst, dass der revolutionäre Weg kein abstrakter Weg ist, nicht abstrakter als die Mechanismen, die Strukturen und die Verantwortlichkeiten der Segregation. Sicher, in der Revolte öffnen sich Räume der Freiheit nicht von selbst, und wir sehen gut, wie subtil die Grenze ist, die sich in der aktuellen sozialen Konfliktualität zwischen der Implosion des Bürgerkrieges und der Explosion des Sozialen Krieges abzeichnet. Aber es ist auch richtig, dass sich nur in einem Moment des Aufstands ein physischer und temporärer Raum auftut, in welchem das Konstruieren und Erfinden der Grundlagen für befreite Beziehungen möglich ist. Die Unterstützung, die gegenüber den Revolten der Gefangenen des sozialen Gefängnis erbracht wird, darf und kann nicht akritisch und verherrlichend bleiben. Sie muss sich unbedingt in eine Möglichkeit konstruktiver Komplizenschaft verwandeln: um es noch einmal zu sagen, die Möglichkeiten, den Weg des sozialen Krieges aufzuzeichnen, zeigen sich in der Dialektik, die sich in einem Moment des Bruches unter den Aufständischen errichtet. «Unser Wunsch» ist, zur Aufspürung des Weges beizutragen, auf dem die Gefangenen nicht mehr als Gefangene des sozialen Gefängnisses revoltieren, sondern als Individuen, die die Vernichtung jeglichen Zwangs anstreben. Es ist nutzlos zu \emph{hoffen}, dem Ziel gewachsen zu sein, wir müssen uns vor allem unverzüglich die Mittel geben, um es zu sein. Und Basta. % begin final page \clearpage % new page for the colophon \thispagestyle{empty} \begin{center} Anarchistische Bibliothek \smallskip Anticopyright \bigskip \includegraphics[width=0.25\textwidth]{logo-yu.pdf} \bigskip \end{center} \strut \vfill \begin{center} Kurze Reise durch das soziale Gefängnis Juli 2009 \bigskip \href{http://acorpsperdu.wikidot.com/kurze-reise-durch-das-soziale-gefaengnis}{http:\Slash{}\Slash{}acorpsperdu.wikidot.com\Slash{}kurze-reise-durch-das-soziale-gefaengnis} Veröffentlicht in \emph{A Corps Perdu}, internationale anarchistische Zeitschrift, Nr. 2, November 2009. Teil des Dossier "Eingeschlossen von allen Seiten". \bigskip \textbf{anarchistischebibliothek.org} \end{center} % end final page with colophon \end{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Feature enabled: %citation-style: vancouver %citation-type: numbered %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{float} \begin{document} \def\RunningAuthor{Singanan M and Sundaram R} \firstPage{1} \articleType{Original Article} \receivedDate{01 Nov 2020} \acceptedDate{12 Jan 2021} \revisedDate{10 Dec 2020} \journalVolume{6} \journalIssue{1} \journalDoi{ijpib.v6i1.1393} \copyrightYear{2021} \def\authorCount{2} \def\affCount{2} \def\journalTitle{International Journal of Pharmacometrics and Integrated Biosciences} \title{\textbf{Investigation on the removal of bivalent cadmium ions from aqueous solution and treatment of industrial wastewater using new alumina interfaced biocarbon }} \author{Sundaram~R\textsuperscript{1}, Singanan~M\textsuperscript{}\textsuperscript{2}~\\[5pt]{\textsuperscript{1}Department of Chemistry\unskip, P.T. Lee C.N. Polytechnic College, Chennai -600007, Tamil Nadu, India}~\\{\textsuperscript{2}Department of Chemistry\unskip, Presidency College (Autonomous), Chennai-600005, Tamil Nadu, India}} \begin{abstract} The presence of heavy metals in water and wastewater is becoming a severe environmental and public health concern. It may contribute variety of adverse environmental and human health effects due to their acute and chronic exposure through air, water and food chain. They are released into the aquatic environment from many industrial activities. The present research paper deals with the adsorption capacity of the biocarbon material produced from the leaves of \textit{Lawsonia inermis} plant. The biocarbon was prepared by the H\ensuremath{_{2}}SO\ensuremath{_{4}} activation process. The adsorption capacity of the biocarbon was evaluated by considering the effect of various parameters such as pH of the solution, biocarbon dose, contact time, and initial metal ions concentration and to optimize the conditions for maximum adsorption. The metal ion uptake capacity of the biocarbon was tested in the stimulated wastewater containing bivalent cadmium ions. The maximum uptake of 97.85\% of the Cd (II) metal ions was observed at the equilibrium time of 3.0 hours at a dose of 3.0 g and at the pH of 4.5 in the stimulated wastewater. In the real sample analysis, electroplating industry wastewater is used for the removal of cadmium (II) ions. The results indicate that 95.16\% of ions were effectively removed at the same experimental conditions. It is also further noted that the metal~sorption~capability~of the adsorbent is higher with rising concentration of~metal ions in the solution. The percentage of adsorption of the metal ions was also significantly increased with rise of temperature of the wastewater. \end{abstract}\def\keywordstitle{Keywords} \begin{keywords}Lawsonia inermis,\newline heavy metal,\newline adsorption,\newline biocarbon,\newline wastewater treatment \end{keywords} \twocolumn[ \maketitle {\printKwdAbsBox}] \makeatletter{\Large$^\ast$}Corresponding Author\par Name:\ Singanan~M~\\ Phone:\ +917200411065~\\ Email:\ [email protected] \par\vspace{-13pt}\hrulefill\par\ifx\@eISSN\@empty\else{\fontsize{12}{14}\selectfont eISSN: \@eISSN}\par\fi% \textsc{DOI:}\ \href{https://doi.org/10.26452/\@journalDoi}{\textcolor{blue}{\underline{\smash{https://doi.org/10.26452/\@journalDoi}}}}\par% \vspace{-12pt}\hrulefill\\[5pt]\hypersetup{allcolors=black}\qrcode[version=4,height=1.5cm]{https://doi.org/10.26452/\@journalDoi}\hypersetup{allcolors=blue} \hspace{10.5pt}\parbox[t]{5cm}{\raisebox{19pt}{\fontsize{9.12}{10.12}\selectfont Production and Hosted by}\\[-13pt]{{\fontsize{12}{14}\selectfont ScienzTech.org \\[-1pt]{\fontsize{9.12}{10.12}\selectfont\textcopyright\ \@copyrightYear\ $\|$ All rights reserved.}\\[-8pt]\hspace{-1pt}\rule{.762\columnwidth}{1.2pt}}}}\hypersetup{allcolors=blue}%{\fontsize{12}{14}\selectfont Pharmascope.org}\par% \makeatother \section{Introduction} The presence of cytotoxic metals in environment is a serious concern. Toxic metal pollutants are discharged into the environment as a consequence of different industrial, aquaculture and other human-made activities \unskip~\cite{986970:21254885}. Toxic metals are considered to be non-biodegradable as well as of an extremely poisonous nature \unskip~\cite{986970:21254869}. Water pollution and environmental degradation is mainly caused by the release of untreated industrial wastewater containing a lot of toxic substances and some other organic contaminants. Hence, the receiving water bodies are highly contaminated and the quality of the water is changed and become unfit any potable uses \unskip~\cite{986970:21254874}. This might cause severe pollution problems. The treatment of industrial wastewater prior to discharge into natural water bodies is therefore very important \unskip~\cite{986970:21254890,986970:21254871}. Cadmium is one of the toxic metal. It is mainly used in many industrial applications. The long-term exposure of cadmium to human beings may lead to serious renal dysfunction and acute disorders like testicular atrophy, hypertension, bones and kidney damage \unskip~\cite{986970:21254876}. In drinking water, the maximum permissible limit (MPL) of cadmium is 0.005 mg/L, as set out in the WHO guideline \unskip~\cite{986970:21254883}. The removal of toxic wastewater containing cadmium is therefore essential. In industrial wastewater treatment process numerous technologies are available and some of them are often used to treat contaminated wastewater. However, most of the currently available methods are not efficient in eliminating heavy metals completely at very low concentration. Moreover, the conventional methods are relatively expensive and further produce the secondary effluent and create additional pollution in the aquatic ecosystem. Simple and green techniques are therefore required for the treatment of industrial wastewater. It is well established that adsorption and biosorption techniques are the simplest and most versatile methods used for the water and wastewater treatment. However, the problem of finding low-cost and effective adsorbent materials is still problem in this fields. Many of the adsorbent materials are very costly and reusable. In these aspects, it is necessary to search for new and low-cost materials for the treatment of the wastewater system. In this field of research, materials such as crab shell \unskip~\cite{986970:21254873}, coconut copra meal \unskip~\cite{986970:21254891}, eggshell \unskip~\cite{986970:21254880}, papaya wood \unskip~\cite{986970:21254882}, sunflower stem \unskip~\cite{986970:21254889}, and tea leaves\unskip~\cite{986970:21254878} are reported as a cheaper adsorbent for the removal and recovery of toxic heavy metals in wastewater. In the present research work, \textit{Lawsonia inermis} leaves are used for the production of biocarbon and are further used for the elimination of cadmium ions in stimulated wastewater and for their implementation to real wastewaters. \section{Materials and Methods} \textbf{Preparation of } \textbf{metal solution} The stock solution (1000 mg/L) of cadmium (II) ion was prepared by dissolving the analytical grade of cadmium nitrate Cd (NO\ensuremath{_{3}}).4H\ensuremath{_{2}}O in double distilled water. The pH values of the working solutions have been adjusted using 0.1 N NaOH and 0.1 N HCl. The pH of the resulting solutions was measured with Hanna pH Instruments (Italy). The concentration of cadmium (II) ions determined by use of AAS. \textbf{Preparation of biocarbon} The \textit{Lawsonia inermis} medicinal plant leaves have been collected and air-dried for 48 hours. Biocarbon was produced by the treatment of leaves with concentrated analytical grade sulphuric acid. The resulting black product was kept in hot air oven at 160 \ensuremath{\pm} 2 \ensuremath{^\circ}C for 6 hours, then washed with distilled water and then dried at 105 \ensuremath{\pm} 2 \ensuremath{^\circ}C. Biocarbon particle sizes between 85 and 130 \ensuremath{\mu }m have been used. In a 500 mL beaker, pure alumina and biocarbon were taken at a ratio of 2:1 and double distilled water was added and heated at 60 \ensuremath{^{o}}C for 30 min and the resulting product was filtered and dried at 200 \ensuremath{\pm} 2 \ensuremath{^{o}}C for 3 hours. The hot air-dried material is finely ground in a range of 100 to 120 microns and maintained in a separate glass container for further use. The biocarbon material is known as alumina interfaced biocarbon (AIBC). \textbf{Batch adsorption process} Batch-wise adsorption experiments were conducted in a series of 250 mL of Erlenmeyer flasks. In the adsorption experiments, the effect of pH, contact time, amount of biocarbon dose and temperature was estimated using an initial metal ion concentration of 100 mg/L with a volume of 100 mL. For the optimization of the amount of adsorbent dose, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5 and 4.0 g of biocarbon was treated separately with 4.5 pH test solutions. All adsorption experiments were performed at 30 \ensuremath{\pm} 2\ensuremath{^\circ}C with the exception of the effect of temperature studies. At 250 rpm, the experimental flasks were constantly agitated up to 180 min to determine the equilibrium condition. Samples were collected at the end of the pre-determined time period (30 min) and the concentration of metal ions was estimated using the AAS technique. Percent removal of cadmium (II) ions and the quantity of metal ions adsorbed from the wastewater system was calculated using the Equations~(\ref{dfg-5c3eca67b6d4}) and~(\ref{dfg-f0caed560e6a}) described by Dada et al., \unskip~\cite{986970:21254875}: \let\saveeqnno\theequation \let\savefrac\frac \def\dispfrac{\displaystyle\savefrac} \begin{eqnarray} \let\frac\dispfrac \gdef\theequation{1} \let\theHequation\theequation \label{dfg-5c3eca67b6d4} \begin{array}{@{}l}q_e=\left(\frac{C_o-C_e}w\right)\times V\end{array} \end{eqnarray} \global\let\theequation\saveeqnno \addtocounter{equation}{-1}\ignorespaces \let\saveeqnno\theequation \let\savefrac\frac \def\dispfrac{\displaystyle\savefrac} \begin{eqnarray} \let\frac\dispfrac \gdef\theequation{2} \let\theHequation\theequation \label{dfg-f0caed560e6a} \begin{array}{@{}l}\%\;Removal=\left(\frac{C_o-C_e}{C_o}\right)\times100\end{array} \end{eqnarray} \global\let\theequation\saveeqnno \addtocounter{equation}{-1}\ignorespaces Where C\ensuremath{_{o}} and C\ensuremath{_{e}} are the initial and equilibrium concentrations of the metal ions (mg/L), w~is mass of biocarbon (g) and V is the volume of the metal containing wastewater (mL) respectively. \textbf{Temperature studies} The impact of temperature was explored using 100 mL of sample solution with an initial concentration of 100 mg/L of Cd (II) ions for 3 hours at an optimised adsorbent dose of 3.0 g at temperatures with 30, 40, 50, 60, 70 and 80 \ensuremath{^{o}}C respectively. \textbf{Desorption experiments} The desorption of the Cd (II) ion study was performed using one of the biocarbon used in the batch process. In these experiments, 50 mL of distilled water was added to the spent biocarbon and the pH of the solution was changed to 5.5 with the 1.0 N HCl and the solution was agitated at 250 rpm for 3 hours. The desorbed cadmium ion in the bulk solution was estimated at an interval of 30 min. \section{Results and Discussion} \textbf{Characterization of biocarbon (AIBC)} \textbf{\space } The characterization of biocarbon is extremely necessary to ascertain the correct surface assimilation capability of the adsorbents in any metal particle removal method. The necessary physico-chemical properties of the \textit{Lawsonia inermis} plant leaves biocarbon are shown in Table~\ref{table-wrap-a710ac9a06d2461bb8630cce9151bd81}. \begin{table}[!htbp] \caption{\boldmath {\textbf{Physico-chemical properties of biocarbon.}} } \label{table-wrap-a710ac9a06d2461bb8630cce9151bd81} \def\arraystretch{1.1} \ignorespaces \centering \begin{tabulary}{\linewidth}{p{\dimexpr.13130000000000003\linewidth-2\tabcolsep}p{\dimexpr.5588\linewidth-2\tabcolsep}p{\dimexpr.3099\linewidth-2\tabcolsep}} \tbltoprule \rowcolor{kwdboxcolor}\textbf{S.No.} & \textbf{Parameters} & \textbf{Values}\\ \tblmidrule 1. & Moisture content (\%) & 54.30 \ensuremath{\pm} 1.25\\ 2. & Bulk density (g/ml) & 0.98 \ensuremath{\pm} 0.06\\ 3. & Total loss of ignition (\%) & 96.35 \ensuremath{\pm} 1.16\\ 4. & Total organic components (\%) & 88.56 \ensuremath{\pm} 1.31\\ 5. & Insoluble components (\%) & 13.25 \ensuremath{\pm} 1.72\\ 6. & Surface area (BET) (m2/g) & 9.65 \ensuremath{\pm} 0.08\\ 7. & C content (\%) & 86.44 \ensuremath{\pm} 1.08\\ 8. & H content (\%) & 9.38 \ensuremath{\pm} 0.04\\ \tblbottomrule \end{tabulary}\par \end{table} \bgroup \fixFloatSize{images/a32d55a4-df72-48d7-a51b-75748969c06e-upicture1.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/a32d55a4-df72-48d7-a51b-75748969c06e-upicture1.png}{\includegraphics{images/a32d55a4-df72-48d7-a51b-75748969c06e-upicture1.png}}{} \makeatother \caption{\boldmath {Effect of pH (C\ensuremath{_{o}} = 100 mg/L, AIBC = 3.0g/100 mL at 30 \ensuremath{\pm} 2\ensuremath{^\circ}C)}} \label{f-cf7a227531b9} \end{figure} \egroup \bgroup \fixFloatSize{images/d5a17d3d-5744-41a6-96b5-8667eca2aeb9-upicture2.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/d5a17d3d-5744-41a6-96b5-8667eca2aeb9-upicture2.png}{\includegraphics{images/d5a17d3d-5744-41a6-96b5-8667eca2aeb9-upicture2.png}}{} \makeatother \caption{\boldmath {Effect of contact time (C\ensuremath{_{o}} = 100 mg/L, pH = 4.5, AIBC = 3.0g/100 mL at 30 \ensuremath{\pm} 2\ensuremath{^\circ}C)}} \label{f-aa71cfccd0b7} \end{figure} \egroup \bgroup \fixFloatSize{images/3a3a8a55-bc3c-459b-a001-369caacfd345-upicture3.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/3a3a8a55-bc3c-459b-a001-369caacfd345-upicture3.png}{\includegraphics{images/3a3a8a55-bc3c-459b-a001-369caacfd345-upicture3.png}}{} \makeatother \caption{\boldmath {Effect of amount of biocarbon (C\ensuremath{_{o}} = 100 mg/L, pH = 4.5 at 30 \ensuremath{\pm} 2\ensuremath{^\circ}C)}} \label{f-a753f024d052} \end{figure} \egroup \bgroup \fixFloatSize{images/05794f71-0b4f-4b07-a15b-86da0e717a13-upicture4.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/05794f71-0b4f-4b07-a15b-86da0e717a13-upicture4.png}{\includegraphics{images/05794f71-0b4f-4b07-a15b-86da0e717a13-upicture4.png}}{} \makeatother \caption{\boldmath {Effect of initial concentration of metal ions (C\ensuremath{_{o}} = 100 mg/L, AIBC = 3.0g/100 mL at 30 \ensuremath{\pm} 2\ensuremath{^\circ}C)}} \label{f-8b5d3583eb99} \end{figure} \egroup \bgroup \fixFloatSize{images/5fdf7111-b76f-4013-82cb-7eb579ce0fa9-upicture5.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/5fdf7111-b76f-4013-82cb-7eb579ce0fa9-upicture5.png}{\includegraphics{images/5fdf7111-b76f-4013-82cb-7eb579ce0fa9-upicture5.png}}{} \makeatother \caption{\boldmath {Effect of temperature (C\ensuremath{_{o}} = 100 mg/L, pH = 4.5, AIBC = 3.0g/100 mL)}} \label{f-d791d82b7b12} \end{figure} \egroup \bgroup \fixFloatSize{images/e9b48a33-41a4-40e5-b89e-a66103ca07e4-upicture6.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/e9b48a33-41a4-40e5-b89e-a66103ca07e4-upicture6.png}{\includegraphics{images/e9b48a33-41a4-40e5-b89e-a66103ca07e4-upicture6.png}}{} \makeatother \caption{\boldmath {Desorption of Cd (II) ions (pH = 7.8 {\textendash} 8.35. BCD = 3.0g/100 mL at 30 \ensuremath{\pm} 2\ensuremath{^\circ}C)}} \label{f-d923e8183c0f} \end{figure} \egroup \begin{table}[!htbp] \caption{\boldmath {The results of treatment of metal plating industrial wastewater} } \label{tw-a0a09ed04fbc} \def\arraystretch{1.1} \ignorespaces \centering \begin{tabulary}{\linewidth}{p{\dimexpr.5936\linewidth-2\tabcolsep}p{\dimexpr.1971\linewidth-2\tabcolsep}p{\dimexpr.2093\linewidth-2\tabcolsep}} \tbltoprule \rowcolor{kwdboxcolor}Wastewater quality parameters (mg/L) & \multicolumn{2}{p{\dimexpr(.4064\linewidth-2\tabcolsep)}}{\cAlignHack Results (mg/L)}\\ \rowcolor{kwdboxcolor} & Before treatment & After treatment\\ \tblmidrule pH & 4.50 \ensuremath{\pm} 0.2 & 5.6 \ensuremath{\pm} 0.3\\ Electrical conductivity (\ensuremath{\mu}mhos/cm) & 4750 \ensuremath{\pm} 1.5 & 950 \ensuremath{\pm} 1.2\\ Total dissolved solids & 3095 \ensuremath{\pm} 1.2 & 620 \ensuremath{\pm} 1.1\\ Turbidity (NTU) & 1.25 \ensuremath{\pm} 0.8 & 0.2 \ensuremath{\pm} 0.7\\ Chloride & 475.62 \ensuremath{\pm} 1.6 & 125 \ensuremath{\pm} 1.3\\ Sulphate & 1150 \ensuremath{\pm} 1.8 & 240 \ensuremath{\pm} 1.5\\ Calcium & 85.54 \ensuremath{\pm} 0.8 & 12 \ensuremath{\pm} 0.6\\ Sodium & 160.34 \ensuremath{\pm} 0.7 & 28 \ensuremath{\pm} 0.5\\ Potassium & 46.43 \ensuremath{\pm} 0.9 & 8.5 \ensuremath{\pm} 0.6\\ Iron & 30.53 \ensuremath{\pm} 1.1 & 3.6 \ensuremath{\pm} 0.8\\ Cadmium & 45.50 \ensuremath{\pm} 0.8 & 2.2 \ensuremath{\pm} 0.3\\ Lead & 25.52 \ensuremath{\pm} 0.5 & 2.5 \ensuremath{\pm} 0.6\\ \tblbottomrule \end{tabulary}\par \end{table} \textbf{Effect of pH} \textbf{\space } The pH is a controlling parameter and plays a greater role in the process of biocarbon adsorption of heavy metals. The principal driving force for metal ion adsorption on the adsorbent surface is the electrostatic interaction between adsorbent and adsorbate. The greater the interaction, the higher the adsorption of heavy metal ions. The pH greatly influences the surface charge of the adsorbent and the degree of ionization of heavy metals in solution \unskip~\cite{986970:21254870}. The trend of removal of Cd (II) ions to the AIBC surface was shown in Figure~\ref{f-cf7a227531b9}. The results indicate that the metal uptake is less near pH 3.0. This is due to the repulsive as well as competitive behaviour of H+ ions with Cd (II) ions on the adsorbent surface. This process delayed the Cd (II) ions to reach the binding sites. In addition, Cd (II) ions were precipitated as Cd (OH)\ensuremath{_{2}} at the higher pH. The results clearly show that 97.85 per cent of metal ions were removed from the wastewater at the pH of 4.5 per 100 mg/L. The results further reveals that the ion - exchange mechanism was involved during the adsorption of metal ions on the surface of the biocarbon. \textbf{Effect of contact time} \textbf{\space } This is the time needed to achieve equilibrium in the adsorption progression and is also called equilibrium time \unskip~\cite{986970:21254879}. The effect of contact time on the removal of Cd (II) ions was investigated by varying the contact time (30-210 min), while other parameters were kept constant. The elimination of Cd (II) ions on the adsorbent matrix is shown in Figure~\ref{f-aa71cfccd0b7}. The results show that the elimination of metal ions increased significantly when the contact time increased from 60 to 180 min. The adsorption process is initially rapid due to the accessibility of rich active sites on the adsorbent \unskip~\cite{986970:21254867}. The similar findings were also observed by Tong et al., \unskip~\cite{986970:21254888}. The mechanism of transfer metal ions to the surface of the adsorbent includes diffusion through the fluid film around the adsorbent particle and through the pores to the internal adsorption sites. In these experimental studies, it is observed that the equilibrium was reached in 180 min. Experimental solutions were left for 24 hours of contact time, but no significant changes were noted in the removal of metal ions. \textbf{Effect of amount of biocarbon} \textbf{\space } The adsorption capacities for different biocarbon doses were determined by keeping all other factors constant, for example, pH, contact time and temperature. The sorption process of Cd (II) ions on the surface of the biocarbon with respect to the initial concentrations of metal ions can be seen in Figure~\ref{f-a753f024d052}. The results show that the uptake of cadmium ions on the surface of the adsorbent was gradually increased from 0.5 g to 4.0 g. This may be due to the greater availability of the exchangeable sites or surface area at higher concentration of the adsorbent. Maximum removal of metal ions was observed at an adsorbent dose of 3.0 g. Further increasing the amount of the adsorbent will not show any significant changes in the removal process. Additionally, the study clearly demonstrates that 3.0 g of the adsorbent is sufficient to remove metal ions. The findings demonstrates that the elimination efficiency of adsorbents is mainly related to the availability of more active sites \unskip~\cite{986970:21254868}. \textbf{Effect of the initial concentration of Cd (II) ions} \textbf{\space } The initial concentration of Cd (II) provides an important driving force to overcome all mass transfer resistances of metal ions between the aqueous and solid phases. It is mandatory to investigate the role of the initial concentration of metal ions in sorption studies. This is because the contamination of water and wastewater has various metal ion concentrations \unskip~\cite{986970:21254872}. Removal of Cd (II) from solution was studied at concentrations of 10, 25, 50, 75 and 100 mg/L, respectively. The percentage of Cd (II) adsorption is shown in Figure~\ref{f-8b5d3583eb99}. The extent of metal ions adsorbed by biocarbon is greatly increased when the initial concentration of metal was enhanced from 10 mg/L to 100 mg/L. In addition, the increasing in uptake capacity of biocarbon with the increasing of Cd (II) ion concentration is due to higher availability of Cd (II) ions in the solution, for the adsorption. This state is often clarified by the fact that there has been a strong possibility of collision at high concentrations between both the adsorbent surface and the metal ions \unskip~\cite{986970:21254886}. \textbf{Effect of temperature} \textbf{\space } The effect of temperature on the removal of Cd (II) ions efficiency was investigated at constant operating parameters by varying the temperature from 30 \ensuremath{^{o}}C to 80 \ensuremath{^{o}}C. The temperature has key effects on the adsorption process. It accelerates the diffusion rate of the adsorbate ions into the external boundary layer and within the pores. Additionally, changing the temperature will modify the equilibrium capacity of the adsorbent. The level of cadmium ion removed from stimulated wastewater at different temperatures is shown in Figure~\ref{f-d791d82b7b12}. The removal of metal ions has been observed to increase significantly while the temperature has risen. This may be due to increased mobility and the spread of ion species. It is also well established that diffusion is an endothermal process \unskip~\cite{986970:21254879}. The findings suggest that, in addition to physical sorption, the adsorption mechanism of Cd (II) ion on the biocarbon surface could be chemical sorption. \textbf{Treatment of industrial wastewater} \textbf{\space } The use of biocarbon in water and wastewater treatment is very important. Biocarbon materials are therefore tested for the elimination of Cd (II) ions in the selected metal plating industrial wastewater. The pH of the wastewater sample was kept at 4.5 for the efficient removal of metal ions and other pollutants. The wastewater sample is subjected to the treatment process with predetermined equilibrium data. The contact time was 3hrs, the adsorbent dose was 3.0 g and also the agitation speed was 250 rpm. The experimental results of electroplating industrial wastewater were presented in Table~\ref{tw-a0a09ed04fbc}. The findings suggest that the disposal of Cd (II) in industrial wastewater is considerably better (p{\textless}0,05). In addition, the results suggest that 95.16 percent Cd metal ions had been separated from the wastewater by adding only 3.0 g of the adsorbent. The results were also in good agreement with the results of the batch experiments conducted for the removal of Cd (II) in aqueous solution. \textbf{Desorption of Cd (II) from AIBC} \textbf{\space } Disposal of the exhausted adsorbent is also a challenging environmental problem may lead to hazardous pollution problems. The saturated adsorbent which contains significant amount of Cd (II) ions is not safe for disposal due to the stringent environmental constraints. Hence, finding a suitable metal recovery process will help greatly to solve this type of waste disposal problems. Adsorption of any solute on adsorbent takes place by physical bonding, ion-exchange, or a combination of both. In the present study, the desorption of Cd (II) ion was carried out 1.0 N HCl as eluent. In the desorption studies, 98.50 percent of metal ions were recovered at a pH of 7.8 and removed completely at 8.5. The result is shown in Figure~\ref{f-d923e8183c0f}. Even though, the desorption of metal pollutants from the adsorbent matrix is not an easy task. This seems to be mainly due to the high adsorption capacity of the adsorbent. The effect of microporous regulation is largely due to presence of microporous filling to cause de-sorption lag \unskip~\cite{986970:21254877}. Furthermore, it was absolutely difficult to recover the metal ions from the micropore structure of the adsorbent. It is extremely difficult to restore the deformed micropores to the original form, which means that some of the Cd (II) ions could not be released from the adsorbent matrix \unskip~\cite{986970:21298998,986970:21254887}. \section{Conclusions} The disposal of Cd (II) ions in metal plating of industry and in stimulated wastewaters using biocarbon technology has been studied in batch experiments. On the basis of the results, the following conclusions can be drawn; \begin{enumerate} \item \relax AIBC is an efficient adsorbent material for the removal of cadmium ions from industrial wastewater. \item \relax The adsorption of metal ions increased with the increase in the initial concentration of Cd (II) ions. \item \relax The maximum percent removal of Cd (II) ions in stimulated wastewater (97.85) and in metal plating industrial wastewater (95.16) was observed by using 3.0 g of adsorbent and the contact time of 180 min. \item \relax During the desorption studies, a complete metal recovery was observed at the pH of 8.5. \item \relax This methodology has been applied successfully to the removal of toxic metals from hazardous wastewater. \item \relax The adsorption methodology is very simple, easy to operate, economically feasible and particularly eco-friendly in nature. \end{enumerate} \section{Acknowledgement} The authors are very much thankful to Dr. P.V. Krupakara, M.Sc., PhD., Vice Principal, Cambridge Institute of Technology (North Campus), Bangalore, Karnataka for his moral support for the completion of the research work. \section{Funding Support} The authors declare that they have no funding support for this study. \section{Competing interests} The authors declare that they have no conflict of interest for this study. \bibliographystyle{vancouver} \bibliography{\jobname} \bioItem[images/a8bcbd09-0011-4852-a4fe-6c296a631885-ucapture]{Singanan M}{ Assistant Professor of Chemistry, Presidency College (Autonomous), Chennai {\textendash} 600 005. Tamil Nadu, India.} \printBio \begin{mdframed}[backgroundcolor=cpboxcolor,hidealllines=true,innerbottommargin=7pt,innerrightmargin=1pt,rightmargin=1pt,innerleftmargin=1pt,leftmargin=2pt,skipabove=1pt,innertopmargin=2pt,innerbottommargin=1pt,skipbelow=1pt]% {\fontsize{8.5}{10}\selectfont\textbf{Copyright:}~\copyrightstmt} \end{mdframed} \begin{mdframed}[backgroundcolor=citeboxcolor,hidealllines=true,innerbottommargin=7pt,innerrightmargin=4pt,rightmargin=4pt,innerleftmargin=2pt,leftmargin=2pt,skipabove=1pt,innertopmargin=2pt,innerbottommargin=4pt,skipbelow=2pt]% {\fontsize{8.5}{10}\selectfont\textbf{Cite~this~article:}~\citeauthor.~\citetitle.\space\makeatletter\abbrvJournalTitle\ \@copyrightYear;\ \ifx\@journalVolume\@empty X\else\@journalVolume\fi\ifx\@journalIssue\@empty\else(\@journalIssue)\fi:\ \ifx\@firstPage\@empty 1\else\@firstPage\fi-\pageref*{LastPage}.\makeatother} \end{mdframed} \vskip-1.1pc {\includegraphics[width=125pt,height=50pt]{scienztech_logo.png}} \vskip-2.5pc ~\\ {\fontsize{9.12}{10.12}\selectfont\textcopyright\ \makeatletter\@copyrightYear\makeatother\ ScienzTech.org.} \end{document}
http://refbase.org/search.php?sqlQuery=SELECT%20author%2C%20title%2C%20type%2C%20year%2C%20publication%2C%20abbrev_journal%2C%20volume%2C%20issue%2C%20pages%2C%20keywords%2C%20abstract%2C%20thesis%2C%20editor%2C%20publisher%2C%20place%2C%20abbrev_series_title%2C%20series_title%2C%20series_editor%2C%20series_volume%2C%20series_issue%2C%20edition%2C%20language%2C%20author_count%2C%20online_publication%2C%20online_citation%2C%20doi%2C%20serial%20FROM%20refs%20WHERE%20serial%20%3D%2043156%20ORDER%20BY%20first_author%2C%20author_count%2C%20author%2C%20year%2C%20title&client=&formType=sqlSearch&submit=Cite&viewType=&showQuery=0&showLinks=1&showRows=10&rowOffset=&wrapResults=1&citeOrder=&citeStyle=APA&exportFormat=RIS&exportType=html&exportStylesheet=&citeType=LaTeX&headerMsg=	refbase.org	CC-MAIN-2017-26	application/x-latex	text/x-php	crawl-data/CC-MAIN-2017-26/segments/1498128320695.49/warc/CC-MAIN-20170626083037-20170626103037-00078.warc.gz	336,334,749	1,457	%&LaTeX \documentclass{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{textcomp} \begin{document} \begin{thebibliography}{1} \bibitem{AliceBranton2015} Alice Branton. (2015). Antibiogram and Genotypic Analysis using 16S rDNA after Biofield Treatment on Morganella morganii. \textit{Advanced Techniques in Biology \& Medicine}, \textit{3}(3), Trivedi MK, Branton A, Trivedi D, Nayak G, Gangwar M, et al. (2015) Antibiogram and Genotypic Analysis using 16S rDNA after Biofield Treatment on Morganella morganii. Adv Tech Biol Med 3: 137. doi: 10.4172/2379-1764.1000137. Retrieved June 26, 2017, from http://dx.doi.org/10.4172/2379-1764.1000137 \end{thebibliography} \end{document}
https://tikz.net/wp-content/uploads/2022/01/jet_tau.tex	tikz.net	CC-MAIN-2022-05	text/x-tex	text/x-matlab	crawl-data/CC-MAIN-2022-05/segments/1642320300010.26/warc/CC-MAIN-20220116180715-20220116210715-00131.warc.gz	646,131,331	2,277	% Author: Izaak Neutelings (November 2021) % Description: jet cones for taus & others \documentclass[border=3pt,tikz]{standalone} \usetikzlibrary{calc} \usetikzlibrary{math} % for \tikzmath \tikzset{>=latex} % for LaTeX arrow head \colorlet{myblue}{blue!70!black} %\colorlet{mydarkblue}{blue!50!black} \colorlet{mygreen}{green!60!black} \colorlet{myred}{red!75!black} \colorlet{isocol}{blue!70!black} % color isolation cone \colorlet{sigcol}{red!90!black} % color isolation cone \tikzstyle{track}=[->,line width=0.6,myred] \tikzstyle{dashed track}=[->,mygreen,line width=0.6,line cap=round, dash pattern=on 2.3 off 2.0] \newcommand\jetcone[6][sigcol]{{ \pgfmathanglebetweenpoints{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#3}{center}} \pgfmathsetmacro\oang{#4/2} % half-opening angle \edef\e{#5} % ratio a/b \def\tmpL{tmpL-#2-#3} % unique coordinate name \edef\vang{\pgfmathresult} % angle of vector OV \tikzmath{ coordinate \C; \C = (#2)-(#3); \x = veclen(\Cx,\Cy)\esin(\oang)^2; % x coordinate P \y = tan(\oang)(veclen(\Cx,\Cy)-\x); % y coordinate P \a = veclen(\Cx,\Cy)sqrt(\e)sin(\oang); % vertical radius \b = veclen(\Cx,\Cy)tan(\oang)sqrt(1-\esin(\oang)^2); % horizontal radius \angb = acos(sqrt(\e)sin(\oang)); % angle of P in ellipse } \coordinate (\tmpL) at ($(#3)-(\vang:\x pt)+(\vang+90:\y pt)$); % tangency \draw[thin,#1!50!black,fill=#1!80!black!50,rotate=\vang] % cone back (\tmpL) arc(180-\angb:180+\angb:{\a pt} and {\b pt}) -- ($(#2)+(0.01,0)$) -- cycle; \draw[thin,#1!50!black,rotate=\vang, % cone inside top color=#1!60!black!60,bottom color=#1!50!black!75,shading angle=\vang] (#3) ellipse({\a pt} and {\b pt}); #6 % extra tracks \draw[thin,#1!50!black,rotate=\vang,fill opacity=0.80, % cone front top color=#1!90!black!20,bottom color=#1!50!black!50,shading angle=\vang] (\tmpL) arc(180-\angb:180+\angb:{\a pt} and {\b pt}) -- ($(#2)+(0.01,0)$) -- cycle; }} \begin{document} % COMMON SETTINGS \small \def\angiso{44} % opening angle of isolation cone \def\angsig{22} % opening angle of isolation cone \def\e{0.11} % a/b ratio of ellipse minor and major radii \foreach \ang [evaluate={\ang; \anang=\ang-90;}] in {90,\angiso/2,0,180}{ % rotate each cone \tikzset{ every picture/.append style={scale=2.4,rotate=\ang-90}, % set scale for all figures every node/.style={inner sep=1,circle} %,draw=black!9,very thin} } % TAU JET - ONE PRONG \begin{tikzpicture} \coordinate (O) at (0,0); \coordinate (O') at (0,-0.01); % shifted \coordinate (I) at (0,0.92); % isolation cone \coordinate (S) at (0,1.00); % signal cone \coordinate (T) at (0,0.02); % tau vertex \jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone \jetcone[sigcol]{O}{S}{\angsig}{\e}{ % signal cone \draw[track] (T) to[out=88,in=-70] (93:1.33) node[anchor=-70+\anang,inner sep={2.5cos(\ang)^2-1.5}] {$\pi^-$}; } } \end{tikzpicture} % TAU JET - ONE PRONG, 2 PI ZEROS \begin{tikzpicture} \jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone \jetcone[sigcol]{O}{S}{\angsig}{\e}{ % signal cone \draw[dashed track] (T) -- (97:1.18) node[anchor=-40+\anang,inner sep={2cos(\ang)^2-1.0}] {$\pi^0$}; \draw[dashed track] (T) -- (82:1.20) node[anchor=-110+\anang,inner sep=0.0] {$\pi^0$}; \draw[track] (T) to[out=88,in=-70] (94:1.33) node[anchor=-100+\anang,inner sep={-sin(\ang)^2}] {$\pi^-$}; } } \end{tikzpicture} % TAU JET - THREE PRONG \begin{tikzpicture} \jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone \jetcone[sigcol]{O}{S}{\angsig}{\e}{ % signal cone \draw[track] (T) to[out=90,in=-55] (103:1.33) node[anchor=-70+\anang,inner sep={2.5cos(\ang)^2-1.5}] {$\pi^-$}; \draw[track] (T) to[out=90,in=-112] (87:1.29) node[anchor=-110+\anang,inner sep={0.6sin(\ang)^2}] {$\pi^+$}; \draw[track] (T) to[out=88,in=-117] (82:1.16) node[anchor=-145+\anang,inner sep={0.6sin(\ang)^2}] {$\pi^+$}; } } \end{tikzpicture} % TAU JET - THREE PRONG, PI ZERO \begin{tikzpicture} \jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone \jetcone[sigcol]{O}{S}{\angsig}{\e}{ % signal cone \draw[dashed track] (T) -- (92:1.18) node[anchor=-85+\anang,inner sep=0.5] {$\pi^0$}; \draw[track] (T) to[out=90,in=-55] (103:1.33) node[anchor=-70+\anang,inner sep={2.5cos(\ang)^2-1.5}] {$\pi^-$}; \draw[track] (T) to[out=93,in=-110] (84:1.29) node[anchor=-110+\anang,inner sep={0.6sin(\ang)^2}] {$\pi^+$}; \draw[track] (T) to[out=88,in=-117] (80:1.16) node[anchor=-145+\anang,inner sep={0.6sin(\ang)^2}] {$\pi^+$}; } } \end{tikzpicture} % ELECTRON JET \begin{tikzpicture} \jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone \jetcone[sigcol]{O}{S}{\angsig}{\e}{ % signal cone %\draw[dashed track] (T) to[out=88,in=-70] (96:1.26) % node[right=0,above=-2] {$\mathrm{e}^-$}; \draw[dashed track] (T) to[out=88,in=-70] (96:1.26) node[anchor=-70+\anang,inner sep={2.5cos(\ang)^2-1.5}] {$\mathrm{e}^-$}; } } \end{tikzpicture} % MUON JET \begin{tikzpicture} \jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone \jetcone[sigcol]{O}{S}{\angsig}{\e}{ % signal cone \draw[track] (T) to[out=88,in=-70] (93:1.33) node[anchor=-70+\anang,inner sep={2.5*cos(\ang)^2-1.5}] {$\mu^-$}; } } \end{tikzpicture} % QUARK/GLUON JET \begin{tikzpicture} \jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone \jetcone[sigcol]{O}{S}{\angsig}{\e}{ % signal cone \draw[dashed track] (T) -- (105:1.18); \draw[dashed track] (T) -- (94:1.22); \draw[dashed track] (T) -- (84:1.22); \draw[track] (T) to[out=105,in=-50] (113:1.18); \draw[track] (T) to[out=90,in=-55] (103:1.33); \draw[track] (T) to[out=98,in=-105] (87:1.29); \draw[track] (T) to[out=68,in=-92] (79:1.20); } } \end{tikzpicture} } % end \foreach \end{document}
http://ofap.ulstu.ru/resources/843/two_certificate.tex?association=resources&parent_scaffold=fremantle%2Fguest%2Fsubdivisions&resource_type_id=38&subdivision_id=76	ulstu.ru	CC-MAIN-2023-06	text/x-tex	text/x-matlab	crawl-data/CC-MAIN-2023-06/segments/1674764499845.10/warc/CC-MAIN-20230131055533-20230131085533-00529.warc.gz	31,411,145	2,653	%% LaTeX2e-файл %% Создано движком Фримантл (https://gitlab.com/korobkov/fremantle) %% в 2023-01-31T11:34:37+04:00 %% Фримантл — Свободный движок репозитория электронных ресурсов %% Copyright © 2009—2018 Лаборатория «Автоматизированные системы» [email protected], УлГТУ %% %% Фримантл is free software: you can redistribute it and/or modify %% it under the terms of the GNU Affero General Public License as published by %% the Free Software Foundation, either version 3 of the License, or %% (at your option) any later version. %% %% Фримантл is distributed in the hope that it will be useful, %% but WITHOUT ANY WARRANTY; without even the implied warranty of %% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the %% GNU Affero General Public License for more details. %% %% You should have received a copy of the GNU Affero General Public License %% along with Фримантл. If not, see <https://www.gnu.org/licenses/>. \documentclass[a4paper,fontsize=18pt]{scrartcl} \usepackage[landscape,left=2cm,right=2cm,top=1cm,bottom=1.5cm,bindingoffset=0cm]{geometry} \usepackage{graphicx, polyglossia, pst-barcode, tabu, wallpaper} \setmainfont{Liberation Serif} \setmonofont{Liberation Mono} \setsansfont{Liberation Sans} \defaultfontfeatures{Scale=MatchLowercase, Mapping=tex-text} \setdefaultlanguage[spelling=modern]{russian} \setotherlanguage{english} \graphicspath{{/srv/http/ofap/releases/20180921145927/app/assets/images/fremantle/two_certificate/}} \CenterWallPaper{1.00}{border.png} \begin{document} \begin{hyphenrules}{nohyphenation} \begin{center} \thispagestyle{empty} {\Large ОФАП УОЦ НИТ} \bigskip\bigskip \begin{tabu}{ b{5cm} >{\centering}b{19cm} } \includegraphics [height=4.5cm]{logo.png} & Ульяновский государственный технический университет Ульяновский областной центр новых информационных технологий Областной фонд алгоритмов и программ \bigskip {\Huge \textit{Свидетельство №\,843}} \bigskip о регистрации программно-информационного продукта \end{tabu} \bigskip \begin{tabu}{ b{5cm} >{\raggedright \itshape}p{19cm} }\hline \\ Наименование: & \textbf{Учебно-методический комплекс по дисциплине 'Теория перевода'} \\ Тип: & --- пока не определён --- \\ URI: & \textbf{http://ofap.ulstu.ru/843} \\ Авторы: & Соснина Екатерина Петровна -- Кафедра «Прикладная лингвистика» (УлГТУ/ГФ) \\ Дата регистрации: & 22 апреля 2005 г. \\ \end{tabu} \vfill \begin{tabu} to 24cm { b{2cm} l X >{\itshape}l } & Директор Ульяновского областного центра НИТ & & \textit{К.В.\,Святов} \\ \psbarcode{2005-04-22 http://ofap.ulstu.ru/843}{format=compact layers=4}{azteccode} \rowfont{\small} & Администратор базы данных ОФАП & & \textit{Ю.А.\,Лапшов} \\ \end{tabu} \end{center} \end{hyphenrules} \clearpage \end{document}
https://www.zentralblatt-math.org/matheduc/en/?id=343&type=tex	zentralblatt-math.org	CC-MAIN-2019-30	text/plain	application/x-tex	crawl-data/CC-MAIN-2019-30/segments/1563195529480.89/warc/CC-MAIN-20190723151547-20190723173547-00397.warc.gz	889,637,723	1,343	\input zb-basic \input zb-matheduc \iteman{ZMATH 2016f.01078} \itemau{Store, Jessie C.; Richardson, Kerri D.; Carter, Tyrette S.} \itemti{Fostering understanding of variable with patterns.} \itemso{Teach. Child. Math. 22, No. 7, 420-427 (2016).} \itemab Summary: Based on a study with six elementary school teachers and 115 students in grades 3, 4, and 5, this article discusses ways that teachers might support an understanding of variable as students explore pattern-finding activities. The practices emerged from interviews with teachers and a yearlong observation of teaching algebraic thinking during an afterschool program at six elementary schools. The task discussed here can be accessible to elementary school students. It supports understanding of different facets of a variable, thereby avoiding misconceptions that students usually have in later grades and allowing flexible understanding that is a core for algebraic thinking. (ERIC) \itemrv{~} \itemcc{H20 C30} \itemut{algebra; variables; algebraic thinking} \itemli{http://www.nctm.org/Publications/Teaching-Children-Mathematics/2016/Vol22/Issue7/Fostering-Understanding-of-Variable-with-Patterns/} \end
http://build.openvpn.net/doxygen/latex/structkey__state__ssl.tex	openvpn.net	CC-MAIN-2018-13	application/octet-stream	application/x-tex	crawl-data/CC-MAIN-2018-13/segments/1521257645248.22/warc/CC-MAIN-20180317155348-20180317175348-00399.warc.gz	44,238,579	1,784	\hypertarget{structkey__state__ssl}{}\subsection{key\+\_\+state\+\_\+ssl Struct Reference} \label{structkey__state__ssl}\index{key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}} {\ttfamily \#include $<$ssl\+\_\+mbedtls.\+h$>$} Collaboration diagram for key\+\_\+state\+\_\+ssl\+:\nopagebreak \begin{figure}[H] \begin{center} \leavevmode \includegraphics[width=203pt]{structkey__state__ssl__coll__graph} \end{center} \end{figure} \subsubsection*{Data Fields} \begin{DoxyCompactItemize} \item mbedtls\+\_\+ssl\+\_\+config \hyperlink{structkey__state__ssl_af07b31e4dab76acec3ea7420e66a3bf2}{ssl\+\_\+config} \begin{DoxyCompactList}\small\item\em mbed\+T\+LS global ssl config \end{DoxyCompactList}\item mbedtls\+\_\+ssl\+\_\+context $\ast$ \hyperlink{structkey__state__ssl_aa9227f00c4139a321564b3ba1e7e4f93}{ctx} \begin{DoxyCompactList}\small\item\em mbed\+T\+LS connection context \end{DoxyCompactList}\item \hyperlink{structbio__ctx}{bio\+\_\+ctx} \hyperlink{structkey__state__ssl_ae5fa226c971d80a2a51eb4571651ef50}{bio\+\_\+ctx} \item S\+SL $\ast$ \hyperlink{structkey__state__ssl_a57b7d5c0e8e97b59ce9cdb84e13e547f}{ssl} \item B\+IO $\ast$ \hyperlink{structkey__state__ssl_a8f5a44beeee25a840aeb7066f3f67872}{ssl\+\_\+bio} \item B\+IO $\ast$ \hyperlink{structkey__state__ssl_a53c8f98bd4ab57d8a84cff856b06bccd}{ct\+\_\+in} \item B\+IO $\ast$ \hyperlink{structkey__state__ssl_aaeae666ec95965ee25625664e2963618}{ct\+\_\+out} \end{DoxyCompactItemize} \subsubsection{Detailed Description} Definition at line 87 of file ssl\+\_\+mbedtls.\+h. \subsubsection{Field Documentation} \mbox{\Hypertarget{structkey__state__ssl_ae5fa226c971d80a2a51eb4571651ef50}\label{structkey__state__ssl_ae5fa226c971d80a2a51eb4571651ef50}} \index{key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}!bio\+\_\+ctx@{bio\+\_\+ctx}} \index{bio\+\_\+ctx@{bio\+\_\+ctx}!key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}} \paragraph{\texorpdfstring{bio\+\_\+ctx}{bio\_ctx}} {\footnotesize\ttfamily \hyperlink{structbio__ctx}{bio\+\_\+ctx} key\+\_\+state\+\_\+ssl\+::bio\+\_\+ctx} Definition at line 90 of file ssl\+\_\+mbedtls.\+h. \mbox{\Hypertarget{structkey__state__ssl_a53c8f98bd4ab57d8a84cff856b06bccd}\label{structkey__state__ssl_a53c8f98bd4ab57d8a84cff856b06bccd}} \index{key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}!ct\+\_\+in@{ct\+\_\+in}} \index{ct\+\_\+in@{ct\+\_\+in}!key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}} \paragraph{\texorpdfstring{ct\+\_\+in}{ct\_in}} {\footnotesize\ttfamily B\+IO$\ast$ key\+\_\+state\+\_\+ssl\+::ct\+\_\+in} Definition at line 47 of file ssl\+\_\+openssl.\+h. Referenced by key\+\_\+state\+\_\+ssl\+\_\+free(), key\+\_\+state\+\_\+ssl\+\_\+init(), and key\+\_\+state\+\_\+write\+\_\+ciphertext(). \mbox{\Hypertarget{structkey__state__ssl_aaeae666ec95965ee25625664e2963618}\label{structkey__state__ssl_aaeae666ec95965ee25625664e2963618}} \index{key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}!ct\+\_\+out@{ct\+\_\+out}} \index{ct\+\_\+out@{ct\+\_\+out}!key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}} \paragraph{\texorpdfstring{ct\+\_\+out}{ct\_out}} {\footnotesize\ttfamily B\+IO$\ast$ key\+\_\+state\+\_\+ssl\+::ct\+\_\+out} Definition at line 48 of file ssl\+\_\+openssl.\+h. Referenced by key\+\_\+state\+\_\+read\+\_\+ciphertext(), key\+\_\+state\+\_\+ssl\+\_\+free(), and key\+\_\+state\+\_\+ssl\+\_\+init(). \mbox{\Hypertarget{structkey__state__ssl_aa9227f00c4139a321564b3ba1e7e4f93}\label{structkey__state__ssl_aa9227f00c4139a321564b3ba1e7e4f93}} \index{key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}!ctx@{ctx}} \index{ctx@{ctx}!key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}} \paragraph{\texorpdfstring{ctx}{ctx}} {\footnotesize\ttfamily mbedtls\+\_\+ssl\+\_\+context$\ast$ key\+\_\+state\+\_\+ssl\+::ctx} mbed\+T\+LS connection context Definition at line 89 of file ssl\+\_\+mbedtls.\+h. \mbox{\Hypertarget{structkey__state__ssl_a57b7d5c0e8e97b59ce9cdb84e13e547f}\label{structkey__state__ssl_a57b7d5c0e8e97b59ce9cdb84e13e547f}} \index{key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}!ssl@{ssl}} \index{ssl@{ssl}!key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}} \paragraph{\texorpdfstring{ssl}{ssl}} {\footnotesize\ttfamily S\+SL$\ast$ key\+\_\+state\+\_\+ssl\+::ssl} Definition at line 45 of file ssl\+\_\+openssl.\+h. Referenced by key\+\_\+state\+\_\+export\+\_\+keying\+\_\+material(), key\+\_\+state\+\_\+ssl\+\_\+free(), key\+\_\+state\+\_\+ssl\+\_\+init(), and print\+\_\+details(). \mbox{\Hypertarget{structkey__state__ssl_a8f5a44beeee25a840aeb7066f3f67872}\label{structkey__state__ssl_a8f5a44beeee25a840aeb7066f3f67872}} \index{key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}!ssl\+\_\+bio@{ssl\+\_\+bio}} \index{ssl\+\_\+bio@{ssl\+\_\+bio}!key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}} \paragraph{\texorpdfstring{ssl\+\_\+bio}{ssl\_bio}} {\footnotesize\ttfamily B\+IO$\ast$ key\+\_\+state\+\_\+ssl\+::ssl\+\_\+bio} Definition at line 46 of file ssl\+\_\+openssl.\+h. Referenced by key\+\_\+state\+\_\+read\+\_\+plaintext(), key\+\_\+state\+\_\+ssl\+\_\+free(), key\+\_\+state\+\_\+ssl\+\_\+init(), key\+\_\+state\+\_\+write\+\_\+plaintext(), and key\+\_\+state\+\_\+write\+\_\+plaintext\+\_\+const(). \mbox{\Hypertarget{structkey__state__ssl_af07b31e4dab76acec3ea7420e66a3bf2}\label{structkey__state__ssl_af07b31e4dab76acec3ea7420e66a3bf2}} \index{key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}!ssl\+\_\+config@{ssl\+\_\+config}} \index{ssl\+\_\+config@{ssl\+\_\+config}!key\+\_\+state\+\_\+ssl@{key\+\_\+state\+\_\+ssl}} \paragraph{\texorpdfstring{ssl\+\_\+config}{ssl\_config}} {\footnotesize\ttfamily mbedtls\+\_\+ssl\+\_\+config key\+\_\+state\+\_\+ssl\+::ssl\+\_\+config} mbed\+T\+LS global ssl config Definition at line 88 of file ssl\+\_\+mbedtls.\+h. The documentation for this struct was generated from the following files\+:\begin{DoxyCompactItemize} \item /root/openvpn/src/openvpn/\hyperlink{ssl__mbedtls_8h}{ssl\+\_\+mbedtls.\+h}\item /root/openvpn/src/openvpn/\hyperlink{ssl__openssl_8h}{ssl\+\_\+openssl.\+h}\end{DoxyCompactItemize}
https://anarchistischebibliothek.org/library/otto-gross-orientierung-der-geistigen-1.tex	anarchistischebibliothek.org	CC-MAIN-2022-49	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2022-49/segments/1669446710777.20/warc/CC-MAIN-20221130225142-20221201015142-00301.warc.gz	127,646,592	5,914	\documentclass[DIV=12,% BCOR=0mm,% headinclude=false,% footinclude=false,open=any,% fontsize=11pt,% oneside,% paper=a4]% {scrbook} \usepackage{fontspec} \usepackage{polyglossia} \setmainfont{Linux Libertine O} % these are not used but prevents XeTeX to barf \setsansfont[Scale=MatchLowercase]{CMU Sans Serif} \setmonofont[Scale=MatchLowercase]{CMU Typewriter Text} \setmainlanguage{german} % global style \pagestyle{plain} \usepackage{microtype} % you need an updated texlive 2012, but harmless \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} % footnote handling \usepackage[fragile]{bigfoot} \usepackage{perpage} \DeclareNewFootnote{default} \DeclareNewFootnote{B} \MakeSorted{footnoteB} \renewcommand\thefootnoteB{(\arabic{footnoteB})} \deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~} % continuous numbering across the document. Defaults to resetting at chapter. Unclear % \usepackage{chngcntr} % \counterwithout{footnote}{chapter} \usepackage[shortlabels]{enumitem} \usepackage{tabularx} \usepackage[normalem]{ulem} \def\hsout{\bgroup \ULdepth=-.55ex \ULset} % https://tex.stackexchange.com/questions/22410/strikethrough-in-section-title % Unclear if \protect \hsout is needed. Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand{\captionformat}{} \renewcommand{\figureformat}{} \renewcommand{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand{\forcelinebreak}{\strut\\{}} \newcommand{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand{\Slash}{\slash\hspace{0pt}} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} % forbid widows/orphans \frenchspacing \sloppy \clubpenalty=10000 \widowpenalty=10000 % http://tex.stackexchange.com/questions/304802/how-not-to-hyphenate-the-last-word-of-a-paragraph \finalhyphendemerits=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{Orientierung der Geistigen} \date{1919} \author{Otto Gross} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={Orientierung der Geistigen},% pdfauthor={Gross, Otto},% pdfsubject={},% pdfkeywords={Anpassung; Revolution; Kompromiss; Demokratie; Räte; Kommunismus; Psychologie; Individualität}% } \begin{document} \begin{titlepage} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge Orientierung der Geistigen\par}}% \vskip 1em \vskip 2em {\usekomafont{author}{Otto Gross\par}}% \vskip 1.5em \vfill {\usekomafont{date}{1919\par}}% \end{center} \end{titlepage} \cleardoublepage Unmessbar allgemein ist das dunkle drängende Ahnen, erstickend beschränkt das klare Begreifen der Urgründe und Erfüllungen des grossen Geschehens das kommen soll. Die schönste neue Erscheinung, die im Bereich extremst gerichteter revolutionärer Gruppierung erblüht, das fortan unverlierbare Erleben tiefsten Einsseins und nicht mehr lösbarer Waffenbrüderschaft der Proletarier und der Geistigen, ist auch das erste Zeichen bewusstseinsnäheren Erkennens der ewig menschlichen Motiven der Revolution. Wo immer geistige Menschen heute noch abseits geblieben sind, wird man sich überzeugen können, dass ihnen jede Kenntnis von anderen als wirtschaftlichen Motiven der revolutionären Bestrebungen fehlt. Fast jeder Hinweis auf den Welt und Leben umfassenden Horizont der wirklichen Perspektive des Kommunismus – von deren Reichtum zu erfahren ihnen in der Tat nur in geringem Masse Gelegenheit geboten wird – vermag hier Wandlung zu schaffen. \emph{Verbindender und trennender als Rasse, Geschlecht, Kultur und Klasse ist der typische Gegensatz zwischen dem revolutionären und dem konservativen Menschen}\textbf{,} sagt Grete Fantl (Neue Rundschau, Berlin, 1919\Slash{}3). Das elementare Prinzip der menschlichen Seele, dessen quantitative individuelle Verschiedenheit, dessen Ausreichen und Versagen also, die Menschen in diese beiden Kategorien trennt und einteilt, dieses im höchsten Sinne Wert und Wesen bestimmende Prinzip ist die Widerstandskraft des einzelnen Menschen, besonders des Menschen im Zustande der Entwicklung, gegen die Suggestionen von aussen her, gegen die aufgedrängten Gefühle, Werturteile und Normen: Die Selbsterhaltungskraft des angeborenen Menschentums, das an der eigenen Individualität wie an der Freude und dem impulsiven Ja zu allem individuellen in allem anderen ringsum, am unbeschränkten eigenen Sein wie an der unbeschränkten Liebe festhält und seinen Widerstand der Vergewaltigung entgegensetzt wie der Verführung dem ewigen und ringsgeschlossenen Druck zur Anpassung an die Anderen\dots{} Das höchste Menschliche ist die Bewahrung dieser liebenden und revolutionären Urkraft im unerhörten Kampf mit dem Milieu, der in der kalten Einsamkeit des Kindes innerhalb der Autoritätsfamilie begonnen, zum Kampf des Seienden und Lebenden mit der entsetzlichen Gewalt des Maschinellen ringsum emporwächst – des Maschinellen als Grundprinzip in aller Ordnung, wie sie jetzt besteht, als Staat, Gesetz und Autorität, als Strafrecht wie als bürgerliches Recht, als Ehe und Prostitution, als Kapital\dots{} Ob diese Kraft zum Widerstand gegen den Anpassungszwang und die Anpassungslockung im einzelnen ausreicht und vorhält, entscheidet also seine Entwicklung zum einen oder anderen Typus, dem Typus des Revolutionären oder des Konservativen – ich möchte sagen: des Angepassten. Und diesen beiden Menschentypen ist nichts auf Erden gemein als das tiefe innere Wissen, dass jedem von ihnen das Leben und Gedeihen nur unter Gesamtbedingungen möglich ist, die für den anderen das Ersticken bedeuten. Die freie grenzenlose Entwicklung des Menschentums, der Liebe und des Geistes setzt eine Ordnung der Welt voraus, welche in Allem und Jedem tödlich ist für die Angepassten an jene andere Ordnung, welche bis jetzt die herrschende ist und immer und überall tödlich war für Menschentum, Lieben und Geist\dots{} Es ist darum stets und ausnahmslos Lüge von vornherein, was immer gesprochen wird von allmählichem Übergang und Ausgleichung der Interessen, von Mässigung und Vergleich – Lüge ist Alles und Jedes, in dem ein einziges gemeinsames Interesse des Revolutionären und des Angepassten als existierend oder auch nur möglich vorausgesetzt wird. Was jeweils die Vermittlungspolitik erreichen kann, das ist allein ein Kompromiss von Interessen von absolut nur wirtschaftlicher Natur – mit ewiger Erhaltung des Unzulänglichen sogar auf diesen Gebiete selbst, mit definitivem Verzicht auf alle Werte des Lebens ausser dem abgrenzbaren der reinen Zahl\dots{} Hier ist der Boden auf welchem die Revolutionen sich auflösen in Verhandlungen zwischen Parteien, hinter welchen kein Unterschied steht von Mensch und Mensch: Verhandlungen zwischen verschieden Situierten, ohne Voraussetzung überhaupt mehr von verschiedenen seelischen Typen und deren verschiedenen Ansprüchen an das Sein. - Noch nie hat eine kämpfende Partei sich einen Namen gegeben, so sehr als Ausdruck eines seelischen Typus geprägt und das gemeinsame psychologische Moment in allen ihren schöpferischen Charakteren bezeichnend, als \emph{der der „Höchstes fordernden“} - das ist \emph{Derer ohne Kompromiss}. In Jedem, dem der Kommunismus innere Berufung ist, wirkt ein lebendiger, ursprungsnaher, von einer Jugendzeit der Menschheit her im besten Blut noch fortgeerbter Urgeist: Ein unmittelbares Wissen vom Unterschied zwischen Mensch und Mensch: Ein selbstverständliches dort ewig heimatlos hier zu Hause Sein, dort losgelöst und hier ins Leben eingegliedert vom dominierenden Element im eigenen Innersten, der revolutionären Menschheitsseele, die jedem Menschen solcher Art den Dienst des unbeschränkten grossen Lebens zur Schicksalsbestimmung macht; ein reflektorisches Sich-Distanzieren von allem Angepassten, der Anpassung an das Inferiore, an Macht und Unterwerfung, Besitz, Gewohnheit, Tradition und Sittefähigen. Deswegen ist uns nichts so wesensinnerlich verhasst, erscheint und keine je noch aufgestellte Politik so furchtbar korrumpierend und gefährlich als diese heutige des Kompromisses, dieser realpolitische Sozialismus der Vielzuvielen, der für das Proletariat und die Bourgeoisie mit einander den Boden gemeinsamer Anpassung herzustellen erraten hat – gemeinsamer Anpassung an den Geist des Bisherigen, um den Preis materieller Auskommensmöglichkeiten ein Mithinüberschleppen alles Wesentlichen aus der alten Ordnung: Mit reduziertem Flügelschlag nun auch der kapitalistischen Ideen ein Realisieren von Durchschnittsmassen in Allem und Jedem, aber basiert wie früher die Selbstverständlichkeit von Macht und Vormacht zwischen Allen, um jeden Einzelnen herum die endlose Einsamkeit. Es ist diese Demokratie des „letzten Menschen“ die Nietzsche prophetisch vorhergesagt hat und vor welcher die Diktatur des Proletariats die Zukunft des Menschengeschlechtes erretten soll. Das Endziel alles Kommunismus ist ein Zustand, in welchem Niemand irgend eine Vormacht politischer, sozialer, ökonomischer, autoritativer Natur über Irgendeinen erhalten kann. Wir wissen, dass es niemals eine Ordnung geben kann, die etwa garantierte, dass nur der seelisch Höhere über den niedriger Organisiert Macht bekäme; und würde eine solche Ordnung je gefunden, so brächte sie die Korruption der hohen Seelen\dots{} Allein die völlig Unmöglichkeit jedweder Vormacht Irgendeines über Irgendeinen gewährt die Sicherheit, dass nie ein Mensch, in dem der freie schöpferische Urgeist lebt, sich Elementen zweiten Ranges beugen muss. \emph{Wir wollen die Macht den Machtlosen geben, den Räten der Armen, damit die Macht wieder ohne Sünde werde, ein Kollektivgefühl der Menschen miteinander und unpersönlicher Besitz des unpersönlichen Gesellschaftskörpers.} Bis einst die Menschen noch einmal beginnen, als Ausdruck eines schrankenlosen Einander-Verstehens und ihrer Freude aneinander einen Turm in den Himmel hinauf zu bauen. Erst dieser Bau wird dann den Namen Tragen dürfen: \emph{Kultur\dots{}} % begin final page \clearpage % new page for the colophon \thispagestyle{empty} \begin{center} Anarchistische Bibliothek \smallskip Anticopyright \bigskip \includegraphics[width=0.25\textwidth]{logo-yu.pdf} \bigskip \end{center} \strut \vfill \begin{center} Otto Gross Orientierung der Geistigen 1919 \bigskip Scan aus: Sowjet, Kommunistische Monatsschrift, Nr. 5, November 1919 \bigskip \textbf{anarchistischebibliothek.org} \end{center} % end final page with colophon \end{document}
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Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand{\captionformat}{} \renewcommand{\figureformat}{} \renewcommand{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand{\forcelinebreak}{\strut\\{}} \newcommand{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand{\Slash}{\slash\hspace{0pt}} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} % forbid widows/orphans \frenchspacing \sloppy \clubpenalty=10000 \widowpenalty=10000 % http://tex.stackexchange.com/questions/304802/how-not-to-hyphenate-the-last-word-of-a-paragraph \finalhyphendemerits=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{Messico: Riflessioni dell’anarchico Fernando Bárcenas nel foglio anti-carcerario “El Canero” (06\Slash{}2016)} \date{} \author{} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={Messico: Riflessioni dell’anarchico Fernando Bárcenas nel foglio anti-carcerario “El Canero” (06\Slash{}2016)},% pdfauthor={},% pdfsubject={},% pdfkeywords={Meksiko; Fernando Barcenas; zatvorenici; zatvori; razmatranja; Italiano}% } \begin{document} \begin{titlepage} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge Messico: Riflessioni dell’anarchico Fernando Bárcenas nel foglio anti-carcerario “El Canero” (06\Slash{}2016)\par}}% \vskip 1em \vskip 2em \vskip 1.5em \vskip 3em \includegraphics[keepaspectratio=true,height=0.5\textheight,width=1\textwidth]{m-r-messico-riflessioni-dell-anarchico-fernando-ba-2.png} \vfill \strut\par \end{center} \end{titlepage} \cleardoublepage Fernando Bárcenas Castillo è un giovane anarchico, musicista e studente della Facoltà di Lettere Vallejo di Città del Messico. Ha vent’anni ed è arrestato il 13 dicembre 2012 durante una protesta contro l’aumento del prezzo dei biglietti della metropolitana. Viene accusato di aver bruciato l’albero natalizio della Coca-Cola, e da allora si trova nel Carcere Nord in Messico. Nel dicembre 2014 è condannato a cinque anni e nove mesi per attacco all’ordine pubblico e per criminalità organizzata. Ha fatto appello e adesso sta aspettando la decisione. In carcere Fernando ha organizzato alcuni progetti informativi come riviste e il foglio anti-carcerario “El Canero”. \emph{\textbf{Riflessioni Fernando Bárcenas sul foglio “El Canero”, Carcere Nord, Città del Messico, giugno 2016}} Il progetto “El Canero” nasce da ore di noia, da discussioni condivise e da riflessioni nelle celle d’isolamento in zona 3 nell’area d’ingresso, osservando la routine e comprendendo che dobbiamo sempre ricominciare; in questo modo è nato il bisogno di ridare qualche significato. Qual era il significato della vera lotta contro il dominio e lo Stato? Significa ancora qualcosa per continuare ciecamente a credere nelle mie idee? La mia testa si era riempita di domande ed allora ho capito che avevo bisogno di trovare un modo per non soccombere all’angoscia e alla disperazione\dots{} All’inizio ho cominciato a scrivere per iniziare un dialogo con me stesso, poi quando ho concepito il modo in cui materializzare la mia libertà interiore l’ho utilizzata come luogo di introspezione, partendo dal punto quando mi sono trovato con i miei carcerieri, le mie carceri soggettive, i miei comportamenti autoritari e remissivi, un luogo che ha acquistato significato solo ritrovando me stesso, e questo è di fatto diventato uno strumento per riconquistare fiducia nella mia individualità unica e libera. Poi, sono arrivate le domande. Ha senso scrivere a sé stessi? Di cosa avevo bisogno per spezzare le sbarre dell’isolamento? Le domande infinite mi hanno portato ad una ed unica risposta: “Scrivere!” Se la libertà è indispensabile e apprezzata come la vita stessa, fino al punto che preferiamo sacrificare la nostra vita che sottometterla alla schiavitù e alle catene, allora perché non lottare per diffondere la libertà e renderla possibile agli altri, per provare la sensazione di libertà e di pienezza che ci dà, scorrendo attraverso il nostro corpo ogni volta che usciamo dai confini legali, dalle norme sociali, qui ed adesso? Noi siamo i protagonisti della rivolta, e in ogni atto decisivo guardiamo a noi stessi come a degli esseri capaci di autodeterminazione, capaci di riprendersi le vite e di andare avanti in modo coerente verso la sperimentazione e la creazione di nuove forme di relazioni, senza trasformasi in istituzioni sociali strada facendo. Per questo motivo dobbiamo, sia fuori che dentro le mura del carcere materiale, riflettere e chiederci: siamo contenti di vivere sottomettendoci a tali condizioni? Vogliamo distruggere la realtà o la vogliamo solo trasformarla? Ma soprattutto dobbiamo sapere se abbiamo davvero fatto questa scelta, se è davvero nostra. \emph{\textbf{Fernando Bárcenas}} \emph{\textbf{Carcere Nord, Città del Messico}} \bigskip \bigskip \textbf{Meksiko: Razmatranja anarhističkog zatvorenika Fernanda Barcenasa u anti-zatvorskom listu “El Canero” (06.2016.)} Fernando Bárcenas Castillo je jedan mladi anarhist, glazbenik i student Filozofskog fakulteta Vallejo u Mexico Cityju. Ima dvadeset godina i uhapšen je 13.12.2012. tokom jednog prosvjeda protiv poskupljenja karte podzemne željeznice. Optužen je za paljenje božićnog drvca Coca-Cole i od tada se nalazi u Sjevernom zatvoru Meksika. U decembru 2014. osuđen je na pet godina i devet mjeseci pod optužbom za napad na javni red i za organizirani kriminal. Uložio je žalbu i sada čeka odluku. U zatvoru je Fernando organizirao nekoliko informativnih projekata kao što su časopisi i anti-zatvorski list “El Canero”. \emph{\textbf{Razmatranja Fernanda Barcenasa u anti-zatvorskom listu “El Canero”, Sjeverni Zatvor, Mexico City, juni 2016.}} Projekt “El Canero” rođen je iz sati dosade, iz dijeljenja diskusija i razmišljanja u izolacijskim ćelijama u zoni 3 na ulazu, promatrajući rutinu i shvačajući da uvijek moramo ponovno početi; tako je rođena potreba da se ponovno daju neka smisla. Koji je bio smisao prave borbe protiv dominacije i države? Da li to još nešto znači da bi nastavio slijepo vjerovati u moje ideje? Moja se glava ispunila pitanjima, i tada sam shvatio da sam trebao pronaći način da ne padnem u tjeskobu i očaj\dots{} Na početku sam započeo pisati kako bih pokrenuo dijalog sa samim sobom, zatim kada sam shvatio kako da materijaliziram moju unutarnju slobodu počeo sam je koristiti kao mjesto introspekcije, započevši od točke kada sam se našao s mojim tamničarima, mojim subjektivnim zatvorenicima, mojim autoritarnim i popuštajućim ponašanjima, mjesto koje je dobilo smisao kada sam pronašao samog sebe i kada je u biti postalo sredstvo kako bih vratio vjeru u moju jedinu i slobodnu individualnost. Onda su došla pitanja. Ima li uopće smisla pisati samom sebi? Što je bilo potrebno da razbijem barijere izolacije? Beskrajna pitanja odvela su me do jednog jedinog odgovora: “Pisati!” Ako je sloboda neophodna i značajna kao sam život, do točke da bi radije žrtvovali naš život nego ga podvrgnuli ropstvu i lancima, onda zašto se ne bi borili da bi je širili i omogućili drugima, da bi osjetili osjećaj slobode i ispunjenja koji daje i kola našim tijelima svaki put kad izađemo iz zakonskih okvira, društvenih normi, ovdje i sada? Mi smo protagonisti pobune i pri svakom odlučnom djelu gledamo na sebe kao na bića koja su sposobna na samo-određenje, na preuzimanje života u vlastite ruke i nastaviti kročiti naprijed na dosljedan način prema eksperimentiranju i stvaranju novih oblika odnosa, bez pretvaranja tim putem u socijalne institucije. Iz tog razloga, kako unutar tako izvan materijalnog zatvora, moramo razmisliti i zapitati se: da li smo zadovoljni živjeti pokoravajući se takvim uvjetima? Da li želimo uništiti stvarnost ili je samo izmijeniti? Ali, povrh svega, sve što trebamo znati je da li smo zaista učinili taj izbor, da li je zaista naš. \emph{\textbf{Fernando Bárcenas}} \emph{\textbf{Sjeverni Zatvor, Mexico City}} \bigskip % begin final page \clearpage % new page for the colophon \thispagestyle{empty} \begin{center} Anarhija.info \strut \end{center} \strut \vfill \begin{center} Messico: Riflessioni dell’anarchico Fernando Bárcenas nel foglio anti-carcerario “El Canero” (06\Slash{}2016) \bigskip \href{http://actforfree.nostate.net/?p=25249}{actforfree.nostate.net} \bigskip \textbf{anarhija.info} \end{center} % end final page with colophon \end{document}
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https://web.ma.utexas.edu/mp_arc/e/01-329.latex.mime	utexas.edu	CC-MAIN-2020-16	application/x-latex	message/rfc822	crawl-data/CC-MAIN-2020-16/segments/1585371662966.69/warc/CC-MAIN-20200406231617-20200407022117-00016.warc.gz	770,081,602	54,595	Content-Type: multipart/mixed; boundary="-------------0109180820111" This is a multi-part message in MIME format. ---------------0109180820111 Content-Type: text/plain; name="01-329.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="01-329.keywords" de Branges space, Schr\"odinger operator, inverse spectral theory ---------------0109180820111 Content-Type: application/x-tex; name="dB.tex" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="dB.tex" \documentclass{amsart} \usepackage{amsmath} \usepackage{amsthm} \usepackage{amsfonts} \usepackage{amssymb} \newtheorem{Theorem}{Theorem}[section] \newtheorem{Proposition}[Theorem]{Proposition} \newtheorem{Lemma}[Theorem]{Lemma} \newtheorem{Definition}[Theorem]{Definition} \newtheorem{Corollary}[Theorem]{Corollary} \numberwithin{equation}{section} \begin{document} \title{Schr\"odinger operators and de~Branges spaces} \author{Christian Remling} \address{Universit\"at Osnabr\"uck\\ Fachbereich Mathematik/Informatik\\ 49069 Osnabr\"uck\\ Germany} \email{[email protected]} \urladdr{www.mathematik.uni-osnabrueck.de/staff/phpages/remlingc.rdf.html} \date{September 18, 2001} \thanks{2000 {\it Mathematics Subject Classification.} 34A55 34L40 46E22} \keywords{de Branges space, Schr\"odinger operator, spectral representation, inverse spectral theory} \thanks{Remling's work was supported by the Heisenberg program of the Deutsche Forschungs\-gemein\-schaft} %\thanks{to appear in {\it Commun.\ Math.\ Phys.} } \begin{abstract} We present an approach to de~Branges's theory of Hilbert spaces of entire functions that emphasizes the connections to the spectral theory of differential operators. The theory is used to discuss the spectral representation of one-dimensional Schr\"odinger operators and to solve the inverse spectral problem. \end{abstract} \maketitle \section{Introduction} In this paper, I will discuss the general direct and inverse spectral theory of one-dimensional Schr\"odinger operators $H=-d^2/dx^2 + V(x)$ from the point of view of de~Branges's theory of Hilbert spaces of entire functions. In particular, I will present a new solution of the inverse spectral problem. Basically, we will obtain a local version of the Gelfand-Levitan characterization \cite{GL} of the spectral data of one-dimensional Schr\"odinger operators (for a modern presentation of the Gelfand-Levitan theory, see Chapter 2 of either \cite{Lev} or \cite{Mar}). However, our treatment is quite different from that of Gelfand-Levitan. On top of that, we do not need continuity assumptions on the potential $V$, but this is not the main point here because this technical improvement should also be possible within the framework of Gelfand-Levitan theory. I have tried to pursue two goals in this paper. First of all, I will emphasize the connections between de~Branges's theory of Hilbert spaces of entire functions and the spectral theory of differential operators from the very beginning, and I hope that this leads to a concrete and accessible introduction to de~Branges's results, at least for people with a background similar to mine. My treatment of de~Branges's theory is, of course, by no means intended to be a replacement for the deeper and more general, but also more abstract and demanding treatment of de~Branges himself in \cite{dB1,dB2,dB3,dB4} and especially \cite{dB}. The second and perhaps more important goal is to give a new view on the (especially inverse) spectral theory of one-dimensional Schr\"odinger operators by recognizing it as a part of a larger picture. More specifically, I believe that one of de~Branges's major results (namely, Theorem \ref{T6.3} below) may be interpreted as the mother of many inverse theorems. In this paper, we will use it to discuss the inverse theory for Schr\"odinger operators, but I think one can discuss along these lines the inverse theory of other operators as well, provided there is a good characterization of the spectral data that occur. In particular, it should be possible to give such a treatment for the one-dimensional Dirac operator. The treatment of the inverse spectral problem given in this paper is neither short nor elementary, the major thrust really is the new picture it provides. It is not short because there are computational parts and technical issues (mainly in Sect.\ 13--15) that need to be taken care of. However, I think that the general strategy, which will be explained in Sect.\ 9, is quite transparent. Our treatment is not elementary, either, because it depends on the machinery of de~Branges spaces and at least two major results from this theory (Theorems \ref{T6.3} and \ref{T6.4}), which will not be proved here. To place this paper into context, let me mention some work on related topics. De~Branges's results from \cite{dB1,dB2,dB3,dB4,dB} are rather complete, so not much has been added since as far as the general, abstract theory is concerned. Dym and Dym-McKean \cite{Dym,DMcK} also use de~Branges spaces to study certain differential operators, and they give independent introductions de~Branges's results. The theory of de~Branges spaces is intimately connected with the theory of so-called canonical systems (also known as Zakharov-Shabat systems), and there exists a considerable literature on this subject. See, for instance, \cite{HdSW,Sakh} and the references cited therein. Sakhnovich's book \cite{Sakh} in fact discusses more general systems, and a study of these systems in the spirit of de~Branges spaces is carried out in \cite{ADym}. As for the inverse spectral theory of one-dimensional Schr\"odinger operators, there is the classical work of Gelfand-Levitan mentioned above \cite{GL}. A different approach -- which so far has been used to attack uniqueness questions, but in principle also gives a procedure for reconstructing the potential from the spectral data -- was recently developed by Simon, partly in collaboration with Gesztesy \cite{GeSi,Si}. This approach emphasizes the role of large $z$ asymptotics and is quite different from both \cite{GL} and the approach used here. However, we will see some connections in Sect.\ 4 of this paper. For still another recent treatment of uniqueness questions, see \cite{Horv}. This paper is organized as follows. We define de~Branges spaces and establish some basic properties in the following section. In Sect.\ 3, we then discuss classical material on the spectral representation of Schr\"odinger operators from this point of view. This gives an immediate intuitive understanding of de~Branges spaces, and it also provides an aesthetically pleasing picture of the spectral representation. Moreover, this material is then used to derive conditions on the spectral data (which are related to the Gelfand-Levitan conditions). The local approach suggested by the theory of de~Branges spaces simplifies this treatment considerably. Here, by ``local'' we roughly mean that instead of studying the problem on the half line $(0,\infty)$ at one stroke, we study the problems on $(0,N)$ for arbitrary $N>0$. In Sect.\ 5, we state the inverse spectral theorem, which is the converse of the results of Sect.\ 4. According to the general philosophy of this paper, this inverse spectral theorem will also be formulated in the language of de~Branges spaces. The proof requires preparatory material; this is presented in Sect.\ 6--8. In particular, in Sect.\ 7 we state, without proof, four theorems on de~Branges spaces on which our treatment of the inverse problem will crucially depend. In Sect.\ 9, we start the proof of the inverse spectral theorem, and we explain the general strategy. This proof is then carried out in Sect.\ 11--16. In Sect.\ 10, we prepare for the proof by a discussion of canonical systems in the style of the treatment of Sect.\ 3. In Sect.\ 17, we discuss the implications of our results for the spectral measures of Schr\"odinger operators on the half line $(0,\infty)$. We do this mainly in order to clarify the relations to the Gelfand-Levitan theory. We conclude this paper with some remarks of a more general character. \section{Elementary properties of de~Branges spaces} One way to understand de~Branges spaces is to interpret them as weighted versions of Paley-Wiener spaces. This point of view is put forward in the introduction of \cite{dB}. So let us recall the Paley-Wiener Theorem. Fix $a>0$, and define $PW_a$ as the space of Fourier transforms $\widehat{f}$ of functions $f\in L_2(-a,a)$ (where $\widehat{f}(k) = (2\pi )^{-1/2} \int f(x) e^{-ikx}\, dx$). For $f\in L_2(-a,a)$, the Fourier transform $\widehat{f}$, originally defined as an element of $L_2(\mathbb R)$, uniquely extends to an entire function. The Paley-Wiener Theorem says that \begin{equation} \label{PW} PW_a = \{ F:\mathbb C\to \mathbb C : F\text{ entire, } \int_{\mathbb R} \left\| F(\lambda)\right\|^2\, d\lambda < \infty, \|F(z)\| \le C_F e^{a\|z\|} \} . \end{equation} An entire function $E:\mathbb C \to \mathbb C$ is called a {\it de~Branges function} if $\|E(z)\| > \|E(\overline{z})\|$ for all $z\in\mathbb C^+ =\{ z\in\mathbb C: \text{Im }z >0 \}$. Note that such an $E$ is root-free on $\mathbb C^+$. Now the {\it de~Branges space} $B(E)$ based on $E$ is defined in analogy to \eqref{PW}: It consists of the entire functions $F$ which are square integrable on the real line with respect to the weight function $\|E\|^{-2}$, \begin{equation} \label{L2} \int_{\mathbb R} \left\| \frac{F(\lambda)}{E(\lambda)} \right\|^2\, d\lambda < \infty, \end{equation} and satisfy a growth condition at infinity. In the presence of \eqref{L2}, there are a number of ways to state this condition. To formulate this result, we need some notions from the theory of Hardy spaces. However, this subject will not play an important role in what follows. A good reference for further information on this topic is \cite{Garn}. We write $N_0$ for the set of those functions from the Nevanlinna class $N$ for which the point mass at infinity in the canonical factorization is non-negative. A more direct, equivalent characterization goes as follows: $f\in N$ precisely if $f$ is holomorphic on $\mathbb C^+$ and can be written as the quotient of two bounded holomorphic functions on $\mathbb C^+$: $f=F_1/F_2$. Such an $f$ is in $N_0$ if in this representation, $F_2$ can be chosen so that \[ \lim_{y\to\infty} \frac{\ln \|F_2(iy)\|}{y} = 0 . \] We will also need the Hardy space $H_2$ (on the upper half plane), which may be defined as follows: $f\in H_2$ precisely if $f$ is holomorphic on $\mathbb C^+$ and \[ \sup_{y>0} \int_{-\infty}^{\infty} \left\| f(x+iy) \right\|^2 \, dx < \infty. \] Equivalently, $H_2$ is the space of Fourier transforms of functions from $L_2(-\infty,0)$. \begin{Proposition} \label{P2.1} Suppose that $F$ is entire and \eqref{L2} holds. Then the following are equivalent:\\ a) $\|F(z)/E(z)\|, \|F^{\#}(z)/E(z)\| \le C_F (\text{{\rm Im }}z)^{-1/2}$ for all $z\in\mathbb C^+$.\\ b) $F/E, F^{\#}/E \in N_0$.\\ c) $F/E, F^{\#}/E \in H_2$. \end{Proposition} Here, we use the notation $F^{\#}(z)=\overline{F(\overline{z})}$. By definition, an entire function $F$ is in $B(E)$ precisely if, in addition to \eqref{L2}, one (and hence all) of these conditions holds. In \cite{dB}, de~Branges uses condition b) to define $B(E)$ (functions from $N$ are called functions of bounded type in \cite{dB}). Condition a) is used in \cite{DMcK}, while c) gives the most elegant description of $B(E)$ as \begin{equation} \label{defdB} B(E) = \{ F:\mathbb C \to \mathbb C : F \text{ entire, } F/E, F^{\#}/E \in H_2 \} . \end{equation} Clearly, \eqref{L2} now follows automatically. \begin{proof} As $H_2 \subset N_0$, c) implies b). Condition c) also implies a) because $H_2$ functions admit a Cauchy type representation \cite[Chapter II]{Garn}: \[ \frac{F(z)}{E(z)} = \frac{1}{2\pi i} \int_{\mathbb R} \frac{F(\lambda)}{E(\lambda)}\, \frac{d\lambda}{\lambda - z} \quad\quad (z\in \mathbb C^+ ) , \] and similarly for $F^{\#}/E$. Taking \eqref{L2} into account, we now get a) by applying the Cauchy-Schwarz inequality. Now assume that a) holds. A standard application of the residue theorem (see \cite[Section 6.1]{DMcK} for the details) shows that \begin{equation} \label{Cauchy} \frac{1}{2\pi i} \int_{\mathbb R} \frac{F(\lambda)}{E(\lambda)}\, \frac{d\lambda}{\lambda - z} = \begin{cases} F(z)/E(z) & z\in\mathbb C^+ \\ 0 & z\in\mathbb C^- \end{cases} . \end{equation} It is well known that \eqref{Cauchy} together with \eqref{L2} implies that $F/E \in H_2$ \cite[Exercise II.2a)]{Garn}. Of course, an analogous argument works for $F^{\#}/E$, so c) holds. Finally, we show that b) implies c). The canonical factorization (see again \cite{Garn}) of $F/E\in N_0$ reads \begin{equation} \label{factor} F(z)/E(z) = e^{i\alpha}e^{ihz} B(z) g(z) S_1(z)/S_2(z), \end{equation} where $\alpha\in\mathbb R$, $h\ge 0$, $B$ is a Blaschke product, $g$ is an outer function, and $S_1$, $S_2$ are the singular factors. Now $F/E$ is meromorphic, and \eqref{L2} prevents poles on the real line, so $F/E$ is actually holomorphic not only on the upper half plane, but on a neighborhood of the closure of $\mathbb C^+$. As a consequence, $S_1=S_2\equiv 1$. To see this, just recall how the singular factors were constructed \cite[Sect.\ II.5]{Garn}. Given this, \eqref{L2} and \eqref{factor} together with Jensen's inequality now imply that $F/E\in H_2$ (compare \cite[Sect.\ II.5]{Garn}). By the same argument, $F^{\#}/E\in H_2$. \end{proof} \begin{Theorem} \label{T2.2} $B(E)$, endowed with the inner product \[ [F,G] = \frac{1}{\pi} \int_{\mathbb R} \overline{F(\lambda)} G(\lambda) \, \frac{d\lambda} {\|E(\lambda)\|^2}, \] is a Hilbert space. Moreover, for any $z\in\mathbb C$, point evaluation is a bounded linear functional. More explicitly, the entire function $J_{z}$ given by \[ J_z(\zeta)= \frac{\overline{E(z)}E(\zeta)- E(\overline{z})\overline{E(\overline{\zeta})}} {2i(\overline{z}-\zeta)} \] belongs to $B(E)$ for every $z\in\mathbb C$, and $[J_z,F]=F(z)$ for all $F\in B(E)$. \end{Theorem} \begin{proof} $B(E)$ is obviously a linear space, and $[\cdot,\cdot]$ is a scalar product on $B(E)$. Also, using condition a) from Proposition \ref{P2.1}, it is not hard to see that $J_z\in B(E)$ for every $z\in\mathbb C$. Now fix $F\in B(E)$. Then, as noted above, $F/E$ obeys the Cauchy type formula \eqref{Cauchy}. A similar computation shows that \[ \frac{1}{2\pi i} \int_{\mathbb R} \frac{F(\lambda)}{E^{\#}(\lambda)}\, \frac{d\lambda}{\lambda - z} = \begin{cases} 0 & z\in\mathbb C^+\\ -F(z)/E^{\#}(z) & z\in\mathbb C^- \end{cases} . \] Combining these equations, we see that indeed \begin{equation} \label{2.1} F(z)=\frac{1}{\pi} \int \overline{J_z(\lambda)}F(\lambda)\frac{d\lambda} {\|E(\lambda)\|^2}, \end{equation} at least if $z\notin\mathbb R$. But the right-hand side of \eqref{2.1} is an entire function of $z$, so \eqref{2.1} must hold for all $z\in\mathbb C$. It remains to prove completeness of $B(E)$. Since entire functions are already determined by their restrictions to $\mathbb R$, the space $B(E)$ may be viewed as a subspace of $L_2(\mathbb R, \pi^{-1}\|E(\lambda)\|^{-2} d\lambda)$. So we only need to show that $B(E)$ is closed in this larger space. To this end, observe that \[ \\|J_z\\|^2=J_z(z)=\frac{\|E(z)\|^2-\|E(\overline{z})\|^2}{4\, \text{Im }z} \] remains bounded if $z$ varies over a compact set. So if $F_n\in B(E)$ converges in norm to some $F\in L_2(\mathbb R, \pi^{-1}\|E(\lambda)\|^{-2} d\lambda)$, then $F_n(z)=\langle J_z, F_n \rangle_{L_2}$ converges uniformly on compact sets to $\langle J_z, F \rangle$, and thus $F(z)=\langle J_z, F \rangle$ defines an entire extension of $F \in L_2(\mathbb R, \pi^{-1}\|E(\lambda)\|^{-2} d\lambda)$. We can now use \eqref{defdB} and completeness of $H_2$ to see that $F$ belongs to $B(E)$. \end{proof} $E_a(z)=e^{-iaz}$ is a de~Branges function. With this choice, we recover the Paley-Wiener space from \eqref{PW}: $PW_a = B(E_a)$. The general de~Branges space $B(E)$ shares many properties with this simple example, as the full blown theory from \cite{dB} shows: $B(E)$ {\it always} consists of transforms of $L_2$ functions with bounded support. However, in the general case, one has to use eigenfunctions of a differential operator instead of the exponentials $e^{ikx}$ and spectral measures instead of Lebesgue measure. These (rather vague) remarks will be made more precise later. Note also that the reproducing kernel $J_z$ for $B(E_a)=PW_a$ is the Dirichlet kernel, \[ J_z(\zeta)=D_a(\overline{z}-\zeta) =\frac{\sin a(\overline{z}-\zeta)}{\overline{z}-\zeta}, \] as a brief computation shows. This is easy to understand: for general $L_2$ functions, convolution with $D_a$ projects onto the frequencies in $(-a,a)$, but for functions in $PW_a$, these are the only frequencies that occur, so $D_a$ acts as a reproducing kernel on this space. There is another simple choice for $E$. Every polynomial without zeros in $\mathbb C^+\cup \mathbb R$ is a de~Branges function. It is clear that in this case $B(E)$ contains precisely the polynomials whose degree is smaller than that of $E$. Basically, the theory of these (finite dimensional) de~Branges spaces is the theory of orthogonal polynomials. Many results from \cite{dB} can be viewed as generalizations of results about orthogonal polynomials. \section{Spectral representation of 1D Schr\"odinger operators} In this section, we show that the spaces used in the usual spectral representation of Schr\"odinger operators on bounded intervals are de~Branges spaces. So consider the equation \begin{equation} \label{se} -y''(x) + V(x)y(x) = zy(x), \end{equation} with $V\in L_1(0,N)$. We will also be interested in the associated self-adjoint operators on $L_2(0,N)$. For simplicity, we will always use Neumann boundary conditions at $x=0$. Thus we consider the operators $H_N^{\beta}=-d^2/dx^2 + V(x)$ on $L_2(0,N)$ with boundary conditions \[ y'(0)=0,\quad y(N)\sin\beta + y'(N)\cos\beta=0 . \] We start by recalling some basic facts about the spectral representation of $H_N^{\beta}$. General references for this material are \cite{CL,WMLN}. The spectrum of $H_N^{\beta}$ is simple and purely discrete. Let $u(x,z)$ be the solution of \eqref{se} with the initial values $u(0,z)=1$, $u'(0,z)=0$ (so $u$ satisfies the boundary condition at $x=0$). Define the Borel measure $\rho_N^{\beta}$ by \begin{equation} \label{rhoN} \rho_N^{\beta} = \sum_{\frac{u'}{u}(N,E)=-\tan \beta} \frac{\delta_E}{\\|u(\cdot,E)\\|_{L_2(0,N)}^2}. \end{equation} Here, $\delta_E$ denotes the Dirac measure (i.e.\ $\delta_E(\{ E\} )=1, \delta_E(\mathbb R\setminus\{ E\} )=0$), and the sum ranges over all eigenvalues of $H_N^{\beta}$, and of course this interpretation also makes sense if $\beta=\pi/2$. The operator $U:L_2(0,N)\to L_2(\mathbb R,d\rho_N^{\beta})$, defined by \begin{equation} \label{U} (Uf)(\lambda) = \int u(x,\lambda) f(x)\, dx, \end{equation} is unitary, and $UH_N^{\beta}U^$ is multiplication by $\lambda$ in $L_2(\mathbb R,d\rho_N^{\beta})$. It is a simple but noteworthy fact that the action of $U$ depends neither on $N$ nor on the boundary condition $\beta$. The adjoint (or inverse) of $U$ acts as \begin{equation} \label{U} (U^F)(x) = \int u(x,\lambda)F(\lambda)\, d\rho_N^{\beta}(\lambda), \end{equation} for $F\in L_2(\mathbb R,d\rho_N^{\beta})$ with finite support. Similar statements hold for half line problems (if a potential $V\in L_{1,loc}([0,\infty))$ is given), except that the construction of the spectral measure $\rho$ is slightly more complicated. One can use, for instance, the limiting procedure of Weyl (see \cite[Chapter 9]{CL}). Also, there is the distinction between the limit point and limit circle cases. In the latter case, one needs a boundary condition at infinity to get self-adjoint operators (see again \cite{CL} or \cite{WMLN}). In either case, $U$, defined by \eqref{U} for compactly supported $f\in L_2(0,\infty)$, extends uniquely to a unitary map $U:L_2(0,\infty)\to L_2(\mathbb R, d\rho)$, and we still have that $UHU^$ is multiplication by the variable in $L_2(\mathbb R, d\rho)$ (in the limit circle case, $\rho$ and $H$ depend on the boundary condition at infinity). Finally, for compactly supported $F\in L_2(\mathbb R, d\rho)$, we also still have \eqref{U}, with $\rho_N^{\beta}$ replaced by $\rho$, of course. In this paper, half line problems will sometimes be lurking in the background, but we will mainly work with problems on bounded intervals. We now identify $L_2(\mathbb R, d\rho_N^{\beta})$ as a de~Branges space. Let \[ E_N(z) = u(N,z)+iu'(N,z). \] Then, since $u(N,\overline{z})=\overline{u(N,z)}$ and similarly for $u'$, \begin{equation} \label{3.1} \frac{\overline{E_N(z)}E_N(\zeta)- E_N(\overline{z})\overline{E_N(\overline{\zeta})}} {2i(\overline{z}-\zeta)} = \frac{\overline{u(N,z)}u'(N,\zeta)-\overline{u'(N,z)} u(N,\zeta)}{\overline{z}-\zeta}. \end{equation} Denote the left-hand side of \eqref{se} by $\tau y$. We have Green's identity \[ \int_0^N\left( \overline{(\tau f)} g - \overline{f} \tau g\right) = \left. \left( \overline{f(x)}g'(x)-\overline{f'(x)}g(x)\right) \right\|_{x=0}^{x=N}, \] and this allows us to write \eqref{3.1} in the form \[ \frac{\overline{E_N(z)}E_N(\zeta)- E_N(\overline{z})\overline{E_N(\overline{\zeta})}} {2i(\overline{z}-\zeta)} = \int_0^N \overline{u(x,z)}u(x,\zeta)\, dx. \] Taking $z=\zeta\in\mathbb C^+$ shows that $E_N$ is a de~Branges function. The de~Branges space based on $E_N$ will be denoted by $S_N\equiv B(E_N)$ ($S$ for Schr\"odinger). By Theorem \ref{T2.2} and the above calculation, the reproducing kernel $J_z$ of $S_N$ is given by \begin{equation} \label{PE} J_z(\zeta)=\int_0^N \overline{u(x,z)}u(x,\zeta)\, dx. \end{equation} \begin{Theorem} \label{T3.1} For any boundary condition $\beta$ at $x=N$, the Hilbert spaces $S_N$ and $L_2(\mathbb R, d\rho_N^{\beta})$ are identical. More precisely, if $F(z)\in S_N$, then the restriction of $F$ to $\mathbb R$ belongs to $L_2(\mathbb R, d\rho_N^{\beta})$, and $F\mapsto F\big\|_{\mathbb R}$ is a unitary map from $S_N$ onto $L_2(\mathbb R, d\rho_N^{\beta})$. \end{Theorem} \begin{proof} Basically, the theorem is true because $J_z$, as given in \eqref{PE}, is the reproducing kernel for both spaces. The formal proof proceeds as follows. Fix $\beta\in [0,\pi)$. We will usually drop the reference to this parameter (and also to $N$) in the notation in this proof. Let $\{\lambda_n\}$ be the eigenvalues of $H_N^{\beta}$; note that $\{\lambda_n\}$ supports the spectral measure $\rho=\rho_N^{\beta}$. We first claim that $J_z\in L_2(\mathbb R, d\rho)$ for every $z\in\mathbb C$. More precisely, by this we mean that the restriction of $J_z$ to $\mathbb R$ (or $\{\lambda_n\}$) belongs to $L_2(\mathbb R, d\rho)$. Indeed, using \eqref{rhoN} and \eqref{PE}, we obtain \begin{align} \left\\| J_z \right\\|^2_{L_2(\mathbb R, d\rho)} & = \sum_n \left\| J_z(\lambda_n) \right\|^2 \rho(\{\lambda_n\} ) \\ & = \sum_n \left\| \langle u(\cdot, z), u(\cdot, \lambda_n) \rangle_{L_2(0,N)} \right\|^2 \left\\|u(\cdot, \lambda_n) \right\\|^{-2}_{L_2(0,N)}\\ & = \left\\|u(\cdot, z) \right\\|^2_{L_2(0,N)}. \end{align} The last equality is Parseval's formula, which applies because the normed eigenfunctions $u(\cdot,\lambda_n)/\\|u(\cdot,\lambda_n)\\|$ form an orthonormal basis of $L_2(0,N)$. A similar computation shows that \[ \langle J_w, J_z \rangle_{L_2(\mathbb R, d\rho)} = \langle u(\cdot,z), u(\cdot, w) \rangle_{L_2(0,N)} = J_z(w) = [J_w, J_z ]_{S_N} . \] By extending linearly, we thus get an isometric restriction map $V_0:L(\{J_z: z\in\mathbb C\} ) \to L_2(\mathbb R,d\rho)$, $V_0J_z=J_z\big\|_{\mathbb R}$. $V_0$ extends uniquely to an isometry $V: \overline{L(\{J_z: z\in\mathbb C\} )} \to L_2(\mathbb R,d\rho)$. Now the finite linear combinations of the $J_z$ are dense both in $L_2(\mathbb R, d\rho)$ and in $S_N$. In fact, as $J_{\lambda_m}(\lambda_n) = \\|u(\cdot,\lambda_n) \\|^2 \delta_{mn}$, the $J_z$ already span $L_2(\mathbb R, d\rho)$ if $z$ runs through the eigenvalues $\lambda_n$. As for $S_N$, we just note that since $[J_z,F]=F(z)$, an $F\in S_N$ that is orthogonal to all $J_z$'s must vanish identically. It follows that $V$ maps $S_N$ unitarily onto $L_2(\mathbb R, d\rho)$. Finally, if $F\in S_N$, then \[ (VF)(\lambda_n)= \langle V_0J_{\lambda_n}, VF \rangle_{L_2(\mathbb R, d\rho)} =[ J_{\lambda_n}, F ] = F(\lambda_n), \] so $V$ (originally defined by a limiting procedure) indeed just is the restriction map on the whole space. \end{proof} Recall that $U$ from \eqref{U} maps $L_2(0,N)$ unitarily onto $L_2(\mathbb R, d\rho_N^{\beta})$. Hence, by using the identification $L_2(\mathbb R, d\rho_N^{\beta}) \equiv S_N$ obtained in Theorem \ref{T3.1}, we get an induced unitary map (which we still denote by $U$) from $L_2(0,N)$ onto $S_N$. We claim that this map is still given by \eqref{U}; more precisely, for $f\in L_2(0,N)$, \begin{equation} \label{UU} (Uf)(z) = \int u(x,z)f(x)\, dx\quad\quad (z\in\mathbb C). \end{equation} To see this, note that \eqref{UU} is correct for $f=u(\cdot,\lambda_n)$, where $\lambda_n$ is an eigenvalue of $H_N^{\beta}$. Indeed, $u(\cdot,\lambda_n)$ is real valued, so in this case the right-hand side of \eqref{UU} equals $J_{\lambda_n}(z)$, which clearly is in $S_N$. It is of course automatic that $Uf$, computed with formula \eqref{UU}, restricts to the right function on $\{ \lambda_n \}$. Now \eqref{UU} follows in full generality by a standard approximation argument. As a consequence, we have the following alternate description of $S_N$ as a set, in addition to the definition \eqref{defdB}: \begin{equation} \label{BN} S_N = \left\{ F(z)= \int u(x,z) f(x)\, dx : f\in L_2(0,N) \right\} . \end{equation} This may be interpreted as a statement of Paley-Wiener type. Originally, $S_N$ was defined as a space of entire functions which are square integrable on the real line with respect to a weight function and satisfy a growth condition; now \eqref{BN} says that these function precisely arise by transforming $L_2$ functions with support in $(0,N)$, using the eigenfunctions $u(\cdot, z)$. In the case of zero potential, one basically recovers the original Paley-Wiener Theorem. A still much more general result along these lines (namely, Theorem \ref{T6.3}) will be discussed later. The material developed so far has some consequences. We continue to denote the de~Branges space associated with a Schr\"odinger equation on an interval $(0,N)$ by $S_N$. \begin{Theorem} \label{T3.2} a) Suppose that $0<N\le N'$. Then $S_N$ is isometrically contained in $S_{N'}$, that is, $S_N \subset S_{N'}$ and $\\|F\\|_{S_N}=\\|F\\|_{S_{N'}}$ for all $F\in S_N$. b) For any boundary condition $\beta\in [0,\pi)$ and any spectral measure $\rho$ for the half line problem (if $V$ is originally defined only on $(0,N)$, one may in fact also choose an arbitrary locally integrable continuation of $V$ to $[0,\infty)$ and possibly also a boundary condition at infinity), we have that \begin{align} \\|F\\|^2_{S_N} & = \frac{1}{\pi} \int_{-\infty}^{\infty} \frac{\|F(\lambda)\|^2}{u^2(N,\lambda) + {u'}^2(N,\lambda)}\, d\lambda\\ & = \int_{-\infty}^{\infty} \|F(\lambda)\|^2\, d\rho_N^{\beta}(\lambda) = \int_{-\infty}^{\infty} \|F(\lambda)\|^2\, d\rho(\lambda) \end{align} for all $F\in S_N$. \end{Theorem} {\it Remarks.} 1.\ Of course, the two parts of the theorem can be combined, and thus in the second part, $N$ on the right-hand sides can be replaced by any $N'\ge N$. 2.\ Part b) says that $S_N$ is embedded in $L_2(\mathbb R, d\mu)$ for many measures $\mu$. In fact, one can give a description of {\it all} such measures $\mu$. This description is an analog of the Nevanlinna parametrization of the solutions of a moment problem. See \cite[Theorem 30]{dB} for a very general version of this statement. 3.\ It is a well known (and often useful) fact that in the limit point case, the (unique) spectral measure $\rho$ of the half line problem can be obtained as \begin{equation} \label{wlim} d\rho(\lambda) = \frac{1}{\pi} \lim_{N\to\infty} \frac{d\lambda}{u^2(N,\lambda) + {u'}^2(N,\lambda)}. \end{equation} More precisely, \eqref{wlim} holds when integrated against continuous functions with compact support. Theorem \ref{T3.2} shows that this convergence takes place in a rather peculiar way. 4.\ The fact that $\\|F\\|_{S_N}$ can be computed by integrating against the discrete measures $\rho_{N}^{\beta}$ may be interpreted as a sampling theorem. In this context, recall that \eqref{BN} indeed says that, in a certain sense, functions from $S_N$ have limited bandwidth. 5.\ Here, we use the term ``spectral measure'' in the sense of Weyl theory. Later, in Sect.\ 17, we will {\it define} spectral measures as those measures that satisfy the conclusion of Theorem \ref{T3.2}b). \begin{proof} a) Obviously, $L_2(0,N)$ is a subspace of $L_2(0,N') =L_2(0,N) \oplus L_2(N,N')$, and the map $U$ from \eqref{UU} maps these spaces unitarily onto $S_N$ and $S_{N'}$, respectively. (Here, we make essential use of the fact that the action of $U$ is independent of $N$.) b) The first integral is the definition of the norm on $S_N$. The second formula gives the correct result because $S_N\equiv L_2(\mathbb R, d\rho_N^{\beta})$ by Theorem \ref{T3.1}. Finally, since $L_2(0,N)$ is isometrically contained in $L_2(0,\infty)$, the argument from the first part of this proof also shows that $S_N$ is isometrically contained in $L_2(\mathbb R, d\rho)$. \end{proof} \section{The spaces $S_N$} We now analyze in more detail the de~Branges spaces $S_N$ that come from a Schr\"odinger equation, as discussed in the previous section. We will prove that $S_N$ as a vector space is independent of the potential $V$. Moreover, the norm on $S_N$ always is a small distortion of the norm for zero potential. In particular, the topology of $S_N$ is also independent of $V$. Along the way, we introduce the function $\phi$ which should be thought of as the spectral data of the Schr\"odinger equation. This function also plays a central role in the Gelfand-Levitan treatment of the inverse problem. The use of $\phi$ instead of the spectral measure (say) has many advantages. For instance, $\phi$ allows us to treat the problem locally: $\phi$ on an interval $[0,2N]$ determines and is determined by $V$ on $[0,N]$. This is also implicit in the Gelfand-Levitan theory, although this aspect is usually not emphasized. The results of this section are basic to our approach to the inverse problem. We assume that a potential $V\in L_1(0,N)$ is given. Then we can make the following statements about the structure of the associated space $S_N$. \begin{Theorem} \label{T4.1} As a set, $S_N$ is given by \[ S_N = \left\{ F(z)=\int f(t) \cos\sqrt{z}t \, dt: f\in L_2(0,N) \right\} . \] \end{Theorem} Note that if $V\equiv 0$, then $u(x,z)=\cos\sqrt{z}x$, so the set from Theorem \ref{T4.1} is just the description \eqref{BN} of the de~Branges space $S_N^{(0)}$ for zero potential. The function $f\in L_2(0,N)$ is of course uniquely determined by the corresponding $F\in S_N$. There are also strong restrictions on the possible scalar products on the de~Branges spaces coming from Schr\"odinger equations. This is the content of the following theorem. We need some notation. Given a continuous, even function $\phi: [-2N,2N]\to\mathbb R$, we define an integral operator $\mathcal{K}_{\phi}$ on $L_2(0,N)$ by \begin{subequations} \label{Kphi} \begin{align} \left( \mathcal{K}_{\phi}f\right) (s) & = \int K(s,t)f(t)\, dt, \\ K(s,t) & = \frac{1}{2}\left( \phi(s-t) + \phi(s+t) \right) . \end{align} \end{subequations} $\mathcal{K}_{\phi}$ is self-adjoint and compact (in fact, Hilbert-Schmidt). \begin{Theorem} \label{T4.2} There exists a function $\phi: [-2N,2N]\to\mathbb R$ which is absolutely continuous, even, and satisfies $\phi(0)=0$, such that for all $F\in S_N$, \[ \\|F\\|^2_{S_N} = \langle f, (1+\mathcal{K}_{\phi}) f\, \rangle_{L_2(0,N)} . \] Here, $f$ is related to $F$ as in Theorem \ref{T4.1}. \end{Theorem} The requirement that $\phi$ be absolutely continuous on $[-2N,2N]$ means that there exists a function $\phi'\in L_1(-2N,2N)$ such that $\phi(x)=\phi(0) + \int_0^x\phi'(t)\, dt$ for all $x\in [-2N,2N]$. Later (Theorem \ref{T8.1}), we will prove that Theorems \ref{T4.1}, \ref{T4.2} have a converse: the conditions formulated in these two theorems actually characterize the de~Branges spaces that come from a Schr\"odinger equation among all de~Branges spaces. Both theorems depend on the fact that the asymptotics of the solutions of \eqref{se} as $\|z\|\to\infty$ are in leading order independent of $V$. \begin{proof}[Proof of Theorem \ref{T4.1}] We first show that $S_N$ is contained in the set on the right-hand side. So let $F\in S_N$; by \eqref{BN}, $F$ is of the form \begin{equation} \label{4.1} F(z)=\int_0^N u(x,z)g(x)\, dx\quad\quad (g\in L_2(0,N)). \end{equation} By a standard asymptotic expansion, we have that \begin{equation} \label{estv} \left\| u(x,z) - \cos\sqrt{z} x \right\| \le \|z\|^{-1/2} \exp( \\|V\\|_{L_1(0,N)} ) \exp ( \|\text{Im }z^{1/2}\|x ) \quad (0\le x\le N). \end{equation} See, for instance, \cite[Chapter 1]{PT} (actually, this reference works in the slightly more restrictive setting $V\in L_2(0,N)$, but the same method yields \eqref{estv}). Define $G(k)=F(k^2)$. Then $G$ is entire, even, and \eqref{4.1}, \eqref{estv} imply that $\|G(k)\| \le C e^{N\|k\|}$. Moreover, again by \eqref{4.1} and \eqref{estv}, \[ G(k) = \int g(x) \cos kx\, dx + O(k^{-1}) \] for $k\in\mathbb R$, $k\to\infty$, so $G\in L_2(\mathbb R)$. Thus the Paley-Wiener Theorem applies: $G$ has the form \[ G(k) = \frac{1}{2} \int f(x) e^{ikx}\, dx, \] where $f\in L_2(-N,N)$. Since $G$ is even, we must also have that $f(-x)=f(x)$, which in turn implies that $G(k)=\int_0^N f(x) \cos kx\, dx$. In other words, $F(z)=G(z^{1/2})=\int_0^N f(x) \cos \sqrt{z}x \, dx$, as desired. To prove the converse inclusion, we first claim that \begin{equation} \label{4.2} \inf_{\lambda\in\mathbb R} \left\| \frac{E(\lambda)}{E_0(\lambda)} \right\| > 0, \end{equation} where $E_0$ is the de~Branges function for zero potential: $E_0(z) =\cos\sqrt{z}N-i\sqrt{z}\sin\sqrt{z}N$. To establish \eqref{4.2}, it clearly suffices to show that \[ \liminf_{\lambda\to\pm\infty}\left\| \frac{E(\lambda)}{E_0(\lambda)} \right\| > 0. \] Consider first the case $\lambda\to\infty$, and put again $\lambda=k^2$, $k\to\infty$. Assume that, contrary to the assertion, there exists a sequence $k_n\to\infty$ so that $E(k_n^2)/E_0(k_n^2)\to 0$. We now use \eqref{estv} and the analogous estimate on $u'$ which reads \begin{equation} \label{estv'} \left\| u'(x,z) + \sqrt{z}\sin\sqrt{z}x \right\| \le \exp( \\|V\\|_{L_1(0,N)} ) \exp ( \|\text{Im }z^{1/2}\|x ) \quad (0\le x\le N) . \end{equation} Since $E(z)=u(N,z)+iu'(N,z)$, we obtain \begin{equation} \label{4.3} \left\| \frac{E(k_n^2)}{E_0(k_n^2)} \right\|^2 = \frac{\left(\cos k_n N + O(k_n^{-1}) \right)^2 + \left( k_n\sin k_n N + O(1) \right)^2}{\cos^2 k_n N + k_n^2 \sin^2 k_n N} . \end{equation} If $k_n \sin k_n N$ remains bounded as $n\to\infty$, then $\|\cos k_n N\| \to 1$, so \eqref{4.3} shows that $\|E(k_n^2)/E_0(k_n^2)\|^2$ is bounded away from zero. Thus, by passing to a subsequence if necessary, we may assume that $k_n\|\sin k_n N\|\to\infty$. But then we see from \eqref{4.3} that $\|E(k_n^2)/E_0(k_n^2)\|^2\to 1$, which is a contradiction to our choice of $k_n$. The argument for $\lambda\to -\infty$ is similar (in fact, easier). Write $\lambda=-\kappa^2$ with $\kappa\to\infty$. One shows that both $E$ and $E_0$ are of the asymptotic form \begin{align} \left\| E(-\kappa^2)\right\|^2 & = \frac{\kappa^2}{4} e^{2\kappa N} +O( \kappa e^{2\kappa N} ), \\ \left\| E_0(-\kappa^2)\right\|^2 & = \frac{\kappa^2}{4} e^{2\kappa N} +O( \kappa e^{2\kappa N} ), \end{align} so $\|E(-\kappa^2)/E_0(-\kappa^2)\| \to 1$. Thus \eqref{4.2} holds. Now if $F(z)=\int f(x) \cos \sqrt{z}x \, dx$ with $f\in L_2(0,N)$, then $F/E_0\in L_2(\mathbb R)$, hence also $F/E\in L_2(\mathbb R)$ by \eqref{4.2}. Moreover, $F$ is obviously entire. It remains to establish one of the conditions of Proposition \ref{P2.1}. To this end, we establish Cauchy type representations for $F/E$, $F^{\#}/E$. As we have already seen in the proof of Proposition \ref{P2.1}, such representations imply condition a) from the Proposition. Write $z=R^2e^{2i\varphi}$, $\sqrt{z}=Re^{i\varphi}$ with $R>0$, $0\le\varphi\le\pi/2$. Then the asymptotic formulae \eqref{estv}, \eqref{estv'} yield \[ E(z) = \cos(NRe^{i\varphi}) - iRe^{i\varphi} \sin (NRe^{i\varphi}) + O(e^{NR\sin\varphi}). \] The constant implicit in the error term is of course independent of $R$ and $\varphi$. It follows that \begin{equation} \label{4.a} \|E(z)\| \ge R \| \sin(NRe^{i\varphi})\| - O(e^{NR\sin\varphi}). \end{equation} Hence there exist constants $C_0,R_0>0$ with the following property: If $R\ge R_0$ and $\sin\varphi\ge C_0/R$, then \begin{equation} \label{4.4} \|E(z)\|\ge \frac{1}{2} R e^{NR\sin\varphi}. \end{equation} In the opposite case of small $\varphi$, we restrict our attention to the radii $R_n=N^{-1}(2\pi n + \pi/2)$, with $n\in\mathbb N$, $n$ large. The assumption $\sin\varphi < C_0/R$ ensures that the error term from \eqref{4.a} is actually bounded, and \begin{align} \sin(NRe^{i\varphi}) & = \sin(NR\cos\varphi + iNR\sin\varphi) = \sin(NR + iNR\sin\varphi) + O(R^{-1})\\ & = \sin(\pi/2 + iNR\sin\varphi) + O(R^{-1}) = \cosh (NR\sin\varphi) + O(R^{-1}). \end{align} As $\cosh x\ge 1$, we thus get from \eqref{4.a} that $\|E(z)\|\ge R_n/2$ for $z$ as above and sufficiently large $n$. Obviously, if $\sin\varphi<C_0/R$, then $e^{-NC_0} e^{NR\sin\varphi} \le 1$, so \eqref{4.4}, possibly with $1/2$ replaced by a smaller constant, actually holds for all $\varphi\in [0,\pi/2]$ if $R$ is restricted to the values $R_n$ from above. Finally, \[ \|F(R^2e^{2i\varphi})\| \le \int_0^N \|f(x)\|\, \|\cos(Re^{i\varphi}x)\|\, dx \le \\|f\\|_2 \sqrt{N} e^{NR\sin\varphi} . \] In conclusion, it follows that $\|F(z)/E(z)\|\le CR^{-1}$ for $R\in \{ R_n \}$ and $\varphi\in [0,\pi/2]$, and this estimate indeed implies the Cauchy formula \[ \frac{F(z)}{E(z)} = \frac{1}{2\pi i} \int_{-\infty}^{\infty} \frac{F(\lambda)}{E(\lambda)} \, \frac{d\lambda}{\lambda - z}\quad\quad (z\in\mathbb C^+) \] by a standard procedure. (Integrate from $-R_n$ to $R_n$ on the real line and close by a semicircle in the upper half plane; let $n\to\infty$. The above estimate ensures that the integral over the semicircle vanishes in the limit.) The same argument works for $F^{\#}/E$. As explained above, this completes the proof. \end{proof} The proof of Theorem \ref{T4.2} will depend on an asymptotic formula for the Titchmarsh-Weyl $m$-function. This subject has been studied systematically and in considerable depth (see, for example, \cite{Atk,GeSi,BJH,HKS,Si}). We will only need a rather straightforward result whose proof we include for the reader's convenience. Given $V\in L_1(0,N)$, we extend $V$ to $(0,\infty)$ by setting it equal to zero on $(N,\infty)$. Denote the spectral measure and the $m$-function of the half line problem (as usual, with Neumann boundary conditions $y'(0)=0$) by $\rho^{(N)}$ and $m^{(N)}$, respectively. We now briefly review some basic facts about $m^{(N)}$ and $\rho^{(N)}$; this material can be found, for example, in \cite{DT,Lev}. We can obtain $m^{(N)}$ as follows: Let $f(x,k)$ be the Jost solution. In other words, $f$ solves \eqref{se} with $z=k^2$ and $f(x,k)=e^{ikx}$ for $x\ge N$. Define a meromorphic function $M_N$ by \[ M_N(k) = -\frac{f(0,k)}{f'(0,k)}. \] Then, since $f(\cdot,k)\in L_2(0,\infty)$ for $k\in\mathbb C^+$, we have that $m^{(N)}(k^2)=M_N(k)$ for these $k$. More precisely, this formula gives the meromorphic continuation of the function $m^{(N)}$, which is originally defined on $\mathbb C^+$, to $\mathbb C \setminus [0,\infty)$. The $m$-function $m^{(N)}$ has only finitely many poles in this region. They all lie on $(-\infty,0)$, and they are just the eigenvalues of $-d^2/dx^2+V(x)$ on $L_2(0,\infty)$. For $k>0$, the limit $\lim_{\epsilon\to 0+} m^{(N)}(k^2+i\epsilon)$ exists. We will denote this limit simply by $m^{(N)}(k^2)$; we then have that $m^{(N)}(k^2)=M_N(k)$ for all $k>0$ (note, however, that $M_N(-k)$ does {\it not} give the correct value but the complex conjugate of $m^{(N)}(k^2)$ because $k^2$ is now approached from the lower half plane). From these facts, we immediately get the following description of $\rho^{(N)}$. Denote the finitely many negative eigenvalues by $-\kappa_n^2$, $\kappa_n > 0$. Then \[ \rho^{(N)}= \sum_n \rho^{(N)}(\{ -\kappa_n^2 \} ) \delta_{-\kappa_n^2} + \frac{1}{\pi}\chi_{(0,\infty)}(\lambda) \text{Im }M_N(\sqrt{\lambda}) \, d\lambda . \] We will also need the $m$-function $m_0$ and the spectral measure $\rho_0$ for zero potential. The following formulae hold: \begin{equation} \label{mrho0} m_0(z) = (-z)^{-1/2},\quad \rho_0 = \chi_{(0,\infty)}(\lambda)\, \frac{d\lambda}{\pi \sqrt{\lambda}}. \end{equation} In the first equation, which holds for $z\in\mathbb C^+$, the square root must be chosen so that $\text{Im }m_0 > 0$. Clearly, $m_0$ can then be holomorphically continued to $\mathbb C \setminus [0,\infty)$. This continuation will also be denoted by $m_0$. Finally, just as for $m^{(N)}$, we put $m_0(\lambda)\equiv \lim_{\epsilon\to 0+} m_0(\lambda+i\epsilon)$ for $\lambda>0$. \begin{Lemma} \label{L4.3} a) The limit $\lim_{k\to 0} k M_N(k)$ exists.\\ b) For $\text{Im }k \ge 0$, $k\notin (-\infty,0]$, we have that \[ m^{(N)}(k^2)-m_0(k^2) = \frac{1}{k^2} \int_0^N V(x) e^{2ikx}\, dx + O(\|k\|^{-3}) . \] \end{Lemma} \begin{proof} a) If $y_1$, $y_2$ both solve \eqref{se}, then the Wronskian $y'_1y_2-y_1y'_2$ is constant. By computing the Wronskian of $f(\cdot,k)$ and $f(\cdot, -k)$ at $x=0$ and $x=N$, we therefore see that \[ f'(0,k)f(0,-k) - f(0,k) f'(0,-k) = 2ik . \] Take the derivative with respect to $k$ (writing $\dot{}\equiv \frac{d}{dk}$) and then set $k=0$. We obtain \[ f(0,0)\dot{f}'(0,0) - \dot{f}(0,0) f'(0,0) = i, \] and thus it is not possible that $f'(0,k)$ and $\dot{f}'(0,k)$ vanish simultaneously at $k=0$. Therefore a possible pole of $M_N$ at $k=0$ must be of order one. b) Put $g(x,k)=f(x,k)e^{-ikx}$. Then, basically by the variation of constants formula, $g$ is the unique solution of the integral equation \[ g(x,k)= 1 + \frac{1}{2ik} \int_x^N \left( e^{2ik(t-x)} - 1 \right) V(t) g(t,k)\, dt . \] If $\text{Im }k\ge 0$ and $\|k\|\ge 2\\|V\\|_{L_1(0,N)}$, this implies the a priori estimate $\\|g\\|_{\infty} \le 2$. So for these $k$, we have $\|g(x,k)-1\|\le 2\\|V\\|_1/\|k\|$. This in turn shows that \[ g'(x,k) = -\int_x^N V(t)e^{2ik(t-x)}\, dt + O(\|k\|^{-1}). \] Hence for large $\|k\|$, \begin{align} m^{(N)}(k^2)=M_N(k) & = -\frac{f(0,k)}{f'(0,k)} = \frac{-g(0,k)}{ikg(0,k)+g'(0,k)}\\ & = \frac{i}{k}\, \frac{1}{1+\frac{g'(0,k)}{ikg(0,k)}} = \frac{i}{k} \left( 1 - \frac{g'(0,k)}{ikg(0,k)} + O(\|k\|^{-2}) \right) \\ & = \frac{i}{k} + \frac{1}{k^2} \int_0^N V(t)e^{2ikt}\, dt + O(\|k\|^{-3}), \end{align} as desired, since $m_0(k^2)=i/k$. For small $k$, there is nothing to prove. \end{proof} \begin{proof}[Proof of Theorem \ref{T4.2}] Suppose that an $F\in S_N$ is given and write, according to Theorem \ref{T4.1}, \[ F(z) = \int f(t) \cos\sqrt{z}t \, dt \] with $f\in L_2(0,N)$. Introduce the (signed) Borel measure $\sigma_N$ by $\sigma_N=\rho^{(N)}-\rho_0$. Theorem \ref{T3.2}b) allows us to compute the norm of $F$ as \begin{equation} \label{4.8} \\|F\\|_{S_N}^2 = \int \|F(\lambda)\|^2\, d\rho^{(N)}(\lambda) = \int\|F(\lambda)\|^2\, d\rho_0(\lambda) + \int \|F(\lambda)\|^2\, d\sigma_N(\lambda) . \end{equation} The two integrals in this last expression converge absolutely because the map $f\mapsto F$ is unitary from $L_2(0,\infty)$ onto $L_2(\mathbb R, d\rho_0)$ -- in fact, it is just the $U$ from \eqref{U} for zero potential. This observation also says that \[ \int\|F(\lambda)\|^2\, d\rho_0(\lambda) = \int_0^N \|f(t)\|^2 \, dt . \] It remains to analyze the last integral from \eqref{4.8}. Using the identity \[ \cos x \cos y = \frac{1}{2} \left( \cos(x-y) + \cos (x+y) \right), \] we can write it in the form \begin{align} \int_{-\infty}^{\infty} \|F(\lambda)\|^2\, & d\sigma_N(\lambda) = \int_{-\infty}^{\infty} d\sigma_N(\lambda) \int ds\int dt \overline{f(s)}f(t) \cos \sqrt{\lambda}s \cos \sqrt{\lambda}t \nonumber \\ \label{4.9} & = \frac{1}{2} \int_{-\infty}^{\infty} d\sigma_N(\lambda) \int ds\int dt \overline{f(s)}f(t) \left( \cos\sqrt{\lambda}(s-t) + \cos\sqrt{\lambda}(s+t) \right) . \end{align} Formally, this is of the desired form with $\phi(x) = \int \cos\sqrt{\lambda}x \, d\sigma_N(\lambda)$, but this needs to be interpreted carefully because the integral ``defining'' $\phi$ will not, in general, be absolutely convergent. Our strategy will be to first define $\phi$ as a distribution and then prove that it is actually an absolutely continuous function. More precisely, the contribution coming from $\lambda\in (0,\infty)$ will be treated in this way. So we define a tempered distribution $\phi_+\in\mathcal{S}'$ as follows. Let $g$ be a test function from the Schwartz space $\mathcal{S}$. Recall that this means that $g$ is infinitely differentiable and $\sup_{x\in\mathbb R} \|x\|^m \|g^{(n)}(x)\| < \infty$ for all $m,n\in\mathbb N_0$. Then $\phi_+$ acts on $g$ by \[ (\phi_+, g) = \int_0^{\infty} d\sigma_N(\lambda) \int_{-\infty}^{\infty} dx\, g(x) \cos\sqrt{\lambda}x . \] This is well defined because $\int g(x) \cos\sqrt{\lambda}x\, dx$ is rapidly decreasing in $\lambda$ and from Lemma \ref{L4.3} and the preceding material we have the a priori estimate $\|\sigma_N \|([0,R]) \le C \sqrt{R}$. Thus the integral certainly converges. It is also clear that $\phi_+$ is linear and continuous in the topology of $\mathcal{S}$, so indeed $\phi_+\in\mathcal{S}'$. Note that formally, $\phi_+$ is just $\phi_+(x)=\int_0^{\infty} \cos\sqrt{\lambda}x \, d\sigma_N(\lambda)$. The Fourier transform of $\phi_+$ is, by definition, the tempered distribution $\widehat{\phi}_+$ acting on test functions $g$ by $(\widehat{\phi}_+,g)= (\phi_+,\widehat{g} )$. We compute \begin{align} (\phi_+,\widehat{g}) & = \frac{1}{2} \int_0^{\infty} d\sigma_N(\lambda) \int_{-\infty}^{\infty} dx\, \widehat{g}(x) \left( e^{i\sqrt{\lambda}x} + e^{-i\sqrt{\lambda}x} \right) \\ & = \sqrt{\frac{\pi}{2}} \int_0^{\infty} d\sigma_N(\lambda) \left( g(\sqrt{\lambda}) + g(-\sqrt{\lambda}) \right) \\ & = \sqrt{\frac{2}{\pi}} \int_0^{\infty} \text{Im } ( m^{(N)}- m_0 )(k^2) \left( g(k) + g(-k) \right) k\, dk \\ & = \sqrt{\frac{2}{\pi}} \int_{-\infty}^{\infty} g(k) \|k\| \text{ Im } (m^{(N)}- m_0)(k^2) \, dk, \end{align} and hence $\widehat{\phi}_+$ is a function and \begin{equation} \label{4.5} \widehat{\phi}_+(k) = \sqrt{\frac{2}{\pi}}\, \|k\| \text{ Im } (m^{(N)}- m_0)(k^2) . \end{equation} From Lemma \ref{L4.3} and the formula for $m_0$, we see that $\widehat{\phi}_+$ is continuous and $\widehat{\phi}_+(k)=O(\|k\|^{-1})$ for large $\|k\|$. In fact, we get the more precise information that \begin{align} \widehat{\phi}_+(k) & = \sqrt{\frac{2}{\pi}} \, \frac{1}{\|k\|} \int_0^N V(x)\sin 2\|k\|x \, dx +O(k^{-2}) \\ & = \frac{1}{\sqrt{2\pi}} \, \frac{1}{ik} \int_0^N V(x) \left( e^{2ikx}- e^{-2ikx} \right) \, dx + O(k^{-2})\\ & =\frac{1}{ik} \widehat{W}_N(k) + O(k^{-2}), \end{align} where \[ W_N(x) = \begin{cases} -(1/2) V(x/2) & 0 < x < 2N \\ (1/2) V(-x/2) & -2N < x < 0 \\ 0 & \|x\| > 2N \end{cases} . \] Therefore the (distributional) derivative $\phi'_+$ of $\phi_+$ has a Fourier transform of the form \[ (\phi'_+)\, \widehat{ }\,(k) = ik\widehat{\phi}_+(k) = \widehat{W}_N(k) + \widehat{R}_N(k), \] where $\widehat{R}_N$ is a continuous function and $\widehat{R}_N(k) = O(\|k\|^{-1})$. It follows that \[ \phi'_+(x) = W_N(x) + R_N(x), \] with $R_N\in L_2$. In particular, $\phi'_+\in\mathcal{S}'$ is a locally integrable function, and as a consequence, $\phi_+$ is an absolutely continuous function. We define \[ \phi(x) = \int_{-\infty}^0 \cos\sqrt{\lambda}x\, d\sigma_N(\lambda) + \phi_+(x) = \sum \rho^{(N)}(\{ -\kappa_n^2 \} ) \cosh \kappa_n x + \phi_+(x), \] and we verify that this $\phi$ has the desired properties. We know already that $\phi_+$ is absolutely continuous. Its Fourier transform, $\widehat{\phi}_+$, is real valued and even (compare \eqref{4.5}), so $\phi_+$ has these properties, too. The (finite) sum $\sum \rho^{(N)}(\{ -\kappa_n^2 \} ) \cosh \kappa_n x$ manifestly is a smooth, real valued, even function, so we have established that $\phi$ is absolutely continuous, real valued, and even. To show that $\phi(0)=0$, we use the formula \[ (m^{(N)} - m_0)(k^2) = \int_{-\infty}^{\infty} \frac{d\sigma_N(\lambda)}{\lambda - k^2}\quad\quad (k\in\mathbb C^+), \] which follows at once from the Herglotz representations of $m^{(N)}$ and $m_0$ (see, e.g., \cite{Lev}). We can Fourier transform the denominator, \[ \frac{1}{\lambda - k^2} = \frac{i}{k} \int_0^{\infty} \cos\sqrt{\lambda}t\, e^{ikt}\, dt\quad\quad (k\in\mathbb C^+, \lambda>0), \] to write this in the form \begin{equation} \label{4.6} (m^{(N)} - m_0)(k^2) = \sum \frac{\rho^{(N)}(\{ -\kappa_n^2 \} )}{-\kappa_n^2 - k^2} + \frac{i}{k} \int_0^{\infty} d\sigma_N(\lambda) \int_0^{\infty} dt\, e^{ikt} \cos\sqrt{\lambda}t . \end{equation} We now take a closer look at this last integral: \begin{align} \int_0^{\infty} d\sigma_N(\lambda) \int_0^{\infty} dt\, e^{ikt} \cos\sqrt{\lambda}t & = \frac{2}{\pi} \int_0^{\infty} dl\, l \text{ Im } (m^{(N)} - m_0)(l^2) \int_0^{\infty} dt\, e^{ikt} \cos lt\\ & = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} dl\, \widehat{\phi}_+(l)\int_0^{\infty} dt\, e^{ikt} \cos lt\\ & = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} dl\, \widehat{\phi}_+(l)\int_0^{\infty} dt\, e^{ikt}e^{-ilt}. \end{align} This last expression equals $\int \widehat{\phi}_+\,\widehat{h}$, where $h(t) = \chi_{(0,\infty)}(t) e^{ikt}$. Since we are assuming that $k\in\mathbb C^+$, this function is in $L_2$, as is $\widehat{\phi}_+$, and thus we may use the Plancherel identity to obtain the final result \[ (m^{(N)} - m_0)(k^2) = \sum \frac{\rho^{(N)}(\{ -\kappa_n^2 \} )}{-\kappa_n^2 - k^2} + \frac{i}{k} \int_0^{\infty} \phi_+(t) e^{ikt}\, dt \quad\quad(k\in\mathbb C^+). \] Note that on a formal level, this may be derived very easily from \eqref{4.6} because the last term of \eqref{4.6} looks like $\phi_+$ applied to $(i/k)h$. However, $h$ is not a test function! If we assume that in addition $\text{Im }k> \max \kappa_n$, then $\int_0^{\infty} \phi(t) e^{ikt} \, dt$ exists and we get the more compact formula \[ (m^{(N)} - m_0)(k^2) = \frac{i}{k} \int_0^{\infty} \phi(t) e^{ikt} \, dt. \] We now specialize to $k=iy$, $y\to\infty$, and integrate by parts. This gives \[ m^{(N)}(-y^2)-m_0(-y^2) = \frac{\phi(0)}{y^2} + \frac{1}{y^2} \int_0^{\infty} \phi'(t) e^{-yt}\, dt . \] Since $\phi'_+\in L_1+ L_2$, the integral goes to zero by dominated convergence, hence \[ m^{(N)}(-y^2)-m_0(-y^2) = \frac{\phi(0)}{y^2} + o(y^{-2}) \quad\quad (y\to\infty) . \] On the other hand, Lemma \ref{L4.3}b) implies that $m^{(N)}(-y^2)-m_0(-y^2) = o(y^{-2})$. Therefore, $\phi(0)=0$. Let $\mathcal{K}_{\phi}: L_2(0,N)\to L_2(0,N)$ be the integral operator defined in \eqref{Kphi}, with the $\phi$ constructed above. We still have to establish the crucial property of $\phi$, namely, the fact that the integral from \eqref{4.9} equals $\langle f, \mathcal{K}_{\phi}f \rangle$ for all $f\in L_2(0,N)$. We first consider the case when $f\in C_0^{\infty}(0,N)$, and we treat explicitly only the first term from \eqref{4.9}, which contains $\cos\sqrt{\lambda} (s-t)$. Introduce the new variables $R=s+t$, $r=s-t$. Then we have \begin{align} \int d\sigma_N(\lambda) \int\int ds\, dt\, & \overline{f(s)} f(t) \cos\sqrt{\lambda}(s-t) \\ & = \frac{1}{2} \int d\sigma_N(\lambda) \int dr\, \cos\sqrt{\lambda} r \int dR\, \overline{f\left( \frac{R+r}{2} \right)} f\left( \frac{R-r}{2} \right) \\ & =\int d\sigma_N(\lambda) \int dr\, g(r) \cos\sqrt{\lambda} r . \end{align} Here, we have put \begin{equation} \label{4.11} g(r) \equiv \frac{1}{2} \int dR\, \overline{f\left( \frac{R+r}{2} \right)} f\left( \frac{R-r}{2} \right) , \end{equation} and all integrals are over $\mathbb R$. Note that $g\in C_0^{\infty} (-N,N)$. In particular, $g$ is an admissable test function, and thus the following manipulations are justified: \begin{align} \int d\sigma_N(\lambda) & \int dr\, g(r) \cos\sqrt{\lambda} r\\ & = \sum \rho( \{ -\kappa_n^2 \} ) \int g(r) \cosh \kappa_n r\, dr +\int_0^{\infty} d\sigma_N(\lambda) \int dr\, g(r) \cos\sqrt{\lambda} r\\ & = \int dr\, g(r) \sum \rho( \{ -\kappa_n^2 \} ) \cosh \kappa_n r + \int \phi_+(r) g(r)\, dr\\ & = \int \phi(r) g(r)\, dr . \end{align} Finally, we can write out $g$ (see \eqref{4.11}) and transform back to the original variables $(s,t)$; we obtain the expression \[ \int\int ds\,dt\, \overline{f(s)} f(t) \phi(s-t) . \] If we combine this with the result of the analogous computation for the term involving $\cos\sqrt{\lambda}(s+t)$, then we get indeed that \begin{align} \frac{1}{2} \int_{-\infty}^{\infty} d\sigma_N(\lambda) \int ds\int dt\, \overline{f(s)} & f(t) \left( \cos\sqrt{\lambda}(s-t) + \cos\sqrt{\lambda}(s+t) \right) \\ & = \frac{1}{2} \int\int ds\,dt\, \overline{f(s)} f(t) \left( \phi(s-t) + \phi(s+t) \right) \\ & = \langle f, \mathcal{K}_{\phi} f \rangle . \end{align} Using this in \eqref{4.8}, \eqref{4.9}, we see that \begin{equation} \label{4.10} \\|F\\|_{S_N}^2 = \langle f, (1+\mathcal{K}_{\phi}) f \rangle_{L_2(0,N)}, \end{equation} as desired. So far, this has been proved for $f\in C_0^{\infty}(0,N)$. To establish \eqref{4.10} in full generality, fix $f\in L_2(0,N)$ and pick $f_n\in C_0^{\infty}(0,N)$ with $\\|f_n-f\\|_{L_2(0,N)} \to 0$. From the proof of Theorem \ref{T4.1} (see, in particular, \eqref{4.2}) we know that there is a constant $C>0$ so that for all $G\in S_N$, the inequality $\\|G\\|_{S_N}\le C\\|G\\|_{S_N^{(0)}}$ holds, where $S_N^{(0)}$ is the de~Branges space for zero potential. Hence, writing $F_n(z)= \int f_n(t) \cos \sqrt{z}t\, dt$, we deduce that \[ \\|F_n-F\\|_{S_N} \le C \\|F_n-F\\|_{S_N^{(0)}} = C \\|f_n-f\\|_{L_2(0,N)} \to 0 . \] Therefore, we can use \eqref{4.10} with $f$ replaced by $f_n$ and then pass to the limit to see that \eqref{4.10} holds for all $f\in L_2(0,N)$. \end{proof} \section{The inverse spectral theorem} Theorem \ref{T4.2} associates with each Schr\"odinger equation a function $\phi$ that determines the scalar product on the corresponding de~Branges spaces $S_N$. Recall also that by Theorem \ref{T3.1}, these de~Branges spaces can be identified with the spaces $L_2(\mathbb R, d\rho_N^{\beta})$ from the spectral representation of the Schr\"odinger operators. So it makes sense to think of $\phi$ (on $[-2N,2N]$) as representing the spectral data of $-d^2/dx^2+V(x)$ (on $L_2(0,N)$, with suitable boundary conditions at the endpoints). Our next result is the converse of Theorem \ref{T4.2}. It says that every function $\phi$ that has the properties stated in Theorem \ref{T4.2} comes from a Schr\"odinger equation. To be able to formulate this concisely, we denote this set of $\phi$'s by $\Phi_N$, so \[ \Phi_N =\{ \phi:[-2N,2N] \to \mathbb R : \phi \text{ absolutely continuous, even, } \phi(0)=0, 1+\mathcal{K}_{\phi}>0 \} . \] The last condition of course refers to the integral operator $\mathcal{K}_{\phi}$ on $L_2(0,N)$ that was introduced in \eqref{Kphi}; we require that the self-adjoint operator $1+\mathcal{K}_{\phi}$ be positive definite. In the situation of Theorem \ref{T4.2}, this condition holds because $\langle f, (1+\mathcal{K}_{\phi}) f\rangle$ is a norm. \begin{Theorem} \label{T8.1} For every $\phi\in \Phi_N$, there exists a $V\in L_1(0,N)$ so that the norm on the de~Branges space $S_N$ associated with \eqref{se} is given by \[ \\|F\\|^2_{S_N} = \langle f, (1+\mathcal{K}_{\phi}) f\, \rangle_{L_2(0,N)} \quad\quad (f\in L_2(0,N)) . \] Here, $F(z)=\int f(t)\cos\sqrt{z}t\, dt$, as in Theorem \ref{T4.1} . \end{Theorem} We will take up the proof of Theorem \ref{T8.1} in Sect.\ 9. Let us first point out that we also have uniqueness in both directions. In fact, uniqueness is, as usual, much easier than existence. \begin{Theorem} \label{T8.2} a) If $V\in L_1(0,N)$ is given, then the $\phi\in\Phi_N$ from Theorem \ref{T4.2} is unique.\\ b) If $\phi\in\Phi_N$ is given, then the $V\in L_1(0,N)$ from Theorem \ref{T8.1} is unique. \end{Theorem} This will also be proved in Sect.\ 9. We need some preparations; this will occupy us for the following three sections. \section{Canonical systems I} A canonical system is a family of differential equations of the following form: \begin{equation} \label{Can} Ju'(x) = zH(x) u(x). \end{equation} Here, $J=\bigl( \begin{smallmatrix} 0 & -1 \\ 1 & 0 \end{smallmatrix} \bigr)$, and $H(x)\in\mathbb R^{2\times 2}$, the entries of $H$ are integrable functions on an interval $(0,N)$, and $H(x)\ge 0$ (i.e., $H(x)$ is a positive semidefinite matrix) for almost every $x\in (0,N)$. We also assume that there is no nonempty open interval $I\subset (0,N)$ so that $H= 0$ almost everywhere on $I$. Finally, $z\in\mathbb C$ is the spectral parameter. As usual, $u:[0,N]\to \mathbb C^2$ is called a solution if $u$ is absolutely continuous and satisfies \eqref{Can} almost everywhere. Usually, one does not assume that $H(x)\not\equiv 0$ on nonempty open sets, but dropping this assumption does not add generality. Indeed, by letting \[ S_0 = \left\{ x\in (0,N): \exists \epsilon >0: H(t)=0\text{ for a.e.\ } t\in (x-\epsilon,x+\epsilon) \right\} \] and introducing the new independent variable \[ \xi(x) = \int_0^x \left( 1 - \chi_{S_0}(t) \right) \, dt, \] one may pass to an equivalent canonical system that satisfies our additional assumption. A fundamental result (namely, Theorem \ref{T6.3}) associates with every de~Branges space a canonical system \eqref{Can}. Therefore, canonical systems are a central object in the theory of de~Branges spaces. Let $u(x,z)$, $v(x,z)$ be the solutions of \eqref{Can} with the initial values $u(0,z)= \bigl( \begin{smallmatrix} 1 \\ 0 \end{smallmatrix} \bigr)$, $v(0,z)= \bigl( \begin{smallmatrix} 0 \\ 1 \end{smallmatrix} \bigr)$. We will mainly work with $u(x,z)$. Just as in Sect.\ 3, we can build a de~Branges function from $u$ by defining $E_N(z)=u_1(n,z)+iu_2(N,z)$. Here, a pathological case can occur: if $H(x)= \bigl( \begin{smallmatrix} 0 & 0 \\ 0 & H_{22}(x) \end{smallmatrix} \bigr)$ on $(0,N)$, then $u(N,z)=\bigl( \begin{smallmatrix} 1 \\ 0 \end{smallmatrix} \bigr)$ and $E_N(z)\equiv 1$. According to our definition in Sect.\ 2, this is not a de~Branges function. So it will convenient to slightly extend this definition and to also admit non-zero constants as de~Branges functions. The corresponding de~Branges space is simply defined to be the zero space. \begin{Proposition} \label{P5.1} $E_N(z)=u_1(N,z)+iu_2(N,z)$ is a de~Branges function. The corresponding reproducing kernel $J_z$ is given by \[ J_z(\zeta) = \int_0^N u^(x,z) H(x) u(x,\zeta) \, dx . \] \end{Proposition} \begin{proof} The formula for $J_z$ follows by a calculation, which is analogous to the discussion preceding Theorem \ref{T3.1}. One uses the fact that $u(x,\overline{z})=\overline{u(x,z)}$; we leave the details to the reader. Also, just as in Sect.\ 3, by taking $z=\zeta\in\mathbb C^+$, the formula for $J_z$ implies that $E_N$ is a de~Branges function. In this context, observe the following fact: if \[ \int_0^N u^(x,z)H(x)u(x,z)\, dx = 0 \] for some $z\in\mathbb C$, then $H(x)u(x,z)=0$ for almost every $x\in (0,N)$, hence $u(x,z)=u(0,z)= \bigl( \begin{smallmatrix} 1 \\ 0 \end{smallmatrix} \bigr)$. This in turn implies that $H_{11}=0$ almost everywhere, and we are in the trivial case $E_N(z)\equiv 1$. In the opposite case, $\int_0^N u^(x,z)H(x)u(x,z)\, dx > 0$ for all $z\in\mathbb C$, and $E_N$ is a genuine de~Branges function. \end{proof} Eventually, we will again identify the corresponding de~Branges space $B(E_N)$ with a space $L_2(\mathbb R, d\rho_N^{\beta})$, where $\rho_N^{\beta}$ is a spectral measure of \eqref{Can}, just as we did in the case of Schr\"odinger equations in Theorem \ref{T3.1}. However, things are more complicated now, basically for two reasons: First of all, if \eqref{Can} is to be interpreted as an eigenvalue equation $Tu=zu$, then, formally, the operator $T$ should be $Tu=H^{-1}Ju'$, but $H(x)$ need not be invertible. Consequently, one has to work with relations instead of operators. Second, on so-called singular intervals, equation \eqref{Can} actually is a difference equation in disguise. These points will be studied in some detail in Sect.\ 10. Our discussion of canonical systems will be modelled on the (simpler) analysis of Sect.~3. For a functional analytic treatment of canonical systems, see \cite{HdSW}. Reference \cite{dB} also contains a lot of material on canonical systems, though in somewhat implicit form. \section{Four theorems of de~Branges} In this section we state, without proof, four general results of de~Branges on de~Branges spaces which will play an important role in our treatment of the inverse problem for Schr\"odinger operators. The first result is a useful tool for recognizing de~Branges spaces. It is Theorem 23 of \cite{dB}. For an alternate proof, see \cite[Sect.\ 6.1]{DMcK}. \begin{Theorem} \label{T6.1} Let $\mathcal{H}$ be a Hilbert space whose elements are entire functions. Suppose that $\mathcal{H}$ has the following three properties:\\ a) For every $z\in\mathbb C$, point evaluation $F\mapsto F(z)$ is a bounded linear functional.\\ b) If $F\in\mathcal{H}$ has a zero at $w\in\mathbb C$, then $G(z)=\frac{z-\overline{w}}{z-w} F(z)$ belongs to $\mathcal{H}$ and $\\|G\\|=\\|F\\|$.\\ c) $F\mapsto F^{\#}$ is an isometry on $\mathcal{H}$. Then $\mathcal{H}$ is a de~Branges space: There exists a de~Branges function $E$, so that $\mathcal{H}=B(E)$ and $\\|F\\|_{\mathcal{H}} =\\|F\\|_{B(E)}$ for all $F\in\mathcal{H}$. \end{Theorem} The converse of Theorem \ref{T6.1} is also true (and easily proved): Every de~Branges space satisfies a), b), and c). In fact, in \cite{dB1}, the conditions of Theorem \ref{T6.1} are used to define de~Branges spaces. The de~Branges function $E$ is not uniquely determined by the Hilbert space $B(E)$. The situation is clarified by \cite[Theorem I]{dB1}. Given $E$, we introduce the entire functions $A$, $B$ by \[ A(z) = \frac{E(z)+E^{\#}(z)}{2},\quad\quad B(z) = \frac{E(z)-E^{\#}(z)}{2i}. \] \begin{Theorem} \label{T6.2} Let $E_1$, $E_2$ be de~Branges functions. Then $B(E_1)=B(E_2)$ (as Hilbert spaces) if and only if there exists $T\in\mathbb R^{2\times 2}$, $\det T=1$, so that \[ \begin{pmatrix} A_2(z) \\ B_2(z) \end{pmatrix} = T \begin{pmatrix} A_1(z) \\ B_1(z) \end{pmatrix}. \] \end{Theorem} The next two results lie much deeper. They are central to the whole theory of de~Branges spaces. We will not state the most general versions here; for this, the reader should consult \cite{dB}. The following definition will be useful to avoid (for us) irrelevant technical problems. A de~Branges space $B(E)$ is called {\it regular} if \begin{equation} \label{regsp} F(z) \in B(E) \Longrightarrow \frac{F(z)-F(z_0)}{z-z_0}\in B(E) . \end{equation} Here $z_0$ is any fixed complex number. The definition is reasonable because it can be shown that if \eqref{regsp} holds for one $z_0\in \mathbb C$, then it holds for all $z_0\in\mathbb C$ (compare \cite[Theorem 25]{dB}). The condition \eqref{regsp} also plays an important role in \cite{dB}. According to (a more general version of) Theorem \ref{T6.3} below, every de~Branges space comes from a (possibly singular) canonical system; the regular spaces are precisely those that come from regular problems, that is, $x=0$ is not a singular endpoint. Jumping ahead, we can also remark that condition \eqref{regsp} ensures the existence of a conjugate mapping. See also \cite{Wo} for other aspects of \eqref{regsp}. \begin{Theorem} \label{T6.3} If $B(E)$ is a regular de~Branges space, $E(0)=1$, and $N>0$ is given, then there exists a canonical system \eqref{Can} (that is, there exists an integrable function $H:(0,N)\to \mathbb R^{2\times 2}$ with $H(x)\ge 0$ almost everywhere, $H\not\equiv 0$ on nonempty open sets), such that $E(z)=E_N(z)$, where $E_N$ is determined from \eqref{Can} as in Proposition \ref{P5.1}. Moreover, $H(x)$ can be chosen so that $\text{tr }H(x)$ is a (positive) constant. \end{Theorem} De~Branges proved various results of this type; see \cite[Theorems V, VII]{dB2} and \cite[Theorems 37, 40]{dB}. The version given here follows by combining \cite[Theorem VII]{dB2} with \cite[Theorem 27]{dB}. In fact, this is not literally true because de~Branges uses the equation \begin{equation} \label{Canint} y(b)J-y(a)J = z \int_a^b y(t) dm(t) \end{equation} instead of \eqref{Can}. Here, $m$ is a matrix valued measure. If $m$ is absolutely continuous, $dm(t)=m'(t)\, dt$, then \eqref{Canint} can be written as a differential equation $y'J=zyH$, with $H=m'$, and the further change of variable $u(x,z)=y^(x,-\overline{z})$ then gives \eqref{Can}. In \cite{dB}, $m$ is only assumed to be continuous, but then one can change the independent variable to $\xi(t)=\text{tr }m((0,t))$ to get an absolutely continuous measure. This transformation automatically leads to a system with $\text{tr }H(x)\equiv 1$, and this is how one proves the last statement of Theorem \ref{T6.3}. A further transformation of the type $\xi\to a\xi$ with a suitable $a>0$ then yields a problem on $(0,N)$ again. There is no apparent reason for preferring one of these equivalent ways of writing canonical systems (see \eqref{Can} and \eqref{Canint}), but it appears that the form we use here (namely, \eqref{Can}) has become the most common. The assumption that $E(0)=1$ is just a normalization; it does not restrict the applicability of Theorem \ref{T6.3}. In fact, one can just use Theorem \ref{T6.2} with $T = \bigl( \begin{smallmatrix} A(0)\|E(0)\|^{-2} & B(0)\|E(0)\|^{-2} \\ -B(0) & A(0) \end{smallmatrix} \bigr)$ to pass to an equivalent $E$ with $E(0)=1$. This will always work because de~Branges functions associated with regular spaces do not have zeros on the real line. Theorem \ref{T6.3}, combined with the material from Sect.\ 10 (especially \eqref{9.b}), is the promised (extremely) general version of the Paley-Wiener Theorem. One can also view Theorem \ref{T6.3} as a basic result in inverse spectral theory: given ``spectral data'' in the form of a de~Branges function $E$, the theorem asserts the existence of a corresponding differential equation. In this paper, we will use Theorem \ref{T6.3} in this second way. As a final remark on Theorem \ref{T6.3}, we would like to point out that $H(x)$ is uniquely determined by $E(z)$ and $N$ if one normalizes appropriately. (One may require that $\text{tr }H(x)$ be constant, as in the last part of Theorem \ref{T6.3}, and $\int_0^{\epsilon} H_{11}(t)\, dt > 0$ for all $\epsilon>0$.) To prove this, the basic idea is to proceed as in the proof of Theorem \ref{T8.2}b) (which will be discussed in Sect.\ 9), but things are more complicated here and one needs material from Sect.\ 10. We do not need this uniqueness statement in this paper. \begin{Theorem} \label{T6.4} Let $B(E)$, $B(E_1)$, $B(E_2)$ be regular de~Branges spaces and assume that $B(E_1)$ and $B(E_2)$ are isometrically contained in $B(E)$. Then either $B(E_1)$ is isometrically contained in $B(E_2)$ or $B(E_2)$ is isometrically contained in $B(E_1)$. \end{Theorem} This is a special case of \cite[Theorem 35]{dB}. See also \cite[Sect.\ 6.5]{DMcK} for a proof. Theorem \ref{T6.4} clearly is a strong structural result. The de~Branges subspaces of a given space are totally ordered by inclusion. As an illustration, take $B(E)=S_N$, the de~Branges space coming from a Schr\"odinger equation on the interval $(0,N)$. Then it can be deduced from Theorem \ref{T6.4} that the chain of spaces $\{ S_x : 0\le x\le N \}$ is a complete list of the de~Branges spaces that are subspaces of $S_N$. \section{Canonical systems II} Theorem \ref{T6.3} associates a canonical system to every (regular) de~Branges space. Conversely, we have seen in Sections 3 and 6 how Schr\"odinger equations and canonical systems generate de~Branges spaces. This recipe works for other equations as well (Dirac, Sturm-Liouville, Jacobi difference equation). So, in a sense, canonical systems are the most general formally symmetric, second order differential systems (here, by ``order'' we mean order of differentiation times number of components). In particular, every Schr\"odinger equation can be written as canonical system by a simple transformation. Namely, given a Schr\"odinger equation \eqref{se}, let $y_1$, $y_2$ be the solutions of \eqref{se} with $z=0$ with the initial values $y_1(0)=y'_2(0)=1$, $y'_1(0)=y_2(0)=0$, and put $T(x) = \bigl( \begin{smallmatrix} y_1(x) & y_2(x) \\ y'_1(x) & y'_2(x) \end{smallmatrix} \bigr)$. Now if $y(x,z)$ solves \eqref{se}, then the vector function $u$ defined by $u(x,z)= T^{-1}(x)\bigl( \begin{smallmatrix} y(x,z) \\ y'(x,z) \end{smallmatrix} \bigr)$ solves \eqref{Can} with \[ H(x) = \begin{pmatrix} y_1^2(x) & y_1(x)y_2(x) \\ y_1(x)y_2(x) & y_2^2(x) \end{pmatrix} . \] This is shown by direct computation. Note that this $H$ has the required properties: its entries are integrable (in fact, they have absolutely continuous derivatives), and $H(x)\ge 0$, $H(x)\not= 0$ for every $x$. Conversely, from a canonical system of this special form, one can go back to a Schr\"odinger equation. We state this separately for later use. By $AC^{(n)}[0,N]$ we denote the set of (locally integrable) functions whose $n$th derivative (in the sense of distributions) is in $L_1(0,N)$. Equivalently, $f\in AC^{(n)}[0,N]$ precisely if $f,f',\ldots, f^{(n-1)}$ are absolutely continuous on $[0,N]$. \begin{Proposition} \label{P7.1} Let $h,k\in AC^{(2)}[0,N]$ be real valued functions, and suppose that $h(0)=1$, $h'(0)=0$, and \begin{equation} \label{7.1} h(x)k'(x) - h'(x)k(x)=1. \end{equation} Let \[ H(x)= \begin{pmatrix} h^2(x) & h(x)k(x) \\ h(x)k(x) & k^2(x) \end{pmatrix}. \] Then, if $u(x,z)$ solves \eqref{Can} with this $H$, then \[ y(x,z) := h(x) u_1(x,z) + k(x) u_2(x,z) \] solves \eqref{se} with $V(x)= h''(x)k'(x)-h'(x)k''(x)$. Moreover, the de~Branges spaces generated by \eqref{se} and \eqref{Can} as in Sect.\ 3 and Proposition \ref{P5.1}, respectively, are identical. \end{Proposition} \begin{proof} The fact that $y$ solves \eqref{se} with $V=h''k'-h'k''$ is checked by direct computation. Note that $hk''=h''k$; this follows by differentiating \eqref{7.1}. Also, $hu'_1+ku'_2=0$ and thus \[ y'(x,z)= h'(x)u_1(x,z)+k'(x)u_2(x,z). \] In particular, this relation shows that $y(\cdot,z)\in AC^{(2)}[0,N]$. To compare the de~Branges spaces, we must specialize to the solution $u$ with the initial values $u_1(0,z)=1$, $u_2(0,z)=0$. The corresponding $y$ satisfies $y(0,z)=1$, $y'(0,z)=0$, and hence is the solution from which the de~Branges function of the Schr\"odinger equation is computed. The values at $x=N$ are related by \[ \begin{pmatrix} y(N,z) \\ y'(N,z) \end{pmatrix} = \begin{pmatrix} h(N) & k(N) \\ h'(N) & k'(N) \end{pmatrix} u(N,z). \] The final claim now follows from Theorem \ref{T6.2}. \end{proof} \section{Starting the proofs} \begin{proof}[Proof of Theorem \ref{T8.2}] a) If we know $V$, we can solve the Schr\"odinger equation \eqref{se} (in principle, that is) and find $E_N(z)$. This function in turn determines the scalar products $[F,G]_{S_N}$, and we have that \[ [F,G]_{S_N} = \langle f, (1+\mathcal{K}_{\phi})g\rangle_{L_2(0,N)}, \] so we know the operator $\mathcal{K}_{\phi}$ on $L_2(0,N)$. Hence we know the kernel $K(s,t)$ almost everywhere on $[0,N]\times [0,N]$ (with respect to two-dimensional Lebesgue measure), but $K$ is continuous, so we actually know the kernel everywhere, and $\phi(2t)=2K(t,t)$, so $\phi$ on $[0,2N]$ is uniquely determined by $V$ on $(0,N)$. As $\phi$ is even, we of course automatically know $\phi$ on $[-2N,2N]$ then. b) Suppose that we have two potentials $V_1,V_2\in L_1(0,N)$, for which the scalar product on the corresponding de~Branges spaces is determined by one and the same $\phi\in\Phi_N$. In other words, $S_N^{(1)}=S_N^{(2)}$ (as de~Branges spaces). Now $\phi$ on $[-2N,2N]$ determines the de~Branges spaces $S_x^{(i)}$ ($i=1,2$) for every $x\in (0,N]$, so we actually have that also $S_x^{(1)}=S_x^{(2)}$ for these $x$. By Theorem \ref{T6.2}, \[ \begin{pmatrix} u_2(x,z) \\ u'_2(x,z) \end{pmatrix} = T(x) \begin{pmatrix} u_1(x,z) \\ u'_1(x,z) \end{pmatrix} \quad\quad (0<x\le N), \] where $T(x)\in\mathbb R^{2\times 2}$, $\det T(x)=1$. Comparison of the large $z$ asymptotics with the help of \eqref{estv}, \eqref{estv'} shows that $T_{11}=1$, $T_{12}=0$, so $u_1=u_2$. As $V_i(x)= u''_i(x,0)/u_i(x,0)$, this of course implies that $V_1=V_2$. \end{proof} We now begin the {\it proof of Theorem \ref{T8.1}}. It is rather obvious how to get started. If the theorem is true, then, taking Theorems \ref{T4.1} and \ref{T4.2} into account, the spaces \begin{equation} \label{Hx} H_x = \left\{ F(z)=\int f(t) \cos\sqrt{z}t \, dt: f\in L_2(0,x) \right\} , \end{equation} endowed with the scalar products \begin{equation} \label{scHx} [F,G]_{H_x} = \langle f, (1+\mathcal{K}_{\phi}) g \rangle_{L_2(0,x)} , \end{equation} must be de~Branges spaces for $0<x\le N$. This can be confirmed right away. \begin{Lemma} \label{L8.3} $H_x$ with the scalar product $[\cdot, \cdot ]_{H_x}$ is a regular de~Branges space. The de~Branges function $E_x$ for which $H_x = B(E_x)$ may be chosen so that $E_x(0)=1$. If $0<x\le y\le N$, then $H_x$ is isometrically contained in $H_y$. \end{Lemma} \begin{proof} We will use Theorem \ref{T6.1}. $H_x$ obviously is a linear space consisting of entire functions. $[\cdot, \cdot ]_{H_x}$ is a scalar product because $1+\mathcal{K}_{\phi}>0$ (strictly speaking, we know this for the operator on $L_2(0,N)$, but $\langle f, (1+\mathcal{K}_{\phi}) g\rangle_{L_2(0,x)}$ for $f,g\in L_2(0,x)$ can of course also be evaluated in the bigger space $L_2(0,N)$). $\mathcal{K}_{\phi}$ is compact, so we actually have that $1+\mathcal{K}_{\phi}\ge \delta >0$. Thus \[ \delta \\|f\\|_{L_2(0,x)}^2 \le \\|F\\|_{H_x}^2 \le C \\|f\\|_{L_2(0,x)}^2, \] and now completeness of $H_x$ follows from the completeness of $L_2(0,x)$. We now verify conditions a), b), c) of Theorem \ref{T6.1}. Condition a) is obvious from \[ \|F(z)\| \le e^{\|z\|^{1/2}x} \int_0^x \|f(t)\|\, dt \le x^{1/2} e^{\|z\|^{1/2}x} \\|f\\| \le (x/\delta)^{1/2} e^{\|z\|^{1/2}x}\\|F\\|_{H_x}. \] It is also clear that c) holds since $F^{\#}(z) = \int\overline{f(t)} \cos \sqrt{z}t\, dt$, so $F^{\#}\in H_x$ and, as $K$ is real valued, \[ \\|F^{\#}\\|^2 = \langle \overline{f}, (1+\mathcal{K}_{\phi})\overline{f} \rangle = \langle f, (1+\mathcal{K}_{\phi}) f \rangle = \\|F\\|^2 . \] To prove b), fix $w\in\mathbb C$ and $F\in H_x$ with $F(w)=0$. Extend the $f\in L_2(0,x)$ corresponding to $F$ to $(-x,x)$ by letting $f(-t)=f(t)$ ($0<t<x$). Then \[ F(k^2) = \frac{1}{2} \int_{-x}^x f(t) e^{-ikt}\, dt = \sqrt{\frac{\pi}{2}}\,\widehat{f}(k). \] The function $\widehat{f}$ is entire, even, obeys $\|\widehat{f}(k)\| \le Ce^{x\|k\|}$, its restriction to $\mathbb R$ belongs to $L_2(\mathbb R)$ and $\widehat{f}(\pm \sqrt{w})=0$. Put \[ \widehat{g}(k) = \frac{k^2-\overline{w}}{k^2-w}\, \widehat{f}(k). \] Then $\widehat{g}$ is also entire, $\|\widehat{g}(k)\|\le Ce^{x\|k\|}$, and the restriction of $\widehat{g}$ to $\mathbb R$ is square integrable. Hence the Paley-Wiener Theorem applies: There exists $g\in L_2(-x,x)$ so that \[ \widehat{g}(k)= \frac{1}{\sqrt{2\pi}} \int_{-x}^x g(t) e^{-ikt}\, dt. \] Since $\widehat{g}$ is even, $g$ must also be even. It follows that \[ \frac{k^2-\overline{w}}{k^2-w}\, F(k^2) = \sqrt{\frac{\pi}{2}}\,\widehat{g}(k) =\frac{1}{2}\int_{-x}^x g(t) e^{-ikt}\, dt = \int_0^x g(t) \cos kt \, dt , \] and hence the function $G(z)=\frac{z-\overline{w}}{z-w} F(z)$ is of the form \[ G(z) = \int_0^x g(t) \cos\sqrt{z}t \, dt, \] with $g\in L_2(0,x)$, so $G\in H_x$. We now calculate the norm of $G$. In this calculation, we extend $\phi$ to a function on $\mathbb R$ by setting it equal to zero outside $[-2x,2x]$. We do this in order to have a well behaved Fourier transform $\widehat{\phi}$. Note that $\mathcal{K}_{\phi}$, viewed as an operator on $L_2(0,x)$, does not depend on the values of $\phi(t)$ for $\|t\| > 2x$. We also rewrite $\langle g, (1+\mathcal{K}_{\phi}) g \rangle_{L_2(0,x)}$. Namely, since $g$ is even and the integral kernel $K$ of $\mathcal{K}_{\phi}$ satisfies \[ K(s,t)=K(-s,t)=K(s,-t)=K(-s,-t), \] we have that \[ \langle \chi_{(0,x)}g, \mathcal{K}_{\phi} \chi_{(0,x)}g \rangle_{L_2(0,x)} = \frac{1}{8} \int_{-x}^x ds \int_{-x}^x dt\, \overline{g(s)}g(t) \left( \phi(s-t)+\phi(s+t) \right) . \] Furthermore, using the substitution $s\to -s$ in the second term, we can write this in the form \[ \langle \chi_{(0,x)}g, \mathcal{K}_{\phi} \chi_{(0,x)}g \rangle_{L_2(0,x)} = \frac{1}{4} \int_{-x}^x ds \int_{-x}^x dt\, \overline{g(s)}g(t)\phi(s-t) = \frac{1}{4} \langle g, \phi g \rangle_{L_2(-x,x)}, \] where, as usual, the star denotes convolution. Having made these preliminary observations and using the fact that $\|\widehat{f}(k)\|=\|\widehat{g}(k)\|$ for real $k$, we obtain \begin{align} 4 \\|G\\|_{H_x}^2 & = 4 \langle \chi_{(0,x)}g, (1+\mathcal{K}_{\phi}) \chi_{(0,x)}g \rangle_{L_2(0,x)} = 2\\|g\\|^2_{L_2(-x,x)} + \langle g, \phi g \rangle_{L_2(-x,x)}\\ & = 2 \\|\widehat{g} \\|_{L_2(\mathbb R)}^2 + \langle \widehat{g}, \widehat{\phi}\,\widehat{g} \rangle_{L_2(\mathbb R)} = \int_{-\infty}^{\infty} \left\| \widehat{g}(k)\right\|^2 \left( 2 + \widehat{\phi}(k) \right)\, dk\\ & = \int_{-\infty}^{\infty} \left\| \widehat{f}(k)\right\|^2 \left( 2 + \widehat{\phi}(k) \right)\, dk\\ & = 2 \\|\widehat{f} \\|_{L_2(\mathbb R)}^2 + \langle \widehat{f}, \widehat{\phi}\,\widehat{f} \rangle_{L_2(\mathbb R)} = 2\\|f\\|_{L_2(-x,x)}^2 + \langle f, \phi * f \rangle_{L_2(-x,x)}\\ & = 4 \langle \chi_{(0,x)}f, (1+\mathcal{K}_{\phi}) \chi_{(0,x)}f \rangle_{L_2(0,x)} = 4 \\|F\\|_{H_x}^2, \end{align} as desired. Theorem \ref{T6.1} now shows that $H_x$ is a de~Branges space. It is clear that for every $\lambda\in\mathbb R$, there exists an $F\in H_x$ with $F(\lambda)\not=0$. Thus, by the definition of de~Branges spaces, the corresponding de~Branges function cannot have zeros on the real line. Using Theorem \ref{T6.2}, we can therefore normalize so that $E_x(0)=1$ (exactly as in the remark following Theorem \ref{T6.3}). We still must show that the de~Branges space $H_x$ is regular. We will check condition \eqref{regsp} with $z_0=0$. So let $F\in H_x$, $F(z)= \int_0^x f(t)\cos\sqrt{z}t\, dt$, with $f\in L_2(0,x)$. Then \[ g(t):= \int_t^x f(s)(t-s)\, ds \] is in $AC^{(2)}[0,x]$ (so, in particular, $g\in L_2(0,x)$), and $g'(t)=\int_t^x f(s)\, ds$, $g''=-f$. By integrating by parts twice, we thus see that \begin{align} \int_0^x g(t)\cos\sqrt{z}t\, dt & = \left. \frac{\sin \sqrt{z}t}{\sqrt{z}} \int_t^x f(s)(t-s)\, ds \right\|_{t=0}^{t=x} - \int_0^x dt\,\frac{\sin \sqrt{z}t}{\sqrt{z}}\int_t^x ds\, f(s)\\ & = \left. \frac{\cos\sqrt{z}t}{z} \int_t^x f(s)\, ds\right\|_{t=0}^{t=x} + \int_0^x f(t) \frac{\cos\sqrt{z}t}{z} \, dt\\ & = \frac{F(z)-F(0)}{z}, \end{align} hence this latter combination is in $H_x$. The final claim of the lemma is obvious from the construction of the spaces $H_x$. We have made this statement explicit mainly because of its importance. \end{proof} The next step in the proof of Theorem \ref{T8.1} is to apply Theorem \ref{T6.3} to the regular de~Branges space $H_N=B(E_N)$. We obtain $H:(0,N)\to \mathbb R^{2\times 2}$, with entries in $L_1(0,N)$ and $H(x)\ge 0$ for almost every $x\in (0,N)$, $\text{tr }H(x)=\tau >0$, such that $E_N(z)$ is exactly the de~Branges function associated with the canonical system \eqref{Can} as in Proposition \ref{P5.1}. Actually, we have obtained much more. We get a whole scale of de~Branges spaces in both cases. On the one hand, we have the spaces $H_x=B(E_x)$ from Lemma \ref{L8.3}. On the other hand, we can consider the canonical system \eqref{Can} on $(0,x)$ only; by Proposition \ref{P5.1}, we get again de~Branges spaces, which we denote by $B_x$. Our next major goal is to show that, possibly after a reparametrization of the independent variable, $H_x=B_x$ for all $x\in [0,N]$ (at the moment, we know this only for $x=N$). One crucial input will be Theorem \ref{T6.4}; however, we will also need additional material on canonical systems. This topic will be resumed in the next section. The proof of Theorem \ref{T8.1} will then proceed as follows. The identity $H_x=B_x$ says that we have two realizations of the same chain of de~Branges spaces: one from Lemma \ref{L8.3} and a second one from the canonical system \eqref{Can}. By comparing objects in these two worlds, we will get information on the matrix elements $H_{ij}(x)$ of the $H$ from \eqref{Can}. This will allow us to verify the hypotheses of Proposition \ref{P7.1}; so the spaces $H_x$ we started with indeed come from a Schr\"odinger equation. \section{Canonical systems III} We now develop some material on the spectral representation of canonical systems. We consider equation \eqref{Can} together with the boundary conditions \begin{equation} \label{bc} u_2(0)=0,\quad\quad u_1(N)\cos\beta + u_2(N)\sin\beta =0 . \end{equation} Here, $\beta\in [0,\pi )$. As usual, $z$ is called an eigenvalue if there is a nontrivial solution to \eqref{Can}, \eqref{bc}. We can considerably simplify the whole discussion by excluding certain ``singular'' values of $\beta$. In particular, it is convenient to assume right away that $\beta\not= \pi/2$. Then zero is not an eigenvalue. In particular, the following holds. If $f\in L_1(0,N)$ is given, then the inhomogeneous problem $Ju'=f$ together with the boundary conditions \eqref{bc} has a unique solution $u$ which can be written in the form \begin{gather} u(x) = \int_0^N G(x,t) f(t)\, dt, \\ G(x,t) = \begin{pmatrix} \tan\beta & -\chi_{(0,t)}(x) \\ -\chi_{(0,x)}(t) & 0 \end{pmatrix} = G(t,x)^* . \end{gather} We can now write the eigenvalue problem \eqref{Can}, \eqref{bc} as an integral equation, which is easier to handle. Of course, this is a standard procedure; compare, for example, \cite[Chapter VI]{GKr}. Let $L_2^H(0,N)$ be the space of measurable functions $y:(0,N)\to\mathbb C^2$ satisfying \[ \\|y\\|_{L_2^H(0,N)}^2 \equiv \int_0^N y^(x) H(x) y(x)\, dx < \infty. \] The quotient of $L_2^H(0,N)$ by $\mathcal{N}=\{ y: \\|y\\|=0 \}$ is a Hilbert space. As usual, this space will again be denoted by $L_2^H(0,N)$, and we will normally not distinguish between Hilbert space elements and their representatives. In a moment, we will also use the similarly defined space $L_2^I$, where $H$ is replaced by the $2\times 2$ identity matrix. The space $L_2^I$ can be naturally identified with $L_2 \oplus L_2$. As a preliminary observation, notice that a nontrivial solution $y$ to \eqref{Can}, \eqref{bc} cannot be the zero element of $L_2^H(0,N)$. Indeed, if $\\|y\\|_{L_2^H}=0$, then $H(x)y(x)=0$ almost everywhere, so \eqref{Can} implies that $y(x)=y(0)$. But since $\beta\not= \pi/2$, the boundary conditions \eqref{bc} then force $y\equiv 0$. A similar argument shows that eigenfunctions associated with different eigenvalues also represent different elements of $L_2^H(0,N)$. We now claim that $\lambda$ is an eigenvalue of \eqref{Can}, \eqref{bc} with corresponding eigenfunction $y$ if and only if $y\in L_2^H(0,N)$ and $y$ solves \begin{equation} \label{9.2} y(x) = \lambda \int_0^N G(x,t) H(t) y(t)\, dt . \end{equation} Note that for $y\in L_2^H(0,N)$, \eqref{9.2} may be considered in the pointwise sense or as an equation in $L_2^H(0,N)$. Fortunately, the two interpretations are equivalent. More precisely, if \eqref{9.2} holds in $L_2^H(0,N)$, then we can simply define a particular representative $y(x)$ by the right-hand side of \eqref{9.2} (this right-hand side does not depend on the choice of representative). It is clear from the construction of $G$ and the fact that solutions of \eqref{Can} are continuous that eigenfunctions lie in $L_2^H(0,N)$ and solve \eqref{9.2} pointwise. Conversely, if $y\in L_2^H(0,N)$, then $Hy\in L_1(0,N)$. So if $y$ in addition solves \eqref{9.2}, then it also solves \eqref{Can}, \eqref{bc} by construction of $G$ again. Now define a map \[ V:L_2^H(0,N) \to L_2^I(0,N),\quad y(x) \mapsto H^{1/2}(x)y(x) . \] Here, $H^{1/2}(x)$ is the unique positive semidefinite square root of $H(x)$. In the sequel, we will often use the fact that $H(x)$ and $H^{1/2}(x)$ have the same kernel. $V$ is an isometry and hence maps $L_2^H$ unitarily onto its range $R(V)\subset L_2^I$. Define an integral operator $\mathcal{L}$ on $L_2^I(0,N)$ by \begin{align} L(x,t) & = H^{1/2}(x) G(x,t) H^{1/2}(t), \\ (\mathcal{L}f)(x) & = \int_0^N L(x,t)f(t)\, dt . \end{align} The kernel $L$ is square integrable (by this we mean that $\int_0^N \!\! \int_0^N \\|L^L\\|\, dx\,dt < \infty$), so $\mathcal{L}$ is a Hilbert-Schmidt operator and thus compact. Since $L(x,t)=L^(t,x)$, $\mathcal{L}$ is also self-adjoint. The following lemma says that the eigenvalues of \eqref{Can}, \eqref{bc} are precisely the reciprocal values of the non-zero eigenvalues of $\mathcal{L}$. The corresponding eigenfunctions are mapped to one another by applying $V$. \begin{Lemma} \label{L9.1} Let $f\in L_2^I(0,N)$, $\lambda\not= 0$. Then the following statements are equivalent:\\ a) $\mathcal{L}f = \lambda^{-1} f$;\\ b) $f\in R(V)$, and the unique $y\in L_2^H(0,N)$ with $Vy=f$ solves \eqref{9.2}. \end{Lemma} \begin{proof} Note that for all $g\in L_2^I$, we have that $(\mathcal{L}g)(x)=H^{1/2}(x)w(x)$, where \[ w(x) = \int_0^N G(x,t)H^{1/2}(t) g(t) \, dt \] lies in $L_2^H$, thus $R(\mathcal{L})\subset R(V)$. Now if a) holds, then $f=\lambda\mathcal{L}f\in R(V)$, so $f=Vy$ for a unique $y\in L_2^H$ and \[ f(x) = H^{1/2}(x) y(x) = \lambda (\mathcal{L}Vy)(x) = \lambda H^{1/2}(x) \int_0^N G(x,t) H(t) y(t)\, dt \] for almost every $x\in (0,N)$. In other words, \[ H^{1/2}(x) \left( y(x) - \lambda \int_0^N G(x,t) H(t) y(t)\, dt \right) = 0 \] almost everywhere, and this says that the expression in parantheses is the zero element of $L_2^H$, that is, \eqref{9.2} holds. Conversely, if b) holds, we only need to multiply \eqref{9.2} from the left by $H^{1/2}(x)$ to obtain a). \end{proof} Let $P:L_2^I\to L_2^I$ be the projection onto the closed subspace $R(V)$ of $L_2^I$. Since \[ R(V)^{\perp} = \{ f\in L_2^I: H(x)f(x)=0 \text{ almost everywhere} \} , \] we have that $\mathcal{L}(1-P)=0$. Also, we have already observed that $R(\mathcal{L})\subset R(V)=R(P)$, so $\mathcal{L}= P\mathcal{L}$. Hence $\mathcal{L}P=P\mathcal{L}$, and thus $R(P)=R(V)$ is a reducing subspace for $\mathcal{L}$. Let $\mathcal{L}_0:R(V)\to R(V)$ be the restriction of $\mathcal{L}$ to $R(V)$. Then $\mathcal{L}_0$ is also compact (in fact, Hilbert-Schmidt) and self-adjoint, and $\mathcal{L}=\mathcal{L}_0 \oplus 0$. If we use this notation, then Lemma \ref{L9.1} says that the eigenfunctions of $\mathcal{L}_0$ with non-zero eigenvalues precisely correspond to the eigenfunctions of \eqref{Can}, \eqref{bc}. The kernel of $\mathcal{L}_0$ will also play a central role. To develop this, we now introduce two important subspaces of $L_2^H$. Namely, let \begin{gather} \begin{split} R_{(0,N)} = \{ y\in L_2^H(0,N): \exists f\in AC^{(1)}[0,N], H(x)f(x)=0 \text{ for a.e.\ } x\in (0,N), \\ f_2(0)=0, f(N)=0, Jf'=Hy \} , \end{split}\\ \begin{split} \widetilde{R}_{(0,N)} = \{ y\in L_2^H(0,N): \exists f\in AC^{(1)}[0,N], H(x)f(x)=0 \text{ for a.e.\ } x\in (0,N), \\ f_2(0)=0, f_1(N)\cos\beta + f_2(N)\sin\beta = 0, Jf'=Hy \} . \end{split} \end{gather} Recall that on a formal level, operators $T$ associated with \eqref{Can} should act as $Tf=H^{-1}Jf'$, so (still formally) the relation $Jf'=Hy$ says that $y$ is an image of $f$. Thus $\widetilde{R}_{(0,N)}$ should be thought of as the space of images of zero; $R_{(0,N)}$ has a similar interpretation. In the following lemma, we identify $\widetilde{R}_{(0,N)}$ as the kernel $N(\mathcal{L}_0)$ of $\mathcal{L}_0$. \begin{Lemma} \label{L9.2} $N(\mathcal{L}_0) = V\widetilde{R}_{(0,N)}$. \end{Lemma} \begin{proof} If $g\in R(V)$ with $\mathcal{L}_0 g=0$ is given, write $g(x)=H^{1/2}(x)y(x)$ with $y\in L_2^H$. Then $y$ obeys \begin{equation} \label{9.a} H^{1/2}(x) \int_0^N G(x,t)H(t)y(t)\, dt = 0 \end{equation} in $L_2^I(0,N)$, that is, for almost every $x\in (0,N)$. Let $f(x)= \int_0^N G(x,t)H(t)y(t)\, dt$. Then, by the construction of $G$, $f\in AC^{(1)}[0,N]$, $f$ satisfies the boundary conditions \eqref{bc}, and $Jf'=Hy$; by \eqref{9.a}, $H(x)f(x)=0$ for almost every $x\in (0,N)$. So $y\in \widetilde{R}_{(0,N)}$ and $g=Vy\in V\widetilde{R}_{(0,N)}$. Conversely, suppose that $g=Vy$ for some $y\in \widetilde{R}_{(0,N)}$. By definition of $\widetilde{R}_{(0,N)}$, there exists $f\in AC^{(1)}[0,N]$, so that $H(x)f(x)=0$ almost everywhere, $f$ satisfies the boundary conditions and $Jf'=Hy$. We have $\mathcal{L}_0 g=\mathcal{L}Vy=V\widetilde{f}$, where $\widetilde{f}(x) = \int_0^N G(x,t)H(t)y(t)\, dt$. Again by construction of $G$, the function $\widetilde{f}\in AC^{(1)}[0,N]$ thus solves the following problem: $\widetilde{f}$ satisfies the boundary conditions and $J\widetilde{f}'=Hy$. However, as noted at the beginning of this section, there is only one function with these properties, hence $\widetilde{f}=f$, and therefore $(\mathcal{L}_0 g)(x)=H^{1/2}(x)f(x)=0$ almost everywhere. \end{proof} \begin{Theorem} \label{T9.3} Suppose that $\beta\not= \pi/2$. Then the normed eigenfunctions of the boundary value problem \eqref{Can}, \eqref{bc}, \[ Jy'(x) = zH(x)y(x),\quad\quad y_2(0)=0,\quad y_1(N)\cos\beta + y_2(N)\sin\beta =0, \] form an orthonormal basis of the Hilbert space $L_2^H(0,N) \ominus \widetilde{R}_{(0,N)}$. \end{Theorem} \begin{proof} As $\mathcal{L}_0$ is compact and self-adjoint, the normed eigenfunctions of $\mathcal{L}_0$ (suitably chosen in the case of degeneracies) form an orthonormal basis of $R(V)$. Also, the normed eigenfunctions belonging to non-zero eigenvalues form an orthonormal basis of $R(V)\ominus N(\mathcal{L}_0)$. Now go back to $L_2^H$, using the unitary map $V^{-1}:R(V)\to L_2^H(0,N)$. By Lemma \ref{L9.2}, $N(\mathcal{L}_0)$ is mapped onto $\widetilde{R}_{(0,N)}$, and by Lemma \ref{L9.1}, the preceding discussion and the fact that $\mathcal{L}=\mathcal{L}_0\oplus 0$, the eigenfunctions of $\mathcal{L}_0$ with non-zero eigenvalues precisely go to the eigenfunctions of \eqref{Can}, \eqref{bc}. \end{proof} As in Sect.\ 3, we can introduce spectral measures $\rho_N^{\beta}$. Define \[ \rho_N^{\beta} = \sum_{\frac{u_1}{u_2}(N,\lambda) = -\tan\beta} \frac{\delta_{\lambda}}{\\|u(\cdot, \lambda) \\|_{L_2^H(0,N)}^2} . \] The sum is over the eigenvalues $\{ \lambda_n \}$ of \eqref{Can}, \eqref{bc} (which also depend on $N$ and $\beta$). Recall also that $u(\cdot,z)$ is the solution of \eqref{Can} with $u(0,z)=\bigl( \begin{smallmatrix} 1 \\ 0 \end{smallmatrix} \bigr)$. The map $U$ defined by \begin{gather} U: L_2^H(0,N) \ominus \widetilde{R}_{(0,N)} \to L_2(\mathbb R, d\rho_N^{\beta}),\\ (Uf)(\lambda) = \int u^(x,\lambda) H(x) f(x) \, dx \end{gather} is unitary. Indeed, this is just a reformulation of Theorem \ref{T9.3} because $U$ computes the scalar products of $f$ with the elements of the basis $\{ u(\cdot,\lambda_n)\}$. The $u(\cdot,\lambda_n)$'s are not normalized here, but this has been taken into account by choosing the correct weights in the definition of $\rho_N^{\beta}$. For a further development of the theory of canonical systems, we need the following definition. Following \cite{dB2,dB}, we call $x_0\in (0,N)$ a {\it singular point} if there exists an $\epsilon >0$, so that on $(x_0-\epsilon, x_0+\epsilon)$, $H$ has the form \[ H(x) = h(x) P_{\varphi}, \quad P_{\varphi} = \begin{pmatrix} \cos^2\varphi & \sin\varphi\cos\varphi \\ \sin\varphi\cos\varphi & \sin^2\varphi \end{pmatrix} \] for some ($x$-independent) $\varphi\in [0,\pi)$ and some $h\in L_1(x_0-\epsilon,x_0+\epsilon)$, $h\ge 0$. Notice that $P_{\varphi}$ is the projection onto $e_{\varphi}=\bigl( \begin{smallmatrix} \cos\varphi \\ \sin\varphi \end{smallmatrix} \bigr)$. Points that are not singular are called {\it regular points}. Clearly, the set $S$ of singular points, \[ S = \{ x\in (0,N): x \text{ is singular} \} , \] is open, so it can be represented as a countable or finite union of disjoint, open intervals: \[ S = \bigcup (a_n, b_n). \] On such an interval $(a_n,b_n)$, the angle $\varphi=\varphi_n$ whose existence is (locally) guaranteed by the definition above must actually have the same value on the whole interval for otherwise there would be regular points on $(a_n,b_n)$. We call the boundary condition $\beta$ at $x=N$ {\it regular} if $\beta\not= \pi/2$ and, in case there should be an $n$ with $b_n=N$, then also $\beta\not= \varphi_n$, where $\varphi_n$ is the angle corresponding to the interval $(a_n,b_n)$. To get a first intuitive understanding of the notion of singular points, consider \eqref{Can} on an interval $(a,b)\subset S$. After multiplying from the left by $J^{-1}=-J$, the equation reads \[ u'(x)= -zh(x) JP_{\varphi}u(x). \] Since the matrices on the right-hand side commute with one another for different values of $x$, the solution is given by \[ u(x)=\exp\left( -z\int_a^x h(t)\, dt\: JP_{\varphi} \right) u(a) . \] However, $P_{\varphi}JP_{\varphi}=0$, as we see either from a direct computation or alternatively from the fact that this matrix is singular, anti-self-adjoint and has real entries. Thus the series for the exponential terminates and \[ u(x)= \left( 1 - z\int_a^x h(t)\, dt\: JP_{\varphi} \right) u(a). \] In particular, letting $u_+=u(b)$, $u_-=u(a)$, $H=\int_a^b H(x)\, dx$, we obtain $J(u_+ - u_-) = zHu_-$, so on a singular interval, \eqref{Can} actually is its difference equation analog in disguise. \begin{Lemma} \label{L9.4} Suppose $y\in\widetilde{R}_{(0,N)}$, and let $f\in AC^{(1)}[0,N]$ be such that $H(x)f(x)=0$ almost everywhere, $f_2(0)=0$, $f_1(N)\cos\beta+ f_2(N)\sin\beta =0$, and $Jf'=Hy$ (the existence of such an $f$ follows from the definition of $\widetilde{R}_{(0,N)}$). Then, if $x_0\in (0,N)$ is regular, then $f(x_0)=0$. Similarly, if $\beta$ is a regular boundary condition, then $f(N)=0$. \end{Lemma} \begin{proof} Fix $y$, $f$, $x_0$ as above, and write $f(x)=R(x)\bigl( \begin{smallmatrix} \sin\varphi(x) \\ -\cos\varphi(x) \end{smallmatrix} \bigr)$. Since $Hf=0$ almost everywhere, either $R(x_0)=0$ or else $H(x)$ must have the form $H(x)=h(x)P_{\varphi(x)}$ in a neighborhood of $x_0$. (Note that this does not say that $x_0$ is singular because $\varphi$ may depend on $x$.) In the first case, we are done. If $R(x_0)\not= 0$, we can solve for $R$, $\varphi$ in terms of $f_1$, $f_2$ in a neighborhood of $x_0$, and we find that these functions are absolutely continuous, too. Hence the condition that $Jf'=Hy$ gives \[ R'(x)\begin{pmatrix} \cos\varphi(x) \\ \sin\varphi(x) \end{pmatrix} + R(x)\varphi'(x) \begin{pmatrix} -\sin\varphi(x) \\ \cos\varphi(x) \end{pmatrix} = h(x) P_{\varphi(x)}y(x) \equiv \alpha(x) \begin{pmatrix} \cos\varphi(x) \\ \sin\varphi(x) \end{pmatrix} . \] We now take the scalar product with $\bigl( \begin{smallmatrix} -\sin\varphi(x) \\ \cos\varphi(x) \end{smallmatrix} \bigr)$ and find that $R(x)\varphi'(x)=0$. Hence $R(x_0)\not=0$ implies that $\varphi'\equiv 0$ on a neighborhood of $x_0$, that is, $x_0$ is singular. This contradiction shows that $f(x_0)=0$. This argument also works at $x_0=N$, provided that $(N-\epsilon,N) \not\subset S$ for all $\epsilon>0$. On the other hand, if $(N-\epsilon,N) \subset (a_n,b_n)\subset S$ for some $\epsilon>0$, then near $N$, the function $f$ must have the form $f(x)=R(x)\bigl( \begin{smallmatrix} \sin\varphi_n \\ -\cos\varphi_n \end{smallmatrix} \bigr)$. But now the boundary condition at $N$ implies that $R(N)=0$ or \[ \sin\varphi_n\cos\beta - \cos\varphi_n\sin\beta = \sin(\varphi_n-\beta)=0 . \] This latter relation, however, cannot hold if $\beta$ is regular. \end{proof} Here is an immediate consequence of the second part of Lemma \ref{L9.4}. \begin{Corollary} \label{C9.5} If $\beta$ is regular, then $\widetilde{R}_{(0,N)}=R_{(0,N)}$. \end{Corollary} We can now prove the promised analog of Theorem \ref{T3.1}. \begin{Theorem} \label{T9.6} For regular boundary conditions $\beta$, the Hilbert spaces $L_2(\mathbb R, d\rho_N^{\beta})$ and $B(E_N)$ (see Proposition \ref{P5.1}) are identical. More precisely, if $F(z)\in B(E_N)$, then the restriction of $F$ to $\mathbb R$ belongs to $L_2(\mathbb R, d\rho_N^{\beta})$, and $F\mapsto F\big\|_{\mathbb R}$ is a unitary map from $B(E_N)$ onto $L_2(\mathbb R, d\rho_N^{\beta})$. \end{Theorem} \begin{proof} Basically, we repeat the proof of Theorem \ref{T3.1}. As $\beta$ and $N$ are fixed throughout, we will again usually drop the reference to these parameters. Let $\{\lambda_n\}$ be the eigenvalues of \eqref{Can}, \eqref{bc}. We claim again that $J_z\in L_2(\mathbb R, d\rho)$ for every $z\in\mathbb C$ and verify this by the following calculation: \begin{align} \left\\| J_z \right\\|^2_{L_2(\mathbb R, d\rho)} & = \sum_n \left\| J_z(\lambda_n) \right\|^2 \rho(\{\lambda_n\} ) \\ & = \sum_n \left\| \langle u(\cdot, z), u(\cdot, \lambda_n) \rangle_{L_2^H(0,N)} \right\|^2 \left\\|u(\cdot, \lambda_n) \right\\|^{-2}_{L_2^H(0,N)}\\ & \le \left\\|u(\cdot, z) \right\\|^2_{L_2^H(0,N)}. \end{align} The estimate follows with the help of Bessel's inequality. Similar reasoning shows that \[ \langle J_w, J_z \rangle_{L_2(\mathbb R, d\rho)} = \langle u(\cdot,z), Q u(\cdot, w) \rangle_{L_2^H(0,N)}, \] where $Q$ is the projection onto $\overline{L(\{ u(\cdot,\lambda_n) \} )}$. By Theorem \ref{T9.3} and Corollary \ref{C9.5}, $\overline{L(\{ u(\cdot,\lambda_n)\} )} = R_{(0,N)}^{\perp}$. We now want to show that $u(\cdot, z)\in R_{(0,N)}^{\perp}$ for all $z\in\mathbb C$. To this end, fix $y\in R_{(0,N)}$, and pick $f\in AC^{(1)}[0,N]$ with $Hf=0$ almost everywhere, $f_2(0)=f(N)=0$, and $Jf'=Hy$. An integration by parts shows that \begin{align} \langle u(\cdot, z) , y \rangle_{L_2^H(0,N)} & = \int_0^N u^(x,z)H(x)y(x)\, dx = \int_0^N u^(x,z)Jf'(x)\, dx\\ & = u^(x,z)Jf(x)\big\|_{x=0}^{x=N} - \int_0^N {u'}^(x,z) Jf(x)\, dx \\ & =\int_0^N \left( Ju'(x,z)\right)^* f(x)\, dx =\overline{z} \int_0^N u^(x,z) H(x) f(x) \, dx = 0, \end{align} as desired. Thus $Qu(\cdot, w)=u(\cdot, w)$ and \[ \langle J_w, J_z \rangle_{L_2(\mathbb R, d\rho)} =\langle u(\cdot,z), u(\cdot, w) \rangle_{L_2^H(0,N)} = J_z(w) = [J_w, J_z]_{B(E_N)} . \] This discussion of $Qu$ and the use of Bessel's inequality (instead of Parseval's identity) were the only modifications that are necessary; the rest of the argument now proceeds literally as in the proof of Theorem \ref{T3.1}. \end{proof} The observations that were made after the proof of Theorem \ref{T3.1} also have direct analogs. By combining Theorem \ref{T9.6} with the remarks following Theorem \ref{T9.3}, we get an induced unitary map, which we still denote by $U$. It is given by \begin{subequations} \begin{gather} \label{9.1a} U: L_2^H(0,N) \ominus R_{(0,N)} \to B(E_N) \\ \label{9.1b} (Uf)(z) = \int u^(x,\overline{z})H(x)f(x)\, dx. \end{gather} \end{subequations} The proof goes as in Sect.\ 3. One first checks that \eqref{9.1b} is correct for $f=u(\cdot,\lambda_n)$. This follows from the following calculation: \begin{align} \left( U u(\cdot, \lambda_n) \right)(z) & = \int_0^N u^(x,\overline{z})H(x) u(x,\lambda_n)\, dx\\ & = \int_0^N \overline{u^(x,z)H(x) u(x,\lambda_n)}\, dx\\ & = \int_0^N \left( u^(x,z)H(x) u(x,\lambda_n)\right)^ \, dx\\ & = \int_0^N u^(x,\lambda_n)H(x)u(x,z)\, dx = J_{\lambda_n}(z). \end{align} Then one extends to the whole space. In this context, recall also that $u(\cdot,\lambda_n)\in R_{(0,N)}^{\perp}$, as we saw in the proof of Theorem \ref{T9.3}. It is remarkable that the technical complications we have had to deal with in this section are, so to speak, automatically handled correctly by the $U$ from \eqref{9.1a}, \eqref{9.1b}. Namely, first of all, the boundary condition $\beta$ does not appear in \eqref{9.1a}, \eqref{9.1b}. Recall that above we needed a regular $\beta$, but once Theorem \ref{T9.6} has been proved, we can get a statement that does not involve $\beta$ by passing from $L_2(\mathbb R, d\rho_N^{\beta})$ to the de~Branges space $B(E_N)$. Next, \eqref{9.1b} also makes sense for general $f\in L_2^H(0,N)$, not necessarily orthogonal to $R_{(0,N)}$. If interpreted in this way, $U$ is partial isometry from $L_2^H(0,N)$ to $B(E_N)$ with initial space $L_2^H(0,N) \ominus R_{(0,N)}$ and final space $B(E_N)$. This follows again from the fact that $u(\cdot,z)\in R_{(0,N)}^{\perp}$ for all $z\in\mathbb C$. We can immediately make good use of these observation to prove the following important fact. \begin{Theorem} \label{T9.reg} The de~Branges spaces $B(E_N)$ coming from the canonical system \eqref{Can} (compare Proposition \ref{P5.1}) are regular. \end{Theorem} \begin{proof} Again, we prove this by verifying \eqref{regsp} for $z_0=0$. As a direct consequence of the discussion above, we have that \begin{equation} \label{9.b} B(E_N) = \left\{ F(z) = \int u^(x,\overline{z})H(x)f(x)\, dx : f\in L_2^H(0,N) \right\} . \end{equation} Thus integration by parts yields \begin{align} & \frac{F(z)-F(0)}{z} = \int_0^N \frac{u^(x,\overline{z})- (1,0)}{z} H(x)f(x)\, dx \\ & \quad\quad = \left. -\frac{u^(x,\overline{z})-(1,0)}{z} \int_x^N H(t)f(t)\, dt \right\|_{x=0}^{x=N} + \frac{1}{z} \int_0^N dx\, {u'}^(x,\overline{z}) \int_x^N dt\, H(t) f(t)\\ & \quad\quad = \int_0^N dx\, u^(x,\overline{z}) H(x)J\int_x^N dt\, H(t) f(t) \equiv \int_0^N u^(x,\overline{z}) H(x) g(x) \, dx , \end{align} with $g(x)=J\int_x^N H(t)f(t)\, dt$. This $g$ is bounded, hence in $L_2^H(0,N)$, so the proof is complete. \end{proof} Note that the relation \eqref{9.b} also makes it clear why it is reasonable to interpret Theorem \ref{T6.3} as a Paley-Wiener Theorem. We are now heading towards the analog of Theorem \ref{T3.2}a). For $0<N_1<N_2$, we define \begin{multline} R_{(N_1,N_2)}= \{ y\in L_2^H(N_1,N_2): \exists f\in AC^{(1)}[N_1,N_2], f(N_1)= f(N_2)=0,\\ H(x)f(x)=0 \text{ for a.e.\ } x\in (N_1,N_2), Jf'=Hy \} . \end{multline} The desired result (see Corollary \ref{C9.8} below) will be a consequence of the following observation. \begin{Lemma} \label{L9.7} Let $0<N_1<N_2$, and suppose that $N_1$ is regular. Then \begin{gather} R_{(0,N_2)} = R_{(0,N_1)} \oplus R_{(N_1,N_2)},\\ L_2^H(0,N_2) \ominus R_{(0,N_2)} = \left( L_2^H(0,N_1) \ominus R_{(0,N_1)} \right) \oplus \left( L_2^H(N_1,N_2) \ominus R_{(N_1,N_2)} \right) . \end{gather} \end{Lemma} \begin{proof} The second equation of course follows from the first one. If $y\in R_{(0,N_2)}$ and $f\in AC^{(1)}[0,N_2]$ is as in the definition of $R_{(0,N_2)}$, then Lemma \ref{L9.4} implies that $f(N_1)=0$. This shows that $\chi_{(0,N_1)}y\in R_{(0,N_1)}$ and $\chi_{(N_1,N_2)}y\in R_{(N_1,N_2)}$ because as the required $f$'s we can just take the corresponding restrictions of the original $f$. Conversely, if $y=y^{(1)}+y^{(2)}$ with $y^{(1)}\in R_{(0,N_1)}$, $y^{(2)}\in R_{(N_1,N_2)}$, then the $f^{(i)}$'s from the definition satisfy $f^{(1)}(N_1)=f^{(2)}(N_1)=0$. Hence $f:= f^{(1)}+f^{(2)}$ is an absolutely continuous function with the properties needed to deduce that $y\in R_{(0,N_2)}$. \end{proof} \begin{Corollary} \label{C9.8} Let $0<N_1<N_2$, and suppose that $N_1$ is regular. Then $B(E_{N_1})$ is isometrically contained in $B(E_{N_2})$. \end{Corollary} \begin{proof} Lemma \ref{L9.7} says that \[ L_2^H(0,N_1)\ominus R_{(0,N_1)} \subset L_2^H(0,N_2)\ominus R_{(0,N_2)}, \] the inclusion being isometric. The unitary operator $U$ from \eqref{9.1b} maps these spaces onto $B(E_{N_1})$ and $B(E_{N_2})$, respectively. \end{proof} We conclude this section with a closer study of the effect of singular points. As above, we first look at the $L_2^H$ spaces and then transfer the results to the scale of de~Branges spaces $B(E_N)$ by applying $U$ from \eqref{9.1b}. \begin{Lemma} \label{L9.9} Let $0<N_1<N_2$, and suppose that $N_1$ is regular and $(N_1,N_2)\subset S$. Then \begin{gather} \dim \left( L_2^H(N_1,N_2) \ominus R_{(N_1,N_2)} \right) = 1 , \\ L_2^H(0,N_2) \ominus R_{(0,N_2)} = \left( L_2^H(0,N_1) \ominus R_{(0,N_1)} \right) \oplus V , \end{gather} where $V$ is a one-dimensional space. \end{Lemma} \begin{proof} On $(N_1,N_2)$, we have that $H(x)=h(x)P_{\varphi}$. So, for an arbitrary $y\in L_2^H(N_1,N_2)$, the function $H(x)y(x)$ has the form $H(x)y(x)=h(x)w(x)e_{\varphi}$, where $\int_{N_1}^{N_2} \|w\|^2 h < \infty$. Here, as introduced above, $e_{\varphi}=\bigl( \begin{smallmatrix} \cos\varphi \\ \sin\varphi \end{smallmatrix} \bigr)$. Now if $f\in AC^{(1)}[N_1,N_2]$ obeys $Jf'=Hy$ and $f(N_1)=0$, then \begin{equation} \label{9.3} f(x)= - Je_{\varphi} \int_{N_1}^x w(t)h(t)\, dt . \end{equation} Thus, the additional condition $f(N_2)=0$ forces \begin{equation} \label{9.4} \int_{N_1}^{N_2} w(t)h(t)\, dt =0 . \end{equation} Conversely, if \eqref{9.4} holds, we can define $f\in AC^{(1)}[N_1,N_2]$ by \eqref{9.3}, and this $f$ satisfies $f(N_1)=f(N_2)=0$ and $Jf'=Hy$. Moreover, since $e_{\varphi}^Je_{\varphi}=0$, it follows that $Hf=0$ on $(N_1,N_2)$. But the integral from \eqref{9.4} is the scalar product in $L_2^H(N_1,N_2)$ of $y$ with the constant function $e_{\varphi}$, so we have proved that \[ R_{(N_1,N_2)} = \left\{ y\in L_2^H(N_1,N_2): \langle e_{\varphi}, y \rangle_{L_2^H(N_1,N_2)} = 0 \right\} = \{ e_{\varphi} \}^{\perp} . \] As $e_{\varphi}$ is not the zero element of $L_2^H(N_1,N_2)$, this is the first assertion. The second claim follows from the first one with the help of Lemma \ref{L9.7}. (Incidentally, the condition that $N_1$ be regular is needed only for this implication.) \end{proof} \begin{Corollary} \label{C9.10} If $N_1>0$ is regular, but $(N_1,N_2)\subset S$, then $B(E_{N_2})=B(E_{N_1})\oplus V$, where $V$ is a one-dimensional space. Similarly, if $(0,N)\subset S$, then either $B(E_N)= \{ 0 \}$ or $B(E_N) \cong \mathbb C$. In the first case, $E_N(z)\equiv 1$. \end{Corollary} \begin{proof}[Sketch of proof] The first part follows in the usual way from Lemma \ref{L9.9} by applying $U$ from \eqref{9.1b}. The second part is established by a similar discussion; we leave the details to the reader. Let us just point out the fact that the case $B(E_N)= \{ 0 \}$ occurs if $H(x)=h(x) \bigl( \begin{smallmatrix} 0 & 0 \\ 0 & 1 \end{smallmatrix} \bigr)$ on $(0,N)$. Here, the boundary condition at zero is not regular, so to speak, and we have that $R_{(0,N)}=\widetilde{R}_{(0,N)}=L_2^H(0,N)$. \end{proof} \section{Matching de~Branges spaces} We resume the proof of Theorem \ref{T8.1}. Recall briefly what we have done already: We have constructed two families of de~Branges spaces, $H_x$ and $B_x$, $0<x\le N$. The spaces $H_x$ are given by \eqref{Hx} and \eqref{scHx}. The spaces $B_x$ come from a canonical system, \begin{equation} \label{Can'} Ju'(x) = zH(x)u(x). \end{equation} This system is trace normed, that is, $\text{tr }H(x)=\tau >0$ for all $x\in (0,N)$. It will be convenient to define $H_0=B_0= \{ 0 \}$. The canonical system \eqref{Can'} was constructed such that $B_N = H_N$; in fact, the corresponding de~Branges functions are equal. We also know that $H_t$ is isometrically contained in $H_x$ if $t\le x$, and for the family $B_x$, we have Corollary \ref{C9.8}. In particular, if $x\in [0,N]$ is arbitrary and if $t\in [0,N]$ is a regular value of \eqref{Can'}, then $H_x$ and $B_t$ are both isometrically contained in $H_N=B_N$. Here, the points $t=0$ and $t=N$ are regular by definition; the claim on $B_t$ is obvious for these $t$'s. (In a different context, it would of course make perfect sense to call $t=0$ singular if there is an interval $(0,s)\subset S$.) Denote this (extended) set of regular values by $R$, that is, $R= [0,N]\setminus S$. By Lemma \ref{L8.3} and Theorem \ref{T9.reg}, all spaces are regular, so Theorem \ref{T6.4} applies: either $H_x\subset B_t$ or $B_t\subset H_x$, the inclusion being isometric in each case. Define, for $t\in R$, a function $x(t)$ by \[ x(t) = \inf \{ x\in [0,N]: H_x \supset B_t \} . \] It is clear that $x(t)$ is increasing, $x(0)=0$, and, since $H_x$ is a proper subspace of $H_N=B_N$ for $x<N$, $x(N)=N$. Our next goal is to prove that $H_{x(t)}=B_t$. A modification of \eqref{Can'} will be useful to avoid certain trivialities. Namely, if $(0,N)$ starts with a singular interval $(0,b)\subset S$ and if $E_b(z)\equiv 1$, we simply delete this initial interval $(0,b)$ (and rescale so that we end up with a problem on $(0,N)$ again). Of course, this does not change the de~Branges space $B_N$. We have just removed an interval on which nothing happens. Next, we show that the spaces $H_x$ depend continuously on $x$ in the following sense. \begin{Lemma} \label{L10.1} For every $x\in (0,N)$, we have that \[ H_x = \overline{\bigcup_{t<x} H_t} = \bigcap_{t>x} H_t . \] \end{Lemma} In the second expression, the closure is taken in $H_N$; recall that this space contains $H_x$ as a subspace for every $x$. \begin{proof} We begin with the first equality. We know already that $H_t$ is isometrically contained in $H_x$ for $t<x$, and this implies that the closure of the union is contained in $H_x$. Conversely, let $F\in H_x$, so $F(z)=\int f(s)\cos\sqrt{z}s\, ds$ for some $f\in L_2(0,x)$. Let $F_n(z) = \int_0^{x-1/n} f(s)\cos\sqrt{z}s\, ds$. Then $F_n\in H_{x-1/n}$ and $F_n\to F$ in $H_x$ because \[ \\|F-F_n\\|_{H_x} \le C \\|f - \chi_{(0,x-1/n)}f\\|_{L_2(0,x)} \to 0 . \] Thus $F\in \overline{\bigcup_{t<x} H_t}$. As for the second assertion, the ordering of the spaces $H_t$ here implies that $H_x\subset \bigcap_{t>x} H_t$. On the other hand, if $F\in \bigcap_{t>x} H_t$, then for all large $n$, we have that $F(z)=\int f_n(s)\cos\sqrt{z}s\, ds$ for some $f_n\in L_2(0,x+1/n)$. But by the uniqueness of the Fourier transform, there can be at most one function $f\in L_2(\mathbb R)$ so that $F(z)=\int f(s) \cos\sqrt{z}s\, ds$, hence $f=f_n$ for all $n$. This $f$ is supported by $(0,x+1/n)$ for all $n$, hence $f\in L_2(0,x)$ and $F\in H_x$. \end{proof} \begin{Proposition} \label{P10.2} The (modified) system \eqref{Can'} has no singular points, and $B_t=H_{x(t)}$ for all $t\in [0,N]$. \end{Proposition} \begin{proof} We first prove that the desired relation $B_t=H_{x(t)}$ holds for all $t\in R$, the set of regular values. For these $t$, we know that for all $x$, either $H_x\subset B_t$ or $B_t \subset H_x$. Now the definition of $x(t)$ implies that the first case occurs for $x<x(t)$ and the second inclusion holds for $x>x(t)$. Hence \[ \overline{\bigcup_{x<x(t)} H_x} \subset B_t \subset \bigcap_{x>x(t)} H_x, \] and now Lemma \ref{L10.1} shows that $B_t=H_{x(t)}$. This argument does not literally apply to the extreme values $t=0$, $t=N$, but the claim is obvious in these cases. If $(a,b)$ is a component of $S$, then the preceding may be applied to the regular values $a$, $b$, and thus \[ H_{x(b)}\ominus H_{x(a)} = B_b \ominus B_a . \] Corollary \ref{C9.10} shows that this latter difference is one-dimensional. (For $a=0$, this statement holds because of our modification of \eqref{Can'}.) On the other hand, $H_{x(b)}\ominus H_{x(a)}$ is isomorphic to $L_2(x(a),x(b))$ and hence either the zero space or infinite dimensional. We have reached a contradiction which can only be avoided if $S=\emptyset$. \end{proof} It is, of course, much more convenient to have $B_t=H_t$; this can be achieved by transforming \eqref{Can'}. More specifically, we will use $x(t)$ as the independent variable. We defer the discussion of the technical details to Sect.\ 15 because we need additional tools which will be developed next. \section{The conjugate function} In regular de~Branges spaces, one can introduce a so-called conjugate mapping, which is a substitute for the Hilbert transform of ordinary Fourier analysis. In this paper, the conjugate mapping will not play a major role. Thus, our treatment of this topic will be very cursory and incomplete; for the full picture, please consult \cite{dB}. Consider a canonical system and the associated de~Branges spaces $B_N\equiv B(E_N)$; for simplicity, we assume that there are no singular points (as in Proposition \ref{P10.2}). Recall that $v$ is the solution of \eqref{Can'} with $v(0,z)=\bigl( \begin{smallmatrix} 0 \\ 1 \end{smallmatrix} \bigr)$, and define \begin{equation} \label{Kz} K_z(\zeta) = \frac{v^(N,z)Ju(N,\zeta) - 1}{\zeta - \overline{z}} . \end{equation} Since $(v^(x,z)Ju(x,\zeta))'=(\zeta-\overline{z})v^(x,z)H(x)u(x,\zeta)$, this may also be written in the form \begin{equation} \label{Kz'} K_z(\zeta) = \int_0^N v^(x,z)H(x)u(x,\zeta)\, dx = \int_0^N u^(x,\overline{\zeta})H(x) v(x,\overline{z})\, dx . \end{equation} In particular, when combined with \eqref{9.b}, the last expression shows that $K_z\in B_N$ for all $z\in\mathbb C$. We can thus define, for $F\in B_N$, the conjugate function $\widetilde{F}$ by $\widetilde{F}(z)=[K_z,F]$. The material of Sect.\ 10 immediately provides us with an interpretation of $\widetilde{F}$. Namely, if $F(z)=\int u^(x,\overline{z})H(x)f(x)\, dx$ with $f\in L_2^H(0,N)$, then $\widetilde{F}(z) = \int v^(x,\overline{z})H(x)f(x)\, dx$, that is, instead of $u$, one uses the solution $v$ satisfying the ``conjugate'' boundary condition at $x=0$. The next lemma says that $\widetilde{F}$ does not depend on the space in which the conjugate function is computed. Notice that since we are assuming that all points are regular, $B_{N_1}$ is isometrically contained in $B_{N_2}$ for $N_1<N_2$ by Corollary \ref{C9.8}. \begin{Lemma} \label{L11.1} Let $0<N_1<N_2$ and $F\in B_{N_1}$. Then \[ \widetilde{F}(z) = [K_z^{(N_1)}, F ]_{B_{N_1}} = [K_z^{(N_2)}, F ]_{B_{N_2}}. \] \end{Lemma} \begin{proof} By \eqref{Kz'}, $K_z^{(N_i)}= U(\chi_{(0,N_i)}v(\cdot, \overline{z}))$, where $U$ is the map from \eqref{9.1b}. Since there are no singular points, $U$ is unitary from $L_2^H(0,N_i)$ onto $B_{N_i}$. Also, $F=Uf$ for some $f\in L_2^H(0,N_1)$, hence \begin{align} [K_z^{(N_1)},F]_{B_{N_1}} & = [U(\chi_{(0,N_1)}v(\cdot,\overline{z})), Uf]_{B_{N_1}}= \langle v(\cdot,\overline{z}), f \rangle_{L_2^H(0,N_1)}\\ & = \langle \chi_{(0,N_2)} v(\cdot,\overline{z}), f \rangle_{L_2^H(0,N_2)} = [ U(\chi_{(0,N_2)} v(\cdot,\overline{z})), Uf]_{B_{N_2}} \\ & = [K_z^{(N_2)}, F ]_{B_{N_2}} . \end{align} \end{proof} For $F\in B_N$, we introduce the abbreviation \[ (RF)(z) = \frac{F(z)-F(0)}{z} . \] Recall from Theorem \ref{T9.reg} that $RF\in B_N$ whenever $F\in B_N$. The following identity, which is a special case of a more general identity (compare \cite[Theorem 27]{dB}), is basically about all we will need about the conjugate function. \begin{Proposition} \label{P11.2} For all $F,G\in B_N$, the following identity holds: \[ \widetilde{F}(0)\overline{G(0)} - F(0)\overline{\widetilde{G}(0)} = [RG,F] - [G,RF] . \] \end{Proposition} \begin{proof} By a standard density argument, it suffices to prove this for $F=J_{\lambda_m}$, $G=J_{\lambda_n}$, where the $\{ \lambda_k \}$ are the eigenvalues of \eqref{Can'}, \eqref{bc}. In that case, \[ \widetilde{F}(0) = [K_0,J_{\lambda_m}] = \overline{K_0(\lambda_m)} =K_0(\lambda_m) = \frac{u_1(N,\lambda_m)-1}{\lambda_m} \] and $\widetilde{G}(0)=(u_1(N,\lambda_n)-1)/\lambda_n$. Also, $F(0)=-u_2(N,\lambda_m)/\lambda_m$ and $G(0)=-u_2(N,\lambda_n)/\lambda_n$. So the left-hand side of the equation that we want to prove equals \[ \frac{1}{\lambda_m\lambda_n} \left[ -(u_1(N,\lambda_m)-1)u_2(N,\lambda_n) +u_2(N,\lambda_m)(u_1(N,\lambda_n)-1) \right] . \] Because $u(\cdot,\lambda_m)$ and $u(\cdot,\lambda_n)$ both satisfy the boundary condition at $x=N$, we have that \[ u_1(N,\lambda_m)u_2(N,\lambda_n)= u_1(N,\lambda_n)u_2(N,\lambda_m), \] and thus the above expression simplifies to \begin{equation} \label{11.1} \frac{u_2(N,\lambda_n)-u_2(N,\lambda_m)}{\lambda_m\lambda_n} . \end{equation} On the other hand, \[ [RG,F] = \overline{(RG)(\lambda_m)} = (RG)(\lambda_m)= \frac{J_{\lambda_n}(\lambda_m) - G(0)}{\lambda_m} , \] and similarly for $[G,RF]$. Since $J_{\lambda_n}(\lambda_m) =\delta_{mn}J_{\lambda_n}(\lambda_n)$, a brief calculation now shows that the right-hand side of the asserted equation also equals \eqref{11.1}. \end{proof} \section{The integral equations} In this section, we study the reproducing kernels $J_z^{(x)}$ and the conjugate kernels $K_z^{(x)}$ of the spaces $H_x$. More specifically, we find integral equations from which further properties of these quantities will be derived later. Actually, it suffices to consider the case when $z=0$. Things are very easy for $J_0^{(x)}$. Introduce $y(x,t)$ by writing \[ J_0^{(x)}(z) = \int_0^x y(x,t)\cos\sqrt{z}t \, dt . \] So for fixed $x$, the function $y(x,\cdot)$ lies in $L_2(0,x)$. Now we use the defining property of $J_0^{(x)}$: $[J_0^{(x)},F]_{H_x}=F(0)$ for all $F\in H_x$. Write $F(z)=\int f(t)\cos\sqrt{z}t\, dt$, where $f\in L_2(0,x)$, and recall that by \eqref{scHx}, \[ [J_0^{(x)},F]_{H_x}=\langle y(x,\cdot), (1+ \mathcal{K}_{\phi}) f\rangle_{L_2(0,x)} . \] We obtain the equation \[ \langle y(x,\cdot), (1+\mathcal{K}_{\phi}) f\rangle_{L_2(0,x)} = F(0) = \langle 1, f \rangle_{L_2(0,x)}, \] where $1$ on the right-hand side denotes the function that is identically equal to $1$ on $(0,x)$. The operator $1+\mathcal{K}_{\phi}$ is self-adjoint and $f\in L_2(0,x)$ is arbitrary, so we conclude that \begin{equation} \label{iey} y(x,t) + \int_0^x K(t,s) y(x,s)\, ds = 1 , \end{equation} and this is the desired integral equation for $y(x,t)$, which, in turn, determines $J_0^{(x)}(z)$. By the way we derived \eqref{iey}, this equation is to be interpreted as an equation in $L_2(0,x)$, where $x\in (0,N]$ is arbitrary, but fixed. However, we can then again define a particular representative $y(x,t)$ by requiring \eqref{iey} to hold pointwise. (Recall that the same procedure was applied in connection with \eqref{9.2}.) From the definition of $y$ we know only that $y(x,\cdot)\in L_2(0,x)$, but then \eqref{iey} in this pointwise sense of course implies much more regularity. This will be discussed in detail in the next section. As for $K_0^{(x)}$, we would like to proceed similarly, but we must first identify a conjugate mapping $F\mapsto \widetilde{F}(0)$ on $H_x$. We do this by exploiting the fact that the identity of Proposition \ref{P11.2} already determines $\widetilde{F}(0)$ up to a multiple of $F(0)$. Let \[ \psi(t) = \int_0^t \phi(s)(t-s)\, ds + t. \] Then $\psi\in AC^{(3)}[0,N]$, $\psi''=\phi$, and $\psi(0)=0$, $\psi'(0)=1$. For $F\in H_N$, so $F(z)=\int_0^N f(t)\cos\sqrt{z}t\, dt$ with $f\in L_2(0,N)$, we define \begin{equation} \label{12.2} \widehat{F}(0) = \int_0^N f(t)\psi(t)\, dt. \end{equation} \begin{Proposition} \label{P12.1} For all $F,G\in H_N$, the following identity holds: \[ \widehat{F}(0)\overline{G(0)} - F(0)\overline{\widehat{G}(0)} = [RG,F] - [G,RF] . \] \end{Proposition} \begin{proof} As usual, let $f,g$ be the $L_2(0,N)$ functions associated with $F$ and $G$, respectively. Plugging in the definitions, we see that the left-hand side of the identity that is to be proved equals \[ \int_0^N\!\!\! \int_0^N dx\, dt\, \overline{g(t)}f(x) \left( x-t + \int_0^x \phi(s)(x-s)\, ds - \int_0^t \phi(s)(t-s)\, ds\right) . \] We have seen in the last part of the proof of Lemma \ref{L8.3} that \[ (RF)(z) \equiv \frac{F(z)-F(0)}{z} = \int_0^N dt\, \cos\sqrt{z}t \int_t^N ds\, f(s)(t-s) . \] Thus, again by a routine calculation, the right-hand side of the above identity is equal to \begin{multline} \int_0^N\!\!\!\int_0^N dx\, dt\, \overline{g(t)}f(x) \left( x-t + \frac{1}{2} \int_0^t \left( \phi(s-x)+\phi(s+x)\right) (s-t)\, ds \right. \\ - \left. \frac{1}{2} \int_0^x \left( \phi(s-t)+\phi(s+t)\right) (s-x)\, ds \right) . \end{multline} So the identity holds for arbitrary $F,G\in B_N$ precisely if \begin{multline} \label{12.1} \int_0^x \left[ \phi(t-s)+\phi(t+s)-2\phi(s)\right] (s-x)\, ds =\\ \int_0^t \left[ \phi(x-s)+\phi(x+s)-2\phi(s)\right] (s-t)\, ds \end{multline} for all $t,x\in [0,N]$. In other words, we need to show that the function \[ H(x,t) = \int_0^x \left[ \phi(t-s)+\phi(t+s)-2\phi(s)\right] (s-x)\, ds \] is symmetric: $H(x,t)=H(t,x)$. We first prove this under the additional assumption that $\phi$ is smooth (let us say, $\phi\in C^2$). Then $H$ has continuous partial derivatives up to order $2$. We have \[ H(0,t)=H_x(0,t)=0,\quad H_{xx}(x,t)= 2\phi(x)-\phi(t-x)-\phi(t+x), \] and, because $\phi$ is even, $H(x,0)=0$. Moreover, \[ H_t(x,0)= \int_0^x \left[ \phi'(-s)+\phi'(s)\right] (s-x)\, ds \] is also equal to zero because the expression in brackets is zero. Finally, \[ H_{tt}(x,t) = \int_0^x \left[ \phi''(t-s)+\phi''(t+s) \right] (s-x)\, ds, \] and by integrating by parts, we may evaluate this as \[ H_{tt}(x,t) = 2\phi(t)-\phi(t-x)-\phi(t+x). \] Fix $t\in [0,N]$ and consider the difference $D(x)=H(x,t)-H(t,x)$. What we have shown in the preceding paragraph says that $D(0)=D'(0)=0$, $D''(x)\equiv 0$. Hence $D\equiv 0$, as desired. To prove \eqref{12.1} in full generality, approximate the given $\phi$ uniformly on $[-2N,2N]$ by even functions $\phi_n\in C^2$. (For example, approximate the odd function $\phi'\in L_1(-2N,2N)$ in $L_1$ norm by odd functions $f_n\in C_0^{\infty}(-2N,2N)$ and let $\phi_n(x)=\int_0^x f_n(t)\, dt$.) Then \eqref{12.1} holds for $\phi_n$, and we can pass to the limit to obtain \eqref{12.1} for $\phi$ as well. \end{proof} We are now ready to introduce $K_0^{(x)}$, the conjugate kernel (for $z=0$) of $H_x$. The map $F\mapsto \widehat{F}(0)$ is a bounded linear functional on $H_x$. Hence there exists a unique $K_0^{(x)}\in H_x$, so that $[K_0^{(x)},F]_{H_x} = \widehat{F}(0)$ for all $F\in H_x$. The use of the symbol $K_0^{(x)}$ for this function will be justified in Sect.\ 15. More precisely, we will show that, possibly after a modification of the canonical system from Proposition \ref{P10.2}, $K_0^{(x)}$ indeed also is the conjugate kernel of $B_x$, which was introduced in Sect.\ 12. \begin{Theorem} \label{T12.3} Let $J_0^{(x)}$ and $K_0^{(x)}$ be the reproducing and conjugate kernels, respectively, of $H_x$. Define $y(x,\cdot),w(x,\cdot)\in L_2(0,x)$ by \begin{align} J_0^{(x)}(z) & = \int_0^x y(x,t)\cos\sqrt{z}t\, dt,\\ K_0^{(x)}(z) & = \int_0^x w(x,t)\cos\sqrt{z}t\, dt. \end{align} Then $y,w$ obey the integral equations \begin{align} y(x,t) + \int_0^x K(t,s) y(x,s)\, ds & = 1 ,\\ w(x,t) + \int_0^x K(t,s) w(x,s)\, ds & = \psi(t). \end{align} \end{Theorem} \begin{proof} The assertions concerning $J_0^{(x)}$ and $y$ have been established at the beginning of this section (compare \eqref{iey}). The argument for $K_0^{(x)}$ and $w$ is completely analogous. By definition of $K_0^{(x)}$, \eqref{12.2}, and the fact that $\psi$ is real, \[ [K_0^{(x)}, F ]_{H_x} = \widehat{F}(0) = \langle\psi, f\rangle_{L_2(0,x)}. \] On the other hand, \[ [K_0^{(x)}, F ]_{H_x} = \langle w(x,\cdot ), (1+\mathcal{K}_{\phi}) f\rangle_{L_2(0,x)} = \langle (1+\mathcal{K}_{\phi})w(x,\cdot ),f \rangle_{L_2(0,x)}, \] and as $f\in L_2(0,x)$ is arbitrary, the integral equation follows. \end{proof} \section{Regularity properties} In this section, we investigate the regularity of the solutions $p(x,t)$ of integral equations of the form \begin{equation} \label{ie} p(x,t) + \int_0^x K(t,s)p(x,s)\, ds = g(t) . \end{equation} Here, $K$ still is the kernel from \eqref{Kphi}. For $g(t)=1$ and $g(t)=\psi(t)$, \eqref{ie} reduces to the equations from Theorem \ref{T12.3}. Since $K(t,s)=(\phi(s-t)+\phi(s+t))/2$ and $\phi\in AC^{(1)}$, we expect that the solutions $p$ have similar regularity, at least if $g$ is sufficiently smooth. In fact, more is true: $p$ has better regularity properties than $K$! The material of this section is of a technical character. It is possible to omit the proof of the following theorem on a first reading. To simplify the notation, we introduce the set \[ \Delta_N = \{ (x,t)\in\mathbb R^2 : 0 \le t \le x \le N \} . \] By continuity in $\Delta_N$, we will always mean that the function under consideration is jointly continuous in $(x,t)\in\Delta_N$. Note that it is also possible to consider \eqref{ie} for $x=0$; we then simply have that $p(0,0)=g(0)$. \begin{Theorem} \label{T13.1} Suppose that $\phi\in\Phi_N$ and $g\in AC^{(2)}[0,N]$. Then, for every $x\in [0,N]$, the integral equation \eqref{ie} has a unique solution $p(x,\cdot)$ in $L_2(0,x)$ which has the following regularity properties:\\ a) $p\in C^1(\Delta_N)$, that is, the first order partial derivatives exist and are continuous in $\Delta_N$.\\ b) $p(x,x)\in AC^{(2)}[0,N]$. \end{Theorem} For reasons of brevity, our formulation in part a) is a little sloppy. The easiest way to get a precise statement is to interpret a) as follows: The first order partial derivatives exist on the interior of $\Delta_N$, and they have continuous extensions to $\Delta_N$. By a limiting argument, this implies that the one-sided partial derivatives exist where they can be reasonably defined. The second order partial derivatives exist in a certain weak sense. Unfortunately, things get messy (for example, the statements are not symmetric in $x$ and $t$), and it is better to avoid these issues as much as possible by using an approximation argument as in the proof of Proposition \ref{P12.1}. Therefore, we have not made these statements explicit. We do need, however, the statement on the existence of the second derivative of the ``diagonal'' function $p(x,x)$. \begin{proof} The integral equation \eqref{ie} is of the form \[ ( 1 + \mathcal{K}_{\phi}^{(x)} ) p(x,\cdot) = g, \] where we write $\mathcal{K}_{\phi}^{(x)}$ for the integral operator in $L_2(0,x)$ that is generated by the kernel $K$. Since $1+\mathcal{K}_{\phi}^{(x)}>0$ by assumption, \eqref{ie} has the unique solution \begin{equation} \label{13.1} p(x,\cdot) = ( 1 + \mathcal{K}_{\phi}^{(x)} )^{-1}g . \end{equation} Note that the roles of the variables $x$ and $t$ are quite different: $t$ is the independent variable, while $x$ is an external parameter. We now observe the important fact that \eqref{13.1} makes sense not only on $L_2(0,x)$, but on each space of the following chain of Banach spaces: \[ C[0,x] \subset L_2(0,x) \subset L_1(0,x) . \] Indeed, first of all, $\mathcal{K}_{\phi}^{(x)}$ is a well defined operator on each of these three spaces; in fact, $\mathcal{K}_{\phi}^{(x)}$ maps $L_1(0,x)$ into $C[0,x]$. Moreover, $\mathcal{K}_{\phi}^{(x)}$ is compact in every case. This follows from the Arzela-Ascoli Theorem: If $f_n\in L_1(0,x)$, $\\|f_n\\|_1\le 1$, then, since the kernel $K$ is uniformly continuous on $[0,x]\times [0,x]$, the sequence of functions $\mathcal{K}_{\phi}^{(x)}f_n$ is equicontinuous and uniformly bounded, hence there exists a uniformly convergent subsequence. So $\mathcal{K}_{\phi}^{(x)}$ is compact even as an operator from $L_1(0,x)$ to $C[0,x]$. The inclusion $\mathcal{K}_{\phi}^{(x)}(L_1(0,x))\subset C[0,x]$ also shows that the spectrum of $\mathcal{K}_{\phi}^{(x)}$ is independent of the space: the eigenfunctions with non-zero eigenvalues are always contained in the smallest space $C[0,x]$. In particular, we always have that $-1\notin \sigma(\mathcal{K}_{\phi}^{(x)})$, so $1+\mathcal{K}_{\phi}^{(x)}$ is boundedly invertible and \eqref{13.1} holds. To investigate the derivatives of $p$, we again temporarily make the additional assumption that $\phi$ and $g$ (and hence also $K$) are smooth. So, let us suppose that $\phi,g\in C^{\infty}$. Then one can show that the solution $p$ is also smooth: $p\in C^{\infty}(\Delta_N)$. We leave this part of the proof to the reader. To investigate the smoothness in $x$, it is useful to transform \eqref{ie} to get an equivalent family of equations on a space that does not depend on $x$. See also \cite[Sect.\ 2.3]{Lev} for a discussion of these issues. Once we know that $p$ is smooth, we can get integral equations for the derivates by differentiating \eqref{ie}. Since, for the time being, all functions are $C^{\infty}$, we may differentiate under the integral sign. Thus we obtain \begin{subequations} \begin{gather} \label{13.1a} p_t(x,t) = - \int_0^x K_t(t,s) p(x,s)\, ds + g'(t), \\ \label{13.1b} p_x(x,t) + \int_0^x K(t,s) p_x(x,s)\, ds = - K(t,x)p(x,x), \\ \label{13.1c} \begin{split} p_{xx}(x,t) + \int_0^x K(t,s) p_{xx}(x,s)\, ds = -K_x & (t,x)p(x,x)\\ & -K(t,x) \left( p_x(x,s) + 2p_s(x,s) \right) \bigr\|_{s=x}, \\ \end{split}\\ \label{13.1d} p_{xt}(x,t) = - K_t(t,x)p(x,x) - \int_0^x K_t(t,s)p_x(x,s)\, ds . \end{gather} \end{subequations} For general $\phi$ and $g$, we approximate $\phi'$ in $L_1(-2N,2N)$ by odd functions $\phi'_n\in C_0^{\infty}(-2N,2N)$, and we put $\phi_n(x)=\int_0^x \phi'_n(t) dt$. Then $\phi_n\to\phi$ in $C[-2N,2N]$ and $K^{(n)}\to K$ in $C(\Delta_N)$ (we use superscripts here because in a moment we will want to denote partial derivatives by subscripts). Similary, we pick $L_1(0,N)$ approximations $g''_n\in C_0^{\infty}(0,N)$ of $g''\in L_1(0,N)$ and put \[ g_n(x)=g(0) + x g'(0) + \int_0^x g''_n(t) (x-t)\, dt . \] The integral operators $\mathcal{K}_{\phi_n}^{(x)}$ converge to $\mathcal{K}_{\phi}^{(x)}$ in the operator norm of any of the spaces we have considered above. In particular, $1+\mathcal{K}_{\phi_n}^{(x)}$ is boundedly invertible for all sufficiently large $n$. In fact, $\mathcal{K}_{\phi_n}^{(x)}$ converges to $\mathcal{K}_{\phi}^{(x)}$ in the norm of $B(L_1(0,x), C[0,x])$. Moreover, this convergence is uniform in $x\in (0,N]$. Let $p^{(n)}$ be the solution of \eqref{ie} with $K$ and $g$ replaced by $K^{(n)}$ and $g_n$, respectively. Then the above remarks together with \eqref{13.1} imply that \[ \\|p^{(n)}(x,\cdot) - p(x,\cdot) \\|_{C[0,x]} \to 0, \] uniformly in $x\in [0,N]$. (Strictly speaking, one needs a separate argument for the degenerate case $x=0$, but things are very easy here because $p^{(n)}(0,0)=g_n(0)=g(0)=p(0,0)$.) In other words, $p^{(n)}$ converges to the solution $p$ of the original problem in $C(\Delta_N)$. In particular, $p\in C(\Delta_N)$. Similar arguments work for the first order partial derivatives. Eq.\ \eqref{13.1b} says that \[ p_x^{(n)}(x,\cdot) = -p^{(n)}(x,x)( 1 + \mathcal{K}_{\phi_n}^{(x)} )^{-1} K^{(n)}(\cdot,x), \] and the right-hand side converges in $C[0,x]$, uniformly with respect to $x$. Again, the case $x=0$ needs to be discussed separately; we leave this to the reader. It follows that the partial derivative $p_x$ exists, is continuous and is equal to this limit function. The argument for the existence and continuity of $p_t$, which uses \eqref{13.1a}, is similar (perhaps easier, because one does not need to invert an operator). We have proved part a) now. Eq.\ \eqref{13.1c} (for $K^{(n)}$ instead of $K$) again has the form \[ ( 1 + \mathcal{K}_{\phi_n}^{(x)} ) p_{xx}^{(n)}(x,\cdot) = h_n(x,\cdot); \] we do not write out the inhomogeneous term $h_n$ here. Since $h_n$ converges in $L_1(0,x)$, but not necessarily in $C[0,x]$, we now only obtain convergence of $p_{xx}^{(n)}$ in $L_1(0,x)$. We denote the limit function by $p_{xx}$, so $p_{xx}(x,\cdot)\in L_1(0,x)$ and \[ \\|p_{xx}^{(n)}(x,\cdot) - p_{xx}(x,\cdot)\\|_{L_1(0,x)} \to 0, \] uniformly in $x$. Note, however, that $p_{xx}$ need not be a partial derivative in the classical sense. Using similar arguments, we deduce from \eqref{13.1d} that $p_{xt}^{(n)}(x,\cdot)$ converges in $L_1(0,x)$ to a limit function, which we denote by $p_{xt}(x,\cdot)$. As usual, the convergence is uniform in $x$. We have that \begin{multline} \label{13.2} p'(x,x) = (p_x+p_t)\bigr\|_{t=x} = -p(x,x)K(x,x) +g'(x) \\ -\int_0^x K(x,s)p_x(x,s)\, ds -\int_0^x K_x(x,s)p(x,s)\, ds. \end{multline} We now show that the individual terms on the right-hand side are in $AC^{(1)}[0,N]$. This is obvious for the first two terms, so we only need to discuss the integrals. If we replace $K$ and $p$ in these integrals by $K^{(n)}$ and $p^{(n)}$, respectively, and then let $n$ tend to infinity, we have convergence to the original terms in $C[0,N]$. We can therefore prove absolute continuity of these terms by showing that the derivatives converge in $L_1(0,N)$. So, consider \begin{multline} \frac{d}{dx} \int_0^x K^{(n)}(x,s)p_x^{(n)}(x,s)\, ds = K^{(n)}(x,x)p_x^{(n)}(x,x)\\ + \int_0^x K_x^{(n)}(x,s) p_x^{(n)}(x,s)\, ds + \int_0^x K^{(n)}(x,s) p_{xx}^{(n)}(x,s)\, ds . \end{multline} It is easy to see that the first two terms on the right-hand side converge in $C[0,N]$. As for the last term, we note that \begin{multline} \int_0^x K^{(n)}(x,s) p_{xx}^{(n)}(x,s)\, ds = \int_0^x K(x,s) p_{xx}^{(n)}(x,s)\, ds\\ + \int_0^x \left( K^{(n)}(x,s)-K(x,s)\right) p_{xx}^{(n)}(x,s)\, ds. \end{multline} Now recall that $\mathcal{K}_{\phi_n}^{(x)}-\mathcal{K}_{\phi}^{(x)}\to 0$ in $B(L_1,C)$ (uniformly in $x$) and $\\|p_{xx}^{(n)}(x,\cdot)\\|_{L_1(0,x)}$ is bounded as a function of $n$ and $x$. Therefore, the last term goes to zero in $C[0,N]$. Similarly, the first term also converges in $C[0,N]$, as we see from the following estimate: \[ \left\| \int_0^x K(x,s) \left( p_{xx}^{(n)}(x,s)- p_{xx}(x,s) \right) \, ds \right\| \le \\|\mathcal{K}_{\phi}^{(x)}\\|_{B(L_1,C)} \\| p_{xx}^{(n)}(x,\cdot) - p_{xx}(x,\cdot) \\|_{L_1} . \] Finally, let us analyze the last term from \eqref{13.2}. By definition of $K$ (see \eqref{Kphi}), \[ K_x(x,s) = \frac{1}{2} \left( \phi'(x-s) + \phi'(x+s) \right) . \] Let us look at the term with $\phi'(x-s)$; the other term is of course treated similarly. An integration by parts gives \[ \int_0^x \phi'(x-s)p(x,s)\, ds = \phi(x)p(x,0) + \int_0^x \phi(x-s)p_s(x,s)\, ds. \] The first term on the right-hand side manifestly is absolutely continuous. To establish absolute continuity of the integral, we argue exactly as above. Namely, we approximate by smooth functions and compute the derivative: \begin{multline} \frac{d}{dx} \int_0^x \phi_n(x-s) p_s^{(n)}(x,s)\, ds =\\ \int_0^x \phi'_n(x-s)p_s^{(n)}(x,s)\, ds + \int_0^x \phi_n(x-s) p_{xs}^{(n)}(x,s) \, ds . \end{multline} Now arguments analogous to those used in the preceding paragraph show that this derivative converges in $C[0,N]$, and, also as above, convergence in $L_1(0,N)$ already would have been sufficient to deduce the required absolute continuity. \end{proof} \section{Some identities} First of all, we can now complete the work of Sect.\ 11. \begin{Theorem} \label{T10.3} There exists $H(x)\in L_1(0,N)$, $H(x)\ge 0$ for almost every $x\in (0,N)$, $H\not\equiv 0$ on nonempty open sets, so that for all $x\in [0,N]$, we have that $B_x=H_x$ (as de~Branges spaces). Here, $B_x$ is the de~Branges space based on the de~Branges function $E_x(z)=u_1(x,z)+iu_2(x,z)$, where \[ Ju'(t)=zH(t)u(t),\quad\quad u(0)=\bigl( \begin{smallmatrix} 1 \\ 0 \end{smallmatrix} \bigr) , \] as in Proposition \ref{P5.1}, and $H_x$ is the space from Lemma \ref{L8.3}. Moreover, $H(x)$ can be chosen so that $\widehat{F}(0)=\widetilde{F}(0)$ for all $F\in B_N=H_N$. \end{Theorem} The last part justifies our definition of $K_0^{(x)}\in H_x$ from Sect.\ 13. Recall also that $\widehat{F}(0)$ is computed in $H_N$, while $\widetilde{F}(0)$ is computed as in Sect.\ 12 by using the realization $B_N$ of this space. \begin{proof} As explained in Sect.\ 11, we use the system from Proposition \ref{P10.2}, but with $x(t)$ as the new independent variable. As the first step of the proof, let us check how far we are from satisfying the last part of Theorem \ref{T10.3}. Propositions \ref{P11.2} and \ref{P12.1} show that \[ \widetilde{F}(0)\overline{G(0)} - F(0)\overline{\widetilde{G}(0)} = \widehat{F}(0)\overline{G(0)} - F(0)\overline{\widehat{G}(0)} \] for all $F,G\in B_N=H_N$. In particular, if $F(0)=0$, then $\widetilde{F}(0)=\widehat{F}(0)$. Since both $F\mapsto \widetilde{F}(0)$ and $F\mapsto \widehat{F}(0)$ are linear maps, it follows that there exists a constant $c\in\mathbb C$, independent of $F$, so that \begin{equation} \label{15-1} \widehat{F}(0)=\widetilde{F}(0)+cF(0). \end{equation} From the definitions, we see that $\widetilde{F^{\#}}(0)= \overline{\widetilde{F}(0)}$ and $\widehat{F^{\#}}(0)=\overline{ \widehat{F}(0)}$, so the $c$ from \eqref{15-1} must actually be real. To avoid confusion, let us temporarily denote the reproducing and conjugate kernels (for $z=0$) of the spaces $B_t$ by $j_0^{(t)}$ and $k_0^{(t)}$ (lowercase letters!), respectively. Note also that the conjugate and reproducing kernels depend only on the de~Branges space, but not on the particular de~Branges function chosen. Therefore \eqref{15-1} says that $K_0^{(N)}(z)=k_0^{(N)}(z)+cj_0^{(N)}(z)$. Since $B_t=H_{x(t)}$ and since by Lemma \ref{L11.1}, $\widetilde{F}(0)$ does not depend on the space in which the conjugate function is computed, we also have that $j_0^{(t)}(z)=J_0^{(x(t))}(z)$ and \begin{equation} \label{15-2} K_0^{(x(t))}(z) = k_0^{(t)}(z) + c j_0^{(t)}(z). \end{equation} Next, we claim that the following analog of Lemma \ref{L10.1} holds: \begin{equation} \label{11-2} B_t = \overline{\bigcup_{s<t} B_s} = \bigcap_{s>t} B_s. \end{equation} We will only prove (and use) this for canonical systems without singular points, where the proof is very easy. However, a similar but -- due to the possible presence of singular points -- somewhat more complicated result holds for general canonical systems. If $S=\emptyset$, then Lemma \ref{L9.4} implies that $R_{(a,b)}=\{ 0 \}$ for arbitrary $a<b$. Thus the $U$ from \eqref{9.1a}, \eqref{9.1b} maps $L_2^H(0,t)$ unitarily onto $B_t$ for all $t\in [0,N]$. In particular, the following obvious fact is equivalent to \eqref{11-2}: \[ L_2^H(0,t) = \overline{\bigcup_{s<t} L_2^H(0,s)} = \bigcap_{s>t} L_2^H(0,s). \] It also follows that $x(t)$ is strictly increasing. Indeed, if $x(t_1)=x(t_2)$, then $B_{t_1}=B_{t_2}$, and these spaces are mapped by $U^{-1}$ onto $L_2^H(0,t_1)$ and $L_2^H(0,t_2)$, respectively, so $t_1=t_2$. The relation \eqref{11-2} allows us to show that $x(t)$ is continuous. Proposition \ref{P10.2} together with \eqref{11-2} imply that \[ B_t = \bigcap_{s>t} B_s = \bigcap_{s>t} H_{x(s)}. \] On the other hand, $B_t=H_{x(t)}$, and now Lemma \ref{L10.1} and the fact that $H_y\ominus H_x$ is not the zero space for $y>x$ show that $\inf_{s>t} x(s) \le x(t)$. A similar argument gives $\sup_{s<t} x(s)\ge x(t)$. Since $x(t)$ is monotonically increasing, these two properties suffice to deduce that $x(t)$ is continuous. Let $t(x)$ be the inverse function of $x(t)$. Then $t$ is also strictly increasing and continuous. We want to show that $t$ is actually absolutely continuous. To this end, we compare $j_0(0)+\widetilde{k_0}(0)$ in the spaces $B_{t(x)}=H_x$. Specializing Proposition \ref{P5.1} to $z=\zeta=0$ (and replacing $N$ by $t(x)$), we see that \[ j_0^{(t(x))}(0) = \int_0^{t(x)} H_{11}(s)\, ds . \] Moreover, arguing as in the proof of Lemma \ref{L11.1}, we obtain \[ \widetilde{k_0^{(t(x))}}(0) = [k_0^{(t(x))},k_0^{(t(x))}]_{B_{t(x)}} =\langle v(\cdot,0), v(\cdot,0)\rangle_{L_2^H(0,t(x))} =\int_0^{t(x)} H_{22}(s)\, ds . \] Hence, still working in $B_{t(x)}$, we have that \begin{equation} \label{15-3} j_0^{(t(x))}(0)+\widetilde{k_0^{(t(x))}}(0) = \int_0^{t(x)} \text{tr }H(s)\, ds = \tau t(x), \end{equation} where $\tau$ is a positive constant. On the other hand, we may use \eqref{15-1}, \eqref{15-2} to evaluate $j_0(0)+\widetilde{k_0}(0)$ in $H_x$. We compute \[ \widetilde{k_0^{(t(x))}}(0) = \widetilde{K_0^{(x)}}(0) - c\widetilde{J_0^{(x)}}(0) = \widehat{K_0^{(x)}}(0) - c K_0^{(x)}(0) - c\widehat{J_0^{(x)}}(0) + c^2 J_0^{(x)}(0). \] By definition of $w$ and the transform $F\mapsto \widehat{F}(0)$, we have $\widehat{K_0^{(x)}}(0)=\int_0^x w(x,t)\psi(t)\, dt$, and this is an absolutely continuous function of $x\in [0,N]$ by Theorem \ref{T13.1}. Similar arguments apply to the other terms and to $j_0^{(t(x))}(0)=J_0^{(x)}(0)=\int_0^x y(x,t)\, dt$. Comparing with \eqref{15-3}, we thus conclude that $t(x)\in AC^{(1)}[0,N]$, as desired. We are now ready to transform \eqref{Can'}. Define $\widetilde{u}(x) =u(t(x))$ and $\widetilde{H}(x)=t'(x) H(t(x))$. Since $t'\ge 0$ almost everywhere, this $\widetilde{H}$ is in $L_1(0,N)$ and positive semidefinite almost everywhere. As $t(x)$ is strictly increasing, $t'$ cannot vanish identically on a nonempty open set, and thus $\widetilde{H}$ also has this property. Moreover, $\widetilde{u}$ solves the corresponding canonical equation: \[ J\widetilde{u}'(x) = Jt'(x)u'(t(x))= zt'(x)H(t(x))u(t(x))= z\widetilde{H}(x)\widetilde{u}(x) . \] By definition of $\widetilde{u}$, the new de~Branges spaces $\widetilde{B}_x$ are related to the old spaces by $\widetilde{B}_x= B_{t(x)}$. Hence $\widetilde{B}_x=H_x$, as desired. Finally, we can get rid of $c$ in \eqref{15-1} by passing to the new matrix \[ H_c(x) = \begin{pmatrix} 1 & 0 \\ c & 1 \end{pmatrix} H(x) \begin{pmatrix} 1 & c \\ 0 & 1 \end{pmatrix} . \] (To avoid clumsy notation, we write $H(x)$ instead of $\widetilde{H}(x)$ for the $H$ constructed above.) Let $u^{(c)}$, $v^{(c)}$ be the solutions of the transformed system \begin{equation} \label{Can''} Jy'(x)=zH_c(x)y(x) \end{equation} with the initial values $u^{(c)}(0,z)=\bigl( \begin{smallmatrix} 1 \\ 0 \end{smallmatrix} \bigr)$, $v^{(c)}(0,z)=\bigl( \begin{smallmatrix} 0 \\ 1 \end{smallmatrix} \bigr)$. These functions are related to the old solutions $u=u^{(0)}$ and $v=v^{(0)}$ by \[ u^{(c)}(x,z) = \begin{pmatrix} 1 & -c \\ 0 & 1 \end{pmatrix} u(x,z), \quad v^{(c)}(x,z) = \begin{pmatrix} 1 & -c \\ 0 & 1 \end{pmatrix} (cu(x,z)+v(x,z)) . \] So, first of all, since the de~Branges functions associated with \eqref{Can''} are given by $E_x^{(c)}(z)= u_1^{(c)}(x,z)+iu_2^{(c)}(x,z)$, it follows from Theorem \ref{T6.2} that \eqref{Can''} still generates the same de~Branges spaces: $B_x\equiv B(E_x^{(0)}) = B(E_x^{(c)})$. So the equality $B_x=H_x$ continues to hold if we replace $H$ by $H_c$. Second, a calculation based on \eqref{Kz} shows that the conjugate kernel $K_z^{(c)}$ of $B(E_N^{(c)})$ (I apologize for the slightly inconsistent notation, but there are so many conjugate kernels in this argument) is given by $K_z^{(c)}(\zeta) = K_z(\zeta) + cJ_z(\zeta)$, and thus for the new system \eqref{Can''}, we have that $\widetilde{F}(0)=\widehat{F}(0)$. \end{proof} \begin{Proposition} \label{P14.1} Let $H$ and $y$, $w$ be as in Theorems \ref{T10.3} and \ref{T12.3}, respectively. Then \begin{gather} H_{11}(x) = y(x,x) + \int_0^x y_x(x,t)\, dt,\\ H_{12}(x) = w(x,x) + \int_0^x w_x(x,t)\, dt = y(x,x)\psi(x) + \int_0^x y_x(x,t)\psi(t)\, dt\\ H_{22}(x) = w(x,x)\psi(x) + \int_0^x w_x(x,t)\psi(t)\, dt . \end{gather} \end{Proposition} \begin{proof} Basically, we have established this already in the preceding proof when we showed that $t(x)$ is absolutely continuous. The idea is to compare reproducing and conjugate kernels in $B_x=H_x$. By Proposition \ref{P5.1}, the reproducing kernel $J_0^{(x)}$ of $B_x$, evaluated at $z=0$, is given by $J_0^{(x)}(0)=\int_0^x H_{11}(t)\, dt$. On the other hand, in $H_x$ we have $J_0^{(x)}(0)=\int_0^x y(x,t)\, dt$, so \[ \int_0^x H_{11}(t)\, dt = \int_0^x y(x,t)\, dt . \] Now take the derivatives with respect to $x$, using Theorem \ref{T13.1} on the right-hand side. The formula for $H_{11}$ follows. Similarly, \eqref{Kz'} shows that in $B_x$, we have $K_0^{(x)}(0)=\int_0^x H_{12}(t)\, dt$, and now the same reasoning applies and gives the first formula for $H_{12}$. To prove the second one, notice that the conjugate of $J_0^{(x)}$, evaluated in $H_x$, is given by \[ \widehat{J_0^{(x)}}(0) = \int_0^x y(x,t)\psi(t)\, dt . \] On the other hand, $\widetilde{J_0^{(x)}}(0) = [K_0^{(x)},J_0^{(x)}]_{B_x}$ by Lemma \ref{L11.1}. This scalar product can be evaluated with the help of the $U$ from \eqref{9.1b}, because $K_0^{(x)}=U(\chi_{(0,x)}v(\cdot,0))$ by \eqref{Kz'} and $J_0^{(x)}=U(\chi_{(0,x)}u(\cdot,0))$ by Proposition \ref{P5.1} (and a simple manipulation). Thus \[ \widetilde{J_0^{(x)}}(0) = \langle v(\cdot,0), u(\cdot,0) \rangle_{L_2^H(0,x)} = \int_0^x H_{21}(t)\, dt = \int_0^x H_{12}(t)\, dt, \] and the second formula for $H_{12}$ now follows. Finally, the formula for $H_{22}$ is proved by an analogous argument, using the conjugate of $K_0^{(x)}$ this time. \end{proof} Our final goal is to verify that $H(x)$ satisfies the hypotheses of Proposition \ref{P7.1}. Proposition \ref{P14.1} gives some hope that this can be done by analyzing the functions $y$, $w$ from Theorem \ref{T12.3}. \begin{Proposition} \label{P14.2} Let $y$, $w$ be as in Theorem \ref{T12.3}. Then $y(0,0)=1$, $w(0,0)=0$, $y'(0,0)=0$, $w'(0,0)=1$, and \[ y(x,x)w'(x,x)-y'(x,x)w(x,x) = 1. \] \end{Proposition} \begin{proof} By the usual approximation argument, it suffices to prove this under the additional assumption that $\phi\in C^{\infty}$. Consider again the general version \eqref{ie} of the integral equations for $y$ and $w$. By differentiating with respect to $x$, we see that $p_x$ satisfies \begin{equation} \label{14.1} \left( 1 + \mathcal{K}_{\phi}^{(x)} \right) p_x(x,\cdot) = - p(x,x) K(\cdot,x). \end{equation} Also, $p_{tt}$ solves \begin{equation} \label{14.2} p_{tt}(x,t) + \int_0^x K_{tt}(t,s) p(x,s)\, ds = g''(t) . \end{equation} Since $K_{tt}(t,s)=K_{ss}(t,s)$, we can use integration by parts to rewrite this equation. In the following calculation, we will use the notation $\partial_i$ for the partial derivative with respect to the $i$th variable ($i=1,2$). \begin{multline} \int_0^x K_{ss}(t,s) p(x,s)\, ds = K_x(t,x)p(x,x) - \partial_2 K(t,0) p(x,0) - \int_0^x K_s(t,s)p_s(x,s)\, ds\\ = K_x(t,x)p(x,x) - K(t,x) \partial_2 p(x,x) + \phi(t) \partial_2 p(x,0) + \int_0^x K(t,s) p_{ss}(x,s)\, ds. \end{multline} We have used the fact that because $\phi$ is even, $\partial_2 K(t,0)=0$. Also, $K(t,0)=\phi(t)$. Plug this into \eqref{14.2} and subtract the resulting equation from the equation \eqref{13.1c} for $p_{xx}$. There are some cancellations, and the function $P=p_{xx}-p_{tt}$ solves the relatively simple equation \begin{equation} \label{14.3} \left( 1 + \mathcal{K}_{\phi}^{(x)} \right) P(x,\cdot) = - 2p'(x,x) K(\cdot,x) +\partial_2 p(x,0)\phi - g'' . \end{equation} By putting $t=0$ in the equation \eqref{13.1a} for $p_t$ and noting that $\partial_1 K(0,s)=0$, we see that $\partial_2 p(x,0)= g'(0)$. Now if $g$ is one of the functions from the equations of Theorem \ref{T12.3} (so $g(t)=1$ or $g(t)=\psi(t)$), then $g'(0)\phi(t)-g''(t)\equiv 0$. Hence \eqref{14.3} says that the functions $Y=y_{xx}-y_{tt}$ and $W=w_{xx}-w_{tt}$ solve \begin{align} \left( 1 + \mathcal{K}_{\phi}^{(x)} \right) Y(x,\cdot) & = - 2y'(x,x) K(\cdot,x),\\ \left( 1 + \mathcal{K}_{\phi}^{(x)} \right) W(x,\cdot) & = - 2w'(x,x) K(\cdot,x). \end{align} Comparison with \eqref{14.1} for $p=y$ and $p=w$ shows that \begin{equation} \label{14.4} \frac{Y(x,t)}{2y'(x,x)} = \frac{W(x,t)}{2w'(x,x)} = \frac{y_x(x,t)}{y(x,x)} = \frac{w_x(x,t)}{w(x,x)} \quad\quad (0\le t\le x \le N) . \end{equation} More precisely, the ratios whose denominators are different from zero are equal to one another; if a denominator equals zero, then the corresponding numerator is identically equal to zero for $t\in [0,x]$. (As usual, the case $x=0$ should be discussed separately, but, also as usual, we leave this to the reader.) It follows from \eqref{14.4} that \begin{equation} \label{id} y_x(x,t)w(x,x)=w_x(x,t)y(x,x)\quad\quad (0\le t\le x \le N), \end{equation} and this holds in all cases. Take derivatives with respect to $x$, \[ y_{xx}(x,t)w(x,x)+y_x(x,t)w'(x,x)=w_{xx}(x,t)y(x,x)+w_x(x,t)y'(x,x), \] and subtract twice this equation from the identity \[ 2w'(x,x)y_x(x,t) = \left( w_{xx}(x,t)-w_{tt}(x,t) \right) y(x,x), \] which follows from \eqref{14.4}. We obtain \begin{equation} \label{14.5} \left( w_{xx}(x,t) + w_{tt}(x,t) \right) y(x,x) = -2w_x(x,t)y'(x,x) + 2w(x,x)y_{xx}(x,t) . \end{equation} If we interchange the roles of $y$ and $w$, we get the analogous identity \begin{equation} \label{14.6} \left( y_{xx}(x,t) + y_{tt}(x,t) \right) w(x,x) = -2y_x(x,t)w'(x,x) + 2y(x,x)w_{xx}(x,t) . \end{equation} Now subtract \eqref{14.5} from \eqref{14.6}. On the right-hand side, we get zero because \begin{multline} -2y_x(x,t)w'(x,x) + 2y(x,x)w_{xx}(x,t) +2w_x(x,t)y'(x,x) - 2w(x,x)y_{xx}(x,t) \\ = 2 \partial_x \left( y(x,x)w_x(x,t) - w(x,x)y_x(x,t) \right) , \end{multline} and the expression in parentheses is zero by \eqref{id}. Hence \[ \left( w_{xx}(x,t) + w_{tt}(x,t) \right) y(x,x) = \left( y_{xx}(x,t) + y_{tt}(x,t) \right) w(x,x) . \] Since $y_{tx}(x,t)w(x,x)=w_{tx}(x,t)y(x,x)$ by \eqref{id} again, we also have that \begin{multline} \label{14.7} \left( w_{xx}(x,t) + 2w_{tx}(x,t) + w_{tt}(x,t) \right) y(x,x) =\\ \left( y_{xx}(x,t) + 2y_{tx}(x,t) + y_{tt}(x,t) \right) w(x,x) . \end{multline} By the chain rule, \[ w''(x,x) = \left( w_{xx}(x,t) + 2w_{tx}(x,t) + w_{tt}(x,t) \right) \bigr\|_{t=x} , \] so taking $t=x$ in \eqref{14.7} yields \[ w(x,x)y''(x,x)-y(x,x)w''(x,x) = \frac{d}{dx} \left( w(x,x)y'(x,x) - w'(x,x)y(x,x) \right) = 0. \] We determine the constant value of $wy'-w'y$ by evaluating at $x=0$. Since $K(0,0)=0$, we see directly from the integral equation \eqref{ie} that $p(x,x)=g(x)+O(x^2)$ for small $x>0$, so $p(0,0)=g(0)$, $p'(0,0)=g'(0)$. Hence \[ y(0,0)=1, \quad w(0,0)=0, \quad y'(0,0)=0, \quad w'(0,0)=1, \] as claimed, and it also follows that $yw'-y'w=1$. \end{proof} \begin{Proposition} \label{P14.3} Let $H$ and $y$, $w$ be as in Theorems \ref{T10.3} and \ref{T12.3}, respectively. Then \[ H_{11}(x)w(x,x) = H_{12}(x)y(x,x),\quad\quad H_{12}(x)w(x,x) = H_{22}(x)y(x,x). \] \end{Proposition} \begin{proof} These identities follow at once from Proposition \ref{P14.1} and \eqref{id}. \end{proof} \section{Conclusion of the proof of Theorem \ref{T8.1}} We are now in a position to verify the hypotheses of Proposition \ref{P7.1} for the $H$ constructed in Theorem \ref{T10.3}. More precisely, we will transform the canonical system one more time to obtain a new system satisfying the assumptions of Proposition \ref{P7.1}. At the end, however, it will turn out that this transformation was actually unnecessary. We know from Theorem \ref{T13.1}b) that the functions $y(x,x)$, $w(x,x)$ belong to $AC^{(2)}[0,N]$, and Proposition \ref{P14.2} implies that if $y(x_0,x_0)=0$, then $y'(x_0,x_0)\not= 0$, $w(x_0,x_0)\not= 0$. Thus $y$, $w$ have only finitely many zeros in $[0,N]$ and they do not vanish simultaneously. Also, Proposition \ref{P14.3} implies that $H_{11}w^2=H_{22}y^2$. So we may consistently define a function $r \ge 0$ by \[ r(x) = \begin{cases} \left\| y(x,x)\right\|^{-1}\sqrt{H_{11}(x)} & \text{ if }y(x,x)\not= 0 \\ \left\| w(x,x)\right\|^{-1}\sqrt{H_{22}(x)} & \text{ if }w(x,x)\not= 0 \end{cases} . \] We now need a certain regularity of $r$ (more precisely, we need that $r\in AC^{(2)}$). This can be established directly by showing that $H_{ij}\in AC^{(2)}[0,N]$. Note, however, that this statement is not obvious at this point because, for example, the second derivative $H''_{11}$, evaluated formally with the help of Proposition \ref{P14.1}, contains the third order derivative $y_{xxx}$, which need not exist. Thus it is again easier to first carry out this final part of the proof of Theorem \ref{T8.1} under the additional assumption that $\phi\in C^{\infty}$ and then pass to the general case by a limiting argument. By Propositions \ref{P14.1}, \ref{P14.2}, $y(0,0)=H_{11}(0)=1$, hence $r(0)=1$. Also, since we are assuming that $\phi\in C^{\infty}$, the function $r$ is also smooth as long as $r>0$. Fix an interval $[0,L]\subset [0,N]$, so that $r>0$ on $[0,L]$. On this interval $[0,L]$, we tranform the canonical system as follows. Let \[ t(x) = \int_0^x r(s)\, ds\quad\quad (0\le x\le L), \] let $x(t)$ be the inverse function, and define the new matrix $\widetilde{H}(t)=H(x(t))/r(x(t))$ for $0\le t \le t(L)$. Let $u(x,z)$ be the solution of the original system \[ Ju'=zHu, \quad\quad u(0,z)=\bigl( \begin{smallmatrix} 1 \\ 0 \end{smallmatrix} \bigr), \] and put $\widetilde{u}(t,z)=u(x(t),z)$. Then $\widetilde{u}$ solves the new equation \begin{equation} \label{Cantr} J\widetilde{u}' = z \widetilde{H} \widetilde{u}, \quad\quad \widetilde{u}(0,z) =\bigl( \begin{smallmatrix} 1 \\ 0 \end{smallmatrix} \bigr); \end{equation} the corresponding de~Branges spaces are related by $\widetilde{B}_t=B_{x(t)}$. Now the first line from the definition of $r$ shows that \begin{equation} \label{15.a} \widetilde{H}_{11}(t) = r(x(t))\frac{H_{11}(x(t))}{r^2(x(t))} = r(x(t)) y^2(x(t)), \end{equation} at least if $y(x(t))\not= 0$. Here, $y(x)$ is short-hand for $y(x,x)$. However, as $y$ and $w$ do not vanish simultaneously, Proposition \ref{P14.3} implies that $H_{11}(x)=0$ if $y(x)=0$, so \eqref{15.a} holds generally. Similar arguments apply to the other matrix elements: \[ \widetilde{H}(t) = r(x(t)) \begin{pmatrix} y^2(x(t)) & (yw)(x(t)) \\ (yw)(x(t)) & w^2(x(t)) \end{pmatrix} \equiv \begin{pmatrix} a^2(t) & (ab)(t) \\ (ab)(t) & b^2(t) \end{pmatrix}, \] where $a(t)=r^{1/2}(x(t))y(x(t))$, $b(t)=r^{1/2}(x(t))w(x(t))$. Now as $r>0$ on $[0,L]$, we have $a,b\in C^{\infty}[0,L]$ and \begin{align} a&(t)b'(t)-a'(t)b(t)\\ & = r^{1/2}(x(t))\left( y(x(t)) \frac{d}{dt} \left( r^{1/2}(x(t))w(x(t)) \right) -w(x(t)) \frac{d}{dt} \left( r^{1/2}(x(t))y(x(t)) \right) \right)\\ & = r(x(t)) \left( y(x(t)) \frac{d}{dt} w(x(t)) - w(x(t)) \frac{d}{dt} y(x(t)) \right)\\ & = \left( y(x)w'(x)-w(x)y'(x)\right) \bigr\|_{x=x(t)} = 1 \end{align} by Proposition \ref{P14.2}. Moreover, $a(0)=r^{1/2}(0)y(0)=1$ and $a'(0)=r^{1/2}(0)y'(0)=0$ also by Proposition \ref{P14.2}. Thus the canonical system \eqref{Cantr} satisfies the assumptions of Proposition \ref{P7.1}. So \eqref{Cantr} comes from a Schr\"odinger equation. In particular, we have the following description of $\widetilde{B}_t$ as a set: \[ \widetilde{B}_t = S_t = \left\{ F(z)=\int_0^t f(s)\cos\sqrt{z}s\, ds: f\in L_2(0,t) \right\} . \] On the other hand, $\widetilde{B}_t=B_{x(t)}=H_{x(t)}$ by Theorem \ref{T10.3}, and, again as sets, $H_{x(t)}=S_{x(t)}$ by the definition of $H_{x(t)}$. We are forced to admit that $x(t)=t$ for all $t\in [0,t(L)]$. In other words, we have shown that if $r>0$ on $[0,L]$, then $r\equiv 1$ on $[0,L]$. Also, as noted at the beginning of the argument, $r(0)=1$, so the set of $L$'s such that $r\equiv 1$ on $[0,L]$ is nonempty and closed and open in $[0,N]$, hence $r\equiv 1$ on all of $[0,N]$. So in reality, there has been no transformation, and the system \eqref{Cantr} is the system from Theorem \ref{T10.3}. This system is equivalent to a Schr\"odinger equation, that is, there exists $V\in L_1(0,N)$, so that $H_x=B_x=S_x$ (as de~Branges spaces). In particular, we may specialize to $x=N$, and we have thus proved Theorem \ref{T8.1} under the additional assumption that $\phi\in C^{\infty}$. The extension to the general case is routine. As usual, approximate $\phi'$ in $L_1(-2N,2N)$ by odd functions $\phi'_n\in C_0^{\infty} (-2N,2N)$ and put $\phi_n(x)=\int_0^x\phi'_n(t)\, dt$. Then $\phi_n \in C^{\infty}\cap \Phi_N$ for all sufficiently large $n$. As a by-product of the above argument, we have the formulae \begin{equation} \label{15.1} H_{11}(x)=y^2(x,x),\quad H_{12}(x)=y(x,x)w(x,x),\quad H_{22}(x)=w^2(x,x), \end{equation} which are valid for smooth $\phi$. So we may use \eqref{15.1} if we replace $\phi$ by $\phi_n$. Now if $n\to\infty$, all quantities converge pointwise to the right limits; for the matrix elements $H_{ij}$, this follows from Proposition \ref{P14.1}. So \eqref{15.1} holds in the general case as well. Now a glance at Theorem \ref{T13.1}b) and Proposition \ref{P14.2} suffices to verify the hypotheses of Proposition \ref{P7.1} (for the canonical system from Theorem \ref{T10.3}; no transformation is needed this time). This completes the proof of Theorem \ref{T8.1}. \section{Half line problems} In this section, we discuss half line problems, that is, operators of the form $-d^2/dx^2 + V(x)$ on $L_2(0,\infty)$. We assume, as usual, that $V\in L_{1,loc}([0,\infty))$. Our presentation in this section will be less detailed. Of course, in a sense, half line problems are contained in our previous treatment because we may analyze the problem on $(0,\infty)$ by analyzing it on $(0,N)$ for every $N$. More precisely, Theorems \ref{T4.1}, \ref{T4.2}, \ref{T8.1}, and \ref{T8.2}, applied with variable $N>0$, give a one-to-one correspondence between functions $\phi\in \bigcap_{N>0} \Phi_N$ and locally integrable potentials $V:[0,\infty) \to \mathbb R$. Here we say that $\phi\in \bigcap_{N>0} \Phi_N$ if the restriction of $\phi$ to $[-2N,2N]$ belongs to $\Phi_N$ for every $N>0$. The uniqueness assertions from Theorem \ref{T8.2} make sure that there are no consistency problems. For example, the following holds: If $N_1<N_2$, $\phi_{N_i}\in \Phi_{N_i}$ and $\phi_{N_1}=\phi_{N_2}$ on $[-2N_1,2N_1]$, then, by Theorem \ref{T8.2}b), the corresponding potentials satisfy $V_1=V_2$ on $(0,N_1)$. This local treatment looks most natural and satisfactory, but it is also reasonable to ask for conditions that characterize the spectral measures of half line problems. In particular, this will relate our results to the Gelfand-Levitan characterization of spectral data. Given a potential $V\in L_{1,loc}([0,\infty))$, we call a positive Borel measure $\rho$ on $\mathbb R$ a {\it spectral measure} of the half line problem if the de~Branges spaces $S_N$ are isometrically contained in $L_2(\mathbb R, d\rho)$ for all $N>0$. In other words, we demand that \[ \\|F\\|_{S_N}^2 = \int \|F(\lambda)\|^2 \, d\rho(\lambda) \quad\quad\forall F\in \bigcup_{N>0} S_N . \] Borrowing the terms commonly used for discrete problems, we may also say that the spectral measures are precisely the solutions of a (continuous version of a) certain moment problem. By Theorem \ref{T3.2}b), the measures from Weyl theory are indeed spectral measures in this sense. In particular, given a potential $V\in L_{1,loc}([0,\infty))$, spectral measures always exist. The spectral measure is unique precisely if $V$ is in the limit point case at infinity. Indeed, if $V$ is in the limit circle case, any choice of a boundary condition at infinity yields a spectral measure, and there are many others. For instance, one can form convex combinations or, more generally, averages of these measures. Conversely, if $V$ is in the limit point case, then uniqueness of the spectral measure follows from the Nevanlinna type parametrization of the measures $\mu$ for which $L_2(\mathbb R, d\mu)$ isometrically contains $S_N$ together with the fact that the Weyl circles shrink to points. The Gelfand-Levitan conditions characterize the spectral measures of half line problems. We now want to demonstrate that such a characterization also follows in a rather straightforward way from our direct and inverse spectral theorems (Theorems \ref{T4.1}, \ref{T4.2}, \ref{T8.1}, and \ref{T8.2}) and some standard material. For a positive Borel measure $\rho$, introduce the signed measure $\sigma=\rho-\rho_0$ (where $\rho_0$ is the measure for zero potential from \eqref{mrho0}), and consider the following two conditions. \begin{enumerate} \item If $F\in \bigcup_{N>0} S_N$, $\int \|F(\lambda)\|^2 \, d\rho(\lambda) =0$, then $F\equiv 0$. \item For every $g\in C_0^{\infty}(\mathbb R)$, the integral $\int d\sigma(\lambda)\int dx\, g(x) \cos\sqrt{\lambda}x$ converges absolutely: \[ \int_{-\infty}^{\infty} d\|\sigma\|(\lambda) \left\| \int_{-\infty}^{\infty} dx\, g(x) \cos\sqrt{\lambda}x \right\| < \infty. \] Moreover, there exists an even, real valued function $\phi\in AC^{(1)}(\mathbb R)$ with $\phi(0)=0$, so that \[ \int d\sigma(\lambda)\int dx\, g(x) \cos\sqrt{\lambda}x = \int g(x) \phi(x)\, dx \] for all $g\in C_0^{\infty}(\mathbb R)$. \end{enumerate} The set of $\rho$'s satisfying these two conditions will be denoted by $GL$, for Gelfand-Levitan. We do {\it not} require that $\bigcup S_N \subset L_2(\mathbb R, d\rho)$, so at this point, we cannot exclude the possibility that for fixed $\rho\in GL$, there exists $F\in \bigcup S_N$ with $\int \|F\|^2\, d\rho = \infty$. However, we will see in moment that actually there are no such $F$'s. Our definition of $GL$ is inspired by Marchenko's treatment of the Gelfand-Levitan theory (see especially \cite[Theorem 2.3.1]{Mar}). Note, however, that Marchenko does not regularize by subtracting $\rho_0$, but by using the analog of the function $\psi$ from Sect.\ 13 instead of $\phi$. Moreover, he uses a space of test functions tailor made for the discussion of Schr\"odinger operators, and he assumes continuity of the potential. \begin{Theorem} \label{T17.1} a) For every $\rho\in GL$, there exists a unique $V\in L_{1,loc}([0,\infty))$ so that $\rho$ is a spectral measure of $-d^2/dx^2+V(x)$.\\ b) If $\rho$ is a spectral measure of $-d^2/dx^2+V(x)$, then $\rho\in GL$. \end{Theorem} \begin{proof} a) A computation using condition 2.\ from the definition of $GL$ shows that for every $f\in C_0^{\infty}(\mathbb R)$, the function \[ F(\lambda)=\int f(x)\cos\sqrt{\lambda}x \, dx \] belongs to $L_2(\mathbb R, d\rho)$ and \[ \\|F\\|_{L_2(\mathbb R,d\rho)}^2 = \\|f\\|_{L_2(\mathbb R)}^2 + \int\!\!\!\int ds\, dt\, \overline{f(s)}f(t) \frac{1}{2}\left( \phi(s-t) + \phi(s+t) \right) . \] In particular, it follows that the identity \begin{equation} \label{17-1} \\|F\\|_{L_2(\mathbb R,d\rho)}^2 = \langle f, (1+\mathcal{K}_{\phi}) f \rangle_{L_2(0,N)} \end{equation} holds if $f\in C_0^{\infty}(0,N)$. By a density argument and the fact that norm convergent sequences have subsequences that converge almost everywhere, condition 1.\ now implies that $1+\mathcal{K}_{\phi}>0$ as an operator on $L_2(0,N)$. So $\phi\in\Phi_N$, and from Theorem \ref{T8.1}, we thus get $V\in L_1(0,N)$, so that \[ \\|F\\|_{S_N}^2 = \langle f, (1+\mathcal{K}_{\phi}) f \rangle_{L_2(0,N)} \] for all $F\in S_N$. Hence $\\|F\\|_{S_N}=\\|F\\|_{L_2(\mathbb R,d\rho)}$ for all $F$ as above with $f\in C_0^{\infty}(0,N)$. Again by a density argument, this relation actually holds on all of $S_N$. The whole argument works for arbitrary $N$, and, as observed above, Theorem \ref{T8.2}b) implies that there are no consistency problems. We obtain a locally integrable potential $V$ on $[0,\infty)$, so that $\\|F\\|_{S_N}=\\|F\\|_{L_2(\mathbb R,d\rho)}$ for all $F\in \bigcup S_N$. In other words, $\rho$ is a spectral measure of $-d^2/dx^2+V(x)$. Uniqueness of $V$ is clear because \eqref{17-1} forces us to take $V$ on $(0,N)$ so that the norm on $S_N$ is the one determined by $\mathcal{K}_{\phi}$; so once $\phi$ is given, there is no choice by Theorem \ref{T8.2}b) again. But clearly $\phi$ is uniquely determined by the measure $\sigma$ and hence also by $\rho$. b) Property 1.\ is obvious from the equality $\\|F\\|_{L_2(\mathbb R,d\rho)}=\\|F\\|_{S_N}$. To establish property 2., we use the well known estimates (\cite[Sect.\ 2.4]{Mar}; compare also \cite{GeSi}) \[ \lim_{L\to\infty} \rho((-\infty,-L)) e^{a\sqrt{L}}=0 \quad\forall a>0,\quad\quad \int \frac{d\rho(\lambda)}{1+\lambda^2} < \infty. \] As $\|\sigma\|\le \rho + \rho_0$, the absolute convergence of $\int d\sigma(\lambda)\int dx\, g(x) \cos\sqrt{\lambda}x$ for $g\in C_0^{\infty}$ follows. Moreover, this integral depends continuously on $g\in \mathcal{D}=C_0^{\infty}(\mathbb R)$ and hence defines a distribution. Now let $f_1,f_2\in C_0^{\infty}(\mathbb R)$ be even functions. Then \[ F_i(z)\equiv \int_{-\infty}^{\infty} f_i(x)\cos\sqrt{z}x\, dx = 2 \int_0^{\infty} f_i(x)\cos\sqrt{z}x\, dx \in \bigcup S_N, \] and by a calculation, \begin{align} [F_1,F_2]_{S_N} & = \langle F_1(\lambda), F_2(\lambda) \rangle_{L_2(\mathbb R,d\rho)}\\ & = 4 \langle f_1, f_2 \rangle_{L_2(0,\infty)} + \int d\sigma(\lambda) \int_{-\infty}^{\infty} dx\, g(x) \cos\sqrt{\lambda}x, \end{align} where $N$ must be chosen so large that $F_1,F_2\in S_N$ and \begin{equation} \label{17.1} g(x) \equiv \frac{1}{2} \int_{-\infty}^{\infty} \overline{f_1\left( \frac{x+y}{2} \right)} f_2\left( \frac{x-y}{2} \right)\, dy. \end{equation} On the other hand, we have that \[ [F_1,F_2]_{S_N} = 4\langle f_1, (1+\mathcal{K}_{\phi}) f_2\rangle = 4 \langle f_1, f_2 \rangle_{L_2(0,\infty)} + \int_{-\infty}^{\infty} g(x)\phi(x)\, dx, \] where $\phi\in\bigcap\Phi_N$ is the function from Theorem \ref{T4.2}. Hence \begin{equation} \label{17.2} \int d\sigma(\lambda) \int dx\, g(x) \cos\sqrt{\lambda}x = \int g(x)\phi(x)\, dx \end{equation} for every $g$ that is of the form \eqref{17.1} with even $f_i\in C_0^{\infty} (\mathbb R)$. We claim that this set of $g$'s is rich enough to guarantee the validity of \eqref{17.2} for arbitrary $g\in C_0^{\infty}(\mathbb R)$. To see this, one can proceed as follows. By a change of variables, \eqref{17.1} becomes \[ g(x) = \int \overline{f_1(x-u)} f_2(u)\, du = \left( \overline{f_1} * f_2 \right) (x). \] We can take $\overline{f_1}$ as an approximate identity, that is, $\overline{f_1(x)}=n\varphi(nx)$, where $\int\varphi =1$ and let $n\to \infty$. It follows that the set of $g$'s of the form \eqref{17.1} is dense (in the topology of $\mathcal{D}=C_0^{\infty}(\mathbb R)$) in the set of even test functions. Moreover, for odd test functions $g$, \[ \int d\sigma(\lambda) \int dx\, g(x)\cos\sqrt{\lambda}x = \int g(x)\phi(x)\, dx = 0. \] By combining these facts, we deduce that \eqref{17.2} holds for every $g\in C_0^{\infty}(\mathbb R)$, as claimed. \end{proof} We have no uniqueness statement in Theorem \ref{T17.1}b): for a given $V$, there may be many $\rho$'s. However, this only comes from the fact that we have insisted on working with spectral measures. Clearly, in addition to the bijection $V\leftrightarrow\phi$ between $L_{1,loc}$ and $\bigcap\Phi_N$ discussed at the beginning of this section, we also have a one-to-one correspondence between potentials $V$ and, let us say, distributions \[ g \mapsto \int d\sigma(\lambda) \int dx\, g(x) \cos\sqrt{\lambda}x . \] However, this distribution determines the measure $\sigma$ (and thus $\rho$) only if (in fact, precisely if) we have limit point case at infinity. This remark again confirms our claim that in inverse spectral theory, the function $\phi$ is the more natural object. \section{Concluding remarks} The proof of Theorem \ref{T8.1} has indicated at least two methods of reconstructing the potential $V$ from the spectral data $\phi$. One consists of solving the integral equation for $y$ (say), \[ y(x,t) + \int_0^x K(t,s)y(x,s)\, ds = 1 . \] By \eqref{15.1} and Proposition \ref{P7.1}, $V=y''w'-w''y'$, and since $yw''=wy''$ and $yw'-y'w=1$, we can compute the potential $V$ from this solution $y$ by $V(x)=y''(x,x)/y(x,x)$. This way of finding $V$ is quite similar to the Gelfand-Levitan procedure, where one solves the integral equation \[ z(x,t) + \int_0^x K(t,s) z(x,s)\, ds = -K(x,t) \] for $z$ and computes the potential as $V(x)=z'(x,x)$ (see \cite[Chapter 2]{Lev}). Loosely speaking, our function $y(x,t)$ is a two-point version of the solution $y(x)$ to $-y''+Vy=0$ with the initial values $y(0)=1$, $y'(0)=0$. Our proof of Theorem \ref{T8.1} also admits a second, completely different interpretation. Namely, the integral equations for $y$, $w$ may be viewed as an auxiliary tool needed to show that the canonical system that was constructed with the aid of Theorem \ref{T6.3} is equivalent to a Schr\"odinger equation. In other words, if one has a constructive proof of Theorem \ref{T6.3}, one may apply the corresponding reconstruction procedure and one automatically obtains a canonical system that satisfies the hypotheses of Proposition \ref{P7.1}, possibly after some modifications: deletion of an initial singular interval, introduction of a new independent variable to match the de~Branges spaces and finally a transformation of the type $H\to H_c$, as in the proof of Theorem \ref{T10.3}. (Actually, this last transformation does not affect $H_{11}(x)$ and, by the above, is thus not needed to compute $V(x)$.) Put differently, this means that work on constructive inverse spectral theory of canonical systems always has implications in the inverse spectral theory of Schr\"odinger operators as well. In \cite{dB2}, Theorem \ref{T6.3} is proved as follows. The first step is to approximate the de~Branges function $E$ by polynomial de~Branges functions $E_n$. The construction of (discrete) canonical systems for $E_n$ can be carried out using elementary methods only (for instance, orthogonalization of polynomials). Finally, one passes to the limit $n\to\infty$. See also \cite{Sakh,Yud} for completely different views on Theorem \ref{T6.3}. As a final remark, we would like to point out that the transformation from a Schr\"odinger equation to a canonical system regularizes the coefficients. Indeed, $H\in AC^{(2)}$, while in general, one only has $V\in L_1$. This effect will be particularly convenient if one considers Schr\"odinger operators with, let us say, measures or even more singular distributions as potentials. 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https://dlmf.nist.gov/1.15.E3.tex	nist.gov	CC-MAIN-2022-21	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2022-21/segments/1652662545326.51/warc/CC-MAIN-20220522094818-20220522124818-00222.warc.gz	262,414,711	695	\[\lim_{x\to 1-}\sum^{\infty}_{n=0}a_{n}x^{n}=s.\]
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https://git.ffmpeg.org/gitweb/ffmpeg.git/blob_plain/36e6842aa63f9cbad3399b26b871589d1258ee43:/doc/libswresample.texi	ffmpeg.org	CC-MAIN-2020-24	application/x-texinfo	application/x-tex	crawl-data/CC-MAIN-2020-24/segments/1590347415315.43/warc/CC-MAIN-20200601071242-20200601101242-00543.warc.gz	354,624,978	1,474	\input texinfo @c -- texinfo -- @settitle Libswresample Documentation @titlepage @center @titlefont{Libswresample Documentation} @end titlepage @top @contents @chapter Description @c man begin DESCRIPTION The libswresample library performs highly optimized audio resampling, rematrixing and sample format conversion operations. Specifically, this library performs the following conversions: @itemize @item @emph{Resampling}: is the process of changing the audio rate, for example from a high sample rate of 44100Hz to 8000Hz. Audio conversion from high to low sample rate is a lossy process. Several resampling options and algorithms are available. @item @emph{Format conversion}: is the process of converting the type of samples, for example from 16-bit signed samples to unsigned 8-bit or float samples. It also handles packing conversion, when passing from packed layout (all samples belonging to distinct channels interleaved in the same buffer), to planar layout (all samples belonging to the same channel stored in a dedicated buffer or "plane"). @item @emph{Rematrixing}: is the process of changing the channel layout, for example from stereo to mono. When the input channels cannot be mapped to the output streams, the process is lossy, since it involves different gain factors and mixing. @end itemize Various other audio conversions (e.g. stretching and padding) are enabled through dedicated options. @c man end DESCRIPTION @chapter See Also @ifhtml @url{ffmpeg.html,ffmpeg}, @url{ffplay.html,ffplay}, @url{ffprobe.html,ffprobe}, @url{ffserver.html,ffserver}, @url{ffmpeg-resampler.html,ffmpeg-resampler}, @url{libavutil.html,libavutil} @end ifhtml @ifnothtml ffmpeg(1), ffplay(1), ffprobe(1), ffserver(1), ffmpeg-resampler(1), libavutil(3) @end ifnothtml @include authors.texi @ignore @setfilename libswresample @settitle audio resampling library @end ignore @bye
http://blog.ac-versailles.fr/jpgoualard/public/2nde-2016-2017-cont-probas.tex	ac-versailles.fr	CC-MAIN-2019-47	text/x-tex	application/x-tex	crawl-data/CC-MAIN-2019-47/segments/1573496664567.4/warc/CC-MAIN-20191112024224-20191112052224-00303.warc.gz	24,529,776	3,220	\documentclass[12pt] {article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath,amssymb,graphicx,multicol,mathrsfs, fancyhdr,enumerate,fourier,eurosym,alterqcm,enumerate,tabularx,variations,numprint} \usepackage[dvips]{color} \usepackage{bclogo} \usepackage{pst-plot,pst-tree,pstricks,pst-node,pstricks-add,pst-math,pst-xkey,pst-eucl} \usepackage{paralist} \usepackage{tabto} \usepackage[francais]{babel} \everymath{\displaystyle} %\usepackage[colorlinks=true,pdfstartview=FitV,linkcolor=blue,citecolor=blue,urlcolor=blue]{hyperref} \textwidth 19cm \textheight 26cm \hoffset -1,4cm \voffset -3.7cm \oddsidemargin 0pt \renewcommand{\thesubsection}{\textcolor{blue}{\Roman{subsection}}} \renewcommand{\thesubsubsection}{\textcolor{blue}{\Roman{subsection}}.\textcolor{blue}{\arabic{subsubsection}}} \pagestyle{fancy} % pour le pied de page central \cfoot{Page \thepage/\pageref{fin}} \begin{document} %\tableofcontents \begin{center}\section{\textcolor{red}{2nde : contrôle sur les probabilités\\ 1 heure}}\end{center} \subsection{} Soit $A$ et $B$ deux événements tels que : \begin{enumerate}[$\bullet$] \item $p(A)=0,7$ \item $p(B)=0,5$ \item $p(A\cap B)=0,3$ \end{enumerate} \begin{enumerate} \item Calculer \NumTabs{3} \begin{inparaenum} \item $p\left(\overline{A}\right)$ \tab\item $p(A\cup B)$ \tab\item $p\left(\overline{A}\cap B\right)$ \end{inparaenum} \medskip \item A et B sont-ils incompatibles ? Expliquer ! \end{enumerate} \subsection{} On considère deux événements $V$ et $F$ tels que : \NumTabs{3} \begin{inparaenum}[a)] \item $p(V)=0,4$ \tab\item $p(F)=0,3$ \tab \item $p(V\cup F)=0,8$ \end{inparaenum} \bigskip Un élève prétend que ce n'est pas possible. Confirmer ou infirmer sa déclaration, en justifiant la réponse. \subsection{\textcolor{blue}{Résultats au bac}} On considère un établissement scolaire de \numprint{2000} élèves, regroupant des collégiens et des lycéens. \begin{itemize} \item 19\:\% de l'effectif total est en classe Terminale; \item parmi ces élèves de Terminale, 55\:\% sont des filles; \item le taux de réussite au baccalauréat dans cet établissement est de 85\:\%; \item parmi les candidats ayant échoué, la proportion des filles a été de $\dfrac{ 8}{19}$. \end{itemize} \begin{enumerate} \item Recopier et compléter le tableau des effectifs regroupant les résultats au baccalauréat : \begin{tabularx}{\linewidth}{\|l\|{4}{>{\centering \arraybackslash}X\|}} \hline Éleves & Garçons & Filles & TOTAL \\ \hline Réussite & & & \\ \hline Échec & & 24 & \\ \hline TOTAL & & & 380 \\ \hline \end{tabularx} Après la publication des résultats, on choisit au hasard un élève parmi l'ensemble des élèves de Terminale. \\ On considère les événements suivants : \begin{itemize} \item $G$: \og l'élève est un garçon \fg; \item $R$: \og l'élève a eu son baccalauréat \fg. \end{itemize} Dans la suite, on donnera les résultats sous forme décimale, arrondis à $10^{-2}$ près. \item Définir les événements suivants par une phrase :\\ \NumTabs{2} \begin{inparaenum}[(a)] \item $R$ \tab\item $\overline{G}\cap R $ \end{inparaenum} \item Calculer les probabilités des événements suivants : \NumTabs{2} \begin{inparaenum}[(a)] \item $\overline{R}$ \tab \item $\overline{G}\cup \overline{R}$ \end{inparaenum} \item On choisit un élève au hasard parmi les bacheliers. Quelle est la probabilité que ce soit une fille? \end{enumerate} \subsection{\textcolor{blue}{Tirage successif avec remise}} On tire au hasard une carte d'un jeu de 32 cartes, on la note, puis on la remet dans le jeu avant d'en tirer une seconde. \emph{On rappelle que les 32 cartes d'un jeu de 2 cartes sont réparties en quatre couleurs (trèfle, carreau, cœur et pique) ; les cartes sont appelées 7~;~8~;~9~;~10~;~Valet~;~Dame~;~Roi et As}. \begin{enumerate} \item Est-ce une situation d'équiprobabilité ? Pourquoi ? \item Combien y a-t-il d'issues ? \item Calculer la probabilité de : \begin{enumerate} \item tirer 2 c\oe urs ; \item ne pas tirer de c\oe ur ; \item tirer exactement 1 c\oe ur ; \item tirer deux fois la même carte ; \item tirer deux cartes différentes ; \item tirer le roi de c\oe ur. \end{enumerate} \end{enumerate} \subsection{} \begin{multicols}{2} \setlength{\columnseprule}{1pt} \setlength{\columnsep}{2 cm} \begin{enumerate} \item Sur le graphique ci-contre, tracer les représentations graphiques $\mathscr{C}_f$ et $\mathscr{C}_g$ des fonctions :\\ $f:x\mapsto f(x)=x^2$ et $g:x\mapsto g(x)= -x+6$. \item Combien les deux courbes ont-elles de points d'intersection ? \\ Quelles semblent être leurs abscisses ? \item Montrer que, pour tout $x\in\mathbb{R}$, on a : \\ \begin{center} $x^2+x-6=(x-2)(x+3)$. \end{center} \item Résoudre l'équation $x^2+x-6=0$ \item Que peut-on en déduire pour les courbes $\mathscr{C}_f$ et $\mathscr{C}_g$ ? \end{enumerate}\begin{center} \newrgbcolor{qqwuqq}{0. 0.39215686274509803 0.} \newrgbcolor{ccqqqq}{0.8 0. 0.} \psset{xunit=1.0cm,yunit=0.75cm,algebraic=true,dimen=middle,dotstyle=o,dotsize=5pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25} \begin{pspicture}(-4.2,-4.)(4.2,12.) \psaxes[labelFontSize=\scriptstyle,xAxis=true,yAxis=true,Dx=1.,Dy=1.,ticksize=-2pt 0,subticks=2,linewidth=2pt]{->}(0,0)(-4.,-4.5)(4.,12.5) \psgrid[subgriddiv=1,gridwidth=.7pt,gridlabels=0](-4.,-4.)(4.,12.) \uput[ul](0,0){0} %\psplot[linewidth=1.2pt,linecolor=qqwuqq,plotpoints=200]{-4.0}{3.0}{x^(2.0)} %\psplot[linewidth=1.2pt,linecolor=ccqqqq,plotpoints=200]{-4.0}{3.0}{6.0-x} \end{pspicture} \end{center} \end{multicols} \label{fin} \end{document}
http://ofap.ulstu.ru/resources/864/three_certificate.tex?association=resources&parent_scaffold=fremantle%2Fguest%2Fresource_types&resource_type_id=26	ulstu.ru	CC-MAIN-2023-06	text/x-tex	text/x-matlab	crawl-data/CC-MAIN-2023-06/segments/1674764500151.93/warc/CC-MAIN-20230204173912-20230204203912-00456.warc.gz	33,074,101	2,704	%% LaTeX2e-файл %% Создано движком Фримантл (https://gitlab.com/korobkov/fremantle) %% в 2023-02-04T21:48:59+04:00 %% Фримантл — Свободный движок репозитория электронных ресурсов %% Copyright © 2009—2018 Лаборатория «Автоматизированные системы» [email protected], УлГТУ %% %% Фримантл is free software: you can redistribute it and/or modify %% it under the terms of the GNU Affero General Public License as published by %% the Free Software Foundation, either version 3 of the License, or %% (at your option) any later version. %% %% Фримантл is distributed in the hope that it will be useful, %% but WITHOUT ANY WARRANTY; without even the implied warranty of %% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the %% GNU Affero General Public License for more details. %% %% You should have received a copy of the GNU Affero General Public License %% along with Фримантл. If not, see <https://www.gnu.org/licenses/>. \documentclass[a4paper,fontsize=18pt]{scrartcl} \usepackage[landscape,left=2cm,right=2cm,top=1cm,bottom=1.5cm,bindingoffset=0cm]{geometry} \usepackage{graphicx, polyglossia, pst-barcode, tabu, wallpaper} \setmainfont{Liberation Serif} \setmonofont{Liberation Mono} \setsansfont{Liberation Sans} \defaultfontfeatures{Scale=MatchLowercase, Mapping=tex-text} \setdefaultlanguage[spelling=modern]{russian} \setotherlanguage{english} \graphicspath{{/srv/http/ofap/releases/20180921145927/app/assets/images/fremantle/three_certificate/}} \CenterWallPaper{1.00}{border.png} \begin{document} \begin{hyphenrules}{nohyphenation} \begin{center} \thispagestyle{empty} {\Large ОФАП УОЦ НИТ} \bigskip\bigskip \begin{tabu}{ b{5cm} >{\centering}b{19cm} } \includegraphics [height=4.5cm]{logo.png} & Ульяновский государственный технический университет Ульяновский областной центр новых информационных технологий Областной фонд алгоритмов и программ \bigskip {\Huge \textit{Свидетельство №\,864}} \bigskip о регистрации программно-информационного продукта \end{tabu} \bigskip \begin{tabu}{ b{5cm} >{\raggedright \itshape}p{19cm} }\hline \\ Наименование: & \textbf{Износостойкие покрытия: свойства, структура, технологии получения} \\ Тип: & Методические указания \\ URI: & \textbf{http://ofap.ulstu.ru/864} \\ Авторы: & Циркин Алексей Валерьевич -- Кафедра «Металлорежущие станки и инструменты» (УлГТУ/МФ) \\ Дата регистрации: & 17 июня 2005 г. \\ \end{tabu} \vfill \begin{tabu} to 24cm { b{2cm} l X >{\itshape}l } & Проректор по научной работе УлГТУ & & \textit{Н.Г.\,Ярушкина} \\ & Директор Ульяновского областного центра НИТ & & \textit{К.В.\,Святов} \\ \psbarcode{2005-06-17 http://ofap.ulstu.ru/864}{format=compact layers=4}{azteccode} \rowfont{\small} & Администратор базы данных ОФАП & & \textit{Ю.А.\,Лапшов} \\ \end{tabu} \end{center} \end{hyphenrules} \clearpage \end{document}
https://ctan.math.washington.edu/tex-archive/info/examples/PSTricks_7_de/13-05-1.ltx	washington.edu	CC-MAIN-2022-27	text/x-tex	text/x-matlab	crawl-data/CC-MAIN-2022-27/segments/1656103329963.19/warc/CC-MAIN-20220627073417-20220627103417-00707.warc.gz	228,863,840	1,591	%% %% Ein Beispiel der DANTE-Edition %% %% 7. Auflage %% %% Beispiel 13-05-1 auf Seite 179. %% %% Copyright (C) 2016 Herbert Voss %% %% It may be distributed and/or modified under the conditions %% of the LaTeX Project Public License, either version 1.3 %% of this license or (at your option) any later version. %% %% See http://www.latex-project.org/lppl.txt for details. %% %% %% ==== % Show page(s) 1 %% %% \documentclass[]{exaarticle} \pagestyle{empty} \setlength\textwidth{193.16928pt} \setlength\parindent{0pt} \usepackage{pstricks,pst-node,pst-xkey} \makeatletter \define@boolkey[psset]{}[Pst@]{zeigeSP}[true]{}% Schwerpunkt markieren? \psset{zeigeSP=true} % Vorgabe \def\Schwerpunkt{\pst@object{Schwerpunkt}} \def\Schwerpunkt@i(#1)(#2)(#3)#4{% \pst@getcoor{#1}\pst@tempA% Punkt A % hole Kordinaten als x y \pst@getcoor{#2}\pst@tempB% Punkt B % " \pst@getcoor{#3}\pst@tempC% Punkt C % " \begin@SpecialObj % Parameter setzen \pnode(!% % setze Knoten \pst@tempA /YA exch \pst@number\psyunit div def /XA exch \pst@number\psxunit div def % x y in user Koordinaten \pst@tempB /YB exch \pst@number\psyunit div def /XB exch \pst@number\psxunit div def \pst@tempC /YC exch \pst@number\psyunit div def /XC exch \pst@number\psxunit div def XA XB XC add add 3.0 div % xSP YA YB YC add add 3.0 div % ySP ){#4} % #5 = Knotenname \ifPst@zeigeSP\qdisk(#4){2pt}\fi% markieren? \end@SpecialObj% \ignorespaces} \makeatother %StartShownPreambleCommands \usepackage{pstricks,pst-node,pst-xkey} % ... Hier obigen Code einf├╝gen %StopShownPreambleCommands \begin{document} \begin{pspicture}[showgrid](4,4) \psset{linewidth=2pt} \pspolygon[linecolor=red](0,0)(2,4)(4,0)% \Schwerpunkt[zeigeSP,linecolor=red](0,0)(2,4)(4,0){SP1}% \pnode(0,0){A}\pnode(0,4){B}\pnode(4,2){C}% \pspolygon[linecolor=blue](A)(B)(C)% \Schwerpunkt(A)(B)(C){SP2}% {\psset{linecolor=blue}\qdisk(SP2){2pt}} \ncline[linewidth=0.2pt]{<->}{SP1}{SP2}% \end{pspicture} \end{document}
https://git.rockbox.org/cgit/rockbox.git/plain/manual/platform/ipodvideo.tex?id=42257940fb69f3cc8e552bcafe8a27ce1696b708	rockbox.org	CC-MAIN-2022-33	text/plain	application/x-tex	crawl-data/CC-MAIN-2022-33/segments/1659882571086.77/warc/CC-MAIN-20220809185452-20220809215452-00113.warc.gz	276,894,607	899	\def\UseOption{ipodvideo} \edef\UseOption{\UseOption,HAVE_LCD_BITMAP} \edef\UseOption{\UseOption,CONFIG_RTC} \newcommand{\playerman}{Apple} \newcommand{\playertype}{iPod Video} \newcommand{\playerlongtype}{\playertype} \newcommand{\genericimg}{320x240x16} \newcommand{\dap}{player}
http://porocila.imfm.si/2014/rac/clani/plestenjak.tex	imfm.si	CC-MAIN-2020-29	text/x-tex	application/x-tex	crawl-data/CC-MAIN-2020-29/segments/1593657142589.93/warc/CC-MAIN-20200713033803-20200713063803-00355.warc.gz	104,292,643	1,903	\clan {Bor Plestenjak} %-------------------------------------------------------- % A. objavljene znanstvene monografije %-------------------------------------------------------- %\begin{skupina}{A} %\disertacija % {NASLOV} % {UNIVERZA} % {FAKULTETA} % {ODDELEK} % {KRAJ} {DRZAVA} {LETO} %\magisterij % {NASLOV} % {UNIVERZA} % {FAKULTETA} % {ODDELEK} % {KRAJ} {DRZAVA} {LETO} %\monografija % {AVTORJI} % {NASLOV} % {ZALOZBA} % {KRAJ} {DRZAVA} {LETO} %\end{skupina} % Ni podatkov za to sekcijo %-------------------------------------------------------- % B. raziskovalni clanki sprejeti v objavo v znanstvenih % revijah in v zbornikih konferenc %-------------------------------------------------------- %\begin{skupina}{B} %\sprejetoRevija % {AVTORJI} % {NASLOV} % {REVIJA} %\sprejetoZbornik % {AVTORJI} % {NASLOV} % {KONFERENCA} % {KRAJ} {DRZAVA} {MESEC} {LETO} %\end{skupina} % Ni podatkov za to sekcijo %-------------------------------------------------------- % C. raziskovalni clanki objavljeni v znanstvenih revijah % in v zbornikih konferenc %-------------------------------------------------------- %\begin{skupina}{C} %\objavljenoRevija % {AVTORJI} % {NASLOV} % {REVIJA} {LETNIK} {LETO} {STEVILKA} {STRANI} %\objavljenoZbornik % {AVTORJI} % {NASLOV} % {KONFERENCA} % {KRAJ} {DRZAVA} {MESEC} {LETO} % {ZBORNIK} {STRANI} %\end{skupina} \begin{skupina}{C} \objavljenoRevija % 1.01: {\bf 1}. MUHI\v{C}, Andrej, PLESTENJAK, Bor. A method for computing all values $\lambda$ such that $A + \lambda B$ has a multiple eigenvalue. %{\it Linear Algebra and its Applications}, 2014, vol. 440, str. 345-359. $[$COBISS.SI-ID 16862553$]$\\ % POZOR: Bibliografija2014A.tex > 2014\rac\clani\plestenjak.tex 8699/80: Ne najdem podatka {STEVILKA} {A.~Muhi\v{c}, \crta} {A method for computing all values $\lambda$ such that $A + \lambda B$ has a multiple eigenvalue} {Linear Algebra Appl.} {440} {2014} {} {345--359} \end{skupina} %-------------------------------------------------------- % D. urednistvo v znanstvenih revijah in zbornikih % znanstvenih konferenc %-------------------------------------------------------- %\begin{skupina}{D} %\urednikRevija % {OPIS} % {REVIJA} %\urednikZbornik % {OPIS} % {KONFERENCA} % {KRAJ} {DRZAVA} {MESEC} {LETO} %\end{skupina} % Ni podatkov za to sekcijo %-------------------------------------------------------- % E. organizacija mednarodnih in domacih znanstvenih % srecanj %-------------------------------------------------------- %\begin{skupina}{E} %\organizacija % {OPIS} % {KONFERENCA} % {KRAJ} {DRZAVA} {MESEC} {LETO} %\end{skupina} % Ni podatkov za to sekcijo %-------------------------------------------------------- % F. vabljena predavanja na tujih ustanovah in % mednarodnih konferencah %-------------------------------------------------------- \begin{skupina}{F} %\predavanjeUstanova % {NASLOV} % {OPIS} % {USTANOVA} % {KRAJ} {DRZAVA} {MESEC} {LETO} \predavanjeKonferenca {Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems} {vabljeno predavanje} {Structured Matrices and Tensors: Analysis, Algorithms and Application} {Taipei} {Tajvan} {december} {2014} \end{skupina} % Ni podatkov za to sekcijo %-------------------------------------------------------- % G. aktivne udelezbe na mednarodnih in domacih % konferencah %-------------------------------------------------------- \begin{skupina}{G} \konferenca {Numerical methods for nonlinear two-parameter eigenvalue problems} {Manchester Workshop on Nonlinear Eigenproblems} {Manchester} {Velika Britanija} {april} {2014} \konferenca {Computing all values $\lambda$ such that $A + \lambda B$ has a multiple eigenvalue} {Householder Symposium XIX} {Spa} {Belgija} {junij} {2014} \end{skupina} % Ni podatkov za to sekcijo %-------------------------------------------------------- % H. strokovni clanki %-------------------------------------------------------- %\begin{skupina}{H} %\clanekRevija % {AVTORJI} % {NASLOV} % {REVIJA} {LETNIK} {LETO} {STEVILKA} {STRANI} %\clanekZbornik % {AVTORJI} % {NASLOV} % {KONFERENCA} % {KRAJ} {DRZAVA} {MESEC} {LETO} % {ZBORNIK} {STRANI} %\end{skupina} % Ni podatkov za to sekcijo %-------------------------------------------------------- % I. razno %-------------------------------------------------------- %\begin{skupina}{I} %\razno % {OPIS} %\end{skupina} % Ni podatkov za to sekcijo %-------------------------------------------------------- % tuji gosti %-------------------------------------------------------- %\begin{seznam} %\gost {IME} {TRAJANJE} {USTANOVA} {KRAJ} {DRZAVA} {MESEC} {LETO} {POVABILO} %\end{seznam} %-------------------------------------------------------- % gostovanja %-------------------------------------------------------- %\begin{seznam} %\gostovanje {Bor Plestenjak} {3 mesece} {Technische Universiteit Eindhoven} {} {Nizozemska} {marec/junij} {2014} %\end{seznam}
http://josephus.hsutx.edu/classes/all/latexhelp/demos/floatfig.tex	hsutx.edu	CC-MAIN-2017-39	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2017-39/segments/1505818690340.48/warc/CC-MAIN-20170925055211-20170925075211-00060.warc.gz	168,999,240	737	% floatfig.tex \documentclass{article} \usepackage{graphics} \begin{document} \begin{figure}[!ht] \centering\includegraphics{2^4cay.eps} \caption{A 4-Dimensional Hypercube Labelled as a Cayley Graph} \label{fig:2^4cay} \end{figure} \end{document}
http://www.mat.uniroma2.it/~difiore/ese.tex	uniroma2.it	CC-MAIN-2022-40	text/x-tex	application/x-tex	crawl-data/CC-MAIN-2022-40/segments/1664030335326.48/warc/CC-MAIN-20220929065206-20220929095206-00058.warc.gz	95,234,685	24,343	\documentclass[10pt,a4paper]{article} \usepackage{amssymb} % for \mathbb (also package 'amsfonts' is ok) \usepackage[dvips]{graphicx} % commands for influencing style: ... \input{mydef} \begin{document} Esercizi ($\&$ teoria): si svolgono dall'ultimo al primo (SMC-STM 2009) \vskip0.2cm $\square$ Siano $$ A = \ba{ccc} 0 & 1 & 2 \\ -2 & 3 & 5 \\ 1 & -1 & 1 \ea,\ \ \b = \ba{c} 3 \\ 6 \\ 1 \ea. $$ \begin{itemize} \item[i] Risolvere il sistema lineare $A\x=\b$ con il metodo di Gauss \item[ii] Trovare matrici $\Pi$ di permutazione, $D$ diagonale, $L$ e $U^T$ triangolari inferiori con $L_{ii}=U_{ii}=1$, $i=1,2,3$, tali che $A=\Pi L U$ \item[iii] Annullare la seconda e la terza componente del vettore $\b$ usando il metodo di Givens \item[iv] Esistono le fattorizzazioni di Cholesky delle matrici $M=A+A^T$ e $N=AA^T$? \item[v] Dire se $-4$ pu\`o essere autovalore di $A$ (non calcolare il polinomio caratteristico di $A$) \item[vi] Studiare la convergenza del metodo di Gauss-Seidel nella risoluzione di $A\x=\b$ \end{itemize} \vskip0.2cm $\ldots$ \qquad $\ldots$ \qquad $\ldots$ \vskip0.4cm ? Maggio 2009 \vskip0.2cm {\it Condizionamento di un sistema lineare vs stabilit\`a dell'algoritmo per la sua risoluzione} (seconda parte) \vskip0.2cm Esempio. Gauss al sistema $$ A(\x+d\x) = \ba{cc} .3\cdot10^{-3} & 1 \\ 1 & 0 \ea \ba{c} x_1+dx_1 \\ x_2+dx_2 \ea = \ba{c} 1 \\ 1 \ea = \b+d\b. $$ Anzich\'e $$ E = \ba{cc} 1 & 0 \\ -1/.3\cdot 10^{-3} & 1 \ea $$ il calcolatore definisce $$ ``E" = \ba{cc} 1 & 0 \\ -.333\cdot 10^4 & 1 \ea. $$ Poi effettua le moltiplicazioni macchina $$ ``E"A = \ba{cc} .3\cdot 10^{-3} & 1 \\ 0 & -.333\cdot 10^4 \ea,\ \ ``E"(\b+d\b) = \ba{c} 1 \\ -.333\cdot 10^4 \ea $$ ($-.333\cdot 10^4``+"1 = -.333\cdot 10^4$). Quindi $``\x+d\x"=$ (cio' che la macchina ha effettivamente ottenuto calcolando $\x+d\x$) $=\ba{c} 0 \\ 1 \ea$ ed errore algoritmico $= \\|``\x+d\x"-(\x+d\x)\\|/\\|\x+d\x\\| = 1/1 =1$. Nota: \`e grande rispetto a $u=0.5\cdot 10^{-2}$ ($\x+d\x = \ba{c} 1 \\ 1 -.3\cdot 10^{-3} \ea$ e si \`e usata la norma infinito). In effetti gli elementi di $$ ``L" = \ba{cc} 1 & 0 \\ .333\cdot 10^4 & 1 \ea,\ ``U" = \ba{cc} .3\cdot 10^{-3} & 1 \\ 0 & -.333\cdot 10^4 \ea $$ sono in modulo molto pi\`u grandi di quelli di $\|A\|$. Conclusione: il problema $A\x=\b$ \`e ben condizionato, ma l'algoritmo di Gauss per la sua risoluzione \`e instabile. \vskip0.1cm Modificando Gauss \`e possibile definire un algoritmo stabile per la risoluzione di $A\x=\b$: Gauss modificato al sistema $$ A(\x+d\x) = \ba{cc} .3\cdot 10^{-3} & 1 \\ 1 & 0 \ea \ba{c} x_1+dx_1 \\ x_2+dx_2 \ea = \ba{c} 1 \\ 1 \ea = \b+d\b. $$ $$ P = \ba{cc} 0 & 1 \\ 1 & 0 \ea,\ PA = \ba{cc} 1 & 0 \\ .3\cdot 10^{-3}& 1 \ea,\ P(\b+d\b) = \ba{c} 1 \\ 1 \ea, $$ $$ E = \ba{cc} 1 & 0 \\ -.3\cdot 10^{-3} & 1 \ea,\ EPA = \ba{cc} 1 & 0 \\ 0 & 1 \ea,\ EP(\b+d\b) = \ba{c} 1 \\ 1 \ea $$ ($-.3\cdot 10^{-3}``+"1 = 1$). Quindi $``\x+d\x" = \ba{c} 1 \\ 1 \ea$ ed errore algoritmo $= \\|``\x+d\x"-(\x+d\x)\\|/\\|\x+d\x\\| = .3\cdot 10^{-3}/1 = .3\cdot 10^{-3}$. Nota: \`e pi\`u piccolo di $u=0.5\cdot 10^{-2}$. In effetti gli elementi di $$ ``L" = \ba{cc} 1 & 0 \\ .3\cdot 10^{-3}& 1 \ea,\ \ ``U" = \ba{cc} 1 & 0 \\ 0 & 1 \ea $$ sono dello stesso ordine di grandezza di quelli di $\|A\|$. Conclusione: l'algoritmo di Gauss modificato per la risoluzione di $A\x=\b$ \`e stabile. \vskip0.2cm 18 Maggio 2009, 9 Maggio 2009, 28 Aprile 2009, 21 Aprile 2009 18 Maggio 2009 \vskip0.2cm {\it Condizionamento di un sistema lineare vs stabilit\`a dell'algoritmo per la sua risoluzione} (prima parte) \vskip0.2cm ``Risultato 1'' (senza dim) sul condizionamento di un sistema lineare $A\x=\b$: Siano $\x$ e $\x+d\x$ tali che $A\x=\b$ e $(A+dA)(\x+d\x)=\b+d\b$ dove $dA$ e $d\b$ sono perturbazioni, rispettivamente, della matrice A e del vettore $b$. Allora $$ \f{\\|d\x\\|}{\\|\x\\|} \leq \mu(A) \f{\\|dA\\|/\\|A\\|+\\|d\b\|/\\|\b\\|} {1-\mu(A)\\|dA\\|/\\|A\\|} $$ dove $\mu(A)=\\|A\\|\\|A^{-1}\\|$ e la norma matriciale \`e quella indotta dalla norma vettoriale utilizzata. [Nota: per $dA=0$ ritroviamo il risultato visto in precedenza, relativo a perturbazioni sul solo vettore dei termini noti: $A\x=\b$ $\&$ $A(\x+d\x)=\b+d\b$ $\then$ $\\|d\x\\|/\\|\x\\| \leq \mu(A) \\|d\b\\|/\\|\b\\|$.] Questo risultato \`e ovviamente utile per valutare l'errore inerente sulla soluzione di un sistema lineare: $\mu(A)$ grande $\then$ errore inerente pu\`o essere molto pi\`u grande dell'errore inerente sui dati; $\mu(A)$ piccolo $\then$ errore inerente deve essere dello stesso ordine dell'errore inerente sui dati. \vskip0.1cm Esempio. Il sistema $$ A\x = \ba{cc} .3\cdot 10^{-3} & 1 \\ 1 & 0 \ea \ba{c} x_1 \\ x_2 \ea = \ba{c} 1+.3\cdot 10^{-3} \\ 1 \ea = \b $$ in $F(10,3,\ldots)$ diventa $$ A(\x+d\x) = \ba{cc} .3\cdot 10^{-3} & 1 \\ 1 & 0 \ea \ba{c} x_1+dx_1 \\ x_2+dx_2 \ea = \ba{c} 1 \\ 1 \ea = \b+d\b $$ ($1+.3\cdot 10^{-3}=.10003\cdot 10^1$, $1``+".3\cdot 10^{-3}=.1\cdot 10^1$) quindi, per il ``Risultato 1'' con $dA=0$, utilizzando la norma infinito, si ottiene la limitazione $$ \f{\\|d\x\\|}{\\|\x\\|} \leq (1+e)^2 \f{\\|d\b\\|}{\\|\b\\|},\ \f{\\|d\b\\|}{\\|\b\\|} =\f{.3\cdot 10^{-3}}{1+.3\cdot 10^{-3}}. $$ Essendo $e=.3\cdot 10^{-3}$, il numero $\mu_{\infty}(A)=(1+e)^2$ \`e poco pi\`u grande di $1$ $\then$ l'errore inerente sulla soluzione \`e dello stesso ordine di grandezza dell'errore inerente sul vettore dei termini noti $\then$ il problema $A\x=\b$ \`e ben condizionato. \vskip0.2cm Vediamo ora come il ``Risultato 1'' pu\`o essere utile anche per valutare l'errore commesso nelle successive operazioni richieste dal metodo di Gauss (errore dovuto ai necessari arrotondamenti operati dalla macchina durante i calcoli) per la risoluzione di $A\x=\b$. Premessa: ``Risultato 2'' (senza dim) sul metodo di Gauss : Dati $A$ $n\times n$ non singolare, $\b$ $n\times 1$, con $a_{ij}$ e $b_i$ numeri macchina, posto $\x =$ soluzione esatta di $A\x=\b$, $``\x" =$ soluzione effettivamente calcolata con Gauss tramite i passi: a) scrittura di $``L", ``U"$ (i fattori della decomposizione LU di $A$ effettivamente calcolati) e di $``\c"$ (la soluzione di $``L"\c=\b$ effettivamente calcolata); b) scrittura di $``\x"$ (la soluzione di $``U"\x=``\c"$ effettivamente calcolata), SI HA CHE $``\x"$ \`e la soluzione esatta di un sistema ottenuto da $A\x=\b$ perturbando $A$ di $DA$, cio\`e vale l'identit\`a $$ (A+DA)``\x"=\b,\ \ \|DA\| \leq 4nu(\|A\|+\|``L"\|\|``U"\|) + O(u^2) $$ ($\|M\|=$ matrice i cui elementi sono i moduli degli elementi di $M$). \vskip0.1cm Il ``Risultato 2'' permette di valutare l'errore dell'algoritmo di Gauss sfruttando la maggiorazione del ``Risultato 1'': $$ \f{\\|``\x"-\x\\|}{\\|\x\\|} \leq \mu(A) \f{\\|DA\\|/\\|A\\|}{1-\mu(A)\\|DA\\|/\\|A\\|} $$ (usa Ris.1 per $dA=DA$, $d\b=\vn$, $\x+d\x=``\x"$). Quest'ultima disuguaglianza e la maggiorazione data per $\|DA\|$ ci dicono che $\\|``\x"-\x\\|/\\|\x\\|$ pu\`o essere grande quando $\|``L"\|$ e $\|``U"\|$ sono grandi rispetto a $\|A\|$; $\\|``\x"-\x\\|/\\|\x\\|$ \`e invece piccolo se $\|``L"\|$ e $\|``U"\|$ sono dello stesso ordine di grandezza di $\|A\|$. \vskip0.2cm \hrule \vskip0.2cm Per risolvere $A\x=\b$ (sempre nel caso $\det(S_k)\neq 0$, $k=1,\ldots, n$) si pu\`o usare anche l'algoritmo: \begin{itemize} \item[(1)] calcolare $L$ ed $U$ tali che $A=LU$, \item[(2)] risolvere il sistema $L\c=\b$ (con il m. di sostituzione in avanti), \item[(3)] risolvere il sistema $U\x=\c$ (con il m. di sostituzione all'indietro). \end{itemize} NOTA: applicare le $E_i$ oltre che ad $A$ anche a $\b$ ( cio\`e calcolare $E_{n-1}\cdots E_2E_1[A\,\|\,\b]$), come si fa nel metodo di Gauss, \`e equivalente ad eseguire i passi (1) e (2) del presente algoritmo contemporaneamente, infatti $E_{n-1}\cdots E_2E_1\b=L^{-1}\b$. \vskip0.2cm 9 Maggio 2009 \vskip0.2cm $\square$ Risolvere con il metodo di Gauss il sistema lineare $$ \ba{ccc} -2 & 4 & -1 \\ 4 &-9 & 0 \\ -4 & 5 &-5 \ea \ba{c} x_1 \\ x_2 \\ x_3 \ea = \ba{c} 12 \\ -32 \\ 3 \ea . $$ \vskip0.2cm $\square$ Calcolare le decomposizioni LU delle matrici $$ A = \ba{cc} -2 & 4 \\ 4 & -8 \ea, \ A = \ba{ccc} 6 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3 \ea,\ A = \ba{cc} 1 & 1/2 \\ 1/2 & 1/3 \ea,\ A = \ba{ccc} 1 & 1/2 & 1/3 \\ 1/2 & 1/3 & 1/4 \\ 1/3 & 1/4 & 1/5 \ea $$ Nota: Le prime due matrici sono singolari, ad esempio nella prima matrice la seconda colonna \`e $-2$ volte la prima colonna, quindi \`e ``linearmente dipendente'' dalla prima. Ne segue che per tali matrici $u_{nn}=0$. \vskip0.2cm {\it Metodo di Gauss: decomposizione LU, risoluzione sistemi lineari} \vskip0.2cm $$ A = \ba{cccc} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ . & . & & . \\ a_{n1} & a_{n2} & \cdots & a_{nn} \ea $$ IPOTESI: $a_{11}\neq 0$ $$ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 E_1 = \ba{ccccc} 1 & 0 & \cdots & & 0 \\ -a_{21}/a_{11} & 1 & . & & . \\ . & 0 & . & . &. \\ . & . & . & . & 0 \\ -a_{n1}/a_{11} & 0 & \cdots & 0 & 1 \ea,\ E_1A = \ba{cccc} a_{11} & a_{12} & \cdots & a_{1n} \\ 0 & a_{22}^2 & \cdots & a_{2n}^2 \\ . & . & & . \\ 0 & a_{n2}^2 & \cdots & a_{nn}^2 \ea =:A^{2}, $$ $a_{ij}^2 = a_{ij} - (a_{i1}/a_{11}) a_{1j}$, $2\leq i,j\leq n$, $a_{i1}^2 = 0$, $2\leq i\leq n$, $a_{ij}^2 = a_{ij}$ altrimenti (per i rimanenti $i$ e $j$). \noindent NOTA: $$ \ba{cc} 1 & 0 \\ -a_{21}/a_{11} & 1 \ea \ba{cc} a_{11} & a_{12} \\ a_{21} & a_{22} \ea = \ba{cc} a_{11} & a_{12} \\ 0 & a_{22}^2 \ea, $$ quindi, passando ai determinanti, $$ a_{22}^2 = \f{1}{a_{11}} \det \ba{cc} a_{11} & a_{12} \\ a_{21} & a_{22} \ea. $$ IPOTESI: $a_{22}^2 \neq 0$ (ovvero $\det\ba{cc} a_{11} & a_{12} \\ a_{21} & a_{22} \ea \neq 0$) $$ E_2 = \ba{ccccc} 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdots & 0 \\ 0 & -a_{32}^2/a_{22}^2 & 1 & . & . \\ . & . & . & . & 0 \\ 0 & -a_{n2}^2/a_{22}^2 & 0 & \cdots 0 & 1 \ea $$ $$ E_2E_1A = \ba{ccccc} a_{11} & a_{12} & a_{13} & \cdots & a_{1n} \\ 0 & a_{22}^2 & a_{23}^2 & \cdots & a_{2n}^2 \\ 0 & 0 & a_{33}^3 & \cdots & a_{3n}^3 \\ . & . & . & & . \\ 0 & 0 & a_{n3}^3 & \cdots & a_{nn}^3 \ea =: A^{3}, $$ $a_{ij}^3 = a_{ij}^2 - (a_{i2}^2/a_{22}^2) a_{2j}^2$, $3\leq i,j\leq n$, $a_{i2}^2 = 0$, $3\leq i\leq n$, $a_{ij}^3 = a_{ij}^2$ altrimenti (per i rimanenti $i$ e $j$). \noindent NOTA: $$ \ba{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 &-a_{32}^2/a_{22}^2 & 1 \ea \ba{ccc} 1 & 0 & 0 \\ -a_{21}/a_{11} & 1 & 0 \\ -a_{31}/a_{11} & 0 & 1 \ea \ba{ccc} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \ea = \ba{ccc} a_{11} & a_{12} & a_{13} \\ 0 & a_{22}^2 & a_{23}^2 \\ 0 & 0 & a_{33}^3 \ea, $$ quindi, passando ai determinanti, $$ a_{33}^3 = \f{1}{a_{11}a_{22}^2} \det \ba{ccc} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \ea. $$ $\ldots$ IPOTESI: $a_{n-1,n-1}^{n-1} \neq 0$ (ovvero $\det\ba{ccc} a_{11} & \cdots & a_{1n-1} \\ . & & . \\ a_{n-11} & \cdots & a_{n-1n-1} \ea \neq 0$) $$ E_{n-1} = \ba{ccccc} 1 & 0 & \cdots & . & 0 \\ 0 & . & . & . & . \\ . & . & . & 1 & 0 \\ 0 & \cdots & 0 & -a_{nn-1}^{n-1}/a_{n-1n-1}^{n-1} & 1 \ea $$ $$ E_{n-1}\cdots E_2E_1A = \ba{cccc} a_{11} & a_{12} & & a_{1n} \\ & a_{22}^2 & & a_{2n}^2 \\ & . & & . \\ & & & a_{nn}^n \ea =: A^{n}, $$ $a_{nn}^n = a_{nn}^{n-1}-(a_{nn-1}^{n-1}/a_{n-1n-1}^{n-1}) a_{n-1n}^{n-1}$, $a_{nn-1}^n = 0$, $a_{ij}^n = a_{ij}^{n-1}$ altrimenti (per i rimanenti $i$ e $j$). \noindent NOTA: si osserva che $$ a_{nn}^n = \f{1}{a_{11}a_{22}^2...a_{n-1n-1}^{n-1}} \det(A). $$ Sia $A$ $n\times n$ e $$ S_k = \ba{ccc} a_{11} & \cdots & a_{1k} \\ . & & . \\ a_{k1} & \cdots & a_{kk} \ea,\ \ k=1,\ldots,n. $$ Teorema. Se $\det(S_k) \neq 0$ per $k=1\ldots n-1$ allora \begin{itemize} \item[(1)] esistono matrici $E_1, E_2,\ldots, E_{n-1}$ ``elementari di Gauss'' tali che $E_{n-1}\cdots E_2E_1A=A^{(n)}=(a_{ij}^n)_{i,j=1}^n$ \`e triangolare superiore \item[(2)] $\det(A)=0$ se e solo se $a_{nn}^n = 0$ \item[(3)] esiste $L$ $n\times n$ triangolare inferiore, $L_{ii}=1$, ed $U$ triangolare superiore tali che $A=LU$: $U=A^{(n)}$ e $$ L = E_1^{-1}E_2^{-1}\cdots E_{n-1}^{-1} = \ba{ccccc} 1 & 0 & \cdots & . & 0 \\ a_{21}/a_{11} & 1 & & . & . \\ . & a_{32}^2/a_{22}^2 & . & & . \\ . & . & & 1 & 0 \\ a_{n1}/a_{11} & a_{n2}^2/a_{22}^2 & . & a_{nn-1}^{n-1}/a_{n-1n-1}^{n-1} & 1 \ea $$ \item[(4)] (metodo di Gauss (a)) considerato il sistema lineare $A\x=\b$, $\b$ $n\times 1$ generico, si pu\`o introdurre un sistema lineare triangolare superiore $U\x=\c$ equivalente ad $A\x=\b$ col seguente algoritmo: $$ \bi{l} [A\ \|\ \b] \\ E_1[A\ \|\ \b] = [E_1A\ \|\ E_1\b] \\ E_2E_1[A\ \|\ \b] = [E_2E_1A\ \|\ E_2E_1\b] \\ \ldots \\ E_{n-1}\cdots E_2E_1[A\ \|\ \b] = [E_{n-1}\cdots E_2E_1A\ \|\ E_{n-1}\cdots E_2E_1\b], \\ U = E_{n-1}\cdots E_2E_1A,\ \ \c = E_{n-1}\cdots E_2E_1\b \ei $$ ovvero: $$ \bi{l} \hbox{per }\ k=1\ldots n-1\ \ \{ \\ a_{ij}^{k+1} = a_{ij}^k - (a_{ik}^k/a_{kk}^k) a_{kj}^k,\ \ k+1\leq i,j\leq n, \\ a_{ik}^{k+1} = 0, \ \ k+1\leq i\leq n, \\ a_{ij}^{k+1} = a_{ij}^k,\ \ \hbox{altrimenti (per i rimanenti i,j)}, \\ b_i^{k+1} = b_i^k - (a_{ik}^k/a_{kk}^k) b_k^k,\ \ k+1\leq i\leq n, \\ b_i^{k+1}= b_i^k,\ \ \hbox{altrimenti }\ (i<=k); \ \} \\ U=A^{n}=(a_{ij}^n)_{i,j=1\ldots n}, \\ \c=\b^n\ . \ei $$ Il costo di questo algoritmo \`e $n^3/3 +O(n^2)$ operazioni moltiplicative. Pi\`u precisamente, per $k$ generico occorre eseguire: $n-k$ divisioni per calcolare i rapporti $l_{ik}=a_{ik}^k/a_{kk}^k$, cio\`e gli elementi della matrice $L$, le $(n-k)^2$ moltiplicazioni $l_{ik}a_{kj}^k$ e le $n-k$ moltiplicazioni $l_{ik}b_k^k$. Quindi $L$ ed $U$ possono essere calcolate con $\sum_{k=1\ldots n-1} (n-k) = n(n-1)/2$ divisioni e $\sum_{k=1\ldots n-1} (n-k)^2 = n(n-1)(2n-1)/6$ moltiplicazioni. Per calcolare anche $\c$ occorre eseguire altre $\sum_{k=1\ldots n-1} (n-k) = n(n-1)/2$ moltiplicazioni \item[(5)] (metodo di Gauss (b)) se $A$ \`e inoltre non singolare i sistemi $A\x=\b$ e $U\x=\c$ oltre ad essere equivalenti ammettono una unica soluzione $\x=A^{-1}\b=U^{-1}\c$, calcolabile, con altre $n(n-1)/2$ moltiplicazioni e $n$ divisioni, applicando il metodo di sostituzione all'indietro al sistema $U\x=\c$ \end{itemize} $\square$ Se $A$ $n\times n$ \`e definita positiva allora $\det(S_k)>0$, $k=1\ldots n$, quindi esiste la decomposizione LU di $A$ ed ogni sistema $A\x=\b$, $\b$ $n\times 1$, pu\`o essere risolto usando il metodo di Gauss \vskip0.2cm $\square$ Un esercizio dell'esonero $A,B$ $n\times n$. Se $\E$ \`e autovalore di $AB$ allora \`e autovalore di $BA$. Infatti $\E$ autovalore di $AB$ $\then$ esiste $\v\neq\vn$ tale che $AB\v=\E\v$ $\then$ $B(AB\v)=B(\E\v)$ $\then$ $(BA)B\v=\E B\v$, ovvero $\E$ \`e autovalore di $BA$ con corrispondente autovettore $B\v$. Quindi $AB$ e $BA$ hanno gli stessi autovalori e gli autovettori di $BA$ si ottengono moltiplicando quelli di $AB$ per $B$ $A$ $n\times n$ invertibile $\then$ $\mu_2(A^A)=\mu_2(A)^2$. Infatti, $$ \bi{rcl} \mu_2(A^A) & = & \\|A^A\\|_2\\|(A^A)^{-1}\\|_2 = \rho(A^A) \rho((A^A)^{-1}) \\ & = & \rho(A^A) \rho(A^{-1}(A^)^{-1}) = \rho(A^A) \rho((A^)^{-1}A^{-1}) \\ & = & \rho(A^A) \rho((A^{-1})^A^{-1}) = \\|A\\|^2 \\|A^{-1}\\|^2 = \mu_2(A)^2 \ei $$ ( risultati utilizzati: $A^A$ \`e hermitiana; $M$ hermitiana $\then$ $M^{-1}$ hermitiana; $MN$ ed $NM$ hanno gli stessi autovalori, quindi $\rho(MN)=\rho(NM)$; ($M^)^{-1}=(M^{-1})^$) \vskip0.2cm 28 Aprile 2009 \vskip0.2cm $\square$ Usando il Teorema di Schur scrivere un algoritmo alternativo per la risoluzione di $A\x=\b$, $A$ $n\times n$, $\b$ $n\times 1$. Si suppone $\det(A)=$ determinante di $A$ diverso da zero. Qual'\`e l'inconveniente di tale algoritmo? \vskip0.1cm {\it Risoluzione}. Algoritmo: \begin{itemize} \item[(1)] calcolare una matrice unitaria $S$ tale che $S^{-1}AS=:U$ \`e triangolare superiore (essa esiste per il Teorema di Schur), \item[(2)] risolvere i due sistemi lineari: $U\y=S^\b$, $S^\x=\y$. \end{itemize} Inconveniente: l'operazione di cui al punto (1) non \`e banale e comunque non pu\`o essere effettuata (in generale) con un numero finito di operazioni aritmetiche. Sappiamo invece che, usando Gauss o una delle sue varianti, o Givens, o Householder, \`e possibile introdurre un sistema lineare triangolare $U\x=\c$ equivalente ad $A\x=\b$ facendo $tot<+\infty$ o.a.. La $U$ ottenuta con tali algoritmi non ha gli autovalori di $A$, ma che importa ! \vskip0.2cm {\it Risolvere sistemi lineari con matrice dei coefficienti triangolare superiore} \vskip0.2cm $U$ $n\times n$ triangolare superiore non singolare, ovvero $[U]_{ii} \neq 0$, per ogni $i$, e $\c$ vettore $n\times 1$: $U\x=\c$ iff $$ \bi{rcl} u_{11}x_1 + u_{12}x_2 +\ldots+ u_{1n}x_n & = & c_1 \\ u_{22}x_2 +\ldots+ u_{2n}x_n & = & c_2 \\ &\vdots& \\ u_{n-1,n-1}x_{n-1} + u_{n-1,n}x_n & = & c_{n-1} \\ u_{nn}x_n & = &c_n \ei $$ iff $$ \bi{l} x_n = c_n / u_{nn} \\ x_{n-1} = ( c_{n-1} - u_{n-1,n}x_n ) / u_{n-1,n-1} \\ \vdots \\ x_2 = ( c_2 - u_{23}x_3 ... - u_{2n}x_n ) / u_{22} \\ x_1 = ( c_1 - u_{12}x_2 .... - u_{1n}x_n ) / u_{11} \ei $$ iff per $i=n,\ldots, 1$: $x_i = (c_i - \sum_{j=i+1,\ldots, n} u_{ij} x_j ) / u_{ii}$. Costo $= n(n+1)/2$ moltiplicazioni-divisioni. \vskip0.2cm {\it Risolvere sistemi lineari con matrice dei coefficienti generica, triangolarizzazione di una matrice} \vskip0.2cm $A$ matrice $n\times n$ non singolare, $\b$ vettore $n\times 1$. $E_k$, $k=1,\ldots, n-1$, matrici $n\times n$ non singolari tali che $$ \bi{l} A \x = \b \hbox{ iff} \\ E_1 A \x = E_1 \b,\ \ E_1A = \ba{cccc} & * & \cdots & * \\ 0 & * & \cdots & * \\ . & . & & . \\ 0 & * & \cdots & * \ea \hbox{ iff} \\ E_2 E_1 A \x = E_2 E_1 \b,\ \ E_2E_1A = \ba{ccccc} * & * & * & \cdots & * \\ 0 & * & * & \cdots & * \\ . & 0 & * & \cdots & * \\ . & . & . & & . \\ 0 & 0 & * & \cdots & * \ea \hbox{ iff} \ei $$ $\ldots$ iff $E_{n-1}\cdots E_2 E_1 A \x = E_{n-1}\cdots E_2 E_1 \b$, ovvero $U \x = \c$, con $$ U = E_{n-1}\cdots E_2E_1A = \ba{ccccc} * & * & * & \cdots & * \\ 0 & * & * & \cdots & * \\ . & 0 & * & \cdots & * \\ . & . & . & . & . \\ 0 & . & . & 0 & * \ea,\ \ \c = E_{n-1}\cdots E_2 E_1 \b. $$ \vskip0.2cm {\it Definizione di $E_k$ (passo $k$ della triangolarizzazione)} \vskip0.2cm Per $k=1,\ldots, n-1$: Al termine del passo $k-1$ \`e stata prodotta la matrice $$ E_{k-1}\cdots E_2E_1A = \ba{cc} T & V \\ 0 & W \ea, $$ $T$ $k-1\times k-1$ triangolare superiore, $W$ $n-k+1\times n-k+1$ (per $k=1$ si ha $A=W$). Si vogliono annullare gli elementi $(k+1,k),\ldots,(n,k)$ di tale matrice, ovvero il secondo, $\ldots$, l'ultimo elemento della prima colonna di $W$: $$ \bi{l} E_k = \ba{cc} I & 0 \\ 0 & F \ea,\ I\ k-1\times k-1,\ \ F\ n-k+1\times n-k+1, \\ E_k(E_{k-1}\cdots E_2E_1A) = \ba{cc} I & 0 \\ 0 & F \ea \ba{cc} T & V \\ 0 & W \ea = \ba{cc} T & V \\ 0 & FW \ea = \ba{cc} T & V \\ 0 & [F\w\ FY] \ea \ei $$ dove $W = [\w\ Y]$. Se $\w$, la prima colonna di $W$, \`e gia' della forma $[\ 0\ \cdots\ 0]^T$ allora porre $F=I$, altrimenti scegliere $F$ come in Gauss semplice, Gauss con pivot parziale, Givens, Householder per ottenere $F\w = [\ 0\ \cdots\ 0]^T$. \vskip0.2cm Costo $= \sum_{k=1\ldots n-1} [$costo del prodotto matrice-matrice $FY$, $F$ $n-k+1\times n-k+1$, $Y$ $n-k+1\times n-k$]. Ad esempio, in Gauss costo($FY)=(n-k)^2$ moltiplicazioni $\then$ costo di Gauss $= n^3/3 + O(n^2)$. \vskip0.2cm {\it Un esempio di triangolarizzazione} \vskip0.2cm $$ A = \ba{cccc} 1 & 0 & 0 & 1 \\ -1 & 1 & 0 & 1 \\ -1 &-1 & 1 & 1 \\ -1 &-1 &-1 & 1 \ea, $$ $$ E_1 = \ba{cccc} 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 1 \ea,\ E_1A = \ba{cccc} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 2 \\ 0 &-1 & 1 & 2 \\ 0 &-1 & -1& 2 \ea\ (F=E_1,\ W=A), $$ $$ E_2 = \ba{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 1 & 0 & 1 \ea,\ E_2E_1A = \ba{cccc} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 4 \\ 0 & 0 & -1 & 4 \ea\ (F = \ba{ccc} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \ea,\ W = \ba{ccc} 1 & 0 & 2 \\ -1 & 1 & 2 \\ -1 & -1 & 2 \ea), $$ $$ E_3 = \ba{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 \ea,\ E_3E_2E_1A = \ba{cccc} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 4 \\ 0 & 0 & 0 & 8 \ea =:U\ \ (F=\ba{cc} 1 & 0 \\ 1 & 1 \ea,\ W = \ba{cc} 1 & 4 \\ -1 & 4 \ea). $$ In questo esempio di triangolarizzazione di una matrice si osserva che Gauss con pivot parziale coincide con Gauss semplice e che $\max\|(FW)_{ij}\| = 2 \max\|(W)_{ij}\|$, cio\`e la disuguaglianza ottenuta prima \`e ottimale. Nota: $\\|A\\|_F = \R{13} < \\|U\\|_F = \R{88}$. Applicando Givens, per triangolarizzare $A$, si ottiene $$ E_3 E_2 E_1 A = U = \ba{cccc} 2 & 1/2 & 0 & -1 \\ 0 & \R{11}/2 & 0 & -1/\R{11} \\ 0 & 0 & \R{2} & 0 \\ 0 & 0 & 0 & \R{2}/\R{11} \ea. $$ (vedi pi\`u avanti). Nota: $\\|A\\|_2 = \\|U\\|_2 \leq \\|A\\|_F = \\|U\\|_F = \R{13}$. Vedremo che per triangolarizzare una matrice $A$ $n\times n$ occorre calcolare dei prodotti del tipo $FW$ con $F$,$W$ matrici $j\times j$, $j=n,\ldots,2$. La prima riga di $FW$ coincide con $[u_{n-j+1,n-j+1} \ldots u_{n-j+1,n}]$ essendo $U$ $n\times n$ la matrice triangolare finale. Gli elementi della prima colonna di $FW$ se si eccettua il primo sono tutti nulli. Inoltre l'elemento $(2,2)$ dell'ultima $FW$ coincide con $u_{nn}$. In Givens e Householder $F$ \`e unitaria, quindi $\\|FW\\|_2=\\|W\\|_2$, ovvero gli elementi di $FW$ e $W$ hanno lo stesso ordine di grandezza. In Gauss $F=GP$, $$ G = \ba{cccc} 1 & 0 & \cdots & 0 \\ m_{21} & 1 & & \\ \vdots & & & 0 \\ m_{j1} & 0 & \ldots 0 & 1 \ea,\ \ P\ j\times j\ \hbox{di permutazione} $$ $\then$ $\\|FW\\|_2 \leq \\|F\\|_2\\|W\\|_2$, dove $$ \bi{rcl} \\|F\\|_2 & = & \\|G\\|_2 = \max_{\x\,j\times1\,\\|\x\\|_2=1} \\|G\x\\|_2 \\ & \geq & \\|G\e_1\\|_2 = \R{1+m_{21}^2+\ldots+m_{j1}^2} > 1\ \ \hbox{se}\ \ G\neq I, \ei $$ ovvero gli elementi di $FW$ possono essere in media pi\`u grandi di quelli di $W$. Nota: poich\'e $m_{k1}=-(P\w)_k/(P\w)_1$, $k=2,\ldots,j$, dove $\w$ \`e il vettore che vogliamo trasformare in $$ F\w = \ba{c} * \\ 0 \\ \vdots \\ . 0 \ea $$ ($\w$=prima colonna di $W$), il numero $\R{1+m_{21}^2+\ldots+m_{j1}^2}$ \`e minimo quando $P$ \`e scelta in modo che $\|(P\w)_1\|=\max_k \|(P\w)_k\|$, ovvero in Gauss con pivot parziale. In Gauss con pivot parziale si ha inoltre: $\max\|(FW)_{ij}\| \leq 2 \max\|(W)_{ij}\|$ (provare a dimostrare questa disuguaglianza) da cui segue il risultato $\max\|u_{ij}\|\leq 2^{n-1}\max\|a_{ij}\|$, cio\`e gli elementi di U non possono essere pi\`u di $2^{n-1}$ volte pi\`u grandi di quelli di $A$. \vskip0.2cm \hrule $$ \ba{cccc} 1/\R{2} & -1/\R{2} & & \\ 1/\R{2} & 1/\R{2} & & \\ & & 1& \\ & & & 1\ea \ba{cccc} 1 & 0 & 0 & 1 \\ -1 & 1 & 0 & 1 \\ -1 &-1 & 1 & 1 \\ -1 &-1 &-1 & 1 \ea = \ba{cccc} \R{2} & -1/\R{2} & 0 & 0 \\ 0 & 1/\R{2} & 0 & \R{2} \\ -1 & -1 & 1 & 1 \\ -1 & -1 &-1 & 1 \ea, $$ $$ \bi{c} \ba{cccc} \R{2}/\R{3} & 0 & -1/\R{3} & \\ 0 & 1 & 0 & \\ 1/\R{3} & 0 & \R{2}/\R{3} & \\ & & & 1 \ea \ba{cccc} \R{2} & -1/\R{2} & 0 & 0 \\ 0 & 1/\R{2} & 0 & \R{2} \\ -1 & -1 & 1 & 1 \\ -1 & -1 &-1 & 1 \ea \\ = \ba{cccc} \R{3} & 0 & -1/\R{3} & -1/\R{3} \\ 0 & 1/\R{2} & 0 & \R{2} \\ 0 &-\R{3}/\R{2}& \R{2}/\R{3}& \R{2}/\R{3} \\ -1 & -1 & -1 & 1 \ea, \ei $$ $$ \bi{c} \ba{cccc} \R{3}/2 & 0 & 0 & -1/2 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1/2 & 0 & 0 & \R{3}/2\ea \ba{cccc} \R{3} & 0 & -1/\R{3} & -1/\R{3} \\ 0 & 1/\R{2} & 0 & \R{2} \\ 0 &-\R{3}/\R{2}& \R{2}/\R{3}& \R{2}/\R{3} \\ -1 & -1 & -1 & 1 \ea \\ = \ba{cccc} 2 & 1/2 & 0 & -1 \\ 0 & 1/\R{2} & 0 & \R{2} \\ 0 & -\R{3}/\R{2}& \R{2}/\R{3} & \R{2}/\R{3} \\ 0 &-\R{3}/2 & -2/\R{3} & 1/\R{3} \ea, \ei $$ $$ \bi{c} \ba{cccc} 1 & 0 & 0 & 0 \\ 0 & 1/2 & -\R{3}/2 & 0 \\ 0 & \R{3}/2 & 1/2 & 0 \\ 0 & 0 & 0 & 1 \ea \ba{cccc} 2 & 1/2 & 0 & -1 \\ 0 & 1/\R{2} & 0 & \R{2} \\ 0 & -\R{3}/\R{2}& \R{2}/\R{3} & \R{2}/\R{3} \\ 0 &-\R{3}/2 & -2/\R{3} & 1/\R{3} \ea \\ = \ba{cccc} 2 & 1/2 & 0 & -1 \\ 0 & \R{2} & -\R{2}/2 & 0 \\ 0 & 0 & (\R{2}/\R{3})/2 & 2\R{2}/\R{3} \\ 0 &-\R{3}/2 & -2/\R{3} & 1/\R{3} \ea, \ei $$ $$ \bi{c} \ba{cccc} 1 & 0 & 0 & 0 \\ 0 & 2\R{2}/\sqrt{11}& 0 &-\R{3}/\sqrt{11} \\ 0 & 0 & 1 & 0 \\ 0 & \R{3}/\sqrt{11} & 0 & 2\R{2}/\sqrt{11} \ea \ba{cccc} 2 & 1/2 & 0 & -1 \\ 0 & \R{2} & -\R{2}/2 & 0 \\ 0 & 0 & (\R{2}/\R{3})/2 & 2\R{2}/\R{3} \\ 0 &-\R{3}/2 & -2/\R{3} & 1/\R{3} \ea \\ = \ba{cccc} 2 & 1/2 & 0 & -1 \\ 0 & \sqrt{11}/2 & 0 & -1/\sqrt{11} \\ 0 & 0 & (\R{2}/\R{3})/2 & 2\R{2}/\R{3} \\ 0 & 0 & -(\sqrt{22}/\R{3})/2 & 2\R{2}/\sqrt{33} \ea, \ei $$ $$ \bi{c} \ba{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & (1/\R{3})/2 & -(\sqrt{11}/\R{3})/2 \\ 0 & 0 & (\sqrt{11}/\R{3})/2 & (1/\R{3})/2 \ea \ba{cccc} 2 & 1/2 & 0 & -1 \\ 0 & \sqrt{11}/2 & 0 & -1/\sqrt{11} \\ 0 & 0 & (\R{2}/\R{3})/2 & 2\R{2}/\R{3} \\ 0 & 0 & -(\sqrt{22}/\R{3})/2 & 2\R{2}/\sqrt{33} \ea \\ = \ba{cccc} 2 & 1/2 & 0 & -1 \\ 0 & \sqrt{11}/2 & 0 & -1/\sqrt{11} \\ 0 & 0 & \R{2} & 0 \\ 0 & 0 & 0 & 4\R{2}/\sqrt{11} \ea. \ei $$ \vskip0.2cm \hrule \vskip0.2cm $\square$ Mostrare che $\\|\y\w^\\|_2 = \\|\y\w^\\|_F = \\|\y\\|_2\\|\w\\|_2$, $\y,\w$ vettori $n\times 1$, ricordando che $\\|M\\|_2=\sqrt{\rho(M^M)}$ e $\\|M\\|_F=\sqrt{\tr(M^M)}$ ($\tr(A)=$ traccia di $A$ $= \sum_i a_{ii}$) \vskip0.1cm {\it Risoluzione}. $$ \\|\x\y^\\|_F^2 = \tr(\y\x^\x\y^) = \x^\x [\tr(\y\y^)] = \x^\x [\y^\y] = \\|\x\\|_2^2 \\|\y\\|_2^2, $$ $$ \\|\x\y^\\|_2^2 = \rho(\y\x^\x\y^) = \x^\x [\rho(\y\y^)] = \x^\x [\y^\y]=\\|\x\\|_2^2 \\|\y\\|_2^2 $$ Nota: a entrambi i risultati si puo arrivare usando solo le definizioni di $\\|\cdot\\|_F$ e $\\|\cdot\\|_2$ e la disuguaglianza di Schwartz: $$ \\|\y\w^\\|_2 = \max_{\x\ n\times 1\ \\|\x\\|_2=1} \\|\y\w^\x\\|_2 = \max_{\x\ n\times 1\ \\|\x\\|_2=1} \|\w^\x\|\\|\y\\|_2 = \\|\y\\|_2 \max_{\x\ n\times 1\ \\|\x\\|_2=1} \|\w^\x\|. $$ Studiamo l'argomento del max: se $\x=\w/\\|\w\\|_2$, allora $\|\w^\x\|=\\|\w\\|_2$; per ogni $\x$, invece, $\\|\w^\x\\| \leq \\|\w\\|_2\\|\x\\|_2 = \\|\w\\|_2$. Ne segue che $\max_{\x\ n\times 1\ \\|\x\\|_2=1} \|\w^\x\| = \\|\w\\|_2$. \vskip0.2cm {\it Esercizi, II Teorema di Gershgorin, matrici normali e Teorema di Schur} \vskip0.2cm $\square$ $A$,$B$ matrici $n\times n$ non singolari. \begin{itemize} \item[a] $\mu(AB)\leq \mu(A)\mu(B)$, $\mu(M)=\\|M\\|\\|M^{-1}\\|$ \item[b] $AB$ e $BA$ hanno gli stessi autovalori (sugg.: dimostrare che $AB$ e $BA$ sono simili) \item[c] $\mu_2(B^B)\leq \mu_2(B)^2$ (sugg.: usare a) e b)) \end{itemize} \vskip0.2cm $\square$ $$ A=\ba{cccc} 1 & 1 & 0 & 1 \\ 1 & 1 & 0 & 1 \\ 1 & 1 & a & 1 \\ 1 & 1 & 0 & 1 \ea,\ a\in\CC. $$ \begin{itemize} \item[a] Trovare $P$ $4\times 4$ di permutazione tale che $$ PAP^T = \ba{cccc} * & * & * & * \\ 0 & * & * & * \\ 0 & * & * & * \\ 0 & * & * & * \ea $$ (Nota: righe di $PA =$ permutazione delle righe di $A$; colonne di $PAP^T =$ permutazione delle colonne di $PA$ con la stessa legge) \item[b] per quali valori di $a$ la matrice $A$ ha un autovalore uguale a $\rho(A)$ ? \end{itemize} \vskip0.2cm $\square$ Dati $\y,\w,\z$ vettori $n\times 1$ dimostrare che il prodotto matrice vettore $(\y\w^)\z$ si pu\`o calcolare con $2n$ moltiplicazioni \vskip0.2cm $\square$ Mostrare che in generale non \`e vera l'identit\`a $AB=BA$, $A,B$ $n\times n$ \vskip0.2cm $\square$ Per $A$ $n\times n$ la misura $\\|A\\|_F = \sqrt{\sum_{i,j=1,\ldots,n}\|a_{ij}\|^2}$ \`e una norma matriciale che non \`e indotta da nessuna norma vettoriale. Mostrare che $\\|A\\|_2\leq\\|A\\|_F$. \vskip0.2cm $\square$ Localizzare nel modo migliore possibile gli autovalori di $$ A = \ba{ccc} 10 & 2 & 3 \\ -1 & 2 & -1 \\ 0 & 1 & 3 \ea. $$ Nota1: $A$ ha elementi reali $\then$ il polinomio caratteristico di $A$ ha coefficienti reali $\then$ se $\E$ \`e autovalore di $A$ anche $\o{\E}$ \`e autovalore di $A$. Nota2: $A$ e $A^T$ hanno gli stessi autovalori \vskip0.2cm $\square$ II Teorema di Gershgorin: Se $m$ cerchi di Gershgorin di $A$ $n\times n$ sono disgiunti dai rimanenti $n-m$, allora $m$ autovalori sono nell'unione di quegli $m$ cerchi e $n-m$ nell'unione di quegli altri \vskip0.2cm $\square$ La matrice $$ A = \ba{cc} 3 & 2 \\ 1 & 2 \ea $$ \`e diagonalizzabile con una trasformazione unitaria? \vskip0.2cm $\square$ $A$ $n\times n$ si dice ``normale'' se $AA^=A^A$, ovvero se commuta con la sua trasposta coniugata. \begin{itemize} \item[(1)] Se $A$ \`e normale e triangolare allora $A$ \`e diagonale. (sugg.: fare il caso $n=2$. Per $n$ generico far vedere che $A$ $n\times n$ triangolare $\then$ $$ A = \ba{cc} a_{11} & \w^T \\ \vn & B \ea $$ con $B$ $n-1\times n-1$ triangolare, e che, se $A$ \`e anche normale allora il vettore $\w$ deve essere nullo e la matrice $B$ deve essere normale. \item[(2)] Sia $A=QTQ^$ con $Q$ unitaria, $T$ triangolare. Allora $A$ \`e normale se e solo se $T$ \`e normale. {\it Teorema di Schur}: Data $A$ $n\times n$ esiste $Q$ unitaria tale che $A=QTQ^$ con $T$ triangolare, ovvero ogni matrice si pu\`o trasformare in triangolare con una trasformazione per similitudine unitaria. Dimostrazione: omessa. \item[(3)] $A$ $n\times n$ si pu\`o diagonalizzare con una trasformazione per similitudine unitaria se e solo se \`e normale (sugg. usare il teorema di Schur e i risultati (1) e (2)) \end{itemize} \vskip0.2cm $\square$ $$ A = \ba{cccc} 9 & 1 & -2 & 1 \\ 0 & 8 & 1 & 1 \\ -1 & 0 & 7 & 0 \\ 1 & 0 & 0 & 1 \ea, \ \ B = \ba{cccc} -9 & 1 &-2 & 0 \\ 1 & 8 & 0 & 1 \\ -2 & 0 & 7 & 0 \\ 0 & 1 & 0 & 2 \ea $$ \begin{itemize} \item[i] osservare che $A$ ha almeno due autovalori reali \item[ii] trovare un limite superiore di $\mu_2(B)$ \end{itemize} \vskip0.2cm $\square$ Sia $p$ un numero naturale. Se $A^p=0$, allora gli autovalori $\E$ di $A$ sono tutti nulli. Se $A^p=I$, allora gli autovalori $\E$ di $A$ devono risolvere l'equazione algebrica $z^p-1=0$ \vskip0.2cm 21 Aprile 2009 \vskip0.2cm {\it Come annullare tutti gli elementi di un vettore eccetto il primo} $\square$ Dato $\w$ vettore $j\times 1$ trovare $F$ matrice $j\times j$ tale che $(F\w)_k=0$, $k=2,\ldots,j$, cio\`e: $$ \w= \ba{c} w_1 \\ w_2 \\ \vdots\\ w_j \ea \quad \to \quad F\w = \ba{c} \\ 0 \\ \vdots\\ 0 \ea. $$ Vediamo quattro matrici $F$ con questa propriet\`a: \begin{itemize} \item[(1)] Metodo di Gauss: $F=GP$ dove $P$ di permutazione tale che $(P\w)_1 \neq 0$ e $$ G = \ba{ccccc} 1 & 0 & & \cdots & 0 \\ -(P\w)_2/(P\w)_1 & 1 & 0 & \cdots & 0 \\ . & 0 &\ddots & & \vdots \\ \vdots & \vdots & & & 0 \\ -(P\w)_j/(P\w)_1 & 0 &\cdots & 0 & 1 \ea $$ \item[(2)] Metodo di Gauss con pivot parziale: come (1), ma si richiede $\|(P\w)_1\|=\max_{k=1,\ldots,j} \|(P\w)_k\|$. Con questa scelta di $P$ gli elementi della matrice $G$ hanno tutti modulo minore o uguale a $1$ $\then$ se $\z$ \`e un vettore affetto da errore questo errore non \`e amplificato nel calcolo di $G\z$ $\then$ pi\`u stabile (meno accumulazione degli errori di arrotondamento) di Gauss \item[(3)] Metodo di Givens ($F$ unitaria): $F=Q_j\cdots Q_3Q_2$, $Q_k$ matrice $j\times j$ di Givens. $a=w_1/\sqrt{w_1^2+w_2^2}$, $b=w_2/\sqrt{w_1^2+w_2^2}$, $$ Q_2\w = \ba{ccccc} a & b & & & \\ -b & a & & & \\ & & 1 & & \\ & & &\ddots & \\ & & & & 1 \ea \ba{c} w_1 \\ w_2 \\ \vdots \\ w_j \ea = \ba{c} \sqrt{w_1^2+w_2^2} \\ 0 \\ w_3 \\ \vdots \\ w_j \ea $$ $a=\sqrt{w_1^2+w_2^2}/\sqrt{w_1^2+w_2^2+w_3^2}$, $b=w_3/\sqrt{w_1^2+w_2^2+w_3^2}$, $$ Q_3Q_2w = \ba{cccccc} a & 0 & b & & & \\ 0 & 1 & 0 & & & \\ -b & 0 & a & & & \\ & & & 1 & & \\ & & & & \ddots & \\ & & & & & 1 \ea \ba{c} \sqrt{w_1^2+w_2^2} \\ 0 \\ w_3 \\ \vdots \\ w_j \ea = \ba{c} \sqrt{w_1^2+w_2^2+w_3^2} \\ 0 \\ 0 \\ w_4 \\ \vdots \\ w_j \ea $$ e cosi' via... \item[(4)] Metodo di Householder ($F$ unitaria): $F =$ matrice di Householder $= I-(2/\u^\u)\u\u^$, $\u$ vettore $j\times 1$ opportuno \end{itemize} \vskip0.2cm $\square$ Utilizzando i metodi (1),(2),(3) trasformare i vettori $$ \w = \ba{c} 0 \\ 1/\sqrt{3} \\ \sqrt{2}/\sqrt{3} \ea,\ \ \w = \ba{c} 1/\sqrt{2} \\ 1/2 \\ 1/2 \ea $$ in un vettore del tipo $$ F\w = \ba{c} * \\ 0 \\ 0 \ea $$ \vskip0.2cm {\it Numero di condizionamento di una matrice} \vskip0.2cm $\square$ Mostrare che le seguenti due matrici $$ \ba{cc} 1 & 1/2 \\ 1/2 & 1/3 \ea, \ \ \ba{ccc} 1 & 1/2 & 1/3 \\ 1/2 & 1/3 & 1/4 \\ 1/3 & 1/4 & 1/5 \ea $$ sono definite positive. Calcolare il loro numero di condizionamento \vskip0.2cm $\square$ Usando l'identit\`a $1/(i+j-1) = \int_0^1 x^{i+j-2}dx$, mostrare che la matrice ``di Hilbert'' $$ A = \ba{cccc} 1 & 1/2 & \cdots & 1/n \\ 1/2 & 1/3 & \cdots & 1/(n+1) \\ & & & \\ 1/n & 1/(n+1) & \cdots & 1/(2n-1) \ea = ( 1/(i+j-1) )_{i,j=1\ldots n} $$ \`e definita positiva. La matrice di Hilbert ha un numero di condizionamento che cresce molto rapidamente con n \vskip0.2cm $\square$ Per $A$ $n\times n$ non singolare sia $\mu(A)=\\|A\\|\\|A^{-1}\\|$ il ``numero di condizionamento'' di $A$. Dal risultato: $A\x=\b$ $\&$ $A(\x+d\x)=\b+d\b$ $\then$ $\\|d\x\\| / \\|\x\\| \leq \mu(A)\\|d\b\\|/\\|\b\\|$ (valido se la norma matriciale \`e indotta da quella vettoriale), segue che $\mu(A)$ misura la sensibilit\`a della soluzione di un sistema lineare a una eventuale perturbazione del vettore dei termini noti. Ad esempio la soluzione del sistema $$ A\x = \ba{cc} 1 & 900 \\ 0 & 1 \ea \ba{c} x_1 \\ x_2 \ea = \ba{c} b_1 \\ b_2 \ea $$ \`e molto sensibile a variazioni di $b_1,b_2$ perch\'e $\mu(A) \approx 10^6$ e, quindi, una perturbazione su $\b$ pu\`o causare una grande perturbazione su $\x$ \vskip0.2cm $\square$ Valgono le seguenti affermazioni: \begin{itemize} \item[(1)] $\mu(A)\geq \max\|\E_i\|/\min\|\E_i\|\geq 1$, $\E_i$ autovalori di $A$ \item[(2)] Se $A$ \`e hermitiana e $\\|\cdot\\|$ \`e la norma spettrale (cio\`e la norma matriciale indotta dalla norma vettoriale euclidea), allora $\mu(A)=\max\|\E_i\|/\min\|\E_i\|$ \item[(3)] Se $A$ \`e definita positiva e $\\|\cdot\\|$ \`e la norma spettrale, allora $\mu(A)=\max \E_i/\min \E_i$ \end{itemize} \vskip0.2cm $\square$ Scrivere una limitazione superiore per $\mu(A)$ essendo $A$ la matrice tridiagonale $$ A = \ba{ccccc} 2+h^2p_1 & -1 & & & \\ -1 & 2+h^2p_2 & -1 & & \\ & -1 & \ddots& \ddots& \\ & & \ddots& \ddots& -1 \\ & & & -1 & 2+h^2p_n \ea , $$ con $p_i$ reali positivi per ogni $i$ \vskip0.2cm $\square$ Il numero di condizionamento delle matrici $$ \ba{cc} 1 & 0 \\ m_{21} & 1 \ea, \ \|m_{21}\|\leq 1,\ \ba{ccc} 1 & 0 & 0 \\ m_{21} & 1 & 0 \\ m_{31} & 0 & 1 \ea,\ \|m_{i1}\|\leq 1, $$ \`e maggiore di $1$. \vskip0.2cm $\square$ Il numero di condizionamento di ogni matrice unitaria, misurato con la norma spettrale, \`e uguale a $1$ \vskip0.2cm {\it Norme matriciali} \vskip0.2cm $\square$ Data $\\|\cdot\\|$ norma vettoriale, per $A$ $n\times n$ si pu\`o usare come misura di $A$ il numero $\\|A\\| = \sup_{\z\ n\times 1\neq\vn} (\\|A\z\\|/\\|\z\\|)$. Questo numero soddisfa le seguenti propriet\`a: \begin{itemize} \item[(1)] $\\|A\\|\geq 0$ \item[(2)] $\\|A\\|=0$ iff $A=0$ \item[(3)] $\\|aA\\|=\|a\|\\|A\\|$ \item[(4)] $\\|A+B\\|\leq\\|A\\|+\\|B\\|$ \item[(5)] $\\|AB\\|\leq\\|A\\|\\|B\\|$ \end{itemize} ($A,B$ $n\times n$, $a$ $1\times 1$) Ogni numero che soddisfa tali propriet\`a \`e detto ``norma matriciale'' \vskip0.2cm $\square$ Dimostrare che $\rho(A)=\max\|\E_i\|$, $\E_i$ autovalori di $A$ $n\times n$, non \`e una norma matriciale \vskip0.2cm $\square$ Per le norme matriciali ``indotte'' dalle norme vettoriali $\\|\cdot\\|_2$, $\\|\cdot\\|_1$, $\\|\cdot\\|_{\infty}$, si dimostra che $\\|A\\|_2 = \sqrt{\rho(A^A)}$, $\\|A\\|_1 = \max_j \sum_i \|a_{ij}\|$, $\\|A\\|_{\infty} = \max_i \sum_j \|a_{ij}\|$. Se $\\|\cdot\\|$ \`e una norma matriciale indotta da una norma vettoriale ed $I$ \`e la matrice identica allora $\\|I\\|=1$. Esempi di norme matriciali che non sono indotte da norme vettoriali sono: $\\|A\\|_F = \sqrt{\sum_{i,j} \|a_{ij}\|^2} = \sqrt{ \tr(A^A) }$ ``norma di Frobenius'' e $\\|A\\| = n \max_{i,j} \|a_{ij}\|$, infatti se si misura la matrice identica con tali norme si ottengono numeri maggiori di $1$. Le norme matriciali, come quelle vettoriali, sono equivalenti tra loro. \vskip0.2cm $\square$ La maggiorazione per il raggio spettrale (di una matrice) ottenuta in precedenza si pu\`o riscrivere come segue: $\rho(A)\leq \min\{\\|A\\|_1,\\|A\\|_{\infty}\}$. Tale risultato si pu\`o generalizzare: per ogni norma matriciale $\\|\cdot\\|$ indotta da una norma vettoriale si ha $\rho(A)\leq\\|A\\|$. In realt\`a la limitazione $\rho(A)\leq\\|A\\|$ \`e vera per ogni norma matriciale $\\|\cdot\\|$. Quindi, ogni cerchio del piano complesso del tipo $\{z\in\CC:\ \|z\|\leq\\|A\\|\}$ (di centro $(0,0)$ e raggio $\\|A\\|$) con $\\|\cdot\\|$ norma matriciale qualsiasi deve contenere tutti gli autovalori di $A$ \vskip0.2cm $\square$ Dimostrare che per $A$ $n\times n$ il numero $\max_{i,j} \|a_{i,j}\|$ \`e una misura di $A$ che non \`e una norma matriciale \vskip0.2cm $\square$ Sia $A$ $n\times n$ generica e $Q$ $n\times n$ unitaria. Allora \begin{itemize} \item[(1)] $\\|Q\\|_2=1$ \item[(2)] $\\|QA\\|_2=\\|AQ\\|_2=\\|A\\|_2$ \item[(3)] $\\|Q\\|_F=\sqrt{n}$ \item[(4)] $\\|QA\\|_F=\\|AQ\\|_F=\\|A\\|_F$ \item[(5)] $\\|A\\|_{2,F}=\\|A^H\\|_{2,F}$ \item[(6)] $(\\|A\\|_2)^2 \leq \\|A\\|_1\\|A\\|_{\infty}$ \item[(7)] esiste $A$ $n\times n$ tale che $\\|A\\|_2>\\|A\\|_{\infty}$ \end{itemize} {\it Risoluzione}. (5) $\\|A\\|_2^2=\rho(A^A)\leq\\|A^A\\|_2\leq\\|A^\\|_2\\|A\\|_2$ $\then$ $\\|A\\|_2\leq\\|A^\\|_2$. Si dimostra allo stesso modo che $\\|A^\\|_2\leq\\|A\\|_2$. \vskip0.1cm (6) $\\|A\\|_2^2=\rho(A^A)\leq\\|A^A\\|_1\leq\\|A^\\|_1\\|A\\|_1=\\|A\\|_{\infty}\\|A\\|_1$. \vskip0.1cm (7) Sia $$ A=\ba{cc} 1 & 10 \\ 1 & 10 \ea $$ Allora $\\|A\\|_{\infty}=11$, $\\|A\\|_1=20$, $\\|A\\|_2\geq\f{\\|A\e_2\\|_2}{\\|\e_2\\|_2}=10\R{2}$ $\then$ $\\|A\\|_2>\\|A\\|_{\infty}$. Un altro esempio. Sia $A=\al\e\e^T+\be\e\e_j^T$, $\e^T=[1\ 1 \cdots 1]$, $\al\geq 0$, $\be>0$ $\then$ $\\|A\\|_{\infty}=n\al+\be$, $\\|A\\|_1=n(\al+\be)$, $\\|A\\|_2\geq\f{\\|A\e_j\\|_2}{\\|\e_j\\|_2}=\R{n}(\al+\be)$. Quindi, se $\be>\R{n}\al$ allora $\\|A\\|_2>\\|A\\|_{\infty}$. Nota: per (6), ogni volta che $\\|A\\|_2>\\|A\\|_{\infty}$ deve essere necessariamente verificata la disuguaglianza $\\|A\\|_2<\\|A\\|_1$. \vskip0.3cm $\square$ Calcolare il numero $\mu_1(A)=\\|A\\|_1 \\|A^{-1}\\|_1$ per $$ A = \ba{cc} 1 & 900 \\ 0 & 1 \ea $$ \vskip0.2cm 7 Aprile 2009, 4 Aprile 2009, 22 Marzo 2009, 15 Marzo 2009, 7 Marzo 2009 \vskip0.2cm 7 aprile era perFra \vskip0.2cm 4 Aprile 2009 \vskip0.2cm $\square$ Sia $A=\u\v^$, con $\u,\v$ vettori $n\times 1$. Dimostrare: \begin{itemize} \item[(1)] $\sqrt{\rho(A^A)}=\\|\u\\|_2\\|\v\\|_2$ \item[(2)] $\max_i \sum_j \|a_{ij}\| = \\|\u\\|_{\infty}\\|\v\\|_1$ \item[(3)] $\max_j \sum_i \|a_{ij}\| = \\|\u\\|_1\\|\v\\|_{\infty}$ \item[(4)] $\rho(A)=\|\v^\u\| \leq \min\{\\|\u\\|_2\\|\v\\|_2, \\|\u\\|_1\\|\v\\|_{\infty},\\|\u\\|_{\infty}\\|\v\\|_1\}$ \item[(5)] Esistono $\u,\v$ per cui $\|\v^\u\|\leq\\|\u\\|_1\\|\v\\|_{\infty}<\\|\u\\|_2\\|\v\\|_2$ \end{itemize} \vskip0.2cm $\square$ Usando il I teorema di Gershgorin osservare che esiste un intervallo positivo della retta reale che contiene i due autovalori di $$ A = \ba{cc} 1 & -1/2 \\ -1/2 & 1 \ea $$ (non calcolare gli autovalori). Essendo $A$ anche hermitiana ne segue che $A$ \`e definita positiva. \vskip0.2cm $\square$ E' possibile stabilire usando il I teorema di Gershgorin se $$ A = \ba{cc} 1 & 1/2 \\ 1/2 & 1/3 \ea $$ \`e definita positiva? Dimostrare che A \`e definita positiva. \vskip0.2cm $\square$ Data $$ A = \ba{cccc} 1 & 1/4 & 2 & 1 \\ 1/2& 2 & 0& 1-\sqrt{2} \\ 0 & 1/2& -3& 0 \\ -\ui/2& 1/2& 1& 1+\ui \ea $$ disegnare i seguenti insiemi, tutti contenenti gli autovalori di $A$: \begin{itemize} \item[(1)] $\{ z:\ \|z\|\leq\min\{\max_i \sum_j \|a_{ij}\|, \max_j \sum_i \|a_{ij}\|\} \}$ \item[(2)] $U_{i=1\ldots n} K_i$, $K_i$ cerchi di Gershgorin di $A$ \item[(3)] $U_{i=1\ldots n} H_i$, $H_i$ cerchi di Gershgorin di $A^T$ \item[(4)] $(U_{i=1\ldots n} K_i)\ \bigcap\ (U_{i=1\ldots n} H_i)$ \end{itemize} Si pu\`o stabilire se $A$ \`e non singolare senza calcolare il suo determinante? \vskip0.2cm $\square$ I T. di Gershgorin: Sia $A$ $n\times n$ generica. Gli autovalori di $A$ sono nell'insieme $U_{i=1\ldots n} K_i$, $K_i = \{z:\ \|z-a_{ii}\| \leq \sum_{j,j \neq i} \|a_{ij}\|\}$ \vskip0.2cm $\square$ Rafforzare il I T.di Gershgorin usando l'osservazione che $A$ e $A^T$ hanno gli stessi autovalori. \vskip0.2cm $\square$ Localizzare gli autovalori della matrice $$ A = \ba{ccc} 1 & 2 & 3 \\ -1 & 1/2 & 1 \\ 4 & 2 & 1 \ea $$ \vskip0.2cm $\square$ Dimostrare, senza calcolare gli autovalori, che la matrice $$ A = \ba{cc} 3 & 2 \\ 1 & 2 \ea $$ ha autovalori reali \vskip0.2cm $\square$ Sia $Q$ unitaria $n\times n$. Dimostrare l'identit\`a $\\|Q\x\\|_2=\\|\x\\|_2$, ovvero applicando una matrice unitaria a un vettore la misura in norma euclidea del vettore non cambia. \vskip0.2cm $\square$ Sia $\w$ $n\times 1$. Se $F$ $n\times n$ unitaria \`e tale che $$ Fw = \ba{c} a \\ 0 \\ \vdots \\ 0 \ea, $$ cio\`e $(F\w)_i=0$, $i=2\ldots n$, allora $\|a\|=\\|w\\|_2$. \vskip0.2cm $\square$ Dare una maggiorazione per $\rho(A)$ essendo $$ A = \ba{ccc} 1 & 2 & 3 \\ -1 & 1/2 & 1 \\ 4 & 2 & 1 \ea $$ \vskip0.2cm $\square$ Scrivere l'inversa della matrice $A$ $n\times n$ $$ a_{i,i}=1,\ i=1\ldots n,\ a_{i,i+1}=-1,\ i=1\ldots n-1,\ a_{n,1}=a,\ a_{i,j}=0\ \hbox{altrimenti}. $$ \vskip0.2cm $\square$ Sia $A=A^$ $n\times n$. Allora le seguenti affermazioni sono equivalenti: \begin{itemize} \item[(1)] $\z^A\z>0$ per ogni vettore $\z$ non nullo \item[(2)] gli autovalori di $A$ sono positivi \item[(3)] le sottomatrici di $A$ $$ \ba{ccc} a_{11} & \cdots & a_{1k} \\ \vdots & & \vdots \\ a_{k1} & \cdots & a_{kk} \ea $$ hanno determinante positivo per $k=1,\ldots,n$. \end{itemize} ($A$ tale che $A=A^$ e vale (1) si dice definita positiva). Vedremo che in certi casi \`e possibile dire che gli autovalori sono positivi senza calcolarli e questo, per la (2), \`e sufficiente per stabilire che $A$ \`e definita positiva \vskip0.2cm $\square$ (PER ME) Sia $A$ la matrice $2\times 2$ $$ A = \ba{cc} c & a \\ \o{a}& b \ea, $$ $a$ numero complesso, $b,c$ reali. Si osserva che $A$ \`e hermitiana. 1) Condizione necessaria affinch\'e $A$ sia definita positiva \`e che $b$ e $c$ siano positivi. 2) Condizione necessaria e sufficiente affinch\'e $A$ sia definita positiva \`e che $c>0$, $b/c>0$, $\sqrt{b/c}-\|a/c\|>0$ ovvero che $c>0$ $\&$ $bc-\|a\|^2>0$. Suggerimento: applicare il risultato ottenuto nell'esercizio precedente \vskip0.1cm {\it Risoluzione} $$ A = \ba{cc} c & a \\ \o{a} & b \ea,\ b,c\in\RR,\ \ A = c \ba{cc} 1 & a/c \\ \o{a/c} & b/c \ea $$ definita positiva iff $$ c>0\ \ \& \ \ \ba{cc} 1 & a/c \\ \o{a/c} & b/c \ea \ \ \pd $$ iff $c>0$, $b/c>0$, $\sqrt{b/c}-\|a/c\|>0$ iff $c>0$ $\&$ $bc-\|a\|^2>0$ \vskip0.2cm $\square$ (PER ME) Sia $A$ la matrice $2\times 2$ $$ A = \ba{cc} 1 & a \\ \o{a} & b \ea, $$ $a$ numero complesso, $b$ reale. Si osserva che $A$ \`e hermitiana 1) Condizione necessaria affinch\'e $A$ sia definita positiva \`e che $b$ sia positivo. 2) Condizione necessaria e sufficiente affinch\'e $A$ sia definita positiva \`e che $b$ sia positivo $\&$ $\sqrt{b}-\|a\|>0$ o, equivalentemente, che $b-\|a\|^2$ sia positivo. Trovare una formula per $\z^A\z$ che consenta di dedurre tale affermazione senza calcolare esplicitamente gli autovalori. \vskip0.1cm {\it Risoluzione} $a$, $b$ numeri complessi $\then$ $$ \z^A\z = \|z_1\|^2 + b\|z_2\|^2 + z_1\o{z_2}\o{a} + \o{z_1}z_2a. $$ b reale positivo $\then$ $$ \z^A\z = (1-\f{\|a\|}{\sqrt{b}})(\|z_1\|^2+b\|z_2\|^2) + \f{\|a\|}{\sqrt{b}} \|z_1+\sqrt{b}\exp{\ui\arg(a)}z_2\|^2. $$ Ne segue che $A$ \`e definita positiva se e solo se $b>0$ $\&$ $\sqrt{b}-\|a\|>0$ se e solo se $b-\|a\|^2>0$ \vskip0.2cm $\square$ La matrice $$ A = \ba{cc} 1 & a \\ \o{a} & 1 \ea, $$ $a$ numero complesso, \`e definita positiva se e solo se $1-\|a\|>0$ (o, equivalentemente, se e solo se $1-\|a\|^2>0$). Trovare una formula per $\z^A\z$ che consenta di dedurre (senza calcolare esplicitamente gli autovalori) tale affermazione. Suggerimento: studiare i casi $a$ reale negativo (vedi $a=-1/2$ del precedente esercizio), poi $a$ reale positivo e infine $a$ generico. \vskip0.1cm {\it Risoluzione} $$ \z^A\z = \|z_1\|^2+\|z_2\|^2+z_1\o{z_2}\o{a}+z_2\o{z_1}a. $$ \begin{itemize} \item[] $a$ reale positivo: $\z^A\z = (1-a)(\|z_1\|^2+\|z_2\|^2)+a\|z_1+z_2\|^2$, \item[] $a$ reale negativo: $\z^A\z = (1+a)(\|z_1\|^2+\|z_2\|^2)-a\|z_1-z_2\|^2$, \item[] $a$ generico: $\z^A\z = (1-\|a\|)(\|z_1\|^2+\|z_2\|^2) +\|a\|\|z_1+\exp{\ui\arg(a)}z_2\|^2$. \end{itemize} Ne segue che $A$ \`e definita positiva se e solo se $1-\|a\|>0$. \vskip0.2cm $\square$ Dimostrare, senza calcolare gli autovalori, che la matrice $$ A = \ba{cc} 1 & -1/2 \\ -1/2 & 1 \ea $$ \`e definita positiva. {\it Risoluzione}: 1) $A$ \`e reale simmetrica, quindi \`e hermitiana. 2) Inoltre, $$ \bi{rcl} \z^A\z & = & [\o{z_1}\ \o{z_2}] \ba{cc} 1 & -1/2 \\ -1/2 & 1 \ea \ba{c} z_1 \\ z_2 \ea = [\o{z_1}-1/2\o{z_2}\ -1/2\o{z_1}+\o{z_2}]\ba{c} z_1 \\ z_2 \ea \\ & = & \|z_1\|^2-1/2z_1\o{z_2}-1/2\o{z_1}z_2+\|z_2\|^2 = 1/2(\|z_1\|^2+\|z_2\|^2) + 1/2(z_1-z_2)(\o{z_1}-\o{z_2}) \\ & = & 1/2(\|z_1\|^2+\|z_2\|^2) + 1/2\|z_1-z_2\|^2 >= 1/2(\|z_1\|^2+\|z_2\|^2). \ei $$ Ne segue che $\z^A\z>0$ per ogni vettore $\z=[z_1\ z_2]^T$ non nullo. \vskip0.2cm {\it Norme vettoriali}: \vskip0.2cm $\square$ $a$ scalare ($1\times 1$), $\|a\|=$ modulo di $a$ $=$ misura della distanza tra i punti $(0,0)$ e $(\Re(a),\Im(a))$ $=\sqrt{\Re(a)^2+\Im(a)^2}$. $\square$ $\z$ $n\times 1$, $\\|\z\\|=\\|\z\\|_2=(\sum_i \|z_i\|^2)^{1/2}=$ misura ``euclidea'' di $\z$. Propriet\`a: \begin{itemize} \item[(1)] $\\|\z\\|\geq 0$ per ogni $\z$ \item[(2)] $\\|\z\\|=0$ iff $\z=\vn$ \item[(3)] $\\|a\z\\|=\|a\|\\|\z\\|$, per ogni $a$ scalare e $\z$ \item[(4)] $\\|\z+\w\\|\leq\\|\z\\|+\\|\w\\|$, per ogni $\z,\w$ \end{itemize} Ogni misura che soddisfa tali propriet\`a \`e detta ``norma vettoriale''. Ad esempio sono norme vettoriali anche $\\|\z\\|=\\|\z\\|_1=\sum_i \|z_i\|$ e $\\|\z\\|=\\|\z\\|_{\infty}=\max_i \|z_i\|$ (verificarlo). Per ogni $\z$ $n\times 1$ non nullo il vettore $\y=\z/\\|\z\\|$ ha norma uguale a $1$, infatti, per la terza propriet\`a delle norme vettoriali, $\\|\z/\\|\z\\|\\|=(1/\\|\z\\|)\\|\z\\|=1$. Esempi: $$ \z = \ba{c} 1/2 \\ 1/2 \ea\ \then\ \\|\z\\|_2=\f{1}{\sqrt{2}},\ \\|\z\\|_1=1, \ \\|\z\\|_{\infty}=1/2 $$ $$ \then\ \y=\z/\\|\z\\|_2 = \ba{c} \sqrt{2}/2 \\ \sqrt{2}/2 \ea,\ \y=\z/\\|\z\\|_1 = \ba{c} 1/2 \\ 1/2 \ea,\ \y=\z/\\|\z\\|_{\infty} = \ba{c} 1 \\ 1 \ea. $$ E' semplice far vedere che, per ogni vettore $\z$ $n\times 1$, $(1/n)\\|\z\\|_1\leq\\|\z\\|_{\infty}\leq\\|\z\\|_1$. Pi\`u in generale comunque prese due norme vettoriali $\\|\cdot\\|_a$ e $\\|\cdot\\|_b$ queste sono equivalenti, cio\`e esistono $c_1$ e $c_2$ costanti positive per cui $c_1\\|\z\\|_b\leq\\|\z\\|_a\leq c_2\\|\z\\|_b$ per ogni $\z$. Ne segue che, se un vettore ha misura grande (piccola) in una norma allora ha misura grande (piccola) in ogni altra norma. Inoltre, se per una certa norma $\\|\cdot\\|_b$ si ha che $\\|\z_k-\z\\|_b\to 0$ (per $k$ che tende a infinito) allora sar\`a anche vero che $\\|\z_k-\z\\|\to 0$ in ogni norma vettoriale $\\|\cdot\\|$. \vskip0.2cm {\it Due limitazioni superiori per il raggio spettrale}: \vskip0.2cm $\square$ $$ A\ n\times n\ \ \then \rho(A) \leq \max_i \sum_j \|a_{ij}\|,\ \ \rho(A)\leq \max_j \sum_i \|a_{ij}\| $$ Dim: $A\v=\E\v$ $\then$ $\sum_j a_{ij}v_j=\E v_i$ per ogni $i$ $\then$ $\|\E\|\|v_i\| \leq \sum_j \|a_{ij}\|\|v_j\| \leq \\|\v\\|_{\infty} \sum_j \|a_{ij}\|$ per ogni $i$ $\then$ esiste $k$ tale che $\|\E\|\leq \sum_j \|a_{kj}\| \leq\max_i \sum_j \|a_{ij}\|$. La seconda disuguaglianza si ottiene applicando la prima ad $A^T$ ed osservando che $\rho(A)=\rho(A^T)$ (gli autovalori di $A^T$ coincidono con quelli di $A$). \vskip0.2cm {\it Teoria(metododellepotenze)} [per il calcolo dell'autovalore in modulo dominante di una matrice e del corrispondente autovettore]: \vskip0.2cm $A$ $n\times n$ diagonalizzabile, ovvero $A\v_i=\E_i\v_i$, $i=1,\ldots,n$, con $\v_1,\ldots,\v_n$ linearmente indipendenti. $\|\E_1\|>\|\E_j\|$ per ogni $j \neq 1$, ovvero c'\`e un solo autovalore il cui modulo \`e uguale al raggio spettrale di $A$ e tale autovalore \`e semplice (cio\`e \`e radice semplice del polinomio caratteristico di $A$). $\x$ $n\times 1$ tale che $a_1$ in $\x=a_1\v_1+a_2\v_2+\ldots+a_n\v_n$ \`e diverso da zero. In queste ipotesi si ha, per $k$ che tende a infinito, \begin{itemize} \item $(1/\E_1^k)A^k\x \to a_1\v_1$, quindi $(\exp{-\ui a})^k A^k\x/\\|A^k\x\\| \to a_1\v_1/\\|a_1\v_1\\|$ dove $a$ \`e l'argomento di $\E_1$ ($\E_1=\|\E_1\|\exp{\ui a}$). \item per ogni $\v$, $\v^T\v_1 \neq 0$, $\v^TA^{k+1}\x/\v^TA^k\x \to \E_1$ (nota: $\v^T\v_1 \neq 0$ $\then$ $\v^TA^k\x \neq 0$ per $k$ grande). \end{itemize} Ne segue che le successioni $\{\z_k\},\{\y_k\}$ generate dall'algoritmo: $$ \bi{l} \y_{-1}=\x \\ \hbox{Per}\ k=0,1\ldots \\ \z_k=\y_{k-1}/\\|\y_{k-1}\\|,\ \y_k=A\z_k\ (\hbox{NOTA}:\ \z_k=A^k\x/\\|A^k\x\\|) \ei $$ soddisfano le propriet\`a: \begin{itemize} \item[(1)] $(\exp{-\ui a})^k \z_k \to a_1\v_1/\\|a_1\v_1\\|$ \item[(2)] $\v^T\y_k/\v^T\z_k \to \E_1$ ($\v^T\v_1 \neq 0$ $\then$ $\v^T\z_k \neq 0$ per $k$ grande) \end{itemize} Dim della NOTA. Per induzione: $$ \z_0=\f{\y_{-1}}{\\|\y_{-1}\\|}=\f{\x}{\\|\x\\|},\ \ ok! $$ $$ \z_{k+1} = \f{\y_k}{\\|\y_k\\|} = \f{A\z_k}{\\|A\z_k\\|} = \f{AA^k\x}{\\|AA^k\x\\|} = \f{A^{k+1}\x}{\\|A^{k+1}\x\\|},\ \ ok! $$ Dim di (1) e (2). Usare la NOTA. Ad esempio, per (2): $$ \f{\v^T\y_k}{\v^T\z_k} = \f{\v^TA\z_k}{\v^T\z_k} = \f{\v^TA^{k+1}\x/\\|A^k\x\\|} {\v^TA^k\x/\\|A^k\x\\|} = \f{\v^TA^{k+1}\x}{\v^TA^k\x}. $$ \vskip0.2cm Esercizi: \vskip0.2cm $\square$ Sia $A$ la matrice $$ \ba{cc} 1 & -1/2 \\ -1/2 & 1 \ea. $$ Scrivere un algoritmo per il calcolo dell'autovalore di modulo massimo e del corrispondente autovettore (usare il metodo delle potenze con $\\|\z\\|=\sum_i \|z_i\|$) {\it Risoluzione}: $A$ \`e diagonalizzabile e $\|\E_1\|>\|\E_2\|$: $A=VDV^{-1}$, $$ D = \ba{cc} 1/2 & 0 \\ 0 & 3/2 \ea, V = \f{1}{\sqrt{2}} \ba{cc} 1 & 1 \\ 1 & -1 \ea $$ (Nota: $V=V^=V^{-1}$). In altri termini $A\v_1=\E_1\v_1$, $A\v_2=\E_2\v_2$, $\v_1=\ba{c} 1 \\ -1 \ea$, $\E_1=3/2$, $\v_2=\ba{c} 1\\ 1 \ea$, $\E_2=1/2$ e $\v_1,\v_2$ sono linearmente indipendenti. Sia $\x$ il vettore $\ba{c} 1 \\ 0 \ea$. $a_1$ in $\x=a_1\v_1+a_2\v_2$ \`e diverso da zero, infatti $$ \ba{c} 1 \\ 0 \ea = \um \ba{c} 1 \\ 1 \ea + \um \ba{c} 1 \\ -1 \ea. $$ Quindi, se $\y_{-1}=\x$ e per $k=0,1,\ldots$ si definisce la coppia di vettori $\z_k=\y_{k-1}/\\|\y_{k-1}\\|$, $\y_k=A\z_k$ (nota: $\z_k=A^k\x/\\|A^k\x\\|$) allora, per $k$ che tende a infinito, $$ \z_k \to a_1\v_1/\\|a_1\v_1\\| = \ba{c} 1/2 \\ -1/2 \ea, \v^T\y_k/\v^T\z_k \to \E_1=3/2 \ \ \fa\,\v,\, \v^T\v_1 \neq 0 $$ (nota: $\v^T\v_1 \neq 0$ $\then$ $\v^T\z_k \neq 0$ per $k$ grande). \vskip0.2cm $\square$ Eseguiamo i primi passi con $\v=\ba{c}1\\0\ea$ ($\v=\ba{c}1\\1\ea$ non ok perch\'e $\v^T\v_1=0$) $$ \bi{l} \z_0 = \ba{c}1\\0\ea,\ \y_0 = \ba{c}1\\-1/2\ea,\ \v^T\y_0/\v^T\z_0=1 \\ \z_1 = \ba{c}2/3\\-1/3\ea,\ \y_1 = \ba{c}5/6\\-4/6\ea,\ \v^T\y_1/\v^T\z_1=5/4 \\ \z_2 = \ba{c}5/9\\-4/9\ea,\ \y_2 = \ba{c}14/18\\-13/18\ea,\ \v^T\y_2/\v^T\z_2=14/10 \ei $$ $\ldots$ \vskip0.2cm $\square$ Ripetere l'esercizio precedente per le matrici $$ \ba{cc} 1 & -1/2 \\ -4 & 1 \ea,\ \ \ba{cc} 1 & 1 \\ 4 & -2 \ea. $$ \vskip0.2cm $\square$ Sia $A$ $n\times n$ definita positiva e $\E_j$, $j=1,\ldots,n$, i suoi autovalori. Nell'ipotesi $\E_1>\E_2\geq \ldots\geq\E_{n-1}>\E_n$ proporre un algoritmo per il calcolo del numero $\max \E_j/\min \E_j$ \vskip0.2cm $\square$ Sia $A$ $n\times n$ hermitiana invertibile e $\E_j$, $j=1,\ldots,n$, i suoi autovalori. Proporre un algoritmo per il calcolo del numero $\max\|\E_j\|/\min\|\E_j\|$ \vskip0.2cm $\square$ (PER ME) Sia $A$ $n\times n$ hermitiana e $\E_1,\E_2,\ldots,\E_n$ i suoi autovalori dove $\E_1$ si suppone diverso da $0$. Sia $\y_1$ $n\times 1$ non nullo tale che $A\y_1=\E_1\y_1$ e $W=A-(\E_1/\y_1^\y_1)\y_1\y_1^$. Allora $W$ \`e hermitiana e i suoi autovalori sono $0,\E_2,\ldots,\E_n$. Dedurre da questo risultato un algoritmo per il calcolo di tutti gli autovalori di $A$ \vskip0.2cm $\square$ (PER ME) Sia $A$ $n\times n$ e $\E_1,\E_2,\ldots,\E_n$ i suoi autovalori dove $\E_1$ si suppone diverso da $0$. Sia $\y_1$ $n\times 1$ non nullo tale che $A\y_1=\E_1\y_1$ e $W=A-(\E_1/\w^\y_1)\y_1\w^$ con $\w$ $n\times 1$ tale che $\w^\y_1 \neq 0$. Allora gli autovalori di $W$ sono, per ogni scelta di $\w$, $0,\E_2,\ldots,\E_n$. ESEMPIO. Se $\w^=\e_i^TA=$ riga $i$ di $A$ con $i$ tale che $(\y_1)_i \neq 0$, allora $\w^\y_1=\E_1(\y_1)_i \neq 0$, quindi gli autovalori di $W=A-(1/(\y_1)_i)\y_1\e_i^TA$ sono $0,\E_2,\ldots,\E_n$. Notare che per tale scelta di $\w$, la riga $i$ di $W$ \`e nulla, cio\`e $$ W = \ba{ccc} W_{11} & W_{12} & W_{13} \\ 0 .. 0 & 0 & 0 .. 0 \\ W_{31} & W_{32} & W_{33} \ea $$ con $W_{11}$ $i-1\times i-1$, $W_{12}$ $i-1\times 1$, $W_{32}$ $n-i\times 1$, $W_{33}$ $n-i\times n-i$. Ne segue che $\E_2,\ldots,\E_n$ sono gli autovalori della matrice $n-1\times n-1$ $$ \ba{cc} W_{11} & W_{13} \\ W_{31} & W_{33} \ea. $$ FINE ESEMPIO Si verifica inoltre che $W\y_1=0$, cio\`e $\y_1$ (autovettore di $A$ relativo a $\E_1$) \`e autovettore di $W$ relativo a $0$. Se poi $\y_i$ son tali che $A\y_i=\E_i\y_i$, $i=2,\ldots,n$, allora per gli $i$ tali che $\E_i \neq 0,\E_1$, posto $\w_i=\y_i-(\E_1/\E_i)(\w^\y_i/\w^\y_1)\y_1$ si ha $W\w_i=\E_i\w_i$. Per\`o, se $A$ \`e singolare ci sono valori di $i$ in $2,\ldots,n$ per cui $\E_i=0$. In questo caso $A\y_i=\vn$ $\then$ $W\w_i=\vn$ con $\w_i=$ ? $\ldots$ Inoltre, $\E_1$ pu\`o essere radice multipla del polinomio caratteristico di $A$, cio\`e ci possono essere valori di $i$ in $2,\ldots,n$ tali che $\E_i=\E_1$. In questo caso $A\y_i=\E_1\y_i$ $i \neq 1$ $\then$ $W\w_i=\E_1\w_i$ con $\w_i=$ ? $\ldots$ \vskip0.2cm {\it Teoria(matrici stocastiche)}: \vskip0.2cm Se $A$ $n\times n$ \`e stocastica per colonne, cio\`e se $a_{ij}\geq 0$ per ogni $i,j$ e $\sum_i a_{ij} = 1$ per ogni $j$, allora: \begin{itemize} \item[(1)] $1$ \`e autovalore di $A$, cio\`e esiste $\z$ non nullo tale che $A\z=\z$ (ma \`e banale calcolarlo solo se $A$ \`e anche stocastica per righe) \item[(2)] $\rho(A)=1$, cio\`e $1\geq\|\E\|$ per ogni autovalore $\E$ di $A$ \item[(3)] per ogni vettore $\x$ $n\times 1$ con tutte le componenti non negative e di somma uguale a $1$ si ha che $A\x\geq \vn$ $\&$ $\sum_i (A\x)_i = 1$ \item[(4)] Teoria(metododellepotenzematricistocastiche): \begin{itemize} \item[] se $A$, inoltre, \`e diagonalizzabile, \item[] se $\E_1=1>\|\E_j\|$ per ogni $j \neq 1$, \item[] se $\x$ \`e tale che $a_1$ in $\x=a_1\v_1+\ldots+a_n\v_n$ \`e diverso da $0$, \item[] se $\\|\cdot\\|$ \`e la norma $\\|\z\\|=\sum_i \|z_i\|$, e \item[] se il vettore iniziale $\x$ \`e scelto tale che $x_i\geq 0$ $\&$ $\sum_i x_i=\\|\x\\|=1$, \end{itemize} ALLORA la successione $\{\z_k\}$ generata dall'algoritmo: $$ \z_0=\x, \quad \z_{k+1}=A\z_k,\ k=0,1\ldots $$ soddisfa le propriet\`a: \begin{itemize} \item[-] $\z_k=A^k\x\geq 0$ e $\\|\z_k\\|=1$ per ogni $k=0,1,\ldots$ e, per $k$ che tende a infinito, $\z_k \to a_1\v_1/\\|a_1\v_1\\|=\z$, $A\z=\z$, $\z\geq\vn$, $\\|\z\\|=1$, \item[-] $\e^T\z_{k+1}/\e^T\z_k=1/1 \to 1$ ($\e^T=[1\ 1\ \ldots\ 1]$). \end{itemize} \end{itemize} \vskip0.2cm Esercizi: \vskip0.2cm $\square$ Sia $$ A = \ba{ccc} 1/2 & 0 & 1/3 \\ 0 & 1/2 & 2/3 \\ 1/2 & 1/2 & 0 \ea. $$ Osservare che per $\z_0=\x=[ 1/3\ 1/3\ 1/3]^T$ si ottiene $$ \z_1=A\z_0=\ba{c} 5/18 \\ 7/18 \\ 1/3 \ea,\ \ \z_2=A\z_1 = \ba{c} 3/12 \\ 5/12 \\ 4/12 \ea,\ \ldots $$ quindi, effettivamente $\z_k$ sta convergendo al vettore $\z$ tale che $A\z=\z$, cio\`e $\z = [2/9\ 4/9\ 3/9]^T$. Verificare che tutte le ipotesi della teoria sulla convergenza sono soddisfatte (gli autovalori di $A$ sono: $1,1/2,-1/2$ $\ldots$) \vskip0.2cm $\square$ Ripetere l'esercizio precedente per $$ A = \ba{ccc} 1/6 & 1/2 & 1/3 \\ 1/6 & 1/4 & 1/3 \\ 2/3 & 1/4 & 1/3 \ea $$ \vskip0.2cm {\it Teoria(Google)} \vskip0.2cm [In un modello per la ricerca di documenti nel web \`e determinante una corretta valutazione delle importanze delle sue pagine. Per eseguirla \`e sufficiente calcolare l'autovettore relativo all'autovalore dominante di una matrice, solo che questa matrice \`e $n\times n$ con $n=$ numero delle pagine del web($\ldots$)]: \vskip0.2cm \begin{itemize} \item $G=\{1,2,\ldots,n\}$ le pagine del web \item $p_i=$ importanza della pagina $i$ \item $\deg(j)=$ numero delle pagine puntate da $j$ \end{itemize} $p_i=\sum_{j:j\to i} p_j/\deg(j)$ ($p_i$ \`e proporzionale alle importanze delle pagine che la puntano e inversamente proporzionale al numero delle pagine puntate da queste). $a_{ij}=1/\deg(j)$ se $j\to i$, $a_{ij}=0$ altrimenti $\then$ $p_i=\sum_{j=1\ldots n} a_{ij}p_j$, cio\`e, in forma vettoriale, $\p=A\p$. Quindi, per determinare il vettore $\p=[p_1\ p_2\ldots p_n]^T$ delle importanze delle pagine web \`e sufficiente trovare l'autovettore di $A$ relativo all'autovalore $1$. Se $A$ fosse stocastica per colonne e soddisfacesse le ipotesi in Teoria(metododellepotenzematricistocastiche), $\p$ si potrebbe calcolare con il metodo delle potenze. Questo in generale non \`e vero (ad esempio, \`e semplice vedere che $\sum_i a_{ij}= 1$ se $\deg(j)>0$ e $\sum_i a_{ij}=0$ altrimenti, cio\`e se vi sono pagine $j$ che non puntano a nulla $A$ non \`e nemmeno stocastica per colonne). Quindi $A$ va sostituita con una matrice $A'$ che soddisfa le propriet\`a dette, con il metodo delle potenze si calcola $\p'$ tale che $\p'=A'\p'$ e si usa $\p'$ come vettore delle importanze ($\ldots$) \vskip0.2cm 22 Marzo 2009 \vskip0.2cm $\square$ $\e_1$ vettore $n\times 1$ con elementi tutti nulli eccetto il primo che \`e uguale a $1$, $\y$ vettore $n\times 1$ con prima componente nulla. Allora $(I+\y\e_1^T)^{-1} = I-\y\e_1^T$ \vskip0.2cm $\square$ Scrivere l'inversa delle matrici $$ \ba{ccccc} 1 & 0 & 0 & 0 & 0 \\ 1/3 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 \\ -2 & 0 & 0 & 1 & 0 \\ 1/2 & 0 & 0 & 0 & 1 \ea,\ \ \ba{ccc} 3 & 0 & 0 \\ 1 & 3 & 0 \\ 1/2 & 0 & 3 \ea $$ \vskip0.2cm $\square$ Il prodotto di due matrici $T$, $U$ triangolari superiori (inferiori) \`e triangolare superiore (inferiore). Una matrice $T$ triangolare \`e invertibile se e solo se i suoi elementi diagonali sono tutti non nulli. L'inversa di una matrice $T$ triangolare superiore (inferiore) invertibile \`e triangolare superiore (inferiore). Inoltre gli elementi diagonali di $T^{-1}$ sono gli inversi degli elementi diagonali di $T$. ($T$, $U$ matrici $n\times n$) \vskip0.2cm $\square$ Trovare i valori di $a$ numero complesso per cui la matrice $A$ $2\times 2$ $$ \ba{cc} a & a \\ a & -a \ea $$ \`e unitaria \vskip0.2cm $\square$ $A$ hermitiana iff esiste $Q$ tale che $Q^{-1}AQ=D$, $Q^=Q^{-1}$, $D$ diagonale reale (dimostrare almeno una delle due implicazioni) \vskip0.2cm $\square$ Dimostrare che le matrici $A$ $$ \ba{cc} 2 & -1 \\ -1 & 2 \ea,\ \ba{cc} 2 & -1 \\ -3 & 2 \ea,\ \ba{cc} 2 & \ui+4 \\ \ui+4 & 7 \ea,\ \ba{cc} 0 & 1 \\ -1 & 0 \ea,\ \ba{ccc} 1/2 & 0 & 1/3 \\ 0 & 1/2 & 2/3 \\ 1/2 & 1/2 & 0 \ea $$ sono diagonalizzabili, cio\`e esiste $S$ non singolare tale che $S^{-1}AS=D$, $D$ diagonale. Dire quali tra di esse \`e diagonalizzabile tramite trasformazione unitaria, cio\`e esiste $S$, $S^H=S^{-1}$, per cui $S^{-1}AS=D$, con $D$ diagonale. Dire quali di esse hanno autovalori tutti reali. \vskip0.2cm $\square$ Mostrare che le matrici $$ A = \ba{cc} 0 & 1 \\ 0 & 0 \ea,\ \ B = \ba{ccc} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \ea $$ non sono diagonalizzabili. Calcolare $A^k$, $B^k$, $k=1,2,\ldots$ Dimostrare che ogni matrice $A$ $n\times n$ hermitiana che abbia tutti gli autovalori nulli deve essere la matrice nulla. \vskip0.2cm $\square$ Descrivere i seguenti insiemi di numeri complessi $z$: $\I_1=\{z:\ \|z-1\|=1\}$, $\I_2=\{z:\ \|z+1\|=3\}$, $\I_3=\{z:\ \|z-1\|>1\}$, $\I_4=\{z:\ \|z+1\|<3\}$, $\I_3 \bigcup \I_4$, $\I_3 \bigcap \I_4$, $\I_1 \bigcap \I_2$, $\I_2 \bigcup \I_4$, $\partial \I_4$, $\o{\I_4}$. \vskip0.2cm $\square$ Se $A=I+\y\w^$ \`e unitaria allora $\w=a\y$ con $a$ complesso \vskip0.2cm $\square$ I valori di $b$ numero complesso per cui la matrice $A=I+b\y\y^$ \`e unitaria sono $b=-2\cos(a)\exp{\ui a}/\y^\y$, $a$ reale. Per $a=0$ (oppure $a=\pi$) si ottengono, in particolare, le matrici di Householder \vskip0.2cm $\square$ Usando la formula $(I+\y\w^)^{-1}=I-(1/(\w^\y+1))\y\w^$, trovare una formula per $(A+\y\w^)^{-1}$, $A$ $n\times n$ non singolare (Sherman-Morrison). Suggerimento: $(A+\y\w^)^{-1}=( A(I+A^{-1}\y\w^) )^{-1}$ \vskip0.2cm $\square$ Se $S^{-1}MS=\diag(a,b,0\ldots 0)$, $S^=S^{-1}$, allora esistono $\y$, $\w$ tali che $M=\y\y^+\w\w^$. \vskip0.2cm $\square$ (PER ME) $A\x=\b$, $A$ hermitiana con autovalori qualsiasi, Sistema equivalente: $R\x=\c$, $R$ hermitiana con autovalori tutti uguali a $1$ eccetto due, $1+a$ e $1+b$ $\then$ $R-I$ hermitiana con autovalori tutti nulli eccetto due, $a$ e $b$ $\then$ $R-I=\y\y^+\w\w^$ $\ldots$ \vskip0.2cm $\square$ Siano $\y$, $\w$ vettori indipendenti. $$ (\y\y^+\w\w^)(a\y+b\w)=c(a\y+b\w), $$ con $a$, $b$ non entrambi nulli, se e solo se $$ \bi{l} a(\y^\y-c)+b(\y^\w)=0, \\ a(\w^\y)+b(\w^\w-c)=0, \ei $$ con $a,b$ non entrambi nulli, se e solo se il determinante della matrice $2\times 2$ $$ \ba{cc} \y^\y-c & \y^\w \\ \w^\y & \w^\w-c \ea \eqno(eq(c)) $$ \`e zero. In altre parole, i due autovalori significativi di $\y\y^+\w\w^$ (cio\`e quelli non nulli) sono i due autovalori della matrice $$ \ba{cc} \y^\y & \y^\w \\ \w^\y & \w^\w \ea $$ e cio\`e $c_{\pm}=\um(\y^\y+\w^\w \pm\R{(\y^\y-\w^\w)^2+4\|\y^\w\|^2})$. Poich\'e $\y$ e $\w$ sono indipendenti, si ha $\|\y^\w\|<\\|\y\\|\\|\w\\|$ (Nota: $(\y^\y)(\w^\w)=\|\y^\w\|^2$ iff $\w=a\y$,infatti $\y^[\w-(\y^\w/\y^\y)\y]=0$, $\w^[\ldots]=0$ $\then$ $[\ldots]=\vn$). Ne segue che $0<c_-\leq c_+$. Agli autovalori $c_+$ e $c_-$ corrispondono, rispettivamente, gli autovettori $\v_+=a_+\y+b_+\w$ e $\v_-=a_-\y+b_-\w$ con $a_{\pm},b_{\pm}$ soluzioni di $eq(c_{\pm})$. \vskip0.1cm $(\y\y^+\w\w^)\z=0\y+0\w=0$ se $\y^\z=\w^\z=0$. Quindi $0$ \`e autovalore di $\y\y^+\w\w^$ e i corrispondenti autovettori sono i $\z\neq\vn$ per cui $\y^\z=\w^\z=0$. Calcoliamoli. Poich\'e $\y$ e $\w$ sono indipendenti, esiste $i<j$ tale che $y_iw_j-y_jw_i \neq 0$. Quindi gli autovettori corrispondenti all'autovalore $0$ sono i $\z\neq\vn$ tali che $$ \ba{c} z_i \\ z_j \ea = \ba{cc} \o{y_i} & \o{y_j} \\ \o{w_i} & \o{w_j} \ea ^{-1} \ba{c} -\sum_{k \neq i,j} \o{y_k}z_k \\ -\sum_{k \neq i,j} \o{w_k}z_k \ea. $$ Tra di essi se ne possono trovare $n-2$ linearmente indipendenti, $\v_1$, $\ldots$, $\v_{n-2}$. Riassumendo $$ \bi{l} (\y\y^+\w\w^)[\v_+\|\v_-\|\v_1\|\ \ldots\ \|\v_{n-2}] \\ \qquad\qquad = [\v_+\|\v_-\|\v_1\|\ \ldots\ \|\v_{n-2}]\diag(c_+,c_-,0,\ldots,0) \ei $$ (Nota: $\y^\w=0$ $\then$ $(\y\y^+\w\w^)\w=(\w^\w)\w$ e $(\y\y^+\w\w^)\y=(\y^\y)\y$.) \vskip0.2cm $\square$ (PER ME) Siano $\y,\w,\z$ vettori indipendenti. $$ (\y\y^+\w\w^+\z\z^)(a\y+b\w+c\z)=d(a\y+b\w+c\z), $$ con $a,b,c$ non tutti nulli, se e solo se $$ \bi{l} a(\y^\y-d)+b(\y^\w)+c(\y^\z)=0 \\ a(\w^\y)+b(\w^\w-d)+c(\w^\z)=0 \\ a(\z^\y)+b(\z^\w)+c(\z^\z-d)=0,\ei $$ con $a,b,c$ non tutti nulli, se e solo se il determinante della matrice $3\times 3$ $$ \ba{ccc} \y^\y-d & \y^\w & \y^\z \\ \w^\y & \w^\w-d & \w^\z \\ \z^\y & \z^\w & \z^\z-d \ea $$ \`e zero. In altre parole, i tre autovalori significativi di $\y\y^+\w\w^+\z\z^$ (cio\`e quelli non nulli) sono i tre autovalori della matrice $$ \ba{ccc} \y^\y & \y^\w & \y^\z \\ \w^\y & \w^\w & \w^\z \\ \z^\y & \z^\w & \z^\z \ea $$ (Nota: quest'ultima matrice ha $0$ come autovalore se e solo se $\ldots$ $\y,\w,\z$ linearmente dipendenti ?) \vskip0.2cm $\square$ (PER ME) Siano $\y,\w$ vettori indipendenti e $\u,\v$ vettori indipendenti. $(\y\u^+\w\v^)(a\y+b\w)=c(a\y+b\w)$, con $a,b$ non entrambi nulli, se e solo se $$ \bi{l} a(\u^\y-c)+b(\u^\w)=0, \\ a(\v^\y)+b(\v^\w-c)=0, \ei $$ con $a,b$ non entrambi nulli, se e solo se il determinante della matrice $2\times 2$ $$ \ba{cc} \u^\y-c & \u^\w \\ \v^\y & \v^\w-c \ea $$ \`e zero. In altre parole, i due autovalori significativi di $\y\u^+\w\v^$ (cio\`e quelli non nulli) sono i due autovalori della matrice $$ \ba{cc} \u^\y & \u^\w \\ \v^\y & \v^\w \ea $$ (Nota: quest'ultima matrice ha $0$ come autovalore se e solo se $(\u^\y)(\v^\w)=(\u^\w)(\v^\y)$ $\then$ $\v^(\w-\f{\u^\w}{\u^\y}\y)=\vn$, $\u^(\w-\f{\u^\w}{\u^\y}\y)=\vn$ $\then$ piano $\u,\v$ ortogonale a piano $\y,\w$ $\ldots$ $0$ autovalore $\then$ $\y\u^+\w\v^$ ha rango $1$ ? Nota sul viceversa: $\y$ e $\w$ ($\u$ e $\v$) dipendenti $\then$ $0$ \`e autovalore.) \vskip0.2cm $\square$ $\y\u^+\w\v^$ \`e uguale a $\x\z^$ se e solo se $\w$ e $\y$ (o $\v$ e $\u$) sono linearmente dipendenti. E' vera tale affermazione ? \vskip0.2cm 15 Marzo 2009 \vskip0.2cm $\square$ $A$ $n\times n$ di dice ``definita positiva'' se soddisfa le due propriet\`a: \begin{itemize} \item[(1)] $A=A^$ ($A$ \`e hermitiana) \item[(2)] $\z^A\z>0$, per ogni vettore $n\times 1$ $\z$ non nullo \end{itemize} (Nota: (1) $\then$ $\o{\z^A\z}=\z^A\z$, cio\`e $\z^A\z$ reale $\then$ ha senso richiedere una condizione sul segno di $\z^A\z$) \vskip0.2cm $\square$ Trovare una condizione su $B$ $n\times n$ per cui $A=B^B$ (oppure $A=BB^$) sia definita positiva \vskip0.2cm $\square$ Se $A$ soddisfa (1) allora valgono le seguenti due implicazioni: (2) $\then$ autovalori di $A$ positivi (Dim: $\E=\v^A\v/\v^\v$, con $\v$ autovettore relativo all'autovalore $\E$ di $A$), autovalori di $A$ positivi $\then$ (2) (Dim: omessa). In altre parole, se $A$ \`e hermitiana, per verificare se $A$ soddisfa la condizione (2) \`e necessario e sufficiente verificare che il segno degli autovalori di $A$ sia positivo \vskip0.2cm $\square$ Dimostrare che $A=I+\y\y^$ \`e definita positiva ed osservare che $A^{-1}=I-(1/(\y^\y+1))\y\y^$. Sotto quali condizioni su $b$ reale la matrice $A=I+b\y\y^$ \`e definita positiva? Scrivere l'inversa della matrice $3I+\y\y^$. Risolvere il sistema $$ \ba{cccc} 4 & -1 & -\ui & 2 \\ -1 & 4 & \ui & -2 \\ \ui & -\ui & 4 & 2\ui \\ 2 & -2 & -2\ui & 7 \ea \ba{c} x_1 \\ x_2 \\ x_3 \\ x_4 \ea = \ba{c} 1 \\ 1 \\ 1 \\ 1 \ea $$ \vskip0.2cm $\square$ Dimostrare che $A=I+\y\w^$ \`e non singolare se $\w^\y \neq -1$ ed osservare che $A^{-1}=I-(1/(\w^\y+1))\y\w^$. Sotto quali condizioni su $b$ reale la matrice $A=I+b\y\w^$ \`e definita positiva? Scrivere, quando esiste, l'inversa della matrice $3I+\y\w^$. Risolvere il sistema $$ \ba{cccc} 4 & -2 & 1 & -1 \\ -1 & 5 & -1 & 1 \\ \ui & -2\ui & \ui+3 & -ui \\ 2 & -4 & 2 & 1 \ea \ba{c} x_1 \\ x_2 \\ x_3 \\ x_4 \ea = \ba{c} 1 \\ 1 \\ 1 \\ 1 \ea $$ \vskip0.2cm $\square$ Siano $M$ $n\times n$ hermitiana e $b$ reale. Mostrare che esistono sempre valori di $a$ reale per cui $A=aI+bM$ \`e definita positiva \vskip0.2cm $\square$ Calcolare autovalori, determinante e inversa della matrice $A$ $n\times n$, con $a_{ii}=2$, per ogni $i$, e $a_{ij}=1$ se $i$ \`e diverso da $j$. \vskip0.2cm $\square$ $Q$ $n\times n$ si dice unitaria se $Q^=Q^{-1}$ (ovvero, se per calcolarne l'inversa basta farne la trasposta coniugata) o, equivalentemente, se $Q^Q=I$ \vskip0.2cm $\square$ Se $Q$ \`e unitaria allora gli autovalori di $Q$ hanno modulo $1$ \vskip0.2cm $\square$ Gli autovalori della ``matrice di Givens'' $$ A = \ba{cc} a & b \\ -b & a \ea,\ a,b\in\RR,\ a^2+b^2=1 $$ sono $a-\ui b$ e $a+\ui b$. Le matrici di Givens hanno determinante 1 \vskip0.2cm $\square$ La matrice $A=I+b\y\y^$, $b$ reale, \`e unitaria se $b=-2/\y^\y$. In tal caso i suoi autovalori sono $1$ ($n-1$ volte) e $-1$. Le ``matrici di Householder'' $A=I-(2/\y^\y)\y\y^$ hanno determinante $-1$. \vskip0.2cm $\square$ $Q$ $n\times n$ si dice ``matrice di permutazione'' se $Q=[\e_{i_1}\, \e_{i_2}\, \ldots\, \e_{i_n}]$ dove $\{i_1,i_2,\ldots,i_n\}$ \`e una permutazione di $\{1,2,\ldots,n\}$ e $\e_j$ \`e il vettore con componenti tutte nulle eccetto la $j$-esima che \`e uguale a $1$. Osservare che le matrici di permutazione sono matrici unitarie (cio\`e $Q^Q=I$) e che il loro determinante deve essere uguale a $1$ oppure a $-1$ \vskip0.2cm Esercizi di base \begin{itemize} \item[-] Se $A$ $m\times n$, $B$ $n\times k$ allora $(AB)^=B^A^$ \item[-] Se $A, B$ sono matrici $n\times n$ allora $(AB)^{-1}=B^{-1}A^{-1}$ \item[-] $a$ numero complesso, $A$ matrice $n\times n$ $\then$ $(aA)^{-1}=a^{-1}A^{-1}$ \item[-] se $\E$ \`e autovalore di $M$ $n\times n$ allora $a_0+a_1\E+\ldots+a_k\E^k$ \`e autovalore di $A=a_0I+a_1M+\ldots+a_kM^k$ ($a_j$ numeri complessi) \item[-] $\det(A)=\det(A^T)$, $\det(\o{A})=\o{\det(A)}$, $\det(A^)=\o{\det(A)}$ \item[-] se $\E$ \`e autovalore di $A$ allora $\E$ \`e autovalore di $A^T$ \item[-] se $\E$ \`e autovalore di $A$ allora $\o{\E}$ \`e autovalore di $\o{A}$ e, quindi, di $A^$ \end{itemize} 7 Marzo 2009 \vskip0.2cm $\square$ Dato $\y$, vettore colonna $n\times 1$, trasposto di $\y$: $\y^T=[y_1\ y_2\ \ldots\ y_n]$, trasposto coniugato di $\y$: $\y^=[\o{y_1}\ \o{y_2}\ \ldots\ \o{y_n}]$ \vskip0.1cm ($\o{y_1}=\o{\Re(y_1)+i\Im(y_1)}=\Re(y_1)-i\Im(y_1)$, $\ldots$) \vskip0.2cm $\square$ Sia $\rho()$ il raggio spettrale di $$. Siano $A$, $B$ matrici $n\times n$, $a$ scalare. Quali delle seguenti propriet\`a sono vere? \begin{itemize} \item[(1)] $\rho(A) \geq 0$ \item[(2)] $\rho(A)=0$ iff $A=0$ \item[(3)] $\rho(aA)=\|a\|\rho(A)$ \item[(4)] $\rho(A+B) \leq \rho(A)+\rho(B)$ \item[(5)] $\rho(AB) \leq \rho(A)\rho(B)$ \end{itemize} \vskip0.1cm {\it Risoluzione} Lapropriet\`a (4) \`e falsa, infatti $$ A = \ba{cc} a & b \\ 0 & 0 \ea,\ B = \ba{cc} 0 & 0 \\ -b & a \ea,\ a,b\in\RR,\ a^2+b^2=1, \quad \rho(A+B)=1,\ \rho(A)+\rho(B)=2\|a\| $$ ($A+B$ is real unitary). Thus, if $\|a\|<1/2$ then $\rho(A+B)>\rho(A)+\rho(B)$. In the complex field: $$ A = \ba{cc} a & b \\ 0 & 0 \ea,\ B = \ba{cc} 0 & 0 \\ -\o{b} & \o{a} \ea,\ a,b\in\CC,\ \|a\|^2+\|b\|^2=1, \quad \rho(A+B)=1,\ \rho(A)+\rho(B)=2\|a\| $$ ($A+B$ is unitary). Thus, if $\|a\|<1/2$ then $\rho(A+B)>\rho(A)+\rho(B)$. \vskip0.1cm La propriet\`a (5) \`e falsa, infatti $$ A = \ba{cc} 1 & 0 \\ 0 & 0 \ea, \ B = \ba{cc} 0 & 0 \\ 0 & 1 \ea, \quad \rho(AB)=0<\rho(A)\rho(B) = 1\cdot 1 = 1, $$ $$ A = \ba{cc} 1 & 1 \\ 1 & 1 \ea, \ B = \ba{cc} 1 & 1 \\ 1 & 1 \ea, \quad \rho(AB)=\rho(2A)=2\rho(A) =2\cdot 2=4=\rho(A)\rho(B), $$ $$ A = \ba{cc} 1 & 1 \\ 0 & 0 \ea,\ B = \ba{cc} 1 & 0 \\ 1 & 0 \ea, \quad \rho(AB)=2>\rho(A)\rho(B)=1\cdot 1=1. $$ \vskip0.2cm $\square$ Discutere se, per ogni $A$, $B$ $n\times n$, (1) $AB=BA$ (2) autovalori di $AB$ coincidono con quelli di $BA$, quindi $\rho(AB)=\rho(BA)$ \vskip0.2cm $\square$ Supponendo $\y$, $\w$ indipendenti, scrivere l'insieme dei $\z$ per cui $\y^\z=0$ $\&$ $\w^\z=0$ \vskip0.2cm $\square$ Discutere l'affermazione: $\|\y^\w\|=\\|\y\\| \\|\w\\|$ iff $\w=a\y$ \vskip0.2cm $\square$ Siano $\y$, $\w$ vettori $n\times 1$ indipendenti. Calcolare esplicitamente \begin{itemize} \item[(1)] determinante, traccia, autovalori e autovettori di $\y\y^$ \item[(2)] {\it idem} di $\y\w^$ \item[(3)] {\it idem} di $\y\y^+\w\w^$ \item[(4)] {\it idem} di $I+\y\w^$ \item[(5)] inversa di $A=I+\y\w^$ (cercarla del tipo $I+a\y\w^$) \end{itemize} \vskip0.1cm {\it Risoluzione} (1): $(\y\y^)\y=\y(\y^\y)=(\y^\y)\y$ $\then$ $\y^\y$ \`e autovalore di $\y\y^$ con corrispondente autovettore $\y$. $(\y\y^)\z=0\y=\vn$ se $\y^\z=0$. Quindi $0$ \`e autovalore di $\y\y^$ e i corrispondenti autovettori sono i $\z\neq\vn$ per cui $\y^\z=0$. Calcoliamoli. Poich\'e $\y\neq\vn$, esiste $i$ t.c. $y_i \neq 0$. Quindi gli autovettori corrispondenti all'autovalore $0$ sono i $\z\neq\vn$ tali che $z_i=(-\sum_{k \neq i} \o{y_k}z_k)/\o{y_i}$. Tra di essi se ne possono trovare $n-1$ linearmente indipendenti, $\v_1$, $\ldots$, $\v_{n-1}$. Riassumendo $$ \y\y^[\y\|\v_1\|\ldots\|\v_{n-1}] = [\y\|\v_1\|\ldots\|\v_{n-1}]\diag(\y^\y,0,\ldots,0). $$ In particolare si ha: $\rho(\y\y^)=\y^\y$ \vskip0.1cm (2): $(\y\w^)\y=\y(\w^\y)=(\w^\y)\y$ $\then$ $\w^\y$ \`e autovalore di $\y\w^$ con corrispondente autovettore $\y$. $\w^\y$ in generale non \`e reale. $(\y\w^)\z=0\y=0$ se $\w^\z=0$. Quindi $0$ \`e autovalore di $\y\w^$ e i corrispondenti autovettori sono i $\z\neq\vn$ per cui $\w^\z=0$. Calcoliamoli. Poich\'e $\w\neq\vn$, esiste $i$ t.c. $w_i \neq 0$. Quindi gli autovettori corrispondenti all'autovalore $0$ sono i $\z\neq\vn$ tali che $z_i=(-\sum_{k \neq i} \o{w_k}z_k)/\o{w_i}$. Tra di essi se ne possono trovare $n-1$ linearmente indipendenti, $\v_1$, $\ldots$, $\v_{n-1}$. Riassumendo $$ \y\w^[\y\|\v_1\|\ldots\|\v_{n-1}] = [\y\|\v_1\|\ldots\|\v_{n-1}]\diag(\w^\y,0,\ldots,0). $$ In particolare si ha: $\rho(\y\w^)=\|\w^\y\|$ \vskip0.1cm Nota: $\rho(\y\w^) = \|\w^\y\| \leq \\|\y\w^\\|_2 = \\|\y\\|_2\\|\w\\|_2$, mentre $\rho(\y\y^)=\y^\y=\\|\y\y^\\|_2=\\|\y\\|_2^2$. \vskip0.1cm (3) (vedi pi\`u avanti). \vskip0.2cm $\square$ Studiare l'andamento del numero $\rho(A)\rho(A^{-1})$, $A=I+\y\w^$ \vskip0.2cm $\square$ Scrivere le matrici $$ \ba{cc} 2 & 1 \\ 1 & 1/2 \ea, \ \ \ba{cccc} 1 & -1 & 2\ui & -3 \\ 2 & -2 & 4\ui & -6 \\ i & -i & -2 & -3\ui \\ 4 & -4 & 8\ui & -12 \ea $$ nella forma $\y\y^$ o $\y\w^$, e calcolare il loro raggio spettrale \vskip0.2cm $\square$ Calcolare $\rho(A)$ dove $A$ \`e la matrice $4\times 4$ $$ \ba{cccc} 1 & -2 & 5 & -1 \\ -2 & 4 & 10& 2 \\ 5 & 10 & 25& -5 \\ -1 & 2 & -5& 1 \ea $$ \vskip0.2cm $\square$ Calcolare gli autovalori $\E$ della matrice $2\times 2$ $$ \ba{cc} a & b \\ -b & a \ea, $$ con $a,b$ reali. Determinare una CNES affinch\'e $\|\E\|=1$ \vskip0.1cm {\it Risoluzione} Gli autovalori sono $a-\ui\|b\|$ e $a+\ui\|b\|$, e il loro modulo \`e $\sqrt{a^2+b^2}$. Quindi, $\|\E\|=1$ se e solo se $a^2+b^2=1$. Gli autovalori di $$ A = \ba{cc} a & b \\ -\o{b} & \o{a} \ea,\ a,b\in\CC, $$ sono $\Re(a) \pm \ui\sqrt{\Im(a)^2+\|b\|^2}$, e il loro modulo vale $\sqrt{\|a\|^2+\|b\|^2}$. Quindi, $\|\E\|=1$ se e solo se $\|a\|^2+\|b\|^2=1$. \vskip0.2cm $\square$ Per $A$ $n\times n$ sia $A^$ la matrice $[A^]_{ij}=\o{[A]_{ji}}$. $A$ $n\times n$ si dice hermitiana, se $a_{ij}=\o{a_{ji}}$ $\fa\,i,j$ (ovvero se $A=A^$). \vskip0.2cm $\square$ $\y\w^$ \`e hermitiana se e solo se $\w=a\y$, $a$ reale \vskip0.2cm $\square$ $A$ $n\times n$ con elementi non negativi tale che $\sum_j a_{ij}=1$ per ogni $i$ si dice stocastica per righe. Se $A$ \`e stocastica per righe allora \begin{itemize} \item[(1)] $1$ \`e autovalore di $A$ con autovettore $[1\ 1\,\ldots\,1]^T$ \item[(2)] $\rho(A)=1$ \item[(3)] $A^k$ \`e stocastica per righe (per induzione su $k$) \item[(4)] $\sum_{k=0}^r y_kA^k$ \`e stocastica per righe, se $y_k\geq 0$ per ogni $k$ e $\sum_k y_k=1$ \end{itemize} \vskip0.2cm Esercizi di base - Ad autovalori distinti corrispondono autovettori indipendenti - Gli autovalori di $aA$ si ottengono moltiplicando gli autovalori di $A$ per $a$ - Gli autovalori di $A^k$ si ottengono facendo le potenze $k$ degli autovalori di $A$ - Gli autovalori di $A^{-1}$ si ottengono invertendo quelli di $A$ - Se $B=S^{-1}AS$ allora $A$ e $B$ hanno gli stessi autovalori - Se $T$ \`e triangolare gli autovalori di $T$ sono i suoi elementi diagonali - Se $S^{-1}AS=T$ con $T$ triangolare allora gli autovalori di $A$ sono gli elementi diagonali di $T$ - Se $S^{-1}AS=D$ con $D$ diagonale allora gli autovalori di $A$ sono gli elementi diagonali di $D$ e i corrispondenti autovettori sono le colonne di $S$ (e $A$ si dice diagonalizzabile) - Esiste sempre $S$, $S^=S^{-1}$, per cui $S^{-1}AS=T$ con $T$ triangolare. Esiste $S$, $S^=S^{-1}$, per cui $S^{-1}AS=D$ se e solo se $AA^=A^A$ (ovvero $A$ \`e normale) - $A=A^$ $\then$ autovalori di $A$ reali - Autovalori di $A$ reali $\&$ $A$ normale $\then$ $A=A^$ \vskip0.2cm \hrule \vskip0.2cm {\it Inizio}: $\y$ vettore colonna $n\times 1$, $\y^T=[y_1\ \ldots\ y_n]$ trasposto di $\y$, $\y^=[\o{y_1}\ \ldots\ \o{y_n}]$ trasposto coniugato di $\y$ Esempio $$ \y = \ba{c} 1 \\ 1-\ui \ea,\quad \y^T=[1\ \ 1-\ui],\quad \y^H=[1\ \ 1+i] $$ $\y^\y=\sum_i \|y_i\|^2$ \`e un numero reale non negativo (che si indica anche $\\|y\\|_2^2$) $\y\y^$ \`e una matrice $n\times n$, ha determinante nullo ($\then$ ha almeno un autovalore uguale a zero), ha traccia uguale a $\\|y\\|_2^2$, \`e un esempio di matrice hermitiana (def di traccia e di matrice hermitiana) matrici hermitiane hanno gli elementi diagonali reali def di autovalori, autovettori, polinomio caratteristico, $A$ $n\times n$ ha $n$ autovalori, gli autovalori di una matrice triangolare sono i suoi elementi diagonali, autovettori di autovalori distinti sono indipendenti, se $A$ \`e simile a $T$ triangolare allora gli autovalori di $A$ sono gli elementi diagonali di $T$ def di raggio spettrale di $A$ $n\times n$: $\rho(A)=\max_i \|\E_i\|$ dove $\E_i$, $i=1,\ldots,n$ sono gli autovalori di $A$. es. $\y$ vettore $n\times 1$ $\then$ $\rho(\y\y^)=\y^*\y$ es. trovare due matrici $2\times 2$ $A$, $B$ per cui $\rho(AB)>\rho(A)\rho(B)$, $<$ , $=$ \end{document}
https://faculty.uml.edu/jpropp/192/A16.tex	uml.edu	CC-MAIN-2021-49	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2021-49/segments/1637964362589.37/warc/CC-MAIN-20211203030522-20211203060522-00251.warc.gz	323,722,778	3,330	\documentclass[12pt]{article} \newcommand{\sign}{{\rm sign}} %\pagestyle{empty} \begin{document} \begin{center} Math 192r, Problem Set \#16: Solutions \end{center} \medskip \begin{enumerate} \item {\it Use Dodgson condensation to prove the Vandermonde determinant formula $$\det(M)=\prod_{1 \leq i < j \leq n} (x_j-x_i)$$ where $M$ is the $n$-by-$n$ matrix whose $i,j$th entry (for $1 \leq i,j \leq n$) is $x_j^{i-1}$.} The claim is easily verified for $n=0$ and $n=1$. We will prove higher cases by induction; hence hereafter we will assume that the formula is true for $n-1$ and $n-2$ in order to prove it for $n>1$. Write the determinant of $M$ as $d_n(x_1,x_2,\dots,x_n)$. If we apply Dodgson condensation to this matrix, we get \begin{eqnarray} d_n(x_1,\dots,x_n) e_{n-2}(x_2,\dots,x_{n-1}) & = & d_{n-1}(x_1,\dots,x_{n-1}) e_{n-1}(x_2,\dots,x_n) \\ & & - d_{n-1}(x_2,\dots,x_n) e_{n-1}(x_1,\dots,x_{n-1}), \end{eqnarray} where $e_m(y_1,\dots,y_m)$ is the determinant of the $m$-by-$m$ matrix whose $i,j$th entry is $x_j^i$. By the multilinearity of the determinant, $$e_m(y_1,\dots,y_m) = y_1 \cdots y_m \, d_m(y_1,\dots,y_m),$$ so the condensation relation may be written as $$ x_2 \cdots x_{n-1} D_1^n D_2^{n-1} = x_2 \cdots x_n D_1^{n-1} D_2^n - x_1 \cdots x_{n-1} D_2^n D_1^{n-1},$$ where $D_i^j$ is short for $d_{j-i+1}(x_i,\dots,x_j)$. Simplifying, we obtain $$D_1^n D_2^{n-1} = x_n D_1^{n-1} D_2^n - x_1 D_2^n D_1^{n-1}$$ or $$D_1^n D_2^{n-1} = (x_n-x_1) D_1^{n-1} D_2^n.$$ Our induction hypothesis implies that $D_1^{n-1} = \left( \prod_{j=2}^{n-1} (v_j-v_1) \right) D_2^{n-1}$ and $D_2^{n} = \left( \prod_{i=2}^{n-1} (v_n-v_i) \right) D_2^{n-1}$, so the right hand side of the preceding inset equation can be rewritten as $$(x_n-x_1) \left( \prod_{j=2}^{n-1} (v_j-v_1) \right) \left( D_2^{n-1} \right) \left( \prod_{i=2}^{n-1} (v_n-v_i) \right) \left( D_2^{n-1} \right) .$$ Hence \begin{eqnarray} D_1^n & = & (x_n-x_1) \left( \prod_{j=2}^{n-1} (v_j-v_1) \right) \left( \prod_{i=2}^{n-1} (v_n-v_i) \right) D_2^{n-1} \\ & = & (x_n-x_1) \left( \prod_{j=2}^{n-1} (v_j-v_1) \right) \left( \prod_{i=2}^{n-1} (v_n-v_i) \right) \left( \prod_{2 \leq i < j \leq n-1} (v_j-v_i) \right) \\ & = & \prod_{1 \leq i < j \leq n} (v_j-v_i), \end{eqnarray} which was to be proved. Someone reading the above might object that there is a flaw in the proof, inasmuch as we are dividing by an expression $D_2^n$ that can vanish (and indeed will vanish if any two of $x_2,\dots,x_{n-1}$ are equal), and that it is invalid to divide by zero. But this objection has no force, since we our conducting our proof in the realm of formal polynomials and formal rational functions. In the field of rational functions in the two variables $x$ and $y$, the expressions $(x^2-y^2)/(x-y)$ and $x+y$ are actually equal; one does not substitute actual values for $x$ and $y$, so one need not worry about ``what if'' $x=y$. On the other hand, once one has proved that a pair of polynomials are equal as formal expressions (namely, the determinant of a certain matrix and a certain product of differences), one can treat the two polynomials as functions and make substitutions for the variables. So the Vandermonde identity that we have proved isn't just true for one particular $n$-by-$n$ matrix in the ring of polynomials in the variables $x_1,\dots,x_n$; it's true for every $n$-by-$n$ matrix whose entries are particular values satisfying certain relations. \item {\it Using Dodgson condensation, Lindstrom's lemma, and the bijection between tilings and routings discussed in class, prove that for all $a,b,c \geq 0$, the number of ways to tile an $a,b,c,a,b,c$ semiregular hexagon with unit rhombuses is equal to $$\frac{H(a+b+c)H(a)H(b)H(c)}{H(a+b)H(a+c)H(b+c)}$$ where $H(0)=H(1)=1$ and $H(n)=1!2!3! \cdots (n-1)!$ for $n > 1$.} Let $T(a,b,c)$ denote the number of rhombus tilings of the $a,b,c,a,b,c$ semiregular hexagon. It is easy to check that for all $a,b \geq 0$, $T(a,b,0) = 1 = \frac{H(a+b+0)H(a)H(b)H(0)}{H(a+b)H(a+0)H(b+0)}$ and $T(a,b,1) = \frac{(a+b)!}{(a)!(b)!} = \frac{H(a+b+1)/H(a+b)}{(H(a+1)/H(a))(H(b+1)/H(b)}$ %kludge $=\frac{H(a+b+1)H(a)H(b)H(1)}{H(a+b)H(a+1)H(b+1)}$. We will prove the claim for $c>1$ using induction on $c$. Rhombus-tilings of the $a,b,c,a,b,c$ semiregular hexagon correspond to routings with $c$ sources and $c$ sinks in a directed graph in which the number of paths from the $i$th source to the $j$th sink equals $a+b \choose b-i+j$. Therefore by Lindstrom's lemma we have $T(a,b,c) = \det M(a,b,c)$ where $M(a,b,c)$ denotes the $c$-by-$c$ matrix whose $i,j$th entry is $a+b \choose b-i+j$. In view of the this, Dodgson condensation tells us that \begin{eqnarray} T(a,b,c) T(a,b,c-2) &=& T(a,b,c-1)^2 \\ & & - T(a+1,b-1,c-1) T(a-1,b+1,c-1). \end{eqnarray} For slight notational convenience, I'll re-index this as $$T(a,b,c+1) T(a,b,c-1) = T(a,b,c)^2 - T(a+1,b-1,c) T(a-1,b+1,c).$$ The problem now reduces to algebraically verifying that $T(a,b,c+1)$ must be given by the $H(\ )$-formula if $T(a,b,c-1)$, $T(a,b,c)$, $T(a+1,b-1,c)$ and $T(a-1,b+1,c)$ are. Equivalently, we must verify that if all five of these $T(\ )$-values are as given by the $H(\ )$-formula, then the expression $$T(a,b,c+1) T(a,b,c-1) - T(a,b,c)^2 + T(a+1,b-1,c) T(a-1,b+1,c)$$ must vanish. If we trust Maple, then we can prove this by noting that the final command in the string of commands \begin{verbatim} H := proc(n) product(k!,k=1..n-1); end; T := proc(a,b,c) H(a+b+c)H(a)H(b)H(c) /H(a+b)/H(a+c)/H(b+c); end; U := T(a,b,c)T(a-2,b,c)-T(a-1,b,c)^2 +T(a-1,b-1,c+1)T(a-1,b+1,c-1); simplify(expand(U)); \end{verbatim} gives the output {\tt{0}}. However, if you're more skeptical, here's a sketch of how you can show by hand that the expression $T(a,b,c+1) T(a,b,c-1) - T(a,b,c)^2 + T(a+1,b-1,c) T(a-1,b+1,c)$ vanishes when each $T(\ )$ is expanded using the $H(\ )$-formula. Write each of the three terms as a fraction, and in each of the terms divide the numerator by $H(a+b+c-1)H(a+b+c)H(a-1)H(a)H(b-1)H(b)H(c-1)H(c)$ and the denominator by $H(a+b)^2 H(a+c-1)H(a+c) H(b+c-1)H(b+c)$, obtaining another messy expression. But we have made progress: where before we had a sum each term of which was a ratio of products each factor of which was a value of the $H$-function, we now have a sum each term of which is a ratio of products each factor of which is a value of the factorial function, Moreover, there are now some factors common to all three terms; removing them gives \begin{eqnarray} & \frac{(a+b+c)!(a-1)!(b-1)!(c)!}{(a+c)!(b+c)!} & \\ & - \frac{(a+b+c-1)!(a-1)!(b-1)!(c-1)!}{(a+c-1)!(b+c-1)!} & \\ & + \frac{(a+b+c-1)!(a)!(b)!(c-1)!}{(a+c)!(b+c)!}. & \end{eqnarray*} Removing common factors again gives us $$(a+b+c-1)(c-1) - (a+c-1)(b+c-1) + (a)(b),$$ which vanishes. \end{enumerate} \end{document}
https://doc.libelektra.org/api/0.8.21/latex/doc_news_2017-03-18_lcdproc_md.tex	libelektra.org	CC-MAIN-2022-40	text/x-tex	application/x-tex	crawl-data/CC-MAIN-2022-40/segments/1664030335124.77/warc/CC-MAIN-20220928051515-20220928081515-00448.warc.gz	243,796,650	6,095	\begin{DoxyItemize} \item guid\+: d52657b5-\/60da-\/4a21-\/9679-\/f8aacf6d6b72 \item author\+: Markus Raab \item pub\+Date\+: Sat, 18 Mar 2017 20\+:43\+:03 +0100 \item short\+Desc\+: Elektrify L\+C\+Dproc \end{DoxyItemize} \begin{quote} L\+C\+Dproc is a piece of open source software that displays real-\/time system information from your Linux/$\ast$\+B\+SD box on a L\+CD. \end{quote} L\+C\+Dproc\textquotesingle{}s \href{http://lcdproc.omnipotent.net/}{\tt website} is a bit outdated but L\+C\+Dproc itself is now well-\/maintained on \href{https://github.com/lcdproc/lcdproc}{\tt Git\+Hub} and had a \href{https://github.com/lcdproc/lcdproc/releases}{\tt release recently}. Like in many projects, it invented its own configuration access and I\+NI parser which did not evolve with the needs of the project. As a consequence inconsistencies and code duplication spread over the source. For example, the L\+C\+Dproc configuration access does not support values that represent display\textquotesingle{}s size (such as {\ttfamily 20x4}). Thus every L\+C\+Dproc\textquotesingle{}s module has its own parsing code for such values. Some days ago (16.\+03.\+2017), we met with Harald Geyer and discussed the current situation. We decided that we will elektrify L\+C\+Dproc and remove all the configuration access and parsing code within L\+C\+Dproc. To {\bfseries elektrify} an application means to change the application so that it uses Lib\+Elektra afterwards. \subsection{Goals} We formulated three goals\+: \begin{DoxyEnumerate} \item We (Elektra Initiative, mainly Thomas Waser) remove as much code as possible from L\+C\+Dproc\textquotesingle{}s code base. \item Users of L\+C\+Dproc should be able to use {\ttfamily L\+C\+Dd.\+conf} as they use it now. \item We avoid the current duplications of configuration specifications. (Currently in {\ttfamily L\+C\+Dd.\+conf}, the docbook, in code checking the limits, and the default parameter in the code.) \end{DoxyEnumerate} Nice-\/to-\/have is\+: \begin{DoxyItemize} \item Safe updates\+: {\ttfamily make install} should not break the current {\ttfamily L\+C\+Dd.\+conf}. (As it is already done in Debian.) \item The robustness of L\+C\+Dproc on misconfiguration should be improved (Thomas Waser writes the specification). \item Automatic reloading of the daemon when using Elektra to update configuration. (Manual {\ttfamily S\+I\+G\+H\+UP}-\/signals will work in any case.) \item Have physical units with metric prefix like {\ttfamily 500ms} for {\ttfamily 0.\+5s} (seconds). \end{DoxyItemize} Possible limitations are\+: \begin{DoxyItemize} \item We break support for systems that only have very old compilers. \item The {\ttfamily -\/c} option to specify a different configuration file is against the abstraction Elektra should deliver. We might create a \href{https://github.com/ElektraInitiative/libelektra/issues/1416}{\tt wrapper script} that emulates {\ttfamily -\/c} via mountpoints. \item L\+C\+Dproc will depend on the yet-\/to-\/be-\/released \href{https://github.com/ElektraInitiative/libelektra/milestone/11}{\tt 0.\+8.\+20}. We will delay the 0.\+8.\+20 release until all parts for L\+C\+Dproc are tested and ready. \end{DoxyItemize} In any case, the \href{https://www.libelektra.org}{\tt advertised benefits of Elektra} will automatically apply (incomplete list)\+: \begin{DoxyItemize} \item Global key database\+: you can connect other configuration files with the L\+C\+Dproc\textquotesingle{}s configuration and validation. \item Allows users to easily modify the specifications, for example to have different command-\/line options, or support for environment variables. \item \href{https://www.libelektra.org/plugins/profile}{\tt Profile support}\+: Having multiple complete configuration settings you can easily choose from. (thanks to Thomas Waser) \item Introspectibility\+: you can check with {\ttfamily kdb}-\/tool which configuration settings L\+C\+Dproc will receive. \item Other configuration file formats can be used instead, e.\+g. J\+S\+ON or X\+ML. (Only if wanted as personal preference, by default I\+NI will be used to remain compatibility with {\ttfamily L\+C\+Dd.\+conf}.) \item Easy migration paths to use other configuration file formats such as Y\+A\+ML as default in future. (thanks to René Schwaiger) \item Elektra\textquotesingle{}s tool can be used to configure L\+C\+Dconf, including\+: \begin{DoxyItemize} \item {\ttfamily kdb set} to modify individual settings within scripts and validation. \item {\ttfamily kdb editor}, which spawns your favourite editor but validates the configuration file before writing it out. \item {\ttfamily kdb qt-\/gui}, the Qt G\+UI (thanks to Raffael Pancheri). \item The web UI of Elektra (thanks to Daniel Bugl). \end{DoxyItemize} \item Elektra\textquotesingle{}s website can be used to share L\+C\+Dproc\textquotesingle{}s configuration files, and you can use the \href{https://www.libelektra.org/plugins/curlget}{\tt curlget plugin} to mount files from the website. (thanks to Marvin Mall) \item You can use Shell, Python, or Lua to write small scripts that are executed on configuration access. \item Elektra allows you to directly read and write from git using the \href{https://www.libelektra.org/plugins/gitresolver}{\tt git plugin}. (Even if {\ttfamily L\+C\+Dd.\+conf} is not checked out, thanks to Thomas Waser) \item We extensively \href{https://www.libelektra.org/devgettingstarted/testing}{\tt test} Elektra with modern techniques such as fuzzing. \end{DoxyItemize} \subsection{Validation} Instead of {\ttfamily if}s within the code, we will use Spec\+Elektra for validation. \href{https://www.libelektra.org/manpages/elektra-glossary}{\tt Spec\+Elektra} is a configuration specification language that allows us to describe which configuration is valid. This specification will be installed as part of L\+C\+Dproc to {\ttfamily /usr/share/elektra/specifications}. It uses the \href{https://www.libelektra.org/docgettingstarted/metadata}{\tt metadata} as defined by the plugins to validate configuration changed via Elektra. For broken installations or when executing L\+C\+Dproc from the source repository, there is also a built-\/in specification. The specification will only be used if the installed one cannot be found. Thus the configuration validation specification is a normal configuration file also integrated in Elektra, also the specification can be introspected\+: useful for system administrators who want to know about valid entries, but also for tools like our newly developed web-\/\+UI by Daniel Bugl. The web-\/\+UI automatically restricts the interface so that only valid entries can be entered. For example, if you should enter a boolean, only a check box is presented to you. \begin{DoxyItemize} \item For more information about validation, see the \href{https://www.libelektra.org/tutorials/validate-configuration}{\tt tutorial} \end{DoxyItemize} \subsection{Code Generation} We (mainly Dominik Hofer) are currently developing \href{https://www.libelektra.org/decisions/high-level-api}{\tt a high-\/level A\+PI}, whose first user will be L\+C\+Dproc. In this A\+PI, we will make sure during compilation, that configuration access is done correctly. This is especially useful when configuration settings get renamed. Then all places where out-\/dated configuration settings are used will fail to compile. In particular using code generation developers do not need to use strings to refer to configuration settings and they get easy-\/to-\/use enums consistent with the configuration specification. Furthermore, code generation will make sure that a specification (and default configuration settings) will be found even if no {\ttfamily /etc} or no {\ttfamily /usr} is found. We also found that we cannot use code generation everywhere. In generic access code, code generation obviously is limited. \begin{DoxyItemize} \item For more information about code generation, see the \href{https://www.libelektra.org/tools/gen}{\tt tutorial} \end{DoxyItemize} \subsection{Risks} Understandably, users might be concerned that such a change will not work or create problems in the future. Here we will discuss some of the concerns. \begin{quote} Elektra might be discontinued. \end{quote} From history perspective, Elektra received steady development since 2004. Elektra is a F\+L\+O\+SS project and welcomes everyone to join. In the last years several people did, with an increasing number per year. Currently following people are working on substantial new features in Elektra (sorted by first name)\+: \begin{DoxyItemize} \item Armin Wurzinger\+: Quality Improvements \item Bernhard Denner\+: \href{https://github.com/ElektraInitiative/puppet-libelektra}{\tt Puppet Module} \item Daniel Bugl\+: \href{https://www.libelektra.org/tools/web}{\tt Web\+UI} \item Dominik Hofer\+: \href{https://www.libelektra.org/decisions/high-level-api}{\tt the high-\/level A\+PI} \item Kurt Micheli\+: Order Preserving Minimal Hash Map \item Markus Raab\+: Maintainer \item Michael Zehender\+: Quality Improvements \item Mihael Pranjić\+: mmap plugin \item Peter Nirschl\+: \href{https://www.libelektra.org/plugins/crypto}{\tt crypto plugin} \item René Schwaiger\+: Y\+A\+ML plugin \item Sebastian Bachmann\+: Shell Completion \item Thomas Waht\+: Notification \item Thomas Waser\+: Validation and Transformations of Configuration \item Vanessa Kos\+: Misconfiguration Bug Database \end{DoxyItemize} Obviously, there are many more casual contributors. Elektra has a large set of \href{https://build.libelektra.org}{\tt automated tests} and only a small amount of technical dept. Elektra has no required external dependencies except libc. So without internal changes, only minimal maintenance cost is required. \begin{quote} Elektra is unfinished. \end{quote} Technically this is true\+: we did not reach \href{https://git.libelektra.org/milestone/12}{\tt 1.\+0}. We are, however, on track to reach this goal within this summer. Now is the best time to join because we can provide more support and are more flexible for changes and wishes. Some https\+://www.libelektra.\+org/news/2016-\/06-\/14\+\_\+0.8.\+17.\+md \char`\"{}time ago\char`\"{} we asked in a survey in which direction Elektra should develop. Most open issues are (in)direct responses from this wanted direction. Some plugins are experimental or proof-\/of-\/concept, but they are clearly marked as such. \begin{quote} It seems a bit to me like \href{https://xkcd.com/927/}{\tt xkcd\+: Standards}. \end{quote} Elektra does not invent a new configuration file format nor new standards where to store configuration files but abstracts over these issues. \begin{quote} Elektra not being available in my distribution. \end{quote} For the following Linux Distributions Elektra 0.\+8 packages are available\+: \begin{DoxyItemize} \item \href{https://github.com/openwrt/packages/tree/master/libs/elektra}{\tt Openwrt} (by Harald Geyer) \item \href{https://admin.fedoraproject.org/pkgdb/package/elektra/}{\tt Fedora} \item \href{http://packages.gentoo.org/package/app-admin/elektra}{\tt Gentoo} \item \href{https://aur.archlinux.org/packages/elektra/}{\tt Arch Linux} \item \href{https://packages.debian.org/de/jessie/libelektra4}{\tt Debian} \item \href{https://launchpad.net/ubuntu/+source/elektra}{\tt Ubuntu} \item \href{https://software.opensuse.org/package/elektra}{\tt Open\+Suse} \item \href{http://sophie.zarb.org/rpms/763d9e52beefaa15b1363d11d836b65c}{\tt P\+L\+D\+Linux} \item \href{https://lede-project.org/packages/pkgdata/libelektra-core?s[]=elektra}{\tt L\+E\+DE} \item \href{https://community.linuxmint.com/software/view/elektra-bin}{\tt Linux Mint} \end{DoxyItemize} See \href{https://www.libelektra.org/docgettingstarted/installation}{\tt I\+N\+S\+T\+A\+LL} for the complete and up-\/to-\/date list. \begin{quote} If Elektra does not take off and achieve world dominance, will we be worse off than before? \end{quote} Making sure that projects will not be worse off is what we did the last years\+: Not only offer an A\+PI and wait for world dominance but to offer an implementation that can compete with any configuration library out there. We are not completely there yet (there are some details where specific other libraries are better than Elektra in specific points) but these are not points that the current configuration system of L\+C\+Dproc supports (not even close). And the libraries that can compete with Elektra have a completely different level on which dependencies they have\+: Elektra is the only one only requiring libc. \begin{quote} Do we retain the old way of configuring things, i.\+e. manually editing a ini file in /etc? \end{quote} Absolutely, you can think of libelektra as a small library in C that reads a configuration file and returns a data structure if you do not use any of its advanced features. \begin{quote} Do we retain the old way reloading/restarting the system service? \end{quote} Elektra does not interfere with restarting. It is a passive library. It provides some techniques for reloading but they are optional (but we recommend that you keep the in-\/memory and persistent configuration in sync via notification). For more information, see the \href{https://www.libelektra.org/manpages/elektra-faq}{\tt F\+AQ}. \subsection{Win-\/\+Win} We can both profit from it\+: \begin{DoxyEnumerate} \item For L\+C\+Dproc it will be a simplification of code while getting many more tools. \item For Elektra it will improve its adoption and packaging. \end{DoxyEnumerate} For oyranos it already worked well on both sides, see our discussions in the issue tracker, for example \href{https://issues.libelektra.org/1134}{\tt \#1134}. If you also maintain an free or open source (F\+L\+O\+SS) project with an out-\/dated configuration system, please contact us. Obviously, we cannot fully port every F\+L\+O\+SS project ourselves, instead we will handle requests on a first come, first serve basis. Earlier projects will also have an higher impact on the feature set of Elektra, thus you will less likely need to implement your own plugin. \subsection{See also} \begin{DoxyItemize} \item Progress can be viewed \href{https://git.libelektra.org/projects/7}{\tt here} \item We discussed about alternatives to Elektra \href{https://issues.libelektra.org/1266}{\tt here}. \end{DoxyItemize} Best regards, Markus
https://dlmf.nist.gov/3.1.E1.tex	nist.gov	CC-MAIN-2018-26	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2018-26/segments/1529267864354.27/warc/CC-MAIN-20180622045658-20180622065658-00371.warc.gz	579,080,043	695	\[x=(-1)^{s}\cdot(b_{0}.b_{1}b_{2}\dots b_{p-1})\cdot 2^{E},\]
https://physics.eou.edu/courses/math_323/mini_proj1b/mini_proj1_template.tex	eou.edu	CC-MAIN-2019-04	text/x-tex	application/x-tex	crawl-data/CC-MAIN-2019-04/segments/1547584334618.80/warc/CC-MAIN-20190123151455-20190123173455-00005.warc.gz	604,478,262	2,027	\documentclass[12pt]{article} \usepackage{graphicx} \usepackage{fancyhdr} \usepackage{lastpage} \setlength{\textheight}{9.5in} \setlength{\topmargin}{0.0in} \setlength{\headheight}{0.3in} \setlength{\headsep}{0.4in} \setlength{\textwidth}{6.5in} \setlength{\oddsidemargin}{0in} \pagestyle{fancy} \fancyfoot{} \fancyhead{} \fancyhf{} % Clear all fiels \renewcommand{\headrule}{} \renewcommand{\footrule}{} % Headers and footers personalization using the `fancyhdr' package \fancyhead[L]{Team Control \# 481} \fancyhead[R]{Page \thepage \hspace{1pt} of \pageref{LastPage}} \begin{document} \begin{titlepage} \title{Modeling Usain Bolt 2009 100 m dash world record} \author{Your Cool Name goes here!\\ \\ Homework \#1b, Math 323\\ Eastern Oregon University\\ Fall 2016\\ with\\ Dr. Tovar } \maketitle \setcounter{page}{0} \thispagestyle{empty} \begin{figure}[h] \begin{center} \includegraphics[scale=0.5]{bolt09.eps} \caption{Here's the cool Figure.} \end{center} \end{figure} \begin{abstract} Insert two to five sentences overviewing what you've done and what you're trying to do. Hint: make sure you mention that you're calculating the initial acceleration. \end{abstract} \end{titlepage} \section{Introduction} A few sentences overviewing Bolt's accomplishment. \section{A Proposed Model} Put the model here, and a sentence or two about it's features. \section{Analysis} Show how you calculate the initial acceleration. \section{Comparison with Race Data} A couple of sentences, then make a table duplicating the data of the web site. Here's a start:\\ \vspace{12pt} \begin{center} \begin{tabular}{\|c\|c\|c\|} \hline Segment (m) & Time (s) & Velocity (m/s) \\ \hline 0-10 & 1.85 & 5.41\\ 10-20 & 1.02 & 9.80\\ \hline \end{tabular} \end{center} Make another table with the corresponding Velocity vs. TIME table (I've done the first two data points for you, complete the rest). \begin{center} \vspace{12pt} \begin{tabular}{\|c\|c\|} \hline Time (s) & Velocity (m/s) \\ \hline 0 & 0 \\ 0.925 & 5.405\\ \hline \end{tabular} \end{center} Now, plot data against your model. \section{Discussion/Conclusion} compare the initial acceleration you got here, you got with the previous model, and that which the web site got. %\section{Future Work} %\section{Appendix} %\newpage %\begin{thebibliography}{References} %\bibitem{bib9} %{\it Handbook of Mathematical Functions with Formulas, Graphs, and %Mathematical Tables,} %Edited by: Abramowitz, M.; Stegun, I.A., U.S. Department of Commerce, 1972. % %\bibitem{bib10} %A. A. Tovar, Propagation of Laguerre-Bessel-Gaussian beams, Journal of the Optical Society of America A, vol. 17, pp. 2010 - 2018 (2000). %% %\bibitem{bib11} %Britney's Guide to Semiconductor Physics, Vertical Cavity Surface %Emitting Lasers (VCSELs), %$\underline{http://britneyspears.ac/physics/vcsels/vcsels.htm}$, %accessed February 3, 2005. %\end{thebibliography} \end{document}
https://mirror.las.iastate.edu/tex-archive/macros/latex/contrib/shipunov/doc/field-form-ex1-ru.tex	iastate.edu	CC-MAIN-2023-14	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2023-14/segments/1679296949107.48/warc/CC-MAIN-20230330070451-20230330100451-00642.warc.gz	462,689,993	2,296	\documentclass[12pt]{article} \usepackage[cp1251]{inputenc} \usepackage[T2A]{fontenc} \usepackage[russian]{babel} \usepackage{array,longtable} \topmargin=-2cm \headheight=0cm \headsep=0cm \textheight=27cm \footskip=.5cm \textwidth=18cm \oddsidemargin=-1.25cm \evensidemargin=-1.75cm \parindent=0pt \renewcommand{\baselinestretch}{.95} \nofiles \pagestyle{empty} \renewcommand{\_}{\mbox{}\hrulefill} \providecommand{\LIN}[1][1]{\leavevmode\hbox to #1.1cm{\hrulefill}} \providecommand{\TI}{\vrule\thinspace} \newcommand*{\PreserveBackslash}[1]{\let\temp=\\#1\let\\=\temp} \newcolumntype{h}[1]{>{\PreserveBackslash\raggedright\hspace{0pt}}p{#1}} \begin{document} {\bfseries\textit{Dactylorhiza}\ \_ --2005: бланк/популяция \No\LIN} Дата \LIN\\ Кто \_\ Влажность (1,2,3) \LIN\ Освещенность (1,2,3) \LIN\\ Фоновые виды всех ярусов \_\\\_\\\_\\\_\\ Где \_\\[-3ex] {\centering\textbf{\textit{Все} измерения проводятся в \textit{миллиметрах}!}\par} \begin{tabular}[c]{% @{\TI}h{.6cm}@{\TI}h{.9cm}@{\TI}h{.8cm} @{\TI}h{.7cm}@{\TI}h{.7cm}@{\TI}h{.8cm} @{\TI}h{.9cm}@{\TI}h{.9cm}@{\TI}h{.8cm}@{\TI}h{.7cm} @{\TI}h{.9cm}@{\TI}h{1cm}@{\TI}h{.9cm} @{\TI}h{.9cm}@{\TI}h{.7cm}@{\TI}h{.7cm}@{\TI}h{.8cm} @{\TI}h{.9cm}@{\TI}h{.8cm}@{\TI}h{.7cm}\|} \hline \No&выс раст&дл сцв& кол лст пл&кол узк лст&дл max лст& шр max лст&плж шр лст&птн лис 1--3&хар птн 0--3& тлщ стбл&дл ниж прцв&дл шпр& шир шпр&шр губ&дл губ&дл срд лоп& мал дл губ&дл бок лоп&цв губ 0--4\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline\hline & & & & & & & & & & & & & & & & & & &\\\hline & & & & & & & & & & & & & & & & & & &\\\hline \end{tabular}\smallskip \textbf{Признаки}: \emph{высота растения} меряется от субстрата; \emph{длина соцветия}~--- от нижнего прицветника; сначала подсчитываются \textbf{все} \emph{листья}, кроме нижних чешуевидных; потом подсчитываются верхние, безвлагалищные \emph{узкие листья}; \emph{основанием} листа считается точка отклонения пластинки от стебля; \emph{положение ширины} измеряется от этой точки; \emph{пятнистость максимального листа}: 1~листья без пятен, 2~площадь пятен меньше трети листа, 3~больше трети листа; \emph{характер пятнистости}: 0~пятен нет; 1~пятна в основном у основания, 2~равномерно, 3~в основном у верхушки; \emph{толщина стебля} измеряется сразу над точкой отклонения пластинки максимального листа; \emph{длина шпорца} измеряется снизу; \emph{ширина шпорца} измеряется сбоку в зеве; \emph{средняя и боковая (левая) лопасти} губы измеряются до выемки (если выемки нет, то длина боковой лопасти =\,0); \emph{малая длина губы} измеряется от зева до конца левой боковой лопасти; \emph{цвет губы}: 0~желтая, 1~почти белая, 2~розовая, 3~темно-розовая, 4~красная. \textbf{Инструкции}: (а) у каждого растения измеряется один цветок из середины соцветия; (б) в силикагель надо брать 4--5 целых наиболее молодых цветков с одного из растений популяции, это растение надо отметить на бланке и загербаризировать; (в) г\'убы со шпорцем всех измеренных цветков надо расправить и заклеить скотчем на обороте бланка; (г) на одном бланке может быть описано более одной популяции, но тогда <<шапку>> бланка надо \emph{повторять}. \end{document}
https://doc.libelektra.org/api/current/latex/doc_help_kdb-help_md.tex	libelektra.org	CC-MAIN-2019-39	text/x-tex	application/x-tex	crawl-data/CC-MAIN-2019-39/segments/1568514573908.70/warc/CC-MAIN-20190920071824-20190920093824-00205.warc.gz	441,384,836	1,056	\subsection{S\+Y\+N\+O\+P\+S\+IS} \begin{DoxyCode} kdb help <tool> kdb --help <tool> kdb -H <tool> \end{DoxyCode} \subsection{D\+E\+S\+C\+R\+I\+P\+T\+I\+ON} Show a man page for one of Elektra‚Äôs tools. Note that {\ttfamily kdb $<$tool$>$ -\/-\/help} might have a different behavior, depending on the tool. Also note that, no additional commandline options are allowed for this kind of invocation. If you want that use {\ttfamily -\/-\/help} or {\ttfamily -\/H} after {\ttfamily $<$tool$>$}. \subsection{K\+DB} \begin{DoxyItemize} \item {\ttfamily /sw/elektra/kdb/\#0/current/man}\+: The man(1) utility to be used. Defaults to /usr/bin/man \end{DoxyItemize} \subsection{E\+X\+A\+M\+P\+L\+ES} Show how to set keys\+: {\ttfamily kdb help set} Use the info program as man page viewer for the current user\+: {\ttfamily kdb set user/sw/elektra/kdb/\#0/current/man /usr/bin/info}
https://www.authorea.com/users/225313/articles/341353/download_latex	authorea.com	CC-MAIN-2022-05	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2022-05/segments/1642320301309.22/warc/CC-MAIN-20220119094810-20220119124810-00161.warc.gz	719,228,081	3,207	\documentclass[10pt]{article} \usepackage{fullpage} \usepackage{setspace} \usepackage{parskip} \usepackage{titlesec} \usepackage[section]{placeins} \usepackage{xcolor} \usepackage{breakcites} \usepackage{lineno} \usepackage{hyphenat} \PassOptionsToPackage{hyphens}{url} \usepackage[colorlinks = true, linkcolor = blue, urlcolor = blue, citecolor = blue, anchorcolor = blue]{hyperref} \usepackage{etoolbox} \makeatletter \patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{% \errmessage{\noexpand\@combinedblfloats could not be patched}% }% \makeatother \usepackage[round]{natbib} \let\cite\citep \renewenvironment{abstract} {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize} {\bigskip} \titlespacing{\section}{0pt}{3}{1} \titlespacing{\subsection}{0pt}{2}{0.5} \titlespacing{\subsubsection}{0pt}{1.5}{0pt} \usepackage{authblk} \usepackage{graphicx} \usepackage[space]{grffile} \usepackage{latexsym} \usepackage{textcomp} \usepackage{longtable} \usepackage{tabulary} \usepackage{booktabs,array,multirow} \usepackage{amsfonts,amsmath,amssymb} \providecommand\citet{\cite} \providecommand\citep{\cite} \providecommand\citealt{\cite} % You can conditionalize code for latexml or normal latex using this. \newif\iflatexml\latexmlfalse \providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}% \AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}} \usepackage[utf8]{inputenc} \usepackage[ngerman,english]{babel} \begin{document} \title{Rese\selectlanguage{ngerman}ñas de las exposiciones:\selectlanguage{english}} \author[1]{Luis Donaldo Valles-Mercado}% \affil[1]{Instituto Tecnológico Superior Zacatecas Occidente}% \vspace{-1em} \date{\today} \begingroup \let\center\flushleft \let\endcenter\endflushleft \maketitle \endgroup \sloppy \selectlanguage{ngerman}\section{Innovación Social:} {\label{462058}} \subsection{Integrantes:~} {\label{791866}} \subsubsection{Dayana Perez} {\label{743631}} \subsubsection{Mayra Flores} {\label{637326}} Mayor enfoque~ en el tema ya que se divagaba mucho, así mismo hacer la presentación mas digerible, con menos texto y mas material visual para comprender mejor el tema. En general me pareció una buena exposición con un tema que tiene un gran potencial. \section{Ventaja Competitiva:~} {\label{987713}} \subsection{Integrantes:} {\label{603349}} \subsubsection{Daniela Terrones} {\label{672996}} \subsubsection{Tania Avila} {\label{516616}} \subsubsection{Alma Hernandez~} {\label{609249}} Buena presentación pero~ era mucho texto y no se comprendía en si que era lo que ellas buscaban hacer, ademas de que al menos una integrante no iba muy bien preparada para explicar el contenido del tema \section{Mercados financieros en Sombrerete:~} {\label{758843}} \subsection{Integrantes:} {\label{526491}} \subsubsection{Yadira García} {\label{601218}} \subsubsection{Moyra~ Fraga} {\label{666177}} \subsubsection{Catalina Fraire} {\label{170709}} Faltas de ortografía y hablaban y leían muy rápido, sin embargo explicaron el contenido de forma clara, aunque se veían un tanto nerviosas y por lo tanto pudo haber influido en la manera en la que se dirigían al publico. \par\null \section{Ética en los Negocios:} {\label{812026}} \subsection{Integrantes:} {\label{388716}} \subsubsection{Rosa Zaldívar} {\label{254292}} \subsubsection{Jacqueline Guitrón} {\label{663546}} \subsubsection{Edith Ávila~} {\label{887223}} Les faltó mayor seriedad durante la exposición ya que continuamente se desviaban del tema y se perdía la seriedad y el enfoque en el tema, también contaban con algunos errores en las referencias y el citado de documentos. \section{Desarrollo de Zonas Rurales:} {\label{765736}} \subsection{Integrantes:} {\label{608030}} \subsubsection{Cristian Gómez} {\label{744180}} \subsubsection{Nancy Díaz} {\label{817938}} En general,~ fue un buen tema sin embargo considero que se podría enfocar más~ y especializar mas, asi como mejorar la metodologia que involucre mas ámbitos del desarrollo de dichas zonas. \section{Modelo de desarrollo de conocimiento para medir el desempeño en la empresa:} {\label{529430}} \subsection{Integrantes:~} {\label{173302}} \subsubsection{Alma Flores~} {\label{325073}} \subsubsection{Elizabeth Arambula~} {\label{677220}} \subsubsection{Francisca Alvarez~} {\label{710573}} Un buen tema sin embargo, a veces solo leían las diapositivas y explicaban poco, asi mismo no se escuchaba mucho y se perdia la concentración y el enfoque en el tema. \section{Pobreza y desigualdad:} {\label{974369}} \subsection{Integrantes:} {\label{893268}} \subsubsection{Alondra Fernandez} {\label{885971}} \subsubsection*{Fernando Gamez~} {\label{684242}} Un tema muy completo que fue cubierto en forma clara, sin embargo a veces explicaban demasiado o en otros casos no explicaban como realizarían ciertas actividades o sus fuentes de información confiables, estaria bien que complementarán aún mas el tema basandose en fenomenos propios de la región que estudiarán asi como las condiciones sociales. \par\null \selectlanguage{english} \FloatBarrier \end{document}
https://people.cs.umass.edu/~freedman/resources/Freedman_LaTeXCheatSheet.tex	umass.edu	CC-MAIN-2022-33	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2022-33/segments/1659882571584.72/warc/CC-MAIN-20220812045352-20220812075352-00448.warc.gz	403,403,447	8,667	%This is a comment. It will not appear in the compiled file. \documentclass[10pt]{article} \usepackage[normalem]{ulem} \title{A Super Brief, Yet Super Awesome, LaTeX Cheat Sheet} \author{Richard (Rick) G. Freedman, \sout{Wake Forest University} University of Massachusetts Amherst\\Philip (Phil) Thomas, University of Massachusetts Amherst} \date{\sout{6 February 2011} 14 June 2013} \begin{document} \maketitle \tableofcontents \section{A Brief Introduction\label{intro}} LaTeX is a programming language that can be used for writing documents. It is especially useful for the mathematics and sciences fields due to its ease of writing special symbols and equations while also making them look good. Most textbooks are actually written in LaTeX. Due to the programming aspect, writing documents in LaTeX allows a lot more freedom to format how the document should look. However, it is important to learn how these formatting techniques function in order to know what to expect (did you notice how Rick's school affilitation goes off the page?). \par In this cheat sheet, we discuss some of the basics for writing documents in LaTeX. We hope it can help you get started with learning this useful language - LaTeX will make writing homework assignments, publications, posters, and many other documents far easier. For additional practice, the actual .tex file is included for you to see what we did. Feel free to modify it and see how your changes affect this document. \subsection{What You Will Need to Get Started\label{gettingStarted}} In order to write documents in LaTeX, you will need to download the standard LaTeX packages and compilers. There are a lot of packages and several compilers, and we barely scratch the surface about a few of them in Sections~\ref{packages} and~\ref{howRickCompiles}. Don't worry about finding all of them scattered across the internet; the essentials can all be found in one place. For Windows users, we suggest downloading MikTex. For Linux (and other *nix) users, we highly recommend TexLive. You can write your code in any text editor as well as any LaTeX IDE. Many of them are out there for free; so play with them and find what you like. We personally use TexMaker. \section{Special Symbols and Their Uses\label{specialSymbols}} To write a comment like the one at the top of the .tex file, use the percent sign (\%). To place symbols like the percent sign into the compiled paper, use the escape character before the symbol (it is the forward slash ($ \setminus $) found above the ENTER key on the keyboard). \par In fact, the escape character is used to begin any command in LaTeX. For example, to start this new paragraph, the command $ \setminus $par was written. However, if you looked at the .tex file itself, you would see that we are writing the escape character for the compiled paper as \$ $ \setminus $setminus \$. This is because two escapes characters in a row indicates a line break \\ that forces us onto the next line as just happened here. However, most journals request that the command $ \setminus $newline is used instead as done \newline here. They look similar in this document, but a journal's style file can modify how the $ \setminus $newline command looks. The two escape character version is unmodifiable. \par So the next question is probably ``Why the dollar signs (\$)?" They place us into a special thing called ``Math Mode." We will explain it later, but it is good to know that the dollar sign is also a special symbol. Other special symbols are the curly braces (\{ and \}) which contain parameters for commands, tilde ($ \sim $) which generates a unit of whitespace that cannot be broken between two lines for word wrapping, carrot (\^) which is used for superscripting in math mode, and underscore (\_) which is used for subscripting in math mode. The ampersand (\&) and pound (\#) are also special symbols, but their uses vary by the context of the document. Just remember to escape these characters (or use \$ $ \setminus $sim \$ for the tilde) when trying to print them in the document; we have done so in the .tex file if you read this paragraph. \section{Formatting Commands\label{formattingCmds}} Many commands in LaTeX will format the compiled paper. In order to understand what is formatted, it is usually bounded in some way just as Math Mode applies to anything between two dollar signs. In particular, there are two ways formatting is done: \subsection{In-Line Formatting Commands\label{inlineFormatCmds}} These format only a little bit of text at a time. Because they only affect a small amount of text, these commands are a single command that receives the text in curly braces (\{ and \}) afterwards. Some important examples we will use are below. To show what they do, the actual command is used on the text in curly braces. \begin{itemize} \item $ \setminus $textbf\{\textbf{Text to write in bold}\} \item $ \setminus $textit\{\textit{Text to write in italics}\} \item $ \setminus $underline\{\underline{Text to underline}\} \item $ \setminus $sout\{\sout{Text to strike out}\} You will need to use the \textit{ulem} package (see Section~\ref{packages}) \item $ \setminus $textsc\{\textsc{Text to write in all capital letters without `shouting'}\} \end{itemize} Best of all, these can be placed within each other (like nested blocks of code). \textbf{\textit{\underline{That is why this sentence is written in bold, italics, and underlined!}}} \subsection{$ \setminus $begin...$ \setminus $end Formatting Commands (Also Called \textit{Environments})\label{envFormattingCmds}} When a large amount of text is formatted at one time with a command, it is easier to not have to contain it within brackets. This is why some formatting commands have two pairs of commands: $ \setminus $begin\{format command\} and $ \setminus $end\{format command\}. Think of them as the left and right curly braces of the in-line formatting commands. Anything between a $ \setminus $begin and $ \setminus $end with the same format command will be formatted. Some examples include: \begin{center} \{center\} centers the text \end{center} \begin{flushright} \{flushright\} moves the text to the right side \end{flushright} \begin{flushleft} \{flushleft\} moves the text to the left side \end{flushleft} \begin{verbatim} \{verbatim\} types everything character for character, including commands. This is great for typing program code since there are so many special symbols that would have been escaped. Notice that we should not have escaped the curly braces around the word `verbatim' and been more careful with margins. \end{verbatim} \begin{tiny} \{tiny\} shrinks the font to a really small size \end{tiny} \begin{huge} \{huge\} enlarges the font to a really large size \end{huge} Besides formatting commands, $ \setminus $begin and $ \setminus $end are used for special segments of the document as well. These (which are far more useful) include: \begin{itemize} \item Creating lists. Each entry is indicated by the $ \setminus $item command. There are many types of lists including: \begin{enumerate} \item \{itemize\} Bulleted lists \item \{enumerate\} Numbered lists \item \{description\} Labelled lists where each item starts with an emphasized word provided in brackets like $ \setminus $item[word]. Here's a secret: the brackets after the command $ \setminus $item can be used for the other list environments. Try them out and see how it looks different from the description environment. \end{enumerate} \item The paper itself is bounded between $ \setminus $begin\{document\} and $ \setminus $end\{document\} and \textsc{this is a required environment} \item \{tabular\} creates a table after providing a little more information. We will briefly explain them in Section~\ref{tableTutorial}. \item \{displaymath\} will also put us in a special Math Mode that gets its own line that can present larger symbols. For example, in-line Math Mode's sum symbol looks like $ \sum_{i = 0}^{n} f\left(i\right) $ while displaymath Math Mode's sum symbol looks less squished $$ \sum_{i = 0}^{n} f\left(i\right) $$ (the shortcut for the displaymath environment is two consecutive dollar signs \$\$ $\ldots$ \$\$ as seen in the .tex file). \end{itemize} The only warning with all these commands is that any $ \setminus $end must have the same command as the most recently unmatched $ \setminus $begin in the file. This will line them up so that they match like the in-line brackets. \section{Math Mode Commands\label{mathModeCmds}} Anything between dollar signs \$ $ \ldots $ \$ is written in math mode. It will accept many commands that are otherwise not available and formats the text to look ``mathy" (so sentences should not go here). Since it is so straightforward, we will just list some commands used in Math Mode for common symbols: \begin{itemize} \item any text is $ any text $ (Note that spaces are ignored in Math Mode since text is assumed to be a string of variables) \item $ \setminus $leq is $ \leq $ \item $ \setminus $geq is $ \geq $ \item $ \setminus $neq is $ \neq $ \item $ \setminus $(Greek letter) makes the Greek letter. Capitalizing the first letter determines whether or not the Greek letter is capital. For example, $ \setminus $Omega is $ \Omega $ and $ \setminus $alpha is $ \alpha $. Not all of them are available, though. Some have alternative designs such as $ \setminus $phi ($ \phi $) and $ \setminus $varphi ($ \varphi $) \item $ \setminus $in is $ \in $ \item $ \setminus $subset is $ \subset $ \item $ \setminus $subseteq is $ \subseteq $ \item $ \setminus $cup is $ \cup $ \item $ \setminus $cap is $ \cap $ \item $ \setminus $vee is $ \vee $ \item $ \setminus $wedge is $ \wedge $ \item $ \setminus $neg is $ \neg $ \item $ \setminus $ldots is $ \ldots $ \item $ \setminus $cdots is $ \cdots $ \item $ \setminus $cdot is $ \cdot $ \item $ \setminus $infty is $ \infty $ \item $ \setminus $sum is $ \sum $ (use superscript and subscript for indexing) \item $ \setminus $prod is $ \prod $ (use superscript and subscript for indexing) \item $ \setminus $int is $ \int $ (use superscript and subscript for limits of integration) \item $ \setminus $partial is $ \partial $ \item $ \setminus $mid is $ \mid $ \item $ \setminus $leftarrow is $ \leftarrow $ (guess what happens if you replace `left' with `up,' `down,' `right,' or `leftright') \item $ \setminus $Leftarrow is $ \Leftarrow $ (guess what happens if you replace `Left' with `Up,' `Down,' `Right,' or `Leftright') \item $ \setminus $; adds extra white space to better separate symbols \end{itemize} $ \setminus $not preceding another Math Mode command slashes through it to get things like `not divisible by:' $ \not\mid $. Also, to help keep track of the left and right grouping symbols, $ \setminus $left and $ \setminus $right may precede parentheses, brackets, curly braces (which must be written as $ \setminus $leftbrace and $ \setminus $rightbrace), vertical bars (above the ENTER key), floor functions (written $ \setminus $lfloor and $ \setminus $rfloor), ceiling functions (written $ \setminus $lceil and $ \setminus $rceil), and period for nothing (which is useful in set notation, conditional probability, and piecewise functions). Another benefit of $ \setminus $left and $ \setminus $right is that they adjust their size appropriately in the displaymath environment: compare $$ (a + \frac{b}{c}] \textnormal{ with } \left(a + \frac{b}{c}\right] $$ which also shows that the symbols do not need to match up. This is the purpose of the period when only one symbol is needed on one side to scale in the displaymath environment. The compiler will complain if the commands $ \setminus $left and $ \setminus $right do not match up correctly. \par There are also some in-line formatting commands for Math Mode. The more useful ones are: \begin{itemize} \item \^\ \{The text to superscript such as 2 in $ x^{2} $\} \item \_\{The text to subscript such as 0 in $ x_{0} $\} \item $ \setminus $frac\{numerator\}\{denominator\} makes a fraction like $ \frac{x}{y} $ when given \{x\}\{y\} \item $ \setminus $textnormal\{any text\} will print the text as though Math Mode is not in use \end{itemize} Notice that the superscript and subscript commands DO NOT have an escape character in front of them! \section{Tables\label{tableTutorial}} To create a table, you will have an extra argument to give when defining $ \setminus $begin\{tabular\}\{layout\}. The \textit{layout} argument will specify how many columns there are, where the text is placed in each column, and if a line separates the columns. A layout example is \{$\|$c$\|$c$\|$lr$\|$c$\|$c\} which will have 6 columns: a line of separation, a centered column, a line of separation, a centered column, a line of separation, a left column (no line of separation), a right column, a line of separation, a centered column, a line of separation, and a centered column (no line of separation). \par When filling in the table, each line is an individual row (columns are separated by ampersands (\&)) and they are separated by the $ \setminus\setminus $ line breaks. To place a horizontal line of separtion, use the $ \setminus $hline command. It may be good to look at the table below both in the compiled document and in the .tex file. It will show the correlation between making the table and its code. You will need to start it on a new line (we use $ \setminus $par to do it here). \par \begin{tabular}{\|c\|c\|lr\|c\|c} \hline Hello & there & person & reading & this & ! \\ \hline This column is & So is this & But here it is & And here it is & Now we are again & As we also are \\ centered & one & left & right & centered & here \\ \hline Above is & 2 columns. & But we did not & separate with & $ \setminus $hline! How cool is & that?! \\ \hline You can also & & have a blank & & column that is & empty \\ \hline \end{tabular} We must be careful. As seen above, the table can be made longer than the page. This is when compiling and editing will become a trial and error task. When in the displaymath environment (see Section~\ref{envFormattingCmds}), the environment name is changed from \textit{tabular} to \textit{array}, but everything else remains the same. \section{More Stuff\label{otherThings}} \subsection{Sections and Subsections\label{sectionInfo}} This whole document has been organized by ``chapters" that have their own numbers and titles. They are generated by two particular commands: \begin{description} \item[$ \setminus $section\{title\}] These are the larger sections. They have a single number and the title. ``More Stuff" is a section. \item[$ \setminus $subsection\{title\}] These are the smaller sections within the section most recently declared in the .tex file. They have two numbers separated by a period (.). ``Sections and Subsections" is a subsection of ``More Stuff." \end{description} \subsection{To Make Quoted Text Look Good\label{quoteText}} LaTeX prints the quote symbols as " and '. These only look good when placed at the end of the text. To get good quotation marks at the beginning of the text, use the backtick ` located below the ESCAPE key on the keyboard. `Thank you very much!' \subsection{Packages\label{packages}} Like in any programming language, other people have made things that can improve our coding lives. Many of these packages already come with a standard LaTeX install (Miktex for Windows and TexLive for Linux), and other ones can be downloaded and placed in the same directory as the .tex file. To use the package in a document, the command $ \setminus $usepackage\{packageName\} must appear after the $ \setminus $documentclass command. Some packages have special parameters that appear in brackets before the package name. Some common packages to include are: \begin{itemize} \item $ \setminus $usepackage\{amsmath\}, $ \setminus $usepackage\{amsfonts\}, and $ \setminus $usepackage\{amssymb\} form the set of AMS (American Mathematics Society) packages that the TexMaker IDE always suggests. With these three packages, almost every math symbol is available. \item $ \setminus $usepackage[margin=XX]\{geometry\} can cheat the margins when you want to save trees or specify particular guidelines. Replace XX with a floating-point number followed by a unit of measurement such as `in' or `cm' (no space between the number and unit). \item $ \setminus $usepackage\{graphicx\} allows graphics to be rendered in the document. It is a necessary evil in LaTeX. \item $ \setminus $usepackage\{epsfig\} allows PostScript images to be rendered in the document. It is a slightly less evil in LaTeX since the bounding boxes can be computed for you. \item $ \setminus $usepackage[normalem]\{ulem\} allows some other emphasis in-line formatting commands such as $ \setminus $sout. \end{itemize} \subsection{Other Useful Commands\label{usefulCmds}} Some commands for formatting look very different from traditional in-line formatting and environments. In particular, they are constants whose values are set such as $ \setminus $parindent=XX for how much to indent paragraphs (with the $ \setminus $par command) and $ \setminus $parskip=XX for how much space to leave between consecutive paragraphs. In both cases, XX is replaced with a floating point and unit as done for the geometry package (see Section~\ref{packages}). \par Also, some documents are better with a tabel of contents and title section (like this one). The command $ \setminus $tableofcontents will generate a table of contents where the command is specified and $ \setminus $maketitle will generate a title section with a given title (use command $ \setminus $title\{title\} beforehand), authors (use command $ \setminus $author\{author(s)\} beforehand), and the date of compilation (unless the command $ \setminus $date\{date\} is specified beforehand). \par Footnotes can be made using the command $ \setminus $footnote\{Text to appear in footnote\}. They are numbered in order and placed at the bottom of the page during compilation. A variation of footnotes that is sometimes used for author information when generating the title section is the command $ \setminus $thanks\{Author Information\}. \subsection{References and Citations\label{references}} When revising a document, it can be common to reorder sections, figures, and tables as well as edit the bibliography. Rather than have to change all the references and citations each time, LaTeX keeps track of them for you! When creating a section or caption, include the command $ \setminus $label\{labelName\} before ending it (as we have done for all sections in the .tex file). Then in the document, feel free to always write Section/Figure/Table$ \sim\setminus $ref\{labelName\} and the compiler will fill in the appropriate name in place of the $ \setminus $ref command. The tilde ($ \sim $) is a special character that makes sure that the number is not separated from the word preceding it. Likewise, the bibtex file's names for each bibliographic entry may be cited in this way in case the reference list changes. Simply use the command $ \setminus $cite\{bibitemName\}. \subsection{Compiling via Command Line\label{howRickCompiles}} For Linux users who want to compile LaTeX documents without the IDE (especially if you code in a text editor instead), there are two paths to take depending on the file format of figures (if no images of either format, then both work). If a compiler error occurs, the best thing to do is make the specified change (warning: LaTeX gives bad error messages) in the .tex file, type a capital `R' in the command line menu, and press ENTER; this terminates the compilation and spits out a lot of text, but avoiding the compiler's debug menu is worth it: \begin{description} \item[PostScript] (.eps and/or .ps) First, compile the .tex file with \textit{latex} in order to get a .dvi file. If you have referenced sections, then a second compilation will be necessary due to the one-pass compiler missing the label of later sections: \begin{verbatim} > latex myfile.tex > #It doesn't hurt to compile again if there are references > latex myfile.tex \end{verbatim} If you have a bibtex file to also compile, then now is the time to synchronize them (since all the other steps convert the .dvi file). When compiling, an auxiliary .aux file is generated that lists which references are cited in each .bib file (since that information is in the .tex file). So synchronize the auxiliary file with the bibtex file: \begin{verbatim} > bibtex myfile.aux \end{verbatim} Now recompile the document \textsc{twice}. The first time generates the bibliography section and a list of citation information (such as `Author Year'), and the second time fills in the $ \setminus $cite commands with this information obtained from the previous compilation. Note that if the bibliography (not the in-text citations) changes, then synchronization needs to be done again by \textsc{deleting the auxiliary file} and then starting over the entire compilation process. \begin{verbatim} > latex myfile.tex > latex myfile.tex \end{verbatim} Second, convert the .dvi file into a .ps file using \textit{dvips} which is `dvi' followed by `ps:' \begin{verbatim} > dvips myfile.dvi \end{verbatim} Lastly, convert the .ps file into a .pdf file using \textit{ps2pdf}: \begin{verbatim} > ps2pdf myfile.ps \end{verbatim} The .pdf file is now ready, and the PostScript images are properly rendered. \item[PDF] First, compile the .tex file with \textit{pdflatex} in order to get a .pdf file. If you have referenced sections, then a second compilation will be necessary due to the one-pass compiler missing the label of later sections: \begin{verbatim} > pdflatex myfile.tex > #It doesn't hurt to compile again if there are references > pdflatex myfile.tex \end{verbatim} If you have a bibtex file to also compile, then now is the time to synchronize them. When compiling, an auxiliary .aux file is generated that lists which references are cited in each .bib file (since that information is in the .tex file). So synchronize the auxiliary file with the bibtex file: \begin{verbatim} > bibtex myfile.aux \end{verbatim} Now recompile the document \textsc{twice}. The first time generates the bibliography section and a list of citation information (such as `Author Year'), and the second time fills in the $ \setminus $cite commands with this information obtained from the previous compilation. Note that if the bibliography (not the in-text citations) changes, then synchronization needs to be done again by \textsc{deleting the auxiliary file} and then starting over the entire compilation process. \begin{verbatim} > pdflatex myfile.tex > pdflatex myfile.tex \end{verbatim} The .pdf file is now ready with all PDF images included. \end{description} \subsection{This Is Only the Beginning\label{conclusion}} LaTeX can do far, far more than these things. However, this should be enough to understand the basics. We can discuss other commands if we need them later, but they will be similar in syntax to the commands discussed above. Enjoy! Happy LaTeX'ing! \end{document}
https://ctan.math.washington.edu/tex-archive/info/examples/PSTricks_en/23-04-5.ltx	washington.edu	CC-MAIN-2022-27	text/x-tex	text/x-matlab	crawl-data/CC-MAIN-2022-27/segments/1656103642979.38/warc/CC-MAIN-20220629180939-20220629210939-00711.warc.gz	236,869,670	1,048	%% %% A DANTE-Edition example %% %% Example 23-04-5 on page 357. %% %% Copyright (C) 2011 Herbert Voss %% %% It may be distributed and/or modified under the conditions %% of the LaTeX Project Public License, either version 1.3 %% of this license or (at your option) any later version. %% %% See http://www.latex-project.org/lppl.txt for details. %% %% %% ==== % Show page(s) 1 %% \documentclass[]{article} \pagestyle{empty} \setlength\textwidth{375.57637pt} \setlength\parindent{0pt} \usepackage{pst-fr3d} \psset{doublesep=0.2} \begin{document} \PstFrameBoxThreeD[FrameBoxThreeDColorHSB=0.8 0.3 0.6]{\textbf{Button}} \PstFrameBoxThreeD[FrameBoxThreeDColorHSB=0.8 0.3 0.6, FrameBoxThreeDBrightnessDistance=0.3]{\textbf{Button}} \PstFrameBoxThreeD[FrameBoxThreeDColorHSB=0.8 0.3 0.6, FrameBoxThreeDBrightnessDistance=0.5]{\textbf{Button}} \PstFrameBoxThreeD[FrameBoxThreeDColorHSB=0.8 0.3 0.8, FrameBoxThreeDBrightnessDistance=0.3]{\textbf{Button}} \PstFrameBoxThreeD[FrameBoxThreeDColorHSB=0.8 0.3 0.6, FrameBoxThreeDBrightnessDistance=-0.2]{\textbf{Button}} \end{document}
http://sokocalo.engr.ucdavis.edu/~jeremic/wwwpublications/CV-T111.tex	ucdavis.edu	CC-MAIN-2020-16	text/x-tex	application/x-tex	crawl-data/CC-MAIN-2020-16/segments/1585370499280.44/warc/CC-MAIN-20200331003537-20200331033537-00523.warc.gz	138,432,459	19,526	\documentclass[fleqn]{beamer} %\documentclass[handout]{beamer} %\usepackage{pgfpages} %\pgfpagelayout{2 on 1}[letterpaper, border shrink=5mm] \mode<handout>{\setbeamercolor{background canvas}{bg=black!3}} \usepackage{epstopdf} % \definecolor{grey}{rgb}{0.6,0.6,0.6} \newcommand\pder[2][]{\ensuremath{\frac{\partial#1}{\partial#2}}} \newcommand\der[2][]{\ensuremath{\frac{d#1}{d#2}}} \newcommand\n{\vspace{0.1in}} %This is a macro to convert eps to pdf files on the fly. % make sure figure syntax uses graphicx syntax NOT epsfig syntax %from http://mailman.mit.edu/pipermail/macpartners/2005-January/000780.html % % \ifx\pdfoutput\undefined % % we are running LaTeX, not pdflatex % \usepackage{graphicx} % \else % % we are running pdflatex, so convert .pdf files to .pdf % \usepackage[pdftex]{graphicx} % \usepackage{epstopdf} % \fi % %***************************************** \usepackage{multimedia} % % % for not showing eq numbers unless eq is references % \usepackage[fleqn,tbtags]{mathtools} % \mathtoolsset{ % showonlyrefs % } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % FEI LOGO definition \newcommand{\FEI} {{\sf \uppercase{F}\kern-0.20em\uppercase{E}\kern-0.20em\uppercase{I}}} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % ovo je za cirilicu % \input vuk.def % %\newfont{\cyr}{wncyr10 scaled 1200} % %\newfont{\cyrimena}{wncyb10 scaled 1800} % %\newfont{\cyrnaslov}{wncyb10 scaled 2600} % %\newfont{\cyrpodnaslov}{wncyr10 scaled 1400} \newfont{\cyr}{wncyss10 scaled 1200} \newfont{\cyrimena}{wncyss10 scaled 2000} \newfont{\cyrnaslov}{wncyss10 scaled 2800} \newfont{\cyrpodnaslov}{wncyss10 scaled 1400} \newfont{\cyrssDvanaest}{wncyss10 scaled 1200 } \newfont{\cyrssJedanaest}{wncyss10 scaled 1100 } \newfont{\cyn}{wncyss10 scaled 2200} %% JB sig \newfont{\cyrjb}{wncyr10 scaled 600} \newcommand{\JB} {{\cyrjb \lower0.50ex\hbox{\uppercase{J}}\kern-.58em\hbox{\uppercase{B}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \setbeamertemplate{navigation symbols}{} \mode<presentation> { % \usetheme{Marburg} % ima naslov i sadrzaj sa desne strane % \usetheme{Hannover} % ima naslov i sadrzaj sa leve strane % \usetheme{Singapore} % ima sadrzaj i tackice gore % \usetheme{Antibes} % ima sadrzaj gore i kao graf ... % \usetheme{Berkeley} % ima sadrzaj desno % \usetheme{Berlin} % ima sadrzaj gore i tackice % \usetheme{Goettingen} % ima sadrzxaj za desne strane % \usetheme{Montpellier} % ima graf sadrzaj gore % \usetheme{Warsaw} % \usetheme{Warsaw} \usetheme{Dresden} \usecolortheme[RGB={20,0,128}]{structure} % or ... \setbeamercovered{transparent} % \setbeamercovered{transparent} % or whatever (possibly just delete it) % \usecolortheme{albatross} % teget sa svetlim slovima % \usecolortheme{beetle} % siva pozadina (vrh plav) \usecolortheme{seagull} % sivo %%%%%%% % \usecolortheme{BorisJeremic} %%%%%%% % \usecolortheme{rose} % \usefonttheme[onlylarge]{structuresmallcapsserif} % \usefonttheme{structuresmallcapsserif} } \definecolor{mycolor}{rgb}{0,0.08,0.45}% \usepackage[greek,english]{babel} %\usepackage[english]{babel} \usepackage{amsmath} \usepackage{mathrsfs} \usepackage{amsfonts} \newcommand{\ud}{{\rm d}} \usepackage{array} %%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF %%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF \definecolor{webgreen}{rgb}{0, 0.15, 0} % less intense green \definecolor{webblue}{rgb}{0, 0, 0.15} % less intense blue \definecolor{webred}{rgb}{0.15, 0, 0} % less intense red %\usepackage[colorlinks=true,linkcolor=webblue,citecolor=webred,urlcolor=webgreen]{hyperref} \usepackage{hyperref} \hypersetup{ pdfmenubar=true, pdftoolbar=true, pdfpagemode={None} } \usepackage{pause} % or whatever %\usepackage{html} %\usepackage{url} \usepackage[latin1]{inputenc} % or whatever \usepackage{times} \usepackage[T1]{fontenc} % Or whatever. Note that the encoding and the font should match. If T1 % does not look nice, try deleting the line with the fontenc. \title[ESSI under Uncertainty] {Modelling and Simulation of Static and Dynamic Soils Structures Interaction Under Uncertainty } %\subtitle %{Include Only If Paper Has a Subtitle} %\author[Author, Another] % (optional, use only with lots of authors) %{F.~Author\inst{1} \and S.~Another\inst{2}} % - Give the names in the same order as the appear in the paper. % - Use the \inst{?} command only if the authors have different % affiliation. \pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm} \pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo} \author[Jeremi{\'c}] % (optional, use only with lots of authors) %{Boris~Jeremi{\'c}} {Boris Jeremi{\'c}} %\institute[Computational Geomechanics Group \hspace{0.3truecm} \institute[\pgfuseimage{university-logo}\hspace{0.1truecm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed) %{ Professor, University of California, Davis\\ { University of California, Davis\\ % and\\ % Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley } Lawrence Berkeley National Laboratory, Berkeley } % - Use the \inst command only if there are several affiliations. % - Keep it simple, no one is interested in your street address. \date[] % (optional, should be abbreviation of conference name) {\small G{\'e}odynamique et Structure, \\ BAGNEUX, France, November 2015} \subject{} % This is only inserted into the PDF information catalog. Can be left % out. % If you have a file called "university-logo-filename.xxx", where xxx % is a graphic format that can be processed by latex or pdflatex, % resp., then you can add a logo as follows: %\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg} %\logo{\pgfuseimage{university-logo}} % \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename} % \logo{\pgfuseimage{university-logo}} % Delete this, if you do not want the table of contents to pop up at % the beginning of each subsection: % \AtBeginSubsection[] %\setcounter{tocdepth}{2} \setcounter{tocdepth}{2} \AtBeginSubsection[] % \AtBeginSection[] { \begin{scriptsize} \begin{frame}<beamer> \frametitle{Outline} \tableofcontents[currentsection,currentsubsection] % \tableofcontents[currentsection] \end{frame} \end{scriptsize} } % If you wish to uncover everything in a step-wise fashion, uncomment % the following command: \begin{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \titlepage \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Outline} \begin{scriptsize} \tableofcontents % You might wish to add the option [pausesections] \end{scriptsize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Structuring a talk is a difficult task and the following structure % may not be suitable. Here are some rules that apply for this % solution: % - Exactly two or three sections (other than the summary). % - At most three subsections per section. % - Talk about 30s to 2min per frame. So there should be between about % 15 and 30 frames, all told. % - A conference audience is likely to know very little of what you % are going to talk about. So simplify! % - In a 20min talk, getting the main ideas across is hard % enough. Leave out details, even if it means being less precise than % you think necessary. % - If you omit details that are vital to the proof/implementation, % just say so once. Everybody will be happy with that. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Motivation} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Introduction} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Motivation} \begin{itemize} %\vspace{0.3cm} \item Improve seismic design of soil structure systems \vspace{1mm} \item {E}arthquake {S}oil {S}tructure {I}nteraction ({ESSI}) in time and space, plays a major role in successes and failures %\vspace{0.1cm} \vspace{1mm} \item Accurate following and directing (!) the flow of seismic energy in ESSI system to optimize for \begin{itemize} \item Safety and \item Economy \end{itemize} %\vspace{0.1cm} \vspace{1mm} \item Development of high fidelity numerical modeling and simulation tools to analyze realistic ESSI behavior: \\ {Real ESSI} simulator % ({\small aka}: {\cyrssDvanaest Stvarno Lako}, % { Muy F{\'a}cil}, % {Molto Facile}, % \raisebox{-1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}}, % \raisebox{-1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Japanese.jpg}}, % {\greektext{Pragmatik'a E'ukolo}}, % \raisebox{-1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Farsi.jpg}}, % {Tr{\`e}s Facile}, % {\cyrssDvanaest Vistinski Lesno} % %{Wirklich Einfach} % ) \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Predictive Capabilities} % \frametitle{High Fidelity Modeling of SFS System: % Verification, Validation and Prediction} \begin{itemize} \item {{ Verification} provides evidence that the model is solved correctly.} Mathematics issue. %\vspace{0.1cm} \vspace{1mm} \item {{ Validation} provides evidence that the correct model is solved.} Physics issue. %\vspace{0.1cm} \vspace{1mm} \item { Prediction under Uncertainty (!)}: use of computational model to predict the state of SSI system under conditions for which the computational model has not been validated. \vspace{1mm} \item Modeling and Parametric Uncertainties \vspace{1mm} \item Predictive capabilities with {low Kolmogorov Complexity} \vspace{1mm} \item Modeling and simulation goal: \\ predict and inform, rather than (force) fit % \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Uncertainties} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Modeling Uncertainty} \begin{itemize} \item Simplified modeling: Features (important ?) are neglected (6D ground motions, inelasticity) \vspace{4mm} \item Modeling Uncertainty: unrealistic and unnecessary modeling simplifications \vspace{4mm} \item Modeling simplifications are justifiable if one or two level higher sophistication model shows that features being simplified out are not important \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Parametric Uncertainty: Material Stiffness} %\vspace{-3mm} \begin{figure}[!hbpt] \begin{center} % \hspace{-7mm} \includegraphics[width=7.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf} % \hfill \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf} % \end{center} \end{figure} % \vspace{-1.8cm} % %\hspace{-3.3cm} % \begin{flushright} % {\tiny % Transformation of SPT $N$-value: \\ % 1-D Young's modulus, $E$ \\ % (cf. Phoon and Kulhawy (1999B))\\ % ~} % \end{flushright} % \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Parametric Uncertainty: Material Strength} % % % \begin{figure}[!hbpt] % \begin{center} % % % \hspace{-7mm} % \includegraphics[width=6.50truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf} % \hspace{-7mm} % % \hfill % \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf} % % % \end{center} % \end{figure} % % % \vspace{-1.8cm} % % %\hspace{-3.3cm} % % \begin{flushright} % % {\tiny % % Transformation of SPT $N$-value: \\ % % 1-D Young's modulus, $E$ \\ % % (cf. Phoon and Kulhawy (1999B))\\ % % ~} % % \end{flushright} % % % % % % \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Parametric Uncertainty: Material Properties} \begin{figure}[!hbpt] \begin{center} % % \hspace{-3mm} \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf} \hspace{-3mm} \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf} \hspace{3mm} \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf} \hspace{-3mm} \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuCdf.pdf} \\ %\vspace{-2mm} \hspace{-2.5cm} \mbox{\tiny Field $\phi$} \hspace{3.5cm} \mbox{\tiny Field $c_u$} %\vspace{45mm} \hspace{-3mm} \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf} \hspace{-3mm} \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf} \hspace{3mm} \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf} \hspace{-3mm} \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuCdf.pdf} \\ %\vspace{-8mm} \hspace{-2.5cm} \mbox{\tiny Lab $\phi$} \hspace{3.5cm} \mbox{\tiny Lab $c_u$} \end{center} \end{figure} \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Realistic ESSI Modeling (Uncertainties)} % % % \begin{itemize} % % % \item Seismic Motions: 6D, inclined, body and surface waves % (translations, rotations) % %; Incoherency % % %\vspace{3mm} % \vspace{1mm} % \item Inelastic material: soil (dry, saturated), rock, concrete, steel % % \vspace{1mm} % \item Inelastic contact: foundation--soil, dry, saturated, slip--gap % % \vspace{1mm} % \item Nonlinear buoyant forces % % \vspace{1mm} % \item Base Isolators, Dissipators % % \vspace{1mm} % \item Uncertain loading and material % % \vspace{1mm} % \item Verification and Validation $\Rightarrow$ Predictions % % % \end{itemize} % % \end{frame} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Modeling and Parametric Uncertainty} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Modeling Uncertainty: 3D Dam/Slope Model} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{3D Dam -- Slope Stability} \begin{itemize} \item 3D earth slope part of a concrete, earth dam % \vspace{3mm} \item Movements recorded during lowering of reservoir % \vspace{3mm} \item 3D slope unstable (?), no one could tell, all commercial software does 2D slope stability % \vspace{3mm} \item 2D vs 3D slope stability % \vspace{3mm} \item Shear strength (?) as the only material parameter \item (")Expert(") increased value of measured shear strength \item Load cases: lowering and raising reservoir, slow and fast \item Dam build using untreated alluvium \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Dam, Satellite Photo} % \begin{figure}[!htbp] \begin{center} \includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SateliteView01.jpg} %\hspace{-0.9cm} %bridge.} \end{center} \end{figure} % \end{frame} %- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Dam, 3D Slope, Satellite Photo} % \begin{figure}[!htbp] \begin{center} \includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SateliteView02.jpg} %\hspace{-0.9cm} %bridge.} \end{center} \end{figure} % \end{frame} %- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{3D Slope} % \begin{figure}[!htbp] \begin{center} \includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SatelliteView_with_slope01.jpg} %\hspace{-0.9cm} %bridge.} \end{center} \end{figure} % \end{frame} %- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{3D Slope, Ground Photo} % \begin{figure}[!htbp] \begin{center} \includegraphics[width=9.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/img-0188.jpg} %\hspace{-0.9cm} %bridge.} \end{center} \end{figure} % \end{frame} %- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Dam, Construction Photo} % \begin{figure}[!htbp] \begin{center} \includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_Q2-61_621_Embankment_Sep_30_48.jpg} %\hspace{-0.9cm} %bridge.} \end{center} \end{figure} % \end{frame} %- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Dam, Section} % \begin{figure}[!htbp] \begin{center} \includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_PerpendicularSection.jpg} %\hspace{-0.9cm} %bridge.} \end{center} \end{figure} % \end{frame} %- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Dam, Model} % \begin{figure}[!htbp] \begin{center} \includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final02.jpg} \includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final04.jpg} // \includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final05.jpg} \includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final_Top.jpg} %\hspace{-0.9cm} %bridge.} \end{center} \end{figure} % \end{frame} %- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Dam Slope, Failure Modes} \vspace{5mm} \begin{itemize} \item 3D failure pattern \item 3D has lower FS than 2D \item Original $S_u$ FS barely enough, \item With "increased" $S_u$ a bit higher \end{itemize} \vspace{-40mm} \begin{figure}[!htbp] \begin{flushright} \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/Undrained-Su440-Vector-Plan_snapshot.jpg} \end{flushright} \end{figure} \vspace{-10mm} % \begin{figure}[!htbp] \begin{center} % \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Drained_3D_AbsVal_L680_E680_Phi18_FS178.jpg} % \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Drained_3D_Vector_L680_E680_Phi18_FS178.jpg} % \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_drained_case_40_FS_1_89_displacement_vectors_factor_42_39.jpg} % \\ % \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Drained_L680_E680_Phi17_FS189.jpg} % \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_undrained_case_41_FS_1_43__displacement_vectors_factor_1_80.jpg} % \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su1200_FS167.jpg} % \\ \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su800_Alluvium_Su1500_FS250.jpg} \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su900_Alluvium_Su1000_FS222.jpg} \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E720_Su1300_FS154.jpg} %\hspace{-0.9cm} %bridge.} \end{center} \end{figure} % \end{frame} %- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \subsection{Modeling Uncertainty: Bridge Model} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % \begin{frame} % \frametitle{Detailed 3D Bridge Model} % % % % \begin{figure}[!htbp] % \begin{center} % \includegraphics[width=8.0cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg} % %\hspace{-0.9cm} % %bridge.} % \end{center} % \end{figure} % % % \end{frame} % %- % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % \begin{frame} % % \frametitle{Model Components} % % % % % % % \begin{itemize} % % \item Soils: elastic--plastic solids (yield land potential surface % % Drucker-Prager, kinematic hardening Armstrong-Frederick) (UCD: Jie and Jeremi{\'c}) % % \vspace{0.2cm} % % \item Structure non--linear beam--column elements (fiber element) % % (UCB: Fenves, UW: Eberhardt) % % % % \vspace{0.2cm} % % \item Piles: non--linear beam--column elements (fiber element) (UCD: Jie and Jeremi{\'c}) % % % % % % \vspace{0.2cm} % % \item Two types of soil: stiff soil (UT, UCD), soft soil (Bay Mud) % % % % \vspace{0.2cm} % % \item Use of the Domain Reduction Method (DRM) (Bielak et al.) for seismic % % input into FEM model % % % % % % \end{itemize} % % % % \end{frame} % % %- % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Modeling Issues} % % \begin{itemize} % % \vspace{0.2cm} % \item Construction process % % \vspace{0.2cm} % \item Deconvolution of given surface ground motions % % \vspace{0.2cm} % \item No artificial damping (only mat. dissipation, radiation) % % \vspace{0.2cm} % \item Element size issues (filtering of frequencies) % % \vspace{-0.4cm} % \begin{table}[!htbp] % %\caption{ } % \begin{center} % \begin{tabular}{\|r\|c\|c\|c\|c\|} % \hline % elem. \# & elem. size & $f_{cutoff}$ & min. $G^{ep}/Gmax$ & $\gamma$ \\ % \hline % % % % % % 100cm element model, f_cuttof=10HZ, G/Gmax=1.0, 12K elements, Gmax model % 12K & 1.00~m & 10~Hz & 1.0 & <0.5~\% \\ % % % % % %~90cm element model, f_cutoff ~= 3Hz, G/Gmax~=0.08, for epsilon ~= 1%, 15K % %elements, now running... % 15K & 0.90~m & >3~Hz & 0.08 & <1.0~\% \\ % % % % % %27.6cm element model, f_cutoff= 10HZ, G/Gmax=0.08, for epsilon = 1%, 150K % %elements, finest model % 150K & 0.30~m & 10~Hz & 0.08 & <1.0~\% \\ % 500K & 0.15~m & 10~Hz & 0.02 & <5.0~\% \\ % % 27.6cm element model, f_cutoff= 10HZ, G/Gmax=0.08, for epsilon = 1%, 150K % %elements, finest model % \hline % \end{tabular} % \end{center} % \end{table} % % \end{itemize} % % % \end{frame} % %- % %-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %- % %-\begin{frame} % %- \frametitle{FEM Mesh (one of)} % %- % %-% % %-\begin{figure}[!htbp] % %-\begin{center} % %-\includegraphics[width=8cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg} % %-%\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend % %-%bridge.} % %-\end{center} % %-\end{figure} % %-% % %-\end{frame} % %- % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % \begin{frame} % % \frametitle{Northridge and Kocaeli Input Motions} % % % % % % \begin{figure}[!htbp] % % \begin{center} % % \hspace{-1cm} % % \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge.pdf} % % \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/LongMotion/InputMotion_Kocaeli.pdf} % % \hspace{-1cm} % % \\ % % \hspace{-1cm} % % \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge_Spectrum.pdf} % % \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/LongMotion/InputMotion_Kocaeli_Spectrum.pdf} % % \hspace{-1cm} % % %bridge.} % % \end{center} % % \end{figure} % % % % % % % \end{frame} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % \begin{frame} % % \frametitle{Simulation Results} % % % % % % \vspace{-0.5cm} % % %\begin{landscape} % % \begin{figure}[!htbp] % % \begin{center} % % \hspace{-1cm} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock1.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent1.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock2.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent2.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock3.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent3.pdf} % % \hspace{-1cm} % % \\ % % \hspace{-1cm} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock1.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent1.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock2.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent2.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock3.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent3.pdf} % % \hspace{-1cm} % % \\ % % \hspace{-1cm} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock1_Spectrum.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent1_Spectrum.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock2_Spectrum.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent2_Spectrum.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock3_Spectrum.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent3_Spectrum.pdf} % % \hspace{-1cm} % % \\ % % \hspace{-1cm} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock1_Spectrum.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent1_Spectrum.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock2_Spectrum.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent2_Spectrum.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock3_Spectrum.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent3_Spectrum.pdf} % % \hspace{-1cm} % % \\ % % \hspace{-1cm} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent1Pile1.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent1Pile2.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent2Pile1.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent2Pile2.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent3Pile1.pdf} % % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent3Pile2.pdf} % % \hspace{-1cm} % % \end{center} % % \end{figure} % % % % \vspace{-0.8cm} % % \begin{figure}[!htbp] % % \begin{center} % % \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg} % % %bridge.} % % \end{center} % % \end{figure} % % \vspace{-2cm} % % % % % % \clearpage % % % % % % % % % % \end{frame} % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Short Period (Northridge) Input Motions} % % % \vspace{-0.7cm} % \begin{figure}[!htbp] % \begin{center} % \hspace{-1cm} % \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge.pdf} % \hspace{-1cm} % \\ % \hspace{-1cm} % \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge_Spectrum.pdf} % \hspace{-1cm} % %bridge.} % \end{center} % \end{figure} % \vspace{-1.0cm} % % % % \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Short Period Eq.: Left Bent, Displacements} % % % % % \vspace{-1cm} % \begin{figure}[!htbp] % \begin{center} % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1.pdf} % %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1.pdf} % \\ % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1.pdf} % %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1.pdf} % %bridge.} % \end{center} % \end{figure} % % % \vspace{-2.9cm} % \hspace{0.2cm} % \begin{figure}[!htbp] % \begin{flushright} % \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg} % %bridge.} % \end{flushright} % \end{figure} % \hspace{-0.5cm} % \vspace{-2.0cm} % % % % \end{frame} % %-- % % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % \begin{frame} % % \frametitle{Short Period E.: Left Bent, Structure and Soil, Acc.} % % % % % % % % % % \vspace{-1cm} % % \begin{figure}[!htbp] % % \begin{center} % % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1.pdf} % % \\ % % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1.pdf} % % %bridge.} % % \end{center} % % \end{figure} % % % % % % \vspace{-2.9cm} % % \hspace{0.2cm} % % \begin{figure}[!htbp] % % \begin{flushright} % % \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg} % % %bridge.} % % \end{flushright} % % \end{figure} % % \hspace{-0.5cm} % % \vspace{-2.0cm} % % % % \end{frame} % % %-- % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % \begin{frame} % % \frametitle{Short Period E.: Left Bent, Structure and Soil, Acc.Sp.} % % % % % % % % % % \vspace{-1cm} % % \begin{figure}[!htbp] % % \begin{center} % % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1_Spectrum.pdf} % % \\ % % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1_Spectrum.pdf} % % %bridge.} % % \end{center} % % \end{figure} % % % % % % \vspace{-2.9cm} % % \hspace{0.2cm} % % \begin{figure}[!htbp] % % \begin{flushright} % % \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg} % % %bridge.} % % \end{flushright} % % \end{figure} % % \hspace{-0.5cm} % % \vspace{-2.0cm} % % % % % % \end{frame} % % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Short Period Eq.: Left Bent, Moments.} % % % % % \vspace{-1cm} % \begin{figure}[!htbp] % \begin{center} % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile1.pdf} % \\ % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile2.pdf} % %bridge.} % \end{center} % \end{figure} % % % % % \vspace{-2.9cm} % \hspace{0.2cm} % \begin{figure}[!htbp] % \begin{flushright} % \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg} % %bridge.} % \end{flushright} % \end{figure} % \hspace{-0.5cm} % \vspace{-2.0cm} % % % \end{frame} % %-- % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Short Period E.: Left Bent, Bending Moments} % % % % % \vspace{-1cm} % \begin{figure}[!htbp] % \begin{center} % \includegraphics[width=11cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile1_25s_SC.pdf} % %bridge.} % \end{center} % \end{figure} % % % \vspace{-2.9cm} % \hspace{0.2cm} % \begin{figure}[!htbp] % \begin{flushright} % \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg} % %bridge.} % \end{flushright} % \end{figure} % \hspace{-0.5cm} % \vspace{-2.0cm} % % % \end{frame} % %-- % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Short Period E.: Left Bent, Free Field vs Real Disp.} % % % % % \vspace{-1cm} % \begin{figure}[!htbp] % \begin{center} % \includegraphics[width=11cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1_15cm_25s_SC.pdf} % %bridge.} % \end{center} % \end{figure} % % % \vspace{-2.9cm} % \hspace{0.2cm} % \begin{figure}[!htbp] % \begin{flushright} % \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg} % %bridge.} % \end{flushright} % \end{figure} % \hspace{-0.5cm} % \vspace{-2.0cm} % % % \end{frame} % %-- % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Long Period (Kocaeli) Input Motions} % % % \vspace{-0.7cm} % \begin{figure}[!htbp] % \begin{center} % \hspace{-1cm} % \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/LongMotion/InputMotion_Kocaeli.pdf} % \hspace{-1cm} % \\ % \hspace{-1cm} % \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/LongMotion/InputMotion_Kocaeli_Spectrum.pdf} % \hspace{-1cm} % %bridge.} % \end{center} % \end{figure} % % % \vspace{-1cm} % % \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Long Period E.: Left Bent, Bending Moments.} % % % % % %\vspace{-1cm} % \begin{figure}[!htbp] % \begin{center} % %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile1.pdf} % %\\ % \includegraphics[width=11cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile2.pdf} % %bridge.} % \end{center} % \end{figure} % % % \vspace{-2.9cm} % \hspace{0.2cm} % \begin{figure}[!htbp] % \begin{flushright} % \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg} % %bridge.} % \end{flushright} % \end{figure} % \hspace{-0.5cm} % \vspace{-2.0cm} % % % \end{frame} % %-- % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % %-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % \begin{frame} % % \frametitle{Long Period E.: Left Bent, Structure and Soil, Disp.} % % % % % % % % % % \vspace{-1cm} % % \begin{figure}[!htbp] % % \begin{center} % % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/DispBent1.pdf} % % \\ % % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/DispSoilBlock1.pdf} % % %bridge.} % % \end{center} % % \end{figure} % % % % % % \vspace{-2.9cm} % % \hspace{0.2cm} % % \begin{figure}[!htbp] % % \begin{flushright} % % \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg} % % %bridge.} % % \end{flushright} % % \end{figure} % % \hspace{-0.5cm} % % \vspace{-2.0cm} % % % % % % % % \end{frame} % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Modeling Uncertainty: Nuclear Power Plant} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Modeling and Simulation of Nuclear Power Plants} \begin{itemize} \item Nuclear Power Plants (NPPs) design based on a number of simplified assumptions! \vspace{1mm} \item Linear elastic material behavior \vspace{1mm} \item Seismic Motions: $1$D or $3 \times 1$D, or real 3D (6D) \vspace{1mm} \item Savings in construction cost possible with more accurate modeling of NPPs \vspace{1mm} \item Improvements in safety of NPPs also possible, even with higher seismic motions, as inelastic effects "eat up" (dissipate) seismic energy \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Nuclear Power Plants: 6D or 1D Seismic Motions} \begin{itemize} \item Assume that a full 6D (3D) motions at the surface are only recorded in one horizontal direction \item From such recorded motions one can develop a vertically propagating shear wave in 1D \item Apply such vertically propagating shear wave to the same soil-structure system \end{itemize} \vspace{-3mm} \begin{figure}[!H] \begin{center} \includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2015/CompDyn/Present/6D_to_1D_01.jpg} \end{center} \end{figure} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{6D Free Field Motions} \vspace{-2mm} \begin{center} %\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop] \hspace{-7mm} \movie[label=show3,width=8.8cm,autostart,showcontrols] {\includegraphics[width=70mm]{BJicon.png}}{movie_input.mp4} \end{center} \begin{flushleft} \vspace{-15mm} \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_01AApr2015/movie_input.mp4} % \href{./homo_50m-mesh_45degree_Ormsby.mp4} {\tiny (MP4)} % \end{flushleft} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{6D Free Field Motions (closeup)} \vspace{-2mm} \begin{center} \hspace{-7mm} \movie[label=show3,width=8.8cm,poster,autostart,showcontrols] {\includegraphics[width=70mm]{BJicon.png}}{movie_input_closeup.mp4} \end{center} \begin{flushleft} \vspace{-15mm} \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_01AApr2015/movie_input_closeup.mp4} % \href{./homo_50m-mesh_45degree_Ormsby.mp4} {\tiny (MP4)} \end{flushleft} % \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{6D Free Field at Location} \vspace{-2mm} \begin{center} \hspace{-7mm} \movie[label=show3,width=8.8cm,poster,autostart,showcontrols] {\includegraphics[width=69mm]{BJicon.png}}{movie_ff_3d.mp4} \end{center} \begin{flushleft} \vspace{-15mm} \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4} % \href{./homo_50m-mesh_45degree_Ormsby.mp4} {\tiny (MP4)} \end{flushleft} % \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{6D Earthquake Soil Structure Interaction} \vspace{-2mm} \begin{center} \hspace{-7mm} \movie[label=show3,width=8.8cm,poster,autostart,showcontrols] {\includegraphics[width=70mm]{BJicon.png}} {movie_npp_3d.mp4} \end{center} \begin{flushleft} \vspace{-15mm} \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_npp_3d.mp4} {\tiny (MP4)} \end{flushleft} % \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{1D Free Field at Location} \vspace{-2mm} \begin{center} \hspace{-7mm} \movie[label=show3,width=8.8cm,poster,autostart,showcontrols] {\includegraphics[width=70mm]{BJicon.png}} {movie_ff_1d.mp4} \end{center} \begin{flushleft} \vspace{-15mm} \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4} {\tiny (MP4)} \end{flushleft} % \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{1D ESSI of NPP} \vspace{-2mm} \begin{center} \hspace{-7mm} \movie[label=show3,width=8.8cm,poster,autostart,showcontrols] {\includegraphics[width=70mm]{BJicon.png}} {movie_npp_1d.mp4} \end{center} \begin{flushleft} \vspace{-15mm} \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_npp_1d.mp4} {\tiny (MP4)} \end{flushleft} % \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{6D vs 1D NPP ESSI Response Comparison} \vspace{-2mm} \begin{center} \hspace{-7mm} \movie[label=show3,width=8.8cm,poster,autostart,showcontrols] {\includegraphics[width=69mm]{BJicon.png}} {movie_2_npps.mp4} \end{center} \begin{flushleft} \vspace{-15mm} \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4} {\tiny (MP4)} \end{flushleft} % \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{6D vs 1D: Containment Displacement Response} % % % \begin{figure}[!hp] % \begin{center} % \hspace{-13mm} % \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/01_displacements_Containment_building_bottom.pdf} % \hspace{-6mm} % \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/02_displacements_Containment_building_top.pdf} % \hspace{-10mm} % \end{center} % \end{figure} % % % % \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{6D vs 1D: Containment Acceleration Response} \begin{figure}[!hp] \begin{center} \hspace{-13mm} \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/01_accelerations_Containment_building_bottom.pdf} \hspace{-6mm} \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/02_accelerations_Containment_building_top.pdf} \hspace{-10mm} \end{center} \end{figure} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\subsection{Parametric Uncertainty: Probabilistic Inelasticity} \subsection{Parametric Uncertainty: Wave Propagation} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Uncertain Material Parameters and Loads} \begin{itemize} \item Decide on modeling complexity \vspace{3mm} \item Determine model/material parameters \vspace{3mm} \item Model/material parameters are uncertain! \begin{itemize} \item Measurements \item Transformation \item Spatial variability \end {itemize} \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Uncertainty Propagation through Inelastic System} % \begin{itemize} \item Incremental el--pl constitutive equation % \begin{eqnarray} \nonumber \Delta \sigma_{ij} = % E^{EP}_{ijkl} E^{EP}_{ijkl} \Delta \epsilon_{kl} = \left[ E^{el}_{ijkl} - \frac{\displaystyle E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}} {\displaystyle n_{rs} E^{el}_{rstu} m_{tu} - \xi_ h_} \right] \Delta \epsilon_{kl} \end{eqnarray} \vspace{5mm} \item Dynamic Finite Elements % \begin{equation} {\bf M} \ddot{\bf u} + {\bf C} \dot{\bf u} + {\bf K}^{ep} {\bf u} = {\bf F} \nonumber \end{equation} \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Critique of our Previous Work, PEP and SEPFEM} % % \begin{itemize} % % \item Constitutive weighted coefficients $N_1$ and $N_2$ do not work well for % stress solution! % % \vspace{1mm} % \item We suggested that $\sigma(t)$ be considered a $\delta$-correlated, and % based on that simplified stiffness equations. Both the assumption and the % resulting equation were not right. % % % \vspace{1mm} % \item On a SEPFEM level, stiffness needs update basis functions and KL % coefficients in each step. We updated the eigenvalues % $\lambda_i$ and kept the same structure (Karhunen-Loeve) in the approximation % of the stiffness, which is not physical % % \vspace{1mm} % \item Implicitly assumed that the stiffness remains Gaussian, which is % not the case % % % \end{itemize} % % % % % % % % \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Gradient Flow Theory of Probabilistic Elasto-Plasticity} % % % Decomposition of an elastoplastic random process: % % into % %the following general form: % % % \begin{eqnarray} % \begin{array}{c c c c c} % \bigg( \displaystyle{\pder[]{t}} - \mathcal{L}_{rev} \bigg) P(\boldsymbol{\sigma},t) &=& 0& \qquad &\text{if } % \boldsymbol{\sigma} \in \Omega^{el} % \\ % ~ % \\ % \bigg( \displaystyle{\pder[]{t}} - \mathcal{L}_{irr} \bigg) P(\boldsymbol{\sigma},t) &=& 0& \qquad &\text{if } % \boldsymbol{\sigma} \in \Omega^{el} \cup \Omega^{pl} % \end{array} % \nonumber % \end{eqnarray} % % % % \begin{itemize} % % \item Reversible ($\mathcal{L}_{rev} $) and Irreversible ($\mathcal{L}_{irr} $) operators % % % % \vspace{2mm} % \item Yield PDF is an attractor, similar to plastic corrector % % \vspace{2mm} % \item Ergodicity of the elastic-plastic process can be proven! % % \end{itemize} % % % % % % \end{frame} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % \begin{frame} % \frametitle{Gradient Flow Theory of Probabilistic Elasto-Plasticity} % % \begin{itemize} % % \item % Elastic, reversible process, Fokker-Planck (forward Kolmogorov) equation % % % \begin{equation} % \pder[P (\boldsymbol{\sigma},t)]{t} % = -\nabla \cdot (\langle \boldsymbol{E} \dot{\boldsymbol{\epsilon}} \rangle P(\boldsymbol{\sigma},t)) % + t ~\text{Var}[\boldsymbol{E}\dot{\boldsymbol{\epsilon}}] \Delta P(\boldsymbol{\sigma},t) % \nonumber % \end{equation} % % % \begin{equation} % \mathcal{L}_{rev} = \nabla \cdot (t \,\text{Var}[\boldsymbol{C}\dot{\boldsymbol{\epsilon}}] \nabla - % \langle \boldsymbol{C} \dot{\boldsymbol{\epsilon}} \rangle) % \nonumber % \end{equation} % % \item % Plastic, irreversible process, Fokker-Planck (forward Kolmogorov) equation % % % \begin{equation} % \pder[P(\boldsymbol{\sigma},t)]{t} = \nabla \cdot (\nabla \Psi(\boldsymbol{\sigma}) % P(\boldsymbol{\sigma},t)) + D \Delta P(\boldsymbol{\sigma},t) % \nonumber % \end{equation} % % % \begin{equation} % \mathcal{L}_{irr} = D \nabla \cdot \bigg(\nabla - \frac{\nabla P_y(\boldsymbol{\sigma})}{P_y(\boldsymbol{\sigma})}\bigg) % \nonumber % \end{equation} % % % % \end{itemize} % % \end{frame} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Gradient Flow Theory of Probabilistic Elasto-Plasticity} % % \begin{itemize} % % \item Limiting (final) distribution % is considered to be known % %(given as a material parameter) and % % \vspace{2mm} % \item Underlying potential leading to this distribution is sought % % \vspace{2mm} % \item Transition from uncertain elastic to uncertain plastic response % % % \vspace{2mm} % \item Only in a 1D elastoplastic problem does one end up with a stationary % distribution % % \vspace{2mm} % \item In higher dimensional problems this yield stress distribution is % only "marginally" stationary along one or a combination of the stress % components. % % \end{itemize} % % % \end{frame} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Probabilistic Elasto-Plasticity: von Mises Surface} % An example of a Mises probabilistic yield surface is given in Fig.~\ref{ProbCylinder}. \begin{figure}[H] \centering \vspace{-5mm} %\hspace{-30mm} \includegraphics % [scale = 0.8, trim = 0.6in 0.4in 0.6in 0.4in, clip=true] [width=12cm] {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Probabilistic_von_Mises_Surface.jpg} % \caption{An example of a probabilistic von Mises yield surface.} \label{ProbCylinder} \end{figure} \end{frame} % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Gradient Theory of Probabilistic Elasto-Plasticity: Numerical Solution} % % % \begin{itemize} % % \item Using radial basis functions (a meshless method) for solving % Fokker-Planck equations for uncertain elastic-plastic response % % % \vspace{6mm} % \item Details in a talk by Mr. Karapiperis later this afternoon (room 2, MS-6, % 17:00-19:00, last talk) % % % \end{itemize} % % % % % % \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Gradient Theory of Probabilistic Elasto-Plasticity: Verification, Elastic-Perfectly Plastic} %\vspace{-3mm} \begin{figure}[H] \centering \includegraphics % [scale = 0.55, trim = 0.0in 0.0in 0.0in 0.0in, clip=true] [width=8cm] {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/M+-SD_1D_Perf_Cyclic.pdf} % \caption{Combining the above plots to get the evolution of mean $\pm$ std. % deviation of stress.} \label{MSD_12} \end{figure} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\subsection{SEPFEM} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % \begin{frame}{Stochastic Elastic-Plastic FEM (SEPFEM)} % % \begin{itemize} % \item<1> KL-PC expansion of material random fields (stiffness, etc) % % % % \begin{equation} % $ % \mathbb{D}(\bold{x}, \theta) = \sum_{i=0}^{M} r_{i}(\bold{x}) \Phi_i[\{\xi_r(\theta)\}] % \label{nonGaussian1} % $ % %\end{equation} % % \item<1> PC expansion of displacement field % % % \begin{eqnarray} % u(\bold{x},\theta) = \sum_{i=0}^p d_i(\bold{x}) \psi_i[\{\xi_r(\theta)\}] % \label{PC1} % \end{eqnarray} % % \item<1> Stochastic Galerkin % % \begin{eqnarray} % \sum_{n = 1} ^ N K'_{mn} d_{ni} + \sum_{n=1}^N \sum_{j=0}^P d_{nj} \sum_{k=1}^M b_{ijk} K''_{mnk} = % \Phi_{m}\langle\psi_i[\{\xi_r\}]\rangle % \label{Lognormal6} % \end{eqnarray} % % \end{itemize} % % % \end{frame} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % \begin{frame}{SEPFEM Statistical linearization} % % Update the FE stiffness in the elastoplastic regime: % % \begin{itemize} % \item Solve elastoplastic FPE for each integration point % % % \begin{eqnarray} % \pder[P^{nl}(\sigma,t)]{t} % &=& \pder[]{\sigma} \bigg(\bigg\langle D^k (1 - P[\Sigma_y \leq \sigma]) \frac{\Delta % \epsilon}{\Delta t} \bigg\rangle P\bigg) \nonumber \\ % & & + \pder[^2]{\sigma^2} \bigg( t Var\bigg[ D^k (1 - P[\Sigma_y \leq \sigma]) \frac{\Delta % \epsilon}{\Delta t} \bigg] P\bigg) % \label{SEPFEMLinearization1} % \end{eqnarray} % % \item Consider an equivalent linear FPE % % % \begin{eqnarray} % \pder[P^{lin}(\sigma,t)]{t} % &=& N_{(1)}^{eq} \pder[P]{\sigma} + N_{(2)}^{eq} \pder[^2 P]{\sigma^2} % \label{SEPFEMLinearization2} % \end{eqnarray} % % \item Linearization of the PC coeff. as an optimization problem % % % \begin{equation} % \pder[P^{lin}(\sigma,t)]{t} % = \pder[P^{nl}(\sigma,t)]{t} % \end{equation} % % % \end{itemize} % % \end{frame} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % \begin{frame}{Dynamic, Time Domain, SEPFEM} % % \begin{itemize} % \item Gaussian formulation inadequate due to occurrence of "probabilistic softening" modes % $\Rightarrow$ Need for positive definite kernel % % \vspace{2mm} % \item Stochastic forcing (e.g. uncertain earthquake) % % \vspace{2mm} % \item Stability of time marching algorithm (Newmark, Rosenbrock, Cubic Hermitian ) analyzed using % amplification matrix % % \vspace{2mm} % \item Long-integration error and higher order statistics phase shift % \end{itemize} % % % \begin{figure}[H] % % \centering % % \includegraphics[scale = 0.4, trim = 0.1in 0.0in 0.0in 0.0in, clip=true]{/home/jeremic/tex/Classes/2015/spring/ECI280A/SEPFEM/odKonstantinosa/figures/Sendai_1Sine_PCk2PCd8.pdf} % % \label{Sendai_1Sine_PCk2PCd8.pdf} % % \end{figure} % % % % % \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Wave Propagation Through Uncertain Soil} \vspace{-2mm} \begin{figure}[H] \centering \includegraphics % [scale = 0.56, trim = 0.0in 0.15in 0.2in 0.16in, clip=true] [width=7cm] {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_profile.png} % % \includegraphics %[scale = 0.56, trim = 0.0in 0.0in 0.0in 0.0in, clip=true] [width=1.5cm] {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/meshes.png} % \caption{Simplified profile and properties for the 1-dimensional profile considered.} \label{Sendai_profile} \end{figure} \vspace{-5mm} \begin{figure}[htbp] \centering %\hspace{-0.2in} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \includegraphics % [scale = 0.37, trim = 0.0in 0.0in 0.0in 0.0in,clip=true] [width=3.5cm] {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/ShearModulusStats.pdf} \hfill \includegraphics % [scale = 0.37, trim = 0.0in 0.0in 0.0in 0.0in, clip=true] [width=3.5cm] {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/ShearStrengthStats.pdf} %\caption{Shear modulus and shear strength statistics in the middle of the soil column.} \hfill \includegraphics % [scale = 0.62, trim = 0in 0.15in 0in 0.22in, clip=true] [width=3.5cm] {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV45_BaseInput.pdf} % \caption{Single sine pulse excitation of the soil column at its base.} % \label{Sendai_1Sine_PCk2PC2_elastic_COV45_BaseInput} \end{figure} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Uncertain Elastic Response at the Surface {\tiny(COV = 120\%)} } \vspace{-2mm} \begin{figure}[H] \centering \includegraphics % [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true] [width=9.3cm] {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120.pdf} % \caption{Mean $\pm$ std. deviation of the elastic response at the top of the % soil column for the conservative COV case (COV = 120\%).} % \label{Sendai_1Sine_PCk2PC2_elastic_COV120} \end{figure} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Displacement PDFs at the Surface {\tiny(COV = 120\%)} } %\vspace{-20mm} %\hspace{-30mm} \begin{figure}[H] \centering \includegraphics %[scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true] [width=10cm] {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_FullPdf.jpg} % \caption{Mean $\pm$ std. deviation of the elastic response at the top of the % soil column for the conservative COV case (COV = 120\%).} % \label{Sendai_1Sine_PCk2PC2_elastic_COV120} \end{figure} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Displacement CDFs (Fragilities) at the Surface {\tiny(COV = 120\%)} } \vspace{-3mm} \begin{figure}[H] \centering \includegraphics % [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true] [width=11cm] {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_FullCdf.jpg} % \caption{Mean $\pm$ std. deviation of the elastic response at the top of the % soil column for the conservative COV case (COV = 120\%).} % \label{Sendai_1Sine_PCk2PC2_elastic_COV120} \end{figure} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Probability of Exceedance, $disp=0.1m$ {\tiny(COV = 120\%)} } \begin{figure}[H] \centering \includegraphics % [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true] [width=9cm] {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_ProbExc.pdf} % \caption{Mean $\pm$ std. deviation of the elastic response at the top of the % soil column for the conservative COV case (COV = 120\%).} % \label{Sendai_1Sine_PCk2PC2_elastic_COV120} \end{figure} \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Real ESSI Simulator System} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Real ESSI Simulator} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Real ESSI Simulator System} \begin{itemize} \item {\bf The Real ESSI-Program} is a 3D, nonlinear, time domain, parallel finite element program specifically developed for Hi-Fi modeling and simulation of Earthquake Soil/Rock Structure Interaction problems for NPPs (infrastructure objects) on ESSI-Computers. \ %The NRC ESSI Program is based on %a number of public domain numerical libraries developed at UCD as well as those %available on the web, that are compiled and linked together to form the %executable program (NRC-ESSI-Program). Significant effort is devoted to development %of verification and validation procedures, as well as on development of %extensive documentation. NRC-ESSI-Program is in public domain and is licensed %through the Lesser GPL. %\vspace{0.3cm} \vspace{1mm} \item {\bf The Real ESSI-Computer} is a distributed memory parallel computer, a cluster of clusters with multiple performance processors and multiple performance networks. %Compute nodes are Shared Memory Parallel %(SMP) computers, that are connected, using high speed network(s), into a %Distributed Memory Parallel (DMP) computer. %\vspace{0.3cm} \vspace{1mm} \item {\bf The Real ESSI-Notes} represent a hypertext documentation system (Theory and Formulation, Software and Hardware, Verification and Validation, and Case Studies and Practical Examples) detailing modeling and simulation of ESSI problems. % %the %NRC-ESSI-Program code API (application Programming Interface) and DSLs (Domain %Specific Language). %%NRC-ESSI-Notes, developed by Boris Jeremic and collaborators, are in public %domain %%and are licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported %%License. % %\vspace{0.3cm} \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Real ESSI Simulator System} \begin{itemize} \item Developed with funding from US-NRC, US-NSF, CNSC-CCSN, and US-DOE \vspace{2mm} \item The Real ESSI simulator system is designed based on premise of high fidelity modeling and simulation \vspace{2mm} \item Reduction of modeling uncertainty and propagation of parametric uncertainty \vspace{2mm} \item Real ESSI simulator, also known as {\small{\cyrssDvanaest Vrlo Prosto}, \raisebox{-1.2mm}{\includegraphics[height=4mm] {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}}, \raisebox{-1.2mm}{\includegraphics[height=4mm] {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Bengali.pdf}}, { Muy F{\'a}cil}, {Molto Facile}, \raisebox{-1.2mm}{\includegraphics[height=4.2mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Japanese.jpg}}, {\greektext{Pragmatik'a E'ukolo}}, \raisebox{-1.6mm}{\includegraphics[height=5mm] {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Hindi.jpg}}, \raisebox{-1.2mm}{\includegraphics[height=5mm] {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Farsi.jpg}}, {Tr{\`e}s Facile}, {\cyrssJedanaest Vistinski Lesno}, {Wirklich Einfach}. %\raisebox{-1.2mm}{\includegraphics[height=4.5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}}, %{ Muy F{\'a}cil}, %{Molto Facile}, %\raisebox{-1.2mm}{\includegraphics[height=4mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Japanese.jpg}}, %{\greektext{Pragmatik'a E'ukolo}}, %\raisebox{-1.2mm}{\includegraphics[height=4.5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Hindi.jpg}}, %\raisebox{-1.2mm}{\includegraphics[height=4mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Farsi.jpg}}, %{Tr{\`e}s Facile}, %{\cyrssDvanaest Vistinski Lesno}, %{Wirklich Einfach}, %\raisebox{-0.80mm}{\includegraphics[height=5.2mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Arabic.jpg}}. } \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Real ESSI Modelling} \vspace{4mm} \begin{figure}[!hbpt] \begin{center} \includegraphics[width=3.2cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf} %\caption{\label{loading_stages-increments_iterations} } \end{center} %\vspace{-0.5cm} \end{figure} % \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Real ESSI Modelling and Simulation Process} % % \begin{itemize} % % %\vspace{4mm} % \item Mesh development: gmsh (UL), gmESSI, FeConv (Vlaski) % % \vspace{2mm} % \item Model Development: sublime text editor % % \vspace{2mm} % \item Model Simulation: % \begin{itemize} % \item Domain Specific Language (DSL) for input % \item Real ESSI % \item output in HDF5 (NCSA...) % \end{itemize} % % \vspace{2mm} % \item Result Visualization: VisIt (LLNL), visitESSI plug-in (all % displacements, stress, strain) % % \end{itemize} % % % \end{frame} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Source Code Development and Management} % % \begin{itemize} % % %\vspace{4mm} % \item Real ESSI sources (finite element, material models, algorithms, DSL % interpreter, \&c.) in a private online repository with version control % % % \vspace{4mm} % \item Real ESSI dependencies (external libraries: solvers, MPI, BLAS, LAPACK, % \&c.) % % % % %\vspace{1mm} % % \item Sequential performance optimization (templates, global linking % % optimization, pipeline parallel, \&c.) % % % % %\vspace{1mm} % % \item Parallel performance optimization (Plastic Domain Decomposition) % % for local clusters as well as large national parallel computers. % % % \end{itemize} % % % \end{frame} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Real ESSI Developers} % % \begin{itemize} % \item UC Davis: % Core system architecture (sequential and % parallel), finite elements, material models, % constitutive integration, deterministic and stochastic elastic plastic % finite elements % % \vspace{2mm} % % \item LBNL: Nonlinear/inelastic beam, Nonlinear/inelastic shell (plate % and wall, deterministic) % % \vspace{2mm} % \item TU Delft: Material Models (deterministic) % \end{itemize} % % % % \end{frame} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Real ESSI Users} % % % \begin{itemize} % \item DOE Project Team: % \begin{itemize} % \item UC Davis: verification, system modeling, \&c. % % \item LBNL: verification, validation, validation system design, system modeling) % % \item UN Reno: validation system design, validation % \end{itemize} % % \vspace{2mm} % \item National Labs % % \vspace{2mm} % \item Companies: AREVA, Shimizu Corp., Rizzo and Assoc. % % \vspace{2mm} % \item Universities: TU Delft, NTUA, UCB % % \end{itemize} % % % % \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\subsection{Real ESSI Simulator: Program} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Real ESSI: Finite Elements} %\vspace{-3mm} \begin{itemize} %\vspace{1mm} \item Dry/single phase solids (8, 20, 27, 8-27 node bricks), elastic and/or inelastic %\vspace{1mm} \item Saturated/two phase solids (8 and 27 node bricks, liquefaction modeling), elastic and/or inelastic %\vspace{1mm} \item Truss, elastic %\vspace{1mm} \item Beams (six and variable DOFs per node), elastic, inelastic %\vspace{1mm} \item Shell (ANDES) with 6DOF per node, linear elastic, inelastic shell soon %\vspace{1mm} \item Contacts (dry and/or saturated soil/rock - concrete, gap opening-closing, frictional slip), inelastic %\vspace{1mm} \item Base isolators (elastomeric, frictional pendulum), inelastic \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Real ESSI: Material Models} %\vspace{-2mm} \begin{itemize} \item Linear and nonlinear, isotropic and anisotropic elastic \vspace{3mm} \item Elastic-Plastic (von Mises, Drucker Prager, Rounded Mohr-Coulomb, Leon Parabolic, Cam-Clay, SaniSand, SaniClay, Pisan{\` o}...). All elastic-plastic models can be used as perfectly plastic, isotropic hardening/softening and kinematic hardening models. \vspace{3mm} \item Viscous damping solids, Rayleigh and Caughey damping \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Real ESSI: Solution Advancement Algorithms} \begin{itemize} %\vspace{-10mm} \item Constitutive \begin{itemize} %\vspace{-1mm} \item Explicit, Implicit, Sub-incrementation, Line Search \end{itemize} \item Nonlinear Static FEM \begin{itemize} %\vspace{-1mm} \item No equilibrium iteration \item Equilibrium Iterations (full Newton, modified N, Initial Stiff.) \item Hyperspherical constraint (arch length, displacement control, load control) \item Line Search \item Convergence criteria: displacement, load, energy \end{itemize} \item Nonlinear Dynamic FEM \begin{itemize} %\vspace{-1mm} \item No equilibrium iteration \item Equilibrium Iterations (full Newton, modified N, Initial Stiff.) \item Constant or variable time stepping \item Convergence criteria: displacement, load, energy \end{itemize} \end{itemize} %\vspace{-60mm} %%\begin{figure}[!hbpt] %\begin{flushright} %\hspace{50mm} %\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf} %%\caption{\label{loading_stages-increments_iterations} } %\end{flushright} %%\vspace{-0.5cm} %%\end{figure} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Real ESSI: Seismic Input} \begin{itemize} %\vspace{-1.5mm} \vspace{4mm} \item Analytic input of seismic motions (both body (P, S) and surface (Rayleigh, Love, etc., waves), including analytic radiation damping using Domain Reduction Method (Bielak et al.) \end{itemize} % %\begin{figure}[!hbpt] \begin{center} \includegraphics[width=8cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/tex_works_psfigures_DRM_NPP_idea01.pdf} %\caption{\label{DRMidea01} Large physical domain with the source of load $P_e(t)$ %and the local feature (in this case a soil-structure system.} \end{center} %\end{figure} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Real ESSI Simulator Program: Parallel, HPC} \begin{itemize} \item High Performance Parallel Computing: both parallel and sequential version available, however, for high fidelity modeling, parallel is really the only option. Parallel Real ESSI Simulator runs on clusters of PCs and on large supercomputers (Distributed Memory Parallel machines, all top national supercomputers). Plastic Domain Decomposition Method (PDD, dynamic computational load balancing) for elastic-plastic computations with multiple types of finite elements and on variable speed CPUs (and networks) % Parallel algorithm uses our % original Plastic Domain Decomposition method (featuring dynamic computational % load balancing) that is efficient for elastic-plastic finite element problems % where elastic-plastic (slow) and elastic (fast) domains change dynamically % during run time. \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Real ESSI Simulator Program: Probabilistic/Stochastic} %\vspace{-2mm} \begin{itemize} %\vspace{-2.5mm} \item Constitutive: Euler-Lagrange form of Fokker-Planck (forward Kolmogorov) equation for probabilistic elasto-plasticity (PEP) %\vspace{-1.5mm} \item Spatial: stochastic elastic plastic finite element method (SEPFEM) \end{itemize} Uncertainties in material and load are analytically taken into account. Resulting displacements, stress and strain are obtained as very accurate (second order accurate for stress) Probability Density Functions. PEP and SEPFEM are not based on a Monte Carlo method, rather they expand uncertain input variables and uncertain degrees of freedom (unknowns) into spectral probabilistic spaces and solve for PDFs of resulting displacement, stress and strain in a single run. \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % \begin{frame} % \frametitle{Real ESSI Simulator Program: Design and Users} % % \begin{itemize} % % %\vspace{0.2cm} % \item Based on a Collection of Useful Libraries (portable) % % \vspace{0.1cm} % \item Library centric software design % % \vspace{0.1cm} % \item Sequential (learning) and Parallel (production modeling and simulation) % % \vspace{0.1cm} % \item Distributed Memory Parallel (DMP) paradigm, scales well to large supercomputers % % % % \vspace{0.1cm} % \item Various public domain licenses (GPL, LGPL, BSD, CC) % % %\vspace{0.3cm} % \vspace{0.1cm} % \item Verification (extensive) and Validation (not much) % % % \vspace{0.1cm} % \item Target users: US-DOE, US-NRC, CNSC, IAEA, Collaborators (AREVA, Shimizu, % Rizzo...), others % % \vspace{0.1cm} % \item Limited use Expert Modeling and Simulation System, and not a public domain % program % % % \end{itemize} % % \end{frame} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame}[fragile] % \frametitle{ESSI Simulator Computer(s)} % % A distributed memory parallel (DMP) computer % designed for high performance, % parallel finite element simulations % % \begin{itemize} % %\vspace{0.1cm} % \item Multiple performance CPUs \\ % and Networks % %\vspace{0.1cm} % \item Most cost-performance \\ % effective % %\vspace{0.1cm} % \item Source compatibility with \\ % any DMP supercomputer % %\vspace{0.1cm} % \item Current systems: % \begin{itemize} % \item 208CPUs, % \item 40CPUs (8+32) % \item 160CPUs (8x5+2x16+24+64) % \item 32CPUs (multiple machines like this) % \end{itemize} % % \end{itemize} % % % \vspace{-4.5cm} % \hspace{0.5cm} % \begin{flushright} % \includegraphics[width=4.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2607.JPG} % %\includegraphics[width=6.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2609.JPG} % %\includegraphics[width=8.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2611.JPG} % \end{flushright} % % % % \end{frame} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \subsection{Near Future Plan} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Real ESSI: Verification and Validation} % \begin{itemize} % %\vspace{-2mm} % \item Verification: % each element, model, algorithm and procedure has been extensively verified % (math issue) % \vspace{4mm} % \item Validation: limited % \begin{itemize} % \item Lotung (!), % % \item PRENOLIN (!?)) % \item UNR tests (!!) % \end{itemize} % \end{itemize} % \end{frame} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Verification and Validation} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{High Fidelity Predictive Capabilities} % \frametitle{High Fidelity Modeling of SFS System: % Verification, Validation and Prediction} \begin{itemize} % \vspace{0.2cm} % \item {\bf Prediction}: use of computational model to foretell the state % of a physical system under consideration under conditions for which the % computational model has not been validated. \vspace{3mm} \item {{Verification} provides evidence that the model is solved correctly.} Mathematics issue. \vspace{3mm} \item {{Validation} provides evidence that the correct model is solved.} Physics issue. \vspace{3mm} \item Goal: predictive capabilities with low information (Kolmogorov) Complexity % %% % \vspace{0.2cm} % % \item {\bf The Finite Element % % Interpreter \FEI{}} might be one such % % predictive tool (application program) \end{itemize} \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{frame} % \frametitle{Fundamentals of Verifications and Validation} % % \frametitle{High Fidelity Modeling of SFS System: % % Verification, Validation and Prediction} % % % \begin{figure}[!h] % \vspace{-0.5cm} % \hspace{-0.5cm} % %\begin{center} % %{\includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2005/OpenSeesWorkshopAugust/DeveloperSymposium/VerifValidFund01.pdf}} % {\includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/VerifValidFund01.pdf}} % %\end{center} % \end{figure} % % % % % % % \end{frame} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Verification} \begin{itemize} \vspace{1mm} \item Code Verification (code coverage, memory leaks and pointer assignment testing, static argument list testing, \&c.) \vspace{1mm} \item Solution verification (finite elements, constitutive integration, material models, algorithms, seismic input, \&c.) based on analytic, closed form solutions \vspace{1mm} \item Method of manufactured solutions for elasto-plastic verification \vspace{1mm} \item Parameter bounds (finite elements, material models, algorithms, \&c.) \vspace{1mm} \item Develop error plots for elements, models, algorithms over a range of parameter \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\subsection{Validation} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Validation} \begin{itemize} \item {Traditional Experiments} \begin{itemize} \item Improve the fundamental understanding of physics involved \item Improve the mathematical models for physical phenomena \item Assess component performance \end{itemize} \vspace{2mm} \item {Validation Experiments} \begin{itemize} \item Model validation experiments \item Designed and executed to quantitatively estimate mathematical model's ability to simulate well defined physical behavior \item The simulation tool (Real ESSI Simulator) (conceptual model, computational model, computational solution) is the customer \item New US-DOE project to validate inelastic seismic wave propagation and soil-structure interaction \end{itemize} \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Summary} \subsection{Summary} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Concluding Remarks} \begin{itemize} %\vspace{2mm} \item Modeling and simulation of infrastructure object requires high sophistication \vspace{3mm} \item Uncertainties (modeling and parametric) influences results \vspace{3mm} \item Those uncertainties need to be addressed and propagated to results and used in decision making \vspace{3mm} \item Goal is to {predict} and {inform}, and not force fit \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Acknowledgement} \begin{itemize} \vspace{2mm} \item Funding from and collaboration with the US-NRC, US-DOE, US-NSF, CNSC, AREVA NP GmbH, and Shimizu Corp. is greatly appreciated, \vspace{2mm} \item Collaborators: % Dr. Budnitz (LBNL), Prof. Yang, Dr Cheng, Dr. Jie, Dr. Tafazzoli, Prof. Pisan{\`o}, Mr. Watanabe, Mr. Vlaski, Mr. Orbovi{\'c}, and UCD students: Mr. Abell, Mr. Karapiperis, Mr. Feng, Mr. Sinha, Mr. Luo, Mr. Lacour, Mr. Yang, Ms. Behbehani % % \vspace*{2mm} \item Real ESSI Simulator: \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/} \end{itemize} \end{frame} \end{document} % %
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http://www.sagemath.org/talks/2005-03-23-pyconn-sage/auto/pycon-sage.tex	sagemath.org	CC-MAIN-2015-18	text/x-tex	null	crawl-data/CC-MAIN-2015-18/segments/1430460544953.41/warc/CC-MAIN-20150501060904-00091-ip-10-235-10-82.ec2.internal.warc.gz	583,709,332	5,474	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % pycon-sage.tex -- pycon talk about SAGE. % % (c) 2005, % William Stein %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \documentclass[landscape]{slides}\usepackage[active]{srcltx} \newcommand{\page}[1]{\begin{slide}#1\vfill\end{slide}} %\renewcommand{\page}[1]{} \newcommand{\apage}[1]{\begin{slide}#1\vfill\end{slide}} \newcommand{\eps}[4]{\rput[lb](#1,#2){% \includegraphics[width=#3\textwidth]{#4}}} \usepackage{fullpage} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsthm} \usepackage{graphicx} \theoremstyle{plain} \newtheorem{theorem}{Theorem} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{claim}[theorem]{Claim} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{conjecture}[theorem]{Conjecture} \usepackage{pstricks} \newrgbcolor{dbluecolor}{0 0 0.6} \newrgbcolor{dredcolor}{0.5 0 0} \newrgbcolor{dgreencolor}{0 0.4 0} \newcommand{\dred}{\dredcolor\bf} \newcommand{\dblue}{\dbluecolor\bf} \newcommand{\dgreen}{\dgreencolor\bf} \title{\bf\dred SAGE: System for Arithmetic Geometry Experimentation\\ {\tt http://modular.fas.harvard.edu/SAGE/}} \author{\large William Stein\\ Asst. Professor of Mathematics, Harvard University} \date{March 24, 2005, PYCON, Washington, D.C.\\ } \bibliographystyle{amsalpha} \newcommand{\section}[1]{\begin{center}{\dblue \bf\Large #1}\end{center}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\defn}[1]{{\em #1}} \renewcommand{\H}{\HH} \newcommand{\hra}{\hookrightarrow} \newcommand{\isom}{\cong} \newcommand{\ds}{\displaystyle} \begin{document} \small \page{ \maketitle } \page{ \section{Arithmetic Geometry} Arithmetic geometry is about geometric questions that have an arithmetic flavor. Sample famous problems: \begin{itemize} \item {\dblue Fermat's Last Theorem:} $x^n+y^n=z^n$ has no solutions with $n\geq 3$ and $x,y,z$ all nonzero integers. Andrew Wiles proved this in 1995 using elliptic curves and modular forms. \item {\dblue The Birch and Swinnerton-Dyer Conjecture:} Discovered from computations in the 1960s. Simple criterion for whether or not for given $a,b$ the elliptic curve $y^2=x^3+ax+b$ has infinitely many rational solutions. (Clay $\$10^6$ dollar problem.) \item {\dblue The Riemann Hypothesis:} Nontrivial zeros of Riemann Zeta function are on line ${\rm Re}(s)=1/2$. Solution gives deep understanding of distribution of the prime numbers $2,3,5,7,11,13,\ldots.$ (Clay million dollar problem.) \item {\dblue Cryptography:} Factor integers quickly. E.g., Hendrik Lenstra, used elliptic curves to give a new algorithms for this. The number field sieve is a sophisticated algorithm for factoring and uses computation in number fields. Also, cryptosystems come from elliptic curves over finite fields. \end{itemize} } %\page{ %\section{Arithmetic Geometers} %{\large %\vfill %Arithmetic geometers are people who spend their lives trying very hard %to solve extremely difficult number theory problems, some of which %have been unsolved for thousands of years. They greatly appreciate good %computational tools. %\vfill %{\tiny Tate, Mazur, Elkies, Coates, Wiles, Fontaine, Stark, %Ribet, Langlands, Skinner, Conrad, Cremona, Poonen, ...} %} %} \page{ \section{The Problem} Create a system for doing computations with the mathematical objects mentioned above. Main Goals: \vfill \begin{itemize} \item {\dblue Efficient:} Be very fast -- comparable to or faster than anything else available. This is very difficult, since most systems are closed source, algorithms are often not published, and finding fast algorithms is often extremely difficult (years of work, Ph.D. theses, luck, etc.) \item {\dblue Open Source:} The source code must be available and readable, so users can understand what the system is really doing and trust the results more. \item {\dblue Comprehensive:} Implements enough different things to be really useful. \item {\dblue Well documented:} Reference manual, API reference with examples for every function, and at least one published book. Make documentation and source a peer reviewed package, so get academic credit like a journal publication. \item {\dblue Extensible:} Be able to define new data types or derive from builtin types, or make code written in your favorite language part of the system. \item {\dblue Free:} Must be sufficiently free (at least GPL). \end{itemize} } \page{ \section{Existing Mature Systems} \begin{itemize} \item {\dblue Mathematica, Maple, and MATLAB:} Arithmetic geometers are not their target audience. Mathematica does well at special functions, and both do calculus very well, which is almost never useful in arithmetic geometry. These systems are {\em closed source, very expensive, for profit}. % \item {\dblue MAGMA:} {\em By far} the best software for arithmetic geometry. It's very efficient, comprehensive, and well documented. Great design and class hierarchy. BUT: It's closed source (but non-profit), expensive, and not easily extensible (no user defined types or C/C++-extension code). I've contributed substantially to MAGMA. \item {\dblue PARI:} Efficient, open source, extendible and free. But the documentation is not good enough and the memory management is not robust enough. Also, PARI does not do nearly as much as what is needed. \item {\dblue Maxima, Octave, etc.:} Open source, but not for arithmetic geometry. \end{itemize} (There's always something else that I don't know about.) {\em All these system use their own custom programming language.} } % end page \page{ \section{SAGE: System for Arithmetic Geometry Experimentation} I am creating a system using Python that will hopefully solve the problem. I've been working on this for one year (and I've been writing arithmetic geometry software since 1998, in C++ and for MAGMA). Please download and try it, though it is still {\em far from ready} for prime time: \begin{center} {\tt http://modular.fas.harvard.edu/SAGE/}. \end{center} \begin{itemize} \item {\em Like SciPy/Numarray but for arithmetic geometry. } \item {\dblue Financial Support:} My NSF Grant DMS-0400386, and hopefully grad students when I go to UC San Diego as a tenured professor in July. I intend to apply for other grants as well. This is a very long-term project. \item {\dblue Tools:} Python, Pyrex, GMP, PARI, mwrank, SWIG, NTL. These are all are GPL'd and SAGE provides (or will provide) a unified interface for using them. Also, I'm writing lots of new code, mainly related to my areas of expertise (modular forms, and linear algebra over exact fields). Not reinventing wheel. Using design ideas from MAGMA. \item {\dblue Current Platforms:} Linux, Solaris, OS X, Windows (cygwin). Architecture independent, so no use of psyco. \end{itemize} } % end page \page{ \section{Advantages to Using Python} Asside from being open source, building an arithmetic geometry system on Python has several advantages. \begin{itemize} \item {\dred Object persistence} is very easy in Python---but very difficult in many other math systems. % \item That function arguments can be of any type is extremely %important in writing mathematics code. E.g., a generic echelon %for matrices over {\em any field} is straightforward to write. \item Good support for {\dred doctest} and automatic extraction of API documentation from docstrings. Having lots of examples that are tested and guaranteed to work as indicated. \item Memory management: MAGMA also does reference counting but does {\em not} deal with {\dred circular references}. Python does. \item Python has {\dred many packages} available now that might be useful to arithmetic geometers: numarray/Numeric/SciPy, 2d and 3d graphics, networking (for distributed computation), database hooks, etc. \item Easy to {\dred compile} Python on many platforms. \end{itemize} } \begin{slide} \section{Standard Python Math Annoyances} \vfill Everybody who does mathematics using Python runs into these problems: \vfill \begin{itemize} \item \verb\|\| versus \verb\|^\| -- easy for me to get used to, but must define \verb\|^\| to give an error on any arithmetic SAGE type. (In IPython shell lines can be pre-parsed, so this can be solved nicely.) \item \verb\|sin(2/3)\| has {\em much} different behavior in Python than in any standard math system. \end{itemize} \vfill I think the best solution is to leave the Python language exactly as is, and write a pre-parser for IPython so that the command line behavior of IPython is what one expects in arithmetic geometry, e.g., typing {\tt a = 2/3} will create {\tt a} as an exact rational number, and typing {\tt a = 3\verb\|^\|4} will set {\tt a} to 81. One must still obey the standard Python rules when writing code in a file. \vfill\end{slide} \begin{slide} \section{Demo} {\tiny \begin{verbatim} was@form:~$ sage ******************************************************** * SAGE Version 0.2 * * System for Arithmetic Geometry Experimentation * * (c) William Stein, 2005 * * http://modular.fas.harvard.edu/SAGE * * Distributed under the terms of the GPL * ********************************************************** Help: object? -> Documentation about 'object'. >>> Q Rational Field >>> a = Q("2/3") >>> a 2/3 >>> a in Q True >>> type(a) <type 'rational.Rational'> >>> 3^4 # illustration of IPython hack! 81 >>> 3\^4 # usual Python behavior (xor) 7 \end{verbatim}} Create a matrix as an element of a space of matrices. {\tiny \begin{verbatim} >>> M = MatrixSpace(Q,3) >>> M Full MatrixSpace of 3 by 3 dense matrices over Rational Field >>> B = M.basis() >>> len(B) 9 >>> B[1] [0 1 0] [0 0 0] [0 0 0] >>> A = M(range(9)); A [0 1 2] [3 4 5] [6 7 8] >>> A.reduced_row_echelon_form() [ 1 0 -1] [ 0 1 2] [ 0 0 0] >>> A^20 [ 2466392619654627540480 3181394780427730516992 3896396941200833493504] ... >>> A.kernel() Vector space of degree 3, dimension 1 over Rational Field Basis matrix: [ 1 -2 1] >>> kernel(A) # functional notation, like in MAGMA \end{verbatim} } Compute with an elliptic curve. {\tiny \begin{verbatim} >>> E = EllipticCurve([0,0,1,-1,0]) >>> E y^2 + y = x^3 - x >>> P = E([0,0]) >>> 10P (161/16, -2065/64) >>> 20P (683916417/264517696, -18784454671297/4302115807744) >>> E.conductor() 37 >>> print E.anlist(30) # coefficients of associated modular form [0, 1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 10, 2, 0, -1, 4, -9, -2, 6, -12] >>> M = ModularSymbols(37) >>> D = M.decomposition() >>> D [Subspace of Modular Symbols of dimension 1 and level 37, Subspace of Modular Symbols of dimension 2 and level 37, Subspace of Modular Symbols of dimension 2 and level 37] >>> D[1].T(2) Linear function defined by matrix: [0 0] [0 0] >>> D[2].T(2) Linear function defined by matrix: [-2 0] [ 0 -2] \end{verbatim} } \end{slide} \end{document}
https://www.apmep.fr/IMG/tex/Corrige-S_Antilles_Guyane_19_juin_2018_JPG.tex	apmep.fr	CC-MAIN-2022-21	text/x-tex	application/postscript	crawl-data/CC-MAIN-2022-21/segments/1652662619221.81/warc/CC-MAIN-20220526162749-20220526192749-00196.warc.gz	752,764,347	10,276	%!TEX encoding = UTF-8 Unicode %\tapuscrit Jean-Paul GOUALARD \documentclass[10p,leqno]{article} %\usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} %\usepackage{SIunits} \usepackage[upright]{fourier} %\usepackage[scaled=0.875]{helvet} \renewcommand{\ttdefault}{lmtt} \usepackage{makeidx} \usepackage{amsmath} \usepackage{variations} \usepackage{enumerate} \usepackage{fancybox} %\usepackage[normalem]{ulem} %\usepackage{pifont} \usepackage{lscape} \usepackage{multicol} \usepackage{mathrsfs} \usepackage{tabularx,array} \usepackage{colortbl} \usepackage{multirow} %\usepackage{textcomp} %\newcommand{\euro}{\eurologo{}} \usepackage{pst-plot,pst-tree,pstricks,pst-node} \usepackage{pst-eucl} \usepackage{pstricks-add} \usepackage{tkz-tab} \usepackage{amssymb} \everymath{\displaystyle} \newcommand{\R}{\mathbb{R}} \newcommand{\N}{\mathbb{N}} \newcommand{\D}{\mathbb{D}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\C}{\mathbb{C}} %\setlength{\textheight}{23.5cm} %\setlength{\voffset}{-1.5cm} % %\addtolength{\textwidth}{1.5cm} \usepackage[left=3.5cm, right=3.5cm, top=3cm, bottom=3cm]{geometry} \renewcommand{\i}{\text{i}} \def\e{\mathrm{e}} \newcommand{\vect}[1]{\overrightarrow{\,\mathstrut#1\,}} \newcommand{\barre}[1]{\overline{\,\mathstrut#1\,}} \renewcommand{\theenumi}{\textbf{\arabic{enumi}}} \renewcommand{\labelenumi}{\textbf{\theenumi.}} \renewcommand{\theenumii}{\textbf{\alph{enumii}}} \renewcommand{\labelenumii}{\textbf{\theenumii.}} \newcommand\alert[1]{{\magenta #1}} \def\Oij{$\left(\text{O}~;~\vect{\imath},~\vect{\jmath}\right)$} \def\Oijk{$\left(\text{O}~;~\vect{\imath},~\vect{\jmath},~\vect{k}\right)$} \def\Ouv{$\left(\text{O}~;~\vect{u},~\vect{v}\right)$} %%%%% commandes personnelles \newcommand{\ssi}{\Leftrightarrow} \newcommand{\SSI}{{\blue~~\Longleftrightarrow~}} \newcommand{\norme}[1]{\left\\|{\vect{#1}}\right\\|} \newcommand{\norm}[1]{\left\\|{#1}\right\\|} \newcommand{\abs}[1]{\left\vert #1\right\vert} \newcommand{\Abs}[1]{\\left\vert #1\right\vert} \newcommand{\limi}[2]{\lim\limits_{#1\rightarrow #2}} \newcommand{\limg}[2]{\lim\limits_{\underset{\scriptstyle #1<#2}{\scriptstyle #1\rightarrow #2}}} \newcommand{\limd}[2]{\lim\limits_{\underset{\scriptstyle #1>#2}{\scriptstyle #1\rightarrow #2}}} \newcommand{\dx}{\mathrm{d}} \newcommand{\integrale}[4]{\int_{#3}^{#4}#1\,\dx#2} \newcommand{\Integrale}[4]{\displaystyle\int_{#3}^{#4}#1\,\dx#2} \makeindex \usepackage{fancyhdr} \usepackage[dvips,colorlinks=true,pdfstartview=FitV,linkcolor=blue,citecolor=blue,urlcolor=blue]{hyperref} \hypersetup{% pdfauthor = {APMEP}, pdfsubject = {Baccalauréat S}, pdftitle = {Baccalauréat S - 2018}, allbordercolors = white, pdfstartview=FitH } \usepackage[frenchb]{babel} \usepackage[np]{numprint} \renewcommand{\labelitemi}{$\blacktriangleright$} \renewcommand{\labelitemii}{$\bullet$} \renewcommand{\labelitemiii}{$\star$} \begin{document} \setlength\parindent{0mm} \rhead{A. P. M. E. P.} \lhead{\small{Baccalauréat S}} \pagestyle{fancy} \thispagestyle{empty} \cfoot{Page \thepage/\pageref{fin}} \begin{center} {\Large\textbf{\decofourleft~ Correction du Baccalauréat S Antilles-Guyane 19 juin 2018 ~\decofourright}} \end{center} \def\labelitemi{$\bullet$} %: EXERCICE 1 \vspace{0,5cm}\textbf{\textsc{Exercice 1} \hfill 5 points} \smallskip \textsc{Commun à tous les candidats} \bigskip L'exploitant d'une forêt communale décide d'abattre des arbres afin de les vendre, soit aux habitants, soit à des entreprises. On admet que: \begin{itemize} \item parmi les arbres abattus, 30~\% sont des chênes, 50~\% sont des sapins et les autres sont des arbres d'essence secondaire (ce qui signifie qu'ils sont de moindre valeur); \item \np{45,9}~\% des chênes et 80~\% des sapins abattus sont vendus aux habitants de la commune; \item les trois quarts des arbres d'essence secondaire abattus sont vendus à des entreprises. \end{itemize} \medskip \textbf{Partie A} \smallskip Parmi les arbres abattus, on en choisit un au hasard. On considère les évènements suivants : \begin{itemize} \item $C$: \og l'arbre abattu est un chêne\fg{}; \item $S$: \og l'arbre abattu est un sapin\fg{}; \item $E$: \og l'arbre abattu est un arbre d'essence secondaire\fg{}; \item $H$: \og l'arbre abattu est vendu à un habitant de la commune\fg{}. \end{itemize} \begin{enumerate} \item %Construire un arbre pondéré complet traduisant la situation. Arbre : \begin{center} \psset{nodesep=0mm,levelsep=30mm,treesep=10mm} \pstree[treemode=R]{\Tdot} { \pstree {\Tdot~[tnpos=a]{$C$}\taput{ $0,3$}} { \Tdot~[tnpos=r]{$H$}\taput{ $0,459$} \Tdot~[tnpos=r]{$\overline{H}$}\tbput{ $0,541$} } \pstree {\Tdot~[tnpos=a]{$S$}\taput{ $0,5$}} { \Tdot~[tnpos=r]{$H$}\taput{ $0,8$} \Tdot~[tnpos=r]{$\overline{H}$}\tbput{ $0,2$} } \pstree {\Tdot~[tnpos=a]{$E$}\tbput{ $0,2$}} { \Tdot~[tnpos=r]{$H$}\taput{ $0,25$} \Tdot~[tnpos=r]{$\overline{H}$}\tbput{ $0,75$} } } \end{center} \item %Calculer la probabilité que l'arbre abattu soit un chêne vendu à un habitant de la commune. $m(C \cap H)=p_C(H)\times p(C)=0,459\times 0,3=\np{0,1377}$. La probabilité que l'arbre abattu soit un chêne vendu à un habitant de la commune est \np{0,1377}. \item %Justifier que la probabilité que l'arbre abattu soit vendu à un habitant de la commune est égale à \np{0,5877}. On applique la formule des probabilités totales : $p(H)=p_C(H)\times p(C)+p_S(H)\times p(S)+p_E(H)\times p(E)=\np{0,1377}+0,8\times 0,5+0,25\times 0,2=\boxed{\textcolor{red}{\np{0,5877}}}$ \item %Quelle est la probabilité qu'un arbre abattu vendu à un habitant de la commune soit un sapin~?\\On donnera le résultat arrondi à $10^{-3}$. $p_H(S)=\dfrac{p(S \cap H)}{p(H)}=\dfrac{0,4}{\np{0,5877}}\boxed{\textcolor{red}{\approx 0,681}}$ à 10$^{-3}$ près. \end{enumerate} \medskip \textbf{Partie B} \smallskip Le nombre d'arbres sur un hectare de cette forêt peut être modélisé par une variable aléatoire $X$ suivant une loi normale d'espérance $\mu=\np{4000}$ et d'écart-type $\sigma=300$. \begin{enumerate} \item %Déterminer la probabilité qu'il y ait entre \np{3400} et \np{4600} arbres sur un hectaure donné de cette forêt. On donnera le résultat arrondi à $10^{-3}$. $p(3400\leqslant X\leqslant 4600)=p(\mu-2\sigma\leqslant X\leqslant \mu+2\sigma)\boxed{\textcolor{red}{\approx 0,954}}$. \item %Calculer la probabilité qu'il y ait plus de \np{4500} arbres sur un hectare donné de cette forêt. %On donnera le résultat arrondi à $10^{-3}$. $p(X\geqslant \np{4500})=1-p(X<\np{4500})\boxed{\textcolor{red}{\approx 0,048}}$ arrondi à $10^{-3}$ \end{enumerate} \medskip \textbf{Partie C} \smallskip L'exploitant affirme que la densité de sapins dans cette forêt communale est de 1 sapin pour 2 arbres. \smallskip %Sur une parcelle, on a compté 106 sapins dans un échantillon de 200 arbres.\ %Ce résultat remet-il en cause l'affirmation de l'exploitant~? La proportion théorique de sapins est $p=0,5$. \begin{enumerate}[$\bullet$] \item La taille de l'échantillon est $n=200\geqslant 25$. \item $np=0,5\times 200=100\geqslant 25$ \item $n(1-p)=100\geqslant 25$ \end{enumerate} Les conditions sont réunies pour qu'on puisse utiliser un intervalle de fluctuation asymptotique au seuil 0,95. Cet intervalle est $I_{0,95}=\left[p-1,96\dfrac{\sqrt{p(1-p)}}{\sqrt{n}}~;~p+1,96\dfrac{\sqrt{p(1-p)}}{\sqrt{n}}\right]=\left[0,5-1,96\dfrac{0,5}{\sqrt{200}}~;~0,5+1,96\dfrac{0,5}{\sqrt{200}}\right]\\ \approx \boxed{\textcolor{red}{[0,430~;~0,570]}}$. La fréquence observée dans cet échantillon est $f=\dfrac{106}{200}=0,53$ ; $\boxed{\textcolor{red}{f\in I_{0,95}}}$. Ce résultat ne remet pas en cause l'affirmation de l'exploitant. %: EXERCICE 2 \vspace{0,5cm}\textbf{\textsc{Exercice 2} \hfill 5 points} \smallskip \textsc{Commun à tous les candidats} \bigskip Un artiste souhaite réaliser une sculpture composée d'un tétraèdre posé sur un cube de 6 mètres d'arête. Ces deux solides sont représentés par le cube $ABCDEFGH$ et par le tétraèdre $SELM$ ci-dessous. \begin{center} \psset{unit=0.8cm} \begin{pspicture}(0,0)(8,8) \pstGeonode[PosAngle=-135](0,0){B} \pstGeonode[PosAngle=135](0,4){F} \pstGeonode[PosAngle=-45](4,0){C} \pstGeonode[PosAngle=0](4,4){G} \pstGeonode[PosAngle=45](2,2){A} \pstTranslation[PosAngle=-45]{B}{A}{C}[D] \pstTranslation[PosAngle=45]{B}{A}{G}[H] \pstTranslation[PosAngle=45]{B}{A}{F}[E] \pstHomO[HomCoef=0.166666666667,PosAngle=-45]{A}{B}[I] \pstHomO[HomCoef=0.166666666667,PosAngle=-45]{A}{D}[J] \pstHomO[HomCoef=0.166666666667,PosAngle=135]{A}{E}[K] \psline(B)(C)(G)(F)(B) \psline[linestyle=dashed](B)(A)(E) \psline[linestyle=dashed](A)(D) \psline(G)(H)(D)(C) \pstHomO[HomCoef=.3333333,PosAngle=45]{E}{H}[M] \pstHomO[HomCoef=.3333333,PosAngle=135]{E}{F}[L] \pstInterLL[PosAngle=90]{B}{L}{M}{D}{S} \psline(S)(L)(M)(S) \psline(F)(L) \psline(M)(H) \psline[linestyle=dashed](L)(E)(S) \psline[linestyle=dashed](E)(M) \psline[linestyle=dashed](L)(B)(D)(M) \psline[linecolor=red]{->}(A)(I) \psline[linecolor=red]{->}(A)(J) \psline[linecolor=red]{->}(A)(K) \end{pspicture} \end{center} On munit l'espace du repère orthonormé $\left(A;\vect{AI},\vect{AJ},\vect{AK}\right)$ tel que: $I\in[AB]$, $J\in[AD]$, $K\in[AE]$ et $AI=AJ=AK=1$, l'unité graphique représentant 1 mètre. Les points $L$, $M$ et $S$ sont définis de la façon suivante: \begin{itemize} \item $L$ est le point tel que $\vect{FL}=\frac23\vect{FE}$; \item $M$ est le point d'intersection du plan $(BDL)$ et de la droite $(EH)$; \item $S$ est le point d'intersection des droites $(BL)$ et $(AK)$. \end{itemize} \begin{enumerate} \item %Démontrer, sans calcul de coordonnées, que les droites $(LM)$ et $(BD)$ sont parallèles. Les droites $(LM)$ et $(BD)$ sont \textbf{\textcolor{red}{coplanaires}} (dans le plan $(BDS)$) et contenues respectivement dans les plans $(ABD)$ et $(EFH)$ qui sont \textbf{\textcolor{red}{parallèles}}, donc elles sont \textbf{\textcolor{red}{parallèles}}. \item %Démontrer que les coordonnées du point $L$ sont $(2~;~0~;~6)$. $\vect{AL}=\vect{AE}+\vect{EL}=6\vect{AK}+\dfrac{1}{3}\vect{AB}=6\vect{AK}+2\vect{AI}=2\vect{AI}+0\vect{AJ}+6\vect{AK}$ donc les coordonnées de $L$ sont $\boxed{\textcolor{red}{L(2~;~0~;~6)}}$. \item \begin{enumerate} \item %Donner une représentation paramétrique de la droite $(BL)$. $\vect{BL}\begin{pmatrix}-4\\0\\6\end{pmatrix}$ et $B(6~;~0~;~0)$. Un représentation paramétrique de $(BL)$ est alors : $\boxed{\textcolor{red}{(BL)\begin{cases}x=6-4t\\y=0\\z=6t\end{cases},~t\in\mathbb{R}}}$. \item %Vérifier que les coordonnées du point $S$ sont $(0~;~0~;~9)$. $S$ appartient au plan $(BDL)$ et à la droite $(AE)$ donc : $\begin{cases}x=6-4t\\y=0\\z=6t\\x=y=0\end{cases}$. On en déduit $t=\dfrac{3}{2}$ d'où $\boxed{\textcolor{red}{S(0~;~0~;~9)}}$. \end{enumerate} \item Soit $\vect{n}$ le vecteur de coordonnées $\begin{pmatrix}3\\3\\2\end{pmatrix}$. \begin{enumerate} \item %Vérifier que $\vect{n}$ est normal au plan $(BDL)$. \begin{enumerate}[$\bullet$] \item $\vect{BD}\begin{pmatrix}-6\\6\\0\end{pmatrix}$ donc $\vect{n}\cdot \vect{BD}=3\times (-6)+3\times 6+2\times 0=0$ donc $\vect{n}\perp \vect{BD}$. \item $\vect{BL}\begin{pmatrix}-4\\0\\6\end{pmatrix}$ donc $\vect{n} \cdot \vect{BL}=3\times (-4)+3\times 0+2\times 6=0$ donc $\vect{n} \perp \vect{BL}$. \item $\vect{n}$ est orthogonal à deux vecteurs non colinéaires du plan $BDL$ donc est normal à ce plan. \end{enumerate} \item %Démontrer qu'une équation cartésienne du plan $(BDL)$ est: %\[ %3x+3y+2z-18=0. %\] Une équation du plan $BDL$ est alors : $3\left(x-x_B\right)+3\left(y-y_B\right)+2\left(z-z_B\right)=0\\ \Leftrightarrow 3(x-6)+3y+2z=0\Leftrightarrow \boxed{\textcolor{red}{3x+3y+2z-18=0}}$. \item On admet que la droite $(EH)$ a pour représentation paramétrique: \[ \left\{ \begin{array}{rcl} x&=&0\\ y&=&s~~~~(s\in\R)\\ z&=&6 \end{array} \right. \] %Calculer les coordonnées du point $M$. $M$ est l'intersection du plan $(BDL)$ et de la droite $EH$ donc ses coordonnées vérifient l'équation du plan et la représentation paramétrique de la droite. On doit avoir : $\begin{cases}x=0\\y=s\\z=6\\3x+3y+2z-18=0\end{cases}\Leftrightarrow \begin{cases}x=0\\y=s\\z=6\\3x+12-18=0\end{cases}\Leftrightarrow \begin{cases}s=2\\x=0\\y=z\\z=6\end{cases}$. $M$ a donc pour coordonnée $\boxed{\textcolor{red}{M(0~;~2~;~6)}}$. \end{enumerate} \item %Calculer le volume du tétraèdre $SELM$. On rappelle que le volume $V$ d'un tétraèdre est donné par la formule suivante: %\[ %V=\frac13\times\text{Aire de la base}\times\text{Hauteur}. %\] L'aire du triangle $ELM$ est $\mathscr{A}(ELM)=\dfrac{EL\times EM}{2}=\dfrac{2\times 2}{2}=2$.\\ La hauteur $SE$ vaut $SE=AS-AE=9-6=3$.\\ Le volume du tétraèdre $SELM$ est alors : $\mathscr{V}=\dfrac{1}{3}\times 2\times 3=2$ m$^3$. \item L'artiste souhaite que la mesure de l'angle $\widehat{SLE}$ soit comprise entre 55\up{o} et 60\up{o}.\\ %Cette contrainte d'angle est-elle respectée~? Le triangle $SLE$ est rectangle en E : $\cos\left(\widehat{SLE}\right)=\dfrac{LE}{LS}$. Or $LS=\sqrt{\left(x_S-x_E\right)^2+\left(y_S-y_L\right)^2+\left(z_S-z_L\right)^2}=\sqrt{2^2+(-3)^2}=\sqrt{13}$. Donc $\cos\left(\widehat{SLE}\right)=\dfrac{2}{\sqrt{13}}$ ; on en déduit que $\widehat{SLE}\approx 56,3\text{\degre}$ ; la contrainte est respectée. \end{enumerate} %: EXERCICE 3 \vspace{0,5cm}\textbf{\textsc{Exercice 3 \hfill 5 points}} \smallskip \textsc{Commun à tous les candidats} \bigskip Un publicitaire souhaite imprimer le logo ci-dessous sur un T-shirt: \begin{center} \psset{xunit=2.0cm,yunit=2.0cm,algebraic=true,dimen=middle,dotstyle=o,dotsize=5pt 0,linewidth=1.6pt,arrowsize=3pt 2,arrowinset=0.25} \begin{pspicture}(-2.,-2.)(5.,1.) \pscustom[linewidth=0.8pt,fillcolor=lightgray!60,fillstyle=solid]{\psplot{-1.57}{4.6}{EXP(-x)(-COS(x)+SIN(x)+1.0)}\lineto(4.6,0)\psplot{4.6}{-1.57}{-EXP(-x)COS(x)}\lineto(-1.57,0)\closepath} \psplot[linewidth=2.pt,plotpoints=200]{-1.57}{4.6}{EXP(-x)(-COS(x)+SIN(x)+1.0)} \psplot[linewidth=2.pt,plotpoints=200]{-1.57}{4.6}{-EXP(-x)COS(x)} \end{pspicture} \end{center} Il dessine ce logo à l'aide des courbes de deux fonctions $f$ et $g$ définies sur $\R$ par: \[ f(x)=\e^{-x}(-\cos x+\sin x+1)\text{~~et~~} g(x)=-\e^{x}\cos x. \] On admet que les fonctions $f$ et $g$ sont dérivables sur $\R$. \medskip \textbf{Partie A — Étude de la fonction $f$} \smallskip \begin{enumerate} \item %Justifier que, pour tout $x\in\R$:\[-\e^{-x}\leqslant f(x)\leqslant 3\e^{-x}.\] Pour tout $x\in\mathbb{R}$ : $\begin{cases}-1\leqslant -\cos x\leqslant 1\\-1\leqslant \sin x\leqslant 1\\1\leqslant 1\leqslant 1\end{cases}$ donc par somme : $\boxed{\textcolor{red}{-1\leqslant -\cos x+\sin x\leqslant 3}}$. Comme $\mathrm{e}^{-x}>0$, on en déduit :\[\boxed{\textcolor{red}{-\mathrm{e}^{-x}\leqslant f(x)\leqslant 3\mathrm{e}^{-x}}}\]. \item %En déduire la limite de $f$ en $+\infty$. $\lim_{x\rightarrow +\infty}\mathrm{e}^{-x}=0$ donc, d'après le théorème des gendarmes, \[\boxed{\textcolor{red}{\lim_{x\rightarrow +\infty}f(x)=+\infty}}\]. \item %Démontrer que, pour tout $x\in\R$, $f'(x)=\e^{-x}(2\cos x-1)$ où $f'$ est la fonction dérivée de $f$. $f$ est le produit de deux fonctions : $\forall x\in\mathbb{R}$ : $f'(x)=-\mathrm{e}^{-x}\left(-\cos x+\sin x+1\right)+\mathrm{e}^{-x}\left(\sin x+\cos x\right)=\mathrm{e}^{-x}\left(2\cos x-1\right)$ donc \[\boxed{\textcolor{red}{f'(x)=\e^{-x}(2\cos x-1)}}\]. \item Dans cette question, on étudie la fonction $f$ sur l'intervalle $[-\pi;\pi]$. \begin{enumerate} \item %Déterminer le signe de $f'(x)$ pour $x$ appartenant à l'intervalle $[-\pi;\pi]$. Comme $\mathrm{e}^{-x}>0$ $f'(x)$ est du signe de $u(x)=2\cos x-1$. $u(x)=0\Leftrightarrow \cos x=\dfrac{1}{2}\Leftrightarrow x=-\dfrac{\pi}{3}$ ou $x=\dfrac{\pi}{3}$. $2\cos x-1>0\Leftrightarrow \cos x>\dfrac{1}{2}\Leftrightarrow x\in\left]-\dfrac{\pi}{3}~;~\dfrac{\pi}{3}\right[$. Signe de $f'(x)$ : \begin{center} \begin{variations} x&\-\pi&&-\dfrac{\pi}{3}&&\dfrac{\pi}{3}&&\pi\\ \filet f'(x)&&+&\z&-&\z&+&\\ \filet \end{variations} \end{center} \item %En déduire les variations de $f$ sur $[-\pi;\pi]$. On en déduit les variations de $f$ sur $\left[-\pi~;~\pi\right]$ : \begin{center} \begin{variations} x&-\pi&&-\dfrac{\pi}{3}&&\dfrac{\pi}{3}&&\pi\\ \filet \m{f(x)}&\h{2\mathrm{e}^{\pi}}&\d&\dfrac{1-\sqrt{3}}{2}\mathrm{e}^{\frac\pi3}&\c&\h{\dfrac{1+\sqrt{3}}{2}\mathrm{e}^{-\frac\pi3}}&\d&2\mathrm{e}^{-\pi}&\\ \filet \end{variations} \end{center} \end{enumerate} \end{enumerate} \medskip \textbf{Partie B — Aire du logo} \smallskip On note $\mathcal{C}_f$ et $\mathcal{C}_g$ les représentations graphiques des fonctions $f$ et $g$ dans un repère orthonormé \Oij. L'unité graphique est de 2 centimètres. Ces deux courbes sont tracées en ANNEXE. \medskip \begin{enumerate} \item %Étudier la position relative dela courbe $\mathcal{C}_f$ par rapport à la courbre $\mathcal{C}_g$ sur $\R$. $\forall x\in\mathbb{R}$, $f(x)-g(x)=\mathrm{e}^{-x}(-\cos x+\sin x+1)-\left(-\mathrm{e}^{-x}\cos x\right)=\mathrm{e}^{-x}(\sin x+1)$. Or, pour tout $x\in\mathbb{R}$, $\sin x\geqslant -1$ donc $\sin x+1\geqslant 0$ donc $f(x)-g(x)\geqslant 0$ donc $f(x)\geqslant g(x)$. La courbe $\mathscr{C}_f$ est au-dessus de la courbe $\mathscr{C}_f$ (avec points communs pour $\sin x=-1$, donc pour $x=-\dfrac{\pi}{2}+2k\pi$). \item Soit $H$ la fonction définie sur $\R$ par: \[ H(x)=\left(-\frac{\cos x}{2}-\frac{\sin x}{2}-1\right)\e^{-x}. \] On admet que $H$ est une primitive de la fonction $x\mapsto (\sin x+1)\e^{-x}$ sur $\R$. On note $\mathcal{D}$ le domaine délimité par la courbe $\mathcal{C}_f$, la courbe $\mathcal{C}_g$ est les droites d'équation $x=-\frac{\pi}{2}$ et $x=\frac{3\pi}{2}$. \begin{enumerate} \item Hachurons le domaine $\mathcal{D}$ sur le graphique en annexe à rendre avec la copie. \psset{xunit=2.0cm,yunit=2.0cm,algebraic=true,dimen=middle,dotstyle=o,dotsize=5pt 0,linewidth=1.6pt,arrowsize=3pt 2,arrowinset=0.25} \begin{pspicture}(-2.,-2.)(5.,1.) \psset{xunit=2.0cm,yunit=2.0cm,algebraic=true,dimen=middle,dotstyle=o,dotsize=5pt 0,linewidth=1.6pt,arrowsize=3pt 2,arrowinset=0.25} \multips(0,-2)(0,1.0){4}{\psline[linestyle=dashed,linecap=1,dash=1.5pt 1.5pt,linewidth=0.4pt,linecolor=lightgray]{c-c}(-2.,0)(5.,0)} \multips(-2,0)(1.0,0){8}{\psline[linestyle=dashed,linecap=1,dash=1.5pt 1.5pt,linewidth=0.4pt,linecolor=lightgray]{c-c}(0,-2.)(0,1.)} \psaxes[labelFontSize=\scriptstyle,xAxis=true,yAxis=true,Dx=1.,Dy=1.,ticksize=-2pt 0,subticks=2]{->}(0,0)(-2.,-2.)(5.,1.) \pscustom[fillstyle=vlines]{\psplot{-1.57}{4.712}{EXP(-x)(-cos(x)+sin(x)+1)}, \psplot{4.712}{-1.57}{-EXP(-x)cos(x)}} \end{pspicture} \item %Calculer, une unité d'aire, l'aire du domaine $\mathcal{D}$, puis en donner une valeur approchée à $10^{-2}$ près en cm\up{2}. L'aire vaut $\mathscr{A}=H\left(\dfrac{3\pi}{2}\right)-H\left(-\dfrac{\pi}{2}\right)=\boxed{\textcolor{red}{-\dfrac{1}{2}\mathrm{e}^{-\frac{3\pi}{2}}+\dfrac{1}{2}\mathrm{e}^{\frac\pi2}}}$. $\mathscr{A}\approx 2,4$ u.a., donc $\mathscr{A}\approx 9,6$ cm\up{2}. \end{enumerate} \end{enumerate} %: EXERCICE 4 \vspace{0,5cm}\textbf{\textsc{Exercice 4 \hfill 5 points}} \smallskip \textsc{Candidats n'ayant pas suivi l'enseignement de spécialité} \bigskip Le directeur d'une réserve marine a recensé \np{3000} cétacés dans cette réserve au 1\up{er} juin 2017. Il est inquiet car il sait que le classement de la zone en \og réserve marine\fg{} ne sera pas reconduit si le nombre de cétacés de cette réserve devient inférieur à \np{2000}. \smallskip Une étude lui permet d'élaborer un modèle selon lequel, chaque année: \begin{itemize} \item entre le 1\up{er} juin et le 31 octobre, 80 cétacés arrivent dans la réserve marine; \item entre le 1\up{er} novembre et le 31 mai, la réserve subit une baisse de 5~\% de son effectif par rapport à celui du 31 octobre qui précède. \end{itemize} On modélise l'évolution du nombre de cétacés par une suite $(u_n)$. Selon ce modèle, pour tout entier naturel $n$, $u_n$ désigne le nombre de cétacés au 1\up{er} juin de l'année $2017+n$. On a donc $u_0=\np{3000}$. \begin{enumerate} \item % Justifier que $u_1=\np{2926}$. $u_1=\left(u_0+80\right)\times 0,95=0,95\times \np{3080}=\np{2926}$. \item %Justifier que, pour tout entier naturel $n$, $u_{n+1}=\np{0,95}u_n+76$. Pour tout $n\in\mathbb{N}$, $u_{n+1}=\left(u_n+80\right)\times 0,95=\boxed{\textcolor{red}{0,95u_n+76}}$. \item À l'aide d'un tableur, on a calculé les 8 premiers termes de la suite $(u_n)$. Le directeur a configuré le format des cellules pour que ne soient affichés que des nombres arrondis à l'unité. \begin{center} \begin{tabular}{\|c\|c\|c\|c\|c\|c\|c\|c\|c\|c\|} \hline \rowcolor{lightgray!50}&A&B&C&D&E&F&G&H&I\\ \hline \cellcolor{lightgray!50}1&$n$&0&1&2&3&4&5&6&7\\ \hline \cellcolor{lightgray!50}2&$u_n$&\np{3000}&\np{2926}&\np{2856}&\np{2789}&\np{2725}&\np{2665}&\np{2608}&\np{2553}\\ \hline \end{tabular} \end{center} %Quelle formule peut-on entrer dans la cellule C2 afin d'obtenir, par recopie vers la droite, les termes de la suite $(u_n)$~? En C2, on doit taper \og{}=0.95B2+76\fg{} \item \begin{enumerate} \item %Démontrer que, pour tout entier naturel $n$, $u_n\geqslant\np{1520}$. Montrons par récurrence que, pour tout $n$, $u_n\geqslant\np{1520}$. \begin{enumerate}[$\bullet$] \item Initialisation : $u_0=3000\geqslant \np{1520}$ donc la propriété est vraie au rang 0. \item On suppose que $u_n\geqslant \np{1520}$ pour un entier $n$ quelconque. Alors : $0,95u_n\geqslant 0,95\times 1520$ d'où $0,95u_n+76\geqslant 0,95\times 1520+76= \np{1520}$ donc la propriété est héréditaire. \end{enumerate} D'après l'axiome de récurrence, la propriété est vraie pour tout $n$. \item %Démontrer que la suite $(u_n)$ est décroissante. Pour tout $n$, $u_{n+1}-u_n=0,95u_n+76-u_n=-0,05u_n+76=-0,05\left(u_n-\np{1520}\right)\leqslant 0$ car on a montré que $u_n\geqslant \np{1520}$. La suite $\left(u_n\right)$ est bien décroissante. \item %Justifier que la suite $(u_n)$ est convergente. On ne cherchera pas ici la valeur de la limite. La suite $\left(u_n\right)$ est décroissante et minée par \np{1250}, donc convergente. \end{enumerate} \item On désigne par $(v_n)$ la suite définie par, pour tout entier naturel $n$, $v_n=u_n-\np{1520}$. \begin{enumerate} \item %Démontrer que la suite $(v_n)$ est une suite géométrique de raison \np{0,95} dont on précisera le premier terme. Pour tout $n$, $v_{n+1}=u_{n+1}-1520=0,95u_n+76-\np{1520}=0,95u_n-\np{1444}=0,95\left(u_n-\np{1520}\right)\\ =\boxed{\textcolor{red}{0,95v_n}}$. La suite $\left(v_n\right)$ est géométrique, de raison $q=0,95$ et de premier terme $v_0=u_0-\np{1520}=\np{3000}-\np{1520}=\np{1480}$. \item %En déduire que, pour tout entier naturel $n$, $u_n=\np{1480}\times\np{0,95}^n+\np{1520}$. Par conséquent, puisque $\left(v_n\right)$ est géométrique, $v_n=v_0q^n=\np{1480}\times 0,95^n$ donc \\ $\boxed{\textcolor{red}{u_n=\np{1480}\times\np{0,95}^n+\np{1520}}}$. \item %Déterminer la limite de la suite $(u_n)$. $-1<0,95<1$ donc $\lim_{n\rightarrow +\infty}0,05^n=0$ d'où $\boxed{\textcolor{red}{\lim_{n\rightarrow +\infty}u_n=1520}}$. \end{enumerate} \newpage \item Recopier et compléter l'algorithme suivant pour déterminer l'année à partir de laquelle le nombre de cétacés présents dans la réserve marine sera inférieur à \np{2000}. \begin{center} \fbox{ \begin{minipage}{4cm} $n\leftarrow 0$\\ $u\leftarrow\np{3000}$\\ Tant que {\red $u > \np{2000}$}\\ \phantom{xxxx}$n\leftarrow {\red n+1}$\\ \phantom{xxxx}$u\leftarrow {\red 0,95u + 76}$\\ Fin de Tant que \end{minipage} } \end{center} %La notation \og $\leftarrow$\fg{} correspond à une affectation de valeur, ainsi \og $n\leftarrow 0$\fg{} signifie \og Affecter à $n$ la valeur $0$\fg{}. \item %La réserve marine fermera-t-elle un jour~? Si oui, déterminer l'année de la fermeture. On a vu que la limite de la suite est \np{1520} donc il y a une valeur de la suite pour laquelle \\ $u_n<1200$. On trouve $\boxed{\textcolor{red}{n=22}}$. \end{enumerate} %: EXERCICE 4 \vspace{0,5cm}\textbf{\textsc{Exercice 4 \hfill 5 points}} \smallskip \textsc{Candidats ayant suivi l'enseignement de spécialité} \bigskip Le droit de pêche dans une réserve marine est réglementé : chaque pêcheur doit posséder une carte d'accréditation annuelle. Il existe deux types de cartes : \begin{itemize} \item une carte de pêche dite « libre » entre parenthèse le pêcheur mais pas limité en nombre de poissons pêchés); \item une carte de pêche dite « avec quota »(le pêcheur ne doit pas dépasser une certaine quantité hebdomadaire de poisson). \end{itemize} On suppose que le nombre total de pêcheurs reste constant d'année en année.\\ On note, pour l'année $2017+n$: \begin{itemize} \item $\ell_n$ la proportion de pêcheurs possédant la carte de pêche libre ; \item $q_n$ la proportion de pêcheurs possédant la carte de pêche avec quota. \end{itemize} On observe que: \begin{itemize} \item chaque année, 65~\% des possesseurs de la carte de pêche libres achètent de nouveau une carte de pêche libre l'année suivante; \item Chaque année, 45~\% des possesseurs de la carte de pêche avec quota achètent une carte de pêche libre l'année suivante ; \item En 2017, 40~\% des pêcheurs ont acheté une carte de pêche libre. On a donc $\ell_0=\np{0,4}$ et $q_0=\np{0,6}$. \end{itemize} On note, pour tout entier naturel $n$, $P_n=\begin{pmatrix} \ell_n\\q_n \end{pmatrix}$. \begin{enumerate} \item %Démontrer que, pour tout entier naturel $n$, $P_{n+1}=MP_n$, où $M$ est la matrice carrée $\begin{pmatrix} %\np{0,65}&\np{0,45}\\ %\np{0,35}&\np{0,55} %\end{pmatrix}$. Il est clair que $P_{n+1}=MP_n$, où $M$ est la matrice carrée $\begin{pmatrix} \np{0,65}&\np{0,45}\\ \np{0,35}&\np{0,55} \end{pmatrix}$. \item %Calculer la proportion de pêcheurs achetant une carte de pêche avec quota en 2019. 2019 correspond à $n=2$. $P_2=M^2P_0=\begin{pmatrix} \np{0,65}&\np{0,45}\\ \np{0,35}&\np{0,55} \end{pmatrix}^2\times \begin{pmatrix}0,4\\0,6\end{pmatrix}=\begin{pmatrix}0,556\\0,444\end{pmatrix}$ (à la calculatrice). La proportion de pêcheurs achetant une carte de pêche avec quota en 2019 est donc $\boxed{\textcolor{red}{q_2=0,444}}$. \newpage \item Un logiciel de calcul formel donne les résultats ci-dessous : \begin{center} \begin{tabular}{cc} \begin{tabular}{\|c\|l\|} \hline \cellcolor{lightgray!50}\begin{tabular}{c}1\\$\circ$\end{tabular} & \begin{tabular}{l} $M:=\{\{\np{0.65},\np{0,45}\},\{\np{0.35},\np{0.55}\}\}$\\ $\checkmark~~ M:=\begin{pmatrix} 0.65&0.45\\0.35&0.55 \end{pmatrix}$ \end{tabular} \\ \hline \cellcolor{lightgray!50}\begin{tabular}{c}2\\$\circ$\end{tabular} & \begin{tabular}{l} $P_0:=\{\{ 0.4 \},\{ 0.6 \}\}$\\ $\checkmark~~ P_0:=\begin{pmatrix} 0.4\\0.6 \end{pmatrix}$ \end{tabular} \\ \hline \cellcolor{lightgray!50}\begin{tabular}{c}3\\$\circ$\end{tabular} & \begin{tabular}{l} $Q:=\{\{ 9,1 \},\{ 7,$-1$ \}\}$\\ $\checkmark~~ Q:=\begin{pmatrix} 9&1\\7&-1 \end{pmatrix}$ \end{tabular} \\ \hline \cellcolor{lightgray!50}\begin{tabular}{c}4\\$\circ$\end{tabular} & \begin{tabular}{l} $T:=\{\{ 1/16,1/16 \},\{ 7/16,$-9/16$ \}\}$\\ $\checkmark~~ T:=\begin{pmatrix} \frac{1}{16}&\frac{1}{16}\\\frac{7}{16}&-\frac{9}{16} \end{pmatrix}$\\[-0.5ex]\quad \end{tabular} \\ \hline \end{tabular} & \begin{tabular}{\|c\|l\|} \hline \cellcolor{lightgray!50}\begin{tabular}{c}5\\$\circ$\end{tabular} & \begin{tabular}{l} $TQ$\\ $\rightarrow~~ \begin{pmatrix} 1&0\\0&1 \end{pmatrix}$ \end{tabular} \\ \hline \cellcolor{lightgray!50}\begin{tabular}{c}6\\$\circ$\end{tabular} & \begin{tabular}{l} $QT$\\ $\rightarrow~~ \begin{pmatrix} 1&0\\0&1 \end{pmatrix}$ \end{tabular} \\ \hline \cellcolor{lightgray!50}\begin{tabular}{c}7\\$\circ$\end{tabular} & \begin{tabular}{l} $D:=TMQ$\\ $\rightarrow~~ D:=\begin{pmatrix} 1&0\\0&\frac15 \end{pmatrix}$ \\[-0.5ex]\quad \end{tabular} \\ \hline \end{tabular} \end{tabular} \end{center} %En vous appuyant sur les résultats précédents, répondre aux deux questions suivantes : \begin{enumerate} \item %Justifier que $Q$ est une matrice inversible et préciser sa matrice inverse.\\ %On notera $Q^{-1}$ la matrice inverse de $Q$. Le déterminant de $Q$ est $9\times (-1)-7\times 1=-16\neq 0$ donc $Q$ est inversible. Alors $Q^{-1}=\dfrac{1}{-16}\begin{pmatrix}-1&-1\\-7&9\end{pmatrix}=\begin{pmatrix}\dfrac{1}{16}&\dfrac{1}{16}\\\dfrac{7}{16}&-\dfrac{9}{16}\end{pmatrix}$ \item %Justifier que $M=QDQ^{-1}$ et démontrer que, pour tout entier naturel $n$ non nul : %\[M^n=QD^nQ^{-1}.\] $QDQ^{-1}=\begin{pmatrix}9&1\\7&-1\end{pmatrix}\begin{pmatrix}1&0\\0&\dfrac{1}{5}\end{pmatrix}\begin{pmatrix}\dfrac{1}{16}&\dfrac{1}{16}\\\dfrac{7}{16}&-\dfrac{9}{16}\end{pmatrix}=\begin{pmatrix}9&\dfrac{1}{5}\\7&-\dfrac{1}{5}\end{pmatrix}\begin{pmatrix}\dfrac{1}{16}&\dfrac{1}{16}\\\dfrac{7}{16}&-\dfrac{9}{16}\end{pmatrix}=\begin{pmatrix}0,65&0,45\\0,35&0,55\end{pmatrix}=M$ donc $\boxed{\textcolor{red}{M=QDQ^{-1}}}$. \end{enumerate} \item On admet que, pour tout entier naturel $n$ non nul, \[ M^n=\frac{1}{16}\begin{pmatrix} 9+7\times\np{0,2}^n&9-9\times\np{0,2}^n\\ 7-7\times\np{0,2}^n&7+9\times\np{0,2}^n \end{pmatrix}. \] \begin{enumerate} \item %Démontrer que pour tout entier naturel $n$, $P_n=M^nP_0$. Démontrons par récurrence que, pour tout $n\in\mathbb{N}$, $P_n=M^nP_0$. \begin{enumerate}[$\bullet$] \item initislisation : Pour $n=0$, $M^0P_0=P_0$ donc la propriété est vraie au rang $0$. \item On suppose que $P_n=M^nP_0$ pour un entier $n$ quelconque. Alors : $P_{n+1}=MP_n=MM^nP_0=M^{n+1}P_0$ donc la propriété est héréditaire. \end{enumerate}`D'après l'axiome de récurrence, la propriété est vraie pour tout $n$. \item %Justifier que, pour tout entier naturel $n$: %\[ %\ell_n=\frac{9}{16}-\frac{13}{80}\times\np{0,2}^n. %\] Par conséquent : $M_n=\begin{pmatrix}l_n\\q_n\end{pmatrix}=M^nP_0=\frac{1}{16}\begin{pmatrix} 9+7\times\np{0,2}^n&9-9\times\np{0,2}^n\\ 7-7\times\np{0,2}^n&7+9\times\np{0,2}^n \end{pmatrix}\begin{pmatrix}0,4\\0,6\end{pmatrix}$. On en déduit que $\ell_n=\dfrac{1}{16}\left[9\times 0,4+7\times 0,2^n\times 0,4+9\times 0,6-9\times 0,6\times 0,2^n\right]=\dfrac{1}{16}\left(9-2,6\times 0,2^n\right)=\boxed{\textcolor{red}{\dfrac{9}{16}-\dfrac{13}{16}\times 0,2^n}}$. \end{enumerate} \item %La proportion de pêcheurs achetant la carte de pêche libre dépassera-t-elle 60~\%~? Pour tout $n$, $\ell_n\leqslant \dfrac{9}{16}=0,5625=\dfrac{56,25}{100}=56,25\:\%$ donc la proportion de pêcheurs achetant la carte de pêche libre ne dépasse pas 60\:\%. \end{enumerate} \label{fin} \end{document}
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http://alandb.darksky.org/search.php?sqlQuery=SELECT%20author%2C%20title%2C%20type%2C%20year%2C%20publication%2C%20abbrev_journal%2C%20volume%2C%20issue%2C%20pages%2C%20keywords%2C%20abstract%2C%20thesis%2C%20editor%2C%20publisher%2C%20place%2C%20abbrev_series_title%2C%20series_title%2C%20series_editor%2C%20series_volume%2C%20series_issue%2C%20edition%2C%20language%2C%20author_count%2C%20online_publication%2C%20online_citation%2C%20doi%2C%20serial%2C%20area%20FROM%20refs%20WHERE%20serial%20%3D%201364%20ORDER%20BY%20created_date%20DESC%2C%20created_time%20DESC%2C%20modified_date%20DESC%2C%20modified_time%20DESC%2C%20serial%20DESC&client=&formType=sqlSearch&submit=Cite&viewType=&showQuery=0&showLinks=1&showRows=5&rowOffset=&wrapResults=1&citeOrder=creation-date&citeStyle=APA&exportFormat=RIS&exportType=html&exportStylesheet=&citeType=LaTeX&headerMsg=	darksky.org	CC-MAIN-2020-10	application/x-latex	application/x-latex	crawl-data/CC-MAIN-2020-10/segments/1581875145989.45/warc/CC-MAIN-20200224224431-20200225014431-00019.warc.gz	8,376,990	1,396	%&LaTeX \documentclass{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{textcomp} \begin{document} \begin{thebibliography}{1} \bibitem{Shapira_etal2013} Shapira, I., Walker, E., Brunton, D. H., \& Raubenheimer, D. (2013). Responses to direct versus indirect cues of predation and competition in na\&$\#$970;ve invasive mice: implications for management. \textit{NZ J. of Ecol.}, \textit{37}(1), 33--40. \end{thebibliography} \end{document}
https://www.authorea.com/users/306619/articles/437594/download_latex	authorea.com	CC-MAIN-2022-05	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2022-05/segments/1642320304686.15/warc/CC-MAIN-20220124220008-20220125010008-00085.warc.gz	689,817,901	2,617	\documentclass[10pt]{article} \usepackage{fullpage} \usepackage{setspace} \usepackage{parskip} \usepackage{titlesec} \usepackage[section]{placeins} \usepackage{xcolor} \usepackage{breakcites} \usepackage{lineno} \usepackage{hyphenat} \PassOptionsToPackage{hyphens}{url} \usepackage[colorlinks = true, linkcolor = blue, urlcolor = blue, citecolor = blue, anchorcolor = blue]{hyperref} \usepackage{etoolbox} \makeatletter \patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{% \errmessage{\noexpand\@combinedblfloats could not be patched}% }% \makeatother \usepackage{natbib} \renewenvironment{abstract} {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize} {\bigskip} \titlespacing{\section}{0pt}{3}{1} \titlespacing{\subsection}{0pt}{2}{0.5} \titlespacing{\subsubsection}{0pt}{*1.5}{0pt} \usepackage{authblk} \usepackage{graphicx} \usepackage[space]{grffile} \usepackage{latexsym} \usepackage{textcomp} \usepackage{longtable} \usepackage{tabulary} \usepackage{booktabs,array,multirow} \usepackage{amsfonts,amsmath,amssymb} \providecommand\citet{\cite} \providecommand\citep{\cite} \providecommand\citealt{\cite} % You can conditionalize code for latexml or normal latex using this. \newif\iflatexml\latexmlfalse \providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}% \AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}} \usepackage[utf8]{inputenc} \usepackage[english]{babel} \usepackage{float} \begin{document} \title{An efficient meshless method based on the Moving Kriging interpolation for two-dimensional variable-order time-fractional mobile/immobile advection-diffusion model} \author[1]{Esmail Hesameddini}% \author[1]{Ali Habibirad}% \author[1]{Mohammad Hossein Heydari}% \author[2]{Reza Roohi}% \affil[1]{Shiraz University of Technology}% \affil[2]{Fasa University}% \vspace{-1em} \date{\today} \begingroup \let\center\flushleft \let\endcenter\endflushleft \maketitle \endgroup \selectlanguage{english} \begin{abstract} in this work, we introduce an efficient meshless technique for solving the two-dimensional variable-order time-fractional mobile/immobile advection-diffusion model with Dirichlet boundary conditions. The main advantage of this scheme is to obtain a global approximation for this problem which reduces such problems to a system of algebraic equations. To approximate the first and fractional variable-order against the time, we use the finite difference relations. The proposed method is based on the Moving Kriging (MK) interpolation shape functions. To discretization this model in space variables, we use the MK interpolation. Duo to the fact that the shape functions of MK have Kronecker's delta property, boundary conditions are imposed directly and easily. To illustrate the capability of the proposed technique on regular and irregular domains, several examples are presented in different kinds of domains and with uniform and nonuniform nodes. Also, we use this scheme to simulating anomalous contaminant diffusion in underground reservoirs.% \end{abstract}% \sloppy \textbf{Hosted file} \verb`Main.pdf` available at \url{https://authorea.com/users/306619/articles/437594-an-efficient-meshless-method-based-on-the-moving-kriging-interpolation-for-two-dimensional-variable-order-time-fractional-mobile-immobile-advection-diffusion-model}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/dom1/dom1} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/dom2/dom2} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/dom3/dom3} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/dom4/dom4} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/dom5/dom5} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/dom6/dom6} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/numexacex1/numexacex1} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/tnumex2/tnumex2} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/terrorex2axt/terrorex2axt} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/tnumex3/tnumex3} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/tabsoluteerror/tabsoluteerror} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Picture1/Picture1} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Picture2/Picture2} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/errorex1/errorex1} \end{center} \end{figure} \selectlanguage{english} \FloatBarrier \end{document}
https://www.authorea.com/users/143341/articles/326810/download_latex	authorea.com	CC-MAIN-2022-49	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2022-49/segments/1669446711336.41/warc/CC-MAIN-20221208114402-20221208144402-00866.warc.gz	666,926,151	7,833	\documentclass[10pt]{article} \usepackage{fullpage} \usepackage{setspace} \usepackage{parskip} \usepackage{titlesec} \usepackage[section]{placeins} \usepackage{xcolor} \usepackage{breakcites} \usepackage{lineno} \usepackage{hyphenat} \PassOptionsToPackage{hyphens}{url} \usepackage[colorlinks = true, linkcolor = blue, urlcolor = blue, citecolor = blue, anchorcolor = blue]{hyperref} \usepackage{etoolbox} \makeatletter \patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{% \errmessage{\noexpand\@combinedblfloats could not be patched}% }% \makeatother \usepackage[round]{natbib} \let\cite\citep \renewenvironment{abstract} {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize} {\bigskip} \titlespacing{\section}{0pt}{3}{1} \titlespacing{\subsection}{0pt}{2}{0.5} \titlespacing{\subsubsection}{0pt}{1.5}{0pt} \usepackage{authblk} \usepackage{graphicx} \usepackage[space]{grffile} \usepackage{latexsym} \usepackage{textcomp} \usepackage{longtable} \usepackage{tabulary} \usepackage{booktabs,array,multirow} \usepackage{amsfonts,amsmath,amssymb} \providecommand\citet{\cite} \providecommand\citep{\cite} \providecommand\citealt{\cite} % You can conditionalize code for latexml or normal latex using this. \newif\iflatexml\latexmlfalse \AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}} \usepackage[utf8]{inputenc} \usepackage[ngerman,english]{babel} \usepackage{siunitx} \usepackage{amsmath} \newcommand{\bra}[1]{\ensuremath{\left\langle#1\right\|}} \newcommand{\ket}[1]{\ensuremath{\left\|#1\right\rangle}} \newcommand{\braket}[1]{\ensuremath{\left\langle#1\right\rangle}} \newcommand{\rhohat}{\hat{\rho}} \newcommand{\tr}[1]{\mathrm{tr}(#1)} \newcommand{\trarb}[2]{\mathrm{tr}_{#1}(#2)} \newcommand{\vv}[1]{\mathbf{#1}} \newcommand\dif{\mathop{}\!\mathrm{d}} \newcommand{\eexp}[1]{\mathrm{e}^{#1}} \begin{document} \title{Lecture 12- Entanglement} \author[1]{Fred Jendrzejewski}% \author[2]{Selim Jochim}% \author[2]{Matthias Weidemüller}% \affil[1]{Kirchhoff-Institut für Physik}% \affil[2]{Physikalisches Institut der Universität Heidelberg}% \vspace{-1em} \date{\today} \begingroup \let\center\flushleft \let\endcenter\endflushleft \maketitle \endgroup \selectlanguage{english} \begin{abstract} We will discuss the creation of entangled photons and how they can be used for the test of Bell's inequalities.% \end{abstract}% \sloppy We have previously discussed how complicated gain media allow for the amplification light \cite{Jendrzejewski}. Here we will discuss how it is used to create entangled photons and then dive into the fundamental test of the Bell inequalities. \section{Parametric down-conversion} Fig. \ref{888919} shows the schematic setup of an experiment where pairs of entangled photons are created by a two-photon source. Two polarizers can be used to probe the polarization of the photons. \subsection{Three-wave mixing} The crystal in the medium is a non-linear crystal, which means that we can write the polarization is not just linear, but higher order terms will play a role. We will consider for starters that there are actually two pump waves in the same direction, which allows us to write: \begin{align} P_{NL}(z) = 2\epsilon_0 \chi^{(2)}\mathcal{E}_1(z)\mathcal{E}_2(z)e^{i(k_1+k_2)z} \end{align} This non-linear polarizability leads to the following equations of motion \cite{grynberg}: \begin{align} \frac{d\mathcal{E}_3}{dz}e^{ik_3 z} &= \frac{i\omega_3}{2\epsilon_0n_3c}P_{NL}(z) \\ \frac{d\mathcal{E}_3}{dz}&= \frac{i\omega_3}{n_3c}\chi^{(2)}\mathcal{E}_1(z)\mathcal{E}_2(z)e^{i(k_1+k_2-k_3)z} \\, \end{align} where $\omega_3 = \omega_1 + \omega_2$. We can now additionally assume that: \begin{itemize} \item The effect of the medium does not change the strong pump to much. \item The amplified field is zero initially. \item The oscillating phase factor $(k_1+k_2-k_3)z$ can be ignored, i.e. where we have: \begin{align} \vec{k}_3 = \vec{k}_1 + \vec{k}_2 \end{align} \end{itemize} We can then simplify to: \begin{align} \frac{d\mathcal{E}_3}{dz}&=\frac{i\omega_3 \chi^{(2)}}{n_3c}\mathcal{E}_1\mathcal{E}_2 \end{align} So the amplitude of the mixed field increases in a linear fashion in the non-linear medium. However, the typical amplitude for production is below 1\% for commonly used crystals. \section{Polarization entangled photons} We will try to observe correlations between the photons. Two optical fibers are collecting the pairs of photons and transmit them to the single photon detectors. Finite collection and detection efficiency causes only one of the two photons to be detected in most cases. Therefore, a coincidence circuit registers events in which two photons arrive within \num{30} \si{\nano \second}. As the rate of detected individual photons is about \num{50} \si{\kilo \hertz}, we assume that photons arriving during such a small time window were created in the same event.\selectlanguage{english} \begin{figure}[h!] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Bildschirmfoto-2018-10-01-um-07-20-45/Bildschirmfoto-2018-10-01-um-07-20-45} \caption{{a) The process of spontaneous parametric down-conversion (SPDC). Inside a nonlinear crystal, two outgoing photons are created from an incoming photon. Momentum and energy conservation apply, resulting in a characteristic emission cone. b) Two photons created by SPDC encounter polarizers. Depending on the polarization, the photons are either absorbed or transmitted. After passing the polarizers, the photons are collected with two optical fibers and detected with single photon counters. The detector indicates a coincidence when both photons arrive within roughly 30 ns. {\label{888919}}% }} \end{center} \end{figure} \subsection{Polarization analysis} To study the quantum nature of the correlations, we will employ polarizers and later dive into Bell's inequalities as well as entanglement in general. The interested reader will have a great time reading through the complement 5.C of \cite{grynberg}. The first emitted photon is analyzed by a rotatable polarizers $\hat{A}(\theta)$, which has two detection paths $\pm1$. The other polarizer will be called $\hat{B}(\theta)$ the only difference is that he only acts on photon 2. Basically, we are following the \textit{Alice} and \textit{Bob} notation here. We can express it then in our basis states of vertical polarization $\ket{V}$ and horizontal polarization $\ket{H}$. The polarizer aligned with $H$ has eigenvalues: \begin{align} \hat{A} \ket{H}= +\ket{H}\\ \hat{A} \ket{V}= -\ket{V} \end{align} To analyse the polarization of each photon in detail we can also rotate the polarizer by an angle of $\theta$. In this case the transmitted eigenstates are: \begin{align} \ket{\theta}_{+} &= \cos(\theta)\ket{H} +\sin(\theta)\ket{V}\\ \ket{\theta}_{-} &= -\sin(\theta)\ket{H} +\cos(\theta)\ket{V} \end{align} Taking as input states $\ket{H}$, we simply find Malus law: \begin{align} P_+(\theta) = \cos(\theta)^2\\ P_-(\theta) = \sin(\theta)^2\\ \end{align} In the rotated basis we can express the polarization operator as: \begin{align} \hat{A}(\theta) = \left(\begin{array}{cc} \cos(2\theta)& \sin(2\theta)\\ \sin(2\theta)& -\cos(2\theta) \end{array}\right) \end{align} We can now employ the two polarizers to investigate the two emitted photons as shown in Fig. \ref{762069}.\selectlanguage{english} \begin{figure}[h!] \begin{center} \includegraphics[width=0.98\columnwidth]{figures/Bildschirmfoto-2018-11-22-um-10-53-25/Bildschirmfoto-2018-11-22-um-10-53-25} \caption{{Polarization analysis of correlated photons {\label{762069}}% }} \end{center} \end{figure} The possible outcome of our experiments are the four states $\{HH, HV, VH, VV\}$ and hence we could decompose our full wavefunction as: \begin{align} \ket{\psi} &= c_0 \ket{HH}+ c_1 \ket{HV} + c_2 \ket{VH} + c_3\ket{VV} \end{align} Using the two polarizers we can now start to investigate the prefactors of the full wavefunction. Let us first look into the results of a polarizer that is not rotated. We find: \begin{align} \bra{\psi}\hat{A}\ket{\psi}&=\|c_0\|^2 + \|c_1\|^2 - \|c_2\|^2-\|c_3\|^2 \end{align} For Bobs polarizer in the same position we would find: \begin{align} \bra{\psi}\hat{B}\ket{\psi}&=\|c_0\|^2+ \|c_2\|^2 - \|c_1\|^2 -\|c_3\|^2 \end{align} \subsection{An equivalent 2 qubit circuit} The optics setup handles two independent photons, with two outcomes each. So we can also see the presented setup as a two qubit system. A circuit diagram would mostly look the following way.\selectlanguage{english} \begin{figure}[h!] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/TwoQubitsCircuit-01/TwoQubitsCircuit-01} \caption{{Realizing the two-photon experiment within a quantum circuit. What are the correlations the two photons have ? {\label{840060}}% }} \end{center} \end{figure} The two photons originate from an unknown source, which is here modelled by photons propagating through some unitary matrix $\hat{U}$. The measurement is performed in the last step, projecting the qubit on its up or down state. The rotation around the x axis $\hat{R}_x$ transforms a qubit state into a superposition. In strong analogy to the polarization \subsection{A naive guess} We know that we have two photons in the system. Both can have some polarization and clearly they are propagation in different directions. So it does not seems to much of a stretch to guess that the total wavefunction is the product of two superposition states: \begin{align}\label{Eq:Separable} \ket{\psi}_{p} &= (c_{H,1}\ket{H} +c_{V,1} \ket{V})\otimes(c_{H,2}\ket{H}+c_{V,2}\ket{V}) \\ &= (c_{H,1}c_{H,2}\ket{HH} + c_{V,1}c_{V,2}\ket{VV} + c_{V,1}c_{H,2}\ket{VH} + c_{H,1}c_{V,2}\ket{HV}) \end{align} \subsection{The experimental observation of entanglement} \begin{itemize} \item We find a lot of counts if both polarizers are set vertical or horizontal. So the state has a $VV$ and a $HH$ component, which tells us that $c_0$ and $c_{3}$ are non-zero. The equal rate of measuring further tells us that they are roughly similiar in amplitude, so we can write for simplicity $\|c_0\| = \|c_3\|$ \item We find zero correlation if the polarizers are opposite. So the mixed terms are zero $c_1 = c_2 = 0$ \end{itemize} In summary we can expect the state to be written as: \begin{align}\label{Eq:BellState} \ket{\psi_B} &= \frac{\ket{HH} +\ket{VV}}{\sqrt{2}} \end{align} This is quite clearly incompatible with our naive guess \eqref{Eq:Separable}, which means that we have an entangled state. \section{Optional: Quantifying entanglement} We will study the properties of the entangled states later in more detail. However, we will take a short moment to cite two ways of quanitfying the entanglement through the density operator: \begin{align} \hat{\rho} = \sum_i \eta_i \ket{i} \bra{i} \end{align} \begin{itemize} \item The reduced density operator, which shows mixed states if there is entanglement: \begin{align} \hat{\rho}_1 = \trarb{2}{\hat{\rho}} \end{align} In this case, $\hat{\rho}$ is the density operator of a pure state and $\textrm{tr}_2$ is the trace over the Hilbert space of particle \num{2}. \item The von Neumann entropy, which measures the remaining uncertainty within a quantum state: \begin{align} S&=-\tr{\hat{\rho}\ln\hat{\rho}}\\ &= - \sum_i \eta_i \ln \eta_i = \sum_i \eta_i \ln \frac{1}{\eta_i} \end{align} \end{itemize} For the Bell states of \eqref{Eq:BellState} we find then: \begin{align} \hat{\rho_B}_1 = \frac{1}{2} \left( \ket{H}\bra{H} + \ket{V}\bra{V} \right) \end{align} Its corresponding entropy is $S=\ln 2$, the entropy of a pure state is $S=0$. \section{Back to the correlation between distant photons} In the last sections we performed measurements on joined detection probabilities between two independent polarizers. Quite importantly we saw that: \begin{itemize} \item Each photon is in a superposition of $\ket{H}$ and $\ket{V}$. \item Both photons are always detected in the same polarization state. \item From Fig. \ref{762069} it seems as if 1 was a bit closer to the source than 2 \footnote{The exact order does not matter, but they are most certainly not at exactly the same distance from the source}. So 1 is detected a bit earlier and projected onto one of the two states. \item Yet, 2 seems to instantaneously on which polarization 1 was projected and choses the same one. \end{itemize} For our set-up the distances are small, but the same observations and arguments hold also for very large distances between the detectors. Einstein, Podolski and Rosen understood this long distance correlation and decided that something was funky about quantum mechanics \cite{Einstein_1935}. Therefore, the idea of an additional hidden shared parameter can be introduced to explain the correlations between distant objects. We will simply assume that the two photons have well-defined polarization with angle $\lambda$ from the starting point, yet this polarization varies randomly from pair to pair between 0 and $2\pi$. Hence we have uniform probability distribution $\rho(\lambda) = \frac{1}{2\pi}$. The measurement of the polarizers can then simply be modelled through \begin{align} A_{hv}(\lambda, \theta) =\text{sign}\left(\cos2 (\theta-\lambda)\right) \end{align} This model reproduces nicely all the tests that we ran previously. Namely, maximum detection for HH and VV as well as zero correlation for $HV$. They can be nicely compared through the correlation coefficient $E(\theta_1,\theta_2)$. The particularly perturbing case is that this simple model for hidden parameters works even perfectly well in the case of $45^\circ$ angles. So is there any measurable difference between our observations and the hidden variable models ?\selectlanguage{english} \begin{figure}[h!] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Bildschirmfoto-2018-11-23-um-13-49-41/Bildschirmfoto-2018-11-23-um-13-49-41} \caption{{Correlation coefficient as taken from~~\protect\cite{grynberg} {\label{649269}}% }} \end{center} \end{figure} \section{Bell's theorem} Bell posed the previous discussion on a more general and quite simple footing \cite{Bell_1964} and later extended by Clauser, Horner, Shimony, Holt \cite{Clauser_1969}. For the hidden parameter we need just a standard density distribution with: \begin{align} \rho(\lambda)\geq 0\\ \int d\lambda \rho(\lambda) = 1 \end{align} We additionally should describe the polarizer by some function that takes the value $\pm 1$ depending on the angle of the polarizer and the hidden variable: \begin{align} \|A(\lambda, \theta_1) \|= \|A(\lambda, \theta_2) \| =1 \end{align} In the experiment we now have two polarizers $A$ for Alice and $B$ for Bob, which we will allow to be in some position $\theta$ as visualized in Fig. \ref{617669}.\selectlanguage{english} \begin{figure}[h!] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/BellConfig-01/BellConfig-01} \caption{{A Bell experiment {\label{617669}}% }} \end{center} \end{figure} We will now calculate the the expectation value for joint detection: \begin{align} E(\theta_1, \theta_2)&=\overline{A(\theta_1)B(\theta_2)}-\overline{A(\theta_1)}~\overline{B(\theta_2)} \end{align} We can simplify further for equal probability of having H or V polarization, which leads too: \begin{align} E(\theta_1, \theta_2)&=\overline{A(\theta_1)B(\theta_2)}\\ &=\int d\lambda A(\lambda, \theta_1)B(\lambda, \theta_2) \end{align} Bells inequalities are then studying the correlations between photons in four different configuations: \begin{align} s(\lambda, \theta_1, \theta_1', \theta_2, \theta_2')&= A(\lambda, \theta_1)B(\lambda, \theta_2)-A(\lambda, \theta_1)B(\lambda, \theta_2') +A(\lambda, \theta_1')B(\lambda, \theta_2)+A(\lambda, \theta_1')B(\lambda, \theta_2')\\ &= A(\lambda, \theta_1)(B(\lambda, \theta_2)-B(\lambda, \theta_2'))+A(\lambda, \theta_1')(B(\lambda, \theta_2)+B(\lambda, \theta_2'))\\ &= \pm 2 \end{align} We actually have no access to the hidden parameter, so we are looking for its average value: \begin{align} S &= \int d\lambda \rho(\lambda) s(\lambda, \theta_1, \theta_1', \theta_2, \theta_2')\\ -2\leq S\leq 2 \end{align} And this value can now be measured experimentally as we can identify: \begin{align} S &= E(\theta_1, \theta_2)-E(\theta_1, \theta_2')+E(\theta_1', \theta_2)+E(\theta_1', \theta_2') \end{align} This is known as the Bell--Clauser--Horn--Shimony--Holt (CHSH) inequalities. \subsection{The inconsistency between hidden parameters and quantum mechanics} We can now go again through the predictions of quantum mechanics and test if there is a region of interest in which we should observe a violation of the CHSH inequalities. Actually there is an important configuration at which we should break them rather violantly namely for: \begin{align} \|\theta_1-\theta_2\| =\frac{\pi}{8}(22.5^\circ)\\ \|\theta_1'-\theta_2\| =\frac{\pi}{8}(22.5^\circ)\\ \|\theta_1'-\theta_2'\| =\frac{\pi}{8}(22.5^\circ)\\ \|\theta_1-\theta_2'\| =\frac{3\pi}{8}(67.5^\circ)\\ \end{align} Here, we expect to have $S= 2\sqrt{2}$. So to test Bells inequalities we have to measure the joint probabilities in rather unusual angles. This also explains why quantum mechanics and local hidden variables seem so similiar in this kind of experiments, the biggest differences are hard to see accidentally. \subsection{The experimental test} We can now study the correlations for the following configuration. \begin{align} \theta_1 = 0 \text{ and }\theta_1' = \frac{\pi}{4}\\ \theta_2 = \frac{\pi}{8} \text{ and }\theta_2' = \frac{3\pi}{8}\\ \end{align}\selectlanguage{english} \begin{figure}[h!] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/displaydata2/displaydata2} \caption{{Correlation measurement between the two photons measured with the setup shown in {\ref{888919}} b) and~{\ref{762069}}. One of the rotatable polarizers stays at an angle $\gamma \in \{ 0^\circ, 45^\circ, 90^\circ, 135^\circ \}$ while the other polarizer is rotated counter-clockwise in small steps between $0^{\circ}$ and $360^{\circ}$. {\label{358356}}% }} \end{center} \end{figure} Experimentally we observe quite frequently value above 2. However, please be aware that there are a lot of loopholes in our test. The most obvious ones are: \begin{enumerate} \tightlist \item Position of the polarizers is not random. \item The detectors are not well separated. \end{enumerate} Other loopholes exist, but all realistically known loopholes have been closed over the course of the last three decades. \cite{Giustina_2015,Shalm_2015,Hensen_2015}. \selectlanguage{english} \FloatBarrier \bibliographystyle{plainnat} \bibliography{bibliography/converted_to_latex.bib% } \end{document}
https://www.zentralblatt-math.org/matheduc/en/?id=79950&type=tex	zentralblatt-math.org	CC-MAIN-2019-43	text/plain	application/x-tex	crawl-data/CC-MAIN-2019-43/segments/1570986661296.12/warc/CC-MAIN-20191016014439-20191016041939-00173.warc.gz	1,202,305,618	1,370	\input zb-basic \input zb-matheduc \iteman{ZMATH 2000b.01013} \itemau{Seel, Norbert M.} \itemti{Educational diagnosis of mental models: assessment problems and technology-based solutions.} \itemso{J. Struct. Learn. Intell. Syst. 14, No. 2, 153-185 (1999).} \itemab This article focuses on central problems of the educational diagnosis of the learning-dependent progression of mental models. Thus, its main purpose is to describe assessment problems concerning the diagnosis of mental model progression in dependence on changing situations of teaching; to describe related problems of controlling the reliability and validity of `measurements of change' as they are involved necessarily in the diagnosis of mental model progression; and to elucidate the appropriateness of causal diagrams as a method to measure `subjective causal models' (discussed in terms of mental models) and their learning-dependent changes. Accordingly, causal diagrams are discussed with regard to the assessment of knowledge transitions and to their validation through structure equation models. Following a short description of procedures to control reliability and validity of causal diagrams, several problems to be still solved are sketched with regard to the educational diagnosis of subjective causal models with the help of causal diagrams. \itemrv{~} \itemcc{D60} \itemut{} \itemli{} \end
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\setlength\bibhang{8pt} \lefthyphenmin = 3 \makeatother \date{} \makeatletter \usepackage{mdframed} %\usepackage{balance} \definecolor{unitednationsblue}{RGB}{222,234,246} \definecolor{cpboxcolor}{RGB}{211,211,211} \definecolor{citeboxcolor}{RGB}{242,242,242} \def\printBio{% %\noindent\begin{mdframed}[innerbottommargin=7pt,backgroundcolor=unitednationsblue,hidealllines=true,frametitle={ABOUT AUTHORS},innerleftmargin=7pt,leftmargin=2pt,skipabove=1pt,innertopmargin=2pt,innerbottommargin=1pt,skipbelow=1pt]% \noindent\begin{mdframed}[innerbottommargin=7pt,backgroundcolor=unitednationsblue,hidealllines=true,frametitle={ABOUT AUTHORS},innerrightmargin=20pt,rightmargin=4,innerleftmargin=7pt,leftmargin=2pt,skipabove=1pt,innertopmargin=2pt,innerbottommargin=1pt,skipbelow=1pt]% \@tempcnta=0 \loop \advance \@tempcnta by 1 \def\aubioCnt{\the\@tempcnta} \vskip1pt % \noindent\hspace{-2pt}%\fbox{ % \vspace{1pt} \raisebox{62pt}%{\begin{minipage}[t]{.35\linewidth}% \expandafter\ifx\csname 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licensed under the identical terms.} \publishedDate{} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Feature enabled: %citation-style: unsrt %citation-type: numbered %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{float} \begin{document} \def\RunningAuthor{Pandala Archana et al.} \firstPage{1} \articleType{Case Report} \receivedDate{25 Nov 2021} \acceptedDate{12 Dec 2021} \revisedDate{11 Dec 2021} \journalVolume{1} \journalIssue{4} \copyrightYear{2021} \eISSN{XXXX-XXXX} \journalDoi{} \def\authorCount{6} \def\affCount{1} \def\journalTitle{International Journal of Clinical Pharmacokinetics and Medical Sciences} \title{A Case Report on Lymphedema} \author{Pandala~Archana\textsuperscript{}\textsuperscript{\href{https://orcid.org/0000-0002-1290-087X}{\XeTeXLinkBox{\includegraphics[height=7pt]{orcid-logo-pharmascope.pdf}}}}, Annabathula~Meghana\textsuperscript{\href{https://orcid.org/0000-0002-7651-3676}{\XeTeXLinkBox{\includegraphics[height=7pt]{orcid-logo-pharmascope.pdf}}}}, Hawashetty~Priyanka\textsuperscript{\href{https://orcid.org/0000-0003-3768-1420}{\XeTeXLinkBox{\includegraphics[height=7pt]{orcid-logo-pharmascope.pdf}}}}, Marella~Priyachandana\textsuperscript{\href{https://orcid.org/0000-0003-0259-0588}{\XeTeXLinkBox{\includegraphics[height=7pt]{orcid-logo-pharmascope.pdf}}}}, Allu~Sree~Reddy\textsuperscript{\href{https://orcid.org/0000-0002-6696-5310}{\XeTeXLinkBox{\includegraphics[height=7pt]{orcid-logo-pharmascope.pdf}}}}, Mogulla~Soujanya\textsuperscript{\href{https://orcid.org/0000-0001-8400-7864}{\XeTeXLinkBox{\includegraphics[height=7pt]{orcid-logo-pharmascope.pdf}}}}~\\[5pt]{St. Mary's Group of Institutions, Deshmukhi (Village), Pochampally (Mandal), Yadadri Bhuvanagiri (Dist)- 508284, Telangana, India}} \begin{abstract} Lymphedema can be a regarding approach about a disorder throughout the vascular system for which explanations femoral lump. Defective ingestion, as well as transportation containing lymph fluid via lymphatic vessels, cause accumulation of protein-wealthy liquid during interstitium, which results in traumatic inflammation of the overall femoral. Underived lymphedema will be regularly nominative at delivery. The rare instances that fact take the floor succeeding historic period 35 years will be terminated as lymphedema tarda. The amazing clients along with edema experience lump going from the decreased limbs top femoral edema will be a group a rare ailment. A 76-yr-old person was once provided along with type a 3-year record containing unilateral lump going from the leftover top limb. Would have been no constitutional indicators as well as no test copy of lymphadenopathy or fundamental skin disorder. Blood exams, carcinoembryonic antigen viva, computer-assisted tomography scans, and venous Doppler ultrasound had also altogether ordinary. The overall trend analysis becomes primary higher femoral lymphedema. The lump that happens in the upper femoral lymphedema is often unchangeable and generally expands up to the hand. Almost 1/3 of those who are victims of the aliment herewith state seem to be treated as well as decreased limb lymphedema. Investigations are going to be allowed in incidents containing unilateral top limb lymphedema to prevent hidden malignancy and intrinsic complaint. \end{abstract}\def\keywordstitle{Keywords} \begin{keywords}Lymphedema,\newline Upper Limb,\newline Systemic Ailment,\newline Swelling \end{keywords} \twocolumn[ \maketitle {\printKwdAbsBox}] \makeatletter{\raggedright{\Large$^\ast$}Corresponding Author\par Name:\ Pandala~Archana~\\ Phone:\ +91 6303015710~\\ Email:\ [email protected] \par}\vspace{-13pt}\hrulefill~\\{\fontsize{12}{14}\selectfont\ifx\@eISSN\@empty\else eISSN: \@eISSN\fi\ifx\@pISSN\@empty\else\hfill pISSN: \@pISSN\fi}\par% \textsc{DOI:}\ \href{https://doi.org/\@journalDoi}{\textcolor{blue}{\underline{\smash{https://doi.org/\@journalDoi}}}}\par% \vspace{-12pt}\hrulefill\\[5pt]\hypersetup{allcolors=black}\qrcode[version=4,height=1.5cm]{https://doi.org/\@journalDoi}\hypersetup{allcolors=blue} \hspace{10.5pt}\parbox[t]{5cm}{\raisebox{19pt}{\fontsize{9.12}{10.12}\selectfont Production and Hosted by}\\[-13pt]{{\fontsize{12}{14}\selectfont\raggedright Pharmasprings.com \\[-1pt]{\fontsize{9.12}{10.12}\selectfont\textcopyright\ \@copyrightYear\ $\|$ All rights reserved.}\\[-8pt]\hspace{-1pt}\rule{.762\columnwidth}{1.2pt}}}}\hypersetup{allcolors=blue}%{\fontsize{12}{14}\selectfont Pharmasprings.com}\par% \makeatother \section{Introduction} Primary top limb lymphedema serves as a rare entity. Almost all reviews about lymphedema affecting the extremities confer with a disorder of one's decreased limbs \unskip~\cite{1295027:23889172}. Incidents will be most of the time categorized since number one or secondary. Primary lymphedema is antiquatedly depicted in particular within the smaller limbs \unskip~\cite{1295027:23889206}. Powerful majority containing instances consisting of underived lymphedema tend to be notion to be nonheritable(congenital). Heritage outmoded set up in several events, and also a gene outmoded recognized in some lives \unskip~\cite{1295027:23889208,1295027:23889209}. Secondary lymphedema serves as some usually identified; relevant instants incorporate affaire of one's limb succeeding inguinal inspection but without therapy the treatment consisting of breast carcinoma \unskip~\cite{1295027:23889211}. Immediate or occipital dysplasia of lymphatics or disorderly hyperplasia outmoded represented \unskip~\cite{1295027:23889213}. Other than primary lymphedema some normally seems to be primal successful lifestyles, critiques containing the biography undergo defined resulting displays of congenital edema \unskip~\cite{1295027:23889246}. Edema happening after age 35 years is now and then often known as lymphedema tarda. A detailed medical assessment has to subtract secondary reasons for lymphedema. Lymphatic define in addition to lymphoscintigraphy is regularly finished to affirm the diagnosis however won't stand by essential inside the bulk containing incidents as soon as secondary reasons of lymphedema will be prohibited. The current document designates the general notecase containing a 76 year-2 months-old affected person along with unpredictable higher limb lymphedema \unskip~\cite{1295027:23889247}. \textbf{Case Presentation} A 76 year 2 months-vintage lady was provided to our health center with 4-11 months precedent days containing a lump of the proper higher femoral. There became nary related ache or intrinsical signs and symptoms. The affected person's precedent days become routine, and she or he stated nary suchlike family ancient times. Expect a mild lump of one's intact left top limb, findings in the investigation were ordinary [Figure~\ref{f-a38bd12a8c5e}]. She turned into in nary seeming distress. Her mucous had been red and wet, and her crucial symptoms had been regular. Work-study of the proper upper femoral (limb) discovered nontender, nonpitting edema. The temperature of a limb changed into ordinary, and there has been no state's evidence consisting of localized cellulitis. Heart rates have been detectable. The apparent venous machine became every day. There were no bizarre conclusions along with a motion study of one's breasts and axillae and nary state's evidence containing generalized lymphadenopathy. A temporary diagnosis containing number one top limb edema became prosperous [Figure~\ref{f-8feba2f2e7ca}]. A full analysis containing blood assessments becomes finished, which includes hematology, electrolytes, liver function, and carcinoembryonic antigen exams. Chest x-rays, contrast computed tomography scans containing the chest and abdomen in each arterial and venous level, and an upper limb blood vessel (venous) Doppler ultrasound had been additionally completed. Entirely consequences have been every day. Mammography findings had been every day. Since the lump changed into symptomless, the overall patient plummeted connive at work operating room nauseant. \bgroup \fixFloatSize{images/0b21272e-da09-4a18-a917-6f9e364b14e8-upicture1.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/0b21272e-da09-4a18-a917-6f9e364b14e8-upicture1.png}{\includegraphics{images/0b21272e-da09-4a18-a917-6f9e364b14e8-upicture1.png}}{} \makeatother \caption{\boldmath {Photograph of upper limbs showing swelling of the left side (dorsal aspect)}} \label{f-a38bd12a8c5e} \end{figure} \egroup \bgroup \fixFloatSize{images/e2e60c51-5ce8-4ce2-afcb-0fd63c81470c-upicture2.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/e2e60c51-5ce8-4ce2-afcb-0fd63c81470c-upicture2.png}{\includegraphics{images/e2e60c51-5ce8-4ce2-afcb-0fd63c81470c-upicture2.png}}{} \makeatother \caption{\boldmath {Photograph of upper limbs showing swelling of the left side (volar aspect)}} \label{f-8feba2f2e7ca} \end{figure} \egroup \section{DISCUSSION} Lymphedema come out from the buildup containing protein-wealthy liquid inside the membrane areas, which explains due to a huge in spite of lymph that exceeds lymphatic machine truking talents. Ordinary drain consisting of lymph within the top limbs tends to occur thru thin-walled lymphatic terminals, which ever drainpipe to axillary nodes. Primary lymphedema could be due to aplasia or hypoplasia containing lymphatics or utilizing renal sickness. Primary lymphedema outmoded hushed in the direction of through to three varieties on the overall prologuize containing age at surprise attack (onset). Lymphedema proposing at delivery may be referred that one may since congenital lymphedema (Milroy disease); from delivery as far as age 35 years, edema praecox (Meige disease); since age 35 years, lymphedema tarda. Primary lymphedema may have in addition also been related to whatever inherited syndromes and cutaneal problems, which come with pancake Turner syndrome, Klinefelter syndrome, and neurofibromatosis kind. Lymphedema outmoded reffered with in triplex websites inside the consistency (body), consisting containing the overall slighter limbs, torso, genital, head, and neck even participation going from intrinsic body parts were found out. Neverthless, preferred lymphedema does have in particular also been defined for arousing influence the decreased extremity. Secondary lymphedema, that's almost commonplace inside the slighter limbs, consequences taken away lymphatic vessel obstruction resulting from a pathogenesis that includes maliciousness, burns, radioactivity, injury, or incision. Elephantiasis, a mosquito-borne contamination resulting from the parasite Wuchereria bancrofti, in particular, includes the slighter limbs and is the overall maximum commonplace form of secondary lymphedema international. Studies containing primary lymphedema that included the higher limbs tend to be aspecial. All but situations containing higher limb lymphedema inside the biograghy comeout surgical lymph node incision for most cancers, malignant percolation, radioactivity, or injury. In girls, edema affiliated malignancy and is a common cause containing one sided limb lump. As a result of affiliation, malignancy has to be taken into consideration in all instances of one sided femoral lump. Ephithelial Ovarian cancer and Endometrial cancer have been most not unusual malignancy. An x-ray of the lymphatic system has superseded lymphography as option in reference to confirmative the diagnosis containing lymphedema. CAT scanner and nuclear magnetic resonance imaging were going to be really useful in indicating the nodule structure and have the additional advantage in reference to capable of leaving aside fundamental ailment. In case, an evaluation computed tomography scan turned into done along with prohibited the general presence of systemic disorder. Such a big amount of techniques as inhabiting lymphedema be mentioned in the literature. Many of those methods(strategies) will be comfirmative in place going from peace offering a specific treatment, further more the result have always been outcomes normally unpredictable. Conservative treatment plans have been tested, and variable residue, further more consist in reference to elevation, sequential compression device, gradient compression stockings, pumps, physical treatment, and rub down. Special strategies known as ``whole decongestive physiotherapy'' undergo additionally had encouraging results. The one in question technique may have fought a reputation in Europe Union as well as comprises multilayer compression bandaging, rubdown, and lengthy-term apply going from compressing garments as well as graded physical activities. Solid result are mentioned long time the one in question approach is administered by way of professional person practitioners. \section{CONCLUSION} Primary lymphedema of one's bigger femoral (higher limb) could be a rare phenomenon. Nearly all of circumstances will be unilateral, and lump (swelling) is often firm further more involves the general handwriting. Most 1/3 going from those who are victims of the aliment are going to be along with primary lymphedema attending and participation going from both upper along with decreased limbs. Serious research can be authorized in situations of individual higher limb lymphedema that one may prevent occult malignity and fundamental ailment. \section{ACKNOWLEDGEMENT\textbf{\space }} I would like to thanks Principal sir (Dr Kamal Hassan) St. Mary's Pharmacy College, Deshmukhi (Village), Pochampally (Mandal), Yadadri Bhuvanagiri (Dist)-508284, Telangana, India. \textbf{Conflict of Interest} \textbf{\space } The authors attest that they have no conflict of interest in this study. \textbf{Funding Support} \textbf{\space } The authors declare that there is no financial support for the current study. \balance \bibliographystyle{unsrt} \bibliography{\jobname}\vspace{20pt} \begin{mdframed}[backgroundcolor=cpboxcolor,hidealllines=true,innerbottommargin=7pt,innerrightmargin=1pt,rightmargin=1pt,innerleftmargin=1pt,leftmargin=2pt,skipabove=1pt,innertopmargin=2pt,innerbottommargin=1pt,skipbelow=1pt]% {\fontsize{8.5}{10}\selectfont\textbf{Copyright:}~\copyrightstmt} \end{mdframed} \begin{mdframed}[backgroundcolor=citeboxcolor,hidealllines=true,innerbottommargin=7pt,innerrightmargin=4pt,rightmargin=4pt,innerleftmargin=2pt,leftmargin=2pt,skipabove=1pt,innertopmargin=2pt,innerbottommargin=4pt,skipbelow=2pt]% {\fontsize{8.5}{10}\selectfont\textbf{Cite~this~article:}~\citeauthor.~\citetitle.\space\makeatletter\abbrvJournalTitle\ \@copyrightYear;\ \ifx\@journalVolume\@empty X\else\@journalVolume\fi\ifx\@journalIssue\@empty\else(\@journalIssue)\fi:\ \ifx\@firstPage\@empty 1\else\@firstPage\fi-\pageref{LastPage}.\makeatother} \end{mdframed} \vskip-1.1pc \vskip.5pc {\includegraphics[width=5cm]{pharmasprings_logo.png}} ~\\ {\fontsize{9.12}{10.12}\selectfont\textcopyright\ \makeatletter\@copyrightYear\makeatother\ Pharma Springs Publication.} \end{document}
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Ogawa ([email protected])% ^^J emulateapj.cls included, Copyright 2000-2015 Alexey Vikhlinin ^^J Rewrite and update of emulateapj.cls, revised and enhanced with table macros, gridlines, draft watermark,^^J track changes, new `modern' style and much more, by Amy Hendrickson,% ^^J ([email protected], http://www.texnology.com) ^^J ^^J }% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% aastex.cls version 2.0 is a based on emulateapj.cls, version January 23, 2015, %% and an older version of aastex.cls, with many additional functionalities. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Options. Document style options, and additional feature options. % These are the General document style options, 6 choices % manuscript : onecolumn, doublespace, 12pt fonts %% Preprints are like manuscript, except they are single spaced. % preprint : onecolumn, single space, 12pt fonts % preprint2 : twocolumn, single space, 12pt fonts %% Modern is new design developed by David Hogg and Daniel Foreman-Mackey % modern : one column, single space, 12pt fonts, more stylish % twocolumn : a two column article, single space, 10pt fonts % Default document style option % onecolumn : a one column article; single space, 10pt fonts %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Additional feature options: % revtex4 : will produce an error message and demand to download revtex4-1. % twocolappendix: make 2 column appendix // produces error message. % onecolappendix: make 1 column appendix is the default. // not needed because it is the default % astrosymb : Loads Astrosymb font and define \astro commands. % tighten : Makes baselineskip slightly smaller, only works with twocolumn option. %% author can also use the commands \tighten, or \singlespace or \doublespace in the body of their article %% to get this change to the baselineskip % times : uses times font as the default % linenumbers : turn on lineno package. % trackchanges : required to see the revision mark up and print output % letteredappendix: (was numbered appendix) Not needed because it is the default, will label appendix sections A, B, ... % numberedappendix: Legacy command, will produce same results as lettered appendix, since we don't want more % than one `section 1' in article: will cause problems for cross referencing. % anonymous: to not list authors/affiliations be listed \newif\ifmanu \newif\iftwelvepoint \newif\ifmodern \newif\ifdoublespace \newif\if@two@col \newif\ifonecolstyle \newif\iftwocolstyle \newif\ifrnaas %% makes modern the style for rnaas \DeclareOption{RNAAS}{\global\rnaastrue} \DeclareOption{rnaas}{\global\rnaastrue} \DeclareOption{manuscript}{\twelvepointtrue\@two@colfalse\doublespacetrue\manutrue}% %% Preprints are like manuscript but are single spaced: \newif\ifpreprint \DeclareOption{preprint}{\@two@colfalse\preprinttrue\twelvepointtrue}% \newif\ifpreprinttwo \DeclareOption{preprint2}{\@two@coltrue\preprinttwotrue\twelvepointtrue}% %% New design suggested by \DeclareOption{modern}{\@two@colfalse\twelvepointtrue\moderntrue} %% left in from older version, in case it could be useful: \DeclareOption{twocolumn}{\onecolstylefalse\twocolstyletrue\@two@coltrue\twelvepointfalse} %% default style \DeclareOption{onecolumn}{\onecolstyletrue\twocolstylefalse} %% obsolete option \DeclareOption{revtex4}{\typeout{=================^^J^^J!!! The revtex4 option no longer allowed!^^J^^J Please download revtex4-1.cls^^J^^J Thank-you!^^J^^J=================}\stop} \newif\if@two@col@app \DeclareOption{twocolappendix}{\@two@col@apptrue} \DeclareOption{onecolappendix}{\@two@col@appfalse}%% this is default \newif\iflongauthor \DeclareOption{longauthor}{\global\longauthortrue} \newlength{\bibbaselineskip}\setlength{\bibbaselineskip}{3.075mm} \DeclareOption{astrosymb}{ \def\astro#1{\leavevmode\hbox{\astro@font#1}}% \def\load@astro@font{% \iftwelvepoint \font\astro@font=astrosym at 8pt \else \font\astro@font=astrosym at 7pt \fi }% \AtBeginDocument{\load@astro@font} } %% Default definition for \astro, in case astrosymb option has not %% been used: \def\astro#1{\typeout{^^J^^J Please use class option `astrosymb' to access fonts for the \string\astro\space command ^^J^^J }\stop} \def\apjsecfont{\normalsize} \def\secnum@size{\small} \def\subsecnum@size{\normalsize} \def\AppendixApjSectionMarkInTitle#1{\relax} \newif\ifletteredappendix \DeclareOption{letteredappendix}{\global\letteredappendixtrue \def\AppendixApjSectionMarkInTitle#1{#1.\ } } %% this option is obsolete, since letteredappendix is a more logical name; %% but keeping it here in case someone uses it, set to be the same as %% letteredappendix. \DeclareOption{numberedappendix}{\global\letteredappendixtrue \def\AppendixApjSectionMarkInTitle#1{#1.\ } } \newif\if@number@appendix@floats\@number@appendix@floatsfalse \DeclareOption{appendixfloats}{ \@number@appendix@floatstrue } %%%%%%%%%%%%% %% AH %% This option changes the baselineskips in the definitions of \normalsize etc %% to make them a bit smaller. \newif\iftighten \DeclareOption{tighten}{\global\tightentrue} %% AH \newif\iftimes \DeclareOption{times}{\global\timestrue} \newif\ifnumlines \DeclareOption{linenumbers}{\global\numlinestrue} \newif\iftrack \DeclareOption{trackchanges}{\global\tracktrue} \newif\ifanonymous \DeclareOption{anonymous}{\global\anonymoustrue} %% End AH Options \ExecuteOptions{onecolumn,onecolappendix,letteredappendix}% \ProcessOptions %%%%%%%%%%%%% % \iftimes %% Might be better to use apjfonts, from Alexey Vikhlinin's website %% http://hea-www.harvard.edu/~alexey/emulateapj/apjfonts.sty %%\usepackage{apjfonts} %% but times.sty is ubiquitous, and many people may not have apjfonts.sty %% or the fonts that it calls. %% default fonts: \usepackage{times} \fi %%%%%%%%%%%%% \IfFileExists{revtex4-1.cls}{ \def\@revtex@cls{revtex4-1} }{ \typeout{^^J^^J Please update your system to include revtex4-1.cls^^J^^J}\stop } \def\@revtex@cls{revtex4-1} \let\@startsection@from@latex=\@startsection %% Passing options to revtex while loading: \iftwelvepoint \iflongauthor \LoadClass[nofootinbib,showkeys,twoside,floatfix,unsortedaddress,flushbottom,12pt,aps,pra] {\@revtex@cls} \else \LoadClass[nofootinbib,showkeys,twoside,floatfix,superscriptaddress,flushbottom,12pt,aps,pra] {\@revtex@cls} \fi \else %not twelvepoint \iflongauthor \LoadClass[nofootinbib,showkeys,twoside,floatfix,unsortedaddress,flushbottom,10pt,aps,pra] {\@revtex@cls} \else \LoadClass[nofootinbib,showkeys,twoside,floatfix,superscriptaddress,flushbottom,10pt,aps,pra] {\@revtex@cls} \fi \fi %%%%%%%%%%%%%%%%%%%% \def\blankaffiliation{~}% %% needed? \def\@eapj@cap@font{\bfseries} \def\@eapj@figname{Figure} \def\@eapj@tabname{Table} % Restore natbib package without sorting. \def\NAT@sort{0} \def\NAT@cmprs{0} % only redefine sort@cites for natbib versions < 2009 \@ifundefined{NAT@sort@cites@}{\def\NAT@sort@cites#1{\edef\NAT@cite@list{#1}}}% \RequirePackage{latexsym}% \RequirePackage{graphicx}% \RequirePackage{amssymb}% \newcommand{\bibstyle@aas}{\bibpunct{(}{)}{;}{a}{}{,}}% \@citestyle{aas}% \let\@startsection=\@startsection@from@latex \def\baselinestretch{1.0} %% Default vertical space between horizontal lines. Can change definition %% of arraystretch in the body of the paper; either for full article or %% for a single table. \AtBeginDocument{\def\arraystretch{1}} %% needed? \def\raggedcolumn@sw#1#2{#2} % implement flushbottom as it was in revtex4 \RequirePackage{epsf,graphicx} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Font families %% modification of bk10.clo, and bk12.clo, standard LaTeX distribution %% %% Implements doublespace used in `manuscript' option %% Implements `tighten' option: make baselineskip smaller if `tighten' is used %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% tighten only works with two column styles: \iftwocolstyle\else\global\tightenfalse\fi %%% preprint, preprint2, manuscript are 12pt %% Modified bk12.clo \iftwelvepoint \renewcommand\normalsize{% \ifdoublespace % manuscript \iftighten \@setfontsize\normalsize\@xiipt{20}% \else \@setfontsize\normalsize\@xiipt{24}% \fi \else \iftighten \@setfontsize\normalsize\@xiipt{13}% \else \ifmodern 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\else \@setfontsize\footnotesize\@xpt\@xiipt \fi\fi \abovedisplayskip 10\p@ \@plus2\p@ \@minus5\p@ \abovedisplayshortskip \z@ \@plus3\p@ \belowdisplayshortskip 6\p@ \@plus3\p@ \@minus3\p@ \def\@listi{\leftmargin\leftmargini \topsep 6\p@ \@plus2\p@ \@minus2\p@ \parsep 3\p@ \@plus2\p@ \@minus\p@ \itemsep \parsep}% \belowdisplayskip \abovedisplayskip } \ifdoublespace % manuscript style \renewcommand\scriptsize{\@setfontsize\scriptsize\@viiipt{14}} \renewcommand\tiny{\@setfontsize\tiny\@vipt{10}} \renewcommand\large{\@setfontsize\large\@xivpt{18}} \renewcommand\Large{\@setfontsize\Large\@xviipt{22}} \renewcommand\LARGE{\@setfontsize\LARGE\@xxpt{25}} \renewcommand\huge{\@setfontsize\huge\@xxvpt{30}} \else \renewcommand\scriptsize{\@setfontsize\scriptsize\@viiipt{9.5}} \renewcommand\tiny{\@setfontsize\tiny\@vipt\@viipt} \renewcommand\large{\@setfontsize\large\@xivpt{22}} \renewcommand\Large{\@setfontsize\Large\@xviipt{24}} \renewcommand\LARGE{\@setfontsize\LARGE\@xxpt{28}} \renewcommand\huge{\@setfontsize\huge\@xxvpt{30}} \fi \let\Huge=\huge %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \else %% not twelvepoint, now tenpoint %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% no doublespace here, because the only doublespace is in `manuscript style' which is 12pt \renewcommand\normalsize{% \iftighten \@setfontsize\normalsize\@xpt{11.5}% \else \@setfontsize\normalsize\@xpt{12.5}% \fi \abovedisplayskip 10\p@ \@plus2\p@ \@minus5\p@ \abovedisplayshortskip \z@ \@plus3\p@ \belowdisplayshortskip 6\p@ \@plus3\p@ \@minus3\p@ \belowdisplayskip \abovedisplayskip \let\@listi\@listI} \normalsize \renewcommand\small{% \iftighten \@setfontsize\small\@ixpt{12}% \else \@setfontsize\small\@ixpt{11}% \fi \abovedisplayskip 8.5\p@ \@plus3\p@ \@minus4\p@ \abovedisplayshortskip \z@ \@plus2\p@ \belowdisplayshortskip 4\p@ \@plus2\p@ \@minus2\p@ \def\@listi{\leftmargin\leftmargini \topsep 4\p@ \@plus2\p@ \@minus2\p@ \parsep 2\p@ \@plus\p@ \@minus\p@ \itemsep \parsep}% \belowdisplayskip \abovedisplayskip } \renewcommand\footnotesize{% \iftighten \@setfontsize\footnotesize\@viiipt{9}% \else \@setfontsize\footnotesize\@viiipt{9.5}% standard eightpoint size \fi \abovedisplayskip 6\p@ \@plus2\p@ \@minus4\p@ \abovedisplayshortskip \z@ \@plus\p@ \belowdisplayshortskip 3\p@ \@plus\p@ \@minus2\p@ \def\@listi{\leftmargin\leftmargini \topsep 3\p@ \@plus\p@ \@minus\p@ \parsep 2\p@ \@plus\p@ \@minus\p@ \itemsep \parsep}% \belowdisplayskip \abovedisplayskip } %% Standard 10pt font sizes \renewcommand\scriptsize{\@setfontsize\scriptsize\@viipt\@viiipt} \renewcommand\tiny{\@setfontsize\tiny\@vpt\@vipt} \renewcommand\large{\@setfontsize\large\@xiipt{14}} \renewcommand\Large{\@setfontsize\Large\@xivpt{18}} \renewcommand\LARGE{\@setfontsize\LARGE\@xviipt{22}} \renewcommand\huge{\@setfontsize\huge\@xxpt{25}} \renewcommand\Huge{\@setfontsize\Huge\@xxvpt{30}} \fi %% End font sizes %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \setlength\smallskipamount{3\p@ \@plus 1\p@ \@minus 1\p@} \setlength\medskipamount{6\p@ \@plus 2\p@ \@minus 2\p@} \setlength\bigskipamount{12\p@ \@plus 4\p@ \@minus 4\p@} \setlength\headheight{12\p@} \def\@listi{\leftmargin\leftmargini \parsep 4\p@ \@plus2\p@ \@minus\p@ \topsep 8\p@ \@plus2\p@ \@minus4\p@ \itemsep4\p@ \@plus2\p@ \@minus\p@} \let\@listI\@listi \@listi \def\@listii {\leftmargin\leftmarginii \labelwidth\leftmarginii \advance\labelwidth-\labelsep \topsep 4\p@ \@plus2\p@ \@minus\p@ \parsep 2\p@ \@plus\p@ \@minus\p@ \itemsep \parsep} \def\@listiii{\leftmargin\leftmarginiii \labelwidth\leftmarginiii \advance\labelwidth-\labelsep \topsep 2\p@ \@plus\p@\@minus\p@ \parsep \z@ \partopsep \p@ \@plus\z@ \@minus\p@ \itemsep \topsep} \def\@listiv {\leftmargin\leftmarginiv \labelwidth\leftmarginiv \advance\labelwidth-\labelsep} \def\@listv {\leftmargin\leftmarginv \labelwidth\leftmarginv \advance\labelwidth-\labelsep} \def\@listvi {\leftmargin\leftmarginvi \labelwidth\leftmarginvi \advance\labelwidth-\labelsep} % **************************************************** % * TWO AND SINGLE ONE COLUMN STYLES: AV * % ************************************************** % %%%%% include atbeginend.sty by AV: % Copy \begin and \end to \BeginEnvironment and \EndEnvironment \let\BeginEnvironment=\begin \let\EndEnvironment=\end %% \ifundefined from TeXbook \def\IfUnDef#1{\expandafter\ifx\csname#1\endcsname\relax} % Null command needed to eat its argument \def\NullCom#1{} \def\begin#1{% % if defined \BeforeBeg for this environment, execute it \IfUnDef{BeforeBeg#1}\else\csname BeforeBeg#1\endcsname\fi% \IfUnDef{AfterBeg#1}% This is done to skip the command for environments % which can take arguments, like multicols; YOU MUST NOT % USE \AfterBegin{...}{...} for such environments! \let\SaveBegEnd=\BeginEnvironment% \else % Start this environment \BeginEnvironment{#1}% % and execute code after \begin{environment} \csname AfterBeg#1\endcsname \let\SaveBegEnd=\NullCom \fi \SaveBegEnd{#1} } \def\end#1{% % execute code before \end{environment} \IfUnDef{BeforeEnd#1}\else\csname BeforeEnd#1\endcsname\fi% % close this environment \EndEnvironment{#1} % and execute code after \begin{environment} \IfUnDef{AfterEnd#1}\else\csname AfterEnd#1\endcsname\fi% } \long\def\BeforeBegin#1#2{\expandafter\gdef\csname BeforeBeg#1\endcsname {#2}} \long\def\BeforeEnd #1#2{\expandafter\gdef\csname BeforeEnd#1\endcsname {#2}} \long\def\AfterBegin #1#2{\expandafter\gdef\csname AfterBeg#1\endcsname {#2}} \long\def\AfterEnd #1#2{\expandafter\gdef\csname AfterEnd#1\endcsname{#2}} %%%% end of atbeginend.sty % ************************************** % * PAGE LAYOUT * % **************************************** % Page size, spacing parameters, etc. \textwidth=7.1in \columnsep=0.3125in \parindent=0.125in \voffset=-20mm \hoffset=-7.5mm \topmargin=0in \headheight=.15in \headsep=0.5in \oddsidemargin=0in \evensidemargin=0in \parskip=0cm \tolerance=600 % 3x "normal" value; cuts down on overfull complaints %% AV,MM, to have 64 lines per column, with textheight 25cm: \textheight=64\baselineskip \textheight=\baselinestretch\textheight \ifdim\textheight>25.2cm\textheight=25.0cm\fi %% so that the margin at the bottom of the page is about equal to margin at top. -- AH \advance\textheight -54pt \topskip\baselineskip \maxdepth\baselineskip \def\eqsecnum{ \@newctr{equation}[section] \def\theequation{\hbox{\normalsize\arabic{section}-\arabic{equation}}}} %% running heads: \def\lefthead#1{\gdef\@versohead{#1}} \lefthead{\relax} \def\righthead#1{\ifanonymous\gdef\@rectohead{Anonymous author(s)}\else\gdef\@rectohead{#1}\fi} \righthead{\relax} \let\shorttitle\lefthead \let\shortauthors\righthead \def\ps@apjheads{\let\@mkboth\markboth \def\@evenfoot{} \def\@evenhead{\lower9mm\hbox to\textwidth{% \rm\thepage\hfill\textsc{\@rectohead}\hfill}}} \def\@oddfoot{} \def\@oddhead{\lower9mm\hbox to\textwidth{ \hfil\rm\textsc{\@versohead}\hfil \rm\thepage}} \pagestyle{apjheads} \@twosidetrue %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % TITLE PAGE % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% October 2017, adding preprint number capability \newcount\rptnum \newcount\rptloopnum \def\reportnum#1{\global\advance\rptnum by 1 \expandafter\gdef\csname report\the\rptnum\endcsname{\hbox to \textwidth{\hskip.75\textwidth\relax#1\relax\hfill}}} \long\def\frontmatter@title@above{ \ifrnaas \vspace{-\headsep}\vspace{\headheight} \footnotesize \noindent{\sc Draft version \today}\\[2pt] {\footnotesize Typeset using \LaTeX\ {\bf RNAAS} style in AASTeX631} \par\vspace{-\baselineskip}\vspace{0.625in} \else \vbox to 0pt{\vskip-48pt\normalsize\rptloopnum=0\loop \global\advance\rptloopnum by 1 \expandafter\ifx\csname report\the\rptloopnum\endcsname\relax \else \csname report\the\rptloopnum\endcsname \vskip1pt \repeat \vss } \ifmodern \vglue-18pt {\footnotesize \raggedright {\sc Draft version \today}\\[2pt] {\footnotesize Typeset using \LaTeX\ {\bf modern} style in AASTeX631} \vskip48pt } \else %% \ifpreprint \vspace{-\headsep}\vspace{\headheight} \footnotesize \noindent{\sc Draft version \today}\\[2pt] {\footnotesize Typeset using \LaTeX\ {\bf preprint} style in AASTeX631} \par\vspace{-\baselineskip}\vspace{0.625in} \else %% \ifpreprinttwo \vspace{-\headsep}\vspace{\headheight} \footnotesize {\footnotesize\textsc{\@journalinfo}}\par {\footnotesize Typeset using \LaTeX\ {\bf preprint2} style in AASTeX631} \par\vspace{-\baselineskip}\vspace{0.625in} \else %% \iftwocolstyle \vspace{-\headsep}\vspace{\headheight} \footnotesize {\footnotesize\textsc{\@journalinfo}}\par {\footnotesize Typeset using \LaTeX\ {\bf twocolumn} style in AASTeX631} \par\vspace{-\baselineskip}\vspace{0.625in} \else \ifmanu \vspace{-\headsep}\vspace{\headheight} \footnotesize \noindent\textsc{\@journalinfo}\\[-8pt] {\footnotesize Typeset using \LaTeX\ {\bf manuscript} style in AASTeX631} \par\vspace{-\baselineskip}\vspace{0.625in} \else %% Default \vspace{-\headsep}\vspace{\headheight} \footnotesize {\footnotesize\textsc{\@journalinfo}}\par {\footnotesize Typeset using \LaTeX\ default style in AASTeX631}%% default style \par\vspace{-\baselineskip}\vspace{0.625in} \fi\fi\fi\fi\fi %% \fi %% ends test to see if rnaas option was used; if rnaas is true %% none of this command will be activated. }% \def\frontmatter@title@produce{% \begingroup \ifnumlines\nolinenumbers\fi \frontmatter@title@above \frontmatter@title@format \@title %% October 2017, was +12pt \@ifx{\@title@aux\@title@aux@cleared}{}{% \ifanonymous\else%% added may 20, 2020 \expandafter\frontmatter@footnote\expandafter{\@title@aux}% \fi }% \par %% \class@warn{Unused short title ignored}% \ifmodern \vskip-42pt \else \ifmanu \vskip-60pt \else \frontmatter@title@below \fi \fi \endgroup }% \newcount\fncount \newcount\endfncount \long\def\tempfootnote#1{\global\advance\fncount by 1\relax% \expandafter\gdef\csname footnote\the\fncount\endcsname{\if@two@col\hsize=.5\textwidth \advance\hsize by -18pt \fi\relax#1}} \def\tempfootnoteintitle#1{} \long\def\ltx@foottext#1#2{% \begingroup \expandafter\ltx@make@current@footnote\expandafter{\@mpfn}{#1}% \@footnotetext{\vtop{\iftwocolstyle\hsize=.5\textwidth \advance\hsize-18pt \fi #2\vskip2pt}}% fixed for two col style, march 15, 2019 \endgroup }% \def\kickoutfootnotes{\c@footnote=0\relax% \loop\advance\endfncount by 1\relax% \expandafter\ifx\csname footnote\the\endfncount\endcsname\relax% \else% \def\thempfn{\fnsymbol{footnote}}% \advance\c@footnote by 1\relax% \unskip\footnote{\csname footnote\the\endfncount\endcsname}% \repeat} %% \renewcommand\title[2][]{% \def\@title{\setbox0=\vbox{\let\footnote\tempfootnote #2}% {\let\footnote\tempfootnoteintitle%\uppercase {#2}}%% right place for kickoutfootnotes below \kickoutfootnotes \ifdoublespace\vskip 3\baselineskip\fi }% \def\@shorttitle{#1}% \let\@AF@join\@title@join }% \def\frontmatter@title@format{ %% No exception for rnaas, May, 2019 %\ifrnaas %\large\scshape\centering %\else \normalsize %% added Mar 2019 \bf\centering %\fi } \def\frontmatter@title@below{\vskip8pt}% \def\frontmatter@authorformat{\small\advance\baselineskip-3pt \parskip=0pt\ifrnaas\else\scshape\fi \ifmodern \vskip48pt \centering \leftskip=.05in plus 1fil \rightskip=.05in plus 1 fil \baselineskip=13pt \else \centering \fi }% \def\frontmatter@affiliationfont{\normalfont\footnotesize %% changed october 2017 \it \iflongauthor\else \ifrnaas\else \rightskip-12pt plus 1fil \leftskip6pt \parindent-4pt \fi\fi }% \def\frontmatter@finalspace{\ifrnaas\vspace{-\baselineskip}\vspace{0.0in} \else \vskip-24pt\fi} \def\@separator{\\}% \newcounter{front@matter@foot@note}\setcounter{front@matter@foot@note}{0} \iflongauthor% \renewcommand\affiliation[1]{% \parskip=2pt \def\@centercr{\vrule depth 3pt width0pt\vskip1sp} \move@AU\move@AF% \iflongauthor\let\@listand\relax\fi \begingroup% \@affiliation{%\hspace{2mm} \ifnum\countauthors<\AuthorCollaborationLimit #1\ifmodern\iflongauthor\baselineskip=12pt\else\vskip2pt\fi\else\baselineskip=11pt \fi\fi \ifnum\countauthors=\AuthorCollaborationLimit #1\ifmodern\iflongauthor\baselineskip=12pt\else\vskip2pt\fi\else\baselineskip=11pt \fi\fi \iflongauthor \vskip-10pt\ifnum\countauthors>\AuthorCollaborationLimit\iftwelvepoint\vskip-3pt\else\iftwocolstyle\else\vskip-6pt\fi\fi\fi% \fi }% \let\@centercr\savecentercr}% \else %% older version \renewcommand\affiliation[1]{% \move@AU\move@AF% \begingroup% \@affiliation{%\hspace{2mm} %% october 2017 changes: \centering #1\ifmodern \baselineskip=9.5pt \else \iftwelvepoint \ifpreprint\baselineskip=12pt\else\ifpreprinttwo\else\baselineskip19pt\fi\fi\else \baselineskip=9.5pt\fi \fi}% }% \fi %% end switch for longauthor % ABSTRACT \def\frontmatter@abstractfont{\normalsize\parindent=9pt }% %% october 2017 \def\frontmatter@abstractwidth{478pt} \def\frontmatter@preabstractspace{12pt} \def\frontmatter@postabstractspace{12pt} \def\abstractname{ABSTRACT} \long\def\frontmatter@abstractheading{% \begingroup \centering \ifmodern\else\hskip34pt \fi \abstractname \vskip 1mm \par \endgroup }% \newif\ifabstract% \renewenvironment{frontmatter@abstract}{% \aftermaketitle@chk{\begin{abstract}}% \global\abstracttrue \global\setbox\absbox\vbox\bgroup \color@begingroup %% width of abstract changed oct 2017 \ifmodern \columnwidth\textwidth \hsize\columnwidth \else \hsize = 478pt \fi \@parboxrestore \def\@mpfn{mpfootnote}\def\thempfn{\thempfootnote)}\c@mpfootnote\z@ % should be footnote, not mpfootnote? % \let\@footnotetext\frontmatter@footnotetext \minipagefootnote@init \let\set@listindent\set@listindent@ \let\@listdepth\@mplistdepth \@mplistdepth\z@ \let@environment{description}{frontmatter@description}% \@minipagerestore \@setminipage \frontmatter@abstractheading \frontmatter@abstractfont % \let\footnote\mini@note \ifmodern\else\everypar={\leftskip=34pt}\fi % \expandafter\everypar\expandafter{\the\everypar\addcontents@abstract\everypar{}}% \ifnumlines\let\go\linenumbers\else\let\go\relax\fi\go }{% \ifnumlines\let\go\endlinenumbers\else\let\go\relax\fi\go \par \unskip \minipagefootnote@here \@minipagefalse %% added 24 May 89 \color@endgroup \egroup% end setbox\absbox }% \let\abstract\frontmatter@abstract \def\frontmatter@abstract@produce{% \par \preprintsty@sw{% \do@output@MVL{% \vskip\frontmatter@preabstractspace \vskip200\p@\@plus1fil \penalty-200\relax \vskip-200\p@\@plus-1fil }% }{% \addvspace{\frontmatter@preabstractspace}% }% \begingroup \dimen@\baselineskip \setbox\z@\vtop{\unvcopy\absbox}% \advance\dimen@-\ht\z@\advance\dimen@-\prevdepth \@ifdim{\dimen@>\z@}{\vskip\dimen@}{}% \endgroup \begingroup \prep@absbox %% centered, oct 2017 \unvbox\absbox \post@absbox \endgroup \@ifx{\@empty\mini@notes}{}{\mini@notes\par}% \addvspace\frontmatter@postabstractspace \global\abstractfalse \vskip12pt }% \newif\ifbib % **************************************** % * KEYWORDS * % **************************************** \def\@keys@name{\textit{Keywords:}\/~\mbox{}}% \newlength{\keys@width} \def\frontmatter@keys@format{\ifmodern\vskip0pt\else\vspace{0.5mm}\fi% \settowidth{\keys@width}{\normalsize\@keys@name}% \ifmodern\else \rightskip=0.5in \leftskip=34pt \fi \parindent=0pt% \hangindent=\keys@width\hangafter=1\normalsize}% \def\@keywords@produce#1{% \showKEYS@sw{% \begingroup% \frontmatter@keys@format% \@keys@name#1 \vrule depth 12pt width 0pt \ifnobreakafterkeywords \vrule depth 24pt width0pt\fi \par \endgroup }{% \@if@empty{#1}{}{% \class@warn{If you want your keywords to appear in your output, use document class option showkeys}% }% }% }% \let\subjectheadings=\keywords % *************************************** % * FOOTNOTES * % **************************************** %% legacy notes and footnote code % Footnotes on the last page: user issues \lastpagefootnotes. It catches all % footnotes and issues them before \begin{refernces} or % \begin{\thebibliography} or \begin{appendix}, whichever comes first, % at the end of right column. \newcounter{lastfootnote} \let\orig@footnote=\footnote % \def\spit@out@footnotes@{\addtocounter{footnote}{-\c@lastfootnote}\vspace{-\baselineskip}\vspace{\skip\footins}\bgroup\footnotesize\lastfootnote\par\egroup\let\footnote=\orig@footnote} % \let\spit@out@footnotes\relax % \long\def\lastpagefootnotes{% \raggedbottom% Have to use flushbottom with revtex4-1 but it eats away % last page footnotes \setcounter{lastfootnote}{0} \long\gdef\lastfootnote{\mbox{}} \let\spit@out@footnotes\spit@out@footnotes@ \long\def\footnote##1{\refstepcounter{lastfootnote}\footnotemark\g@addto@macro\lastfootnote{\\[\footnotesep]\refstepcounter{footnote}\mbox{}\hspace{3mm}\textsuperscript{\thefootnote}~##1}} % We need to mess with footnotes in appendix only if it is in a % different mode (twocol vs onecol) than the main text \def\mess@with@appendix@footnotes{ \BeforeBegin{appendix}{\spit@out@footnotes\let\spit@out@footnotes\relax} \BeforeEnd{appendix}{\spit@out@footnotes\let\spit@out@footnotes\relax} \AfterEnd{appendix}{\let\footnote=\orig@footnote} } \if@two@col \if@two@col@app\else \mess@with@appendix@footnotes \fi \fi \BeforeBegin{references}{\spit@out@footnotes\let\spit@out@footnotes\relax} \BeforeBegin{thebibliography}{\spit@out@footnotes\let\spit@out@footnotes\relax} % in case \lastpagefootnotes were given inside \begin{appendix}\end{appendix}, \AfterEnd{references}{\let\footnote=\orig@footnote} \AfterEnd{thebibliography}{\let\footnote=\orig@footnote} } \let\lastpagefootnote=\lastpagefootnotes %% probably not needed: \def\notetoeditor#1{}% % We do not need notes to editor in the preprint \def\placetable#1{}% % We do not need notes to editor in the preprint \def\placefigure#1{}% % We do not need notes to editor in the preprint %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \ifdoublespace %used for manuscript \footnotesep 12pt \skip\footins 36pt \else \footnotesep 12pt \skip\footins 24pt \fi \let\footnoterule\relax \def\@makefntext#1{\hsize=\columnwidth\mbox{}\hspace{3mm}\@makefnmark~#1} % **************************************** % * SECTIONS * % **************************************** \setcounter{secnumdepth}{3} \newcount\tempsectnum \newif\if@firstsection \@firstsectiontrue \def\section{% \ifanonymous\nocollaboration{0}\fi \if@firstsection %% In case no collaboration is listed: \ifcollaborationon\else\let\doauthor\olddoauthor \ifanonymous \else \let\allauthors=\oldallauthors\fi \fi %\edef\currauthorlimit{\the\AuthorCollaborationLimit} %\collaboration{\currauthorlimit}{} \maketitle \global\@firstsectionfalse \setcounter{footnote}{\thefront@matter@foot@note}% \let\footnotetext=\old@foot@note@text \let\footnotemark=\old@foot@note@mark \ifnobreakafterkeywords \ifmodern\vskip24pt \else \vskip12pt\fi%% \goodbreak \else \ifrnaas\else \clearpage\fi \fi \if@two@col \twocolumngrid \fi \fi \tempsectnum=\the\c@section \advance\tempsectnum by 1 \xdef\cref@currentlabel{section \the\tempsectnum} \@startsection{section}{1}{\z@}{9pt plus 1pt minus 1pt}{4pt}{\apjsecfont\center}} \def\subsection{\@startsection{subsection}{2}{\z@}{9pt plus 1pt minus 1pt}{4pt}% {\normalsize\itshape \center}} \def\subsubsection{\@startsection{subsubsection}{3}{\z@}% {2ex plus 1ex minus .2ex}{1ex plus .2ex}{\small\itshape \center}} \def\paragraph{\@startsection{paragraph}{4}{\z@}% {1.5ex plus 1ex minus .2ex}{0pt}{\small\itshape}} \def\subparagraph{\@startsection{subparagraph}{5}{\z@}% {1ex plus 1ex minus .2ex}{-0.5\parindent}{\small\itshape}} \def\thesection{\arabic{section}} \def\thesubsection{\thesection.\arabic{subsection}} \def\thesubsubsection{\thesubsection.\arabic{subsubsection}} \def\theparagraph{\thesubsubsection.\arabic{paragraph}} \def\p@section {} \def\p@subsection {} \def\p@subsubsection {} \def\p@paragraph {} \def\p@subparagraph {} \def\sec@upcase#1{\uppercase{#1}} \def\subsec@upcase#1{\relax{#1}} % % How the section number will appear in the section title - AV \def\ApjSectionMarkInTitle#1{\ifrnaas\else #1.\ \fi} \def\ApjSectionpenalty{0} \def\@sect#1#2#3#4#5#6[#7]#8% {\ifnum#2=1\setbox0=\hbox{\def\label##1{\gdef\templabel{##1}}#7}\fi \@tempskipa #5\relax \ifdim \@tempskipa >\z@ \begingroup #6\relax \ifnum #2>\c@secnumdepth \def \@svsec {}\else \refstepcounter{#1} \edef \@svsec {\ApjSectionMarkInTitle {\csname the#1\endcsname}}\fi \@hangfrom {\hskip #3\relax \ifnum #2=1{\secnum@size {\rm\@svsec~}}% \else {\subsecnum@size {\rm\@svsec~}}\fi }% {\interlinepenalty \@M \ifnum #2=1\sec@upcase{#8}% \else \subsec@upcase{#8}\fi\par}\endgroup \csname #1mark\endcsname {#7}\addcontentsline{toc}{#1}% {\ifnum #2>\c@secnumdepth \else \protect \numberline {\csname the#1\endcsname }\fi #7}% \else \ifnum #2>\c@secnumdepth \def \@svsec {}\else \refstepcounter{#1} \edef \@svsec {\ApjSectionMarkInTitle {\csname the#1\endcsname}}\fi \def \@svsechd {#6\hskip #3% \ifnum #2=1{\secnum@size{\rm\@svsec~}}\else{\subsecnum@size{\rm\@svsec~}}\fi% \ifnum #2=1\sec@upcase{#8}\else\subsec@upcase{#8}\fi% \ifnum #2=4\hskip 0.4ex{\rm ---}\fi% \csname #1mark\endcsname {#7}\addcontentsline{toc}{#1}% {\ifnum #2>\c@secnumdepth \else \protect \numberline {\csname the#1\endcsname }\fi #7}}\fi \@xsect {#5} \penalty \ApjSectionpenalty %-refstepcounter is now within a group. So \@currentlabel, which is normally %-set by \refstepcounter is hidden within a group. Need to set it manually. \protected@edef\@currentlabel{\csname p@#1\endcsname\csname the#1\endcsname} \expandafter\ifx\csname templabel\endcsname\relax \let\go\relax \else \def\go{\label{\templabel}}\fi\go \let\templabel\relax } \def\@ssect#1#2#3#4#5{\@tempskipa #3\relax \ifdim \@tempskipa>\z@ \begingroup #4\@hangfrom{\hskip #1}{\interlinepenalty \@M \sec@upcase{#5}\par}\endgroup \else \def\@svsechd{#4\hskip #1\relax \sec@upcase{#5}}\fi \@xsect{#3} % MM: \penalty \ApjSectionpenalty} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% changed to begin...end form, May 20,2020, AH %% Acknowledgments, use \begin{acknowledgments}...\end{acknowledgments} %% or \begin{acknowledgements}...\end{acknowledgements} {\catcode`#=12 \gdef\hashmark{#}} \def\xacknowledgments{acknowledgments} \def\xacknowledgements{acknowledgements} \newbox\ackbox \def\acknowledgments{% \ifx\@currenvir\xacknowledgments\let\go\relax\else \let\go\stop \typeout{x^^J^^J^^J^^J^^J^^J^^J^^J ===================^^J In AASTeX v6.3.1 the \string\acknowledgments\space command has been deprecated.^^J^^J Instead, please use the begin/end form:^^J^^J "\string\begin\string{acknowledgments\string}...\string\end\string{acknowledgments\string}"^^J^^J when using acknowledgments.^^J^^J See here: \url{https://journals.aas.org/aastexguide/\hashmark acknowledgments} ^^J^^J for more details.^^J ===================^^J }% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Printed error \vskip12pt \hrule height 1pt \vskip12pt \noindent ERROR: In AASTeX v6.3.1 the {\tt\string\acknowledgments} command has been deprecated.\\ Instead, please use the begin/end form:\\ {\tt \string\begin\string{acknowledgments\string}...\string\end\string{acknowledgments\string}}\\ when using acknowledgments. For more details, see:\\ \url{https://journals.aas.org/aastexguide/\hashmark acknowledgments} % \fi\go %% \global\setbox\ackbox=\vbox\bgroup \expandafter\ifx\csname internallinenumbers\endcsname\relax\else \begin{internallinenumbers} \fi \vskip 5.8mm plus 1mm minus 1mm \vskip1sp %\section{Acknowledgments} \noindent\ignorespaces} \def\endacknowledgments{ \expandafter\ifx\csname internallinenumbers\endcsname\relax\else \end{internallinenumbers} \fi \egroup%% completes ackbox \ifanonymous \vskip 5.8mm plus 1mm minus 1mm \vskip1sp %\section{Acknowledgments} \centerline{(Acknowledgments anonymized for review)} \else \vbox{\unvbox\ackbox} \fi\vskip6pt} %% alternate spelling \def\acknowledgements{% \ifx\@currenvir\xacknowledgements\let\go\relax\else \let\go\stop \typeout{x^^J^^J^^J^^J^^J^^J^^J^^J ===================^^J In AASTeX v6.3.1 the \string\acknowledgements\space command has been deprecated.^^J^^J Please use the begin/end form:^^J^^J "\string\begin\string{acknowledgements\string}...\string\end\string{acknowledgements\string}"^^J^^J when using acknowledgements.^^J^^J See here: \href{https://journals.aas.org/aastexguide/\hashmark acknowledgments} {https://journals.aas.org/aastexguide/\hashmark acknowledgments} ^^J^^J for more details.^^J ===================^^J }% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Printed error \vskip12pt \hrule height 1pt \vskip12pt \noindent ERROR: In AASTeX v6.3.1 the {\tt\string\acknowledgements} command has been deprecated.\\ Instead, please use the begin/end form:\\ {\tt \string\begin\string{acknowledgements\string}...\string\end\string{acknowledgements\string}}\\ For more details, see:\\ \url{https://journals.aas.org/aastexguide/\hashmark acknowledgments} % \fi\go %% \global\setbox\ackbox=\vbox\bgroup \expandafter\ifx\csname internallinenumbers\endcsname\relax\else \begin{internallinenumbers} \fi \vskip 5.8mm plus 1mm minus 1mm \vskip1sp %\section{Acknowledgments} \noindent\ignorespaces} \def\endacknowledgements{ \expandafter\ifx\csname internallinenumbers\endcsname\relax\else \end{internallinenumbers} \fi \egroup%% completes ackbox \ifanonymous \vskip 5.8mm plus 1mm minus 1mm \vskip1sp %\section{Acknowledgements} \centerline{(Acknowledgements anonymized for review)} \else \vbox{\unvbox\ackbox} \fi\vskip6pt} % **************************************** % * APPENDIX * % ************************************** \newcounter{remember@figure@num} \newcounter{remember@table@num} % this was an environment earlier, which doesn't make sense since we don't % do \begin{appendix}...\end{appendix}. Changed to \appendix which is how it is used. % numberedappendix: Needed to label appendix sections A, B, . % appendixfloats: Needed. ?? \newif\ifappendixon \def\appendix{\global\appendixontrue \if@two@col \onecolumngrid \noindent\mbox{}\vrule height 24pt width0pt\hfill{\apjsecfont APPENDIX}\hfill\mbox{}\par \vskip18pt \if@two@col@app\global\@two@coltrue\twocolumngrid \fi % above, we want onecolumngrid to be default. Only twocolumn is asked for in documentclass option \else \noindent\mbox{}\vrule height 24pt width0pt\hfill{\apjsecfont APPENDIX}\hfill\mbox{}\par \vskip18pt \if@two@col@app\global\@two@coltrue\twocolumngrid \fi\fi % \vrule used for extra space; otherwise revtex4-1 sometimes eats % away the last line before appendix \nopagebreak\medskip\@nobreaktrue\def\ApjSectionpenalty{\@M} \@firstsectionfalse \setcounter{section}{0} \setcounter{subsection}{0} \setcounter{equation}{0} %% \ifletteredappendix \def\thesection{\Alph{section}} \def\theequation{\hbox{\Alph{section}\arabic{equation}}} %% these are NOT supposed to reset to zero %\setcounter{table}{0} %\setcounter{figure}{0} \fi %% \if@number@appendix@floats % we don't want to set equations to zero in appendix, because there % might then be two equation 1's, etc., confusing for cross referencing. %\setcounter{equation}{0} \def\thesection{\Alph{section}} \def\theequation{\hbox{\Alph{section}\arabic{equation}}} \def\section{\@startsection {section}{1}{\z@} {10pt}{5pt}{\centering\scshape\apjsecfont}} \else % Do not use appendix numbers in the titles \def\ApjSectionMarkInTitle{\AppendixApjSectionMarkInTitle} \fi \ifappletter \let\savesection\section \def\section{\resetapptablenumbers\savesection} \fi } % %% % ************************************** % * BIBLIOGRAPHY * % **************************************** \renewenvironment{references}[0]{ \onecolumngrid \par \vspace{10pt plus 3pt} \noindent \makebox[\textwidth][c]{\small\scshape REFERENCES} \par \vspace{4pt plus 3pt} \set@column@hsize{2}\twocolumngrid %% Jan29, 2021, added \ifonecolstyle, \ifpreprinttwo \ifnumlines \ifonecolstyle \ifpreprinttwo\else \advance\linenumbersep-12pt\fi\fi\fi \parindent=0cm \parskip=0cm \def\baselinestretch{1.0} \footnotesize \baselineskip=\baselinestretch\bibbaselineskip plus 1pt minus 1pt \interlinepenalty \@M \hyphenpenalty=10000 \frenchspacing % AV - to get right spacing after ``et al.'' \def\refpar{\par\hangindent=1.2em\hangafter=1}} { \onecolumngrid } % redefine thebibliography % remove numbers from the reference list \def\@biblabel#1{\relax} \newskip\bibskip \bibskip=0pt plus 1pt \let\savebibitem\bibitem \def\bibitem{\vskip\bibskip\savebibitem} \newdimen\bibindent \renewenvironment{thebibliography}[1]{\global\bibtrue %%\ifrnaas\newpage\fi% Not wanted, March 2019 \onecolumngrid \vspace{20pt} \goodbreak \hbox to\textwidth{\hss\normalsize REFERENCES\hss} \vspace{6pt}\parskip=0pt \twocolumngrid %% Jan29, 2021, added \ifonecolstyle \ifnumlines \ifonecolstyle \ifpreprinttwo\else \advance\linenumbersep-12pt\fi\fi\fi \par \raggedright \small \ifmodern\else \vspace{10pt plus 3pt}\fi \par \topsep=0pt \list{}% { \parindent=0pt \parskip=1pt plus 1pt \parsep=0pt % AV \bibindent=0pt % \ifmodern\vskip-12pt \baselineskip=13pt plus 1pt \else \ifdoublespace \baselineskip=20pt \else \baselineskip=13pt plus 1pt \fi\fi \interlinepenalty \@M % AV \frenchspacing % AV - to get right spacing after ``et al.'' \hyphenpenalty=10000 \itemindent=-1.0em % \itemsep=0pt % \listparindent=0pt % \settowidth\labelwidth{0pt} % \labelsep=0pt % \leftmargin=1.0em \advance\leftmargin\labelsep %%% \usecounter{enumiv}% \let\p@enumiv\@empty \renewcommand\theenumiv{\relax}}% \sloppy\clubpenalty10000\widowpenalty10000% \sfcode`\.\@m\relax %%%\item[] This May be necessary, but causes extra vertical space in first column %%% of the bibliography. } {\def\@noitemerr {\@latex@warning{Empty `thebibliography' environment}}% \endlist \onecolumngrid % to balance references \global\bibfalse \newpage } % %% AV: \def\reference{\@ifnextchar\bgroup {\@reference} {\@latexerr{Missing key on reference command} {Each reference command should have a key corresponding to a markcite somewhere in the text}}} \def\@reference#1{\refpar} %% subtitle header and journal info, legacy, probably not needed % \def\submitted#1{\gdef\@submitted{#1}} % \let\slugcomment\submitted % slugcomment == submitted % \submitted{Draft version \today} % \journalinfo{\@submitted} \def\journalinfo#1{\gdef\@journalinfo{#1}} \journalinfo{Draft version \today} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Equations % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % EQNARRAY with reduced spacing around tab characters - AV \def\eqnarray{% \stepcounter{equation}% \def\@currentlabel{\p@equation\theequation}% \global\@eqnswtrue \setlength{\arraycolsep}{0.25\arraycolsep} \m@th \global\@eqcnt\z@ \tabskip\@centering \let\\\@eqncr $$\everycr{}\halign to\displaywidth\bgroup \hskip\@centering$\displaystyle\tabskip\z@skip{##}$\@eqnsel &\global\@eqcnt\@ne\hskip \tw@\arraycolsep \hfil${##}$\hfil &\global\@eqcnt\tw@ \hskip \tw@\arraycolsep $\displaystyle{##}$\hfil\tabskip\@centering &\global\@eqcnt\thr@@ \hb@xt@\z@\bgroup\hss##\egroup \tabskip\z@skip \cr } % *************************************** % * TABLES AND FIGURES * % **************************************** \def\@arstrut@hline@clnc{0.5\p@}% % Klootch: magic number \setcounter{topnumber}{7} \setlength{\belowcaptionskip}{4pt}% \setlength{\abovecaptionskip}{5pt} \setlength{\textfloatsep}{9pt} \setlength{\dbltextfloatsep}{0pt} % \addtolength{\textfloatsep}{17mm plus 10mm minus 10mm} % \addtolength{\dbltextfloatsep}{7mm plus 10mm minus 10mm} \renewcommand{\topfraction}{1.0} \renewcommand{\bottomfraction}{1.0} \renewcommand{\textfraction}{0.0} \renewcommand{\dbltopfraction}{0.85} \renewcommand{\dblfloatpagefraction}{0.85} \setcounter{topnumber}{9} \setcounter{bottomnumber}{9} \setcounter{totalnumber}{20} \setcounter{dbltopnumber}{9} % Copied from revtex4.cls; without it, captions are centered \def\@xfloat@prep{% \let\footnote\footnote@latex \def\@mpfn{mpfootnote}% \def\thempfn{\thempfootnote}% \c@mpfootnote\z@ \let\@footnotetext\@mpfootnotetext \let\H@@footnotetext\@mpfootnotetext \let\@makefntext\@mpmakefntext }% %%%%%%%%%%%% \cutinhead %% Number of \pt@ncol set when \tablecolumns{} used at beginning of %% deluxetable. \def\@ptabularcr{\\} \newcommand\cutinhead[1]{% \noalign{\vskip 1.5ex}% \hline \@ptabularcr \noalign{\vskip -1.5ex}% \multicolumn{\pt@ncol}{c}{#1}% \@ptabularcr \noalign{\vskip .8ex}% \hline \@ptabularcr \noalign{\vskip -2ex}% }% \newcommand\sidehead[1]{% \noalign{\vskip 1.5ex}% % \hline % \@ptabularcr % \noalign{\vskip -1.5ex}% \multicolumn{\pt@ncol}{l}{#1}% \@ptabularcr \noalign{\vskip .8ex}% % \hline % \@ptabularcr % \noalign{\vskip -2ex}% }% %% these don't seem to be relevant: \newcommand\figcaption{\@testopt{\@xfigcaption}{}}% %% suggested by Joern Wilms \def\@figcaption#1{{\def\@captype{figure}\caption{\footnotesize #1}}} \def\@xfigcaption[#1]#2{{\def\@captype{figure}\caption{\footnotesize #2}}} \def\thefigure{\@arabic\c@figure} \def\fnum@figure{{\footnotesize{\@eapj@cap@font\rm \mbox{\@eapj@figname~\thefigure}% <== was period here }}} \def\thetable{\@arabic\c@table} %%% Table captions without making a floating table \def\tabcaption{\@ifnextchar[{\@xtabcaption}{\@tabcaption}} \def\@tabcaption#1{{\def\@captype{table}\caption{#1}}} \def\@xtabcaption[#1]#2{{\def\@captype{table}\caption{#2}}} %% redefined below \def\fnum@table{{\@eapj@cap@font \@eapj@tabname~\thetable}} \let\fnum@ptable=\fnum@table \def\fnum@ptablecont{{\centering{\scshape Table~\thetable}---{\itshape Continued}}}% \long\def\@make@caption@text#1#2{% {\small\centering#1{\scshape #2}\par\vskip1.4ex} }% \long\def\@makecaption@plano@cont#1#2{% {\small \centering#1\par}\vskip1.4ex\relax }% %% Commands from aastex.cls: % This has been redefined below %\newcommand\dataset{\@testopt\@dataset{[}}% %\def\@dataset[#1]#2{#2}% \newcommand\facility{\@testopt\@facility{[}}% \def\@facility[#1]#2{{\vskip6pt{\large\it Facility:} #2}}% \newcommand\facilities{\@testopt\@facilities{[}}% \def\@facilities[#1]#2{{\vskip6pt{\large\it Facilities:} #2}}% \long\def\software{\bgroup\@testopt \@software {[}} \def\@software[#1]#2{\vskip 6pt{ \frenchspacing \iftwelvepoint \font\foo=cmr12 \else \font\foo=cmr10\fi %% \fontdimen2\foo=3pt %% Changed from 1.5pt to 3pt, March12, 2019 %% {\large \it Software: } #2 %% returning to original fontdimen \iftwelvepoint \fontdimen2\foo=3.91663pt \else \fontdimen2\foo=3.33333pt \fi }\egroup} \newcommand\object{\@testopt\@object{[}}% \def\@object[#1]#2{#2}% \newcommand\objectname{\@testopt\@objectname{[]}}% \def\@objectname[#1]#2{#2}% \newlength{\plot@width} \def\eps@scaling{1.0}% \newcommand\epsscale[1]{\def\eps@scaling{#1}}% \newcommand\plotone[1]{% \centering \leavevmode \setlength{\plot@width}{0.85\linewidth} \includegraphics[width={\eps@scaling\plot@width}]{#1}% }% \newcommand\plottwo[2]{% \centering \leavevmode \setlength{\plot@width}{0.425\linewidth} \includegraphics[width={\eps@scaling\plot@width}]{#1}% \hfil \includegraphics[width={\eps@scaling\plot@width}]{#2}% }% \newcommand\plotfiddle[7]{% \centering \leavevmode \vbox\@to#2{\rule{\z@}{#2}}% \includegraphics[% scale=#4, angle=#3, origin=c ]{#1}% }% \newcommand\figurenum[1]{% \def\thefigure{#1}% \let\@currentlabel\thefigure \addtocounter{figure}{\m@ne}% }% \newcommand\phn{\phantom{0}}% \newcommand\phd{\phantom{.}}% \newcommand\phs{\phantom{$-$}}% \newcommand\phm[1]{\phantom{#1}}% \let\la=\lesssim % For Springer A&A compliance... \let\ga=\gtrsim \newcommand\sq{\mbox{\rlap{$\sqcap$}$\sqcup$}}% \newcommand\arcdeg{\mbox{$^\circ$}}% \newcommand\arcmin{\mbox{$^\prime$}}% \newcommand\arcsec{\mbox{$^{\prime\prime}$}}% \newcommand\fd{\mbox{$.\!\!^{\mathrm d}$}}% \newcommand\fh{\mbox{$.\!\!^{\mathrm h}$}}% \newcommand\fm{\mbox{$.\!\!^{\mathrm m}$}}% \newcommand\fs{\mbox{$.\!\!^{\mathrm s}$}}% \newcommand\fdg{\mbox{$.\!\!^\circ$}}% \newcommand\farcm@mss{\mbox{$.\mkern-4mu^\prime$}}% \let\farcm\farcm@mss \newcommand\farcs@mss{\mbox{$.\!\!^{\prime\prime}$}}% \let\farcs\farcs@mss \newcommand\fp{\mbox{$.\!\!^{\scriptscriptstyle\mathrm p}$}}% \newcommand\micron{\mbox{$\mu$m}}% \def\farcm@apj{% \mbox{.\kern -0.7ex\raisebox{.9ex}{\scriptsize$\prime$}}% }% \def\farcs@apj{% \mbox{% \kern 0.13ex.% \kern -0.95ex\raisebox{.9ex}{\scriptsize$\prime\prime$}% \kern -0.1ex% }% }% \newcommand\ion[2]{#1$\;${% \ifx\@currsize\normalsize\small \else \ifx\@currsize\small\footnotesize \else \ifx\@currsize\footnotesize\scriptsize \else \ifx\@currsize\scriptsize\tiny \else \ifx\@currsize\large\normalsize \else \ifx\@currsize\Large\large \fi\fi\fi\fi\fi\fi \rmfamily\@Roman{#2}}\relax}% \renewcommand\case[2]{\mbox{$\frac{#1}{#2}$}}% \renewcommand\slantfrac{\case}% \newcommand\onehalf{\slantfrac{1}{2}}% \newcommand\onethird{\slantfrac{1}{3}}% \newcommand\twothirds{\slantfrac{2}{3}}% \newcommand\onequarter{\slantfrac{1}{4}}% \newcommand\threequarters{\slantfrac{3}{4}}% \newcommand\ubvr{\mbox{$U\!BV\!R$}}%% UBVR system \newcommand\ub{\mbox{$U\!-\!B$}}% % U-B \newcommand\bv{\mbox{$B\!-\!V$}}% % B-V \renewcommand\vr{\mbox{$V\!-\!R$}}% % V-R \newcommand\ur{\mbox{$U\!-\!R$}}% % U-R %% need this change so that it works correctly in tables: {\catcode`\$=\active \gdef\nodata{ ~$\cdots$~ }}% \newcommand\diameter{\ooalign{\hfil/\hfil\crcr\mathhexbox20D}}% \newcommand\degr{\arcdeg}% \newcommand\Sun{\sun}% \newcommand\Sol{\sun}% \newcommand\sun{\odot}% \newcommand\Mercury{\astro{\char1}}% Mercury symbol, "1" \newcommand\Venus{\astro{\char2}}% Venus symbol, "2" \newcommand\Earth{\earth}% \newcommand\Terra{\earth}% \newcommand\earth{\oplus}% \newcommand\Mars{\astro{\char4}}% Mars symbol, "4" \newcommand\Jupiter{\astro{\char5}}% Jupiter symbol, "5" \newcommand\Saturn{\astro{\char6}}% Saturn symbol, "6" \newcommand\Uranus{\astro{\char7}}% Uranus symbol, "7" \newcommand\Neptune{\astro{\char8}}% Neptune symbol, "8" \newcommand\Pluto{\astro{\char9}}% Pluo symbol, "9" \newcommand\Moon{\astro{\char10}}% Moon symbol, "M" \newcommand\Luna{\Moon}% \newcommand\Aries{\astro{\char11}}% \newcommand\VEq{\Aries}% vernal equinox (Aries) \newcommand\Taurus{\astro{\char12}}% \newcommand\Gemini{\astro{\char13}}% \newcommand\Cancer{\astro{\char14}}% \newcommand\Leo{\astro{\char15}}% \newcommand\Virgo{\astro{\char16}}% \newcommand\Libra{\astro{\char17}}% \newcommand\AEq{\Libra}% autumnal equinox (Libra) \newcommand\Scorpius{\astro{\char18}}% \newcommand\Sagittarius{\astro{\char19}}% \newcommand\Capricornus{\astro{\char20}}% \newcommand\Aquarius{\astro{\char21}}% \newcommand\Pisces{\astro{\char22}}% \newcommand\sbond{\chem@bnd{\@sbnd}}% \newcommand\dbond{\chem@bnd{\@dbnd}}% \newcommand\tbond{\chem@bnd{\@tbnd}}% \def\chem@bnd#1{% {% \kern.1em\relax \setbox\z@\hbox{M}% \[email protected]\relax \p@=.1em\relax \[email protected]\ht\z@\dimen@i-\dimen@ \advance\[email protected]\p@\advance\[email protected]\p@ #1% \kern.1em\relax }% }% \def\@sbnd{% \advance\[email protected]\p@\advance\[email protected]\p@ \vrule\@height\dimen@\@depth\dimen@i\@width\dimen@ii\nobreak }% \def\@dbnd{% \advance\[email protected]\p@\advance\[email protected]\p@ \vrule\@height\dimen@\@depth\dimen@i\@width\dimen@ii\nobreak \advance\[email protected]\p@\advance\[email protected]\p@ \hskip-\dimen@ii \vrule\@height\dimen@\@depth\dimen@i\@width\dimen@ii\nobreak }% \def\@tbnd{% \vrule\@height\dimen@\@depth\dimen@i\@width\dimen@ii\nobreak \advance\[email protected]\p@\advance\[email protected]\p@ \hskip-\dimen@ii \vrule\@height\dimen@\@depth\dimen@i\@width\dimen@ii\nobreak \advance\[email protected]\p@\advance\[email protected]\p@ \hskip-\dimen@ii \vrule\@height\dimen@\@depth\dimen@i\@width\dimen@ii\nobreak }% %\newcommand\anchor[2]{#2}% %\renewcommand\url{\@dblarg\@url}% %\def\@url[#1]{\anchor{#1}}% \let\jnl@style=\rmfamily \def\ref@jnl#1{{\jnl@style#1}}% \newcommand\aj{\ref@jnl{AJ}}% % Astronomical Journal \newcommand\psj{\ref@jnl{PSJ}}% % Planetary Science Journal \newcommand\araa{\ref@jnl{ARA\&A}}% % Annual Review of Astron and Astrophys \renewcommand\apj{\ref@jnl{ApJ}}% % Astrophysical Journal \newcommand\apjl{\ref@jnl{ApJL}} % Astrophysical Journal, Letters \newcommand\apjs{\ref@jnl{ApJS}}% % Astrophysical Journal, Supplement \renewcommand\ao{\ref@jnl{ApOpt}}% % Applied Optics \newcommand\apss{\ref@jnl{Ap\&SS}}% % Astrophysics and Space Science \newcommand\aap{\ref@jnl{A\&A}}% % Astronomy and Astrophysics \newcommand\aapr{\ref@jnl{A\&A~Rv}}% % Astronomy and Astrophysics Reviews \newcommand\aaps{\ref@jnl{A\&AS}}% % Astronomy and Astrophysics, Supplement \newcommand\azh{\ref@jnl{AZh}}% % Astronomicheskii Zhurnal \newcommand\baas{\ref@jnl{BAAS}}% % Bulletin of the AAS \newcommand\icarus{\ref@jnl{Icarus}}% % Icarus \newcommand\jaavso{\ref@jnl{JAAVSO}} % The Journal of the American Association of Variable Star Observers \newcommand\jrasc{\ref@jnl{JRASC}}% % Journal of the RAS of Canada \newcommand\memras{\ref@jnl{MmRAS}}% % Memoirs of the RAS \newcommand\mnras{\ref@jnl{MNRAS}}% % Monthly Notices of the RAS \renewcommand\pra{\ref@jnl{PhRvA}}% % Physical Review A: General Physics \renewcommand\prb{\ref@jnl{PhRvB}}% % Physical Review B: Solid State \renewcommand\prc{\ref@jnl{PhRvC}}% % Physical Review C \renewcommand\prd{\ref@jnl{PhRvD}}% % Physical Review D \renewcommand\pre{\ref@jnl{PhRvE}}% % Physical Review E \renewcommand\prl{\ref@jnl{PhRvL}}% % Physical Review Letters \newcommand\pasp{\ref@jnl{PASP}}% % Publications of the ASP \newcommand\pasj{\ref@jnl{PASJ}}% % Publications of the ASJ \newcommand\qjras{\ref@jnl{QJRAS}}% % Quarterly Journal of the RAS \newcommand\skytel{\ref@jnl{S\&T}}% % Sky and Telescope \newcommand\solphys{\ref@jnl{SoPh}}% % Solar Physics \newcommand\sovast{\ref@jnl{Soviet~Ast.}}% % Soviet Astronomy \newcommand\ssr{\ref@jnl{SSRv}}% % Space Science Reviews \newcommand\zap{\ref@jnl{ZA}}% % Zeitschrift fuer Astrophysik \renewcommand\nat{\ref@jnl{Nature}}% % Nature \newcommand\iaucirc{\ref@jnl{IAUC}}% % IAU Cirulars \newcommand\aplett{\ref@jnl{Astrophys.~Lett.}}% % Astrophysics Letters \newcommand\apspr{\ref@jnl{Astrophys.~Space~Phys.~Res.}}% % Astrophysics Space Physics Research \newcommand\bain{\ref@jnl{BAN}}% % Bulletin Astronomical Institute of the Netherlands \newcommand\fcp{\ref@jnl{FCPh}}% % Fundamental Cosmic Physics \newcommand\gca{\ref@jnl{GeoCoA}}% % Geochimica Cosmochimica Acta \newcommand\grl{\ref@jnl{Geophys.~Res.~Lett.}}% % Geophysics Research Letters \renewcommand\jcp{\ref@jnl{JChPh}}% % Journal of Chemical Physics \newcommand\jgr{\ref@jnl{J.~Geophys.~Res.}}% % Journal of Geophysics Research \newcommand\jqsrt{\ref@jnl{JQSRT}}% % Journal of Quantitiative Spectroscopy and Radiative Trasfer \newcommand\memsai{\ref@jnl{MmSAI}}% % Mem. Societa Astronomica Italiana \newcommand\nphysa{\ref@jnl{NuPhA}}% % Nuclear Physics A \newcommand\physrep{\ref@jnl{PhR}}% % Physics Reports \newcommand\physscr{\ref@jnl{PhyS}}% % Physica Scripta \newcommand\planss{\ref@jnl{Planet.~Space~Sci.}}% % Planetary Space Science \newcommand\procspie{\ref@jnl{Proc.~SPIE}}% % Proceedings of the SPIE \newcommand\actaa{\ref@jnl{AcA}}% % Acta Astronomica \newcommand\caa{\ref@jnl{ChA\&A}}% % Chinese Astronomy and Astrophysics \newcommand\cjaa{\ref@jnl{ChJA\&A}}% % Chinese Journal of Astronomy and Astrophysics \newcommand\jcap{\ref@jnl{JCAP}}% % Journal of Cosmology and Astroparticle Physics \newcommand\na{\ref@jnl{NewA}}% % New Astronomy \newcommand\nar{\ref@jnl{NewAR}}% % New Astronomy Review \newcommand\pasa{\ref@jnl{PASA}}% % Publications of the Astron. Soc. of Australia \newcommand\rmxaa{\ref@jnl{RMxAA}}% % Revista Mexicana de Astronomia y Astrofisica %% added feb 9, 2016 \newcommand\maps{\ref@jnl{M\&PS}}% Meteoritics and Planetary Science \newcommand\aas{\ref@jnl{AAS Meeting Abstracts}}% American Astronomical Society Meeting Abstracts \newcommand\dps{\ref@jnl{AAS/DPS Meeting Abstracts}}% American Astronomical Society/Division for Planetary Sciences Meeting Abstracts \let\astap=\aap \let\apjlett=\apjl \let\apjsupp=\apjs \let\applopt=\ao \newcommand\ulap[1]{\vbox\@to\z@{{\vss#1}}}% \newcommand\dlap[1]{\vbox\@to\z@{{#1\vss}}}% \newcounter{table@save} %% March 25, 2019 %% Old v5.2 way, From Greg, This allows a number like 33N to be used %% for a table, and the cross-references will work correctly \newcommand\tablenum[1]{% \def\thetable{#1}% \xdef\@currentlabel{\thetable} \global\advance\c@table-1\relax }% \let\savetablenum\tablenum \def\tabletypesize#1{\gdef\currtabletypesize{#1} \def\@table@type@size{#1}}% \tabletypesize{\small} \let\tablefontsize=\tabletypesize % for compatibility with old documents \gdef\@tablecaption{} \def\tablecaption#1{\gdef\@tablecaption{#1}} \def\LT@endpbox{% \@finalstrut\@arstrutbox \egroup \the\LT@p@ftn \global\LT@p@ftn{}% \hfil} %% Used for longtable \def\LT@makecaption#1#2#3{% \LT@mcol\LT@cols c{\hbox to\z@{\hss\parbox[t]\LTcapwidth {% \xdef \@currentlabel{\thetable} \sbox\@tempboxa{\small #2. %% disable trackchanges commands here, so they aren't entered 2 times: \let\added\relax \let\deleted\relax \let\replaced\relax #3}% \ifdim\wd\@tempboxa>\hsize \small#2. #3% \else \hbox to\hsize{\hfil\box\@tempboxa\hfil}% \fi \endgraf\vskip\baselineskip}% \hss}} }%% \let\LT@makecaption@rtx=\LT@makecaption % to fight redefinition in Revtex-4.1 \def\xfigure{figure} %% from book.cls/ used?? \long\def\@makecaption#1#2{% \vskip\abovecaptionskip %% \small added to keep currtabletypesize from determining size of caption \sbox\@tempboxa{\small %% disable trackchanges commands here, so they aren't entered 2 times: \let\added\relax \let\deleted\relax \let\replaced\relax {\bf #1.} #2}% \ifdim \wd\@tempboxa >\hsize \small {\bf #1.} #2\par \else \global \@minipagefalse \hb@xt@\hsize{\hfill\box\@tempboxa\hfill}% \fi \vskip\belowcaptionskip } \newdimen\@abovenoteskip \newcommand\tablerefs[1]{\ifdim\@abovenoteskip=0pt\global\@abovenoteskip=10pt\fi {\small\@tableref{\parfillskip\z@ plus1fil\relax #1\endgraf}}}% \def\@tableref#1{% \par \vspace{3ex}% {%\parbox{\pt@width} %%%% {\hskip1em\rm References. --- #1}\par}% }% %% march 2019, added \it to tablenotemark \global\def\tablenotemark#1{{\normalfont\textsuperscript{\normalsize\it #1}}} \global\def\tablenotetext#1#2{\footnotetext[#1]{\currtabletypesize\relax#2}} %% redefined by AH below, since it wasn't working with tabular table \global\def\tablenotetext#1#2{\vskip-8pt\vskip1sp\flushleft{\currtabletypesize \noindent\hskip1em $^{#1}$ #2}\vskip1sp} %% this version of \tablehead doesn't seem to be used, so set to \xyztablehead{} \def\xyztablehead#1{\@table@not@headedfalse% \kill \caption{\\% \@tablecaption\gdef\@currentlabel{\thetable}(0)} \\\hline\hline% #1\vrule height 12pt depth 10pt width 0pt\relax \hskip\tabcolsep\\[.7ex] \hline\\[-1.5ex] \endfirsthead \caption[]{--- \emph{Continued}}\\ \hline \hline\\[-1.7ex] #1\hskip\tabcolsep\\[.7ex] \hline\\[-1.5ex] \endhead \hline \endfoot% } \newif\if@table@not@headed \newlength{\table@note@skip} \setlength{\table@note@skip}{0.5ex} \newlength{\deluxe@table@width} \newlength{\@d@t@a} \newcounter{deluxe@table@num} \newdimen\LTcapwidth %% \ignorespaces necessary ++== depth 6pt was depth 3pt, == added height 12pt, nov 2017 \def\colhead#1{\multicolumn{1}{c}{\vrule depth 6pt height 12pt width 0pt\relax#1}\ignorespaces} \def\twocolhead#1{\multicolumn{2}{c}{\hss\vrule depth 6pt height 12pt width 0pt\relax#1\hss}\ignorespaces} \def\nocolhead#1{\multicolumn{1}{h}{}\ignorespaces} \def\dcolhead#1{\multicolumn{1}{c}{$\vrule depth 6pt height12pt width0pt\relax#1$}\ignorespaces} %\newcounter{LT@tables} \def\tablewidth#1{% \ifdim#1=\z@ \else \gdef\@d@t@@flag{1} \if@filesw\immediate\write\@auxout{% \gdef\expandafter\noexpand \csname deluxe@table@width@\romannumeral\c@LT@tables\endcsname {#1}} \fi \fi } \def\save@natural@width{% \ifnum\@d@t@@flag=0 \setlength{\@d@t@a}{0pt}% \let\@d@t@b=\LT@entry% \def\LT@entry##1##2{\addtolength{\@d@t@a}{##2}% }% \expandafter\csname LT@\romannumeral\c@deluxe@table@num\endcsname \setlength{\@d@t@a}{-\@d@t@a} \tablewidth{\the\@d@t@a} \def\LT@entry{\@d@t@b} \fi } \def\lt@expand@linewidth@one{\setlength\LTleft{0pt}\setlength\LTright{0pt}} \def\lt@expand@linewidth@two{@{\extracolsep{0pt plus 1filll}}} \def\find@table@width{% %%% set table width using aux file and command \tablewidth \setcounter{deluxe@table@num}{\c@LT@tables} \refstepcounter{deluxe@table@num} \expandafter\ifx\csname deluxe@table@width@\romannumeral\c@deluxe@table@num\endcsname\relax \def\@d@t@{0.999\linewidth} \else \edef\@d@t@{\expandafter\csname deluxe@table@width@\romannumeral\c@deluxe@table@num\endcsname} \fi \ifdim\@d@t@<\z@% then natural width is used \setlength{\deluxe@table@width}{-\@d@t@} \setlength{\LTcapwidth}{-\@d@t@} \def\lt@expand@linewidth{\relax} \def\lt@expand@linewidth@{} \else% we will enclose table in the minipage of the given width and make % longtable to span the full minipage width \ifdim\@d@t@>\z@\else\def\@d@t@{0.999\linewidth}\fi \setlength{\deluxe@table@width}{\@d@t@} \setlength{\LTcapwidth}{\@d@t@} \def\lt@expand@linewidth{\lt@expand@linewidth@one} \def\lt@expand@linewidth@{\lt@expand@linewidth@two} \fi } \newlength{\abovedeluxetableskip} \newlength{\belowdeluxetableskip} \setlength{\abovedeluxetableskip}{0pt} \setlength{\belowdeluxetableskip}{0pt} \setlength{\tabcolsep}{5pt} \setlength\doublerulesep{1.5pt} \newdimen\lastrowheight \def\set@last@row@height{\setlength{\lastrowheight}{\ht\strutbox}\addtolength{\lastrowheight}{\dp\strutbox}\setlength{\lastrowheight}{-\arraystretch\lastrowheight}} \let\tableline=\colrule % Revtex said: Command \tableline is obsolete; Use \colrule instead.. %% \newtoks\DT@p@ftn \global\def\xtablenotetext@DT#1#2{ \edef\@tempa{\the\DT@p@ftn\noexpand\tablenotemark{#1}~} \global\DT@p@ftn\expandafter{\@tempa{\@table@type@size#2}\par}}% %%% AH %%%%%%%%%%%%%%%%%%%%% \let\savedollar$ \catcode`\$=\active \let$\savedollar %% \def\resetdecimals{\global\let\zdoit\relax\global\let\ddoit\relax} \def\tableheadfrac#1{} \newcount\pt@column \newcount\pt@ncol \newcommand\tablecolumns[1]{% \pt@column=#1\relax \pt@ncol=#1\relax \global\let\pt@addcol\@empty }% %% from older version, probably can delete: \def\@tablecom#1{% \vspace{\table@note@skip} \par {\parbox{\linewidth}{\hskip1em\rmfamily {\@eapj@cap@font Note}. --- #1}\par}% }% \def\@tableref#1{% \vspace{\table@note@skip} \par {\parbox{\linewidth}{\hskip1em\rmfamily {\@eapj@cap@font References}. --- #1}\par}% }% \def\spew@tblnotes{% \@ifx@empty\tblref@list{}{% \@tablenotes{\tblref@list}% \vspace{\table@note@skip}% \global\let\tblref@list\@empty }% \@ifx@empty\tblnote@list{}{% \@tablenotes{\tblnote@list}% \vspace{\table@note@skip}% \global\let\tblnote@list\@empty } \the\DT@p@ftn% }% %% for notes on emulateapj please see http://hea-www.harvard.edu/~alexey/emulateapj %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% End of code taken from emulateapj.cls %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% New as of august 2015: %% These commands requested AAS \newcommand{\noprint}[1]{} \newcommand{\figsetstart}{{\bf Fig. Set} } \newcommand{\figsetend}{} \newcommand{\figsetgrpstart}{} \newcommand{\figsetgrpend}{} \newcommand{\figsetnum}[1]{{\bf #1.}} \newcommand{\figsettitle}[1]{ {\bf #1}} \newcommand{\figsetgrpnum}[1]{\noprint{#1}} \newcommand{\figsetgrptitle}[1]{\noprint{#1}} \newcommand{\figsetplot}[1]{\noprint{#1}} \newcommand{\figsetgrpnote}[1]{\noprint{#1}} \usepackage{url} %% if we take away the xx before UrlBreaks we will get a url that breaks %% at any letter or number. It might be better to break only at / however... \expandafter\def\expandafter\xxUrlBreaks\expandafter{\UrlBreaks% save the current one \do\a\do\b\do\c\do\d\do\e\do\f\do\g\do\h\do\i\do\j% \do\k\do\l\do\m\do\n\do\o\do\p\do\q\do\r\do\s\do\t% \do\u\do\v\do\w\do\x\do\y\do\z\do\A\do\B\do\C\do\D% \do\E\do\F\do\G\do\H\do\I\do\J\do\K\do\L\do\M\do\N% \do\O\do\P\do\Q\do\R\do\S\do\T\do\U\do\V\do\W\do\X% \do\Y\do\Z\do\1\do\2\do\3\do\4\do\5\do\6\do\7\do\8\do\9} %% for tables continuing over pages \usepackage{longtable} %% for editing changes \usepackage{xcolor} % hyperref link defaults to "blue" (0000ff) as this matches our publisher produced pdf style \definecolor{xlinkcolor}{cmyk}{1,1,0,0} \PassOptionsToPackage{hyphens}{url} %% In response to request from AAS \usepackage[bookmarks=true, % show bookmarks bar?/ Changed March 22, 2019 for % improved accessibility pdfnewwindow=true, % links in new window colorlinks=true, % false: boxed links; true: colored links linkcolor=xlinkcolor, % color of internal links citecolor=xlinkcolor, % color of links to bibliography filecolor=xlinkcolor, % color of file links urlcolor=xlinkcolor, % color of external links final=true, ]{hyperref} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Additions to AASTeX by Amy Hendrickson, TeXnology Inc, August 17, 2015 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Table Tools, written by Amy Hendrickson %% for American Astronomical Society %% August 17, 2015 %% array package is necessary: \usepackage{array} %%%%%%%% %% 1) h in table preamble will makes text in that column ignored. %%%%%%%% %% 2) uppercase C L or R will make those columns in math mode. %%%%%%%% %% 3) \begin{splittabular}{<preamble B preamble>}...\end{splittabular} %% `B' in the preamble will show where the table should be broken. It may %% be used once in a preamble to break the table into two parts, or %% two times in a preamble to break the table into three parts. %% The resulting table will position left half of table above right half of table. %% Care should be taken with \multicolumn so that it won't be broken between %% the two parts of the table. You may need to shorten the \multicolumn argument %% for number of columns to be appropriate to the number of columns in %% the new split table. %% In this example, for instance, we start with: %% \begin{tabular}{ccccccc} %% \multicolumn{7}{c}{\textsc{Table 1}} %% and change it to: %% \begin{splittabular}{ccccBccc} %% \multicolumn{4}{c}{\textsc{Table 1}}\\ %% %% If you'd like to have a table number in the second half of the table, %% you can ask for a second multicolumn command that will position at the %% top of the second half of the table: %% %% \begin{splittabular}{ccccBccc} %% \multicolumn{4}{c}{\textsc{Table 1}}&\multicolumn{3}{c}{\textsc{Table 1, Continued}}\\ %% %% You can do the same for the caption, and give a Continued caption for %% the second half of the table. Originally: %% \multicolumn{7}{c}{\textsc{Log of \textit{HST} Observations for %% NGC~6388}} %% Now, changed so that we get a caption on both halves of the table: %% \multicolumn{4}{c}{\textsc{Log of \textit{HST} Observations for %% NGC~6388}}&\multicolumn{3}{c}{\textsc{Log of \textit{HST} Observations for %% NGC~6388, Continued}}\\ %% %% Similarly, you can rearrange table notes to appear at the bottom of %% the appropriate half of the table. For instance, starting with this, %% which would make table notes both appear at the bottom of the top half %% of the table: %% \multicolumn{4}{l}{\small{$\dagger$ Average distance of data set from %% cluster center.}}\\ %% \multicolumn{4}{l}{$^{\rm a}$SNAP program.}\\ %% %% We may substitute the following: %% \multicolumn{4}{l}{$^{\rm a}$SNAP program.}&\multicolumn{3}{l}{\small{$\dagger$ Average distance of data set from %% cluster center.}}\\ %% %% Which will produce the first endnote underneath the top half of the %% table, and the second underneath the bottom half. %% %% Another option would be to have both endnotes appear below the bottom %% half of the table. Easily done: %% &&&&\multicolumn{3}{l}{$^{\rm a}$SNAP program.}\\ %% &&&&\multicolumn{3}{l}{\small{$\dagger$ Average distance of data set from %% cluster center.}}\\ %% %% %% %% %% %% %% %%%%%%%% %% 4) \colnumbers will make line with column numbers automatic. It will work with splittabular %% and splitdeluxetable as well as tabular. %% To use: type in \colnumbers within the table whereever you'd like it to appear, typically %% underneath the column headers, before the lines of data. %%%%%%%% %% 5) Easy Decimal numbering %% How to make decimal numbers in tables line up on the period: %% Use D (for decimal column) in table preamble for every decimal number. The decimal %% numbers will use two columns, one for the left part of the decimal %% number and one for the right part. %% D may be used more than once in a table preamble. %% If you want to type in a column header over the decimal %% numbers, please use \multicolumn2c{} to span both columns. %% After the column headers, to start decimal numbering, %% type in \decimals in the body of the table. %% When entering decimal numbers %% remember to leave a space after the decimal number, before the following &. %% For instance: &22.3 &35.96 \\ %% If you'd like an empty entry, please supply a period and a space: & . &. You %% will not see the period in the resulting table. %% example: % \begin{tabular}{rDD} % \hline % &&&\multicolumn2c{\bf More}\\ % &\multicolumn2c{\bf Decimals}&\multicolumn2c{\bf Decimals}\\ % \hline % \hline % \decimals % one& . &34.2 \\ % two &567.0 &21345 \\ % three&.0 &62.5 \\ % four&245 &5034.349923 \\ % five&21 & \\ % six& &21.6 % \end{tabular} %% % Decimal numbering works within \begin{splittabular}...\end{splittabular} % \begin{splitdeluxetable} and \end{splitdeluxetable} for tables broken into two % or three parts. \colnumbers will number the columns counting both sides % of the decimal number as one column; \tablehead{\colhead{}...} will make % the column headers position above the two columns used for one decimal % number as well. % % Decimal numbers will be in math mode so that plus and minus signs are printed % correctly, expressions like `$\pm$ 1.2' or `\pm 1.2', will both work %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \let\savedollar$ \catcode`\$=\active \let\savetabular\tabular \def\tabular{\catcode`\&=\active\relax\catcode`\$=\active\relax\hskip\movetableright \savetabular} \long\gdef\eatone{\setbox0=\hbox\bgroup\savedollar\let$\relax} \gdef\endeatone{\savedollar\egroup\hskip-2\tabcolsep} %% Hide, important because it allows us to split tables horizontally \newcolumntype{h}{>\eatone c<\endeatone} \newcolumntype{C}{>{\bgroup\savedollar\let$\relax}c<{\savedollar\egroup}} \newcolumntype{L}{>{\bgroup\savedollar\let$\relax}l<{\savedollar\egroup}} \newcolumntype{R}{>{\bgroup\savedollar\let$\relax}r<{\savedollar\egroup}} \newcolumntype{B}{>\eatone c<\endeatone} %% used for \splittabular to indicate break in %% two or three parts of table %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Split tables into 2 or 3 parts; stack the parts %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Process table preamble %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Count number of columns in preamble \newcount\colcount \newcount\firstcolcount \newcount\secondcolcount \newcount\thirdcolcount \newcount\columncount %% \makeatother is necessary to keep @ from being treated as a letter %% when counting the number of columns in table. \makeatother \def\xD{D} \def\xaster{} \newcount\howmanyDs \newcount\firsthowmanyDs \newcount\secondhowmanyDs \newif\ifD \def\countcols#1{\ifcat#1c \global\advance\colcount by 1\relax\fi %% \def\lookforD{#1} \ifx\lookforD\xD \global\advance\howmanyDs by 1 \global\advance\colcount by1\relax \fi %% \futurelet\next\lookatnext } \makeatletter \def\xeatone#1{\countcols} \def\xrelax{\relax} %% second conditional deals with expressions like @{} in %% the preamble. \def\lookatnext{\if\next\xrelax\let\go\relax \else \ifx\next\bgroup\let\go\xeatone\else \let\go\countcols\fi\fi\go} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% reset line counting at \\ %% arraycr redefined to match revtex4-1 \def\new@arraycr{\relax \global\columncount=0\relax \global\colheadcount=0\relax \iffalse {\fi \ifnum 0=`}\fi \@ifstar {\global \@tbpen \@M \@xarraycr} {\global \@tbpen \intertabularlinepenalty \@xarraycr}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Redefining & is necessary to get around \omit in \multicolumn, %% which prevents @{} from being used to change the meaning of multicolumn. %% Now column number and top or bottom table is used to determine whether %% multicolumn should be turned on or off. \let\saveampersand& \newif\iffirstbox \newif\ifsecondbox \newif\ifthirdbox \long\gdef\CheckNumberAndSwitch{\unskip\global\advance\columncount by 1\relax% \saveampersand} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Parse and count preamble \def\catchfirstpreamble#1B#2Z{%firstpreamble \def\leftpreamble{#1\relax} \colcount=0 \global\howmanyDs=0\relax \expandafter\countcols\leftpreamble \global\firstcolcount\the\colcount \global\firsthowmanyDs\the\howmanyDs \ifnum\firstcolcount>25 \typeout{^^J ----------------------------------------------------- ^^J Warning! ^^J^^J Too many columns in first part of table! ^^J^^J Maximum number of columns in each part of the table is 25. Each `D' counts as two columns. ^^J ----------------------------------------------------- }\fi \global\howmanyDs=0\relax \global\colcount=0\relax \newcolumntype{A}{#1}} \def\catchsecondpreamble#1B#2Z{%secondpreamble \def\rightpreamble{#2\relax} \colcount=0 \expandafter\countcols\rightpreamble \global\secondcolcount\colcount \global\secondhowmanyDs\the\howmanyDs \ifnum\secondcolcount>25 \typeout{^^J----------------------------------------------------- ^^J Warning! ^^J^^J Too many columns in second part of table! ^^J^^J Maximum number of columns in each part of the table is 25. Each `D' counts as two columns. ^^J ----------------------------------------------------- }\fi \global\totalcolumns=\firstcolcount \global\advance\totalcolumns by \secondcolcount \global\colcount=0\relax \newcolumntype{Z}{#2}} \def\catchsecondofthreepreamble#1B#2B#3Z{%secondpreamble \def\rightpreamble{#2\relax} \colcount=0 \howmanyDs=0 \expandafter\countcols\rightpreamble \global\secondcolcount\colcount \global\secondhowmanyDs\the\howmanyDs \global\totalcolumns=\firstcolcount \global\advance\totalcolumns by \secondcolcount \global\colcount=0\relax \newcolumntype{Z}{#2}} \def\catchthirdpreamble#1B#2B#3Z{%firstpreamble \def\thirdpreamble{#3} \colcount=0 \expandafter\countcols\thirdpreamble \global\thirdcolcount\the\colcount \global\advance\totalcolumns by \thirdcolcount \global\colcount=0\relax \newcolumntype{z}{#3}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Define splittabular/endsplittabular \newcount\PartsOfTable \newif\ifbreaktab \def\checkforB #1B#2B#3B{ %% defaults, may be used in \colnumbers \gdef\tabfullpreamble{#1#2#3\relax} \gdef\firstpreamble{#1} \gdef\secondpreamble{#2} \gdef\thirdpreamble{#3} \ifx\thirdpreamble\empty \global\PartsOfTable=2 \else \global\PartsOfTable=3 \fi } \def\lookforD#1{\def\zone{#1}\ifx\zone\xD \global\Dtrue\else\Dfalse\fi} \newcount\columnoneandtwo \newif\ifdonullmulticol \newcount\colnumsused \newcount\loopnum \catcode`\&=\active \let&\CheckNumberAndSwitch \let$\savedollar %sss \def\splittabular{\catcode`\&=\active \catcode`\$=\active \global\colnumbersonfalse \let\colnumbers\savesplitplaincolnumbers \let\splitdecimalcolnumbers\savesplitdecimalcolnumbers \def\decimalcolnumbers{\splitdecimalcolnumbers} \xsplittabular} \def\xsplittabular#1#2\end{{ \global\firsttimetrue \let&\CheckNumberAndSwitch \let$\savedollar %%% \def\endtabular{\endarray \global\let\zdoit\relax \global\let\ddoit\relax \global\Dfalse} \setbox0=\hbox{\def\firstarg{#1}\expandafter\lookforD\firstarg} \PartsOfTable=0 \def\tempfullpreamble{#1BB} \setbox0=\hbox{\expandafter\checkforB\tempfullpreamble} %% Now PartsOfTable is either =2 or 3 %% \global\colnumsused=0 \global\breaktabtrue \global\colcount=0 %% \ifnum\PartsOfTable=3 \let\multicolumn\threebreakmulticolumn \else \let\multicolumn\breakmulticolumn \fi %% \def\one{#1Z}%% full preamble \ifnum\PartsOfTable=3 \expandafter\catchfirstpreamble\one \expandafter\catchsecondofthreepreamble\one \expandafter\catchthirdpreamble\one \makefirstdummycolumns %f \makeseconddummycolumns %F \makethirddummycolumns %E \else %% PartsOfTable=2 \expandafter\catchfirstpreamble\one \expandafter\catchsecondpreamble\one \makefirstdummycolumns %f \makeseconddummycolumns %F \fi %%% \global\columncount=0 \ifnum\PartsOfTable=3 %% For table divided into three parts !! \firstboxtrue\secondboxfalse\thirdboxfalse % \setbox\firsttablebox=\hbox{% \begin{tabular}{AFE}% #2\crcr \end{tabular}} % \hbox to \hsize{\hss\unhbox\firsttablebox\hss} \vskip6pt \hrule \vskip6pt \global\columncount=0 \firstboxfalse\secondboxtrue\thirdboxfalse \ifcolnumberson \let\colnumbers\xplain \setbox\secondtablebox=\hbox{% \begin{tabular}{fZE}% fZE #2\crcr\end{tabular}} \else \setbox\secondtablebox=\hbox{ \begin{tabular}{fZE}% fZE #2 \end{tabular}} \fi \hbox to \hsize{\hss\unhbox\secondtablebox\hss} %% \vskip6pt \hrule \vskip6pt \firstboxfalse\secondboxfalse\thirdboxtrue \global\columncount=0 \ifcolnumberson \let\colnumbers\xplain \setbox\thirdtablebox=\hbox{% \begin{tabular}{fFz}% fFz #2\crcr\end{tabular}} \else \setbox\thirdtablebox=\hbox{ \begin{tabular}{fFz}% fFz #2 \end{tabular}} \fi \hbox to \hsize{\hss\unhbox\thirdtablebox\hss} \else %% %% For table divided into two parts: %% \global\columncount=0 \secondboxfalse \setbox\firsttablebox=\hbox{% \begin{tabular}{AF}% should be AF #2 \end{tabular} } \hbox to \hsize{\hss\unhbox\firsttablebox\hss} \vskip6pt \hrule \vskip6pt \global\columncount=0 \secondboxtrue \ifcolnumberson \setbox\secondtablebox=\hbox{\let\colnumbers\xplain \begin{tabular}{fZ}% should be fZ #2 \end{tabular} } \else \setbox\secondtablebox=\hbox{ \begin{tabular}{fZ}% should be fZ #2 \end{tabular} } \fi \hbox to \hsize{\hss\unhbox\secondtablebox\hss} %% %% end of conditional testing for 2 or 3 part table: \fi %\global\breaktabfalse } \firsthowmanyDs=0 \secondhowmanyDs=0 \resetdecimals \end } %yyy \def\endsplittabular{\global\firsttimefalse\global\colnumbersonfalse \global\let\splitplaincolnumbers\savesplitplaincolnumbers \global\breaktabfalse} \long\gdef\breakmulticolumn#1#2#3{% \multispan{#1}% \let&\CheckNumberAndSwitch \ifsecondbox% \ifnum\columncount<\firstcolcount% \global\donullmulticoltrue% \else% \global\donullmulticolfalse% \fi% %%% \else% first box \ifnum\columncount<\firstcolcount% \global\donullmulticolfalse% \else% \global\donullmulticoltrue% \fi% \fi% \ifdonullmulticol% \global\advance\colheadcount by 1\relax \begingroup \def\@addamp{\if@firstamp \@firstampfalse \else \@preamerr 5\fi}% \@mkpream{h}\@addtopreamble\@empty \endgroup \def\@sharp{}% %% comment out \@arstrut to prevent blank line where multicolumn was found %% on other parts of the table, but not on the current part. \@arstrut \@preamble \null\ignorespaces \else% \begingroup \def\@addamp{\if@firstamp \@firstampfalse \else \@preamerr 5\fi}% \@mkpream{#2}\@addtopreamble\@empty \endgroup \def\@sharp{#3}% \@arstrut \@preamble \null\ignorespaces \fi% \global\donullmulticolfalse% \global\advance\columncount by #1\relax% \global\advance\columncount-1\relax% } \long\gdef\threebreakmulticolumn#1#2#3{% \multispan{#1}% \columnoneandtwo=\firstcolcount\relax% \advance\columnoneandtwo by \secondcolcount\relax% %% \global\donullmulticoltrue\relax% \iffirstbox\relax% \ifnum\columncount<\firstcolcount% \global\donullmulticolfalse% \fi\relax% \ifnum\columncount=\firstcolcount\relax% \donullmulticoltrue\fi\relax% \else\relax% %% \ifsecondbox% \ifnum\columncount=\firstcolcount\relax% \global\donullmulticolfalse\fi\relax% \ifnum\columncount>\firstcolcount% \ifnum\columncount<\columnoneandtwo\relax% \global\donullmulticolfalse\relax% \fi\fi\relax% \else\relax% %%% \ifthirdbox% \ifnum\columncount<\columnoneandtwo% \global\donullmulticoltrue% \else\relax% \global\donullmulticolfalse% \fi\relax% \fi%% end if third box \fi%% end if second box \fi%% end if first box %% \ifdonullmulticol% \begingroup\relax% \global\advance\colheadcount by 1\relax% \def\@addamp{\if@firstamp \@firstampfalse \else% \@preamerr 5\fi}% \@mkpream{h}\@addtopreamble\@empty% \endgroup% \def\@sharp{}% %% comment out \@arstrut to prevent blank line where multicolumn was found %% on other parts of the table, but not on the current part. \@arstrut \@preamble% \null\ignorespaces \else% \begingroup% \def\@addamp{\if@firstamp \@firstampfalse \else% \@preamerr 5\fi}% \@mkpream{#2}\@addtopreamble\@empty% \endgroup% \def\@sharp{#3}% \@arstrut \@preamble% \null\ignorespaces \fi% \global\donullmulticolfalse% \global\advance\columncount by #1\relax% \global\advance\columncount-1\relax% } %% First dummy columns is the part of the table that will not print, %% in this case the first part to the left. %%\makefirstdummycolumns %% %% and second dummy columns %% \makeseconddummycolumns. \gdef\makefirstdummycolumns{ \ifcase\firstcolcount \or% 1 \newcolumntype{f}{h} % no D possible %%%%%%%%%%%%%%%%%% \or% 2 \ifcase\firsthowmanyDs \newcolumntype{f}{hh}%% 0 \or \newcolumntype{f}{d} %% 1 \fi %%%%%%%%%%%%%%%%%% \or% 3 \ifcase\firsthowmanyDs% \newcolumntype{f}{hhh}% 0 \or% \newcolumntype{f}{dh}% 1 \fi% %%%%%%%%%%%%%%%%%% \or% 4 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhh} % 0 \or \newcolumntype{f}{dhh} % 1 \or \newcolumntype{f}{dd} % 2 \fi %%%%%%%%%%%%%%%%%% \or% 5 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhh} % 0 \or \newcolumntype{f}{dhhh} % 1 \or \newcolumntype{f}{ddh} % 2 \fi %%%%%%%%%%%%%%%%%% \or% 6 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhh} % 0 \or \newcolumntype{f}{dhhhh} % 1 \or \newcolumntype{f}{ddhh} % 2 \or \newcolumntype{f}{ddd} % 3 \fi %%%%%%%%%%%%%%% \or % 7 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhhh} % 0 \or \newcolumntype{f}{dhhhhh} % 1 \or \newcolumntype{f}{ddhhh} % 2 \or \newcolumntype{f}{dddh} % 3 \fi %%%%%%%%%%%%%%%%%% \or % 8 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhhhh} % 0 \or \newcolumntype{f}{dhhhhhh} % 1 \or \newcolumntype{f}{ddhhhh} % 2 \or \newcolumntype{f}{dddhh} % 3 \or \newcolumntype{f}{dddd} % 4 \fi %%%%%%%%%%%%%%%%%% \or % 9 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhhhhh} % 0 \or \newcolumntype{f}{dhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhh} % 2 \or \newcolumntype{f}{dddhhh} % 3 \or \newcolumntype{f}{ddddh} % 4 \fi %%%%%%%%%%%%%%%%%% \or %10 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhhhhhh} % 0 \or \newcolumntype{f}{dhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhh} % 2 \or \newcolumntype{f}{dddhhhh} % 3 \or \newcolumntype{f}{ddddhh} % 4 \or \newcolumntype{f}{ddddd} % 5 \fi %%%%%%%%%%%%%%%%%% \or % 11 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhhhhhhh} % 0 \or \newcolumntype{f}{dhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhh} % 3 \or \newcolumntype{f}{ddddhhh} % 4 \or \newcolumntype{f}{dddddh} % 5 \fi %%%%%%%%%%%%%%%%%% \or % 12 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhhhhhhhh} % 0 \or \newcolumntype{f}{dhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhh} % 4 \or \newcolumntype{f}{dddddhh} % 5 \or \newcolumntype{f}{dddddd} % 6 \fi %%%%%%%%%%%%%%%%%% \or %13 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhhhhhhhhh} % 0 \or \newcolumntype{f}{dhhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhhh} % 4 \or \newcolumntype{f}{dddddhhh} % 5 \or \newcolumntype{f}{ddddddh} % 6 \fi %%%%%%%%%%%%%%%%%% \or %14 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhhhhhhhhhh} % 0 \or \newcolumntype{f}{dhhhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhhhh} % 4 \or \newcolumntype{f}{dddddhhhh} % 5 \or \newcolumntype{f}{ddddddhh} % 6 \or \newcolumntype{f}{ddddddd} % 7 \fi %%%%%%%%%%%%%%%%%% \or %15 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhhhhhhhhhhh} % 0 \or \newcolumntype{f}{dhhhhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhhhhh} % 4 \or \newcolumntype{f}{dddddhhhhh} % 5 \or \newcolumntype{f}{ddddddhhh} % 6 \or \newcolumntype{f}{dddddddh} % 7 \fi %%%%%%%%%%%%%%%%%% \or %16 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhhhhhhhhhhhh} % 0 \or \newcolumntype{f}{dhhhhhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhhhhhh} % 4 \or \newcolumntype{f}{dddddhhhhhh} % 5 \or \newcolumntype{f}{ddddddhhhh} % 6 \or \newcolumntype{f}{dddddddhh} % 7 \or \newcolumntype{f}{dddddddd} % 8 \fi %%%%%%%%%%%%%%%%%% \or %17 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhhhhhhhhhhhhh} % 0 \or \newcolumntype{f}{dhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhhhhhhh} % 4 \or \newcolumntype{f}{dddddhhhhhhh} % 5 \or \newcolumntype{f}{ddddddhhhhh} % 6 \or \newcolumntype{f}{dddddddhhh} % 7 \or \newcolumntype{f}{ddddddddh} % 8 \fi %%%%%%%%%%%%%%%%%% \or %18 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhhhhhhhhhhhhhh} % 0 \or \newcolumntype{f}{dhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhhhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhhhhhhhh} % 4 \or \newcolumntype{f}{dddddhhhhhhhh} % 5 \or \newcolumntype{f}{ddddddhhhhhh} % 6 \or \newcolumntype{f}{ddddddhhhh} % 7 \or \newcolumntype{f}{ddddddddhh} % 8 \or \newcolumntype{f}{ddddddddd} % 9 \fi %%%%%%%%%%%%%%%%%% \or %19 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhhhhhhhhhhhhhhhh} % 0 \or \newcolumntype{f}{dhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhhhhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhhhhhhhhh} % 4 \or \newcolumntype{f}{dddddhhhhhhhhh} % 5 \or \newcolumntype{f}{ddddddhhhhhhh} % 6 \or \newcolumntype{f}{dddddddhhhhh} % 7 \or \newcolumntype{f}{ddddddddhhh} % 8 \or \newcolumntype{f}{ddddddddddh} % 9 \fi %%%%%%%%%%%%%%%%%% \or %20 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhh hhhhh hhhhh hhhhh} % 0 \or \newcolumntype{f}{dhhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhhhhhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhhhhhhhhhh} % 4 \or \newcolumntype{f}{dddddhhhhhhhhhh} % 5 \or \newcolumntype{f}{ddddddhhhhhhhh} % 6 \or \newcolumntype{f}{dddddddhhhhhh} % 7 \or \newcolumntype{f}{ddddddddhhhh} % 8 \or \newcolumntype{f}{dddddddddhh} % 9 \or \newcolumntype{f}{dddddddddd} % 10 \fi %%%%%%%%%%%%%%%%%% \or %21 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhh hhhhh hhhhh hhhhh h} % 0 \or \newcolumntype{f}{dhhhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhhhhhhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhhhhhhhhhhh} % 4 \or \newcolumntype{f}{dddddhhhhhhhhhhh} % 5 \or \newcolumntype{f}{ddddddhhhhhhhhh} % 6 \or \newcolumntype{f}{dddddddhhhhhhh} % 7 \or \newcolumntype{f}{ddddddddhhhhh} % 8 \or \newcolumntype{f}{ddd ddd ddd hhh} % 9 \or \newcolumntype{f}{ddd ddd ddd d h} % 10 \fi %%%%%%%%%%%%%%%%%% \or %22 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhh hhhhh hhhhh hhhhh hh} % 0 \or \newcolumntype{f}{dhhhhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhhhhhhhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhhhhhhhhhhhh} % 4 \or \newcolumntype{f}{dddddhhhhhhhhhhhh} % 5 \or \newcolumntype{f}{ddddddhhhhhhhhhh} % 6 \or \newcolumntype{f}{dddddddhhhhhhhh} % 7 \or \newcolumntype{f}{ddddddddhhhhhh} % 8 \or \newcolumntype{f}{ddd ddd ddd hhhh} % 9 \or \newcolumntype{f}{ddd ddd ddd dhh} % 10 \or \newcolumntype{f}{ddddddddddd} % 11 \fi %%%%%%%%%%%%%%%%%% \or %23 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhh hhhhh hhhhh hhhhh hhh} % 0 \or \newcolumntype{f}{dhhhhhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhhhhhhhhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhhhhhhhhhhhhh} % 4 \or \newcolumntype{f}{dddddhhhhhhhhhhhhh} % 5 \or \newcolumntype{f}{ddddddhhhhhhhhhhh} % 6 \or \newcolumntype{f}{dddddddhhhhhhhhh} % 7 \or \newcolumntype{f}{ddddddddhhhhhhh} % 8 \or \newcolumntype{f}{ddd ddd ddd hhhhh} % 9 \or \newcolumntype{f}{ddddddddddhhh} % 10 \or \newcolumntype{f}{ddddd ddddd dh} % 11 \fi %%%%%%%%%%%%%%%%%% \or %24 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhh hhhhh hhhhh hhhhh hhhh} % 0 \or \newcolumntype{f}{dhhhhhhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhhhhhhhhhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhhhhhhhhhhhhhh} % 4 \or \newcolumntype{f}{dddddhhhhhhhhhhhhhh} % 5 \or \newcolumntype{f}{ddddddhhhhhhhhhhhh} % 6 \or \newcolumntype{f}{dddddddhhhhhhhhhh} % 7 \or \newcolumntype{f}{ddddddddhhhhhhhh} % 8 \or \newcolumntype{f}{ddd ddd ddd hhhhhh} % 9 \or \newcolumntype{f}{ddddddddddhhhh} % 10 \or \newcolumntype{f}{ddddd ddddd dhh} % 11 \or \newcolumntype{f}{ddddd ddddd dd} % 12 \fi %%%%%%%%%%%%%%%%%% \or %25 \ifcase\firsthowmanyDs \newcolumntype{f}{hhhhh hhhhh hhhhh hhhhh hhhhh} % 0 \or \newcolumntype{f}{dhhhhhhhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{f}{ddhhhhhhhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{f}{dddhhhhhhhhhhhhhhhhhhh} % 3 \or \newcolumntype{f}{ddddhhhhhhhhhhhhhhhhh} % 4 \or \newcolumntype{f}{dddddhhhhhhhhhhhhhhh} % 5 \or \newcolumntype{f}{ddddddhhhhhhhhhhhhh} % 6 \or \newcolumntype{f}{dddddddhhhhhhhhhhh} % 7 \or \newcolumntype{f}{ddddddddhhhhhhhhh} % 8 \or \newcolumntype{f}{ddd ddd ddd hhhhhhh} % 9 \or \newcolumntype{f}{ddddddddddhhhhh} % 10 \or \newcolumntype{f}{dddddddddddhhh} % 11 \or \newcolumntype{f}{ddddddddddddh} % 12 \fi %%%%%%%%%%%%%%%%%% \else \typeout{^^J----------------------------------------------------- ^^J Warning!^^J^^J Too many Columns using in Splittabular. ^^J 25 column maximum in each part of the table.^^J Each`T' counts as two columns. ^^J-----------------------------------------------------^^J} \fi } %% Second dummy columns is the part of the table that will not print, %% in this case the part to the right. %%\makeseconddummycolumns \gdef\makeseconddummycolumns{% \ifcase\secondcolcount %0 \or %1 \newcolumntype{F}{h} % no D possible %%%%%%%%%%%%%%%%%% \or %2 \ifcase\secondhowmanyDs \newcolumntype{F}{hh}%% 0 \or \newcolumntype{F}{d} %% 1 \fi %%%%%%%%%%%%%%%%%% \or %3 \ifcase\secondhowmanyDs \newcolumntype{F}{hhh} % 0 \or \newcolumntype{F}{dh} % 1 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhh} % 0 \or \newcolumntype{F}{dhh} % 1 \or \newcolumntype{F}{dd} % 2 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhh} % 0 \or \newcolumntype{F}{dhhh} % 1 \or \newcolumntype{F}{ddh} % 2 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhh} % 0 \or \newcolumntype{F}{dhhhh} % 1 \or \newcolumntype{F}{ddhh} % 2 \or \newcolumntype{F}{ddd} % 3 \fi %%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhhh} % 0 \or \newcolumntype{F}{dhhhhh} % 1 \or \newcolumntype{F}{ddhhh} % 2 \or \newcolumntype{F}{dddh} % 3 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhhhh} % 0 \or \newcolumntype{F}{dhhhhhh} % 1 \or \newcolumntype{F}{ddhhhh} % 2 \or \newcolumntype{F}{dddhh} % 3 \or \newcolumntype{F}{dddd} % 4 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhhhhh} % 0 \or \newcolumntype{F}{dhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhh} % 2 \or \newcolumntype{F}{dddhhh} % 3 \or \newcolumntype{F}{ddddh} % 4 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhhhhhh} % 0 \or \newcolumntype{F}{dhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhh} % 2 \or \newcolumntype{F}{dddhhhh} % 3 \or \newcolumntype{F}{ddddhh} % 4 \or \newcolumntype{F}{ddddd} % 5 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhhhhhhh} % 0 \or \newcolumntype{F}{dhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhh} % 3 \or \newcolumntype{F}{ddddhhh} % 4 \or \newcolumntype{F}{dddddh} % 5 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhhhhhhhh} % 0 \or \newcolumntype{F}{dhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhh} % 4 \or \newcolumntype{F}{dddddhh} % 5 \or \newcolumntype{F}{dddddd} % 6 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhhhhhhhhh} % 0 \or \newcolumntype{F}{dhhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhhh} % 4 \or \newcolumntype{F}{dddddhhh} % 5 \or \newcolumntype{F}{ddddddh} % 6 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhhhhhhhhhh} % 0 \or \newcolumntype{F}{dhhhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhhhh} % 4 \or \newcolumntype{F}{dddddhhhh} % 5 \or \newcolumntype{F}{ddddddhh} % 6 \or \newcolumntype{F}{ddddddd} % 7 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhhhhhhhhhhh} % 0 \or \newcolumntype{F}{dhhhhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhhhhh} % 4 \or \newcolumntype{F}{dddddhhhhh} % 5 \or \newcolumntype{F}{ddddddhhh} % 6 \or \newcolumntype{F}{dddddddh} % 7 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhhhhhhhhhhhh} % 0 \or \newcolumntype{F}{dhhhhhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhhhhhh} % 4 \or \newcolumntype{F}{dddddhhhhhh} % 5 \or \newcolumntype{F}{ddddddhhhh} % 6 \or \newcolumntype{F}{dddddddhh} % 7 \or \newcolumntype{F}{dddddddd} % 8 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhhhhhhhhhhhhh} % 0 \or \newcolumntype{F}{dhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhhhhhhh} % 4 \or \newcolumntype{F}{dddddhhhhhhh} % 5 \or \newcolumntype{F}{ddddddhhhhh} % 6 \or \newcolumntype{F}{dddddddhhh} % 7 \or \newcolumntype{F}{ddddddddh} % 8 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhhhhhhhhhhhhhh} % 0 \or \newcolumntype{F}{dhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhhhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhhhhhhhh} % 4 \or \newcolumntype{F}{dddddhhhhhhhh} % 5 \or \newcolumntype{F}{ddddddhhhhhh} % 6 \or \newcolumntype{F}{dddddddhhhh} % 7 \or \newcolumntype{F}{ddddddddhh} % 8 \or \newcolumntype{F}{ddddddddd} % 9 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhhhhhhhhhhhhhhhh} % 0 \or \newcolumntype{F}{dhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhhhhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhhhhhhhhh} % 4 \or \newcolumntype{F}{dddddhhhhhhhhh} % 5 \or \newcolumntype{F}{ddddddhhhhhhh} % 6 \or \newcolumntype{F}{dddddddhhhhh} % 7 \or \newcolumntype{F}{ddddddddhhh} % 8 \or \newcolumntype{F}{dddddddddh} % 9 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhh hhhhh hhhhh hhhhh} % 0 \or \newcolumntype{F}{dhhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhhhhhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhhhhhhhhhh} % 4 \or \newcolumntype{F}{dddddhhhhhhhhhh} % 5 \or \newcolumntype{F}{ddddddhhhhhhhh} % 6 \or \newcolumntype{F}{dddddddhhhhhh} % 7 \or \newcolumntype{F}{ddddddddhhhh} % 8 \or \newcolumntype{F}{dddddddddhh} % 9 \or \newcolumntype{F}{dddddddddd} % 10 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhh hhhhh hhhhh hhhhh h} % 0 \or \newcolumntype{F}{dhhhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhhhhhhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhhhhhhhhhhh} % 4 \or \newcolumntype{F}{dddddhhhhhhhhhhh} % 5 \or \newcolumntype{F}{ddddddhhhhhhhhh} % 6 \or \newcolumntype{F}{dddddddhhhhhhh} % 7 \or \newcolumntype{F}{ddddddddhhhhh} % 8 \or \newcolumntype{F}{ddd ddd ddd hhh} % 9 \or \newcolumntype{F}{ddd ddd ddd d h} % 10 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhh hhhhh hhhhh hhhhh hh} % 0 \or \newcolumntype{F}{dhhhhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhhhhhhhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhhhhhhhhhhhh} % 4 \or \newcolumntype{F}{dddddhhhhhhhhhhhh} % 5 \or \newcolumntype{F}{ddddddhhhhhhhhhh} % 6 \or \newcolumntype{F}{dddddddhhhhhhhh} % 7 \or \newcolumntype{F}{ddddddddhhhhhh} % 8 \or \newcolumntype{F}{ddd ddd ddd hhhh} % 9 \or \newcolumntype{F}{ddddddddddhh} % 10 \or \newcolumntype{F}{ddddddddddd} % 11 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhh hhhhh hhhhh hhhhh hhh} % 0 \or \newcolumntype{F}{dhhhhhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhhhhhhhhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhhhhhhhhhhhhh} % 4 \or \newcolumntype{F}{dddddhhhhhhhhhhhhh} % 5 \or \newcolumntype{F}{ddddddhhhhhhhhhhh} % 6 \or \newcolumntype{F}{dddddddhhhhhhhhh} % 7 \or \newcolumntype{F}{ddddddddhhhhhhh} % 8 \or \newcolumntype{F}{ddd ddd ddd hhhhh} % 9 \or \newcolumntype{F}{ddddddddddhhh} % 10 \or \newcolumntype{F}{ddddd ddddd dh} % 11 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhh hhhhh hhhhh hhhhh hhhh} % 0 \or \newcolumntype{F}{dhhhhhhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhhhhhhhhhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhhhhhhhhhhhhhh} % 4 \or \newcolumntype{F}{dddddhhhhhhhhhhhhhh} % 5 \or \newcolumntype{F}{ddddddhhhhhhhhhhhh} % 6 \or \newcolumntype{F}{dddddddhhhhhhhhhh} % 7 \or \newcolumntype{F}{ddddddddhhhhhhhh} % 8 \or \newcolumntype{F}{ddd ddd ddd hhhhhh} % 9 \or \newcolumntype{F}{ddddddddddhhhh} % 10 \or \newcolumntype{F}{ddddd ddddd dhh} % 11 \or \newcolumntype{F}{ddddd ddddd dd} % 12 \fi %%%%%%%%%%%%%%%%%% \or \ifcase\secondhowmanyDs \newcolumntype{F}{hhhhh hhhhh hhhhh hhhhh hhhhh} % 0 \or \newcolumntype{F}{dhhhhhhhhhhhhhhhhhhhhhhh} % 1 \or \newcolumntype{F}{ddhhhhhhhhhhhhhhhhhhhhh} % 2 \or \newcolumntype{F}{dddhhhhhhhhhhhhhhhhhhh} % 3 \or \newcolumntype{F}{ddddhhhhhhhhhhhhhhhhh} % 4 \or \newcolumntype{F}{dddddhhhhhhhhhhhhhhh} % 5 \or \newcolumntype{F}{ddddddhhhhhhhhhhhhh} % 6 \or \newcolumntype{F}{dddddddhhhhhhhhhhh} % 7 \or \newcolumntype{F}{ddddddddhhhhhhhhh} % 8 \or \newcolumntype{F}{ddd ddd ddd hhhhhhh} % 9 \or \newcolumntype{F}{ddddddddddhhhhh} % 10 \or \newcolumntype{F}{ddddd ddddd dhhh} % 11 \or \newcolumntype{F}{ddddd ddddd ddh} % 12 \fi %%%%%%%%%%%%%%%%%% \else \typeout{^^J----------------------------------------------------- ^^J Warning!^^J^^J Too many Columns using in Splittabular. ^^J 25 column maximum in each part of the table.^^J Each`D' counts as two columns. ^^J-----------------------------------------------------^^J} \fi } %% we don't have to worry about D's in this section, fortunately. \gdef\makethirddummycolumns{ \ifcase\thirdcolcount \or\newcolumntype{E}{h} \or\newcolumntype{E}{hh} \or\newcolumntype{E}{hhh} \or\newcolumntype{E}{hhhh} \or\newcolumntype{E}{hhhhh} \or\newcolumntype{E}{hhhhhh} \or\newcolumntype{E}{hhhhhhh} \or\newcolumntype{E}{hhhhhhhh} \or\newcolumntype{E}{hhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhhhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhhhhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhhhhhhhhhhhhhh} \or\newcolumntype{E}{hhhhhhhhhhhhhhhhhhhhhhhhh} %% up to 25 columns \else \typeout{^^J-----------------------------------------------------^^J Warning! ^^J^^J Too many Columns in Splittabular. ^^J 25 column maximum in each part of the table.^^J Each `D' counts as two columns. ^^J-----------------------------------------------------^^J}\fi } %%%%%%%%%%%%%%%%% %% Colnums %% defaults \gdef\settabnumdefaults{% \loopnum=0\relax\loop% \ifnum\loopnum<31\relax% \expandafter\gdef\csname tab\the\loopnum\endcsname{% \multicolumn1{c}{\global\advance\colnumsused by 1\relax% (\the\colnumsused)}}% \global\advance\loopnum by1\repeat} %%%%%%%%%%%%%%%%%%%%%%%%% %% this version of countcols is for \colnumbers \newcount\totalcolumncount \def\xH{h} \makeatother \def\tabcountcols#1{\ifcat#1c \global\advance\colcount by 1\relax\fi% %% \def\lookforD{#1}% \ifx\lookforD\xD% \expandafter\gdef\csname tab\the\colcount\endcsname{% \multicolumn2{c}{\global\advance\colnumsused by 1\relax% (\the\colnumsused)}}% \fi% \ifx\lookforD\xH% \expandafter\gdef\csname tab\the\colcount\endcsname{% \multicolumn1{h}{}}% \fi% %% \futurelet\next\tablookatnext} \def\tabxeatone#1{\tabcountcols} %% second conditional deals with expressions like @{} in %% the preamble. \def\tablookatnext{\if\next\xrelax\let\xgo\relax\else% \ifx\next\bgroup\let\xgo\tabxeatone\else\let\xgo\tabcountcols\fi\fi\xgo} \makeatletter %%%%%%%%%%%%%%% \newcount\totalcolumns \newbox\firsttablebox \newbox\secondtablebox \newbox\thirdtablebox \newif\ifdbreaktab %% A loop would be more elegant, of course, but using & in a loop %% within a table column produces errors. %% was\tabnumberline, now \colnumbers %% Is this test necessary? %\newif\ifcolumnums \newif\ifcolnumberson \def\deluxecolnumbers{\global\colnumbersontrue} \def\colnumbers{\omit\\\omit\xcolnumbers} \def\xcolnumbers{\global\let\colnumbers\xcolnumbers% \global\colnumbersontrue\let&\CheckNumberAndSwitch% \global\colcount=0\relax% \global\totalcolumncount=0\relax% %% above here \settabnumdefaults% %% Now, change the columns that have `D' to be \multicolumn2c, by redefining %% the \csname tab<number>\endcsname %% \expandafter\tabcountcols\tabfullpreamble% \global\totalcolumncount=\the\colcount\relax% \global\colcount=0\relax% \ifbreaktab\else\ifdbreaktab\else\global\colnumsused=0\relax\fi\fi% %% % \ifdeluxe\ifbreaktab\\\else\\[-6pt]\fi%\hline% not above \else% \\[-14pt]\fi% \ifcase\totalcolumncount% \or% \csname tab1\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&%% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname% \or \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname% \or%22 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname% \or% 24 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname% \or% 25 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname% \or% 27 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname&% \csname tab27\endcsname% \or% 28 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname&% \csname tab27\endcsname&\csname tab28\endcsname% \or% 29 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname&% \csname tab27\endcsname&\csname tab28\endcsname&% \csname tab29\endcsname% \or% 30 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname&% \csname tab27\endcsname&\csname tab28\endcsname&% \csname tab29\endcsname&\csname tab30\endcsname% \else% \typeout{^^J^^J Sorry, more than 30 columns cannot be numbered with^^J \string\colnumbers. Please number the columns manually.^^J Thank you!^^J}\fi% %\ifbreaktab \\\hline% below, hline is wanted %\else \noalign{\vskip-8pt} %\vrule height 28pt width0pt %the \vrule is in the line below colnumbers; % it causes all the vrules on that line to grow to 28pt. % The -14pt will cause the lower line to overlap the upper line. % Complication, needed to add this vrule to Z and z in order to % have it also work for split tabular. %\fi } \let\savecolnumbers\colnumbers \gdef\plaincolnumbers{% \omit\\\omit% \global\colnumbersontrue\let&\CheckNumberAndSwitch% \global\colcount=0\relax% \global\totalcolumncount=0\relax% %% above here \settabnumdefaults% %% Now, change the columns that have `D' to be \multicolumn2c, by redefining %% the \csname tab<number>\endcsname %% \expandafter\tabcountcols\tabfullpreamble% \global\totalcolumncount=\the\colcount\relax% \global\colcount=0\relax% \ifbreaktab\else\ifdbreaktab\else\global\colnumsused=0\relax\fi\fi% %% \\\ifcase\totalcolumncount% \or% \csname tab1\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&%% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname% \or \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname% \or%22 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname% \or% 24 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname% \or% 25 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname% \or% 27 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname&% \csname tab27\endcsname% \or% 28 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname&% \csname tab27\endcsname&\csname tab28\endcsname% \or% 29 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname&% \csname tab27\endcsname&\csname tab28\endcsname&% \csname tab29\endcsname% \or% 30 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname&% \csname tab27\endcsname&\csname tab28\endcsname&% \csname tab29\endcsname&\csname tab30\endcsname% \else% \typeout{^^J^^J Sorry, more than 30 columns cannot be numbered with^^J \string\colnumbers. Please number the columns manually.^^J Thank you!^^J}\fi% \\\hline% below, hline is wanted \\\noalign{\vskip-30pt }%%%%% %\vrule height 28pt width0pt %the \vrule is in the line below colnumbers; % it causes all the vrules on that line to grow to 28pt. % The -14pt will cause the lower line to overlap the upper line. % Complication, needed to add this vrule to Z and z in order to % have it also work for split tabular. } \let\saveplaincolnumbers\plaincolnumbers \def\splitplaincolnumbers{% \omit\\\omit% \xplain} \let\savesplitplaincolnumbers\splitplaincolnumbers \newif\iffirsttime \firsttimetrue \gdef\xplain{% \global\let\plaincolnumbers\xplain% \global\colnumbersontrue\let&\CheckNumberAndSwitch% \global\colcount=0\relax% \global\totalcolumncount=0\relax% %% above here \settabnumdefaults% %% Now, change the columns that have `D' to be \multicolumn2c, by redefining %% the \csname tab<number>\endcsname %% \expandafter\tabcountcols\tabfullpreamble% \global\totalcolumncount=\the\colcount\relax% \global\colcount=0\relax% \ifbreaktab\else\ifdbreaktab\else\global\colnumsused=0\relax\fi\fi% %% \iffirsttime \\%\hline% above not wanted \else \\[-12pt]%\hline% above not wanted \fi \ifcase\totalcolumncount% \or% \csname tab1\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&%% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname% \or \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname% \or%22 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname% \or% 24 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname% \or% 25 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname% \or% \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname% \or% 27 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname&% \csname tab27\endcsname% \or% 28 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname&% \csname tab27\endcsname&\csname tab28\endcsname% \or% 29 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname&% \csname tab27\endcsname&\csname tab28\endcsname&% \csname tab29\endcsname% \or% 30 \csname tab1\endcsname&\csname tab2\endcsname&% \csname tab3\endcsname&\csname tab4\endcsname&% \csname tab5\endcsname&\csname tab6\endcsname&% \csname tab7\endcsname&\csname tab8\endcsname&% \csname tab9\endcsname&\csname tab10\endcsname&% \csname tab11\endcsname&\csname tab12\endcsname&% \csname tab13\endcsname&\csname tab14\endcsname&% \csname tab15\endcsname&\csname tab16\endcsname&% \csname tab17\endcsname&\csname tab18\endcsname&% \csname tab19\endcsname&\csname tab20\endcsname&% \csname tab21\endcsname&\csname tab22\endcsname&% \csname tab23\endcsname&\csname tab24\endcsname&% \csname tab25\endcsname&\csname tab26\endcsname&% \csname tab27\endcsname&\csname tab28\endcsname&% \csname tab29\endcsname&\csname tab30\endcsname% \else% \typeout{^^J^^J Sorry, more than 30 columns cannot be numbered with^^J \string\colnumbers. Please number the columns manually.^^J Thank you!^^J}\fi% \\\hline% below, hline is wanted \iffirsttime \\\noalign{\vskip-30pt}%% %\noalign{\vskip-8pt} \vrule height 28pt width0pt %the \vrule is in the line below colnumbers; % it causes all the vrules on that line to grow to 28pt. % The -14pt will cause the lower line to overlap the upper line. % Complication, needed to add this vrule to Z and z in order to % have it also work for split tabular. \fi\global\firsttimefalse } \def\decimalcolnumbers{\crcr\saveplaincolnumbers\\% \noalign{\global\savetabskip\tabskip \tabskip=0pt \global\let\extracolsep\relax \global\let\ddoit\saveddoit \global\let\zdoit\savezdoit \vskip-32pt }{\vrule height28pt depth0pt width0pt}\relax} \def\splitdecimalcolnumbers{\\[-15pt]% \savesplitplaincolnumbers \global\colnumbersonfalse \\\noalign{\vskip-32pt %!!! \global\savetabskip\tabskip \tabskip=0pt \global\let\extracolsep\relax \global\let\ddoit\saveddoit \global\let\zdoit\savezdoit }\vrule height 28pt width0pt %!!! \global\let\splitdecimalcolnumbers\secondsplitdecimalcolnumbers} \def\secondsplitdecimalcolnumbers{\omit\\ \plaincolnumbers \global\colnumbersonfalse \\\noalign{\vskip-26pt %!!! was -28pt \global\savetabskip\tabskip \tabskip=0pt \global\let\extracolsep\relax \global\let\ddoit\saveddoit \global\let\zdoit\savezdoit }\\\relax} \let\savesplitdecimalcolnumbers\splitdecimalcolnumbers %%AAA \newif\ifdeluxestar \expandafter\def\csname deluxetable\endcsname{\deluxestartrue\bgroup\floattrue \hsize=\textwidth \deluxetable} \expandafter\def\csname enddeluxetable\endcsname{\enddeluxetable \egroup \null% added june 2020 \global\colnumbersonfalse \global\deluxedecimalsfalse \global\deluxestarfalse } \def\deluxedecimalcolnumbers{\deluxedecimalstrue\colnumbersontrue} \def\deluxetablecaption#1{\gdef\@tablecaption{#1}} \newif\ifstartlongtable \def\startlongtable{\vskip1sp\global\startlongtabletrue} \newif\iffloat \def\floattable{\global\deluxestartrue\global\floattrue} %% for equivalent but in \begin...\end form. \def\floatrotatetable{\global\deluxestartrue\global\floattrue} \let\endfloatrotatetable\relax \def\deluxetable{\global\deluxetrue \catcode`\&=\active \catcode`\$=\active %% Mar 30, 2019, to make label outside of \caption work correctly {\advance\c@table by 1 \xdef\@currentlabel{\thetable}} \let\tablecaption\deluxetablecaption \deluxetablecaption{} %% july 2016 % \iffloat % \let\go\ydeluxetable % \else\let\go\longdeluxetable\fi\go%} %% aug 2016 \ifstartlongtable %% this works for both deluxetable and deluxetable: %% nov 2017: \def\arraystretch{1.1} %% March 2019 \if@two@col\global\returntotwocoltrue\vskip1pt \ifdeluxestar\onecolumngrid\fi\fi %% \ifdeluxestar \vskip12pt \fi \let\go\longdeluxetable \else \let\go\ydeluxetable \fi\go } \def\ydeluxetable#1{% \@ifnextchar[{\xdeluxetable{#1}}{\zdeluxetable{#1}}} %% % x and z are the same, except that xdeluxetable allows optional square bracket arg, like [h]. \def\xdeluxetable#1[#2]{\global\breaktabtrue %% not here \let\colnumbers\deluxecolnumbers \global\deluxedecimalsfalse \let\decimals\deluxedecimals \let\decimalcolnumbers\deluxedecimalcolnumbers \let\tablehead\ztablehead \gdef\tabfullpreamble{#1}%<<== needed \def\endtabular{\endarray \global\let\zdoit\relax \global\let\tdoit\relax \global\Dfalse} \global\colnumsused=0 \global\breaktabtrue \global\colcount=0 %% %%%%%%%%%%%% \lineskiplimit=\z@ % restore default setting \ifdeluxestar \gdef\two{#2}\gdef\checkh{h} \ifx\two\checkh\onecolumngrid\fi \begin{table}[#2]\hsize=\textwidth\else \begin{table}[#2]\fi \noindent\setbox\splitbox=\vtop\bgroup% \currtabletypesize \vspace{\abovedeluxetableskip} %% \def\startdata##1\enddata{% \currtabletypesize \setbox0=\hbox{ \begin{tabular}{#1} \pt@head ##1\end{tabular}} \expandafter\ifx\csname @tablecaption\endcsname\empty\else %% \noindent\hbox to\hsize{\hss\vtop{\hsize=\wd0 \caption{\@tablecaption}}\hss}\vskip3pt\fi %% not here \global\setbox3\hbox{% \begin{tabular}{#1}% \hline\hline\noalign{\vskip-9pt}% \pt@head% ##1\crcr% added october 2017 \omit\\\omit\\\hline\end{tabular}} %\noindent\hskip-1.25em %% kludge! but seems necessary \hbox to\hsize{\hss\copy3\hss} \global\setbox4\vtop\bgroup\ifdeluxestar\hsize=\textwidth\else\hsize=\wd0\fi\leftskip6pt\parindent-6pt }} \def\zdeluxetable#1{\global\breaktabtrue \let\colnumbers\deluxecolnumbers \global\deluxedecimalsfalse \let\decimals\deluxedecimals \let\decimalcolnumbers\deluxedecimalcolnumbers \let\tablehead\ztablehead \gdef\tabfullpreamble{#1}%<<== needed \def\endtabular{\endarray \global\let\zdoit\relax \global\let\tdoit\relax \global\Dfalse} \global\breaktabtrue \global\colnumsused=0 \global\colcount=0 %% %%%%%%%%%%%% \lineskiplimit=\z@ % restore default setting \ifdeluxestar \begin{table}\hsize=\textwidth\else \begin{table}\fi \noindent\setbox\splitbox=\vtop\bgroup% \currtabletypesize \vspace{\abovedeluxetableskip} %% \def\startdata##1\enddata{% \currtabletypesize \setbox0=\hbox{\colnumbersonfalse \begin{tabular}{#1} \pt@head %% ##1\end{tabular}}% not here \expandafter\ifx\csname @tablecaption\endcsname\empty\else \noindent\hbox to\hsize{\hss\vtop{\hsize=\wd0 \caption{\@tablecaption}}\hss}\vskip3pt\fi \global\setbox3\hbox{% \begin{tabular}{#1}% \hline\hline\noalign{\vskip-9pt}% \pt@head% ##1\crcr%% added October 2017 \omit\\\omit\\\hline\end{tabular}}%%<<== original \vskip-\parskip \noindent\hbox to\hsize{\hss\copy3\hss} \global\setbox4\vtop\bgroup\hsize=\wd0\relax \leftskip6pt\parindent-6pt }} %% go to \end{deluxetable}, after longdeluxetable %%@@@@ %% Variation on definition found in revtex4-1.cls \def\LT@start@new{% \let\LT@start\endgraf \endgraf \markthr@@{}% \LT@pre \@ifvoid\LT@firsthead{\LT@top}{\hbox{\ifdim\movetableright>0pt\relax\hskip\movetableright\fi\box\LT@firsthead} \nobreak}% \mark@envir{longtable}% }% %%% \newbox\longtablebox \def\longdeluxetable#1{ \global\rotateonfalse \let\colnumbers\deluxecolnumbers \global\deluxedecimalsfalse \let\decimals\deluxedecimals \let\decimalcolnumbers\deluxedecimalcolnumbers \let\tablehead\ztablehead \gdef\tabfullpreamble{#1}%<<== needed \def\endtabular{\endarray \global\let\zdoit\relax \global\let\tdoit\relax \global\Dfalse} \global\colnumsused=0 \global\colcount=0 %% %%%%%%%%%%%% \lineskiplimit=\z@ % restore default setting \let\enddeluxetable\endlongdeluxetable \vspace{\abovedeluxetableskip} %% \def\startdata##1\enddata{% \global\setbox\longtablebox=\hbox{\currtabletypesize \tabcolsep=3pt \begin{tabular}{#1} \pt@head ##1\end{tabular}} %%% \bgroup\centering \def\table@hook{\currtabletypesize} \LTcapwidth=\wd\longtablebox %% march 2019, added [c] and these terms: \ifcenterwidetable\global\centerwidetablefalse \def\LT@LR@c{\LTleft=0pt minus1fill \let\LTright\LTleft}% \else %% default, will center table that is narrower than text width \def\LT@LR@c{\LTleft=0pt plus1fill \LTright\LTleft}% \fi %% % \begin{longtable}[c]{#1}%% \ifdim\movetableright>0pt \noalign{\ifdim\movetableright>0pt \global\LTleft=\movetableright \fi} % \noalign{\hbox to \wd\longtablebox{ \vtop{\hsize=.8\wd\longtablebox \advance\baselineskip4pt \raggedright {\bf \fnum@table}.\vrule depth 6pt width0pt\ \@tablecaption}\hss}\vskip-3pt }\\ \hline \hline\noalign{\vskip-9pt} \pt@head% \else \caption{\hsize=\wd\longtablebox \advance\baselineskip2pt \@tablecaption}\\ % \hline\hline\noalign{\vskip-9pt}% prob ok \pt@head% \fi \endfirsthead \noalign{\centerline{\small \hskip\movetableright{\bf \fnum@table}\ \it(continued)}\vskip6pt} \hline\hline \noalign{\vskip-12pt} \pt@head% \endhead \hline \multicolumn{\totalcolumns}{c}{\vrule height 24pt width0pt\small\it \fnum@table\ continued \if@two@col\else on next page\fi}\\ \endfoot \hline%\nobreak \endlastfoot ##1 \end{longtable} \vglue-\LTpost \vskip-6pt \egroup \global\setbox4=\vtop\bgroup \ifdim\wd\longtablebox>\textwidth \hsize=\textwidth \else \hsize=\wd\longtablebox\fi \leftskip=6pt \parindent=-6pt \currtabletypesize \global\startlongtablefalse \global\movetableright=0pt }% end data, endlongtable } \def\endlongdeluxetable{ %% \vrule depth 6pt width 0pt \vskip1sp \egroup \ifdim\dp4>6pt \vglue-6pt \vbox{\hbox to \columnwidth{\hfill \vtop{\hsize\wd\longtablebox \leftskip=6pt\parindent-6pt \copy4 }\hfill}%% } \fi \vglue\ht4 \global\colnumbersonfalse \global\deluxedecimalsfalse \global\rotateonfalse %% \relax\null%% \null is an empty hbox. %% This keeps final page(s) of startlongtable/deluxetable %% from begin thrown away when at end of article. % \global\advance\c@table-1\relax %% % %% march 2019 \ifreturntotwocol\global\returntotwocolfalse \twocolumngrid\fi %% May 2020 \ifappendixon \if@two@col@app \twocolumngrid \else \onecolumngrid\fi\fi \null }%% %% bbb %% \end{deluxetable}: \def\enddeluxetable{% \egroup%end box 4 \ifdim\dp4>6pt \hbox to\hsize{\hss\copy4\hss} \fi \egroup% end splitbox \centering \ifrotateon\global\rotateonfalse \rotatebox{90}{\hbox to\textheight{\hfill\vbox{ \unvbox\splitbox \vspace{\belowdeluxetableskip}}\hfill}} \else \centering\unvbox\splitbox \vspace{\belowdeluxetableskip} \vspace{24pt} \fi \ifdeluxestar\end{table}\global\deluxestarfalse \if@two@col \twocolumngrid\hsize=\columnwidth\fi%% check this!! \else \end{table}\fi \null % added june 2020 \gdef\colnumbers{\saveplaincolnumbers} \global\breaktabfalse \global\deluxefalse \global\colnumbersonfalse \global\deluxedecimalsfalse \global\rotateonfalse \startlongtablefalse \global\movetableright=0pt %\global\floatfalse %\global\advance\c@table by -1\relax %% check this!! } %%@@@ ??? \newbox\splitbox \newif\ifdeluxe \def\splitdeluxetable{ %% Mar 30, 2019, to make label outside of \caption work correctly {\advance\c@table by 1 \xdef\@currentlabel{\thetable}} \global\deluxetrue\catcode`\&=\active \catcode`\$=\active \xsplitdeluxetable} \def\xsplitdeluxetable#1{ \global\breaktabtrue \let\colnumbers\deluxecolnumbers \let\decimals\deluxedecimals \global\deluxedecimalsfalse \let\decimalcolnumbers\deluxedecimalcolnumbers \let\tablehead\xtablehead \gdef\tabfullpreamble{#1} \def\endtabular{\endarray \global\let\zdoit\relax \global\let\tdoit\relax \global\Dfalse} %%% modification of emulateapj \deluxetable %%%% \setbox0=\hbox{\def\firstarg{#1}\expandafter\lookforD\firstarg} \gdef\temppreamble{#1\relax} \PartsOfTable=0 \def\tempfullpreamble{#1BB} \setbox0=\hbox{\expandafter\checkforB\tempfullpreamble} %% Now PartsOfTable is either =2 or 3 %% \gdef\one{#1Z} \global\colnumsused=0 \global\breaktabtrue \global\colcount=0 %% \ifnum\PartsOfTable=3 \let\multicolumn\threebreakmulticolumn \else \let\multicolumn\breakmulticolumn \fi %%%%%%%%%%%% \lineskiplimit=\z@ % restore default setting \gdef\tblnote@list{} \gdef\tblref@list{} \ifsplitstar \begin{table}\else \begin{table}\fi \noindent\setbox\splitbox=\vtop\bgroup% \currtabletypesize \vspace{\abovedeluxetableskip} \let\startdata\xstartdata} %% \end{splitdeluxetable}: \newdimen\movetabledown \def\endsplitdeluxetable{\vskip1sp\egroup%% end box with tablenotes \hbox to \hsize{\hss\copy4\hss} \egroup \vskip1pt \ifrotateon\global\rotateonfalse \vskip\movetabledown\rotatebox{90}{\vbox{\noindent\unvbox\splitbox % \vspace{\belowdeluxetableskip} }}\global\movetabledown=0pt\else \noindent\unvbox\splitbox \vspace{\belowdeluxetableskip} \fi \ifsplitstar \end{table} \else \end{table}\fi \gdef\colnumbers{\saveplaincolnumbers} \tabletypesize{\small} \global\breaktabfalse \global\deluxefalse \global\splitstarfalse \global\colnumbersonfalse \global\deluxedecimalsfalse } \newif\ifsplitstar \expandafter\def\csname splitdeluxetable\endcsname{\global\splitstartrue\splitdeluxetable} \expandafter\def\csname endsplitdeluxetable\endcsname{\endsplitdeluxetable\global\splitstarfalse \global\colnumbersonfalse \global\deluxedecimalsfalse } \newdimen\maxtablewidth \gdef\NoTableCaption{\global\@table@not@headedtrue} %% For splitdeluxetable %%% ====================================================== %%% \gdef\dbreaktabular{\catcode`\&=\active \let&\CheckNumberAndSwitch\xdbreaktabular} \long\gdef\xdbreaktabular#1{%% #1=contents of table {\global\maxtablewidth=0pt \let&\CheckNumberAndSwitch \let$\savedollar \global\colnumsused=0 %% \global\dbreaktabtrue \global\colcount=0 %% \ifnum\PartsOfTable=3 \let\multicolumn\threebreakmulticolumn \else \let\multicolumn\breakmulticolumn \fi %% \ifnum\PartsOfTable=3 \expandafter\catchfirstpreamble\one \expandafter\catchsecondofthreepreamble\one \expandafter\catchthirdpreamble\one \makefirstdummycolumns \makeseconddummycolumns \makethirddummycolumns \else %% PartsOfTable=2 \ifnum\PartsOfTable=2 \expandafter\catchfirstpreamble\one \expandafter\catchsecondpreamble\one \makefirstdummycolumns \makeseconddummycolumns \fi\fi %%% \global\columncount=0 \ifnum\PartsOfTable=3 %% For table divided into three parts \firstboxtrue\secondboxfalse\thirdboxfalse \setbox\firsttablebox=\hbox{% \begin{tabular}{AFE} \ifx\csname pt@head\endcsname\relax\else \pt@head\fi#1\crcr\end{tabular}} \global\maxtablewidth=\wd\firsttablebox \noindent\hbox to \hsize{\hss\unhbox\firsttablebox\hss} \vskip6pt \hrule \vskip6pt \global\columncount=0 \firstboxfalse\secondboxtrue\thirdboxfalse \ifcolnumberson% \setbox\secondtablebox=\hbox{% \let\savecolnumbers\xcolnumbers% \notfirsttrue% \begin{tabular}{fZE} %fZE !!! \ifx\csname pt@head\endcsname\relax\else% \pt@head\fi#1\crcr\end{tabular}} \else %% \setbox\secondtablebox=\hbox{% \begin{tabular}{fZE}% \ifx\csname pt@head\endcsname\relax\else% \pt@head\fi\\ [-14pt]% #1\crcr% \end{tabular}} \fi \ifdim\wd\secondtablebox>\maxtablewidth \global\maxtablewidth\wd\secondtablebox\fi \noindent\hbox to \hsize{\hss\unhbox\secondtablebox\hss} %% \vskip6pt \hrule \vskip6pt \firstboxfalse\secondboxfalse\thirdboxtrue \global\columncount=0 \ifcolnumberson \notfirsttrue \setbox\thirdtablebox=\hbox{ \let\savecolnumbers\xcolnumbers \notfirsttrue \begin{tabular}{fFz} \ifx\csname pt@head\endcsname\relax\else \pt@head\fi#1\crcr\end{tabular}} \else \setbox\thirdtablebox=\hbox{ \begin{tabular}{fFz} \ifx\csname pt@head\endcsname\relax\else \pt@head\fi\\[-14pt] #1 \end{tabular}} \fi \ifdim\wd\thirdtablebox>\maxtablewidth \global\maxtablewidth\wd\thirdtablebox\fi \noindent\hbox to \hsize{\hss\unhbox\thirdtablebox\hss} \vskip6pt \hrule \else %% Original for table divided into two parts \global\columncount=0 \secondboxfalse \setbox\firsttablebox=\hbox{% \begin{tabular}{AF} \ifx\csname pt@head\endcsname\relax\else \pt@head\fi% #1\end{tabular}} \global\maxtablewidth=\wd\firsttablebox \hbox to \hsize{\hss\unhbox\firsttablebox\hss} \vskip6pt \hrule \vskip6pt \global\columncount=0 \secondboxtrue \ifcolnumberson \setbox\secondtablebox=\hbox{% \let\savecolnumbers\xcolnumbers \notfirsttrue \begin{tabular}{fZ}%% \ifx\csname pt@head\endcsname\relax\else% \pt@head\fi#1\crcr%%= tablecontents \end{tabular}}% \else \setbox\secondtablebox=\hbox{% \begin{tabular}{fZ}%% was 12 \ifx\csname pt@head\endcsname\relax\else% \pt@head\fi\\[-14pt]% #1%%= tablecontents \end{tabular}}\fi \ifdim\wd\secondtablebox>\maxtablewidth \global\maxtablewidth\wd\secondtablebox\fi \noindent\hbox to \hsize{\hss\unhbox\secondtablebox\hss} \vskip6pt \hrule \secondboxtrue %% %% end of conditional testing for 2 or 3 part table: \fi %% \global\dbreaktabfalse}} %%% ====================================================== %%% \newif\ifnotfirst %% @@@@ %% xstartdata, modified from \startdata in emulateapj, for splitdeluxetable \gdef\xstartdata#1\enddata{\def\tablecontents{% \ifcolnumberson% \\\savecolnumbers\\[2pt]\fi% this is for top level split \ifdeluxedecimals\savedecimals\fi% #1}% \currtabletypesize% \setbox2=\vtop{\dbreaktabular{\tablecontents}}% % \expandafter\ifx\csname @tablecaption\endcsname\empty\else \noindent\hbox to\hsize{\hss\vtop{\hsize=\maxtablewidth\caption{\@tablecaption}}\hss}\vskip3pt\fi \dbreaktabular{\tablecontents\noalign{\global\let\zdoit\relax \global\let\ddoit\relax}} \parindent=0pt \global\setbox4=\vtop\bgroup% egroup in enddeluxetable \currtabletypesize \ifsplitstar \hsize=\textwidth\else\hsize=245.3pt\fi \parindent=-6pt \leftskip=6pt } \def\tablecomments#1{\vskip1pt{\small\vskip1sp\indent\vrule height 11pt depth 2pt width 0pt\currtabletypesize{\sc Note}---{#1}\vskip1pt}} \def\tablenotetext#1#2{\vskip1pt{\currtabletypesize\vskip1pt\indent\vrule height 11pt depth 2pt width0pt\relax$^{\hbox to 5pt{$#1$}}$#2\vskip1pt}} \def\tablerefs#1{{\small\vskip3pt\indent\vrule height 11pt depth 2pt width 0pt\currtabletypesize{\bf References}---{#1}\vskip1sp}} \let\tablereferences\tablerefs %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 5. Simple entry decimal numbers %% extra unused args are to get rid of unnecessary commands revtex puts in \gdef\lookfordecimal#1#2#3#4.#5 {\gdef\xone{{\let$\relax\savedollar#4\savedollar}} \gdef\xtwo{#5}\ifx\xtwo\empty\else\gdef\xtwo{{\let$\relax\savedollar#5\savedollar}}\fi} %% D \def\newdoit{\setbox0=\hbox\bgroup\zdoit} \def\endnewdoit{\egroup\unhbox0} \long\gdef\zdoit#1 {\let$\relax \def\bothcols{#1 }% \setbox0=\hbox{\let$\relax\expandafter\lookfordecimal\bothcols{}{}{}{}.{} }% \xdoit} \global\let\savezdoit\zdoit \let\zdoit\relax \gdef\xdoit{\relax\hskip\tabcolsep\relax\xone&\tabskip=0pt% \ifx\xtwo\empty\let\go\relax\else.\def\go{\xtwo}\fi\go} %% d \def\xnewdoit{\setbox0=\hbox\bgroup\ddoit} \def\xendnewdoit{\egroup} \long\gdef\ddoit#1#2#3{\xxdoit} \let\saveddoit\ddoit \let\ddoit\relax %% to delete all D material: \gdef\xxdoit{&} \newcolumntype{D}{>\newdoit r<{\endnewdoit} @{}l}%% \newcolumntype{d}{>\xnewdoit h<{\xendnewdoit} @{}h} %% \newdimen\savetabskip \gdef\decimals{\noalign{\global\savetabskip\tabskip \tabskip=0pt \global\let\extracolsep\relax \global\let\ddoit\saveddoit \global\let\zdoit\savezdoit }} \let\savedecimals\decimals %% to allow \decimals to be used before \startdata: \newif\ifdeluxedecimals \def\deluxedecimals{\global\deluxedecimalstrue} %%%%%%%%% %% This needed to be redefined so that \colhead in \tablehead would span both parts %% of decimal numbers. %% in case there isn't a table head \let\pt@head\relax %% for splitdeluxetable \def\xtablehead{\catcode`\&=\active% \catcode`\$=\active% \xxtablehead} %% \def\xxtablehead#1{% \let&\CheckNumberAndSwitch% \gdef\pt@head{% \hline\hline% \multicolumn1c{\vrule height 12pt width0pt\relax\tempcounter=0 \expandafter\getDs\tabfullpreamble\relax \global\colcount=0 \global\colheadcount=0}% \\ \iftwelvepoint% \ifpreprint% \iflongrotateon\else\noalign{\vskip-6.5pt}\fi% \else% \ifpreprinttwo% \iflongrotateon\else\noalign{\vskip-6.5pt}\fi% \else% \ifmanu% \iflongrotateon\noalign{\vskip-8pt}\else\noalign{\vskip-17pt}\fi% \else% \ifmodern\iflongrotateon\else\noalign{\vskip-9pt}\fi% \else% \fi%% end ifmodern \fi%% end ifmanu \fi%% end ifpreprinttwo \fi%% end ifpreprint \else% %% not twelvepoint \iftwocolstyle% \iflongrotateon\else\noalign{\vskip-5pt}\fi% \else% \ifonecolstyle% default \iflongrotateon\noalign{\vskip2pt}\else\noalign{\vskip-4.5pt}\fi% \fi% end ifonecol \fi%endiftwocolstyle \fi%end iftwelvepoint #1\ifcolnumberson% \ifnotfirst\\[-22pt]\fi \else\\\hline\\[-8pt]\fi% space below hline for 2nd and 3rd part of split table }% % } \def\ztablehead{\catcode`\&=\active% \catcode`\$=\active% \zztablehead} \def\zztablehead#1{\let&\CheckNumberAndSwitch% \gdef\pt@head{% %% this is needed: \multicolumn1c{\vrule height12pt width0pt\relax\expandafter\getDs\tabfullpreamble\relax \global\tempcounter=0 \global\colcount=0 \global\colheadcount=0}\\ \iftwelvepoint% \ifpreprint% \iflongrotateon\else\noalign{\vskip-6.5pt}\fi% \else% \ifpreprinttwo% \iflongrotateon\else\noalign{\vskip-6.5pt}\fi% \else% \ifmanu% \iflongrotateon\noalign{\vskip-8pt}\else\noalign{\vskip-17pt}\fi% \else% \ifmodern \iflongrotateon\else\noalign{\vskip-5pt}\fi% \else% \fi%% end ifmodern \fi%% end ifmanu \fi%% end ifpreprinttwo \fi%% end ifpreprint \else% %% not twelvepoint \iftwocolstyle% \iflongrotateon\else\noalign{\vskip-5pt}\fi% \else% \ifonecolstyle% default \iflongrotateon\noalign{\vskip2pt}\else\noalign{\vskip-4.5pt}\fi% \fi% end ifonecol \fi%endiftwocolstyle \fi%end iftwelvepoint #1\unskip% \ifcolnumberson\\[6pt] \savecolnumbers\vrule height 11pt depth 4pt width 0pt\relax% \\\ifmanu\noalign{\vskip-15pt}\fi% \ifdeluxedecimals\\[-14pt]% \savedecimals\fi% \else \vrule depth 6pt width0pt\\\ifdeluxedecimals\savedecimals\fi\hline\fi% }} \newcount\tempcounter \gdef\getDs#1{\let&\CheckNumberAndSwitch \def\lookforD{#1}% \ifx\lookforD\xD% \expandafter\gdef\csname col\the\tempcounter\endcsname{2}\else \expandafter\gdef\csname col\the\tempcounter\endcsname{1}\fi \global\advance\tempcounter by 1 \futurelet\next\checkingpreamble} \gdef\checkingpreamble{\ifx\next\relax \let\go\relax\else\let\go\getDs\fi\go} %%% Something like this could be used to automate the width of colheads in the tablehead, %% making those that match the D in preamble are multicolumn2c instead of %% multicolumn 1c. \newcount\colheadcount \newcommand\xcolhead[1]{\multicolumn{\expandafter\ifx\csname col\the\colheadcount\endcsname\relax 1\else\expandafter% \csname col\the\colheadcount\endcsname\fi}{c}{\vrule depth 4pt width0pt\relax#1\relax\global\advance\colheadcount by 1\relax}\ignorespaces}% % %% \extrarowheight=2pt %% from revtex4-1, additions on top %% fix for \usepackage{amsmath} and %% any matrix environment \def\matrixpreamble{\c@MaxMatrixCols c} %% this causes problem, must be fixed! %\let\save@array@array@new\@array@array@new \def\@array@array@new[#1]#2{% \ifbreaktab \else %%% added so that we can use \colnumbers in any tabular environment %%% and avoid error messages for breaktabular \def\catchpreamble{#2\relax} \gdef\tabfullpreamble{#2\relax} {\colcount=0 %% important fix, makes it possible to use amsmath and matrices. \def\two{#2} \ifx\matrixpreamble\two \else \expandafter\countcols\catchpreamble \global\totalcolumns=\colcount\fi} \fi %%% end of additions \@tempdima\ht\strutbox \advance\@tempdima by\extrarowheight \setbox\@arstrutbox\hbox{% \vrule \@height\arraystretch\@tempdima \@depth \arraystretch\dp\strutbox \@width \z@ }% \begingroup \@mkpream{#2}% \xdef\@preamble{\@preamble}% \endgroup \prepdef\@preamble{% \tabskip\tabmid@skip \@arstrut }% \appdef\@preamble{% \tabskip\tabright@skip \cr \array@row@pre }% \@arrayleft \@nameuse{@array@align@#1}% \m@th \let\\\new@arraycr %<<== defined above, original plus reset counters \let\tabularnewline\\% \let\par\@empty \let\@sharp##% \set@typeset@protect \lineskip\z@\baselineskip\z@ \tabskip\tableft@skip \everycr{}% \expandafter\halign\expandafter\@halignto\expandafter\bgroup\@preamble }% %% \rotate \newif\ifrotateon \def\rotate{\global\floattrue\iffloat\global\let\go\relax\global\rotateontrue\else \global\rotateonfalse \let\go\relax %\def\go{\vskip48pt\huge %{\tt \string\floattable\space must precede table using %\string\rotate !!}} \fi\go} \def\colnumbers{\plaincolnumbers} %% add 6pt of space between table and following text: \let\saveendtable\endtable \def\endtable{\vskip6pt\saveendtable} \expandafter \let \csname endtable\endcsname = \endtable %% %%% \movetabledown works \newbox\rotatetablebox \def\rotatetable{% \clearpage \global\startlongtabletrue\setbox\rotatetablebox=\vbox\bgroup } \def\endrotatetable{\egroup \vglue\movetabledown \hbox to \textwidth{\hss\rotatebox{90}{\hbox{\box\rotatetablebox}}\hss} \global\movetabledown=0pt\relax \global\startlongtablefalse } %%% \movetabledown works \expandafter\def\csname rotatetable\endcsname{% \clearpage \global\startlongtabletrue\setbox\rotatetablebox=\vbox to \textwidth\bgroup\vfill} \expandafter\def\csname endrotatetable\endcsname{\vfill\egroup \vbox to \textheight{\vfill \vglue\movetabledown \hbox to \textwidth{\hss\rotatebox{90}{\box\rotatetablebox}\hss}\global\movetabledown=0pt\relax \vfill} \clearpage \if@two@col \twocolumngrid \global\startlongtablefalse } % %%% \movetabledown works \newif\iflongrotateon \def\longrotatetable{% \global\longrotateontrue \if@two@col\onecolumngrid\clearpage \fi \clearpage \clearpage \begingroup \expandafter\def\csname deluxetable\endcsname{\deluxetable} \expandafter\def\csname enddeluxetable\endcsname{\enddeluxetable} \global\floatfalse \global\startlongtabletrue \def\LS@rot{% \setbox\@outputbox\vbox{\vskip\movetabledown\hbox{\rotatebox{90}{\box\@outputbox}}}} \let\LS@makecol=\@makecol \let\LS@makefcolumn=\@makefcolumn \vsize=\textwidth \hsize=\textheight \linewidth=\hsize \columnwidth=\hsize \@colroom=\vsize \textheight=\vsize \@colht=\vsize \def\@makecol{\LS@makecol\LS@rot}% \def\@makefcolumn##1{\LS@makefcolumn{##1}\LS@rot}} \def\endlongrotatetable{% \onecolumngrid %% ?? \clearpage \ifGin@pdftex \pdfpageattr{/Rotate 90} \fi \clearpage \endgroup \if@two@col\twocolumngrid\fi \clearpage \global\longrotateonfalse \global\movetabledown=0pt \global\@colht=\textheight \global\vsize=\textheight \global\@colroom=\textheight} \newif\ifGin@pdftex \Gin@pdftexfalse \DeclareOption{pdftex}{% \PassOptionsToPackage\CurrentOption{graphicx} \Gin@pdftextrue } \DeclareOption{\PassOptionsToPackage\CurrentOption{graphicx}} \ProcessOptions %% set &, $ catcode back to normal: \catcode`&=4 \catcode`$=3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% end table tools %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Gridlines for positioning multiple illustrations in %% one figure environment. \def\gridline#1{\vskip6pt\hbox to\hsize{#1}\vskip6pt} \def\boxedfig#1#2#3{\hfill\fbox{\vbox{\parskip=0pt\relax \hsize=#2 \includegraphics[width=#2]{#1}\vskip2pt\vtop{\hsize=#2 \centerline{#3}}}}\hfill} \def\fig#1#2#3{\hfill\vbox{\parskip=0pt\hsize=#2 \includegraphics[width=#2]{#1}\vskip2pt\vtop{\centering \footnotesize \hsize=#2 #3\vskip1pt }}\hfill} \def\leftfig#1#2#3{\vbox{\parskip=0pt\relax\hsize=#2 \includegraphics[width=#2]{#1}\vskip2pt\vtop{\hsize=#2 \centering #3\vskip1sp\vskip1sp}}\hfill} \def\rightfig#1#2#3{\hfill\vbox{\parskip=0pt\relax\hsize=#2 \includegraphics[width=#2]{#1}\vskip2pt\vtop{\hsize=#2 \centering#3\vskip1sp}}} \def\rotatefig#1#2#3#4{\hfill\vbox{\centering\parskip=0pt\hsize=#3 \includegraphics[width=#3,angle=#1]{#2}\vskip2pt\vtop{\centering \footnotesize \hsize=#3 #4\vskip1pt }}\hfill} %%%%%%%%%% End Grid line Macros %%%%%%%%%% %%%%%%%%%% Color Editing Macros %%%%%%%%%% %% \turnoffedit or \turnoffedits %% will prevent all \edit<number>{text}, all %% \collaborationcomment<number>{text}, and all %% \authorcomment<number>{text} from producing any text. \newif\ifturnoffedit \def\turnoffedit{\global\turnoffedittrue} \def\turnoffedits{\global\turnoffedittrue} \let\turnoffediting\turnoffedits \newif\ifturnoffone \newif\ifturnofftwo \newif\ifturnoffthree %% \turnoffeditone to only turn off only \edit1, \collaborationcomment1 and \authorcomment1 : \def\turnoffeditone{\turnoffonetrue} %% \turnoffedittwo to only turn off only \edit2, \collaborationcomment2 and \authorcomment2 : \def\turnoffedittwo{\turnofftwotrue} %% \turnoffeditthree to only turn off only \edit3, \collaborationcomment3 and \authorcomment3 : \def\turnoffeditthree{\turnoffthreetrue} %% Other choices can be made, but this should be %% standardized, so didn't make an user interface %% to change the colors easily. \expandafter\def\csname editcolor1\endcsname{black}% was magenta \expandafter\def\csname editcolor2\endcsname{black}% was blue \expandafter\def\csname editcolor3\endcsname{black}% was violet \let\newgo\relax \newcount\colorcount \newcount\editnum \def\edit#1#2{\ifcase#1\or\ifturnoffone% \unskip% \else% \texorpdfstring{{\bf#2}}{#2}\fi\or% \ifturnofftwo% \unskip% \else\texorpdfstring{{\bfseries\itshape#2}}{#2}\fi% \or% \ifturnoffthree\unskip\else% \texorpdfstring{{\bfseries\underline{#2}}}{#2}\fi\fi} \def\collaborationcomment#1#2{{\colorcount=#1 \ifturnoffedit\let\go\ignorespaces\else% \let\go\relax% \color{\csname editcolor\the\colorcount\endcsname} \ifnum\colorcount=1{\ifturnoffone\else\bf (Collaboration~note: #2)\ \fi}\else \ifnum\colorcount=2{\ifturnofftwo\else\it (Collaboration~note: #2)\ \fi}\else \ifnum\colorcount=3{\ifturnoffthree\else (Collaboration~note: #2)\ \fi}\fi\fi\fi\fi% \go}} \def\authorcomment#1#2{{\colorcount=#1 \ifturnoffedit\let\go\ignorespaces\else% \let\go\relax% \color{\csname editcolor\the\colorcount\endcsname} \ifnum\colorcount=1{\ifturnoffone\else\bf (Author~note 1: #2)\ \fi}\else \ifnum\colorcount=2{\ifturnofftwo\else\it (Author~note 2: #2)\ \fi}\else \ifnum\colorcount=3{\ifturnoffthree\else (Author~note 3: #2)\ \fi}\fi\fi\fi\fi% \go}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Draft watermark \definecolor{ltgray}{gray}{.9}% .89 \font\bighelv=phvr at 2in % \def\setwatermarkfontsize#1{\font\bighelv=phvr at #1} \def\watermark#1{\def\thewatermark{\hbox to\textwidth{\vtop to 1.1\textheight{\vss \hskip24pt\rotatebox{60}{\hbox{\bighelv \color{ltgray} \uppercase{#1}}}\vss}}\hss}} \let\thewatermark\empty %% Used in titlepage definition, as \pagestyle{titlepage} \def\ps@titlepage{% \let\@mkboth\@gobbletwo \def\@oddhead{\ifx\thewatermark\empty\hfill\else \hbox to \textwidth{\rlap{\thewatermark}\hfill}\fi} \let\@oddfoot\@empty \let\@evenhead\@empty\let\@evenfoot\@empty} % end of watermark definitions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newcommand\submitjournal[1] {\def\@submitted{Submitted to #1}}% %% this one is used &&& \def\titleblock@produce{% \begingroup \ltx@footnote@pop \def\@mpfn{mpfootnote}% \def\thempfn{\thempfootnote}% \c@mpfootnote\z@ \let\@makefnmark\frontmatter@makefnmark \frontmatter@setup \thispagestyle{titlepage}\label{FirstPage}% \ifmodern\leftskip=0pt\rightskip\leftskip\fi \frontmatter@title@produce \groupauthors@sw{% \frontmatter@author@produce@group }{% \frontmatter@author@produce@script }% \frontmatter@RRAPformat{% \vskip12pt \expandafter\produce@RRAP\expandafter{\@date}% \expandafter\produce@RRAP\expandafter{\@received}% \expandafter\produce@RRAP\expandafter{\@revised}% \expandafter\produce@RRAP\expandafter{\@accepted}% \expandafter\produce@RRAP\expandafter{\@published}% }% \expandafter\ifx\csname @submitted\endcsname\relax\else \vskip6pt \expandafter\produce@RRAP\expandafter{\centerline{\@submitted\hbox to 20pt{\hfill}}\vskip12pt}% \fi \frontmatter@abstract@produce \@ifx@empty\@pacs{}{% \@pacs@produce\@pacs }% \@ifx@empty\@keywords{}{% \@keywords@produce\@keywords }% \par \frontmatter@finalspace \endgroup% }% % needed?? \gdef\specialbibitem#1[#2]#3#4{ {\tt\string\bibitem}[#2]{\tt\string{\string}} #4} %%%%%%%%%%%%%%%%%%%%%%%%% %% Track Changes %% Amy Hendrickson, Nov 2015 %% Change Jan 2016, to allow list of changes %% to give line and page numbers for more than one entry on the same line. %% Change Feb 2016, to allow optional argument for time/date, and/or editor initials, etc. \providecolor{trackchange}{cmyk}{0,0,0,1} \providecolor{explain}{cmyk}{0,0,0,1} \newif\ifsilent \newcount\refchangenumber \def\added{\@ifnextchar[{\xadded}{\yadded}} \long\def\xadded[#1]#2{% \iftrack {\global\advance\refchangenumber by 1\relax% \vtop to 0pt{\vss \hypertarget{link\the\refchangenumber}{} \vskip14pt}% \ifnumlines% \ifabstract\else% \xdef\doit{\noexpand\linelabel{\the\refchangenumber}}\doit\fi\else% \xdef\doit{\noexpand\label{\the\refchangenumber}{}{}{}}\doit\fi}% {\color{trackchange}\bf(Added: [#1] #2)}%% \ifabstract\label{\the\refchangenumber}% \expandafter\gdef\csname changenum\the\refchangenumber\endcsname{\bf Added: [#1] \textcolor{trackchange}\bf\relax{#2}\global\silenttrue}% \else\expandafter\gdef\csname changenum\the\refchangenumber\endcsname{\bf\relax Added: [#1] \textcolor{trackchange}\bf\relax{\let\bibitem\specialbibitem #2}\global\silentfalse}\fi% \else#2\fi} \long\def\yadded#1{% \iftrack{\global\advance\refchangenumber by 1\relax% \vtop to 0pt{\vss \hypertarget{link\the\refchangenumber}{} \vskip14pt}% \ifnumlines\ifabstract\else% \xdef\doit{\noexpand\linelabel{\the\refchangenumber}}\doit\fi\else% \xdef\doit{\noexpand\label{\the\refchangenumber}{}{}{}}\doit% \fi}% {\color{trackchange}\bf(Added: #1)}%% \ifabstract% \label{\the\refchangenumber}% \expandafter\gdef\csname changenum\the\refchangenumber\endcsname{\bf Added: \textcolor{trackchange}\bf\relax{#1}, \global\silenttrue}\else \expandafter\gdef\csname changenum\the\refchangenumber\endcsname{\bf Added: \textcolor{trackchange}{\bf\relax\let\bibitem\specialbibitem #1},% \global\silentfalse}\fi% \else#1\fi} \def\deleted{\@ifnextchar[{\xdeleted}{\ydeleted}} \long\def\xdeleted[#1]#2{\iftrack{\global\advance\refchangenumber by 1\relax% \vtop to 0pt{\vss \hypertarget{link\the\refchangenumber}{} \vskip14pt}% \ifnumlines\ifabstract\else% \xdef\doit{\noexpand\linelabel{\the\refchangenumber}}\doit\fi% \else% \xdef\doit{\noexpand\label{\the\refchangenumber}}\doit\fi% }% {\color{trackchange}\bf% \ifbib\let\sout\relax\fi% (Deleted: [#1] \sout{#2}) }% \ifabstract\label{\the\refchangenumber}% \expandafter\gdef\csname changenum\the\refchangenumber\endcsname{Deleted: [#1] {\color{trackchange}\bf% \sout{#2}}\global\silenttrue}% \else \expandafter\gdef\csname changenum\the\refchangenumber\endcsname{Deleted: [#1] {\color{trackchange}% \let\bibitem\specialbibitem% \sout{#2} }\global\silentfalse}\fi% \fi} \long\def\ydeleted#1{\iftrack{\global\advance\refchangenumber by 1\relax% \vtop to 0pt{\vss \hypertarget{link\the\refchangenumber}{} \vskip14pt}% \ifnumlines\ifabstract\else% \xdef\doit{\noexpand\linelabel{\the\refchangenumber}}\doit\fi% \else% \xdef\doit{\noexpand\label{\the\refchangenumber}{}{}{}}\doit% \fi}% %% {\color{trackchange}\bf% \ifbib\let\sout\relax\fi% (Deleted: \sout{#1})}% \ifabstract\label{\the\refchangenumber}% \expandafter\gdef\csname changenum\the\refchangenumber\endcsname{Deleted: {\color{trackchange}\bf \sout{#1}}\global\silenttrue}% \else \expandafter\gdef\csname changenum\the\refchangenumber\endcsname{Deleted: {\color{trackchange}\bf% \sout{#1}}\global\silentfalse}\fi% \fi} \def\replaced{\@ifnextchar[{\xreplaced}{\yreplaced}} \long\def\xreplaced[#1]#2#3{% \iftrack\global\advance\refchangenumber by 1\relax% \vtop to 0pt{\vss \hypertarget{link\the\refchangenumber}{} \vskip14pt}% \ifnumlines\ifabstract\else\xdef\doit{\noexpand\linelabel{\the\refchangenumber}}\doit\fi\else% \xdef\doit{\noexpand\label{\the\refchangenumber}}\doit\fi% {\ifbib\let\sout\relax\fi \color{trackchange}\bf(Replaced: [#1] \sout{#2}}% {\color{black}replaced with:} { \color{trackchange}\bf\relax #3)}% \ifabstract\label{\the\refchangenumber}% \expandafter\gdef\csname changenum\the\refchangenumber\endcsname{Replaced: [#1] {\color{trackchange}\bf\relax\sout{#2}} {\color{black} replaced with:} {\color{trackchange}\bf\relax#3}, \global\silenttrue}% \else \expandafter\gdef\csname changenum\the\refchangenumber\endcsname{Replaced: [#1] {\ifbib\let\sout\relax\fi \color{trackchange}\bf\relax\sout{#2} } {\color{black} replaced with:} {\color{trackchange}\bf\relax#3}, \global\silentfalse}\fi% \else#3\fi} \long\def\yreplaced#1#2{% \iftrack\global\advance\refchangenumber by 1\relax% \vtop to 0pt{\vss \hypertarget{link\the\refchangenumber}{} \vskip14pt}% \ifnumlines\ifabstract\else\xdef\doit{\noexpand\linelabel{\the\refchangenumber}}\doit\fi\else% \xdef\doit{\noexpand\label{\the\refchangenumber}}\doit\fi% {\ifbib\let\sout\relax\fi \color{trackchange}\bf\relax(Replaced: \sout{#1} }% {\color{black}replaced with:} {\color{trackchange}\bf\relax #2)}% \ifabstract\label{\the\refchangenumber}% \expandafter\gdef\csname changenum\the\refchangenumber\endcsname{Replaced: {\color{trackchange}\bf\relax \sout{#1}} {\color{black} replaced with:} {\color{trackchange}\bf\relax#2},\global\silenttrue}% \else \expandafter\gdef\csname changenum\the\refchangenumber\endcsname{Replaced: {\ifbib\let\sout\relax\fi \color{trackchange}\bf\relax\sout{#1} } {\color{black} replaced with:} {\let\bibitem\specialbibitem\color{trackchange}\bf\relax#2}, \global\silentfalse}\fi% \else#2\fi} \def\explain{\@ifnextchar[{\xexplain}{\yexplain}} \def\xexplain[#1]#2{\iftrack\ {\bfseries\itshape\color{explain} [Explanation of change: #2 (#1)]\ }\fi} \def\yexplain#1{\iftrack\ {\bfseries\itshape\color{explain} [Explanation of change: #1]\ }\fi} \newcount\listchangenum \def\listofchanges{ \clearpage \iftrack \ifnum\refchangenumber>0 \ifnumlines\nolinenumbers\fi \vskip36pt \hrule \noindent{\vrule height 14pt width0pt depth 6pt\large\bf List of Changes} \hrule \vskip18pt \nobreak {\parskip=4pt \parindent=0pt \loop \global\silentfalse \vskip-1pt\relax \global\advance\listchangenum by 1\relax \expandafter\ifx\csname changenum\the\listchangenum\endcsname\relax \else \csname changenum\the\listchangenum\endcsname\ on page %% can't get hyperlink to work correctly for page numbers, works but error messages. \hyperlink{link\the\listchangenum}{\bf\pageref{\the\listchangenum}}% \ifnumlines% \ifsilent\global\silentfalse \else% \setbox0=\hbox{\lineref{\the\listchangenum}}% \ifdim\wd0<20pt% , line\ \hyperlink{link\the\listchangenum}{\lineref{\the\listchangenum}}% \fi \fi\fi.\relax \repeat} \fi\fi \thispagestyle{empty} } \PassOptionsToPackage{normalem}{ulem} \usepackage{ulem} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% From earlier version of AASTeX, for usefulness and %% backward compatibility, with some requested additions \let\jnl@style=\rmfamily \def\ref@jnl#1{{\jnl@style#1}}% %%% \renewcommand\memsai{\ref@jnl{Mem.~Soc.~Astron.~Italiana}}% % Mem. Societa Astronomica Italiana %% longer version: \newcommand\memsocai{Mem. Societ\`a Astronomica Italiana} \newcommand\aspconf{Ast. Soc. of the Pac. Conference Series} \let\astap=\aap \let\apjlett=\apjl \let\apjsupp=\apjs \let\applopt=\ao %%% More useful commands from Earlier version of Aastex: \let\la=\lesssim % For Springer A&A compliance... \let\ga=\gtrsim \let\farcm\farcm@mss \let\farcs\farcs@mss \def\farcm@apj{% \mbox{.\kern -0.7ex\raisebox{.9ex}{\scriptsize$\prime$}}% }% \def\farcs@apj{% \mbox{% \kern 0.13ex.% \kern -0.95ex\raisebox{.9ex}{\scriptsize$\prime\prime$}% \kern -0.1ex% }% }% \def\chem@bnd#1{% {% \kern.1em\relax \setbox\z@\hbox{M}% \[email protected]\relax \p@=.1em\relax \[email protected]\ht\z@\dimen@i-\dimen@ \advance\[email protected]\p@\advance\[email protected]\p@ #1% \kern.1em\relax }% }% \def\@sbnd{% \advance\[email protected]\p@\advance\[email protected]\p@ \vrule\@height\dimen@\@depth\dimen@i\@width\dimen@ii\nobreak }% \def\@dbnd{% \advance\[email protected]\p@\advance\[email protected]\p@ \vrule\@height\dimen@\@depth\dimen@i\@width\dimen@ii\nobreak \advance\[email protected]\p@\advance\[email protected]\p@ \hskip-\dimen@ii \vrule\@height\dimen@\@depth\dimen@i\@width\dimen@ii\nobreak }% \def\@tbnd{% \vrule\@height\dimen@\@depth\dimen@i\@width\dimen@ii\nobreak \advance\[email protected]\p@\advance\[email protected]\p@ \hskip-\dimen@ii \vrule\@height\dimen@\@depth\dimen@i\@width\dimen@ii\nobreak \advance\[email protected]\p@\advance\[email protected]\p@ \hskip-\dimen@ii \vrule\@height\dimen@\@depth\dimen@i\@width\dimen@ii\nobreak }% \renewcommand\LaTeX{% \leavevmode L% \raise.42ex\hbox{% \count@=\the\fam $\fam\count@\scriptstyle\kern-.3em A$% }% \kern-.15em\TeX }% %% added Feb 2, 2016, redefining definition of \caption made with hyperref %% package. Making \caption[] be the default, to prevent sending caption %% text to listoftables or listoffigures, which we are not going to use %% anyway. This change enables track changes commands to work in captions. \def\xtable{table} \def\caption{\numlinesfalse \ifx\@captype\@undefined \@latex@error {\noexpand \caption outside float}\@ehd \expandafter \@gobble \else \H@refstepcounter \@captype \let \Hy@tempa \@caption \@ifundefined {float@caption}{} {\expandafter \ifx \csname @float@c@\@captype\endcsname \float@caption\let\Hy@tempa\Hy@float@caption\fi} \expandafter\@firstofone\fi {\@dblarg {\Hy@tempa \@captype}}[]} \def\@caption#1[#2]#3{{\small\rm\expandafter \ifx \csname if@capstart\expandafter \endcsname \csname iftrue\endcsname \global \let \@currentHref \hc@currentHref \else \hyper@makecurrent {\@captype }\fi \@ifundefined {NR@gettitle}{\def \@currentlabelname{\thesection\relax #2}} {\NR@gettitle {#2}}\par %\addcontentsline {\csname ext@#1\endcsname }{#1}{\protect \numberline {\csname the#1\endcsname }{\ignorespaces #2}} \begingroup \@parboxrestore \if@minipage \@setminipage \fi \normalsize \expandafter\ifx \csname if@capstart\expandafter \endcsname \csname iftrue\endcsname \global \@capstartfalse \@makecaption {\bf\csname fnum@#1\endcsname }{\ignorespaces #3} \else \@makecaption {\bf\csname fnum@#1\endcsname }{\ignorespaces \ifHy@nesting \expandafter \hyper@@anchor \expandafter {\@currentHref }{#3}\else \Hy@raisedlink {\expandafter \hyper@@anchor \expandafter {\@currentHref }{\relax }}{#3}\fi }\fi \par \endgroup}} %% changed, March 23, 2019, took out \\ at end of definition: \newcommand\tablebreak{\\[-11pt]\noalign{\break}} %% As suggested by Greg Schwarz, August Meunch, Feb 11 \def\dataset{\def\doi##1{https://doi.org/##1} \@ifnextchar[{\ydataset}{\xdataset}} \def\xdataset#1{\ydataset[]{#1}\let\doi\savedoi} \def\ydataset[#1]#2{\def\one{#1}\ifx\one\empty \href{#2}{[DATASET]}\else \href{#2}{#1}\fi\let\doi\savedoi} %% this seems in the middle of nowhere... \advance\columnsep6pt %%%%%%%%%% %% macros to give hyperref link to authors when orcid numbers %% are supplied with \author[0000-2345-3333-0023]{author name} \def\lookforbracket{\ifx\next[\let\go\xauthor\else\let\go\yauthor\fi\go} \newcount\entriesinthiscollab \newcount\allentries \newif\ifseesmessage \def\author{\global\advance\entriesinthiscollab by 1\relax% \global\advance\allentries by 1\relax\futurelet\next\lookforbracket} \def\new@author@def#1#2{% \move@AU\move@AF\move@AUAF \let\@AF@join\@author@join \def\@author{{\href{http://orcid.org/#1}{#2% \openin1 Orcid-ID.png \ifeof1 %% message for authors?? %\typeout{^^J^^J ! Missing File: Orcid-ID.png; needed for Orcid Author icon ! %^^J} \else% \hskip2pt\includegraphics[width=9pt]{Orcid-ID.png}\fi}}{}}% }% \def\orciderrormessage{% \typeout{^^J^^J [\firstarg]\space Invalid ORCID Identifier!^^J^^J The ID should consist of four sets of four digits,^^J separated with -, ie, 0000-0012-3245-1234 or ^^J 0000-0012-3245-123X ^^J^^J Please fix, or don't use square bracket argument with \string\author[]\string{\string} ^^J^^J}% } %% Tests to see if author gave reasonable Orcid number; %% if not, stops processing and gives error message. \newif\ifbadOrcid \def\lookatOrcid #1-#2-#3-#4-{% \def\one{#1}\def\two{#2}\def\three{#3}\def\four{#4}% \ifx\one\empty% \global\badOrcidtrue% \else% \ifx\two\empty% \global\badOrcidtrue% \else% \ifx\three\empty% \global\badOrcidtrue% \else% \ifx\four\empty% \global\badOrcidtrue% \fi\fi\fi\fi} \def\lookforDigits #1#2#3#4{ \def\xone{#1}\def\xtwo{#2}\def\xthree{#3}\def\xfour{#4} %% \ifx\xone\empty \global\badOrcidtrue \else \ifcat \xone 1\else \global\badOrcidtrue\fi \fi %%% \ifx\xtwo\empty \global\badOrcidtrue \else \ifcat \xtwo 1\else \global\badOrcidtrue\fi \fi %%% \ifx\xthree\empty \global\badOrcidtrue \else \ifcat \xthree 1\else \global\badOrcidtrue\fi \fi %%% \ifx\xfour\empty \global\badOrcidtrue \else \ifcat \xfour 1\else \global\badOrcidtrue\fi \fi} \def\FinallookforDigits #1#2#3#4{ \def\xone{#1}\def\xtwo{#2}\def\xthree{#3}\def\xfour{#4} %% \ifx\xone\empty \global\badOrcidtrue \else \ifcat \xone 1\else \global\badOrcidtrue\fi \fi %%% \ifx\xtwo\empty \global\badOrcidtrue \else \ifcat \xtwo 1\else \global\badOrcidtrue\fi \fi %%% \ifx\xthree\empty \global\badOrcidtrue \else \ifcat \xthree 1\else \global\badOrcidtrue\fi \fi %%% \ifx\xfour\empty \global\badOrcidtrue \else \ifcat \xfour 1\else \if\xfour X \else \global\badOrcidtrue\fi% \fi% \fi} %% Last digit might be X \def\xauthor[#1]#2{\def\testone{#1-}\def\firstarg{#1}% \setbox0=\hbox{\expandafter\lookatOrcid\testone {}-{}-{}-{}- \expandafter\lookforDigits\one {}{}{}{}% \expandafter\lookforDigits\two {}{}{}{}% \expandafter\lookforDigits\three {}{}{}{}% \expandafter\FinallookforDigits\four {}{}{}{}}% %% \ifbadOrcid\let\go\orciderrormessage \else\let\go\relax\fi\go% \ifbadOrcid\let\go\stop\else\let\go\relax\fi\go% \new@author@def{#1}{#2}}%% oct 7, this doesn't seem to work \def\yauthor{\@author@def{}} \def\altaffilmark#1{\typeout{^^J^^J\string\altaffilmark\space is no longer needed. It will not do anything.^^J Please use \string\altaffiliation\string{\string} instead.^^J^^J}\stop} \def\altaffiltext#1{\typeout{^^J^^J\string\altaffiltext\space is no longer needed. It will not do anything.^^J Please use \string\altaffiliation\string{\string} instead.^^J^^J}\stop} %% We do not need \and in list of authors. It is taken care of %% automatically. Below is the definition from revtex4-1: % %\renewcommand\frontmatter@and{\class@err{\protect\and\space is not % supported}} \newcount\AuthorCollaborationLimit \let\AuthorCallLimit\AuthorCollaborationLimit %% no limit for default \AuthorCollaborationLimit=10000 \newcount\largestAffilNum \def\lookfornumbers#1#2#3#4#5#6#7#8#9{\def\one{#1} \def\two{#2} \def\three{#3} \def\four{#4} \def\five{#5} \def\six{#6} \def\seven{#7} \def\eight{#8} \def\nine{#9} \ifnum\one>\largestAffilNum \global\largestAffilNum=\one\fi %%% \ifx\two\empty\else \ifnum\two>\largestAffilNum \global\largestAffilNum=\two\fi\fi %%% \ifx\three\empty\else \ifnum\three>\largestAffilNum \global\largestAffilNum=\three\fi\fi %%% \ifx\four\empty\else \ifnum\four>\largestAffilNum \global\largestAffilNum=\four\fi\fi %%% \ifx\five\empty\else \ifnum\five>\largestAffilNum \global\largestAffilNum=\five\fi\fi %%% \ifx\six\empty\else \ifnum\six>\largestAffilNum \global\largestAffilNum=\six\fi\fi %%% \ifx\seven\empty\else \ifnum\seven>\largestAffilNum \global\largestAffilNum=\seven\fi\fi %%% \ifx\eight\empty\else \ifnum\eight>\largestAffilNum \global\largestAffilNum=\eight\fi\fi %%% \ifx\nine\empty\else \ifnum\nine>\largestAffilNum \global\largestAffilNum=\nine\fi\fi } %\gdef\newcomma@space{\hskip-3pt\textsuperscript{,}}% \def\doEtAl{\rm et al.\gdef\doEtAl{\relax}} %% ===================== \newif\iffirsttime \firsttimetrue \newcount\totalentries \newcount\docollabnum \newcount\tempauthornumber \newcount\countauthors \newif\ifdothis \def\doAnd{} \newcount\testnum \def\olddoauthor#1#2#3{% \iflongauthor\vskip6pt\fi \global\advance\countauthors by 1 \ifnum\countauthors>\AuthorCollaborationLimit \doEtAl \else \ifnum\AuthorCollaborationLimit=1 \let\@listand\relax \fi \ignorespaces\leavevmode\hbox{#1\unskip\@listcomma}% nice, keeps name from breaking across lines \fi \begingroup \ifnum\countauthors>\AuthorCollaborationLimit\else #3% all affil numbers \ifx\@affilID@temp\empty \else% \setbox0=\hbox{\expandafter\lookfornumbers\@affilID@temp{}{}{}{}{}{}{}{}{}}% \fi\fi %% #2= \altaffiliation{} or \email{} or %% possibly anything other than author, affiliation, or collaboration \@if@empty{#2}{\endgroup{}{}} {\ifnum\countauthors>\AuthorCollaborationLimit\endgroup{}{}%% <<< bug fix, added \endgroup{}{} \else \endgroup{\comma@space}{}\frontmatter@footnote{#2}\fi}% \ifnum\countauthors>\AuthorCollaborationLimit\else \space \@listand\fi }% \newif\ifaddspace \def\doauthor#1#2#3{% \iflongauthor\vskip6pt\fi%%% \ifanonymous% \iffirsttime% \global\firsttimefalse% Anonymous author(s)% \fi% \else%% ends at end of this def %%% \ifnum\docollabnum< 1 \global\AuthorCollaborationLimit\expandafter\csname currCollabLimit0\endcsname% %% this won't change until after collaboration name at end \fi %% end ifnum\docollabnum %% %%%%%%%%%%%%%%%% \global\advance\totalentries by 1\relax% \global\advance\countauthors by 1\relax% %%% \ifallauthors\global\AuthorCollaborationLimit=9999 \fi% %%% % for testing % [author number=\the\countauthors/ auth collab limit % =\the\AuthorCollaborationLimit] % \gdef\xone{#1}% \ifnum\countauthors < \AuthorCollaborationLimit \global\addspacetrue \gdef\docomma{,}\else\gdef\docomma{}\fi% ok %%% \ifnum\countauthors = \AuthorCollaborationLimit \ifnum\AuthorCollaborationLimit=1\else \gdef\doAnd{And }\fi% \ifnum\tempauthornumber= 1 \gdef\doAnd{ } \fi\fi% %% {\tempauthorminusone=\AuthorCollaborationLimit \advance\tempauthorminusone by -1 \ifnum\countauthors=\tempauthorminusone \gdef\doAnd{And }% \gdef\docomma{}\fi}% %%% \global\dothisfalse% %% if num countauthors is less than or equal to \AuthorCollaborationLimit, print name \ifnum\countauthors< \AuthorCollaborationLimit %%% \ifx\xone\empty\else% \global\dothistrue% %\expandafter\gdef\csname %dothisaffil-\the\countauthors\the\docollab\endcsname{dothisone} \ignorespaces\leavevmode\hbox{#1\unskip\docomma}% nice, keeps name from breaking across lines \fi% \fi% %% \ifnum\countauthors= \AuthorCollaborationLimit %%% \ifx\xone\empty\else \global\dothistrue \ignorespaces\leavevmode\hbox{\doAnd #1\unskip\docomma}%nice, keeps name from breaking across lines \fi% \fi% %% ++++ %% \ifsuppressAffiliations\else% \ifx\xone\empty\else% \begingroup% \ifnum\countauthors>\AuthorCollaborationLimit\else #3% all affil numbers \ifx\@affilID@temp\empty %% number following author \else% \setbox0=\hbox{\expandafter\lookfornumbers\@affilID@temp{}{}{}{}{}{}{}{}{}}% \fi\fi% %% #2= \altaffiliation{} or \email{} or %% possibly anything other than author, affiliation, or collaboration \@if@empty{#2}{\endgroup{}{}}% {\ifnum\countauthors>\AuthorCollaborationLimit\endgroup{}{}%% <<< bug fix, added \endgroup{}{} \else \endgroup{\comma@space}{}\frontmatter@footnote{#2}\fi}% \fi%% end test of empty \fi%% end test of suppressAffiliations %%%%%%%%%%%%%%%%%%%%%%%% %%% Collaboration name is always used if available: \expandafter\ifx\csname currCollabName\the\totalentries\endcsname\relax\else %%% %%% %%% %% changed locally: {\advance\docollabnum 1 \advance\countauthors-1 %%% %%% We need to test to see if more than one author in collaboration %%% and if the number of authors is greater than the \AuthorCollaborationLimit. %%% If both of these are true, than use `et al.' , otherwise do not: \expandafter\ifx\csname CollabTotalAuthors\the\docollabnum\endcsname\relax \else \expandafter\ifnum\csname CollabTotalAuthors\the\docollabnum\endcsname < 2 %%%%% Don't use et al if there is only one author \else \expandafter\ifnum\csname CollabTotalAuthors\the\docollabnum\endcsname >\AuthorCollaborationLimit\relax% \ifnum\AuthorCollaborationLimit=0\else \vskip3pt {\rm et al.} \vskip-3pt \fi\fi\fi\fi% }%% end local change to docollabnum %%%% \expandafter\ifx\csname currCollabName\the\totalentries\endcsname\empty \vskip-3pt \else \vskip6pt \expandafter\csname currCollabName\the\totalentries\endcsname\vskip8pt \affiliation{testing} \fi% %%%%%%%% \global\countauthors=0 %%% %%% \global\advance\docollabnum by 1 %% Set up counters for next time through this loop: {\advance\docollabnum by1 \expandafter\ifx\csname specificCollabLimit\the\docollabnum\endcsname\relax \else \global\AuthorCollaborationLimit=\csname specificCollabLimit\the\docollabnum\endcsname \fi% \expandafter\ifx\csname CollabTotalAuthors\the\docollabnum\endcsname\relax \else \global\tempauthornumber=\csname CollabTotalAuthors\the\docollabnum\endcsname \fi}% \fi %% ends test to see if it is time to use collaboration name \fi %% ends ifanonymous \ifaddspace\ \fi\global\addspacefalse}% oct 7, 2020, allows multiple names to break over lines, %but no extra space if \collaboration{1} %%%% ++++==== \newcount\tempauthorminusone %% +++ \def\doAllauthors#1#2#3{% \global\suppressAffiliationsfalse \iflongauthor\vskip6pt\fi %%% \ifanonymous \iffirsttime \global\firsttimefalse Anonymous author(s) \fi \else %% ends at end of this def %%% \ifnum\docollabnum< 1 %% these won't change until after collaboration name at end \global\AuthorCollaborationLimit\expandafter\csname currCollabLimit0\endcsname \global\tempauthornumber=\csname CollabTotalAuthors1\endcsname \fi%% end ifnum\docollabnum %% %%%%%%%%%%%%%%%% \global\advance\totalentries by 1 \global\advance\countauthors by 1 %%% \ifallauthors\global\AuthorCollaborationLimit=9999 \fi %%% % for testing %[author number=\the\countauthors/ temp author %=\the\tempauthornumber] \def\one{#1} {\tempauthorminusone=\tempauthornumber \advance\tempauthorminusone by -1 \ifnum\countauthors < \tempauthornumber \gdef\xdocomma{,}% \else\gdef\xdocomma{}\fi% %%% \ifnum\countauthors = \tempauthornumber \gdef\xdoAnd{And}\gdef\xdocomma{}% \else\gdef\xdoAnd{}\fi% \ifnum\tempauthornumber= 1 \gdef\xdoAnd{}\gdef\xdocomma{}\fi% \ifnum\countauthors=\tempauthorminusone \gdef\xdocomma{}\fi% } %%% %% if num countauthors is less than or equal to \AuthorCollaborationLimit, print name \ifnum\countauthors< \AuthorCollaborationLimit %%% \ifx\one\empty\else \ignorespaces\leavevmode\hbox{\unskip\xdoAnd\ #1\unskip\xdocomma}% nice, keeps name from breaking across lines \fi\fi% %% \ifnum\countauthors= \AuthorCollaborationLimit %%% \ifx\one\empty\else \ignorespaces\leavevmode\hbox{\unskip\xdoAnd\ #1\unskip\xdocomma}% nice, keeps name from breaking across lines \fi% \fi% %% \ifx\one\empty\else \begingroup \ifnum\countauthors>\AuthorCollaborationLimit\else #3% all affil numbers \ifx\@affilID@temp\empty \else% \setbox0=\hbox{\expandafter\lookfornumbers\@affilID@temp{}{}{}{}{}{}{}{}{}}% \fi\fi %% #2= \altaffiliation{} or \email{} or %% possibly anything other than author, affiliation, or collaboration \@if@empty{#2}{\endgroup{}{}} {\ifnum\countauthors>\AuthorCollaborationLimit\endgroup{}{}%% <<< bug fix, added \endgroup{}{} \else \endgroup{\comma@space}{}\frontmatter@footnote{#2}\fi}% \fi%% end test of empty %%%%%%%%%%%%%%%%%%%%%%%% %%% Collaboration name is always used if available: \expandafter\ifx\csname currCollabName\the\totalentries\endcsname\relax\else %%% %% No et al in allauthors, because all authors are listed! %% \expandafter\ifx\csname currCollabName\the\totalentries\endcsname\empty \else \vskip6pt \expandafter\csname currCollabName\the\totalentries\endcsname\vskip6pt \fi \global\countauthors=0 %%% %%% \global\advance\docollabnum by 1 %% Set up counters for next time through this loop: {\advance\docollabnum by1 \expandafter\ifx\csname specificCollabLimit\the\docollabnum\endcsname\relax \else \global\AuthorCollaborationLimit=\csname specificCollabLimit\the\docollabnum\endcsname \fi % \expandafter\ifx\csname CollabTotalAuthors\the\docollabnum\endcsname\relax \else \global\tempauthornumber=\csname CollabTotalAuthors\the\docollabnum\endcsname \fi} \fi %% ends test to see if it is time to use collaboration name \fi %% ends ifanonymous }% %%% %% set \affil to match \affiliation found in revtex, since authors are accustomed to using \affil{} \let\affil\affiliation \newif\iffirstaffil \firstaffiltrue \newcount\affilnum %% +++! \def\@affil@script#1#2#3#4{% \ifsuppressAffiliations\else \iffirstaffil % Oct 2017 \vskip2pt \global\firstaffilfalse\fi \@ifnum{#1=\z@}{}{% \par \begingroup \frontmatter@affiliationfont \@ifnum{\c@affil<\affil@cutoff}{}{% \def\one{#1} %% %% \ifnum\one<\largestAffilNum %% this makes the numbers \def\@thefnmark{#1}\@makefnmark\fi \ifnum\one=\largestAffilNum \def\@thefnmark{#1}\@makefnmark\fi }% \ifnum\one<\largestAffilNum \ignorespaces#3% \fi \ifnum\one=\largestAffilNum \ignorespaces#3% \fi \@if@empty{#4}{}{\frontmatter@footnote{#4}}% \par \endgroup }% \fi}% \newif\ifnobreakafterkeywords \def\NoNewPageAfterKeywords{\global\nobreakafterkeywordstrue} \NoNewPageAfterKeywords \def\NewPageAfterKeywords{\global\nobreakafterkeywordsfalse} %%%+++!!! \def\frontmatter@maketitle{% %% \@author@finish needs to be here: \@author@finish \if@firstsection% not appendix, in other words \title@column\titleblock@produce \onecolumngrid \else % \global\firstaffiltrue \title@column\secondtitleblock@produce \fi \suppressfloats[t]% %% Prevent these from being turned off so that %% we can use \maketitle again for \AllAuthors. %% % \let\and\relax \let\affiliation\@gobble \let\author\@gobble % \let\@AAC@list\@empty % \let\@AFF@list\@empty % \let\@AFG@list\@empty % \let\@AF@join\@AF@join@error % \let\email\@gobble % \let\@address\@empty % \let\maketitle\relax % \let\thanks\@gobble \if@firstsection \let\abstract\@undefined\let\endabstract\@undefined \titlepage@sw{% \ifnobreakafterkeywords \else \vfil \ifrnaas\else \clearpage\fi \fi }{}% \fi }% \let\maketitle\frontmatter@maketitle \def\secondtitleblock@produce{% \begingroup \ltx@footnote@pop \def\@mpfn{footnote}% \def\thempfn{\thefootnote}% \c@footnote\z@ \let\@makefnmark\frontmatter@makefnmark % \frontmatter@setup \thispagestyle{titlepage}%\label{FirstPage}% % \frontmatter@title@produce \groupauthors@sw{% \frontmatter@author@produce@group }{% \frontmatter@author@produce@script }% \endgroup }% %% no club or widow lines \widowpenalty=10000 \clubpenalty\widowpenalty \setlength{\footnotesep}{8pt} \ifmodern \setlength{\voffset}{0in} \setlength{\hoffset}{0in} \setlength{\textwidth}{6in} \setlength{\textheight}{9.2in} \setlength{\headheight}{0ex} \setlength{\headsep}{36pt} % this is 2 lines in ``manuscript'' \setlength{\footnotesep}{0in} \setlength{\topmargin}{-\headsep} \setlength{\oddsidemargin}{0.25in} \setlength{\evensidemargin}{0.25in} \setlength{\parindent}{0.54\baselineskip} \sloppy\sloppypar \fi \def\figurename{Figure} \def\tablename{Table} \def\fnum@figure{{\bf\figurename~\thefigure}} \def\fnum@table{{\bf\tablename~\ifappletter\thesection\fi\thetable}} \def\tempfootmark#1{} \newcount\c@affilcount \renewcommand\altaffiliation[2][]{% \@AF@join{\ifanonymous\else #1#2\ifmodern\baselineskip=14pt\fi \if@two@col\hsize=.5\textwidth \advance\hsize by -18pt \fi\fi}% }% \def\correspondingauthor#1{{\ifanonymous \else \renewcommand\thefootnote{\hskip-12pt} \footnote{Corresponding author: #1\ifmodern\vrule depth 5pt width 0pt\relax\fi}\fi}} \let\saveemail\email \def\email#1{\ifanonymous \else{\let\ltx@footmark\tempfootmark \saveemail{}} {\renewcommand\thefootnote{\hskip-12.1pt} \footnote{\href{mailto: #1}{#1}\ifmodern\vrule depth 7pt width 0pt\relax\else\ifmanu\vskip-4pt\else\vrule depth 7pt width 0pt\fi\fi}}\fi} \def\nocollaboration#1{% \collaboration{#1}{\vbox to 0pt{\vss\centerline{---}\vskip2pt}} } %% May 19 %% \AuthorsAndCollaboration changed to \FullCollaborationID %% June 6 \FullCollaborationID changed to \xcollaboration{}{} %% june 7 \collaboration changed to \xcollaboration; fullcollaborationid changed to \collaboration %% here just in case we need it in the future... \def\xcollaboration#1#2{ \global\advance\allentries by 1 \expandafter\def\csname currCollabLimit\the\allentries\endcsname{#1} \@author@def{\@booleantrue \collaboration@sw}{#2} } \let\savelistand\@listand \newcount\numauthors \newcount\collabnum \newbox\collabnamebox \newif\iffirstcollab \global\firstcollabtrue \newif\ifcollaborationon \def\collaboration#1#2{\global\collaborationontrue \global\advance\collabnum by 1 \iffirstcollab\global\firstcollabfalse \expandafter\xdef\csname currCollabLimit0\endcsname{#1} \fi %% make this def so that we can use it when we want in doauthor: \expandafter\gdef\csname specificCollabLimit\the\collabnum\endcsname{#1} %% This allows us access the number of authors per collaboration: \expandafter\xdef\csname CollabTotalAuthors\the\collabnum\endcsname{\the\entriesinthiscollab} \global\entriesinthiscollab=0 %% \global\advance\allentries by 1 %% %% we should have only one of these with this number; this used to say when %% use specificCollabLimit: \expandafter\gdef\csname currCollabLimit\the\allentries\endcsname{#1} %% we should have only one of these with this number \expandafter\gdef\csname currCollabName\the\allentries\endcsname{%\ifnum#1>0 %\sc And the\vskip4pt\fi #2} %% \let\doEtAl\relax %% not here \@author@def{\@booleanfalse \collaboration@sw}{}} \def\and{ \centerline{\vbox {\vrule height 12pt width0pt and\vskip2pt}} } %\def\andthe{% %\collaboration{\vbox {\vrule height 12pt width0pt and %the\vskip2pt}}\vskip4pt %} %% gets rid of () around collaboration \def\@collaboration@present#1#2#3#4{% \par \begingroup \vskip3pt \iflongauthor\vskip-4pt\ifmodern\vskip-6pt\fi\fi \frontmatter@collaboration@above \@affilID@def{}% \@tempcnta\z@ \@author@present{}{\ignorespaces#3\unskip}{#4}% %% October 2017 \par \ifmodern%\vskip-4pt \else \iflongauthor\else\vskip-6pt\fi\fi \endgroup \iflongauthor \else\vskip8pt\fi \set@listcomma@list#1% \vskip1pt %% was \vskip9pt }% %%% These lines were commented out until a fix could be applied that %%% addresses the underlying issues. The problem is that on Linux systems %%% you can not write a "hidden" .bib file. There is no issue with this %%% on Mac OS X nor Windows. %%% get rid of \jobname Notes being sent to .aux file: %\let\bibdata@app\relax %\def\pre@bibdata{} %% This is the underlying issue: %% Redefining \@bibdataout@init will keep useless file, \jobnameNotes, from being written. \let\@bibdataout@init\relax %% redefining and simplifying RevTeX4-1 definition, so that bibliography is not looking for %% \jobnameNotes: \def\bibliography#1{\bibliography@latex{#1}}% %%% \newif\iffrontmatterfirsttime \global\frontmatterfirsttimetrue \let\savecentercr\@centercr \def\frontmatter@author@produce@script{% \begingroup \let\@author@present\@author@present@script \frontmatterverbose@sw{\typeout{\string\frontmatter@author@produce@script:}\say\@AAC@list\say\@AFF@list\say\@AFG@list}{}% \let\AU@temp\@empty \@tempcnta\z@ \let\AF@opr \@gobble \def\AU@opr{\@author@count\@tempcnta}% \def\CO@opr{\@collaboration@count\AU@temp\@tempcnta}% \@AAC@list \expandafter\CO@opr\@author@cleared \begingroup \frontmatter@authorformat \let\AF@opr \@affilID@def \let\AU@opr \@author@present \def\CO@opr{\@collaboration@present\AU@temp}% \set@listcomma@list\AU@temp \@AAC@list %% \, added to definition taken from revtex4-1 to prevent error message. \, \unskip\unskip \par \endgroup %% below \begingroup \frontmatter@above@affiliation@script \let\AFF@opr \@affil@script {\parskip=2pt \def\@centercr{\vrule depth 3pt width0pt\vskip1sp} \@AFF@list} \let\@centercr\savecentercr %% sept 14, 2020 \iffrontmatterfirsttime \frontmatter@footnote@produce \global\frontmatterfirsttimefalse \fi \par \endgroup \endgroup }% \let\auto@bib\relax \newif\iffirstaffil \firstaffiltrue %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% These commands were in aastex earlier; I redefined. \def\tighten{\global\tightentrue\normalsize} \let\tightenlines=\tighten \def\singlespace{\par\global\doublespacefalse\global\tightenfalse\normalsize} \def\doublespace{\par\global\doublespacetrue\global\tightenfalse\normalsize} \bibliographystyle{aasjournal} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% October 2017 \renewenvironment{widetext}{% \if@two@col \par\ignorespaces \setbox\widetext@top\vbox{% \hb@xt@\hsize{% \leaders\hrule\hfil \vrule\@height6\p@ }% }% \setbox\widetext@bot\hb@xt@\hsize{% \vrule\@depth6\p@ \leaders\hrule\hfil }% \onecolumngrid \vskip10\p@ \dimen@\ht\widetext@top\advance\dimen@\dp\widetext@top \cleaders\box\widetext@top\vskip\dimen@ \vskip6\p@ \prep@math@patch \fi}{% \if@two@col \par \vskip6\p@ \setbox\widetext@bot\vbox{% \hb@xt@\hsize{\hfil\box\widetext@bot}% }% \dimen@\ht\widetext@bot\advance\dimen@\dp\widetext@bot \cleaders\box\widetext@bot\vskip\dimen@ \vskip8.5\p@ \twocolumngrid\global\@ignoretrue \@endpetrue \fi}% \newbox\widetext@top \newbox\widetext@bot \urlstyle{rm} \def\doi#1{\href{https://doi.org/#1}{https://doi.org/#1}} \let\savedoi\doi \def\mdash{---} \newif\ifcenterwidetable %% these two definitions are the same, but it might %% be convenient to have both \def\centerwidetable{\global\centerwidetabletrue} %% this doesn't seem to be documented, assume we don't need it: %\def\centernarrowtable{\global\centerwidetablefalse} %% default, center within width of text on both sides \def\LT@LR@c{\LTleft=0pt plus1fill \LTright\LTleft}% \def\widetable{\def\LT@LR@c{\LTleft=0pt minus1fill \let\LTright\LTleft}} \newif\ifreturntotwocol %%%%%%%%% %% to help with graceful linebreaks in two column text: \tolerance 9999% %% sloppy defines emergencystretch to be 3 em, this is a bit %% more conservative: \emergencystretch 1em \hfuzz .5\p@ %%%%%%%%% %% Nominal Conversion Constants %% \boldmath inside the \hbox ?? \def\nomSolarEffTemp{\leavevmode\hbox{\boldmath$\mathcal{T}^{\rm N}_{\mathrm{eff}\odot}$}} \def\nomTerrEqRadius{\leavevmode\hbox{\boldmath$\mathcal{R}^{\rm N}_{E\mathrm e}$}} \def\nomTerrPolarRadius{\leavevmode\hbox{\boldmath$\mathcal{R}^{\rm N}_{E\mathrm p}$}} \def\nomJovianEqRadius{\leavevmode\hbox{\boldmath$\mathcal{R}^{\rm N}_{J\mathrm e}$}} \def\nomJovianPolarRadius{\leavevmode\hbox{\boldmath$\mathcal{R}^{\rm N}_{J\mathrm p}$}} \def\nomTerrMass{\leavevmode\hbox{\boldmath$(\mathcal{GM})^{\rm N}_{\mathrm E}$}} \def\nomJovianMass{\leavevmode\hbox{\boldmath$(\mathcal{GM})^{\rm N}_{\mathrm J}$}} \def\Qnom{\leavevmode\hbox{\boldmath$\mathcal{Q}^{\rm N}_{\odot}$}} \let\Qn\Qnom %% Generic commands that can be given an argument: \def\nom#1{\leavevmode\hbox{\boldmath$\mathcal{#1}^{\rm N}_{\odot}$}} \def\Eenom#1{\leavevmode\hbox{\boldmath$\mathcal{#1}^{\rm N}_{Ee}$}} \def\Epnom#1{\leavevmode\hbox{\boldmath$\mathcal{#1}^{\rm N}_{Ep}$}} \def\Jenom#1{\leavevmode\hbox{\boldmath$\mathcal{#1}^{\rm N}_{Je}$}} \def\Jpnom#1{\leavevmode\hbox{\boldmath$\mathcal{#1}^{\rm N}_{Jp}$}} %%%%%%%%%%%%%%%% %% Ability to have tables, equations, figures in appendix start from 1, and use appendix section letter. \newif\ifappletter \def\apptablenumbers{\global\applettertrue \setcounter{table}{0} \setcounter{figure}{0} \setcounter{equation}{0} \def\thetable{\thesection\the\c@table}% \def\fnum@table{{\bf\tablename~\thetable}}% \def\thefigure{\thesection\the\c@figure}% \def\fnum@figure{{\bf\figurename~\thefigure}}% }% %%% easier to remember than \apptablenumbers \let\restartappendixnumbering\apptablenumbers \def\resetapptablenumbers{\global\c@table=0 \global\c@figure=0 \global\c@equation=0 \def\thetable{\thesection\the\c@table} \def\fnum@table{{\bf\tablename~\thetable}}% \def\thefigure{\thesection\the\c@figure} \def\fnum@figure{{\bf\figurename~\thefigure}}% } %% written for aastex63 \newif\ifallauthors \def\allauthors{ \global\allauthorstrue \let\doauthor\doAllauthors \ifanonymous \vskip6pt\vskip1sp\centerline{\large\bf All Authors and Affiliations\vrule depth 18pt width0pt}\nobreak \centerline{Anonymous author(s)} \else \ifnumlines\nolinenumbers\fi \onecolumngrid \clearpage {\vskip6pt\vskip1sp\centerline{\large\bf All Authors and Affiliations\vrule depth 18pt width0pt}\nobreak \global\docollabnum=0 \global\totalentries=0 \global\countauthors=0 \maketitle }\fi} %% written for AASTeX62 \def\oldallauthors{%% this conditional keeps \allauthors from turning on %% unless \AuthorCollaborationLimit is used: \ifnumlines\nolinenumbers\fi \onecolumngrid \clearpage \AuthorCollaborationLimit=10000 %\largestAffilNum=10000 <<== not needed {\vskip6pt\vskip1sp\centerline{\large\bf All Authors and Affiliations\vrule depth 18pt width0pt}\nobreak \maketitle }} \let\AllAuthors\allauthors %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Highlight Figure \definecolor{ltblue}{cmyk}{.5,.1,.1,0} \newdimen\currwidth \long\def\highlightfigure#1{ \bgroup \fboxrule=4pt \fboxsep=12pt \vskip6pt \global\currwidth=\hsize \global\advance\currwidth by -32pt \noindent\hbox to\currwidth{\fcolorbox{ltblue}{white}{% $\vcenter{\hbox to\currwidth{\hss#1\hss}}$}} \egroup} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% New interactive command: \def\xlc{lc} \def\xjs{js} \def\xanimation{animation} \newbox\interactbox \newif\ifcorrectentries \def\interactive#1#2{ \global\correctentriesfalse\def\checkone{#1} \ifx\checkone\xlc\correctentriestrue\fi \ifx\checkone\xjs\correctentriestrue\fi \ifx\checkone\xanimation \correctentriestrue\fi \def\checktwo{#2} \ifx\checktwo\empty\global\correctentriesfalse\fi \ifcorrectentries \else\hrule height1pt\vskip12pt\bf ERROR: The command {\tt\string\begin\string{interactive\string}\string{\string}\string{\string}} needs two arguments. The first describes the interactive type and the only allowed choices are lc, js, or animation.\\ The second argument is the movie file or package containing the interactive figure components. See\\ \url{https://journals.aas.org/aastexguide/\hashmark interactivefig} for more details. \vskip12pt\hrule height1pt \fi \global\currwidth\hsize \global\advance\currwidth by -32pt %% we need to set \currwidth here because interactbox expands %% before highlightfigure \global\setbox\interactbox=\vbox\bgroup\hsize=\currwidth\relax\centering } \def\endinteractive{\egroup \ifcorrectentries\highlightfigure{\copy\interactbox}\fi } %%%% For cases in which footnotes are called in full width environment %% but are used in two cols. This keeps them from overwriting the %% second column: \let\savefootnote\footnote \def\onecolfootnote#1{\savefootnote{\hsize=.5\textwidth\advance\hsize by-18pt\relax#1}} \def\onecolumnfootnotes{\let\footnote\onecolfootnote} \newdimen\movetableright %% for anonymous option \newif\ifsuppressAffiliations \def\suppressAffiliations{\global\suppressAffiliationstrue} %% new definition to be used in trackchanges: \def\sout#1{\raise5pt\hbox{\underline{\vbox to 0pt{\vskip-4pt\hbox{#1\vrule height 8.5pt depth 3.5pt width0pt}\vss}}}} %% changes for affiliations when anonymous option is used: \ifanonymous \suppressAffiliationstrue \gdef\affiliation#1{}%% may 20, 2020 \def\xauthor[#1]#2{} \let\yauthor\@gobble \def\lookforbracket{\ifx\next[ \let\go\xauthor\else\let\go\yauthor\fi\go} \def\author{\futurelet\next\lookforbracket} \fi %%%%%%%%%%%%% %% Line numbering \ifnumlines \usepackage[mathlines]{lineno}%% dec 20 %% \linenumbers[1] %%\linenumbersep default=10pt \if@two@col \advance\linenumbersep -6pt \else \advance\linenumbersep 12pt \fi \fi %% Use when line numbers are on, and after \usepackage{amsmath}. %% Will make line numbering work on math as it would without amsmath. \def\fixmathlinenumbering{ \let\saveopensqbracket\[ \def\[{\linenomath\saveopensqbracket} \let\saveequation\equation \let\saveendequation\endequation %% \let\savealign\align \let\saveendalign\endalign %% \let\savealigned\aligned \let\saveendaligned\endaligned %% \def\align{\linenomath\savealign} \def\endalign{\saveendalign} \def\aligned{\linenomath\savealigned} \def\endaligned{\linenomath\saveendaligned} %% \def\equation{\linenomath\saveequation} \def\endequation{\linenomath\saveendequation} \usepackage[mathlines]{lineno} } \AtBeginDocument{\expandafter\ifx\csname @amsmath@err\endcsname\relax\else\fixmathlinenumbering\fi} \endinput %% Change Log ============================ Jan 29, 2021 added \ifonecolstyle to see if reference numberlines need to be closer to text Dec 20, 2020 Line numbering solutions: Line numbering equations and \[ \] works fine. $$math $$ does not work, and should be replaced with \[ math \] If author has \usepackage{amsmath} the equations will not number; amsmath and lineno are incompatible. June 28 For using \edit{}{} in section heads; new command, \simpleedit that will prevent errors in section heads and in bookmarks. \edit is set to be equal to \simpleedit{}{} in \section definition, so nothing needs to be done by user. \protect used in section head, as \protect\edit{}{}, is not necessary. June 27 \null added to \end{deluxetable} and \csname enddeluxetable\endcsname to force final page of multipage table to print. June 26 Acknowledgments: remember to use \begin{acknowledgments}...\end{acknowledgments} form OR \begin{acknowledgements}...\end{acknowledgements} Now have an error message built in if someone uses just \acknowledgments or \acknowledgements June 4, 2020 Added \nocollaboration{0} to first section head, if anonymous was true. This allowed correct titlepage for anonymous if any style option was used. Acknowledgments: remember to use \begin{acknowledgments}...\end{acknowledgments} form %% Change Log ============================ May 19, 2020 Changed definition of \sout (strike out) so that it works with a variety of citations in argument of \deleted and \replaced without complaint. Made anonymous work with \longauthor, and without \collaboration or \nocollaboration. Changed \acknowledgements to \begin{acknowledgements}...\end{acknowledgements} (More error proof, and standard mark up) ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ June 8, 2019 Changed \author and \collaboration macros. Collaboration now takes two arguments: #1= number of authors to be listed before the name of the collaboration; #2 = name of the collaboration \nocollaboration{} has one argument, #1= the number of authors above it that we want to print on the title page. June 6, 2019 \acknowledgments does not use \begin{}...\end{} form, now just \acknowledgments command. Acknowledgments text ends with \par, so if author wants more than one paragraph in acknowledgment he/she should surround text with curly bracket: \acknowledgments text... or \acknowledgments {text... more text...} ------ ============================ June 3, 2019 \let\footnote\onecolfootnote on page where references start, but before footnotes are entered, will allow footnotes to break in the right place (one column's width). ============================ May 15, 2019 \centerwidetable is now \movetableover at Greg's suggestion. ============================ Nov 27, 2017 1) Change to \begin{widetext}...\end{widetext} to return the horizontal lines before and after the environment. 2) \NoNewPageAfterKeywords is now default; authors wanting a new page after keywords can use the \NewPageAfterKeywords command. 3) Change in definition names, returning to earlier version: \turnoffediting will turn off colors for all levels of editing mark up made with \edit1{}, \edit2{}, or \edit3{}. You can turn off any level of editing with \turnoffeditone, \turnoffedittwo, and \turnoffeditthree. 4) It is now possible to use \doi{} as an argument of \dataset. \dataset[]{\doi{10.5281/zenodo.831784}} and \dataset[\doi{10.5281/zenodo.831784}]{\doi{10.5281/zenodo.831784}} will work. ============================ October 15, 2017 1) \movetabledown now works with longrotatetable as it does with rotatetable. \movetabledown=<dimen> before either \begin{rotatetable} or \begin{longrotatetable} Added \clearpage before \begin{rotatetable} and \begin{rotatetable*} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2) \NoNewPageAfterKeywords, used after \documentclass{AASTeX62}, will keep a new page from starting after keywords. Extra vertical space before first section in Modern option. Solution suggested by Alex Drlica-Wagner. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 3)\edit1{}, \edit2{} and \edit3{} will add color to the edited text. To get rid of the color, but not the text, authors should use \turnoffeditonecolor (for \edit1{}) \turnoffedittwocolor (for \edit2{}) \turnoffeditthreecolor (for \edit3{}) These commands have the same results as \turnoffeditone, \turnoffedittwo, and \turnoffeditthree which are not disabled, but the new commands make the action to be produced more descriptive. Similarly, instead of \turnoffedit or \turnoffedits we now have \turnoffeditcolors. The original two commands still work, but the new command is more descriptive of the results. Authors should be instructed to put these commands before \begin{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 4) \begin{widetext}...\end{widetext} \begin{widetext} will go from twocolumngrid to onecolumngrid, centered. \end{widetext} will turn off centering and go back to twocolumngrid. Only needed in twocolumn styles; nothing will happen in single column styles. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 5) Sean Lake's problem with \mag was solved by Barbara Beeton online, ``the latest edit identifies the problem unambiguously: \mag is a tex primitive, and shouldn't be redefined. why this didn't appear in the logs you posted is beyond me, but if you rename your command to (say) \Mag it should stop having a problem. � barbara beeton Feb 22'' \mag is a tex primitive, and it is expecting to be followed by a number. This had nothing to do with AASTeX61.cls %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 6) \def\arraystretch{.9} as requested will make the space between lines in tables shrink to 90% of the original space. I think what is really wanted is \def\arraystretch{1.1} which will still give us 110% of the original space, a little extra vertical space, but not as much as we had before. Meanwhile, an author can change the definition of \arraystretch{} for a single table or all the tables in his paper, if he wants more or less space. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 7) Abstract is now the same width as in emulateapj in all styles, with the exception of the modern option which is unchanged. Abstracts in all styles will break over pages in this version. Thanks to suggestion by Patricio Cubillos. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 8) Center and tighten affiliations, changed and tested for all styles, including longauthor option. samples.zip show examples titlepage of each style with and without longauthor option. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 9) preprintnumbers activated. No need to use a documentclass option. Just enter \reportnum{<text>}, before \begin{document} and repeat as many times as needed. The entries will stack in the top right hand corner of the titlepage, for all styles. ie \reportnum{YOUR-INST-REP-789} \reportnum{MY-INST-REP-123} %% author can continue with as many entries as desired. % \reportnum{A number of other numbers} % \reportnum{More Numbers} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 10) Title is no longer uppercase by default. It is now title case, which means all important words are capitalized by author. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 11) \AuthorCollaborationLimit now set to default of 10,000. If smaller number of authors wanted, \AuthorCollaborationLimit can be set to the number wanted; \allauthors typed at end of article will make every author and affiliation print. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 12) \startlongtable\deluxetable now works in appendix, even when it is the last entry in the paper. Added \null to \endlongdeluxetable which has the effect of making last page print. This works in my test, but it may be useful to see the example from author, github #54 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 13) Deluxetable no longer crashes if author has neglected to put in \\ before \enddata. I added the non-redundant \\ command, \crcr, and sample now works. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 14) \tablehead in deluxetable had too much space underneath double horizontal lines. Made custom negative skip based on each style, tested, and supplied tabsamples.zip showing tableheads in each style. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 15) \urlstyle{rm} is set so that url and href produce the same fonts. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 16) Fix to \dataset so that square brackets are not printed in the case of argument in square brackets. Now \dataset[]{http://www.texnology.com} produces [DATASET] linked to www.texnology.com \dataset[TeXnology]{http://www.texnology.com} produces TeXnology linked to www.texnology.com %% This will also work, % same results as \dataset[]{http://www.texnology.com} % but using the more common LaTeX syntax: \dataset{http://www.texnology.com} also produces [DATASET] linked to www.texnology.com %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 17) New version of DOI: \doi{10.5281/zenodo.831784} now produces hyperlinked https://doi.org/10.5281/zenodo.831784 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 18) Added to definition of \software, working with sample from August Muench, reduced the space between words, and got rid of extra space after punctuation with the \frenchspacing command. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 19) August Muench entered a bug report complaining that \clearpage doesn't always work, but he didn't have a sample, so I am not able to debug this one. It may be that the problem isn't with the code, but with the way the commands were entered, but without a sample I have no way of knowing. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 20) Tested \startlongtable in all styles and didn't find a problem with centering. I did add a skip at the beginning of \startlongtable in case someone didn't leave a blank line before using the command. ============================ September 21, 2016 Finishing Version 6.1 update ===================== August 27, 2016 Many changes ===================== August 17 Many changes: %% note: %% this keeps tables from being set to \small, code used in Revtex4-1 \let\table@hook\relax ===================== Feb 29, changes to table macros to center caption even if table is wider than width of text; give error message if user asks to rotate table but forgets to use \floattable before table; make rotating table be full text width even if called for in double columns. March 1, reworking figure and table numbering for appendices. Deleted recent definition of \appendix, returned to earlier version with additions. ================ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% New interactive command: \def\xlc{timeseries} \def\xjs{js} \def\xanimation{animation} \newbox\interactbox \newif\ifcorrectentries \def\interactive#1#2{ \global\correctentriesfalse\def\checkone{#1} \ifx\checkone\xlc\correctentriestrue\fi \ifx\checkone\xjs\correctentriestrue\fi \ifx\checkone\xanimation \correctentriestrue\fi \ifcorrectentries \else\hrule height1pt\vskip12pt\bf ERROR: Your choices for the first argument for {\tt\string\interactive} are timeseries, js, or animation.\\[6pt] Please choose one of these terms.\vskip12pt \fi %%% \def\checktwo{#2} \ifx\checktwo\empty \vskip12pt \bf ERROR: The command {\tt\string\interactive} needs two arguments, with the second argument for the graphics file or files needed.\vskip12pt\hrule height1pt \else\global\correctentriestrue\fi \global\currwidth\hsize \global\advance\currwidth by -32pt %% we need to set \currwidth here because interactbox expands %% before highlightfigure \global\setbox\interactbox=\vbox\bgroup\hsize=\currwidth\centering} \def\xxinteractive#1#2{\global\correctentriesfalse\def\checkone{#1} \ifx\checkone\xlc\correctentriestrue\fi \ifx\checkone\xjs\correctentriestrue\fi \ifx\checkone\xanimation \correctentriestrue\fi \ifcorrectentries \else\hrule height1pt\vskip12pt\bf \noindent ERROR:\\[6pt] Your choices for the first argument for {\tt\string\begin\string{\string\interactive\string}} are timeseries, js, or animation.\\[6pt] Please choose one of these terms.\vskip12pt \fi %%% \def\checktwo{#2} \ifx\checktwo\empty \vskip12pt \bf \noindent ERROR:\\[6pt] The second argument of %{\tt\string\begin\string{interactive\string}} is the file containing the interactive component. Please check your LaTeX to be sure it conforms. See %\href{https://journals.aas.org/aastexguide/interactivefig}{stuff} %{https://journals.aas.org/aastexguide/\#interactivefig} for more details. \vskip12pt\hrule height1pt \else\global\correctentriestrue\fi \global\currwidth\hsize \global\advance\currwidth by -32pt %% we need to set \currwidth here because interactbox expands %% before highlightfigure \global\setbox\interactbox=\vbox\bgroup\hsize=\currwidth\centering} \def\endinteractive{\egroup \ifcorrectentries\highlightfigure{\copy\interactbox}\fi}
https://cforall.uwaterloo.ca/trac/export/86c1f1c39dec46dad2d3904ab9144ce3de4805ab/doc/theses/thierry_delisle_PhD/thesis/text/intro.tex	uwaterloo.ca	CC-MAIN-2022-27	text/x-latex	application/x-tex	crawl-data/CC-MAIN-2022-27/segments/1656103626162.35/warc/CC-MAIN-20220629084939-20220629114939-00699.warc.gz	225,373,067	817	\chapter{Introduction}
http://demo.refbase.net/search.php?sqlQuery=SELECT%20author%2C%20title%2C%20type%2C%20year%2C%20publication%2C%20abbrev_journal%2C%20volume%2C%20issue%2C%20pages%2C%20keywords%2C%20abstract%2C%20thesis%2C%20editor%2C%20publisher%2C%20place%2C%20abbrev_series_title%2C%20series_title%2C%20series_editor%2C%20series_volume%2C%20series_issue%2C%20edition%2C%20language%2C%20author_count%2C%20online_publication%2C%20online_citation%2C%20doi%2C%20serial%20FROM%20refs%20WHERE%20serial%20%3D%2096577%20ORDER%20BY%20first_author%2C%20author_count%2C%20author%2C%20year%2C%20title&client=&formType=sqlSearch&submit=Cite&viewType=&showQuery=0&showLinks=1&showRows=5&rowOffset=&wrapResults=1&citeOrder=&citeStyle=APA&exportFormat=RIS&exportType=html&exportStylesheet=&citeType=LaTeX&headerMsg=	refbase.net	CC-MAIN-2022-27	application/x-latex	application/x-latex	crawl-data/CC-MAIN-2022-27/segments/1656104676086.90/warc/CC-MAIN-20220706182237-20220706212237-00097.warc.gz	16,526,960	1,357	%&LaTeX \documentclass{article} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} \usepackage{textcomp} \begin{document} \begin{thebibliography}{1} \bibitem{Mercatelli_etal2017} Mercatelli, N., Galardi, S., \& Ciafre, S. A. (2017). MicroRNAs as Multifaceted Players in Glioblastoma Multiforme. \textit{Int Rev Cell Mol Biol}, \textit{333}, 269--323. \end{thebibliography} \end{document}
https://www.apmep.fr/IMG/tex/STTACCACANlleCaledodec-2001-2.tex	apmep.fr	CC-MAIN-2022-21	text/x-tex	application/x-tex	crawl-data/CC-MAIN-2022-21/segments/1652662539049.32/warc/CC-MAIN-20220521080921-20220521110921-00391.warc.gz	731,811,567	2,816	\documentclass[10pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{fourier} \usepackage[scaled=0.875]{helvet} \renewcommand{\ttdefault}{lmtt} \usepackage{amsmath,amssymb,makeidx} \usepackage[mathscr]{eucal} \usepackage{fancybox} \usepackage[normalem]{ulem} \usepackage{pifont} \usepackage{lscape} \usepackage{dcolumn} \usepackage{multicol} \usepackage{tabularx} \usepackage{diagbox} \usepackage{multirow} \usepackage{textcomp} \newcommand{\euro}{\eurologo{}} %Tapuscrit : Denis Vergès \usepackage{pstricks,pst-plot,pst-text,pst-tree,multido} \newcommand{\R}{\mathbb{R}} \newcommand{\N}{\mathbb{N}} \newcommand{\D}{\mathbb{D}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\C}{\mathbb{C}} \setlength{\textheight}{23.5cm} \setlength{\voffset}{-1,5cm} \newcommand{\vect}[1]{\mathchoice% {\overrightarrow{\displaystyle\mathstrut#1\,\,}}% {\overrightarrow{\textstyle\mathstrut#1\,\,}}% {\overrightarrow{\scriptstyle\mathstrut#1\,\,}}% {\overrightarrow{\scriptscriptstyle\mathstrut#1\,\,}}} \renewcommand{\theenumi}{\textbf{\arabic{enumi}}} \renewcommand{\labelenumi}{\textbf{\theenumi.}} \renewcommand{\theenumii}{\textbf{\alph{enumii}}} \renewcommand{\labelenumii}{\textbf{\theenumii.}} \def\Oij{$\left(\text{O},~\vect{\imath},~\vect{\jmath}\right)$} \def\Oijk{$\left(\text{O},~\vect{\imath},~ \vect{\jmath},~ \vect{k}\right)$} \def\Ouv{$\left(\text{O},~\vect{u},~\vect{v}\right)$} \usepackage{fancyhdr} \usepackage[frenchb]{babel} \usepackage[np]{numprint} \begin{document} \setlength\parindent{0mm} \rhead{A. P. M. E. P.} \lhead{\small Baccalauréat STT A.C.C.-A.C.A.} \lfoot{\small{Nouvelle-Calédonie}} \rfoot{\small{novembre 2001}} \renewcommand \footrulewidth{.2pt} \pagestyle{fancy} \thispagestyle{empty} \begin{center}{\Large \textbf{\decofourleft~Baccalauréat STT ACC - ACA Nouvelle-Calédonie~\decofourright\\ novembre 2001}} \end{center} \vspace{0,5cm} \textbf{Exercice 1 \hfill 9 points} \medskip Un club de vol libre compte 150 membres. Chacun des membres pratique un seul des trois sports suivants : le parapente, le deltaplane, le cerf-volant. De plus on sait que : \setlength\parindent{5mm} \begin{itemize} \item[$\bullet~$] 42\:\% des membres ont 35 ans ou plus, \item[$\bullet~$] 20\:\% des membres pratiquent le deltaplane, \item[$\bullet~$] $\dfrac{1}{3}$ des moins de 35 ans pratiquent le cerf-volant, \item[$\bullet~$] $\dfrac{2}{5}$ des pratiquants du deltaplane ont moins de 35 ans, \item[$\bullet~$] le nombre de parapentistes est le double de celui des pratiquants du cerf-volant. \end{itemize} \setlength\parindent{0mm} \begin{enumerate} \item Recopier et complèter le tableau suivant : \begin{center} \begin{tabularx}{\linewidth}{\|c\|{4}{>{\centering \arraybackslash}X\|}}\cline{2-5} \multicolumn{1}{c\|}{} &Parapente &Deltaplane & Cerf-volant & Total\\ \hline Moins de 35 ans & & & & \\ \hline 35 ans et plus & & & & \\ \hline Total & & & & 150\\ \hline \end{tabularx} \end{center} On justifiera le résultat : 40~membres pratiquent le cerf-volant. \emph{Les résultats des questions} 2 \emph{et} 3 \emph{seront donnés sous forme d'une fraction irréductible puis sous la forme décimale arrondie } à $10^{-2}$ \emph{près}. \item On choisit au hasard un membre de ce club, calculer les probabilités des évènements suivants : A : \og ce membre a moins de 35 ans \fg ; B : \og ce membre ne pratique pas le parapente \fg ; C : \og ce membre a moins de 35 ans et pratique le parapente \fg ; D : \og ce membre a moins de 35 ans ou pratique le parapente \fg. \item Quelle est la probabilité qu'un membre du club choisi au hasard parmi ceux qui pratiquent le parapente ait 35 ans ou plus ? \end{enumerate} \vspace{0,5cm} \textbf{Exercice 1 \hfill 12 points} \medskip Un artisan se lance dans la fabrication en série d'un petit objet. Il calcule que le coût de fabrication de $n$~objets est donné en francs par \[ C(n) = - 0,2n^2 + 50n + \np{2000}. \] \vspace{0,25cm} \textbf{Partie A} \medskip \begin{enumerate} \item On note $C'$ la dérivée de la fonction $C$. Calculer $C'(n)$ et montrer que la fonction $C$ est croissante sur l'intervalle [0~;~100]. \item Reproduire et complèter le tableau suivant : \[ \begin{tabularx}{\linewidth}{\|{7}{>{\centering \arraybackslash}X\|}}\hline $n$ & 0 & 20 & 40 & 60 & 80 & 100 \\ \hline $C(n)$ & & & & & & \\ \hline \end{tabularx} \] \item Construire la courbe représentative de $C$ dans un repère orthogonal pour $n \leqslant 100$. Unités : 1~cm représente 5~objets en abscisse, 1~cm représente 250~francs en ordonnée. \end{enumerate} \vspace{0,25cm} \textbf{Partie B} \begin{enumerate} \item Tous les objets fabriqués sont vendus 80~ francs pièce. Quel est le montant $R(n)$ des rentrées d'argent pour la vente de $n$ objets ? Tracer la droite représentative de $R$ dans le m\^eme repère que celui de la question \textbf{A 3}. \item Lire graphiquement : \begin{enumerate} \item Pour quelles valeurs de $n$ l'artisan réalise un bénéfice. \item Pour quelle valeur de $n$ l'artisan subit une perte de \nombre{1000}~francs. \end{enumerate} \end{enumerate} \vspace{0,25cm} \textbf{Partie C} \medskip \begin{enumerate} \item Montrer que le bénéfice réalisé pour la vente de $n$ objets est donné par \[ B(n) = 0,2n^2 + 30n - \nombre{2000}.\] \item Montrer que $B(n) = 0,2(n - 50)(n + 200)$. Expliquer comment on retrouve le résultat du \textbf{B 2 a}. \end{enumerate} \end{document}
http://dlmf.nist.gov/18.5.E8.tex	nist.gov	CC-MAIN-2016-50	application/x-tex	null	crawl-data/CC-MAIN-2016-50/segments/1480698543030.95/warc/CC-MAIN-20161202170903-00341-ip-10-31-129-80.ec2.internal.warc.gz	71,005,829	727	\[\mathop{P^{(\alpha,\beta)}_{n}\/}\nolimits\!\left(x\right)=2^{-n}\sum_{\ell=0}% ^{n}\binom{n+\alpha}{\ell}\binom{n+\beta}{n-\ell}(x-1)^{n-\ell}(x+1)^{\ell}=% \frac{\left(\alpha+1\right)_{n}}{n!}\left(\frac{x+1}{2}\right)^{n}\mathop{{{}_% {2}F_{1}}\/}\nolimits\!\left({-n,-n-\beta\atop\alpha+1};\frac{x-1}{x+1}\right),\]
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https://www.zentralblatt-math.org/matheduc/en/?id=108139&type=tex	zentralblatt-math.org	CC-MAIN-2019-43	text/plain	application/x-tex	crawl-data/CC-MAIN-2019-43/segments/1570987822098.86/warc/CC-MAIN-20191022132135-20191022155635-00135.warc.gz	1,149,092,958	1,055	\input zb-basic \input zb-matheduc \iteman{ZMATH 1993a.01812} \itemau{McGarry, S.} \itemti{Removing the fear of numbers. Die Angst vor Zahlen nehmen.} \itemso{Train. Off. (Jun 1992) v. 28(5) p. 149-151. [ISSN 0041-090X]} \itemab \itemrv{~} \itemcc{M38} \itemut{Financial Mathematics; Book-Keeping; Curriculum Development; Content Selection; Courses; Further Education; ; Finanzmathematik; Buchfuehrung; Curriculumentwicklung; Stoffauswahl; Lehrgang; Weiterbildung} \itemli{} \end
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http://ctan.sharelatex.com/tex-archive/info/examples/Math/6-19-4.ltx	sharelatex.com	CC-MAIN-2014-23	text/x-tex	null	crawl-data/CC-MAIN-2014-23/segments/1405997883905.99/warc/CC-MAIN-20140722025803-00105-ip-10-33-131-23.ec2.internal.warc.gz	91,516,571	998	%% %% Der Mathematiksatz mit LaTeX, 1. Auflage 2009 %% %% Example 6-19-4 on page 130. %% %% Copyright (C) 2009 Herbert Voss %% %% It may be distributed and/or modified under the conditions %% of the LaTeX Project Public License, either version 1.3 %% of this license or (at your option) any later version. %% %% See http://www.latex-project.org/lppl.txt for details. %% \documentclass[]{ttctexa} \pagestyle{empty} \setcounter{page}{6} \setlength\textwidth{194.59192pt} \AtBeginDocument{\setlength\parindent{0pt}} \StartShownPreambleCommands \usepackage{amsmath} \StopShownPreambleCommands \begin{document} \[ \begin{gathered}\relax [p] = 100 \\ [v] = 200 \end{gathered} \] \end{document}
http://dlmf.nist.gov/25.11.E34.tex	nist.gov	CC-MAIN-2014-10	application/x-tex	null	crawl-data/CC-MAIN-2014-10/segments/1394011103144/warc/CC-MAIN-20140305091823-00065-ip-10-183-142-35.ec2.internal.warc.gz	54,112,882	652	\[n\int_{0}^{a}{\mathop{\zeta\/}\nolimits^{{\prime}}}\!\left(1-n,x\right)dx={% \mathop{\zeta\/}\nolimits^{{\prime}}}\!\left(-n,a\right)-{\mathop{\zeta\/}% \nolimits^{{\prime}}}\!\left(-n\right)+\frac{\mathop{B_{{n+1}}\/}\nolimits-% \mathop{B_{{n+1}}\/}\nolimits\!\left(a\right)}{n(n+1)},\]
https://mirror.anarhija.net/pl.anarchistlibraries.net/mirror/a/ak/anonim-kobiety-powinny-stracic-prawa-wyborcze-tak-jak-i-mezczyzni-16-1-2002.tex	anarhija.net	CC-MAIN-2021-31	application/octet-stream	application/x-tex	crawl-data/CC-MAIN-2021-31/segments/1627046153892.74/warc/CC-MAIN-20210729172022-20210729202022-00605.warc.gz	423,416,574	7,468	\documentclass[DIV=12,% BCOR=0mm,% headinclude=false,% footinclude=false,open=any,% fontsize=10pt,% oneside,% paper=210mm:11in]% {scrbook} \usepackage[noautomatic]{imakeidx} \usepackage{microtype} \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} \usepackage[shortlabels]{enumitem} \usepackage{tabularx} \usepackage[normalem]{ulem} \def\hsout{\bgroup \ULdepth=-.55ex \ULset} % https://tex.stackexchange.com/questions/22410/strikethrough-in-section-title % Unclear if \protect \hsout is needed. Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand{\forcelinebreak}{\strut\\{}} \newcommand{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand{\Slash}{\slash\hspace{0pt}} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} \usepackage{fontspec} \usepackage{polyglossia} \setmainlanguage{polish} \setmainfont{cmunrm.ttf}[Script=Latin,% Ligatures=TeX,% Path=/usr/share/fonts/truetype/cmu/,% BoldFont=cmunbx.ttf,% BoldItalicFont=cmunbi.ttf,% ItalicFont=cmunti.ttf] \setmonofont{cmuntt.ttf}[Script=Latin,% Ligatures=TeX,% Scale=MatchLowercase,% Path=/usr/share/fonts/truetype/cmu/,% BoldFont=cmuntb.ttf,% BoldItalicFont=cmuntx.ttf,% ItalicFont=cmunit.ttf] \setsansfont{cmunss.ttf}[Script=Latin,% Ligatures=TeX,% Scale=MatchLowercase,% Path=/usr/share/fonts/truetype/cmu/,% BoldFont=cmunsx.ttf,% BoldItalicFont=cmunso.ttf,% ItalicFont=cmunsi.ttf] \newfontfamily\polishfont{cmunrm.ttf}[Script=Latin,% Ligatures=TeX,% Path=/usr/share/fonts/truetype/cmu/,% BoldFont=cmunbx.ttf,% BoldItalicFont=cmunbi.ttf,% ItalicFont=cmunti.ttf] \renewcommand{\partpagestyle}{empty} % global style \pagestyle{plain} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand{\captionformat}{} \renewcommand{\figureformat}{} \renewcommand{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} \deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} \frenchspacing % avoid vertical glue \raggedbottom % this will generate overfull boxes, so we need to set a tolerance % \pretolerance=1000 % pretolerance is what is accepted for a paragraph without % hyphenation, so it makes sense to be strict here and let the user % accept tweak the tolerance instead. \tolerance=200 % Additional tolerance for bad paragraphs only \setlength{\emergencystretch}{30pt} % (try to) forbid widows/orphans \clubpenalty=10000 \widowpenalty=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{Kobiety powinny stracić prawa wyborcze – tak, jak i mężczyźni} \date{25.08.2019} \author{Barry Macleod-Cullinane} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={Kobiety powinny stracić prawa wyborcze – tak, jak i mężczyźni \#16 (1\Slash{}2002)},% pdfauthor={Barry Macleod-Cullinane},% pdfsubject={},% pdfkeywords={Inny Świat; feminizm; prawo; demokracja}% } \begin{document} \begin{titlepage} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge Kobiety powinny stracić prawa wyborcze – tak, jak i mężczyźni\par}}% \vskip 1em \vskip 2em {\usekomafont{author}{Barry Macleod-Cullinane\par}}% \vskip 1.5em \vfill {\usekomafont{date}{25.08.2019\par}}% \end{center} \end{titlepage} \cleardoublepage Dwusetna rocznica \emph{Vindication of the Rights of Woman}\footnote{\emph{“A Vindication of the Rights of Woman: with Structures on Political and Moral Subjects [1792]”} Penguin, Harmondsworth, Middlesex, 1992.} Mary Wollstonecraft wydaje się być dobrą okazją do przypomnienia czytelniczkom i czytelnikom prostej, acz często zapominanej prawdy. To, że kobiety powinny mieć takie samo prawo do stanowienia praw jak mężczyźni jest poza dyskusją. Tu kobiety i mężczyźni naprawdę są równi: \emph{“Nikt nie ma prawa stanowić Praw”}\footnote{Opinie wyrażone w artykule są zbliżone do tych wyrażanych przez czolowego XIX-wiecznego teoretyka wolnościowego Lysandra Spoonera w eseju \emph{“A Right to Make Laws?”} opublikowanym w \emph{“Liberty”} i \emph{“The New Age”} J. M. L. Babcocka, i ponownie w znakomitej antologii Wendy McElroy \emph{“Freedom, Feminism, and the State: An Overview of Individualist Feminism”} Cato Institute, Washington, D.C., 1982 [1st edition]. Książka McElroy jest być może ostatecznym zbiorem tekstów z tej dziedziny.}. Spadkobierczynie sufrażystek, współczesne feministki głównego nurtu twierdzą, że aby skończyć z uciskiem cierpianym przez kobiety i ich dyskryminacją konieczne są prawa stanowione przez państwo. Obojętnie, czy tą dyskryminacją są różnice w zarobkach, szansach na zatrudnienie, przysługujących prawach do posiadania majątku czy, co najważniejsze, przyzwolenie (męskiego) społeczeństwa na przemoc wobec ich osób i własności, feministki zwracają się o środki zaradcze i sprawiedliwość do państwowego prawodawstwa\footnote{McElroy w swym artykule \emph{“You’ve slid a long way, baby!”}, opublikowanym w \emph{“No Statesman”}, Vol. 1, No. 1 (1990) oferuje szczególnie bezlitosną krytykę poglądu socjalistycznych feministek, że ucisk ma swe źródło w procesie rynkowym. Pokazuje ona, że ucisk nie jest konsekwencją działalności rynkowej, ale wynika z przemocy państwa i jego ingerencji w rynek. Jako że proces rynkowy karze po pewnym czasie dobrowolną dyskryminację jednostek, to wprowadza on, jak to ujął Ludwig von Mises, harmonię właściwie rozumianych interesów. Przewagi i przywileje mogą być zatem utrzymywane w obliczu tego procesu jedynie poprzez używanie przemocy, czy to indywidualne, czy zinstytucjonalizowane w formie państwa. Zob. także klasyczne rozróżnienie pomiędzy Państwem a Rynkiem nakreślone przez Franza Oppenheimera w \emph{„The State”} Vanguard Press, New York, 1926.}. Społeczeństwo może być oparte na jednym z dwóch wzajemnie wykluczających się aksjomatów: przymusie albo zgodzie. Przymus tworzy hierarchiczne, oparte na sile stosunki między jednostkami, przybierające zwykle formę kradzieży, niewolnictwa i morderstwa – i jest on zinstytucjonalizowany w państwie. Zgoda jest podstawą wolnego handlu czy też laissez-faire z tylko jedną zasadą, prawem natury, które zachowuje prawo każdego do kontrolowania swej osoby i majątku pod warunkiem, że nie ingeruje on w podobne prawo kogoś innego do swobodnego posługiwania się własnym ciałem i majątkiem, i kontrolowania ich. Męski szowinistyczny pracodawca, potępiany przez “politycznie poprawnych” intelektualistów za odmowę zatrudniania kobiet, jest karany za swe uprzedzenia, musząc oferować wyższe płace dla przyciągnięcia dodatkowych pracowników – mężczyzn. Jego zwiększone koszty i zmniejszona konkurencyjność pozwalają firmom zatrudniającym tańszych pracowników-kobiety sprzedawać taniej od niego, co po pewnym czasie podnosi płace kobiet i obniża płace mężczyzn\footnote{Argument ten jest nakreślony dokładniej przez Waltera Blocka, który pokazuje, dlaczego “Męska Szowinistyczna Świnia” powinna być uznana za współczesnego bohatera – znajduje się on w jego godnym uwagi i głęboko przenikliwym przesłaniu tolerancji: \emph{„Defending the Undefendable: The Pimp, Prostitute, Scab, Slumlord, Libeler, Moneylender, and Other Scapegoats in the Rogue’s Gallery of American Society”} Fleet Press Corporation, New York,1976.}. Ustawy o \emph{“równych płacach”} dają całkiem odmienny rezultat. Zakaz zastępowania kosztownych mężczyzn tańszymi pracownikami-kobietami zmniejsza szanse zatrudnienia kobiet; zatrudnieni już pracownicy wyciągają płace powyżej stawki rynkowej, co równa się przymusowej redystrybucji od biednych do bogatych. Nic dziwnego, że związki zawodowe popierają ustawy o płacach minimalnych. Takie ustawodawstwo, czy roszczenia do majątku innych, wskrzesza na powrót sytuację, w której zdaniem feministek cierpią kobiety, tj. zalegalizowany przymus przypominający niewolnictwo – i popierając to feministki wydają się wypierać swych wcześniejszych zasad. Amerykański feminizm wyłonił się z XIX-wiecznego, radykalnie indywidualistycznego antyniewolniczego ruchu związanego z pismem \emph{“The Liberator”} Williama Lloyda Garrisona\footnote{Jeśli chodzi o historyczne szkice na temat wyłaniania się myśli indywidualistycznego feminizmu, zob. \emph{“The True Mothers of Feminism”} Wendy McElroy, opublikowane w \emph{“Reason”}, lipiec 1983, str. 39-42, oraz jej późniejszy traktat na ten temat, \emph{“The Roots of Individualist Feminism in 19th Century America”}, str. 3-26, który stanowi początkowy rozdział \emph{„Freedom, Feminism, and the State”}. Dr Stephen Davies napisał podobną znakomitą historię wolnościowego feminizmu w Wielkiej Brytanii, \emph{„Libertarian Feminism in Britain, 1860}\emph{-1910}\emph{”} LA Pamphlet No. 7, Libertarian Alliance, London, 1987. Ten ostatni tekst służy do obalania mitów współczesnych socjalistycznych feministek na temat pochodzenia ruchu feministycznego w Wielkiej Brytanii.}. Siostry Grimke, Sarah i Angelina, pokazywały w broszurach i prelekcjach, jak prawa kobiet i prawa niewolników na równi nie istnieją wobec państwowego prawa. A jednak niektóre feministki popierają przywrócenie ustawowego niewolnictwa, wyrażając to bardziej w języku roszczeń niż prawa do władania sobą. Jest to konsekwencja kampanii na rzecz ustawowego \emph{“prawa do aborcji na żądanie”}\footnote{Jeśli chodzi o argument na rzecz prawa do aborcji wynikający jawnie z zasady władania sobą, patrz wystąpienie McElroy, \emph{“What Does it Mean To Be An Individual?} \emph{(}\emph{Self-Ownership} \emph{Is Key To Abortion Issue)”} w debacie z Doris Gordon z Libertarians for Life, organizacji antyaborcyjnej, w \emph{“Rampart Individualist”}, Vol. 1, No. 4, jesien, 1983, str. 3-9.}. Naturę tego zadania ujawnia następujący scenariusz: wyobraźmy sobie, że wszyscy lekarze odmawiają z takiej czy innej przyczyny przeprowadzania aborcji. Przy \emph{“prawie do aborcji na żądanie”} konieczne byłoby zmuszenie kilku lub wszystkich opornych lekarzy do przeprowadzenia operacji i tym samym ustanowienie stosunków międzyludzkich opartych na przemocy, sprowadzające zmuszanych do roli niewolników. Pogląd, że takie roszczenia można wywieść z reguł demokracji jest fałszywy z tej przyczyny, że jest obojętne, czy czyjeś prawo do władania sobą przywłaszcza sobie jedna osoba, czy milion osób, które to przegłosowują i wtrącają tego kogoś w niewolnictwo. Feministki domagające się sprawiedliwości i wolności powinny uzmysłowić sobie fakt, że sprawiedliwość nie może być stanowiona w drodze przymusu państwa nad jednostkami, musi natomiast być odkryta poprzez usunięcie owego zgubnego prawodawstwa, które unieważnia prawo kobiet i mężczyzn do władania sobą\footnote{Ten pogląd na państwo, prawo i sprawiedliwość jest poglądem Woluntarystów, z którymi Wendy McElroy mocno się utożsamia. Użyteczny zbiór pism Woluntarystów został opublikowany jako \emph{„Neither Bullets nor Ballots: Essays on Voluntaryism, The Voluntaryists”} Baltimore, Maryland, 1983; znajdują się tam eseje McElroy, George’a H. Smitha i Carla Watnera. Woluntaryści dążą do \emph{“delegitymizacji państwa przez edukacje”} i \emph{“orędują za wycofaniem się ze współpracy i milczącej zgody, na której ostatecznie opiera się władza państwa”}. Powinno się jednak tu zaznaczyć, że nie jest to ostatnia nowinka strategiczna wśród wolnościowców i, jak podkreślają to współcześni Woluntaryści, pochodzi z klasycznego dzieła \emph{„Etienne’a de la Boetie The Will to Bondage [trans.} \emph{A Discourse on Voluntary Servitude]”,} 1577, [1735], \emph{Libertarian Broadsides} No. 6, Ralph Myles Publisher, Colorado Springs, 1974. Za część tej tradycji można uznać też Lysandra Spoonera; jego \emph{“No Treason: The Constitution of No Authority and Natural Law: The Science of Justice”} są ostatnio dostępne w znakomitym zbiorze pod redakcja George’a H. Smitha \emph{“The Lysander Spooner Reader, Fox \& Wilkes”} San Francisco, 1992.}. Jak zauważył Lysander Spooner, \emph{“jeśli kobiety, zamiast wnosić petycje o dopuszczenie do udziału we władzy ustanawiającej więcej praw, obwieszczą obecnym prawodawcom, że one, kobiety, pójdą do parlamentu i cisną w ogień wszystkie istniejące kodeksy, to zrobią bardzo rozsądną rzecz – jedną z najrozsądniejszych rzeczy, jakie są w stanie zrobić. I będą miały ze sobą tłum mężczyzn – przynajmniej wszystkich rozsądnych i uczciwych mężczyzn w tym kraju – którzy z nimi pójdą”}\footnote{Lysander Spooner, \emph{“A Right to Make Laws?”}, str. 330.}. W niniejszym artykule próbowałem przedstawić parę idei i ogólny “wydźwięk” argumentów charakteryzujących tradycje indywidualistycznego feminizmu używając jej jako tła do przeegzaminowania rozpowszechnionych roszczeń współczesnego socjalistycznego feminizmu. Chociaż tekst ten broni się sam i nie potrzebuje wielu przypisów, zdecydowałem się włączyć doń – dla zainteresowanych – opatrzony przypisami przewodnik bibliograficzny, który odnosi poszczególne argumenty zawarte w tekście do materiałów źródłowych. % begin final page \clearpage % new page for the colophon \thispagestyle{empty} \begin{center} Anarcho-Biblioteka \smallskip Dobry pieróg to wywrotowy pieróg \bigskip \includegraphics[width=0.25\textwidth]{logo-pl.pdf} \bigskip \end{center} \strut \vfill \begin{center} Barry Macleod-Cullinane Kobiety powinny stracić prawa wyborcze – tak, jak i mężczyźni 25.08.2019 \bigskip https:\Slash{}\Slash{}innyswiat.com.pl\Slash{}kobiety-powinny-stracic-prawa-wyborcze-tak-jak-i-mezczyzni-16-1-2002\Slash{} Tłum. J. Sierpinski \bigskip \textbf{pl.anarchistlibraries.net} \end{center} % end final page with colophon \end{document} % No format ID passed.
https://engineering.purdue.edu/~mark/PurdueThesis/template/ap-figures.tex	purdue.edu	CC-MAIN-2021-17	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2021-17/segments/1618038461619.53/warc/CC-MAIN-20210417162353-20210417192353-00572.warc.gz	347,881,555	1,841	\ProvidesFile{ap-figures.tex}[2021-02-04 figures appendix] \begin{VerbatimOut}{z.out} \chapter{FIGURES} \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} The \verb+h+ specifier used in all the examples below tells \LaTeX\ to put the figure ``here'' instead of trying to find a good spot at the top or bottom of a page. Specifiers can be combined, for example, ``\verb+\begin{figure}[htbp!]+''. \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} The complete list of specifiers: \vspace{6pt} \begin{center} \begin{tabular}{@{}ll@{}} \toprule \bf Specifier& \bf Description\cr \midrule \noalign{\vspace{2pt}} \tt b& bottom of page\cr \tt h& here on page\cr \tt p& on separate page of figures\cr \tt t& top of page\cr \tt !& try hard to put figure as early as possible\cr \bottomrule \end{tabular} \end{center} \end{VerbatimOut} \MyIO % !!!! Label ``fi:not-centered'' is ``\ref{fi:not-centered}''. % !!!! Label ``sf:four-parts-c'' is ``\ref{sf:four-parts-c}''. \begin{VerbatimOut}{z.out} % MyRepeat is defined in MyRepeat.sty. \MyRepeat{This is the first paragraph. }{5} \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} \begin{figure}[ht] \includegraphics{gr-plot.pdf} \caption{% By default figures are not centered. This is a long caption to demonstrate that captions are single spaced.% } \label{fi:not-centered} \end{figure} \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} \MyRepeat{This is the second paragraph. }{10} \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} \begin{figure}[ht] \centering \includegraphics{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} \MyRepeat{This is the third paragraph. }{15} \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} \begin{figure}[ht] \centering \includegraphics{gr-plot.pdf} \caption{This is another figuure.} \label{fi:another} \end{figure} \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} \MyRepeat{This is the fourth paragraph. }{10} \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} \begin{figure}[ht] \centering \subcaptionbox {First subcaption.\label{sf:two-parts-a}}% [2in]% {\bfseries First subfigure.}% \hskip 0.5truein \subcaptionbox {Second subcaption.\label{sf:two-parts-b}}% [2in]% {\bfseries Second subfigure.}% \caption{This figure has two parts.} \label{fi:two-parts} \end{figure} \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} \MyRepeat{This is the fifth paragraph. }{10} \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} \newpage \begin{figure}[ht] \centering \subcaptionbox {First subcaption.\label{sf:four-parts-a}} [2in]% {\bfseries First subfigure.}% \hskip 0.5truein \subcaptionbox {Second subcaption.\label{sf:four-parts-b}} [2in]% {\bfseries Second subfigure.}% \vspace{\baselineskip} \subcaptionbox {Third subcaption.\label{sf:four-parts-c}} [2in]% {\bfseries Third subfigure.}% \hskip 0.5truein \subcaptionbox {Fourth subcaption.\label{sf:four-parts-d}} [2in]% {\bfseries Fourth subfigure.}% \caption{This figure has four parts.} \label{fi:four-parts} \end{figure} \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} \MyRepeat{This is the sixth paragraph. }{10} \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} \newpage \begin{figure}[ht] \centering % Use a 5" font. {\fontsize{5in}{5in}\selectfont$\hspace{-0.07em}\sqrt 2$} \caption{% \LaTeX\ can make output big enough for T-shirts or posters. Square roots are printed with space before them, I put some negative horizontal space before this one to center it.% } \end{figure} \end{VerbatimOut} \MyIO \begin{VerbatimOut}{z.out} \newpage The remainder of this file tests having lots of figures. There are 20 figures in this test. \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.1]{gr-plot.pdf} \caption{Use {\tt \char'134centering\/} to center figures.} \label{fi:centered} \end{figure} \end{VerbatimOut} \MyIO
http://cr.yp.to/bib/1995/abrash.tex	yp.to	CC-MAIN-2022-40	text/plain	application/x-tex	crawl-data/CC-MAIN-2022-40/segments/1664030337625.5/warc/CC-MAIN-20221005105356-20221005135356-00554.warc.gz	15,592,162	647	\bib{1995/abrash} \yr 1995 \isbn 188357708X \by Michael Abrash \book Zen of graphics programming \publ Coriolis Group \publaddr Scottsdale, Arizona \endref
http://arxmliv.kwarc.info/sty/aaspp4_rj.sty	kwarc.info	CC-MAIN-2018-39	text/x-tex	text/x-matlab	crawl-data/CC-MAIN-2018-39/segments/1537267161638.66/warc/CC-MAIN-20180925123211-20180925143611-00156.warc.gz	19,882,622	6,334	% Converted by doc2sty Mon May 15 13:45:55 PDT 1995. % This file is not intended for human consumption. % AASPP4.STY -- AAS preprint substyle definition for LaTeX. \def\revtex@ver{4.0} \def\revtex@date{25 Apr 95} \def\revtex@org{AAS} \def\revtex@jnl{AAS} \def\revtex@genre{preprint} \typeout{\revtex@org\space \revtex@genre\space substyle, v\revtex@ver\space <\revtex@date>.} \def\revtex@pageid{\xdef\@thefnmark{\null} \@footnotetext{This \revtex@genre\space was prepared with the \revtex@org\space \LaTeX\ macros v\revtex@ver.}} \def\genre@MS{manuscript} \def\genre@PP{preprint} \ifx\revtex@genre\genre@PP \ifnum\@ptsize<1 \typeout{Warning: Undersize \revtex@genre\space font (1\@ptsize\space pts). 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\setcounter{cureqno}{\value{equation}}% \let\@curtheeqn\theequation% \edef\cur@eqn{\theequation}% \def\theequation{\cur@eqn\alph{equation}}% \setcounter{equation}{0}}% {\let\theequation\@curtheeqn% \setcounter{equation}{\value{cureqno}}} \def\eqnum#1{\def\theequation{#1}\let\@currentlabel\theequation \addtocounter{equation}{\m@ne}} \def\references{\subsection{REFERENCES} \bgroup\parindent=\z@\parskip=\itemsep \def\refpar{\par\hangindent=3em\hangafter=1}} \def\endreferences{\refpar\egroup\revtex@pageid} \def\thebibliography#1{\subsection{REFERENCES} \list{\null}{\leftmargin 3em\labelwidth\z@\labelsep\z@\itemindent -3em \usecounter{enumi}} \def\refpar{\relax} \def\newblock{\hskip .11em plus .33em minus .07em} \sloppy\clubpenalty4000\widowpenalty4000 \sfcode`\.=1000\relax} \def\endthebibliography{\endlist\revtex@pageid} \def\@biblabel#1{\relax} \def\@cite#1#2{#1\if@tempswa , #2\fi} \def\reference{\@ifnextchar\bgroup {\@reference} {\@latexerr{Missing key on reference command} {Each 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\footnoterule \vspace{.5ex} {\footnotesize\tblnote@list} \gdef\tblnote@list{} \fi} \def\endtable{\spew@tblnotes\end@float} \@namedef{endtable}{\spew@tblnotes\end@dblfloat} \let\tableline=\hline \long\def\@makecaption#1#2{\vskip 2ex\noindent #1 #2\par} \def\tablenum#1{\def\thetable{#1}\let\@currentlabel\thetable \addtocounter{table}{\m@ne}} \def\figurenum#1{\def\thefigure{#1}\let\@currentlabel\thefigure \addtocounter{figure}{\m@ne}} \let\placetable=\@gobble \let\placefigure=\@gobble \let\placeplate=\@gobble \def\figcaption{\@ifnextchar[{\@xfigcaption}{\@figcaption}} \def\@figcaption#1{{\def\@captype{figure}\caption{#1}}} \def\@xfigcaption[#1]#2{{\def\@captype{figure}\caption{#2}}} \def\dummytable{\refstepcounter{table}} \newbox\pt@box \newdimen\pt@width \newcount\pt@line \newcount\pt@column \newcount\pt@nlines \newcount\pt@ncol \newcount\pt@page \def\colhead#1{\multicolumn{1}{c}{#1}\pt@addcol} \def\tablecolumns#1{\pt@column=#1\pt@ncol=#1\gdef\pt@addcol{\relax}} \def\tablecaption#1{\gdef\pt@caption{#1}} \def\pt@caption{\relax} \def\tablehead#1{\gdef\pt@head{\hline\hline\relax\\[-1.7ex] #1\hskip\tabcolsep\\[.7ex]\hline\relax\\[-1.5ex]}} \def\pt@head{\relax} \def\tabletail#1{\gdef\pt@tail{#1}} \def\pt@tail{\relax} \def\tablewidth#1{\pt@width=#1} \pt@width\textwidth \def\tableheadfrac#1{\gdef\pt@headfrac{#1}} \def\pt@headfrac{.1} \def\pt@calcnlines{\@tempdima\pt@headfrac\textheight \@tempdimb\textheight\advance\@tempdimb by-\@tempdima \@tempdima\arraystretch\baselineskip \divide\@tempdimb by\@tempdima \global\pt@nlines\@tempdimb} \def\pt@tabular{\hbox \bgroup $\let\@acol\@ptabacol \let\@classz\@tabclassz \let\@classiv\@tabclassiv \let\\\@tabularcr\@tabarray} \def\@ptabacol{\edef\@preamble{\@preamble \hskip \tabcolsep\tabskip\fill}} \def\fnum@ptable{Table \thetable} \def\fnum@ptablecont{Table \thetable---{\rm Continued}} \newdimen\pt@tmpcapwidth \def\set@mkcaption{\long\def\@makecaption##1##2{\ifdim\pt@width>\z@% \pt@tmpcapwidth\pt@width\else\pt@tmpcapwidth\textwidth\fi% \center\parbox{\pt@tmpcapwidth}{\center\rm##1.\quad##2\endcenter}% \endcenter}} \def\set@mkcaptioncont{\long\def\@makecaption##1##2{ \center\rm##1\endcenter\vskip 2.5ex}} \newenvironment{deluxetable}[1]{\def\pt@format{\string#1}% \set@tblnotetext\global\pt@ncol=0\global\pt@column=0\global\pt@page=1% \def\pt@addcol{\global\advance\pt@ncol by\@ne}}% {% \pt@width\wd\pt@box\box\pt@box\spew@ptblnotes% \typeout{Page \the\pt@page\space of table \thetable\space has been set to width \the\pt@width\space with \the\pt@nlines\space lines per page}% \endcenter\end@float} \let\planotable=\deluxetable \let\endplanotable=\enddeluxetable \def\startdata{\pt@line=0\pt@calcnlines% \ifdim\pt@width>\z@\def\@halignto{to \pt@width}\else\def\@halignto{}\fi% \let\fnum@table=\fnum@ptable\set@mkcaption% \@float{table}\center\caption{\pt@caption}\leavevmode% \setbox\pt@box=\pt@tabular{\pt@format}\pt@head} \def\enddata{\crcr\noalign{\vskip .7ex}\hline\endtabular} \def\pt@nl{\global\advance\pt@line by\@ne% \ifnum\pt@line=\pt@nlines% \endtabular\pt@width\wd\pt@box\box\pt@box \typeout{Page \the\pt@page\space of table \thetable\space has been set to width \the\pt@width}% \global\advance\pt@page by\@ne% \endcenter\end@float\clearpage% \addtocounter{table}{\m@ne}% \let\fnum@table=\fnum@ptablecont\set@mkcaptioncont% \@float{table}\center\caption{\pt@caption}\leavevmode% \global\pt@ncol=\pt@column \global\pt@line=0% \setbox\pt@box=\pt@tabular{\pt@format}\pt@head% \else\\ \fi} \let\nl=\pt@nl \let\nextline=\pt@nl \def\tablevspace#1{\noalign{\vskip#1}} \def\tablebreak{\pt@line\pt@nlines\advance\pt@line by\m@ne\pt@nl} \def\cutinhead#1{\noalign{\vskip 1.5ex} \hline\pt@nl\noalign{\vskip -2.0ex} \multicolumn{\pt@ncol}{c}{#1}\pt@nl \noalign{\vskip .8ex} \hline\pt@nl\noalign{\vskip -2ex}} \def\sidehead#1{\noalign{\vskip 1.5ex} \multicolumn{\pt@ncol}{@{\hskip\z@}l}{#1}\pt@nl \noalign{\vskip .5ex}} \def\set@tblnotetext{\def\tablenotetext##1##2{{% \@temptokena={{\parbox{\pt@width}{\hskip1em$^{\rm ##1}$##2}}\par}% \@temptokenb=\expandafter{\tblnote@list} \xdef\tblnote@list{\the\@temptokenb\the\@temptokena}}}} \def\spew@ptblnotes{ \ifx\tblnote@list\@empty\relax \else \par \vspace{2ex} {\parskip=1.5ex% \tblnote@list} \gdef\tblnote@list{} \fi} \def\tablerefs#1{\@temptokena={\vspace{3ex}{% \parbox{\pt@width}{\hskip1em\rm References. --- #1}\par}}% \@temptokenb=\expandafter{\tblnote@list} \xdef\tblnote@list{\the\@temptokenb\the\@temptokena}} \def\tablecomments#1{\@temptokena={\vspace{3ex}{% \parbox{\pt@width}{\hskip1em\rm Note. --- #1}\par}}% \@temptokenb=\expandafter{\tblnote@list} \xdef\tblnote@list{\the\@temptokenb\the\@temptokena}} \newcounter{plate} \def\theplate{\@arabic\c@plate} \def\fps@plate{bp} \def\ftype@plate{4} \def\ext@plate{lof} \def\fnum@plate{{\bf Plate \theplate.}} \def\plate{\@float{plate}} \let\endplate\end@float \@namedef{plate}{\@dblfloat{plate}} \@namedef{endplate}{\end@dblfloat} \let\platewidth=\tablewidth \def\platenum#1{\def\theplate{#1}\let\@currentlabel\theplate \addtocounter{plate}{\m@ne}} \def\thefigure{\@arabic\c@figure} \def\fnum@figure{{\rm Fig.\space\thefigure.---}} \def\thetable{\@arabic\c@table} \def\fnum@table{{\rm Table \thetable:}} \def\fps@figure{bp} \def\fps@table{bp} \@ifundefined{epsfbox}{\@input{epsf.sty}}{\relax} \def\eps@scaling{.95} \def\epsscale#1{\gdef\eps@scaling{#1}} \def\plotone#1{\centering \leavevmode \epsfxsize=\eps@scaling\columnwidth \epsfbox{#1}} \def\plottwo#1#2{\centering \leavevmode \epsfxsize=.45\columnwidth \epsfbox{#1} \hfil \epsfxsize=.45\columnwidth \epsfbox{#2}} \def\plotfiddle#1#2#3#4#5#6#7{\centering \leavevmode \vbox to#2{\rule{0pt}{#2}} \special{psfile=#1 voffset=#7 hoffset=#6 vscale=#5 hscale=#4 angle=#3}} \let\jnl@style=\rm \def\ref@jnl#1{{\jnl@style#1}} \def\aj{\ref@jnl{AJ}} \def\araa{\ref@jnl{ARA\&A}} \def\apj{\ref@jnl{ApJ}} \def\apjl{\ref@jnl{ApJ}} \def\apjs{\ref@jnl{ApJS}} \def\ao{\ref@jnl{Appl.~Opt.}} \def\apss{\ref@jnl{Ap\&SS}} \def\aap{\ref@jnl{A\&A}} \def\aapr{\ref@jnl{A\&A~Rev.}} \def\aaps{\ref@jnl{A\&AS}} \def\azh{\ref@jnl{AZh}} \def\baas{\ref@jnl{BAAS}} \def\jrasc{\ref@jnl{JRASC}} \def\memras{\ref@jnl{MmRAS}} \def\mnras{\ref@jnl{MNRAS}} \def\pra{\ref@jnl{Phys.~Rev.~A}} \def\prb{\ref@jnl{Phys.~Rev.~B}} \def\prc{\ref@jnl{Phys.~Rev.~C}} \def\prd{\ref@jnl{Phys.~Rev.~D}} \def\pre{\ref@jnl{Phys.~Rev.~E}} \def\prl{\ref@jnl{Phys.~Rev.~Lett.}} \def\pasp{\ref@jnl{PASP}} \def\pasj{\ref@jnl{PASJ}} \def\qjras{\ref@jnl{QJRAS}} \def\skytel{\ref@jnl{S\&T}} \def\solphys{\ref@jnl{Sol.~Phys.}} \def\sovast{\ref@jnl{Soviet~Ast.}} \def\ssr{\ref@jnl{Space~Sci.~Rev.}} \def\zap{\ref@jnl{ZAp}} \def\nat{\ref@jnl{Nature}} \def\iaucirc{\ref@jnl{IAU~Circ.}} \def\aplett{\ref@jnl{Astrophys.~Lett.}} \def\apspr{\ref@jnl{Astrophys.~Space~Phys.~Res.}} \def\bain{\ref@jnl{Bull.~Astron.~Inst.~Netherlands}} \def\fcp{\ref@jnl{Fund.~Cosmic~Phys.}} \def\gca{\ref@jnl{Geochim.~Cosmochim.~Acta}} \def\grl{\ref@jnl{Geophys.~Res.~Lett.}} \def\jcp{\ref@jnl{J.~Chem.~Phys.}} \def\jgr{\ref@jnl{J.~Geophys.~Res.}} \def\jqsrt{\ref@jnl{J.~Quant.~Spec.~Radiat.~Transf.}} \def\memsai{\ref@jnl{Mem.~Soc.~Astron.~Italiana}} \def\nphysa{\ref@jnl{Nucl.~Phys.~A}} \def\physrep{\ref@jnl{Phys.~Rep.}} \def\physscr{\ref@jnl{Phys.~Scr}} \def\planss{\ref@jnl{Planet.~Space~Sci.}} \def\procspie{\ref@jnl{Proc.~SPIE}} \let\astap=\aap \let\apjlett=\apjl \let\apjsupp=\apjs \let\applopt=\ao \def\phn{\phantom{0}} \def\phd{\phantom{.}} \def\phs{\phantom{$-$}} \def\phm#1{\phantom{#1}} \def\sun{\hbox{$\odot$}} \def\earth{\hbox{$\oplus$}} \def\lesssim{\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{$<$}}}} \def\gtrsim{\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{$>$}}}} \def\sq{\hbox{\rlap{$\sqcap$}$\sqcup$}} \def\arcdeg{\hbox{$^\circ$}} \def\arcmin{\hbox{$^\prime$}} \def\arcsec{\hbox{$^{\prime\prime}$}} \def\fd{\hbox{$.\!\!^{\rm d}$}} \def\fh{\hbox{$.\!\!^{\rm h}$}} \def\fm{\hbox{$.\!\!^{\rm m}$}} \def\fs{\hbox{$.\!\!^{\rm s}$}} \def\fdg{\hbox{$.\!\!^\circ$}} \def\farcm{\hbox{$.\mkern-4mu^\prime$}} \def\farcs{\hbox{$.\!\!^{\prime\prime}$}} \def\fp{\hbox{$.\!\!^{\scriptscriptstyle\rm p}$}} \def\micron{\hbox{$\mu$m}} \let\la=\lesssim \let\ga=\gtrsim \def\case#1#2{\hbox{$\frac{#1}{#2}$}} \def\slantfrac#1#2{\hbox{$\,^#1\!/_#2$}} \def\onehalf{\slantfrac{1}{2}} \def\onethird{\slantfrac{1}{3}} \def\twothirds{\slantfrac{2}{3}} \def\onequarter{\slantfrac{1}{4}} \def\threequarters{\slantfrac{3}{4}} \def\ubvr{\hbox{$U\!BV\!R$}} \def\ub{\hbox{$U\!-\!B$}} \def\bv{\hbox{$B\!-\!V$}} \def\vr{\hbox{$V\!-\!R$}} \def\ur{\hbox{$U\!-\!R$}} \def\ion#1#2{#1$\;${\small\rm\@Roman{#2}}\relax} \def\nodata{ ~$\cdots$~ } \newcount\lecurrentfam \def\LaTeX{\lecurrentfam=\the\fam \leavevmode L\raise.42ex \hbox{$\fam\lecurrentfam\scriptstyle\kern-.3em A$}\kern-.15em\TeX} \def\sizrpt{ (\fontname\the\font): em=\the\fontdimen6\font, ex=\the\fontdimen5\font \typeout{ (\fontname\the\font): em=\the\fontdimen6\font, ex=\the\fontdimen5\font }}
https://mirror.anarhija.net/usa.anarchistlibraries.net/mirror/b/bc/bonfire-collective-affinity-identity-tactics.tex	anarhija.net	CC-MAIN-2021-10	application/octet-stream	application/x-tex	crawl-data/CC-MAIN-2021-10/segments/1614178360745.35/warc/CC-MAIN-20210228084740-20210228114740-00010.warc.gz	454,248,003	9,953	\documentclass[DIV=12,% BCOR=10mm,% headinclude=false,% footinclude=false,open=any,% fontsize=11pt,% twoside,% paper=210mm:11in]% {scrbook} \usepackage{microtype} \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} \usepackage[shortlabels]{enumitem} \usepackage{tabularx} \usepackage[normalem]{ulem} \def\hsout{\bgroup \ULdepth=-.55ex \ULset} % https://tex.stackexchange.com/questions/22410/strikethrough-in-section-title % Unclear if \protect \hsout is needed. Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand{\forcelinebreak}{\strut\\{}} \newcommand{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand{\Slash}{\slash\hspace{0pt}} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} \usepackage{fontspec} \usepackage{polyglossia} \setmainlanguage{english} \setmainfont{LinLibertine_R.otf}[Script=Latin,% Path=/usr/share/fonts/opentype/linux-libertine/,% BoldFont=LinLibertine_RB.otf,% BoldItalicFont=LinLibertine_RBI.otf,% ItalicFont=LinLibertine_RI.otf] \setmonofont{cmuntt.ttf}[Script=Latin,% Scale=MatchLowercase,% Path=/usr/share/fonts/truetype/cmu/,% BoldFont=cmuntb.ttf,% BoldItalicFont=cmuntx.ttf,% ItalicFont=cmunit.ttf] \setsansfont{cmunss.ttf}[Script=Latin,% Scale=MatchLowercase,% Path=/usr/share/fonts/truetype/cmu/,% BoldFont=cmunsx.ttf,% BoldItalicFont=cmunso.ttf,% ItalicFont=cmunsi.ttf] \newfontfamily\englishfont{LinLibertine_R.otf}[Script=Latin,% Path=/usr/share/fonts/opentype/linux-libertine/,% BoldFont=LinLibertine_RB.otf,% BoldItalicFont=LinLibertine_RBI.otf,% ItalicFont=LinLibertine_RI.otf] \renewcommand{\partpagestyle}{empty} % global style \pagestyle{plain} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand{\captionformat}{} \renewcommand{\figureformat}{} \renewcommand{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} \deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} \frenchspacing % avoid vertical glue \raggedbottom % this will generate overfull boxes, so we need to set a tolerance % \pretolerance=1000 % pretolerance is what is accepted for a paragraph without % hyphenation, so it makes sense to be strict here and let the user % accept tweak the tolerance instead. \tolerance=200 % Additional tolerance for bad paragraphs only \setlength{\emergencystretch}{30pt} % (try to) forbid widows/orphans \clubpenalty=10000 \widowpenalty=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{Affinity Identity Tactics} \date{2018} \author{Bonfire Collective} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={Affinity Identity Tactics},% pdfauthor={Bonfire Collective},% pdfsubject={},% pdfkeywords={affinity; affinity groups; identity; tactics; diversity of tactics; organizing; the left; identity politics}% } \begin{document} \begin{titlepage} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge Affinity Identity Tactics\par}}% \vskip 1em \vskip 2em {\usekomafont{author}{Bonfire Collective\par}}% \vskip 1.5em \vfill {\usekomafont{date}{2018\par}}% \end{center} \end{titlepage} \cleardoublepage \tableofcontents % start a new right-handed page \cleardoublepage When movements for social and political change gather to work together, there are always three essential elements that movements should keep in mind: Affinity, Identity, and Tactics. Affinity refers to your political goals, that is, your vision of a what a good society looks like. Communism, anarchism, and mainstream liberalism are all different Affinities with different political projects. Identity is created by your position in your society, and is made up of facts about you that affect your experience of life. Your race, gender, (dis)ability, and socioeconomic status are all parts of your Identity in a political sense. Tactics are the methods that you are willing to use to bring about the political goals set by your Affinity. Boycotts, public educational campaigns, voting in elections, and black bloc are all Tactics. Planning successful political campaigns and actions requires that we pay attention to all three of these elements without leaving any of them out. How and why should we address each one? \section{Affinity} Do you want to live in a society in which everyone can get medical care without having to worry about whether they will go bankrupt? What about a society in which police aren’t just another kind of predator? A society that seriously works protect the future of this planet and the beings that inhabit it? Your answers to these questions and others like them define your Affinity. As people learn more about the history and current reality of movements, they tend to define their Affinity more precisely and start to use words like “anarchist” and “socialist” to refer to themselves and their comrades. Sometimes we combine terms to emphasize what we think is important, such as “eco-socialist” or “anarcho-communist.” We choose these Affinities because we share the goals of larger movements. Consider some choices of Affinity within the Left: \emph{If you oppose capitalism but not the State, then your Affinity is authoritarian communism. If you believe that the State can limit the worst parts of capitalism and that both can coexist in a reformed version of our current society, then you are a liberal. If you oppose both capitalism and the State, then you are an anarchist. These are just some of the choices of Affinity available to you.} While activism can work by just being reactive, that is, by seeing that some problem needs fixing and working on it together, it is hard to broaden and sustain our movements without a clear idea of where we are going together. For example, if we are working together to fight the spread of dangerous opiates around our community, will it be a good solution for the local police to promise to arrest more people who sell drugs? An activist group built entirely around “solving” this problem will likely split on this issue. Liberals and authoritarian communists may be satisfied, while anarchists will not be, because anarchists believe that police don’t solve problems at their root. Understanding the big picture of what you and others in your group believe will help you explain your disagreements, find common ground, and reject inadequate solutions. We want to see the big picture, not just the little issues. If you haven’t yet, begin the work to understand your Affinity. Read about diverse political movements, follow politically active people on Twitter, watch historical documentaries and go to university lectures. Revolutionary Left Radio is a podcast with a big archive of people having smart conversations about their political Affinity. Remember that the Left has more commonalities than differences, but that the differences are still very important. Most people change their Affinity as they learn more, and that’s alright too. Political traditions offer rich lessons, ideas, and inspiration. The work and sacrifice of others in the struggle for justice was meant to nourish us, and when we understand our political beliefs, it does. \section{Identity} Our Identities are produced by the interaction of individuals with positive and negative aspects of our society. In society, individuals are seen as members of groups, and this group membership affects us whether or not we want it to or not. Privileges flow from being seen as part of a dominant group (Whites, men, colonizers, wealthy, first-world, citizen, straight, cisgender) and oppression flows from being a member of an oppressed group (people of color, women, colonized, poor, third-world, undocumented, queer, transgender). Experiences of solidarity within identity groups come from shared worldviews, literature, art, and history, and are not reducible to shared experiences of oppression and hardship. This is true of the solidarity of people of color, queer folks, women, and other identity groups. People with privileged identities, such as men, white people, and middle-class and rich people are also members of identity groups, even if they do not feel solidarity with other members of those groups. Consider the negative and positive experiences of being a person with a disability. On one hand, the life of a person with a physical disability may be negatively defined by the way in which buildings are constructed - there are social spaces that cannot be entered, extra assistance that may be needed from other people, and forms of discrimination faced in seeking work. On the other hand, physically disabled people form communities based on their shared experiences and have positive experiences of solidarity - there is a deaf community, a physically disabled community, and non-neurotypical community. This mixture of positive and negative experiences creates the common ground needed for communities to form, and these communities become Identity groups. Because culture comes from close social interaction between people in group settings, it shouldn’t be surprising that people who belong to identity groups have specific knowledge that comes from their community. People with hearing really don’t know the daily reality of what it is like to be deaf. White people really don’t know the daily reality of what it is like to be Black. Especially relevant for political organizing is knowledge about how a group’s social position has affected their struggles for freedom and self-determination within dominant cultures. Oppressed people often know more about how their community has been affected by police, laws, corporations, and powerful individuals. Although it is possible for outsiders to learn about these things through patient study, it is still very hard to see the big picture from the perspective of the insiders. There is a misconception among some Leftist circles that all “identity politics” is counterproductive and doomed to fail because it emphasizes difference over shared interests. Our view is that identity-based movements have historically succeeded or failed by virtue of how clearly they send also messages about Affinity and Tactics. In identity movements these messages are often recoded into specific and relevant terms, such as the disability-rights slogans “You do not exist to be used” and “Nothing about us, without us” - messages which point to anticapitalism and representation. Although Identity movements are not always Left-aligned, historically most have been, and the work they have accomplished has significantly advanced the goals of the Left at large. \section{Tactics} Tactics are the methods by which we strive to achieve our political goals. Mainstream Tactics include running political candidates, voting, signing petitions, media appearances, and the occasional well-mannered demonstration. More radical political Tactics include highjacking time and space on mainstream media, closing down essential services like airports and highways, attacking dangerous enemy politicians, hacking and exposing incriminating information about opponents, or destroying property for symbolic or practical reasons. When Tactics include intervening directly to stop an objectionable event or to alleviate an evil, these Tactics are known as “direct action.” Direct Actions include personally feeding the hungry or destroying the offices of a military recruiter. When choosing Tactics, consider the three R’s: reward, risk, and reach. The rewards for using a particular Tactic should be clear. For example, publicizing personally embarrassing information about a political opponent has the obvious reward of damaging his reputation and making his job a little harder. At the same time, you should do everything you reasonably can to reduce the risks of your actions. While some older activists still seem to think that getting mass- arrested to “overload the system” is a good tactic, the criminal punishment system has grown so much in recent years that it can handle mass arrests without difficulty. When you plan to get arrested, you risk thousands of dollars that will have to be raised by you and your community for your defense - all of which will go to rich lawyers or to the State. Even if you end up being released quickly, the police will use the opportunity of having you custody to fingerprint you, document who you were with, search your phone, perhaps sexually assault you, and generally waste your day. It should be a red flag when rewards and risks seem to balance out. Publicly attacking a political opponent for taking a position with which many reactionaries agree may actually help his reputation to grow among your enemies. Watch out for these expensive victories. Finally, consider the reach of your Tactics, that is, how many people will find out about your actions. Even an action with a small reward for those involved, such as temporarily stopping the construction of a pipeline, can have a huge reach if it is expertly timed, executed, and publicized. Actions long in reach multiply the rewards for the movement as a whole. When you undertake an action, you can amplify its reach by preparing a statement for the media or anonymously uploading pictures to Twitter. Tactics are most effective they are tailored to the political climate, time, and place. During the Nazi occupation, it was appropriate for the French resistance to assassinate enemies, set off bombs in public places where innocent people were hurt, kill informants within their ranks, and fight to the death rather than be captured. Such Tactics would be ineffective and ruinous for movements in the US and Europe today. Consider what one of us saw at a demonstration for climate justice in Paris in 2015: \emph{When we arrived at the Place de la Republique, there were hundreds of pairs of shoes littering the plaza with no owners. Parents with strollers and old pacifists hunched and clutching purses with concern, well- meaning, were taking pictures. One man had climbed the statue at the center of the square with a Lebanese flag and was draping it over a shrine of votive candles. The gendarmes were still in their vans, though their ranks were silently growing. An hour later I was rushing an elderly woman toward the sidelines as a tear gas canister landed three paces away. The appearance of the black bloc in no way justified the violence exhibited on the crowd by the French police, but they had escalated the demonstration, and in the news reports and hostel lobbies the following day, they would be blamed for getting a bunch of peaceful protestors mixed up in a lot of violence for no good reason.} It should be clear that baby strollers and black blocks don’t mix. On the other hand, the idea that resistance must sink to the lowest common denominator of polite inaction surely gets us nowhere. The lesson here is this: to make sure that Tactics are well-suited to the situation, we will need to join in solidarity across tactical differences. To facilitate better collaboration, groups should be explicit about their level of commitment and ability to take risks, refrain from making simplistic judgements about the relative morality of different tactics, and implement a variety of complimentary tactics. Had the passive marchers and the black bloc communicated about, for instance, the timing of their very different Tactical moves, people could have done a better job at taking care of each other. Coordination should not be confused with unanimity here. If the peaceful marchers and the black bloc tried to arrive at a single consensus regarding their tactics, it is likely that neither group would have gotten what they wanted. When communicating about Tactics, be firm in your commitment while remaining flexible to the requests of others. Start these planning sessions with a commitment to help your allies carry out their ideas while not giving up on your own. A diversity of Tactics makes your movement harder to outmaneuver and makes it more likely to gain traction. \section{Affinity, Identity, Tactics} Up until this point, we have argued for the importance of Affinity, Identity, and Tactics separately, but the key insight is that we should not consider any of these three elements in isolation. Let’s explore the practical consequences of doing this for each one of the three elements in order to understand why this is true. First, paying attention to Affinity to the exclusion of Identity and Tactics may seem like a logical way to assert the unity of your group, but it’s ultimately too narrow. People from different Identities bring different knowledge to the group. When Identity issues are ignored, communication differences can turn into problems that reproduce oppressive power relationships found in society, or failing that, simply breed confusion and hurt. Within your Affinity, you will also find that people who fly the same flag are fond of different Tactics. There are more pacifist and more confrontational flavors of every Affinity. Some members of your group may be able to take more risks than others because of privilege, immigration or parole status, or because they are undercover in enemy territory (e.g. an informant in a corporation). Assuming that everyone is ready and willing to take the same risks will likely push out valuable members of your group who might otherwise be able to support your actions. When working within your Affinity group, you will still need to talk through issues of Identity and Tactics, and you may need to get creative to accommodate everyone. Remember that it is usually better to split your group into allied factions that have clarity about their Affinity and Tactics than to stay together and accomplish nothing because of infighting. Another way of saying that we can’t just organize around Affinity is that we need to remember to put Affinity in context. Next, what happens when we pay attention to Identity while ignoring Affinity and Tactics? As Zora Neale Hurston once said, “All my skinfolk ain’t kinfolk.” People within the same Identity group are almost always divided about both Affinity and Tactics. It is very difficult for people to work within the same groups when they want radically different worlds and are not willing to use similar methods to further their cause. Those who believe that capitalism is not responsible for their oppression may oppose shutting down a busy street in protest because of the harm done to businesses. Those who believe that all protests should be peaceful may give information to the police when a window gets broken. Huey Newton was murdered in his sleep by the FBI because one of his friends put sleeping medication in his dinner, trusting the agents when they said they wanted to take him alive. Failures like this happen because we don’t pay attention to forming groups around Affinities and Tactics, and they have certainly happened within Identity-based movements. \emph{Milo Yiannopoulos is not an ally of the LGBTQ community, Ben Carson is not an ally to Black folks, Marco Rubio is not an ally to Latinx people, and Condoleeza Rice is not an intersectional hero.} There is a common misconception that the only movements worth pursuing today are identity-based, and that questions about Affinity and Tactics can be avoided until the “right people” hold power. In practice, this idea mainly serves to steamroll important disagreements from within the ranks of identity-based movements. Should feminism and the LGBTQ movement reject capitalism? Is it a good idea for racial justice groups to be hierarchical or should they be direct democracies? These are essential issues that aren’t going away. Identity-based movements need to know where they are going and how they intend to get there. Finally, what happens when we join together as Tactical allies without thinking of Affinity and Identity? In a word, you’ll have strange bedfellows. There are many groups who want to delegitimize the government, expand access to birth control, or demand more ecological ways of living - and we promise that some of them have really terrible views. Focusing only on the immediate objective may seem like “pragmatic” politics, but take a look to make sure that you are truly in the presence of allies. When you win fights alongside people who differ with you on fundamental issues, remember that they will also claim victory, that their reputations will be elevated, and that other groups will begin to associate you with them. Some differences of opinion are probably healthy, but here’s a rule of thumb: never collaborate with people who think you shouldn’t have rights, shouldn’t be safe, or shouldn’t be listened to. Not all groups deserve to be included as part of “Left unity.” We hope what we have said about the relationship between Affinity, Identity, and Tactics will help bring some nuance to our talk about organizing. Our theory that when we lose sight of any one of these three elements we are vulnerable to avoidable mistakes, co-optation, and self-destruction. When we create organizations that know how to make these Affinity, Identity, and Tactics work harmoniously, we can win the big victories of moving together and the small victory of respecting current comrades and winning new ones to the struggle. % begin final page \clearpage % if we are on an odd page, add another one, otherwise when imposing % the page would be odd on an even one. \ifthispageodd{\strut\thispagestyle{empty}\clearpage}{} % new page for the colophon \thispagestyle{empty} \begin{center} The Anarchist Library (Mirror) \smallskip Anti-Copyright \bigskip \includegraphics[width=0.25\textwidth]{logo-yu.pdf} \bigskip \end{center} \strut \vfill \begin{center} Bonfire Collective Affinity Identity Tactics 2018 \bigskip \bigskip \textbf{usa.anarchistlibraries.net} \end{center} % end final page with colophon \end{document} % No format ID passed.
http://www1.combinatorics.org/Volume_17/Abstracts/v17i1r155.abs.tex	combinatorics.org	CC-MAIN-2013-20	application/x-tex	null	crawl-data/CC-MAIN-2013-20/segments/1368704933573/warc/CC-MAIN-20130516114853-00039-ip-10-60-113-184.ec2.internal.warc.gz	761,809,641	905	\documentclass[12pt]{article} \usepackage{amsmath,mathrsfs,bbm} \usepackage{amssymb} \textwidth=4.825in \overfullrule=0pt \thispagestyle{empty} \begin{document} \noindent % % {\bf Zhicheng Gao} % % \medskip \noindent % % {\bf A Formula for the Bivariate Map Asymptotics Constants in terms of the Univariate Map Asymptotics Constants} % % \vskip 5mm \noindent % % % % The parameters $t_g$, $p_g$, $t_g(r)$ and $p_g(r)$ appear in the asymptotics for a variety of maps on surfaces and embeddable graphs. In this paper we express $t_g(r)$ in terms of $t_g$ and $p_g(r)$ in terms of $p_g$. \end{document}
http://edshare.soton.ac.uk/2079/3/MA222Exam85qu3.tex	soton.ac.uk	CC-MAIN-2021-49	text/x-tex	application/x-tex	crawl-data/CC-MAIN-2021-49/segments/1637964363332.1/warc/CC-MAIN-20211207014802-20211207044802-00406.warc.gz	25,092,850	2,062	\documentclass[a4paper,12pt]{article} \newcommand{\ds}{\displaystyle} \newcommand{\pl}{\partial} \newcommand{\un}{\underline} \newcommand{\undb}{\underbrace} \newcommand{\df}{\ds\frac} \parindent=0pt \begin{document} {\bf Question} \begin{description} \item[(a)] A Markov chain has three states, and transition probability matrix $$P=\left(\begin{array}{ccc} 0 & 1 & 0\\ 1-p & 0 & p\\ 0 & 1 & 0 \end{array}\right)$$ where $0<p<1$. Find the probability distribution for state occupancy at the nth step $(n \geq 1)$ if initially all the states are equally likely to be occupied. \item[(b)] A Markov chain has the transition probability matrix given below. Classify the states and find the mean recurrence times for all recurrent states. (Label the states 1,2,3,4,5,6,7 in order) $$P=\left(\begin{array}{ccccccc} 0 & 0 & \frac{1}{4} & \frac{1}{2} & \frac{1}{8} & \frac{1}{8} & 0 \\ 0 & \frac{1}{4} & \frac{3}{4} & 0 & 0 & 0 & 0 \\ 0 & \frac{1}{3} & \frac{2}{3} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0\\ \frac{1}{3} & 0 & \frac{1}{3} & 0 & \frac{1}{6} & \frac{1}{6} & 0\\ 0 & 0 & 0 & \frac{1}{4} & 0 & \frac{3}{4} & 0\\ 1 & 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right)$$ \end{description} \vspace{.25in} {\bf Answer} \begin{description} \item[(a)] $P^2=\left(\begin{array}{ccc} 1-p & 0 & p\\ 0 & 1 & 0\\ 1-p & 0 & p\end{array}\right)$ and $P^3=P$ so $P^n=P$ if $n$ is odd and $P^n=P^2$ if $n$ is even. So if the initial distribution is $\left(\df{1}{3},\ \df{1}{3},\ \df{1}{3}\right)$ the distribution at step $n$ is: $\left(\df{1}{3}(1-p),\ \df{2}{3},\ \df{1}{3}p\right)$ if $n$ is odd. $\left(\df{2}{3}(1-p),\ \df{1}{3},\ \df{2}{3}p\right)$ if $n$ is even. \item[(b)] The transition diagram is as follows: PICTURE \vspace{2in} $\{2,3\}$ and $\{4,6\}$ both form irreducible closed aperiodic sets of states, and so are ergodic. States 1,\ 5 intercommunicate and are of the same type. The probability of return to state 1 is $\begin{array}{rcl} f_{11} & = & \df{1}{8} \cdot \df{1}{3}+\df{1}{8} \cdot \df{1}{6} \cdot \df{1}{3}+\df{1}{8} \cdot \left(\df{1}{6}\right)^2 \cdot \df{1}{3}+\cdots\\ & = & \df{1}{8} \cdot \df{1}{3}\left(1+\df{1}{6}+\df{1}{6^2}+\cdots\right)\\ & = & \df{1}{8}\cdot \df{1}{3}\cdot \df{1}{1-\frac{1}{6}}\\ & = & \df{1}{8}\cdot \df{1}{3}\cdot \df{6}{5}=\df{1}{20}<1 \end{array}$ Hence states 1 and 5 are transient. OR: The probability of leaving state 1 initially to a state other than 5 is $\df{7}{8}$. Return is only possible from state 5. So the probability of return is at most $\df{1}{8}<1$. State 7 is transient since the probability of return is zero. To calculate mean recurrence times $\begin{array}{rcl} \mu_2 & = & \df{1}{4}+2 \cdot \df{3}{4}\cdot \df{1}{3}+3 \cdot \df{3}{4} \cdot \df{2}{3} \cdot \df{1}{3}+4 \cdot \df{3}{4} \cdot \left(\df{2}{3}\right)^2 \cdot \df{1}{3}+\cdots\\ & = & \df{1}{4}+\df{3}{4} \cdot \df{1}{3} \left[2+3 \cdot \df{2}{3}+4\left(\df{2}{3}\right)^2+\cdots\right] \end{array}$ ${}$ $\begin{array}{rcrcrcrcl} s & = & a & + & (a+1)r & + & (a+2)r^2 & + & \cdots\\ rs & = & & & ar & + & (a+1)r^2& + & \cdots\\ s-rs & = & a & + & r & + & r^2 & +& \cdots \\ & = & a & + & \df{r}{1-r}\end{array}$ $$s = \df{a}{1-r} + \df{r}{(1-r)^2}$$ ${}$ so $\mu_2=\df{1}{4}+\df{3}{4} \cdot \df{1}{3} \left[3 \cdot 2+9 \cdot \df{2}{3} \right]=3\df{1}{4}$ ${}$ $\begin{array}{rcl}\mu_3 & = & \df{2}{3}+\df{1}{3}\cdot \df{3}{4} \left[2+3\cdot \df{1}{4}+4 \cdot \left(\df{1}{4}\right)^2+\cdots \right]\\ & = & \df{2}{3}+\df{1}{3}\cdot \df{3}{4}\left[2 \cdot \df{4}{3}+\df{1}{4}\cdot \left(\df{4}{3}\right)^2\right]\\ & = & \df{2}{3}+\left(\df{2}{3}+\df{1}{9}\right]\\ & = & 1\df{4}{9} \end{array}$ ${}$ $\begin{array}{rcl}\mu_4 & = & \df{1}{2}+\df{1}{2}\cdot \df{1}{4} \left[2+3\cdot \df{3}{4}+4 \cdot \left(\df{3}{4}\right)^2+\cdots \right]\\ & = & \df{1}{2}+\df{1}{2}\cdot \df{1}{4}\left[2 \cdot 4+\df{3}{4}\cdot 4^2\right]\\ & = & \df{1}{2}+\df{1}{2}\cdot 5=3 \end{array}$ ${}$ $\begin{array}{rcl}\mu_6 & = & \df{3}{4}+\df{1}{2}\cdot \df{1}{4} \left[2+3\cdot \df{1}{2}+4 \cdot \left(\df{1}{2}\right)^2+\cdots \right]\\ & = & \df{3}{4}+\df{1}{2}\cdot \df{1}{4}\left[2 \cdot 2+\df{1}{2}\cdot 2^2\right]\\ & = & \df{3}{4}+\left(\df{1}{4}+3\right]\\ & = & \df{3}{2}\end{array}$ \end{description} \end{document}
https://theanarchistlibrary.org/library/dot-matrix-reviews.tex	theanarchistlibrary.org	CC-MAIN-2019-26	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2019-26/segments/1560627999838.23/warc/CC-MAIN-20190625112522-20190625134522-00260.warc.gz	627,662,354	11,470	\documentclass[DIV=12,% BCOR=10mm,% headinclude=false,% footinclude=false,open=any,% fontsize=11pt,% twoside,% paper=210mm:11in]% {scrbook} \usepackage{fontspec} \usepackage{polyglossia} \setmainfont{Linux Libertine O} % these are not used but prevents XeTeX to barf \setsansfont[Scale=MatchLowercase]{CMU Sans Serif} \setmonofont[Scale=MatchLowercase]{CMU Typewriter Text} \setmainlanguage{english} % global style \pagestyle{plain} \usepackage{microtype} % you need an updated texlive 2012, but harmless \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} % footnote handling \usepackage{bigfoot} \usepackage{perpage} \DeclareNewFootnote{default} \DeclareNewFootnote{B} \MakeSorted{footnoteB} \renewcommand\thefootnoteB{(\arabic{footnoteB})} % continuous numbering across the document. 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Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand{\captionformat}{} \renewcommand{\figureformat}{} \renewcommand{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand{\forcelinebreak}{\strut\\{}} \newcommand{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand{\Slash}{\slash\hspace{0pt}} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} % forbid widows/orphans \frenchspacing \sloppy \clubpenalty=10000 \widowpenalty=10000 % http://tex.stackexchange.com/questions/304802/how-not-to-hyphenate-the-last-word-of-a-paragraph \finalhyphendemerits=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{Reviews} \date{} \author{dot matrix} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={Reviews},% pdfauthor={dot matrix},% pdfsubject={},% pdfkeywords={A Problem of Memory; Creating Anarchy; critique; Killing the Artist; Passion Fruit; Politics is Not a Banana; post-civ; review; The Rag}% } \begin{document} \begin{titlepage} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge Reviews\par}}% \vskip 1em \vskip 2em {\usekomafont{author}{dot matrix\par}}% \vskip 1.5em \vfill \strut\par \end{center} \end{titlepage} \cleardoublepage \tableofcontents % start a new right-handed page \cleardoublepage \chapter{Passion Fruit} \begin{quote} \emph{Passion Fruit: Anti-Authoritarian (Con)sensuous Games}\forcelinebreak PO Box 63232\forcelinebreak St. Louis, MO 63163\forcelinebreak 83 pages; \$4 \end{quote} This zine describes physical, sexual and flirtatious games people can play with each other that are creative and as safe as seems reasonable. It discusses issues of consent, communication, and disease. It tries to be fun and responsible. I have a soft spot in my heart for the thinking behind this zine. I grew up in the time before AIDS, when the shots from the Sexual Revolution were still reverberating (including the ones of penicillin). My early feminist years were spent thinking and reading about how breaking the corporate, button-down affect, getting in touch with our bodies, refusing to abide by suburban morality, were all practices that would liberate us, as well as celebrate our liberation. There is still something to these arguments — the understanding that we are animals not floating brains, that bodies are to be embodied, that the control implied by suits and high heels may be what we need to attain to destroy this society, but will destroy us as it has the people who believe in it. And \emph{Passion Fruit} is explicit in its desire to open up people’s options around forms of relationships, which I can only appreciate. But too much emphasis on sexuality is problematic too. Over-hyped sexuality is the haven of a corporatized world; it is the award and the consolation for our (presumed) powerlessness in the rest of our lives. Acknowledging the power of sex in human life is one thing; understanding how this culture has forced even more significance into sex is another. Understanding how we are all taught to manipulate (and be manipulated by) sex is part of that. \emph{PF} might have worked better for me if it had used different graphics. The images drop you into the middle of a party full of strangers. Of course some people love that jump-in-over-your-head approach, but I prefer to go in one step at a time. Perhaps the most serious question is about \emph{PF’}s attempt to marry hedonism with responsibility. Talking to people about how to have fun while they relate in loaded, physical ways with people who they don’t know is a tricky and frequently explosive business. This zine takes the de rigueur approach of cautioning everyone to make sure that everyone consents to everything before anybody does anything, and encouraging people to opt out if they feel uncomfortable. This is the standard approach made popular by sexual harassment suits everywhere: the approach that says that we can have hedonistic fun while dotting i’s and crossing t’s, that trust comes from having signed on the dotted line. Perhaps this approach is the best we can do. But I would love to see an analysis that challenges that perspective on safety, on consent, and on play. \chapter{Politics is Not a Banana} \begin{quote} Politics is Not a Banana\forcelinebreak journal of vulgar discourse\forcelinebreak \href{http://issuu.com/the.institute/docs/banana\_pages}{issuu.com} \end{quote} One of a spate of zines that are being distributed primarily online as PDFs, leaving it up to the reader whether to read it online or download and print it out, PiNaB is a pretty, clean, light-hearted, insurrection-inspired, thoughtful publication with a heavy design element. It is so designed in fact that the design becomes one of the loudest (if ambiguous) facets of the content. For example, the footnotes are larger than the body text, and are set off in bright red. Message: perhaps that our roots and\Slash{} or tangents are important? Or perhaps that we should pay attention to things that are normally considered secondary? Or perhaps, that size and color are not in fact a measure of importance? Documents that are published online (with the goal of people printing them out themselves) have different (not fewer) challenges than pieces designed for hardcopy. Instead of having to make decisions based on price (of ink, of paper type, of shipping, etc), online documents have to negotiate the differences between reading on a screen (short text sections to suit reading on a monitor, a clunkier page change process, etc) with reading in hardcopy. Pages need to work as well in color (for the screen) as in black and white (per the limitations of most home printers — unless your audience is primarily people who will be scamming color copies). PiNaB’s design means that it is not especially easy to read, either on screen or in hard copy. The main problem was one running thread (apparently a subpiece called “politics is not a banananotes”?) that streams along the bottom of the pages. This piece is particularly hard to read — as it’s very broken up — and distracts from the other articles above it. Furthermore, the argument for design is that reading as a sensual experience is worth focusing on, which is contradicted by presenting the document in a way that de-emphasizes touch. But life is full of compromise. This document negotiates territory between appealing and funny, and between sincerity and jargon. One of the first images is an apparently appreciative, but perhaps ironic, picture of a masked frat-looking white boy grabbing his crotch in good wigger style. There’s an argument that this sets a theme for this publication. There is a lot of talk about sex, and some about shit, in what is clearly attempting to reflect a transgressive integration of body and theory. Sometimes this works, but sometimes it just turns the body into another rhetorical device. \chapter{Post-Civ!} \begin{quote} A brief philosophical and political introduction to the concept of post-civilization\forcelinebreak \href{http://tangledwilderness.org}{tangledwilderness.org} \end{quote} Another of the PDF \Slash{} online documents that are becoming more common, Post-Civ! comes from one of the people who brought us the excellent magazine, Steampunk. That magazine floated above the conflicts that come from appealing to a broad base of people who frequently don’t get along with each other (science fiction aficionados, DIYers, crafters, anti-civ idealogues, etc). Post-Civ! is a more direct approach to the question of critiquing civilization while not necessarily being anti-tech, and promotes a civilization-critique-without-modifiers. “It’s about the anarchist urban hunter-gatherer squatting the ruins of the city living side-by-side with the micro-hydro engineer who has rigged the water running through the sewers to power her gristmill\dots{} It’s about never laboring again. (In this case, we are defining labor as ‘unnecessary, unenjoyable work’.) Frankly, it‘s about destroying civilization and saving the world and living a life of adventure and fulfillment.” This attempt has honorable precedents. Historically Voltairine de Cleyre is the exemplar of anarchy without adjectives and the utopian novel ‘bolo ‘bolo by p.m. posits a future world in which contradictory lifeways will coexist as long as certain fundamentals (eg community size) remain stable. While ideologues will be frustrated by the crossing of certain lines, it’s hard to argue with the three basic premises put forth for the definition of post-civilized thought: Civilization is unsustainable and unsalvageable; it is neither possible nor desirable to return to a pre-civilized state of being; figuring out a good post-civilization is therefore appropriate. There are people who are so attached to the definition of pre-civilization as meaning all things good that they will have a hard time getting past number two, but rhetoric aside, there is nothing to argue with. The writer(s?) of Post-Civ! takes the route that is more complicated in practice: not rejecting all technology but picking and choosing what works for a specific situation and what doesn’t, not rejecting science but also “not worshiping it.” This will stick in the craw of those who see science and\Slash{}or technology as an overarching philosophy, part and parcel of the problems that we face today, but the conflict may be a semantic one, something to determine as (and ii) the project continues. If we agree that we have been irretrievably shaped by our world, then the best we will ever be able to do in overcoming it is to be skeptical of and challenging toward the things that seem to push us to (or keep us in) the status quo. Since being purist and heady is one way to support the status quo, and since being unreflective and action- or product-oriented is another way to also support the status quo, we will always be in the position of doing the best we can in any given situation. Post-Civ! seems to err on the side of getting along in a milieu of people who don’t worry much about making friends, and therefore may not satisfy many of their most obvious audience (and will probably be the center of some conflict). But this is a fine little publication. The question is whether the producers are prepared to weather the conflict as bravely as de Cleyre did, and continue to flesh out the bones of their interesting idea. \chapter{The Rag \#1 Autumn 2006} \begin{quote} PO Box 10785\forcelinebreak Dublin 1, Ireland\forcelinebreak www.ragdublin.org \end{quote} I visited Ireland for a few weeks many years ago. I don’t have a strong knowledge of the place. I know the basics. It’s strongly Catholic: everything shuts down on Sundays, abortions are even more inaccessible there than they are in the US (unlike the rest of Europe, which in general has no question about whether women should be able to have them). The violence of ongoing warfare; its status as one of the earliest colonies; these realities make Ireland a very different place than the US. So it is hard to position myself relative to the feminist theory that I have read from Ireland, which, to my eyes, seems so reminiscent of the 1970s. \emph{The Rag} has articles, like so many dozens of other feminist zines, on herbal medicines, on domestic violence, on why there are so few women in anarchist scenes, on midwives, on the value of anger, and so on. Sadly, the content is no more unusual than the topics. Women don’t want to be part of anarchist scenes because there is a culture of macho posturing, for example. If I had a penny for every time I’ve heard that\dots{} I don’t know if it’s true, although some of the best anarchist posturing I know is done by women, myself included — what I do know is that I would love to read something that doesn’t talk about boys making room for girls, bur perhaps talks about girls taking their own room. Power, in any meaningful sense, can not be given. It must be claimed. The one different thing in this publication is the article on sexworkers. While still couched uncomfortably in “men shouldn’t see women as meat” language, it is at least one indication that feminist arguments have moved incrementally farther than they were when good feminists didn’t talk about decriminalizing sex work. There is a strong need for people, in groups and individually, to reconsider how women and men, girls, boys, and other, people in general, interact with each other and themselves. There are ongoing, decades-old, centuries-old, problems that relate to how we value ourselves and each other. The urgency of that need is only covered up, concealed, by rhetoric that was tired 20, even 30, years ago. Like I said, I don’t know. Maybe this stage of dialog is an important part of what needs to happen in Ireland. But it would be great if somehow we could learn more from each other, instead of having to go over the same road again and again, reading the same tired signs that don’t seem to get us to where we want to go. \chapter{Killing the Artist} \begin{quote} 12 pages, no price listed\forcelinebreak [email protected] \end{quote} This reprint of a chapter from a book in French, A mort l’artiste, is a brief and scathing indictment of the artist-as-advanced-individual ideal. Starting with the history of artists under the patronage of the wealthy and powerful (whether noble or church-based), the author(s) move on to point out that currently artists are merely workers with attitude. “Presenting themselves as the victims of the commodification of culture, they are actually simultaneously its result and one of its principal agents\dots{} being the social category recognized notably for its ‘right’ to subversion and transgression, the artist remains the best agent for the neutralisation of critique and its aesthetic recycling.” While there is not that much that is new here — particularly lacking is an acknowledgment of the impact that aesthetics do have on our lives or the possibilities inherent in something like Oscar Wilde’s determined dandy-ism — it could serve as an wake-up call for any self-righteous liberal arts major you want to smack down. Available online (in French) at \href{http://lafeteestfinie.free.fr/}{lafeteestfinie.free.fr} \chapter{Creating Anarchy} \begin{quote} Ron Sakolsky\forcelinebreak Fifth Estate Books\forcelinebreak Liberty, TN\forcelinebreak \$15, paper, 215 pages \end{quote} \emph{Creating Anarchy} works on a few levels — for example Sakolsky’s concise and clear critique of issues like democracy and voting are refreshing and valuable in these days of “anybody but Bush.” The first pieces in this book are bite size, e.g. interviews with Sakolsky and others that don’t go very deeply into any of the things that they talk about, and descriptions of Sakolsky’s experiences teaching or working on free radio projects. These are fine examples of lessons learned, but lessons that are easy to come by in most of our lives, so the audience is apparently young people without a lot of experience in this arena. The best parts of this book come later, and are on the history and relationship between surrealism and anarchist (or anti-state) thinking. Sakolsky is a fine historian, intimately connected with his topic(s), knowledgeable and accessible in tone. These pieces are not just his thoughts about the connections between these two fields, but also introductions to various surrealist painters, poets and musicians, for readers who want more information about this tradition. Some discordant notes \begin{quote} interpreting quotations. Sakolsky quotes people and then explains what the quotation means. Is this because Sakolsky’s history with the authors gives him an understanding of what they mean that is better than what they actually say? Perhaps that is the case, but if so, using quotations is a confusing way to make the given points. word play. I don’t know why someone who has a background in, and information about, poetry would do some of the goofiness that Sakolsky does here. Phrases like “snivilization” “realpolitricks,” and “evil of two lessers” are neither funny (although of course humor is in the perspective of the beholder) nor interesting commentary. Particularly irritating are simplistic references to animals as in any way relevant to state tendencies, as in “United Snakes of America.” It’s cheesiness like this that gives play a bad name. \end{quote} Among the complicated philosophical concepts that are bounced around uncritically in this book are the tropes of building-an-anarchist-movement, and life=good\Slash{}death=bad. It is easy and problematic to use the word “movement” as the way to talk about increasing the strength of anarchist ideas. The word has enough baggage, along the lines of democracy and glorification of the masses, to sound alarms. Nor is life is always good, or death always bad, but those associations too are taken for granted in this culture. Someone who has been around as long as he has, and who is conversant in the significance of dreams and storytelling, might be expected to have a more sophisticated understanding. Life and death are part of a whole, made significant by each other. Making one good and the other bad denies both. The book also includes pictures from various surrealist artists, including Don La Coss, Clifford Harper, Sue Simensky Bietila, Cathy Stoyko, and others. \chapter{A Problem of Memory} \begin{quote} by Taylor Sparrow\forcelinebreak Eberhardt Press \end{quote} \emph{Only a Nod} If you are looking for a current, accessibly written book that talks about the history of US racism against black people, doesn’t demonize all white people, and gives some examples of projects for education reform, this could be the book for you. The author spent some time in a class in Douglas High School (in the 9\textsuperscript{th} Ward of New Orleans), and examples from that class provide descriptions of where some kids are right now in their suspicion and boredom with school (and presumably with their options in general). The history of British colonization of Scotland and Ireland gives context to the history of Black people in the US. And projects like Students At the Center (SAC), Young People’s Project (YPP), and the Algebra Project are given as examples of people making a system that works for students — apparently in hope that such an educational system will encourage students to make a better world. This book gets some important things right: a) schools are not failing but succeeding at their goal (which is to manage and create people who believe they have no options); b) that this is true regardless of the economic background of the students (although the tactics might be different for different classes); c) that saviors and charity don’t actually create serious change, and d) that memory is a big deal. But if you’re looking for deep thoughts about memory and history and how we address or experience being cut off from our past, or stories that might actually (as promised) end some nightmares, then this book will disappoint. The book’s most significant weakness is that it conceives of race as black and white. Asian people are not mentioned once, and native and latin people are thrown in as “and them too.” While of course engaged readers can make some connections, this lack indicates unsophisticated thinking about race and power. Race here and now is about so much more than Manichean “your team vs my team”. And the rhetoric of race, especially in activist circles, has so far to go to coherently address the issues of what is currently called “internalized racism” that it was very disappointing to have this book be so simple on this facet of the topic. APoM’s most ironic failure is in its nod to a hopeful future. If educational projects like SAC, YPP and the Algebra Project are the best hope for a better future, how are they different from multiple previous education reform projects? History has shown that these kinds of projects are so easily integrated into the status quo as to be swallowed without a ripple. A quote from one of the author’s mentors, Kalamu Ya Salaam: “Unless and until [disenfranchised youth] can honestly recognize and confront their own realities, they will never be able to truly transform themselves and their communities.” Of course, the rub is that what some people mean by transformation is really not what others mean. Educational projects are a fine liberal goal, one that is easy to find support for since it is a deeply-held liberal concept that more information will solve all problems. There have been multiple efforts to empower students through various levels of student participation, from students organizing against wars to members of radical groups becoming teachers to effect change from within. A brief foray into a library reveals that in past decades there have been many high school students who were articulate about the racism and classism of the school system and who had hope that society could be changed. The efforts that are cited in APoM are working at getting students just to that level of analysis (by giving them skills and confidence), and there is no evidence (when and if they get there) that any more change will be effected than was 35 years ago. The question of reform vs. revolution, of what makes change, is only alluded to in this book, and the allusions don’t make a compelling argument. The author’s failure to acknowledge the history that exists here is in direct contradiction to the title of the book. Finally, there is always a push and pull to memory. Remembering where we came from is crucial to knowing where we are, but we also best remember what best suits us or what we best understand, and what we best remember doesn’t necessarily help us to create different ways of being. Taught to be within structures that despise both us and what we long for, we are not necessarily capable of remembering the things that might be most important to who we want to be. This conservative role of memory is another nuance that is never acknowledged here. The title of this work gives a nod to significant and powerful topics, a rich menu, but then offers up potato chips and miniature cucumber sandwiches, leaving the reader not starving but ready for something more. % begin final page \clearpage % if we are on an odd page, add another one, otherwise when imposing % the page would be odd on an even one. \ifthispageodd{\strut\thispagestyle{empty}\clearpage}{} % new page for the colophon \thispagestyle{empty} \begin{center} The Anarchist Library \smallskip Anti-Copyright \bigskip \includegraphics[width=0.25\textwidth]{logo-en} \bigskip \end{center} \strut \vfill \begin{center} dot matrix Reviews \bigskip Anarchy: a journal of desire armed \bigskip \textbf{theanarchistlibrary.org} \end{center} % end final page with colophon \end{document}
https://fkurz.net/et/MatheII/mathe.tex	fkurz.net	CC-MAIN-2022-05	text/x-tex	application/x-tex	crawl-data/CC-MAIN-2022-05/segments/1642320305420.54/warc/CC-MAIN-20220128043801-20220128073801-00060.warc.gz	316,469,938	50,716	\documentclass[11pt,a4paper]{report} \usepackage[ansinew]{inputenc} \usepackage{amssymb} \usepackage{makeidx} \makeindex \usepackage{wasysym} \usepackage{ngerman,latexsym,alltt,graphicx,textcomp} \usepackage[bookmarks, colorlinks=false, pdftitle={Mitschrift Mathematik I/2 Prof. Dr. Sasvari}, pdfauthor={Fabian Kurz}, pdfsubject={Mathematik}, pdfkeywords={Mathematik Elektrotechnik}, linkbordercolor={1 1 1}]{hyperref} \usepackage{xy} \input xy \xyoption{all} \date{Zuletzt aktualisiert:\\\today} \author{Fabian~Kurz\\\href{http://fkurz.net/}{http://fkurz.net/}} \title{Mathematik I/2 für Elektrotechniker -- SS 04\\Prof. Dr. Sasv\'ari\\Mitschrift} \begin{document} \maketitle \pagenumbering{Roman} \tableofcontents \setcounter{chapter}{9} \chapter{Differentialrechnung für Funktionen mehrerer Variablen} \pagenumbering{arabic} \section{Grundbegriffe} \subsection{Der zweidimensionale Raum} Unter dem \emph{zweidimensionalen} Raum $\mathbb{R}^2$ versteht man die Menge aller geordneten Paare reeller Zahlen. Seine Elemente heißen \emph{Punkte}. $$\mathbb{R}^2 = \left\{(x,y):x\in \mathbb{R} , y \in \mathbb{R}\right\}$$ \begin{tabular}{lll} \index{Koordinaten, kartesische} \index{kartesische Koordinaten} \index{Polarkoordinaten} \index{Koordinaten, Polar} $x$ und $y$ &:& \emph{kartesische Koordinaten}\\ $(r,\; \varphi)$ &:& \emph {Polarkoordinaten}, $r \geq 0,\; 0 \leq \varphi \leq 2\pi$ \end{tabular} \subsubsection{Es gilt:} \begin{tabular}{ll} $x = r\cdot \cos \varphi$ & $y = r \cdot \sin \varphi$\\\\ $r = \sqrt{x^2 + y^2}$ & $\tan\varphi = \frac y x \quad (x \ne 0)$\\\\ $\varphi = \frac{\pi}{2}$ wenn $x = 0$, $y > 0$ & $\varphi = \frac{3\pi}{2}$ wenn $x = 0$, $y < 0$ \end{tabular} \vspace{0.5cm} \begin{flushleft} \emph{Abstand} des Punktes $P(x,\,y)$ vom Nullpunkt $(0,\,0,\,0)$: $$\|P\| = \sqrt{x^2+y^2}$$ Abstand der Punkte $P_1(x_1,\,y_1)$ und $P_2(x_2,\,y_2)$: $$\|P_1-P_2\| = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}$$ \begin{minipage}[c]{9.5cm} Es sei $P_0 \in \mathbb{R}^2$ und $\varepsilon > 0$. Die Menge $$U_{\varepsilon}(P_0) = \left\{P\in\mathbb{R}^2:\|P-P_0\| < \varepsilon\right\}$$ heißt die (offene) \emph{$\varepsilon$--Umgebung} des Punktes $P_0$ (Kreisscheibe ohne Berandung). \end{minipage} \begin{minipage}[c]{80pt} \begin{picture}(80,80) \setlength{\unitlength}{1.5pt} \put(30,30){\circle{30}} \put(30,30){\circle{1}} \put(23,24){$P$} \put(34,31){$\varepsilon$} \qbezier(30,30)(30,30)(38.4,40) \end{picture} \end{minipage} \bigskip \begin{minipage}[c]{9.5cm} Es sei $D \subset \mathbb{R}^2$. Der Punkt $P\in\mathbb{R}^2$ heißt \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \index{innerer Punkt} \index{Punkt, innerer} \index{Punkt, Randpunkt} \index{Randpunkt} \item \emph{innerer Punkt} von $D$, wenn es eine Umgebung $U_{\varepsilon}(P)$ gibt, die in $D$ liegt (z.B. $P_1$) \item \emph{Randpunkt} von $D$, wenn in jeder Umgebung $U_{\varepsilon}(P)$ sowohl ein Punkt von $D$ als auch von $\mathbb{R}^2\smallsetminus D$ liegt (z.B. $P_2$) \end{enumerate} \end{minipage} \begin{minipage}[c]{85pt} \begin{picture}(80,100) \qbezier(15,80)(40,115)(65,75) \qbezier(15,80)(0,55)(20,35) \qbezier(20,35)(25,30)(20,25) \qbezier(20,25)(5,12)(30,4) \qbezier(30,4)(110,-8)(65,75) \put(3,85){$D$} \put(32,31){$P_1$} \put(45,28){\circle{2.5}} \put(65.75,74){\circle{2.5}} \put(67,76){$P_2$} \end{picture} \end{minipage} \end{flushleft}\index{Rand} \index{offene Menge} \index{Menge, offen} \index{abgeschlossene Menge} \index{Menge, abgeschlossen} Die Menge aller Randpunkte heißt der \emph{Rand} von $D$. Die Menge $D$ heißt \emph{offen}, wenn jeder Punkt $P \in D$ ein innerer Punkt ist. $D$ heißt \emph{abgeschlossen}, wenn $\mathbb{R}^2 \smallsetminus D$ offen ist. \subsubsection{Beispiele} \begin{flushleft} \begin{minipage}[c]{8.5cm} $D_1 = \left\{(x,\,y) : 1 < x < 3,\; -1 < y < 2\right\} \subset \mathbb{R}^2$ \bigskip $(2,1)$ : innerer Punkt $(1,1)$ : Randpunkt, $(1,1) \not\in D_1$ \smallskip $D_1$ ist offen \end{minipage} \begin{minipage}[c]{100pt} \begin{picture}(100,80) \setlength{\unitlength}{1pt} \put(0,25){\vector(1,0){100}} \put(15,0){\vector(0,1){80}} \multiput(14,5)(0,20){4}{\line(1,0){2}} \put(0,2){$-1$} \put(7,42){$1$} \put(7,62){$2$} \put(20,74){$y$} \multiput(35,24)(20,0){3}{\line(0,1){2}} \put(27,13){$1$} \put(52,13){$2$} \put(78,13){$3$} \multiput(35,5)(40,0){2}{\multiput(0,0)(0,4){15}{\line(0,1){2}}} \multiput(35,5)(0,60){2}{\multiput(0,0)(4,0){10}{\line(1,0){2}}} \end{picture} \end{minipage} \vspace{0.75cm} \begin{minipage}[c]{8.5cm} $D_2 = \left\{(x,\,y) : 1 \leq x \leq 3,\; -1 \leq y \leq 2\right\}$ \bigskip $D_2$ ist abgeschlossen \vspace{0.75cm} \end{minipage} \begin{minipage}[c]{100pt} \begin{picture}(100,80) \setlength{\unitlength}{1pt} \put(0,25){\vector(1,0){100}} \put(15,0){\vector(0,1){80}} \multiput(14,5)(0,20){4}{\line(1,0){2}} \put(0,2){$-1$} \put(7,42){$1$} \put(7,62){$2$} \put(20,74){$y$} \multiput(35,24)(20,0){3}{\line(0,1){2}} \put(27,13){$1$} \put(52,13){$2$} \put(78,13){$3$} \multiput(35,5)(40,0){2}{\multiput(0,0)(0,4){15}{\line(0,1){4}}} \multiput(35,5)(0,60){2}{\multiput(0,0)(4,0){10}{\line(1,0){4}}} \end{picture} \end{minipage} \vspace{0.75cm} \begin{minipage}[c]{8.5cm} $D_3 = \left\{(x,\,y) : 1 \leq x < 3,\; -1 < y \leq 2\right\}$ \bigskip $D_3$ ist weder abgeschlossen noch offen \vspace{0.75cm} \end{minipage} \begin{minipage}[c]{100pt} \begin{picture}(100,80) \setlength{\unitlength}{1pt} \put(0,25){\vector(1,0){100}} \put(15,0){\vector(0,1){80}} \multiput(14,5)(0,20){4}{\line(1,0){2}} \put(0,2){$-1$} \put(7,42){$1$} \put(7,62){$2$} \put(20,74){$y$} \multiput(35,24)(20,0){3}{\line(0,1){2}} \put(27,13){$1$} \put(52,13){$2$} \put(78,13){$3$} \multiput(75,5)(0,4){15}{\line(0,1){2}} \multiput(35,5)(4,0){10}{\line(1,0){2}} \put(35,5){\line(0,1){60}} \put(35,65){\line(1,0){40}} \end{picture} \end{minipage} \end{flushleft} \index{beschränkte Menge} \index{Menge, beschränkt} \index{Menge, unbeschränkt} \index{unbeschränkte Menge} $D \subset \mathbb{R}^2$ heißt \emph{beschränkt}, wenn es eine Zahl $A$ gibt, so daß für alle $P \in D$ gilt $\|P\| \leq A$, andernfalls heißt $D$ \emph{unbeschränkt}. \subsection[Der drei-- und der n--Dimensionale Raum]{Der drei-- und der $n$--Dimensionale Raum} Unter dem \emph{dreidimensionalen Raum} $\mathbb{R}^3$ versteht man die Menge aller geordneten Tripel reeller Zahlen. $$\mathbb{R}^3 = \left\{(x,\,y,\,z) : x \in \mathbb{R},\; y \in \mathbb{R},\; z \in \mathbb{R}\right\}$$ Abstand der Punkte $P_1 = (x_1,\,y_1,\,z_1)$ und $P_2 = (x_2,\,y_2,\,z_2)$: $$\|P_1-P_2\| = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2 + (z_1-z_2)^2}$$ Die Definitionen aus 10.1.1. lassen sich einfach auf $\mathbb{R}^3$ übertragen ($\varepsilon$--Umge\-bung, innerer Punkt, \ldots). \subsubsection{Zylinderkoordinaten ($r$, $\varphi$, $z$)} \index{Zylinderkoordinaten} \index{Koordinaten, Zylinder} \smallskip \begin{flushleft} \begin{minipage}[c]{7.2cm} Es sei $P = (x,\,y,\,z) \in \mathbb{R}^3$. \bigskip Dann bezeichnen: \begin{description} \item[$r$] den Abstand des Punktes $P$ von der $z$--Achse. $r = \sqrt{x^2+y^2}$ \item[$\varphi$] den Winkel der Strecke von $(0,\,0,\,0)$ nach $P'=(x,\,y,\,0)$ gegen die positive Richtung der $x$--Achse, im mathematisch positiven Sinn mit $0 \leq \varphi \leq 2\pi$. \item[$z$] wie bei den kartesischen Koordinaten \end{description} \end{minipage} \begin{minipage}[c]{150pt} \begin{picture}(150,170) \put(75,50){\vector(2,-1){60}} \put(75,50){\vector(-2,-1){60}} \put(75,50){\vector(0,1){90}} \put(49,37){\line(2,-1){45}} \put(94,14.5){\line(2,1){26}} \put(94,14.5){\line(0,1){75}} \multiput(75,50)(0,75){2}{\qbezier(0,0)(0,0)(19,-35.5)} \put(10,25){$x$} \put(137,25){$y$} \put(80,138){$z$} \multiput(94,14.5)(0,75){2}{\circle{2}} \put(96,7){$\scriptstyle P'(x,\,y,\,0)$} \put(97,91){$\scriptstyle P(x,\,y,\,z)$} \put(63,22){$\scriptstyle y$} \put(109,17){$\scriptstyle x$} \put(70,40){$\scriptstyle \varphi$} \multiput(87,33)(0,75){2}{$\scriptstyle r$} \qbezier(61,43)(67,33)(82,36) \end{picture} \end{minipage} \subsubsection{Umrechnungsformeln} $x = r \cdot \cos \varphi$ \smallskip $y = r \cdot \sin \varphi$ \smallskip $z = z$ \subsubsection{Kugelkoordinaten ($r$, $\varphi$, $\vartheta$)} \index{Kugelkoordinaten} \index{Koordinaten, Kugel} Es sei $P = (x,\,y,\,z) \in \mathbb{R}^3$. \bigskip Dann bezeichnen: \begin{description} \item[$r$] den Abstand des Punktes $P$ vom Ursprung $(0,\,0,\,0)$. \item[$\varphi$] wie bei den Zylinderkoordinaten \item[$\vartheta$] der Winkel, den die Strecke vom Ursprung $(0,\,0,\,0)$ nach $P \ne (0,\,0,\,0)$ mit der positiven Richtung der $z$--Achse bildet, wobei $0 \leq \vartheta \leq \pi$. \end{description} \begin{minipage}[c]{7.2cm} Das sind die sogenannten \emph{astronomischen Kugelkoordinaten}. Geographische Kugelkoordinaten: $\vartheta = \frac{\pi}{2} - \vartheta$. \subsubsection{Umrechnungsformeln} $x = r\cdot \cos \varphi \cdot \sin \vartheta$ \smallskip $y = r\cdot \sin \varphi \cdot \sin \vartheta$ \smallskip $z = r\cdot \cos \vartheta$ \smallskip $r = \sqrt{x^2+y^2+z^2}$ \end{minipage} \begin{minipage}[c]{150pt} \begin{picture}(150,170) \put(75,50){\vector(2,-1){60}} \put(75,50){\vector(-2,-1){60}} \put(75,50){\vector(0,1){90}} \put(49,37){\line(2,-1){45}} \put(94,14.5){\line(2,1){26}} \put(94,14.5){\line(0,1){75}} \multiput(75,50)(0,75){2}{\qbezier(0,0)(0,0)(19,-35.5)} \put(10,25){$x$} \put(137,25){$y$} \put(80,138){$z$} \multiput(94,14.5)(0,75){2}{\circle{2}} \put(96,7){$\scriptstyle P'(x,\,y,\,0)$} \put(97,91){$\scriptstyle P(x,\,y,\,z)$} \put(63,22){$\scriptstyle y$} \put(109,17){$\scriptstyle x$} \put(70,40){$\scriptstyle \varphi$} \put(87,109){$\scriptstyle r \cdot \sin \vartheta$} \qbezier(61,43)(67,33)(82,36) \qbezier(75,50)(75,50)(94,89.5) \qbezier(75,75)(81,77)(86,73) \put(77,65){$\scriptstyle \vartheta$} \put(86,64){$\scriptstyle r$} \end{picture} \end{minipage} \end{flushleft} \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Die Kreisscheibe\\ %% bah!! aber so gehts am schnellsten \begin{minipage}[c]{7cm} $$D = \left\{(x,\,y) : x^2 + y^2 < 9\right\}$$ wird in Polarkoordinaten durch $$0 \leq r < 3 \qquad 0 \leq \varphi < 2\pi$$ beschrieben. \end{minipage} \begin{minipage}[c]{130pt} \begin{picture}(120,80) \put(00,30){\vector(1,0){120}} \put(60,0){\vector(0,1){80}} \put(60,30){\circle{40}} \thicklines \put(80,27){\line(0,1){6}} \put(79,18){$3$} \put(57,50){\line(1,0){6}} \put(63,51){$3$} \put(110,21){$x$} \put(63,72){$y$} \end{picture} \end{minipage} \item \begin{minipage}[c]{7cm} $$2 < r \leq 5 \qquad 0 < \varphi < \pi$$ \end{minipage} \begin{minipage}[c]{4cm} \includegraphics[width=4cm]{20040407-1} %% bahpfui!! x-fig. \end{minipage} \item Die Menge $\{(x,\,y,\,z) : 1 \leq x \leq 3,\; 0 \leq y \leq 3, \; 1 \leq z \leq 4\}$ ist ein Quader. \begin{center} \begin{picture}(150,150) \put(50,50){\vector(1,0){90}} \put(50,50){\vector(0,1){90}} \put(50,50){\vector(-1,-1){40}} \multiput(45,55)(4,0){15}{\line(1,0){2}} \multiput(45,55)(0,4){15}{\line(0,1){2}} \put(45,115){\line(1,0){60}} \put(105,115){\line(0,-1){60}} \qbezier(45,55)(45,55)(44,54) \qbezier(43,53)(43,53)(42,52) \qbezier(41,51)(41,51)(40,50) \qbezier(39,49)(39,49)(38,48) \qbezier(37,47)(37,47)(36,46) \qbezier(35,45)(35,45)(34,44) \qbezier(33,43)(33,43)(32,42) \qbezier(31,41)(31,41)(30,40) \qbezier(29,39)(29,39)(28,38) \qbezier(27,37)(27,37)(26,36) \put(85,35){\line(1,1){20}} \multiput(45,115)(60,0){2}{\line(-1,-1){20}} \multiput(25,35)(60,0){2}{\line(0,1){60}} \multiput(25,35)(0,60){2}{\line(1,0){60}} \put(95,35){\vector(1,1){20}} \put(115,55){\vector(-1,-1){20}} \put(117,56){$\scriptstyle 1$} \put(87,27){$\scriptstyle 3/3$} \put(25,30){\vector(1,0){60}} \put(85,30){\vector(-1,0){60}} \put(12,28){$\scriptstyle 1/0$} \put(15,97){$\scriptstyle 4$} \put(18,35){\vector(0,1){60}} \put(18,95){\vector(0,-1){60}} \put(53,132){$z$} \put(132,41){$y$} \put(16,8){$x$} \end{picture} \end{center} \item Der Kreiszylinder ist durch ein System von Ungleichungen zu beschreiben. $$Z = \left\{(x,\,y,\,z) : \sqrt{x^2 + y^2} \leq R,\, 1 \leq z \leq 4\right\}$$ $$Z = \left\{(x,\,y,\,z) : - R \leq x \leq R,\; \sqrt{R^2-x^2} \leq y \leq \sqrt{R^2-x^2}\right\}$$ \begin{minipage}[c]{100pt} \begin{picture}(100,100) \put(50,20){\vector(1,0){50}} \put(50,70){\vector(0,1){30}} \put(50,20){\line(0,1){15}} \multiput(50,37)(0,4){10}{\line(0,1){2}} \put(50,20){\vector(-1,-1){20}} \put(92,11){$y$} \put(53,93){$z$} \put(22,0){$x$} \put(50,70){\line(1,0){20}} \put(55,76){$R$} \put(50,40){\circle{2}} \put(50,70){\circle{2}} \qbezier(70,70)(70,75)(50,75) \qbezier(70,70)(70,65)(50,65) \qbezier(30,70)(30,75)(50,75) \qbezier(30,70)(30,65)(50,65) \qbezier(70,40)(70,35)(50,35) \qbezier(30,40)(30,35)(50,35) \multiput(30,40)(40,0){2}{\line(0,1){30}} \qbezier(30,40)(30.5,42)(32,42.8) \qbezier(35,43.7)(36,44)(37,44.2) \qbezier(40,44.6)(41,44.7)(42,44.8) \qbezier(45,44.9)(46,44.9)(47,45) \qbezier(70,40)(69.5,42)(68,42.8) \qbezier(65,43.7)(64,44)(63,44.2) \qbezier(60,44.6)(59,44.7)(58,44.8) \qbezier(55,44.9)(54,44.9)(53,45) \put(49,45.2){\line(1,0){2}} \end{picture} \end{minipage} \begin{minipage}[b]{8cm} \center In Zylinderkoordinaten: $$0 \leq r \leq R, \quad 0 \leq \varphi < 2\pi, \quad 1 \leq z \leq 4$$ \vspace{0.3cm} \end{minipage} \item Der Kegel ist in Zylinderkoordinaten zu beschreiben \bigskip \begin{minipage}[c]{100pt} \begin{picture}(100,100) \put(50,20){\vector(1,0){50}} \put(50,70){\vector(0,1){30}} \multiput(50,20)(0,4){20}{\line(0,1){2}} \put(50,20){\vector(-1,-1){20}} \put(92,11){$y$} \put(53,93){$z$} \put(22,0){$x$} \put(50,70){\line(1,0){20}} \put(55,76){$R$} \put(50,70){\circle{2}} \qbezier(70,70)(70,75)(50,75) \qbezier(70,70)(70,65)(50,65) \qbezier(30,70)(30,75)(50,75) \qbezier(30,70)(30,65)(50,65) \qbezier(50,20)(30,70)(30,70) \qbezier(50,20)(70,70)(70,70) \end{picture} \end{minipage} \begin{minipage}[c]{8cm} $$0 \leq r \leq R$$ $$0 \leq \varphi < 2\pi$$ $$\frac{h}{R}\cdot r = z \leq h$$ \end{minipage} \item Eine Kugel vom Radius $R$ mit Mittelpunkt $(0,\,0,\,0)$ wird in Kugelkoordinaten $(r,\,\varphi,\,\eta)$ durch $$a \leq r \leq R, \quad 0 \leq \varphi < 2\pi,\quad 0 \leq \eta < 2\pi$$ beschreiben. \item Kugelausschnitt mit dem Öffnungswinkel $\frac{\pi}{2}$ \bigskip \begin{minipage}[c]{100pt} \begin{picture}(100,100) \put(50,20){\vector(1,0){50}} \put(50,85){\vector(0,1){15}} \multiput(50,22)(0,4){20}{\line(0,1){2}} \put(50,20){\vector(-1,-1){20}} \put(92,11){$y$} \put(53,93){$z$} \put(22,0){$x$} \qbezier(90,70)(90,65)(50,65) \qbezier(10,70)(10,65)(50,65) \qbezier(50,20)(10,70)(10,70) \qbezier(50,20)(90,70)(90,70) \qbezier(10,70)(20,85)(50,85) \qbezier(90,70)(80,85)(50,85) \end{picture} \end{minipage} \begin{minipage}[c]{8cm} $$ 0 \leq r \leq R,\quad 0 \leq \varphi < 2\pi , \quad 0 \leq \eta \leq \frac{\pi}{4}$$ \end{minipage} \end{enumerate} \subsection{Definition} \index{Raum, $n$--Dimensional} Unter dem \emph{$n$--Dimensionalen Raum} ($n = 1,\,2,\ldots$) versteht man die Menge aller geordneten $n$--Tupel ($x_1,\, \ldots \, , \, x_n$) reeler Zahlen. Die Zahl $$\|P-Q\| = \sqrt{(x_1 - y_1)^2 + \cdots + (x_n-y_n)^2}$$ heißt der \emph{Abstand} der Punkte $P = (x_1,\, \ldots ,\, x_n)$ und $Q = (y_1,\, \ldots\, ,\,y_n)$. Man übernimmt die Bezeichnungen aus dem dreidimensionalen Fall. $U_{\varepsilon}(P)$ heißt eine ($n$--dimensionale) \emph{Kugel} vom Radius $\varepsilon$ mit Mittelpunkt $P$. \smallskip Es sei $P_k = \left(x_1^{(k)}, \ldots, x_n^{(k)}\right),\; k = 1,\,2,\, \ldots$ eine Punktfolge in $\mathbb{R}^n$ und $P = (a_1,\, \ldots ,\, a_n) \in \mathbb{R}^n$. Die Punktfolge $\Big\{P_k\Big\}^{\infty}_{k=1}$ heißt \emph{konvergent} gegen den Punkt $P$ wenn $\lim\limits_{k \to \infty} \|P_k - P\| = 0$. \bigskip Schreibweise: $\lim\limits_{k \to \infty} P_k = P$ \bigskip Man kann zeigen: $$\lim_{k \to \infty} P_k = P \Leftrightarrow \lim\limits_{k \to \infty} x^{(k)}_i = a_i \quad (i = 1,\,\ldots \, , \, n)$$ \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item \quad \\ \begin{tabular}{l@{$\,$}c@{$\,$}l@{}c@{$\,$}l@{$\;$}c@{$\,$}l@{$\;$}c@{}l} $P_k$ & $=$ & $\Big($ &$\frac{k}{k+1}$ &, &$\left(\frac{2}{3}\right)^k $&, &$\frac{2}{k}$ &$\Big) \in \mathbb{R}^3 \qquad (k = 1,\,2,\,3,\, \ldots)$\\ & & &$\Big\downarrow$ & & $\Big\downarrow$ & & $\Big\downarrow$\\ $P$ & $=$ & $\Big($ & 1 & , & 0 & , & 0 & $\Big)$ \end{tabular} $\lim\limits_{k \to \infty} P_k = (1,\,0,\,0)$ \item $P_k = \Big(\frac{1}{k},\; k\Big) \in \mathbb{R}^3$ nicht konvergent (die Punkte $P_k$ liegen auf der Hyperbel $y = \frac{1}{x}$). \bigskip $\{P_k\}$ ist unbeschränkt. \item $P_k = (\cos k,\; \sin k) \in \mathbb{R}^2$ \bigskip $\|P_k\| = 1$ \qquad Punkte liegen auf Einheitskreis. \bigskip Man kann zeigen: $\{P_k\}$ ist nicht konvergent. \end{enumerate} \newpage \section{Stetige Funktionen mehrerer Variablen} Im Folgenden: $D_f \subset \mathbb{R}^n$ : Definitionsbereich der Funktion $f: D_f \longrightarrow \mathbb{R}$ \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $$\displaystyle f(x,\,y,\,z) = x + \frac{y\cdot z}{y+z}$$ $$D_f = \left\{(x,\,y,\,z) : y + z \ne 0\right\} = \mathbb{R}^3 \smallsetminus \{\textnormal{die Ebene } y + z = 0\}$$ \item $$f(x,\,y) = (x-2)^2 + 2y \qquad D_f = \mathbb{R}^2$$ \item $$f(x,\,y) = \frac{x\cdot y}{x^2 + y^2} \qquad D_f = \mathbb{R}^2 \smallsetminus \{(0,0)\}$$ Mit Polarkoordinaten $(r,\,\varphi)$: $$x = r\cdot \cos \varphi, \quad y = r\cdot \sin \varphi, \quad r^2 = x^2 + y^2$$ $$f(x,\,y) = \frac{r\cdot \cos \varphi \cdot r \cdot \sin \varphi}{r^2} = \cos \varphi \cdot \sin\varphi = \frac{1}{2} \cdot \sin 2\varphi$$ $\Rightarrow \|f(x,\,y)\| \leq \frac{1}{2} \Rightarrow f$ ist beschränkt. Funktionswert unabhängig vom Abstand zu $(0,\,0,\,0)$. \end{enumerate} \subsection{Definition}\index{Stetigkeit} Eine Funktion $f$ heißt \emph{im Punkt $P \in D_f$ stetig}, wenn für jede gegen $P$ konvergierende Punktfolge $\{P_K\}$ gilt: $$\lim_{K \to \infty}f(P_K) = f(P)$$ $f$ heißt \emph{in $D_f$ stetig}, wenn $f$ in jedem Punkt $P$ aus $D_f$ stetig ist. Äquivalente Definition: Zu jedem $\varepsilon > 0$ existiert ein $\delta > 0$, so daß für alle Punkte $Q$ aus $U_{\delta}(P) \cap D_f$ gilt: $$\left\| f(P) - f(Q)\right\| < \varepsilon$$ \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Die Funktion $f(x,\,y,\,z) = x$ ist auf $\mathbb{R}^3$ stetig. Die Funktion $f(x,\,y) = x\cdot y$ ist auf $\mathbb{R}^2$ stetig. \item Die Funktion $f(x,\,y) = \left\{\begin{array}{ll}\frac{xy}{x^2+y^2} & (x,\,y) \ne (0,\,0)\\0 & (x,\,y) = (0,\,0)\end{array}\right.$ ist im Punkt $P(0,0)$ nicht stetig. \newpage Wähle $P_K = \left(\frac{1}{k},\,\frac{1}{k}\right)$ die gegen $(0,\,0)$ konvergiert. Dann ist $$f(P_K) =\frac{\frac{1}{k}\cdot\frac{1}{k}}{\left(\frac{1}{k}\right)^2 + \left(\frac{1}{k}\right)^2} = \frac{1}{2} \ne 0 = f(0,\,0)$$ Wähle $P_K = \left(\frac{1}{k},\,\frac{a}{k}\right)$, $y = ax$. Dann ist $$f(P_K) =\frac{\frac{a}{k^2}}{\frac{1}{k^2} \cdot (1 + a^2)}= \frac{a}{(1+a^2)} = \frac{1}{2} \ne 0 \textnormal{ für } a \ne 0$$ \item Die Funktion $f(x,\,y) = \left\{\begin{array}{ll}\frac{(xy)^2}{x^2+y^2} & (x,\,y) \ne (0,\,0)\\0 & (x,\,y) = (0,\,0)\end{array}\right.$ ist stetig auf $\mathbb{R}^2$. \smallskip Wähle $P_K = (x_k,\,y_k)$ beliebig. $$\lim_{x_k,\,y_k \to 0} \frac{(x_ky_k)^2}{{x_k}^2+{y_k}^2} = \lim_{x_k,\,y_k \to 0} \frac{1}{\left(\frac{1}{x_k}\right)^2+ \left(\frac{1}{y_k}\right)^2} = 0$$ \end{enumerate} \subsection{Satz} $(f,\,g : \mathbb{R}^n \longrightarrow \mathbb{R})$ \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item Sind $f$ und $g$ stetig im Punkt $P$, so sind auch $f+g$, $f\cdot g$ und $c\cdot g$ $(c \in \mathbb{R})$ in $P$ stetig. \item Ist $g(P) \ne 0$, dann ist auch $\frac{f}{g}$ in $P$ stetig. \item Ist die Funktion $F:\mathbb{R} \longrightarrow \mathbb{R}$ auf $\mathbb{R}$ stetig, so ist auch $F(f)$ in $P$ stetig. \end{enumerate} Beispiele: \smallskip $e^{x^2+y^2}$ ist stetig auf $\mathbb{R}^2$ \smallskip $\sin(x^2+y^2+e^z)$ ist stetig auf $\mathbb{R}^3$ \subsection{Definition: Beschränktheit}\index{Beschränktheit} Die auf $D_f \subset \mathbb{R}^n$ definierte Funktion $f$ heißt \emph{beschränkt}, wenn es eine Zahl $A$ gibt, so daß für alle $P \in D_f$ gilt: $$\left\|f(P)\right\| \leq A$$ {\flushleft Beispiele:} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $f(x,\,y) = \sin (x+e^{xy}) \qquad \|f(x,\,y)\| \leq 1 \Rightarrow f$ ist beschränkt \item Die Funktion $f(x,\,y) = \frac{xy}{x^2+y^2} \qquad D_f = \mathbb{R}^2 \smallsetminus \{0,\,0\}$ $\displaystyle f(x,\,y) = \tilde{f}(r,\,\varphi) = \frac{r^2\cos\varphi\sin\varphi}{r^2(\cos^2\varphi + \sin^2\varphi)} = \cos\varphi\cdot\sin\varphi = \frac{1}{2} \sin 2\varphi$ \end{enumerate} \subsection{Satz} Der Wertebereich einer auf einer abgeschlossenen beschränkten Menge stetigen Funktion ist beschränkt. Die Funktion nimmt auf dieser Menge ihr Maximum und auch ihr Minimum an. {\flushleft Beispiel: Die Funktion $f(x,\,y) = \displaystyle\frac{1}{x}+y$ ist auf der Menge $D_f = \{(x,\,y) : 0 < x \leq 2,\; 0\leq y \leq 1\}$ stetig aber nicht beschränkt, da $D_f$ \emph{nicht} abgeschlossen ist.} \subsection{Höhenlinien (Niveaulinien), Niveauflächen}\index{Höhenlinien} \index{Niveaulinien, flächen} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \begin{minipage}[c]{8cm} \item $f(x,\,y) = (x-2)^2 + 2y \qquad D_f = \mathbb{R}^2$ \bigskip In der $x$--$y$--Ebene markieren wir alle Punkte mit gleichem Funktionswert $c$. \bigskip $(x-2)^2 + 2y = c\quad \Rightarrow\quad y = -\frac{1}{2}(x-2)^2 + \frac{c}{2}$ \end{minipage} \begin{minipage}[c]{100pt} \begin{picture}(100,80) \put(23,74){$\scriptstyle y$} \put(89,34){$\scriptstyle x$} \put(0,40){\vector(1,0){95}} \put(20,0){\vector(0,1){80}} \multiput(18.5,10)(0,10){7}{\line(1,0){3}} \put(12,47){$\scriptstyle 1$} \put(12,67){$\scriptstyle 3$} \put(5,17){$\scriptstyle -2$} \put(40,38.5){\line(0,1){3}} \put(38,31){$\scriptstyle 2$} \multiput(0,0)(0,10){4}{\qbezier(40,40)(22,38)(14,0)} \multiput(0,0)(0,10){4}{\qbezier(40,40)(58,38)(66,0)} \put(69,0){$\scriptstyle c = 0$} \put(69,10){$\scriptstyle c = 1$} \put(69,20){$\scriptstyle c = 2$} \put(69,30){$\scriptstyle c = 3$} \end{picture} \end{minipage} \item $(f(x,\,y,\,z)\; , c\in \mathbb{R})$ Die Menge aller Punkte $(x,\,y,\,z) \in D_f = \mathbb{R}^3$ für die $f(x,\,y,\,z) = c$ ist, heißt \emph{Niveaufläche}. Beispiel: $f(x,\,y,\,z) =\displaystyle \frac{1}{[(x+2)^2 + (y+3)^2 + z^2]^2} = c \qquad c > 0$ \smallskip $(x-2)^2 + (y+3)^2 + z^2 = \sqrt{\frac{1}{c}}$ : Kugelfläche vom Radius $\left(\frac{1}{c}\right)^{\frac{1}{4}}$ um den Mittelpunkt $(2,\,-3,\,0)$. \smallskip Im Fall $c \leq 0$ ist die Niveaufläche die leere Menge. \end{enumerate} \section{Partielle Ableitungen} \index{partielle Ableitung} Graphische Darstellung einer Funktion $f$ von einer Variablen: Kurve mit den Punkten $(x,\,f(x)),\; x\in D_f$. Graphische Darstellung einer Funktion von zwei Variablen: Fläche mit den Punkten $(x,\,y,\,f(x,\,y)) \in D_f$. Die Frage "`Welche Steigung hat die Fläche an der Stelle $(x,\,y,\,f(x,\,y)) = (P_0,\,f(P_0))?$"' ist sinnlos, denn die Steigung hängt von der Richtung ab, in der man sich von $(P_0,\,f(P_0))$ aus bewegt. Sinnvoll ist aber die Frage "`Welche Steigung hat die Fläche in Richtung der $x$--Achse und welche in Richtung der $y$--Achse?"' oder "`In welcher Richtung ist der Anstieg am größten?"' \subsection{Definition} Es sei $f$ eine auf der offenen Menge $D_f \in \mathbb{R}^2$ definierte Funktion und im Punkt $P_0(x_0,\,y_0) \in D_f$ gegeben. Die Funktion $f$ heißt in diesem Punkt $P_0$ nach $x$ \emph{partiell differenzierbar}, wenn die Funktion $x \to f(x,\,y_0)$ im Punkt $x_0$ differenzierbar ist. Deren Ableitung heißt \emph{partielle Ableitung} von $f$ nach $x$ im Punkt $P_0$. {\flushleft \textbf{Schreibweise:} $f_x(P_0) \quad $oder$\displaystyle\quad\frac{\partial f}{\partial x}$} {\flushleft \textbf{Bemerkung:}} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $f_x$ liest man "`$f$ partiell nach $x$"' oder "`$f$ nach $x$"' \item $\displaystyle f_x(x_0,y_0) = \lim_{h\to 0} \frac{f(x + h,\, y_0) - f(x,\,y_0)}{h}$ \smallskip $\displaystyle f_y(x_0,y_0) = \lim_{h\to 0} \frac{f(x_0 ,\, y+h) - f(x_0,\,y)}{h}$ \end{enumerate} \subsection{Definition} Es sei $f$ eine auf der offenen Menge $D_f \subset \mathbb{R}^n$ definierte Funktion, $P_0 = (u_1,\, u_2,\, \ldots \, ,\,u_n) \in D_f$. $f$ heißt im Punkt $P_0$ nach $x_i$ \emph{partiell differenzierbar}, wenn $x\longrightarrow f(u_1,\, u_2,$ $\ldots \, ,\, u_{i-1},\,u_{i},\,u_{i+1},\, \ldots \, ,\, u_n)$ an der Stelle $u_i$ differenzierbar ist. Ihre Ableitung an der Stelle $u_i$ heißt dann die partielle Ableitung von $f$ nach $x_i$ im Punkt $P_0$. \begin{flushleft} \textbf{Schreibweise}: $f_{x_i}(P_0) = \displaystyle\frac{\partial f}{\partial x_i}(P_0)$ \end{flushleft} \subsection{Beispiel} \begin{eqnarray} f(x,\,y,\,z) & = & \sin^2 x + z\cdot e^y\cdot \sqrt{x} +23\\ f_x(x,\,y,\,z) & = & 2 \sin x \cos x + z \cdot e^y \cdot \frac{1}{2} \frac{1}{\sqrt{x}}\\ f_y(x,\,y,\,z) & = & z\cdot e^y \cdot \sqrt{x}\\ f_z(x,\,y,\,z) & = & e^y\cdot\sqrt{x} \end{eqnarray} \subsection{Definition} $f$ sei eine auf der offenen Menge $D_f \subset \mathbb{R}^n$ definierte Funktion und dort nach $x$ partiell differenzierbar. Wenn $f_{x_i}$ in $P \in D_f$ nach $x_i$ partiell differenzierbar ist, so heißt diese Ableitung die \emph{zweite partielle Ableitung} von $f$ nach $x_i,\,x_j$ im Punkt $P$. Schreibweise: $f_{{x_i}{x_j}}(P) = \frac{\partial^2 f}{\partial x_i\partial x_j}(P)$. \subsection{Beispiel} Gegeben sei die Funktion: $f(x,y,z) = x^2y + z\cdot\sin(x+y^2)$ \vspace{6pt} Erste partielle Ableitungen: \smallskip $f_x(x,y,z) = 2xy + z\cdot\cos(x+y^2) \cdot 1$ $f_y(x,y,z) = x^2 + z\cdot\cos(x+y^2) \cdot 2y$ $f_z(x,y,z) = 0 + \cos(x+y^2)$ \vspace{6pt} Zweite partielle Ableitungen: \smallskip $\left.\begin{array}{l} f_{xy} = 2x - 2yz\cdot\sin(x+y^2)\\ f_{yx} = 2x - 2yz\cdot\sin(x+y^2) \end{array}\right\} f_{xy} = f_{yx}$ \vspace{2pt} $\;\,f_{zz} = 0$ \subsection{Satz} Die Funktion $f$ sei auf der offenen Menge $D_f \subset \mathbb{R}^n$ definiert und dort mögen sämtliche partielle Ableitungen bis zur Ordnung $k$ existieren und stetig sein. Dann hängen die partiellen Ableitungen der Ordnung $\leq k$ nicht von der Reihenfolge der Differentiation ab. \subsection{Satz (Leibnitzsche Regel)} \index{Leibnitzsche Regel} \begin{minipage}[c]{8cm} Sei $D_f = \{(x,t) \in \mathbb{R}^2 : a \leq x \leq b,\; \alpha \leq t \leq \beta\}$ und $g$ eine auf $D$ definierte stetige Funktion, $g_x$ auf $D$ stetig. Ferner seien $u$ und $v$ auf $[a,b]$ stetig differenzierbare Funktionen und für alle $x \in [a,b]$ sei $\alpha \leq u(x)\leq \beta$ und $\alpha \leq v(x) \leq \beta$. Dann wird durch \end{minipage} \begin{minipage}[c]{115pt} \flushright \begin{picture}(100,85) \put(10,5){\vector(0,1){80}} \put(5,10){\vector(1,0){95}} \multiput(9,25)(0,40){2}{\line(1,0){2}} \multiput(25,9)(50,0){2}{\line(0,1){2}} \multiput(25,25)(50,0){2}{\line(0,1){40}} \multiput(25,25)(0,40){2}{\line(1,0){50}} \put(22,0){$a$} \put(72,0){$b$} \put(0,23){$\alpha$} \put(0,63){$\beta$} \qbezier(25,30)(30,35)(50,31) \qbezier(50,31)(60,28)(75,37) \put(46,33){$\scriptstyle u(x)$} \qbezier(25,58)(30,55)(50,60) \qbezier(50,60)(60,63)(75,63) \put(43,53){$\scriptstyle v(x)$} \put(90,1){$x$} \put(2,76){$t$} \put(76,66){$D$} \end{picture} \end{minipage} $$f(x) = \int\limits_{u(x)}^{v(x)}g(x,t)\;dt$$ eine auf $[a,b]$ differenzierbare Funktion definiert. Weiterhin gilt $$f'(x) = \int\limits_{u(x)}^{v(x)} g(x)(x,t)\;dt + g(x,\,v(x)) \cdot v'(x) - g(x,u(x))\cdot u'(x) \qquad (x \in [a,b])$$ \subsubsection{Spezialfälle} \begin{itemize} \item $\frac{d}{dx} \int\limits_{c}^{d}g(x,t)\,dt = \int\limits_c^d g_x(x,t)\,dt$ \item $\frac{d}{dx}\int\limits_c^xg(x,t)\,dt = \int\limits_c^xg_x(x,t)\,dt + g(x,x) \cdot 1$ \end{itemize} \subsection{Beispiel} $$f(x) = \int\limits_x^{x^2} e^{(x-t)^2}\,dt \qquad f'(x) = ?$$ \begin{eqnarray} f'(x) &=& \int\limits_x^{x^2} \underbrace{2\cdot (x-t) \cdot e^{(x-t)^2}}_{\textnormal{\small Subst. } y=x-t} \, dt + e^{(x-x^2)}\cdot 2x -1\\ & & [\ldots] \\ & = & (2x - 1) \cdot e^{(x-x)^2} \end{eqnarray} \section{Extrema der Funktionen mehrerer Variablen}\index{Extrema} \index{absolutes Maximum} \index{Maximum, absolutes} \index{Minimim, absolutes} \index{absolutes Minimum} \index{Minimum, lokales} \index{Maximim, lokales} \index{lokales Maximum} \subsection{Definition} Die Funktion $f$ sei auf $D_f \subset \mathbb{R}^n$ definiert und $P_0 \in D_f$. Wenn $f(P_0) \geq f(P)$ \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item für alle $P\in D_f$ gilt, so sagt man, $f$ habe in $P_0$ ein \emph{absolutes Maximum}. \item für alle $P\in D_f \cap U$ gilt, wobei $U$ eine geeignete Umgebung von $P_0$ ist, so sagt man, $f$ habe in $P_0$ ein \emph{lokales (relatives) Maximum}. \end{enumerate} Die Zahl $f(P_0)$ ist dann (absolutes oder relatives) \emph{Maximum} von $f$. \smallskip Absolutes Minimum, lokales Minimum analog. \subsubsection{Beispiel} $f(x,y) = (x-3)^2 + y^4 \qquad D_f \in \mathbb{R}^2$ \bigskip $f(x,y) \geq 0 \quad (\forall x,y), \quad f(3,0) = 0$ \bigskip $\Rightarrow $ absolutes Minimum im Punkt $P_0=(3,0)$ \subsection{Satz} Die Funktion $f$ sei auf der offenen Menge $D_f \subset \mathbb{R}^n$ definiert und besitze in $P \in D_f$ ein relatives Extremum. Wenn die partielle Ableitung $f_{x_i}$ in $P$ existiert, so ist sie Null. \begin{description} \item[Beweis:] $f$ hat in $P=(a_1,\ldots , a_n)$ ein relatives Extremum $\Rightarrow g(x) = (a_1, \ldots , a_{i-1} , x , \ldots , a_n)$ hat an der Stelle $a_i$ ein relatives Extremum $\Rightarrow g'(a_i) = 0 = f_{x_i}(a_1,\ldots , a_n)$ \end{description} \subsection{Beispiel} Gesucht sind die Extrema der Funktion $f(x,y) = 2x^3-3x^2+y^2$. \bigskip $f_x = 6x^2 - 6x = 0 \Rightarrow x = 0$ oder $x = 1$ \smallskip $f_y = 2y = 0 \Rightarrow y = 0$ \bigskip Die beiden Lösungen $P_1 = (0,0)$ und $P_2 = (1,0)$ sind Kandidaten für relative Extrema. \subsection{Satz} Die Funktion $f$ sei auf der offenen Menge $D_f \subset \mathbb{R}^2$ definiert, im Punkt $P \in D_f$ seien alle partiellen Ableitungen bis zur zweiten Ordnung stetig, ferner sei $f_x(P) = f_y(P) = 0$ und $\Delta(P) = f_{xx}(P) \cdot f_{yy}(P) - f_{xy}(P)^2$. \newline Dann gilt: \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item Ist $\Delta(P) > 0$, so besitzt $f$ in $P$ ein relatives Extremum, und zwar ein relatives Maximum, wenn $f_{xx}(P) < 0$ (bzw. $f_{yy}(P) < 0$) ist, ein relatives Minimum, wenn $f_{xx}(P) > 0$ (bzw. $f_{yy}(P) > 0$) ist \item Ist $\Delta(P) < 0$, so hat $f$ in $P$ kein Extremum \item Im Fall $\Delta (P) = 0$ kann ein Extremum vorliegen oder nicht. \end{enumerate} \subsection{Beispiele} $f$ aus 10.4.3 \smallskip $f_{xx} = 12x-6, \quad f_{yy} = 2, \quad f_{xy} = 0 \quad \Rightarrow \Delta(x,y) = 24x - 12$ \bigskip $\Delta (0,0) = -12 < 0 \quad \Rightarrow$ keine Extremstelle \smallskip $\Delta (1,0) = 12 > 0, \quad f_{yy}(1,0) = 2 > 0 \quad \Rightarrow $ rel. Maximum \subsection{Anwendung: Ausgleichsrechnung}\index{Ausgleichsrechnung}\index{Methode der kleinsten Quadrate} Gegeben seien $n$ Produkte $P_i = (x_i,y_i) \; i = 1, \ldots , n \; (n > 1)$ die $x_i$ seien nicht alle einander gleich. Es soll eine Gerade $g : y = ax + b$ durch diese Punkte so gelegt werden, daß sie "`möglichst gut"' hindurch geht. \begin{center} \begin{picture}(180,110) \put(5,10){\vector(1,0){180}} \put(15,0){\vector(0,1){110}} \put(32,0){5} \put(59,0){10} \put(89,0){15} \put(119,0){20} \put(149,0){25} \multiput(35,9)(30,0){5}{\line(0,1){2}} \multiput(14,20)(0,15){6}{\line(1,0){2}} \put(8,17){5} \put(2,32){10} \put(2,47){15} \put(2,62){20} \put(2,77){25} \put(2,92){30} \put(6,104){$y$} \put(174,3){$x$} \put(5,2){\line(2,1){150}} \put(35,20){\circle{2}} \put(65,25){\circle{2}} \put(95,70){\circle{2}} \put(125,52){\circle{2}} \put(155,75){\circle{2}} \put(95,70){\line(0,-1){23}} \put(84,57){$d_3$} \put(28,25){$P_1$} \put(58,38){$P_2$} \put(88,75){$P_3$} \put(119,41){$P_4$} \put(149,63){$P_5$} \end{picture} \end{center} Der Punkt $P_i$ hat in $y$--Richtung den Abstand $d_i = \|ax_i + b - y_i\|$ von $g$. "`Möglichst gute"' Annäherung heißt, die Summe $$\sum_{i=1}^{n} {d_i}^2 = \sum_{i=1}^n (ax_i + b - y_i)^2 = f(a,b)$$ soll klein sein, d.h. $a$ und $b$ sollen so bestimmt werden, daß $f(a,b)$ das absolute Minimum annimmt (\emph{Methode der kleinsten Quadrate}). \smallskip \begin{description}\item[Notwendige Bedingung:] $f_a(a,b) = 0 \quad f_b(a,b) = 0)$ \end{description} \begin{eqnarray} f_a(a,b) &\!\!=\!\!& \sum_{i=1}^n 2 (ax_i + b -y) \cdot x_i = 2 \left[a\!\cdot\!\sum_{i=1}^n {x_i}^2 + b\!\cdot\!\sum_{i=1}^n x_i - \sum_{i=1}^n x_i y_i\right] = 0\\ f_b(a,b) &\!\!=\!\!& 2 \sum_{i=1}^n (ax_i + b -y) = 2 \left[a\cdot\sum_{i=1}^n {x_i} + n\cdot b - \sum_{i=1}^n y_i\right] = 0 \end{eqnarray} \bigskip $\Rightarrow$ lineares Gleichungssystem für $a$ und $b$. Lösung: $$a = \frac{n \sum\limits_{i=1}^n x_i \cdot y_i - \left(\sum\limits_{i=1}^n x_i\right)\cdot\left(\sum\limits_{i=1}^n y_i\right)}{n\cdot \sum\limits_{i=1}^n {x_i}^2 - \left(\sum\limits_{i=1}^n x_i\right)^2} $$ \begin{description} \item[Beispiel:] An eine Feder hängt man ein Gewicht, sie wird gedehnt. Die Länge $y$ der Feder wird in Abhängigkeit vom Gewicht $x$ gemessen. Hooksches Gesetz: $y = ax + b$ \qquad Anzahl der Messwerte: $n = 6$ \begin{center} \begin{tabular}{l\|llllll} & $P_1$ & $P_2$ & $P_3$ & $P_4$ & $P_5$ & $P_6$ \\ \hline $x$ & 5 &10 &15 &20 &25 &30\\ $y$ & 34 & 52 &66 &79 & 97 & 110 \end{tabular} \end{center} $\Rightarrow a \approx 3,02$ und $b \approx 20,2$ \quad $\sum {d_i}^2 = 9,37$ \end{description} \subsection{Extrema mit Nebenbedingungen} Ein Punkt bewege sich in der Ebene $x+y+z = 0$, sein Abstand zum Nullpunkt betrage $A$. Welches ist sein kleinst-- bzw. größtmöglicher Abstand von der $z$--Achse? \bigskip Abstand von der $z$--Achse: $\sqrt{x^2+y^2}$ \bigskip \begin{description} \item[Aufgabe:] $f(x,y,z) = \sqrt{x^2+y^2} \longrightarrow $ Maximum, Minimum \item[Nebenbedingungen:] $x+y+z = 0$ und $x^2+y^2+z^2 -1 = 0$ \end{description} \subsubsection{Allgemeine Berechnung} \begin{description} \item[Aufgabe:] $f(x_1,\ldots ,x_n) \longrightarrow$ Extremstellen berechnen \item[Nebenbedingungen:] \quad \\ $g_1(x_1, \ldots, x_n) = 0$ $\quad\qquad \vdots$ $g_k(x_1, \ldots, x_n) = 0$ \end{description} \subsubsection{Lösungsmethode} (Multiplikatorenregel von Lagrange) \begin{enumerate} \item Man setzt $$F(x_1, \ldots , x_n, \lambda_1, \ldots , \lambda_k) = f(x_1,\ldots , x_n) + \sum_{j=1}^{k} \lambda_j \cdot g(x_1,\ldots ,x_n)$$ \item Dann wird das Gleichungssystem \begin{eqnarray} \frac{\partial F}{\partial x_i} (x_1,\ldots,x_n,\lambda_1,\ldots ,\lambda_k) &=& 0 \hspace{3.58cm}(i = 1,\ldots,n)\\ \frac{\partial F}{\partial \lambda_i} (x_1,\ldots,x_n,\lambda_1,\ldots ,\lambda_k) & = & g_j(x_1,\ldots , x_n) = 0 \qquad (j = 1,\ldots, k ) \end{eqnarray} gelöst. \item An den gefundenen Stellen $(x_1,\ldots,x_n)$ können die Extremstellen liegen. \end{enumerate} \subsection{Beispiel} wie oben: $f(x,y,z) = \sqrt{x^2 + y^2} = r$ \bigskip $\displaystyle f_x = \frac{1}{2}(x^2 + y^2)^{-\frac{1}{2}} \cdot 3x = \frac{x}{r}$ \hfill $\displaystyle f_y = \frac{y}{r}$ \hfill $\displaystyle f_z = 0$\quad $$F(x,y,z) = f(x,y,z) + \lambda_1 (x^2+y^2+z^2 +1) + \lambda_2 (x+y+z)$$ Es ergibt sich das Gleichungssystem: \begin{eqnarray} F_x = \frac{x}{r} + 2x\lambda_1 + \lambda_2 &=& 0 \qquad (a)\\ F_y = \frac{y}{r} + 2y\lambda_1 + \lambda_2 &=& 0 \qquad (b)\\ F_z = 0 + 2z\lambda_1 + \lambda_2 &=& 0 \qquad (c) \vphantom{\frac{a}{b}}\\ x^2+y^2+z^2-1 & = & 0 \qquad (d) \vphantom{\frac{a}{b}}\\ x+y+z &=& 0 \qquad (e) \vphantom{\frac{a}{b}} \end{eqnarray} Lösung des Gleichungssystems: \smallskip $(a) \cdot y - (b) \cdot x : (y-x) \cdot \lambda_2 = 0 \Rightarrow \lambda_2 = 0$ oder $y = x$ \begin{enumerate} \renewcommand{\labelenumi}{\textbf{(\arabic{enumi})}} \item $\lambda_2 = 0$: A aus $(c)$ folgt dann: $z \cdot \lambda_1 = 0 \Rightarrow \lambda_1 = 0$ oder $z=0$ \begin{enumerate} \renewcommand{\labelenumii}{\textbf{(\arabic{enumi}.\arabic{enumii})}} \item $z = 0$ dann folgt aus $(e) \Rightarrow x = -y$ $(d) \Rightarrow x = \pm \frac{\sqrt{2}}{2}$ \smallskip $\Longrightarrow P_1\left(\frac{\sqrt{2}}{2};-\frac{\sqrt{2}}{2};0\right) \quad P_2\left(-\frac{\sqrt{2}}{2};\frac{\sqrt{2}}{2};0\right) $ \item $\lambda_1 = 0$ dann folgt aus $(a)$ und $(b) \Rightarrow x = y = 0$ $(e) \Rightarrow z = 0$ dann ist aber $(d)$ nicht erfüllt! \end{enumerate} \item $y = x$ dann folgt aus $(e)$ und $(d) \Rightarrow x=y=\pm\frac{\sqrt{6}}{6} ;\; z = \mp\frac{\sqrt{6}}{3}$ $\Longrightarrow P_1\left(\frac{\sqrt{6}}{6};\frac{\sqrt{6}}{6};-\frac{\sqrt{6}}{3}\right) \quad \Longrightarrow P_2\left(-\frac{\sqrt{6}}{6};-\frac{\sqrt{6}}{6};\frac{\sqrt{6}}{3}\right) $ \end{enumerate} \smallskip $f(P_1) = f(P_2) = 1 \qquad f(P_3) = f(P_4) = \frac{\sqrt{3}}{3}$ \begin{flushleft} Aus geometrischen Gründen ist klar: $P_1$ und $P_2$ haben den größten Abstand, $P_3$ und $P_4$ haben den kleinsten Abstand. \end{flushleft} \section{Vollständiges Differential, Anwendungen}\index{vollständiges Differential} \index{Differential, vollständiges} \index{totales Differential} \setlength{\parindent}{0pt} In diesem Abschnitt: $D_f \subset \mathbb{R}^n$ ist offen, $f_{x_i}$ stetig. \smallskip Im Abschnitt 5.3. haben wir gesehen: $$f(x-h) - f(x) \approx f'(x) \cdot h$$ ($h$ "`klein"'), $f'(x)\cdot h$ : Differential von $f$ an der Stelle $x$ zum Zuwachs $h$. \smallskip Jetzt werden wir die Differenz ($n$ beliebig) $$f(x_1+h_1,\ldots , x_n+h_n) - f(x_1,\ldots ,x_n)$$ abschätzen ($h$ "`klein"'). \subsection{Definition} Es sei $P = (x_1,\ldots ,x_n) \in D_f$. Man nennt $$df(P) = f_{x_1}(P)\cdot h_1 + \cdots + f_{x_n}(P)\cdot h_n$$ \emph{vollständiges} (oder \emph{totales}) \emph{Differential} von $f$ an der Stelle $P$ zum Zuwachs $(h_1,\ldots ,h_n)$. Oft schreibt man $dx_i$ anstelle von $h_i$: $$df(P) = f_{x_1}(P)\cdot dx_1 + \cdots + f_{x_n}(P)\cdot dx_n$$ Sind die Zuwächse $dx_i$ klein, so gilt: $$f(x_1 + dx_1 , \ldots , x_n + dx_n) - f(x_1,\ldots ,x_n) \approx df(P)$$ oder $$f(x_1 + dx_1 , \ldots , x_n + dx_n) \approx f(x_1,\ldots ,x_n) + df(P)$$ \subsection{Beispiel} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $f(x,y) = 2x^2 + xy^2 \qquad P = (3;\,-1)$ Vollständiges Differential im Punkt $P$: $$df(P) = f_x(P) dx + f_y(P) dy = 13dx + 6dy$$ $$(f_x = 4x + y^2 \qquad f_y =2xy)$$ \item Man berechne näherungsweise: $1,\!002 \cdot 2,\!003^2 \cdot 3,\!004^3$ Ansatz: $f(x,y,z) = x\cdot y^2 \cdot z^3$ $x_0 = 1, \; y_0 = 2, \; z_0 = 3 \; \Rightarrow \; P = (x_0,y_0,z_0) = (1,\,2,\,3)$ $f(P) = 1\cdot 2^2 \cdot 3^3 = 108 $ $dx = 0,002,\; dy = 0,003,\; dz = 0,004 \Rightarrow f(x_0 + dx,y_0 +dy , z_0 + dz)$ $f(1,\!002,\,2,\!003,\,3,\!004) \approx f(P) + f_x(P)dx + f_y(P)dy + f_z(P)dz =$ $108 + {y_0}^2\cdot {z_0}^3\cdot dx + 2x_0\cdot y_0\cdot {z_0}^3\cdot dy + 3x_0\cdot {y_0}^2\cdot {z_0}^2\cdot dz = 108,\!972$ Analog kann man näherungsweise $\sqrt{1,\!02^3+1,\!97^3}$ ($x_0 = 1,\; y_0 = 2$) oder $0,\!97^{1,05}$ ($x_0=y_0=1$) berechnen. \end{enumerate} \subsection{Definition: Tangentialebene} \index{Tangentialebene} Die Ebene $E$ mit der Gleichung $$z = f(P_0) + f_x(P_0)(x-x_0) + f_y(P_0)(y-y_0) \qquad (P_0 = (x_0,y_0) \in D_f)$$ heißt die \emph{Tangentialebene}, die durch $z\! =\! f(x,y)$ definierte Fläche im Flächenpunkt $(x_0,y_0, \underbrace{f(x_0,y_0)}_{z_0})$. Die Tangentialebene geht durch einen Punkt $(x_0,y_0,z_0)$ und \emph{berührt} die Fläche im folgenden Sinne: Jede zur $xy$--Ebene senkrechte Ebene $S$ durch den Punkt $P_0 = (x_0,y_0,z_0)$ schneidet die Tangentialebene $E$ in einer Geraden, die Tangente an die Schnittkurve von $S$ mit der Fläche ist (z.B. die Ebenen $x=x_0$ oder $y=y_0$). \subsubsection{Beispiel} $z = f(x,y) = 2x^2 + xy^2 \qquad P(3,\,-1,\,f(3,\,-1)) = (3,\,-1,\,21)$ $f_x = 4x + y^2 \quad \Rightarrow \quad f_x(3,-1) = 13$ $f_y = 2xy \quad \Rightarrow \quad f_y(3,-1) = -6$ Tangentialebene: $z = 21 + 13\cdot (x-3) - 6\cdot (y+1) = 13x - 6y -24$ \subsection{Für implizit angegebene Funktionen} Oft ist eine Fläche in der impliziten Form $F(x,y,z) = 0$ gegeben. Zum Beispiel: Kugelfläche (Radius 1): $F(x,y,z) = x^2 + y^2 + z^2 - 1 = 0$. Dann lautet die Gleichung der Tangentialebene im Punkt $(x_0,y_0,z_0)$: $$(x-x_0)\cdot F_x(x_0,y_0,z_0) + (y-y_0)\cdot F_y(x_0,y_0,z_0) + (z-z_0)\cdot F(x_0,y_0,z_0) = 0$$ \begin{description} \item[Beispiel:] $F$ wie oben, $(x_0,y_0,z_0)$ beliebig. Tangentialebene: $$(x-x_0)\cdot 2x_0 + (y-y_0) \cdot 2y_0 + (z-z_0)\cdot 2z_0 = 0$$ \item[Speziell:] $x_0=1,\, y_0 = z_0 = 0$ : $2(x-1) = 0$ oder die Ebene $x=1$. \end{description} \subsection{Definition: Differentialform} \index{Differentialform} Es seien $Q_1,\ldots, Q_n$ auf der offenen Menge $D \subset \mathbb{R}^n$ definierte stetige Funktionen. Dann heißt der Ausdruck $$Q_1(x_1,\ldots , x_n) \cdot dx_1 + \cdots + Q_n(x_1,\ldots ,x_n)\cdot dx_n$$ eine \emph{Differentialform} (ein vollständiges Differential ist zum Beispiel eine Differentialform). Eine wichtige Frage: Unter welchen Bedingungen über $Q_i$ ist eine Differentialform vollständiges Differential einer Funktion $f$ (d.h. $Q_1 = f_{x_1}, \ldots , Q_n = f_{x_n}$)? \subsection{Satz} Wenn die Funktionen $Q_1,\ldots ,Q_n$ stetige partielle Ableitungen besitzen, so ist $Q_1\cdot dx_1 + \cdots + Q_n dx_n$ genau dann vollständig differenzierbar, wenn $$\frac{\partial Q_i}{x_j} = \frac{\partial Q_j}{x_i} \qquad (i,\,j = 1,\ldots , n)$$ erfüllt ist. \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $\underbrace{(y + \cos x)}_{P} \cdot dx + \underbrace{(x+2y)}_{Q}\cdot dy$ $P_y = Q_x = 1 \Rightarrow$ Differentialform ist ein vollständiges Differential, d.h. es exisitert $f$ mit $f_x = P$ und $f_y = Q$. \smallskip Bestimmung von $f$: $f_x = y + \cos x \Rightarrow$ Integration nach $x$ ergibt $f = yx + \sin x + c(y)$, einsetzen in $f_y = x + 2y$: $x + c'(y) = x + 2y$ $c'(y) = 2y \Rightarrow c(y) = y^2 + c_0 \Rightarrow f(x,y) = yx + \sin x +y^2+c_0$ \item $\underbrace{2xy}_{P}\cdot dx + \underbrace{y}_{Q}\cdot dy \qquad P_y = 2x \ne Q_x = 0$ $\Rightarrow$ \emph{kein} vollständiges Differential \end{enumerate} \section{Kettenregel, Richtungsableitung, Gradient} \index{Kettenregel} Wir setzen stets voraus: $D_f \subset \mathbb{R}^n$ ist offen, $f_{x_i}$ existiert und ist stetig \\($i = 1,\ldots ,n$). \subsection{Satz: Kettenregel} \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item $v_1, \ldots , v_n$ seien auf dem Intervall $(a,b)$ definierte und differenzierbare Funktionen und für alle $t \in (a,b)$ sei $(v_1(t), \ldots , v_n(t)) \in D_f$. Dann ist die Funktion $g(t) = f(v_1(t),\ldots ,v_n(t))$ auf $(a,b)$ differenzierbar mit \[g'(t) = \sum\limits_{i=1}^n f_{x_i} (v_1(t), \ldots , v_n(t)) \qquad t \in (a,b)\] \item $v_1,\ldots , v_n$ seien auf der offenen Menge $M \subset \mathbb{R}^k$ definierte und partiell stetig differenzierbare Funktionen und für alle $(t_1,\ldots , t_k) = P \in M$ sei $(v_1(P),\ldots , v_n(P)) \in D_f$. Dann ist die Funktion $$h(P) = f(v_1(P),\ldots , v_n(P))$$ nach $t_j$ ($j = 1,\ldots, k$) auf $M$ differenzierbar und es gilt: $$\frac{\partial h}{\partial t_j}(P) = \sum\limits_{i=1}^n f_{x_i} (v_1(P),\ldots , v_n(P)) \cdot \frac{\partial v_i}{\partial t_j} \qquad P \in M$$ \end{enumerate} \subsubsection{Merkregel} \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item $\displaystyle\frac{df}{dt} = \sum\limits_{i=1}^n \frac{\partial f}{\partial x_i}\cdot\frac{dx_i}{dt}$ \item $\displaystyle\frac{\partial f}{\partial t_j} = \sum\limits_{i=1}^n \frac{\partial f}{\partial x_i}\cdot \frac{\partial x_i}{\partial t_j} \qquad (t = 1,\ldots , k)$ \end{enumerate} \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $f(x,y)$ beliebig (z.B. $f(x,y) = \sqrt{x^2+y^2}$) $v_1(t) = t^2,\; v_2(t) = t^3 \quad \Rightarrow g(t) = f(t^2,t^3)$ \smallskip $g'(t) = f_x(t^2,t^3)\cdot 2t + f_y(t^2+t^3)\cdot 3t^2$ \item $f(x,y)$ beliebig, $v_1(t_1,t_2) = t_1+t_2$, $v_2(t_1,t_2) = t_1\cdot t_2$ $h(t_1, t_2) = f(t_1+t_2, t_1\cdot t_2)$ \smallskip $\displaystyle\frac{\partial h}{\partial t_1} = f_x(t_1+t_2, t_1\cdot t_2) \cdot 1 + f_y(t_1+t_2, t_1\cdot t_2) \cdot t_2$ \smallskip $\displaystyle\frac{\partial h}{\partial t_2} = f_x(t_1+t_2, t_1\cdot t_2) \cdot 1 + f_y(t_1+t_2, t_1\cdot t_2) \cdot t_1$ \end{enumerate} \subsection{Richtungsableitung}\index{Richtungsableitung} $f(x_1,\ldots , x_n), \quad P_0(x_1,\ldots , x_n) \in D_f, \quad \vec a = (a_1,\ldots ,a_n)^T, \quad \|\vec a\| = 1$ \smallskip Parameterdarstellung der Geraden mit der Richtung $\vec a$, die durch $P_0$ geht: $$P_0 + t\cdot \vec a = (x_1 + t \cdot a_1, \ldots x_n + t \cdot a_n) \qquad t\in \mathbb{R}$$ Wir betrachten $f$ nur auf dieser Geraden: $$g(t) \stackrel{\mathrm{Def.}}{=} f(x_1+t\cdot a_1, \ldots , x_n + t\cdot a_n) \qquad t \in \mathbb{R}$$ \begin{description} \item[Definition:] Unter der \emph{Richtungsableitung} von $f$ im Punkt $P_0$ in Richtung $\vec a$ mit $\|\vec a\| = 1$ versteht man die Zahl $g'(0)$ (für $t = 0$ erhalten wir dem Punkt $P_0$) \item[Schreibweise:] \quad $\displaystyle\frac{\partial f}{\partial \vec a}(P_0)$ \qquad Nach der Kettenregel $$g'(t) = f_{x_1}(x_1+ta_1, \ldots , x_n + ta_n)\cdot a_1 + \ldots + f_{x_n}(x_1+ta_1, \ldots , x_n + ta_n)\cdot a_n$$ $\Rightarrow \displaystyle \frac{\partial f}{\partial \vec a}(P_0) = f_{x_1}(P_0)\cdot a_1 + \ldots + f_{x_n}(P_0)\cdot a_n$ \end{description} Ist ein beliebiger Richtungsvektor $\|\vec a\| \ne 0$ gegeben, so ersetzen wir $\vec a$ durch $\frac{\vec a}{\|\vec a\|}$ (= normierter Vektor). \hspace{1.5cm} \fbox{\qquad $\displaystyle \frac{\partial f}{\partial \vec a}(P) = \frac{1}{\|\vec a\|} \cdot \left(f_{x_1}(P)\cdot a_1 + \ldots + f_{x_n}(P)\cdot a_n\right)$\qquad} \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $\vec a = (1,0,0,\ldots)^T \qquad \|a\| = 1$ $\displaystyle\frac{\partial f}{\partial \vec a} = f_{x_1}(P)$ \item $f(x,y) = x\cdot y + x^2 \qquad P_0 = (1,2)$ \begin{tabular}{lll} $f_x = y+2x$ & $\Rightarrow$ & $f_x(P_0) = f_x(1,2) = 4$\\ $f_y = x$ & $\Rightarrow$ & $f_y(P_0) = f_y(1,2) = 1$\\ \end{tabular} \bigskip $\vec a = (1,1)^T \quad \|\vec a\| = \sqrt{2} \quad \Rightarrow \quad \frac{\partial f}{\partial\vec a}(P_0) = \frac{1}{\sqrt{2}}(4\cdot 1 + 1\cdot 1)\approx 3,\!535$ $\vec a = (5,1)^T \quad \|\vec a\| = \sqrt{26} \quad \Rightarrow \quad \frac{\partial f}{\partial\vec a}(P_0) = \frac{1}{\sqrt{26}}(4\cdot 5 + 1\cdot 1)\approx 4,\!118$ \end{enumerate} \subsection{Definition: Gradient} \index{Gradient} Der Vektor $(f_{x_1}(P), \ldots , f_{x_n}(P))^T$ heißt \emph{Gradient} von $f$ im Punkt $P$. \begin{description} \item[Bezeichnung:] $\mathrm{grad} f(P)$ \item[Bemerkung:] $\displaystyle\frac{\partial f}{\partial \vec a} (P) = \frac{1}{\|\vec a\|} \cdot \vec a \cdot \mathrm{grad} f(P)$ \end{description} \subsection{Satz} \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item Der Vektor $\mathrm{grad} f(P)$ zeigt in die Richtung des stärksten Anstiegs von $f$ im Punkt $P$. $-\mathrm{grad} f(P)$ zeigt in die Richtung des stärksten Gefälles. \item $\|\mathrm{grad} f(P)\|$ gibt den größten Anstieg im Punkt $P$ an. \end{enumerate} \subsection{Beispiel} In jedem Körper, in dem kein Temperaturgleichgewicht herrscht, treten Wärmeströmungen auf. Der Wärmefluß im Punkt $P$ wird durch einen Vektor $\vec q(P)$, dessen Richtung die der Wärmeströmung, und dessen Länge die Intensität ist dargestellt. Es sei $T(P)$ die Temperatur im Punkt $P$. Es zeigt sich, daß \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item Der Wärmefluß hat die Richtung des stärksten Gefälles der Temperatur in $P$ und \item die Stärke des Wärmeflusses ist proportional zum Temperaturgefälle. Der Vektor $-\mathrm{grad} T(P)$ hat diese Eigenschaften $\Rightarrow$ \emph{Grundgesetz der Wärmeleitung}. $$\vec q(P) = - \lambda(P) \cdot \mathrm{grad} T(P)$$ wobei $\lambda(P)$ die Wärmeleitfähigkeit ist. \end{enumerate} \section{Die Taylorsche Formel}\index{Taylorsche Formel} \index{Nabla--Operator} \index{Laplace--Operator} Zur Erinnerung: Taylorsche Formel ($f : \mathbb{R} \to \mathbb{R}$): $$f(x_0+h) = \sum\limits_{k=0}^n \frac{f^{(k)}(x_0)}{k!}\cdot h^k + \underbrace{R_n(x_0)}_{\mathrm{Restglied}}$$ Mit $\nabla$ (\emph{Nabla-Operator}) bezeichnen wir den formalen Ausdruck $$\nabla = \left(\frac{\partial}{\partial x_1}+ \cdots + \frac{\partial}{\partial x_n}\right)^T$$ Ist $f(x_1,\ldots, x_n)$ eine Funktion (für die alle partiellen Ableitungen existieren), so sei $$\nabla f(P) = \left(\frac{\partial f}{\partial x_1}(P) + \cdots + \frac{\partial f}{\partial x_n}(P)\right)^T$$ (formale Multiplikation des "`Vektors"' $\nabla$ mit dem Skalar $f$). Bemerkung: grad$\,f = \nabla f$. Mit $\nabla$ rechnet man ähnlich mit einem Vektor, einige Formeln lassen sich mit diesem Operator übersichtlicher darstellen. Sei z.B. $h = (h_1,\ldots, h_n)\in\mathbb{R}^n$. Dann ist $$(h\cdot \nabla)f(P) = \left(h_1\cdot\frac{\partial}{\partial x_1} + \cdots + h_n \frac{\partial}{\partial x_n}\right)\cdot f(P) = h_1\cdot f_{x_1}(P) + \cdots + h_n\cdot f_{x_n}(P)$$ (das Differential von $f$ im Punkt $P$ zum Zuwachs $h$). \bigskip Weitere Beispiele: $$(h\cdot \nabla)^2 \cdot f(P) = \left(h_1\cdot\frac{\partial}{\partial x_1} + \cdots + h_n \cdot \frac{\partial}{\partial x_n}\right)^2 \cdot f(P) = \sum\limits_{i,j=1}^n h_i\cdot h_j \cdot f_{x_i\,x_j}(P)$$ mit $\left[h_i\cdot \frac{\partial}{\partial x_i} \cdot h_j\cdot\frac{\partial}{\partial x_j} = h_i\cdot h_j \frac{\partial^2}{\partial x_i\cdot\partial x_j}=f_{x_i\,x_j}\cdot h_i\cdot h_j\right]$ \smallskip Oder: $\nabla \cdot \nabla \; f = \frac{\partial^2 f}{\partial {x_1}^2} + \cdots +\frac{\partial^2 f}{\partial {x_n}^2}$ \smallskip $\nabla \cdot \nabla$ wird auch mit $\Delta$ bezeichnet und heißt \emph{Laplace-Operator}. \subsection{Satz: Mehrdimensionale Taylorsche Formel} Die Funktion $f$ sei auf der offenen Menge $D_f \in\mathbb{R}^n$ $(n+1)$--mal stetig partiell differenzierbar nach allen Variablen. Es sei $h \in \mathbb{R}^n$, $x_0 \in D_f$ und $x=x_0 + h \in D_f$. Dann existiert ein $t \in (0,1)$ so, daß $$f(x_0+h) = \sum\limits_{k=0}^n \frac{1}{k!}(h\cdot \nabla)^k f(x_0) + \frac{1}{(n+1)!}\cdot\left(h\cdot \nabla\right)^{n+1}f(x_0+t\cdot h)$$ \subsection{Beispiel} $f(x,y) = e^x \cdot \sin y$ \smallskip Taylorentwicklung an der Stelle $P = (0,0)$ bis zu Gliedern dritter Ordnung. \begin{description} \item[$k=0$]:\newline $f(P) = f(0,0) = 0$ \item[$k=1$]:\newline $f_x = e^x\cdot \sin y \qquad f_x(P) = 0$ $f_y = e^x\cdot \cos y \qquad f_y(P) = 1$ \item[$k=2$]:\newline $f_{xx} = e^x \cdot \sin y \qquad f_{xx}(P) = 0$ $f_{xy} = e^x \cdot \cos y \qquad f_{xy}(P) = f_{yx}(P) = 1$ \quad (2 $\times$) $f_{yy} = e^x \cdot \sin y \qquad f_{yy}(P) = 0$ \item[$k=3$]:\newline $f_{xxx} = e^x \cdot \sin y \qquad f_{xxx}(P) = 0$ $f_{xxy} = e^x \cdot \cos y \qquad f_{xxy}(P) = f_{xyx}(P) = f_{yxx}(P) = 1$ \quad (3 $\times$) $f_{xyy} = e^x \cdot \sin y \qquad f_{xyy}(P) = f_{yxy}(P) = f_{yyx}(P) = 0$ \quad (3 $\times$) $f_{yyy} = e^x \cdot \cos y \qquad f_{yyy}(P) = -1$ \end{description} Mit $x_0 = y_0 = 0$, $h_1 = x-x_0 = x$, $h_2 = y-y_0 = y$ gilt: \bigskip $\displaystyle f(x,y) = \underbrace{0}_{k=0} + \underbrace{\frac{1}{1!} \cdot 0 \cdot x + \frac{1}{1!} \cdot 1 \cdot y}_{k=1} + \frac{1}{2!}\Big(\underbrace{0\cdot x^2 + 2\cdot 1 \cdot x\cdot y + 0\cdot y^2}_{k=2}\Big) + $ \smallskip \hfill $ + \frac{1}{3!} \cdot \Big(\underbrace{0\cdot x^3 + 3\cdot 1 \cdot x^2\cdot y + 3\cdot 0 \cdot x\cdot y^2 + (-1)\cdot y^3}_{k=3}\Big) + R_3$ \smallskip $f(x,y) = y+xy+\frac{1}{6}\cdot(3x^2y - y^3) +R_3$ \bigskip Bemerkung: In diesem Spezialfall hätten wir auch die Taylorentwicklung der Funktionen $e^x$ und $\sin y$ multiplizieren können. \newpage \section{Implizite Funktionen} \index{implizite Funktionen} \index{Funktionen, implizit} Wir betrachten die Auflösbarkeit einer Gleichung $F(x,y) = 0$ nach einer Variablen. \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $F(x,y) = ax + by + c = 0$ Auflösung nach $y$ genau dann möglich, wenn $b \ne 0$. $y= f(x) = -\frac{a}{b}\cdot x - \frac{c}{b}$ \qquad Bemerkung: $b = F_y$ \item $F(x,y) = x^2+y^2 + 1 = 0$ \begin{minipage}{8cm} \index{lokale Auflösbarkeit} Nur eine sogenannte \emph{lokale Auflösbarkeit} in einer Umgebung einer Stelle $(x_y.y_0)$. \bigskip Wenn $y_0>0$, dann $y = f_1(x) =\sqrt{1-x^2}$ Wenn $y_0<0$, dann $y = f_2(x) =-\sqrt{1-x^2}$ \end{minipage} \begin{minipage}{3.5cm} \begin{picture}(100,75) \put(50,0){\vector(0,1){75}} \put(50,35){\circle{40}} \put(0,35){\vector(1,0){100}} \put(64,49){\circle{2}} \multiput(30,35)(40,0){2}{\circle{2}} \put(66,49){$\scriptstyle (x_0,y_0)$} \put(44,69){\line(1,-1){40}} \put(90,28){$x$} \put(53,70){$y$} \end{picture} \end{minipage} In den Punkten $(\pm1,0)$ ist eine lokale Auflösung nicht möglich! In diesen Punkten ist die Tangente parallel zur $x$--Achse. Die $y$--Koordinate des Gradienten $(F_x,F_y) = (2x, 2y)$ verschwindet in diesen Punkten. \end{enumerate} \subsection{Satz} Sei $F(x,y)$ stetig nach $x$ und $y$ differenzierbar, $F(x_0,y_0) =\! 0$ und $F_y(x_0,y_0)\! \ne 0$. Dann existiert eine Umgebung $U$ von $x_0$, für die gilt: Es gibt genau eine Funktion $y = f(x)$ auf $U$ mit $$F(x,f(x)) = 0 \qquad x \in U$$ Die Funktion $f$ ist dann differenzierbar und $\displaystyle f'(x) = - \frac{F_x(x,f(x))}{F_y(x,f(y))}$ \paragraph{Beweis der letzten Gleichung:} $h(x) = F(x,h(x)) = 0 \Rightarrow h'(x) = 0$ \[\frac{dh}{dx} = F_x \cdot 1 + F_y \cdot f'(x) = 0 \qquad \textrm{(Kettenregel)}\] \subsection{Beispiel} \begin{minipage}{275pt} $F(x,y) = x^3 + y^3 - 3axy, \quad (a \ne 0)$, \quad "`Kartesisches Blatt"' \index{kartesisches Blatt} Wir bestimmen diejenigen Kurvenpunkte, für die $F_y = 0$ wird: \end{minipage} \begin{minipage}{80pt} \flushright \begin{picture}(60,70) \qbezier(0,55)(15,25)(30,35) \qbezier(30,35)(38,42)(33,50) \qbezier(33,50)(22,62)(15,50) \qbezier(15,50)(10,40)(13,10) \put(12.4,37.2){\circle{2}} \put(13,26){$\scriptstyle P_1 = (0,0)$} \put(35.2,42.4){\circle{2}} \put(38,40){$\scriptstyle P_2$} \end{picture} \end{minipage} \begin{enumerate} \renewcommand{\labelenumi}{(\arabic{enumi})} \item $F(x,y) = x^3 + y^3 -3axy = 0$ \item $F_y(x,y) = 3y^2 - 3ax = 0 \quad \Rightarrow \quad x = \frac{y^2}{a}$ in (1) \end{enumerate} $\Rightarrow \displaystyle \frac{y^6}{a^3} + y^3 - 3y^3 = 0$ \bigskip $y^6 = 2a^3y^3 \qquad /\,: y^3$ (für $y \ne 0$) \qquad $\Rightarrow \qquad y^3 = 2a^3 \quad \Rightarrow \quad y = \sqrt[3]{2} a$ \bigskip $\Rightarrow P_1 = (0,0), \; P_2 = a\cdot (4^{\frac{1}{3}}, 2^{\frac{1}{3}})$ \subsubsection{Verallgemeinerung} Auflösbarkeit aus Gleichungssystemen: \bigskip $F_1(x_1,\ldots , x_n , y_1 , \ldots y_m) = 0$ $\quad \vdots$ $F_m(x_1,\ldots , x_n , y_1 , \ldots y_m) = 0$ \bigskip nach den Variablen $y_1, \ldots, y_m$ auflösen, d.h. \bigskip $y_1 = f_1(x_1,\ldots,x_n)$ $\quad \vdots $ $y_m = f_m(x_1,\ldots,x_n)$ \chapter{Integralrechnung der Funktionen mehrerer Variablen} \section{Mehrfache Integrale} \index{Doppelintegrale} \index{Integrale, mehrfach} \subsection{Doppelintegrale} Es sei $G \subset \mathbb{R}^2$ eine beschränkte abgeschlossene Menge und $f$ eine auf $G$ definierte beschränkte Funktion. Es sei $f(P) \geq 0$ $(P \in G)$. Wir wollen das Volumen desjenigen Körpers bestimmen, der durch die Menge $$\left\{(x,y,z) \in \mathbb{R}^3 : (x,y) \in G ,\; 0 \leq z \leq f(x,y) \right\}$$ definiert ist. \begin{enumerate} \item $Z$ sei eine Zerlegung von $G$ in $n$ Teilmengen $g_1,\ldots,g_n$ für die folgendes gilt: \begin{enumerate} \item Jede Teilmenge $g_i$ hat einen Flächeninhalt $\Delta g_i$ \item Die Vereinigung aller $g_i$ ist $G$ \item Die $g_i$ sind disjunkt \item Sei $\delta_i =\sup\{\|P-Q\| : P,\,Q \in g_i\}$ (\emph{Durchmesser} von $g_i$) und $\Delta(Z) = \max\{\delta_1,\ldots ,\delta_n\}$ (\emph{Feinheit} der Zerlegung) \end{enumerate} \item \begin{enumerate} \item In jeder Menge $g_i$ wird ein "`Zwischenpunkt"' $P_i \in g_i$ gewählt und das Produkt $f(P_i) \cdot \Delta g_i$ gebildet (Volumen der "`Säulen"') \item Es wird die Zwischensumme $$S(Z) = \sum\limits_{i=1}^{n} f(P_i) \cdot \Delta g_i$$ gebildet (Näherung für das gesuchte Volumen). \end{enumerate} \end{enumerate} \subsection{Definition} Die Funktion $f$ heißt über $G$ \emph{integrierbar}, wenn es eine Zahl $I$ gibt, so daß $$\lim\limits_{\Delta(Z) \to 0} S(Z) =I$$ Die Zahl $I$ nennt man das \emph{Integral von $f$ über $G$}. $G$ heißt \emph{Integrationsbereich}. \begin{description} \item[Schreibweise:] $\displaystyle \int\limits_G \! f\,dP \qquad oder \qquad \iint\limits_{G} f(x,y) \,dx\,dy$ \item[Bemerkung:] $\int\limits_G\! 1 \, dP = $ Flächeninhalt von $G$ \end{description} \subsection{Satz} \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item Die Aussagen in (5.8.5) bleiben auch für Doppelintegrale gültig, wenn man $[a,b]$ durch $G$ und $b-a$ durch den Flächeninhalt von $G$ ersetzt. \item Jede stetige Funktion auf $G$ ist integrierbar \end{enumerate} \subsection{Definition (Normalbereich)}\index{Normalbereich} $g$ und $h$ seien auf $[a,b]$ definierte und stetige Funktionen, für die gilt $g(t) \leq h(t)$ $(t \in [a,b])$. Dann heißt jede der Mengen $G_1 = \{(x,y) : a \leq x \leq b,\; g(x) \leq y \leq h(x)\}$ und $G_2 = \{(x,y) : a \leq y \leq b,\; g(x) \leq x \leq h(x)\}$ ein \emph{Normalbereich} in der Ebene. \subsubsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $h(t) = \frac{1}{4}t^2 \qquad g(t) = -\sin t \qquad [a,b] = [0,2]$ \begin{picture}(100,90) \put(0,40){\vector(1,0){80}} \put(15,0){\vector(0,1){80}} \multiput(13.5,20)(0,40){2}{\line(1,0){3}} \multiput(15,38.5)(20,0){3}{\line(0,1){3}} \qbezier(15,40)(40,45)(55,60) \qbezier(15,40)(35,20)(46.5,20) \qbezier(46.5,20)(52,20)(55,21) \multiput(55,21)(0,4){10}{\line(0,1){2}} \put(71,31){$x$} \put(19,73){$y$} \put(33,31){$\scriptstyle 1$} \put(8,57.5){$\scriptstyle 1$} \put(27,52){$G_1$} \qbezier(19,36)(19,36)(25.5,42.5) \qbezier(23.5,32.5)(23.5,32.5)(38.8,47.8) \qbezier(38,39)(38,39)(54.5,55.5) \qbezier(28,29)(28,29)(32,33) \qbezier(33,25)(33,25)(54.5,46.5) \qbezier(38.5,22)(38.5,22)(54.5,38) \qbezier(44.5,20)(44.5,20)(54.5,30.5) \put(58,58){$\scriptstyle h(t)$} \put(58,17){$\scriptstyle g(t)$} \end{picture} \qquad \begin{picture}(100,90) \put(50,0){\vector(0,1){80}} \put(10,15){\vector(1,0){80}} \multiput(30,13.5)(20,0){3}{\line(0,1){3}} \multiput(48.5,15)(0,20){3}{\line(1,0){3}} \qbezier(50,15)(55,40)(70,55) \qbezier(50,15)(30,35)(30,46.5) \qbezier(30,46.5)(30,52)(31,55) \qbezier(46,19)(46,19)(52.5,25.5) \qbezier(42.5,23.5)(42.5,23.5)(57.8,38.8) \qbezier(49,38)(49,38)(65.5,54.5) \qbezier(39,28)(39,28)(43,32) \qbezier(35,33)(35,33)(56.5,54.5) \qbezier(32,38.5)(32,38.5)(48,54.5) \qbezier(30,44.5)(30,44.5)(40.5,54.5) \put(44,32.5){$\scriptstyle 1$} \multiput(31,55)(4,0){10}{\line(1,0){2}} \put(54,73){$y$} \put(82,6){$x$} \put(68,6){$\scriptstyle 1$} \put(10,59){$\scriptstyle x= - \sin t$} \put(65,59){$\scriptstyle x= \frac{1}{4}y^2$} \put(60,30){$G_2$} \end{picture} \item Der Kreis $K$ mit dem Mittelpunkt $(0,0)$ und dem Radius $2$ ist ein Normalbereich, da $$K = \{(x,y) : -2 \leq x \leq 2, -\sqrt{4-x^2} \leq y \leq \sqrt{4-x^2}\}$$ oder $$K = \{(x,y) : -2 \leq y \leq 2, -\sqrt{4-x^2} \leq x \leq \sqrt{4-x^2}\}$$ $[a,b] = [-2,2]$. Kreisgleichung $x^2 + y^2 = 4 \Rightarrow y = \sqrt{4-x^2}$ (für $y \geq 0$) bzw. $y = -\sqrt{4-x^2}$ (für $y \leq 0$). \end{enumerate} \subsection{Satz} Mit den Bezeichnungen von (11.1.4) gilt: $$\int\limits_{G_1}\! f\,dP = \int\limits_a^b \left[\int\limits_{g(x)}^{h(x)} f(x,y)\,dy\right]dx \qquad \qquad \int\limits_{G_2}\! f\,dP = \int\limits_a^b \left[\int\limits_{g(y)}^{h(y)} f(x,y)\,dx\right]dy$$ \subsection{Beispiel} \begin{enumerate} \renewcommand{\labelenumi}{\alph{enumi})} \item $G = \{(x,y) : 0 \leq x \leq 1,\; -x \leq y \leq x^2\} \qquad f(x,y) = x$ $\int\limits_{G} f\,dP = \int\limits_0^1 \int\limits_x^{x^2} x \, dy\,dx = \int\limits_0^1 x\cdot y\Big\|_{y=x}^{y=x^2} dx = \int\limits_0^1 x^3 + x^2 \,dx = \frac{x^4}{4} + \frac{x^3}{3}\Big\|_{0}^{1} = \frac{7}{12}$ \item Ist der Integrationsbereich $G$ ein Rechteck, also alle vier Integrationsgrenzen konstant, so kommt es auf die Reihenfolge der Integration nicht an. Zum Beispiel: $$\int\limits_0^{2\pi}\!\int\limits_0^1 e^{x^2} \cdot \sin y \; dx\,dy = \int\limits_0^1\!\underbrace{\int\limits_0^{2\pi} e^{x^2} \cdot \sin y \; dy}_{= -e^{x^2} \cos y\big\|_{y=0}^{2\pi} = 0} dx = 0$$ \end{enumerate} \subsection{Satz} Die Funktion $f$ sei auf der abgeschlossenen Menge $G \subset \mathbb{R}^2$ stetig, $g$ und $h$ seien auf $[a,b]$ definierte stetige Funktionen, für alle $t \in [a,b]$ sei $0 \leq g(t) \leq h(t) \leq 2\pi$. Ferner bezeichnen $r$ und $\varphi$ Polarkoordinaten. \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item Wenn $G$ durch die Ungleichung $0 \leq a \leq r \leq b$ und $g(r) \leq \varphi \leq h(r)$ beschrieben wird, so gilt $$\int\limits_{G}\!f(x,y) \; dx\,dy = \int\limits_{a}^{b} \!\int\limits_{g(r)}^{h(r)} f(r\cdot \cos \varphi, r\cdot \sin \varphi) \cdot r\,d\varphi \, dr$$ \item Wenn $G$ durch die Ungleichung $0 \leq a \leq \varphi \leq b$ und $0 \leq g(\varphi) \leq r \leq h(\varphi)$ beschrieben wird, so gilt $$\int\limits_{G}\!f(x,y) \; dx\,dy = \int\limits_{a}^{b} \!\int\limits_{g(\varphi)}^{h(\varphi)} f(r\cdot \cos \varphi, r\cdot \sin \varphi) \cdot r\,dr\,d\varphi$$ $r\,dr \, d\varphi$ : \emph{Flächenelement} in Polarkoordinaten \index{Flächenelement} \end{enumerate} \subsection{Beispiele} $G: 1 \leq r \leq 2 \quad (r-1)\cdot \pi \leq \varphi \leq r\cdot \pi$ Flächeninhalt $F$ von $G$: \begin{eqnarray} F & =& \int\limits_{G} 1 \, dP = \int\limits_1^2\!\int\limits_{(r-1)\pi}^{r\pi}\!\! 1 \; r\,\,r\varphi\,\,dr = \int\limits_1^2 r\cdot \varphi\bigg\|_{\varphi=(r-1)\pi}^{\varphi=r\cdot\pi} dr\\ & = & \pi\int\limits_1^2 r\;dr = \pi\frac{r^2}{2} \bigg\|_1^2 = \frac{3}{2}\;\pi \end{eqnarray} \subsection{Dreifache Integrale} \index{Integrale, dreifach} \index{Dreifachintegrale} $G \subset \mathbb{R}^3$ sei eine beschränkte, abgeschlossene Menge und $f$ eine auf $G$ definierte beschränkte Funktion. Wir zerlegen $G$ in Teilmengen $g_1,\ldots,g_n$ die die selben Eigenschaften wie in (11.1.1) haben (dabei ist "`Flächeninhalt"' durch "`Rauminhalt"' zu ersetzen). \smallskip Die Definition (11.1.2) wird nun wörtlich übernommen ($\mathbb{R}^2 \longrightarrow \mathbb{R}^3$). \begin{description} \item[Bemerkung:] $\displaystyle \int\limits_{G} 1\; dP =$ Volumen von $G$. \item[Definition:] Es seien $f_1$ und $f_2$ in $[a,b] \subset \mathbb{R}$ und $g_1$ und $g_2$ in $G = \{(x,y) \in \mathbb{R}^3:x\in[a,b], f_1(x) \leq y \leq f_2(x)\}$ stetige Funktionen. Dann heißt die Menge $$K\! =\! \{(x,y,z)\! \in\! \mathbb{R}^3 : a\!\leq\! x\! \leq\! b,\, f_1(x)\! \leq\! y\! \leq\! f_2(x),\, g_1(x,y)\! \leq\! z\! \leq\! g_2(x,y)\}$$ ein \emph{Normalbereich} in $\mathbb{R}^3$. Vertauscht man $x,y,z$ untereinander, so entstehen weitere Mengen, die man auch Normalbereiche nennt ($3! = 6$ Möglichkeiten). \end{description} \subsection{Satz} Die Funktion $f$ sei auf dem Normalenbereich $K$ aus (11.1.9) stetig. Dann ist $f$ über $K$ integrierbar und es gilt: $$\int\limits_{K} f(P)\,dP = \int\limits_a^b\int\limits_{f_1(x)}^{f_2(x)}\int\limits_{g_1(x,y)}^{g_2(x,y)} f(x,y,z) \; dz\,dy\,dx$$ Sind alle Integrationsgrenzen konstant, so kommt es auf die Reihenfolge der Integrationen nicht an. \subsection{Beispiel} $K = \{(x,y,z) : 0\leq x \leq 2,\, 0 \leq y \leq x,\, 0 \leq z \leq x+y+1\}$ \smallskip $f(x,y,z) = 2xz + y^2$ \bigskip $\displaystyle \int\limits_G f(P)\, dP = \int\limits_0^2 \int\limits_0^x \int\limits_0^{x+y+1} 2xz + y^2 \; dz\,dy\,dx =$ \bigskip $\displaystyle\int\limits_0^2\int\limits_0^x 2x \cdot \frac{z^2}{2} + y^2z\bigg\|_{z=0}^{z=x+y+1}\;dy\,dx = \int\limits_0^2\int\limits_0^x x(x+y+1)^2 + y^2(x+y+1)\;dy\,dx =$ \smallskip $\displaystyle\int\limits_0^2\int\limits_0^x x^3 + 2x^2y+2x^2+xy^2+2xy+x+y^2x+y^3+y^2\;dy\,dx =$ \smallskip $\displaystyle\int\limits_0^2 x^4 + \frac{x^4}{3}+x^2+x^4+2x^3+x^3+\frac{x^4}{3}+ \frac{x^4}{4} + \frac{x^3}{3}\;dx \stackrel{[\ldots]}{=} \frac{104}{4}$ \subsection{Substitution der Variablen} \index{Substitution (Dreifachint.)} $$\int\limits_K f(P)\;dP = \iiint\limits_K f(x,y,z) \;dx\,dy\,dz$$ \begin{description} \item[Zylinderkoordinaten:] ($r$, $\varphi$, $z$) Substitution: \begin{enumerate} \item $x \longrightarrow r\cdot \cos \varphi,\quad y \longrightarrow r\cdot\sin \varphi$, $z$ unverändert \item $dP \longrightarrow r\cdot dr\,d\varphi\,dz$ \end{enumerate} \item[Kugelkoordinaten:] ($r$, $\varphi$ $\eta$) Substitution: \begin{enumerate} \item $x \longrightarrow r\cdot \cos \varphi \cdot \sin \eta,\quad y \longrightarrow r \cdot\sin \varphi \cdot \sin\eta,\quad z = r\cdot \cos\eta$ \item $dP \longrightarrow r^2\cdot\sin\eta\,d\varphi\,d\eta\,dr$ \item Neue Grenzen einsetzen \end{enumerate} \end{description} \subsubsection{Beispiel} \begin{minipage}{246pt} Das schraffierte Flächenstück rotiere man um die $z$--Achse, der entstehende Körper sei $K$. $$f(x,y,z) = x^2+y^2 = r^2\!\int\limits_K f(P) \; dP =\; ?$$ \end{minipage} \begin{minipage}{110pt} \flushright \begin{picture}(100,85) \put(10,15){\vector(1,0){80}} \put(15,10){\vector(0,1){70}} \put(65,13){\line(0,1){4}} \put(13,60){\line(1,0){4}} \put(6,70){$z$} \put(62,3){$1$} \put(6,56.5){$1$} \qbezier(15,15)(20,50)(65,60) \multiput(15,60)(4,0){13}{\line(1,0){2}} \put(66,63){$\scriptstyle z=\sqrt{x}$} \qbezier(15,55)(15,55)(20,60) \qbezier(15,50)(15,50)(25,60) \qbezier(15,45)(15,45)(30,60) \qbezier(15,40)(15,40)(35,60) \qbezier(15,35)(15,35)(40,60) \qbezier(15,30)(15,30)(45,60) \qbezier(15,25)(15,25)(19,29) \qbezier(15,20)(15,20)(16,21) \qbezier(42,52)(50,60)(50,60) \qbezier(51,56)(55,60)(55,60) \qbezier(59,59)(60,60)(60,60) \end{picture} \end{minipage} $K$ in Zylinderkoordinaten: $0 \leq r \leq 1$, $0 \leq \varphi \leq 2\pi$, $\sqrt{x} \leq z \leq 1$ $$\int\limits_Kf(P)\;dP =\int\limits_0^1\int\limits_0^{2\pi}\int\limits_{\sqrt{r}}^1 \underbrace{r^2}_{f} \underbrace{r\,dz\,d\varphi\,dr}_{\textnormal{\tiny Flächenelement}} =\frac{1}{18}\pi$$ Man kann auch $K$ beschreiben als: $0 \leq \varphi \leq 2\pi,\; 0\leq z\leq 1,\; 0\leq r\leq z^2$ \subsubsection{Beispiel} Es sei $K$ die obere Hälfte der Kugel vom Radius $R$ mit dem Mittelpunkt $(0,0,0)$. $$f(x,y,z) = x^2+y^2 - xz \qquad \int\limits_K f(P)\,dP =\; ?$$ Beschreibung von $K$ in Kugelkoordinaten ($r$, $\varphi$, $\eta$): $$K: \quad 0 \leq \varphi \leq 2\pi, \quad 0 \leq \eta \leq \frac{1}{2}\pi,\quad 0 \leq r \leq R$$ $$(x=r\cdot\cos\varphi\cdot\sin\eta,\;y=r\cdot\sin\varphi\cdot\sin\eta,\;z=r\cdot\cos\eta)$$ \begin{eqnarray} \int\limits_K\! f(P)\,dP &=& \int\limits_{0}^{2\pi}\int\limits_{0}^{\frac{\pi}{2}}\int\limits_{0}^{R}( \underbrace{r^2\cdot \sin^2\eta}_{x^2+y^2} - r^2\cdot\cos \varphi \cdot \sin \eta \cdot \cos \eta) \; r^2\,\sin\eta\,dr\,d\eta\,d\varphi\\ & = & \frac{R^5}{5}\int\limits_0^{\frac{\pi}{2}}\int\limits_0^{2\pi}\sin^3\eta - \underbrace{\cos\varphi \cdot \sin^2\eta\cdot\cos\eta}_{0}\;d\varphi\,d\eta\\ & = & \frac{R^5}{5}\cdot2\pi\int\limits_0^{\frac{\pi}{2}} \sin^3\eta\,d\eta \stackrel{[\ldots]}{=} \frac{4}{15}\cdot\pi\cdot R^5 \end{eqnarray} \section{Anwendungen dreifacher Integrale} \subsection{Satz} \index{Volumen} \index{Masse} \index{Schwerpunkt} \index{Trägheitsmoment} Ein Körper $K (\in\mathbb{R}^3)$ mit der Massendichte $\varrho$ hat das Volumen $V = \int\limits_K 1\,dP$, die Masse $M = \int\limits_K \varrho(P)\,dP$, den Schwerpunkt $(x_s,y_s,z_s)$ mit $x_s = \frac{1}{M}\cdot\int\limits_K x\cdot\varrho(P)\,dP$, $y_s = \frac{1}{M}\cdot\int\limits_K y\cdot\varrho(P)\,dP$, $z_s = \frac{1}{M}\cdot\int\limits_K z\cdot\varrho(P)\,dP$, das Trägheitselement bezüglich der $z$--Achse als Drehachse $\Theta = \int\limits_K (x^2+y^2)\cdot\varrho(P)\,dP$. Für eine beliebige Drehachse gilt: $\Theta = \int\limits_K a^2(P) \cdot \varrho(P)\,dP$, wobei $a(P)$ den Abstand von $P$ von der Drehachse bezeichnet. Analoge Formeln gelten in $\mathbb{R}^2$ (mit Doppelintegralen). \subsection{Beispiel} \begin{minipage}[c]{110pt} \begin{picture}(100,100) \put(50,20){\vector(1,0){50}} \put(50,70){\vector(0,1){30}} \multiput(50,20)(0,4){20}{\line(0,1){2}} \put(50,20){\vector(-1,-1){20}} \put(92,11){$y$} \put(53,93){$z$} \put(22,0){$x$} \put(50,70){\line(1,0){20}} \put(55,76){$R$} \put(52,50){$h$} \put(50,70){\circle{2}} \qbezier(70,70)(70,75)(50,75) \qbezier(70,70)(70,65)(50,65) \qbezier(30,70)(30,75)(50,75) \qbezier(30,70)(30,65)(50,65) \qbezier(50,20)(30,70)(30,70) \qbezier(50,20)(70,70)(70,70) \end{picture} \end{minipage} \begin{minipage}[c]{245pt} Es ist der Schwerpunkt des Kegels zu berechnen, $\varrho = 1$. Beschreibung von $K$ in Zylinderkoordinaten (siehe 10.1.3.e): $$K: 0 \leq r \leq R, \quad 0 \leq \varphi \leq 2\pi,\quad \frac{h}{R}r \leq z \leq h$$ Aus Symmetriegründen: $x_s = y_s = 0$. \end{minipage} \begin{eqnarray} z_s &=& \frac{1}{M}\int\limits_K\!z \,dP = \frac{1}{M} \int\limits_0^{2\pi}\!\int\limits_0^{R}\!\int\limits_{\frac{hr}{R}}^h z \cdot r\,dz\,dr\,d\varphi = \\ &\stackrel{[\ldots]}{=}& \frac{\pi}{M}\int\limits_0^{R}\!\left(h^2-\frac{h^2}{R^2}r^2\right)r\,dr = \frac{\pi}{4} \cdot h^2 \cdot R^2 \cdot \frac{1}{M} \end{eqnarray} Wobei $M = \frac{\pi}{3} \cdot R^3 \cdot h$ (Masse = Volumen, da $\varrho =1$): \bigskip $\Rightarrow \displaystyle z_s = \frac{3}{4}\cdot h$ \chapter{Vektoranalysis} \section{Skalar-- und Vektorfelder} \index{Skalarfeld} \index{Vektorfeld} \index{Felder, Skalar--, Vektor--} \subsection{Definition} Es sei $D \subset \mathbb{R}^3$. Eine Abbildung $\vec V$, die jedem Punkt $P = (x,y,z) \in D$ einem dreidimensionalen Vektor $\vec V(P) = \vec V (x,y,z) = (v_1(x,y,z),\,v_2(x,y,z),$ $\,v_3(x,y,z))$ zuordnet, heißt ein (räumliches) \emph{Vektorfeld} auf $D$. Eine Abbildung $F$, die jeden Punkt $P \in D$ eine reelle Zahl $F(P)$ zuordnet, heißt ein (räumliches) \emph{Skalarfeld} auf $D$. Ist $D \subset \mathbb{R}^2$ und sind die Vektoren $\vec V(P)$ zweidimensional $\vec V(P) = \vec V(x,y) = (v_1(x,y),\,v_2(x,y))$, so spricht man von einem \emph{ebenen Vektorfeld} bzw. \emph{ebenen Skalarfeld}. \subsection{Beispiele} \subsubsection{Skalare Felder} \begin{itemize} \item Temperaturverteilung in einem Raum \item elektrostatisches Potential in der Umgebung einer geladenen Kugel \item Dichteverteilung im innern der Erdkugel \item Betrag eines Vektorfeldes \end{itemize} \subsubsection{Vektorfelder} \begin{itemize} \item Gravitationfeld der Erde \item elektrostatisches Feld in einem Kondensator \item Geschwindigkeit einer Strömung \item Gradient eines Skalarfeldes $\vec C = \mathrm{grad}\, F = (F_x,F_y,F_z)^T$ \end{itemize} Weitere Beispiele in \textsc{SigMath}, \textsf{http://www.math.tu-dresden.de/$\sim$sasvari/} \subsection{Definition: Rotation} \index{Rotation, Rotor} Es sei $\vec V = (v_1,v_2,v_3)^T$ ein auf der offenen Menge $D$ definiertes und dort partiell differenzierbares Vektorfeld. Dann heißt das Vektorfeld $$\mathrm{rot}\, \vec V = \left( \frac{\partial v_3}{\partial y} - \frac{\partial v_2}{\partial z}, \frac{\partial v_1}{\partial z} - \frac{\partial v_3}{\partial x}, \frac{\partial v_2}{\partial x} - \frac{\partial v_1}{\partial y} \right)^T$$ die \emph{Rotation} (oder \emph{Rotor}) von $\vec V$. Gilt $\mathrm{rot}\,\vec V = (0,0,0)^T$ in $D$, so heißt $\vec V$ ein wirbelfreies Vektorfeld. Die Rotation läßt sich formal durch das Vektorprodukt darstellen: $$\mathrm{rot}\,\vec V = \nabla \times \vec V = \left(\frac{\partial}{\partial x},\,\frac{\partial}{\partial y},\,\frac{\partial}{\partial z}\right)^T\times (v_1,v_2,v_3)^T = \left\| \begin{array}{ccc} \vec e_1 & \vec e_2 & \vec e_3\\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y}& \frac{\partial}{\partial z}\\v_1 & v_2 & v_3 \end{array}\right\|$$ (Entwicklung nach der ersten Zeile) \subsubsection{Rechenregeln} \begin{tabular}{lcl} $\mathrm{rot}\,(\vec V + \vec W)$ & = & $\mathrm{rot}\,\vec V + \mathrm{rot}\,\vec W $\\ $\mathrm{rot}\,(c \cdot \vec V)$& = & $c \cdot \mathrm{rot}\,\vec V$\\ $\mathrm{rot}\,(F \cdot \vec V)$& = & $(\mathrm{grad}\, F)\times \vec V + F\cdot \mathrm{rot}\,\vec V$ \end{tabular} \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Bezeichne $\vec H$ das mangnetische Feld eines geraden, unendlich langen, von einem gleichstromdurchflossenen Leiters. Wir legen das Koordinatensystem so, daß die $z$--Achse mit dem Leiter zusammenfällt und ihre Richtung gleich der Stromrichtung ist. \begin{minipage}{230pt} $$\vec H(x,y,z) = \frac{k}{x^2+y^2} \cdot (x,y,0)^T$$ $$\|\vec H\| = \frac{k}{\sqrt{x^2+y^2}} \qquad \vec H \perp (x,y,z)^T$$ $$\frac{\partial v_1}{\partial y} = k\cdot\frac{y^2-x^2}{(x^2+y^2)^2} = \frac{\partial v_2}{\partial y}$$ \end{minipage} \begin{minipage}{100pt} \begin{picture}(100,100) \put(0,50){\vector(1,0){100}} \put(50,0){\vector(0,1){100}} \qbezier(80,50)(80,62.426408)(71.213204,71.213204) \qbezier(050,80)(62.426408,80)(71.213204,71.213204) \qbezier(20,50)(20,37.573592)(28.786796,28.786796) \qbezier(050,20)(37.573592,20)(28.786796,28.786796) \qbezier(20,50)(20,62.426408)(28.786796,71.213204) \qbezier(050,80)(37.573592,80)(28.786796,71.213204) \qbezier(80,50)(80,37.573592)(71.213204,28.786796) \qbezier(050,20)(62.426408,20)(71.213204,28.786796) \put(50,50){\circle{30}} \put(66,50){\vector(0,1){20}} \put(34,50){\vector(0,-1){20}} \put(50,66){\vector(-1,0){20}} \put(50,34){\vector(1,0){20}} \put(80.25,50){\vector(0,1){15}} \put(20,50){\vector(0,-1){15}} \put(50,80){\vector(-1,0){15}} \put(50,20){\vector(1,0){15}} \put(71.21,71.21){\vector(-1,1){10}} \put(71.21,71.21){\circle{2}} \put(73,72){$\scriptstyle \vec H(x,y)$} \put(92,43){$x$} \put(53,93){$y$} \end{picture} \end{minipage} \bigskip $\mathrm{rot}\, \vec H = (0,0,0)^T \Rightarrow$ Vektorfeld wirbelfrei \item $\vec V (x,y,z) = (x^2+xyz,\,y^2-x^2,\,x+y\cdot\sin z)^T$ $$\mathrm{rot}\,\vec V = \left\|\begin{array}{ccc}\vec e_1&\vec e_2 & \vec e_3\\\frac{\partial}{\partial x} &\frac{\partial}{\partial y} &\frac{\partial}{\partial z}\\\scriptstyle x^2+xyz & \scriptstyle y^2-x^2&\scriptstyle x+y\sin z \end{array}\right\| = (\sin z-0,\,-1+xy,\,-2x-xz)^T$$ $\Rightarrow$ Vektorfeld $\vec V$ ist nicht wirbelfrei. \end{enumerate} \subsection{Definition: Divergenz} \index{Divergenz (Vektorfeld)} \index{Quelldichte (Vektorfeld)} \index{Ergiebigkeit (Vektorfeld)} \index{Quelle (Vektorfeld} \index{Senke (Vektorfeld)} Es sei $\vec V = (v_1,\,v_2,\,v_3)^T$ ein auf der offenen Menge $D \subset \mathbb{R}^3$ definiertes und dort partiell differenzierbares Vektorfeld. Dann heißt das Skalarfeld $$\mathrm{div}\, \vec V = \frac{\partial v_1}{\partial x} + \frac{\partial v_2}{\partial y} + \frac{\partial v_3}{\partial z}$$ die \emph{Divergenz} (\emph{Quelldichte}, \emph{Ergiebigkeit}) von $\vec V$. Man nennt diejenigen Punkte, für die $\mathrm{div}\,\vec V(P) > 0$ bzw. $\mathrm{div}\,\vec V(P) < 0$ gilt die \emph{Quellen} bzw. \emph{Senken} des Feldes $\vec V$. Ist $\mathrm{div}\,\vec V = 0$ in $D$, so heißt $\vec V$ ein \emph{quellenfreies Feld}. Die Divergenz läßt sich formal als Skalarprodukt darstellen: $$\mathrm{div}\,\vec V = \nabla \cdot\vec V = \left(\frac{\partial}{\partial x}+\frac{\partial}{\partial y}+\frac{\partial}{\partial z}\right)^T \cdot (v_1,\,v_2,\,v_3)^T$$ Analog für ebene Vektorfelder ($z = 0$). \paragraph{Physikalische Deutung:} Es sei durch $\vec V(x,y,z) = (0,\,0,\, z\cdot (1-x^2-y^2))^T$ ein Vektorfeld auf dem Zylinder $D = \{(x,y,z) : x^2 + y^2 \leq 1\}$ definiert. \smallskip $\vec V$ : Geschwindigkeit einer das Rohr (Zylindermantel) durchströmenden Flüs\-sigkeit. \bigskip \begin{minipage}{235pt} Wir denken uns einen Zylinder $Z$ in die Strömung gelegt. "`Volumengewinn"' in $Z$ pro Zeiteinheit = abgeflossene $-$ zugeflossene Menge: $$\int_Z\mathrm{div}\,\vec V(P)\,dP = \iiint_Z 1-x^2-y^2\;dx\,dy\,dz$$ \end{minipage} \begin{minipage}{120pt} \flushright \begin{picture}(110,75) \put(0,10){\vector(1,0){110}} \put(50,0){\vector(0,1){70}} \multiput(10,9)(80,0){2}{\line(0,1){51}} \linethickness{0.2pt} \qbezier(10,10)(50,35)(90,10) \multiput(18,10)(64,0){2}{\vector(0,1){4.5}} \multiput(26,10)(48,0){2}{\vector(0,1){8}} \multiput(34,10)(32,0){2}{\vector(0,1){10.5}} \multiput(42,10)(16,0){2}{\vector(0,1){12}} \put(50,10){\vector(0,1){13}} \qbezier(10,30)(50,75)(90,30) \put(10,30){\line(1,0){80}} \multiput(18,30)(64,0){2}{\vector(0,1){8}} \multiput(26,30)(48,0){2}{\vector(0,1){14}} \multiput(34,30)(32,0){2}{\vector(0,1){18.7}} \multiput(42,30)(16,0){2}{\vector(0,1){21.3}} \put(50,30){\vector(0,1){22}} \thinlines \multiput(0,0)(0,-25){2}{\qbezier(38,40)(38,42)(50,42) \qbezier(62,40)(62,42)(50,42)} \multiput(0,0)(0,-25){2}{\qbezier(38,40)(38,38)(50,38)\qbezier(62,40)(62,38)(50,38)} \put(2,0){$-1$} \put(87,0){$1$} \put(103,0){$x$} \put(53,63){$z$} \put(65,21.5){$Z$} \multiput(38,15)(24,0){2}{\line(0,1){25}} \end{picture} \end{minipage} \bigskip $\mathrm{div}\,\vec V(P)$ wird auch als \emph{Quellenstärke pro Volumen} bezeichnet. \subsubsection{Rechenregeln} \begin{tabular}{lcl} $\mathrm{div}\,(\vec V + \vec W) $ & = & $\mathrm{div}\,\vec V + \mathrm{div}\,\vec W$\\ $\mathrm{div}\,(c\cdot\vec V) $ & = & $c \cdot \mathrm{div}\,\vec V$\\ $\mathrm{div}\,(F\cdot\vec V)$ & = & $(\mathrm{grad}\,F)\cdot\vec V + F\cdot \mathrm{div}\,\vec V$ \end{tabular} \smallskip \ \ wobei $F$ ein Skalarfeld ist. \paragraph{Beispiele:} $\vec r = (x,y)^T = 1+1=2, \quad \vec r = (x,y,z)^T = 1+1+1 =3$ \bigskip $\displaystyle\vec H(x,y,z) = \frac{k}{x^2+y^2}\cdot(-y,x,0)^T \qquad$ (magnetisches Feld, s. 12.1.4) $$\frac{\partial v_1}{\partial x} = k\cdot \frac{2xy}{(x^2+y^2)^2},\quad \frac{\partial v_2}{\partial y} = -k\cdot\frac{2xy}{(x^2+y^2)^2},\quad \frac{\partial v_3}{\partial z} = 0 $$ $\Rightarrow \mathrm{div}\,\vec H = 0 \Rightarrow$ Feld ist quellenfrei \subsection{Satz} \index{quellenfrei (Vektorfeld)} \index{Vektorpotential} \index{wirbelfrei (Vektorfeld)} \index{Skalarpotential} Ein Vektorfeld $\vec V$ ist genau dann quellenfrei, wenn es sich als Rotation eines Vektorfeldes $\vec W$ darstellen läßt: $$\mathrm{div}\,\vec V = 0 \quad \Leftrightarrow \quad \vec V = \mathrm{rot}\,\vec W$$ $\vec W$ heißt \emph{Vektorpotenzial} (und ist bis auf den Gradienten einer skalaren Funktion eindeutig bestimmt). \bigskip Ein Vektorfeld $\vec V$ ist genau dann wirbelfrei, wenn es sich als Gradient eines Skalarfeldes darstellen läßt: $$\mathrm{rot}\,\vec V = 0 \quad \Leftrightarrow \quad \vec V = \mathrm{grad}\,\vec F$$ $F$ heißt \emph{Skalarpotenzial} (und ist bis auf einem Konstanten eindeutig bestimmt). \quad /siehe Satz 10.5.6 mit $n = 3$/ \section{Kurvenintegrale} \subsection{Kurven im Raum (Wiederholung)} Parameterdarstellung: $\vec r(t) = (x(t),\,y(t),\,z(t)), \quad t \in [a,\,b]$ Sind $x$, $y$, $z$ differenzierbar, so sei $$\vec {r'}(t) = \dot{\vec{r}}(t) = (x'(t),\,y'(t),\,z'(t))$$ $\vec{r'}(t_0)$ ist Tangentialvektor an die Kurve im Kurvenpunkt $\vec r(t_0)$. Parameterdarstellung der Tangente: $$\vec r(t_0) + t\cdot\vec{r'}(t_0) \qquad t\in\mathbb{R}$$ \subsubsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Schraublinie: $\vec r(t) = (R\cdot \cos t,\,R\cdot \sin t,\,h\cdot t)^T, \quad t \in \mathbb{R}, (R>0, h >0)$ \smallskip \begin{minipage}{220pt} Abstand von der $z$--Achse: \smallskip $\sqrt{R^2\cos^2 t + R^2 \sin^2 t} = R$. \bigskip Ein Umlauf: $2\pi \Rightarrow$ Ganghöhe: $2\pi\cdot h$. \bigskip Tangentialvektor: $\vec{r'} = (-R\cdot \sin t,\, R \cdot \cos t,\,h)^T$ \bigskip Bei $t=0$: $\vec r(0) = (R,\,0,\,0)^T$ \smallskip $\vec{r'}(0) = (0,\,R,\,h)^T$ \smallskip $\Rightarrow$ Tangente: $(R,\,0,\,0)^T + t\cdot(0,\,R,\,h)^T$ \end{minipage} \begin{minipage}{110pt} \flushright \begin{picture}(100,120) \setlength{\unitlength}{1.5pt} \put(30,20){\vector(2,-1){25}} \put(30,20){\vector(-2,-1){25}} \put(30,20){\vector(0,1){60}} \put(0,2.5){$x$} \put(56,2.5){$y$} \put(32,75){$z$} \multiput(0,0)(0,10){4}{ \qbezier(17.5,13.25)(20,10)(30,10) \qbezier(30,10)(40,10)(45,16) \qbezier(45,27.5)(50,23)(45,16) \qbezier(45,27.5)(40,32)(30,32) \qbezier(17.5,23.25)(13,31)(30,32) } \qbezier(17.5,13.25)(17.5,13.25)(16.5,14.25) \put(12,15.5){$R$} \multiput(47,23)(0,10){2}{\line(1,0){5}} \put(52,23){\vector(0,1){10}} \put(52,33){\vector(0,-1){10}} \put(54,25.5){$2\pi h$} \end{picture} \end{minipage} \newpage \item Schraublinie auf einem Kegelmantel: $\vec r(t)\! =\! (t\cdot \cos t,\, t\cdot \sin t,\, h\cdot t)^T,\; t \in \mathbb{R}$ \begin{minipage}{220pt} Abstand von der $z$--Achse: $\|t\|$ \bigskip Ein Umlauf: $2\pi \Rightarrow$ Ganghöhe: $2\pi\cdot h$. \bigskip Tangentialvektor: $\vec{r'} =(t\cdot\cos,\,t\cdot\sin t,\,h\cdot t)^T$ \bigskip \end{minipage} \begin{minipage}{100pt} \flushright \begin{picture}(100,120) \setlength{\unitlength}{1.5pt} \put(40,20){\vector(2,-1){30}} \put(40,20){\vector(-2,-1){30}} \put(40,20){\vector(0,1){60}} \linethickness{0.15pt} \put(40.1,20){\line(1,2){18}} \put(40,20){\line(-1,2){18}} \qbezier(57.9,56)(57.9,53)(40,53) \qbezier(22,56)(22,53)(40,53) \qbezier(57.9,56)(57.9,59)(40,59) \qbezier(22,56)(22,59)(40,59) \thinlines \qbezier(40,20)(44,27)(43,32) \qbezier(43,32)(42,34)(40,34) \qbezier(40,34)(34,34.3)(34,32) \qbezier(34,32)(34,29.7)(40,30) \qbezier(40,30)(46,30)(48.5,38) \qbezier(48.5,38)(50,45)(40,46) \qbezier(40,46)(29,46.5)(28,44) \qbezier(28,44)(29,42)(40,42) \qbezier(40,42)(53,41.5)(53,48) \qbezier(53,48)(53,58)(40,58) \qbezier(40,58)(22,58)(22,56) \put(5,0){$x$} \put(72,0){$y$} \put(42,75){$z$} \end{picture} \end{minipage} \bigskip \item Gerade: $\vec r(t) = \mathbf{a} + t\cdot \mathbf{b}$ ,\qquad $t\in \mathbb{R}$,\quad$(a,b \in \mathbb{R}^3)^T$ \qquad $\mathbf{r}'(t) = \mathbf{b}$ \quad Tangentialvektor der Geraden \end{enumerate} \subsection{Kurvenintegrale (Linienintegral)} \index{Kurvenintegral} \index{Linienintegral} \index{Integral, Kurven--} \begin{description} \item[Motivation:] Berechnung der Arbeit, die von einem Kraftfeld $\vec F$ beim Verschieben eines Massenpunktes verrichtet wird (entlang einer Kurve). \end{description} \begin{minipage}{220pt} \begin{tabular}{lcl} Arbeit &=& Kraft mal Weg\\ $W$ & = &$ F \cdot s$ \end{tabular} \end{minipage} \begin{minipage}{135pt} \begin{picture}(130,49) \put(10,15){\vector(1,0){110}} \put(120,15){\vector(-1,0){110}} \put(63,17){$s$} \put(55,3){Weg} \put(0,35){\line(1,0){130}} \multiput(10,33)(110,0){2}{\line(0,1){4}} \multiput(10,35)(20.5,0){2}{\line(0,1){8}} \put(10,43){\line(1,0){20}} \put(5,23){$A$} \put(115,23){$B$} \qbezier(10,39)(14,43)(14,43) \qbezier(26,35)(30,39)(30,39) \multiput(0,0)(4,0){4}{\qbezier(10,35)(10,35)(18,43)} \put(30,39){\vector(1,0){30}} \put(50,43){$F$} \end{picture} \end{minipage} \paragraph{Spezialfall:} Verschiebung längs einer Geraden durch eine konstante Kraft \begin{minipage}{220pt} \begin{tabular}{l@{\,\,}c@{\,\,}l} Arbeit = $W$ &=& $F\cdot s = \|\vec F\| \cdot \cos\varphi \cdot s$\\ &=& $\vec F \cdot \vec s$ \end{tabular} \end{minipage} \begin{minipage}{135pt} \begin{picture}(130,52) \put(10,12){\vector(1,0){110}} \put(63,2){$\vec s$} \put(0,12){\line(1,0){130}} \multiput(10,10)(110,0){2}{\line(0,1){4}} \put(5,0){$A$} \put(115,0){$B$} \put(10,12){\vector(3,2){40}} \put(52,37){$\vec F$} \put(22,15){$\varphi$} \qbezier(32,12)(33,18)(30,25) \end{picture} \end{minipage} \vspace{0.3cm} Es sei nun $C : \vec r (t) = (x_1(t),\,x_2(t),\,x_3(t))^T$, $t = [a,\,b]$ eine Kurve und auf $C$ sei ein Vektorfeld $\vec F$ definiert. \vspace{0.3cm} \begin{minipage}{192pt} Sei $Z : a = t_0 < t_1 < t_2 < \cdots < t_n = b$ eine Zerlegung des Intervalls $[a,\,b]$. Die geradlinige Verbindung der Punkte $\vec r(t_i)$ ergibt einen eingeschriebenen Streckenzug. \end{minipage} \begin{minipage}{165pt} \begin{picture}(165,53) \put(0,0){$\scriptstyle A = \vec{r}(t_0)$} \put(125,0){$\scriptstyle B = \vec{r}(t_n)$} \put(15,10){\circle{2}} \qbezier(15,10)(35,70)(68,25) \qbezier(68,25)(87,3)(110,30) \qbezier(110,30)(128,50)(140,10) \put(140,10){\circle{2}} \qbezier(15,10)(15,10)(44,44.5) \put(42,47){$\scriptstyle \vec r(t_1)$} \put(80,7){$\scriptstyle \vec r(t_2)$} \put(44,44){\circle{2}} \put(86,15){\circle{2}} \qbezier(44,44.5)(86,15)(86,15) \end{picture} \end{minipage} \vspace{0.3cm} In jedem Teilintervall $[t_{i-1},\,t_i]$ wählen wir eine beliebige Zwischenstelle $\eta_i$. Näherung für $\vec F$ auf der $i$--ten Teilstrecke: $\vec F(\vec r(\eta_i))$. Wir bilden die Summe (Näherung für die Arbeit): $$S(Z) = \sum\limits_{i=1}^n\vec F(\vec r(\eta_i))\cdot(\vec r(t_i)-\vec r(t_{i-1}))$$ \paragraph{Definiton:} Existiert der Grenzwert $\lim\limits_{\Delta Z \to 0} S(Z)$, so nennt man ihn \emph{Kurvenintegral von $\vec F$ längs $C$}. \subparagraph{Bezeichnung:} $\displaystyle\int\limits_C \vec F\cdot d\vec r$ \subsection{Satz} Ist $\vec F = (F_1,\,F_2,\,F_3)^T$ stetig und $C$ eine stückweise stetig differenzierbare Kurve, so ist $\vec F$ längs $C$ integrierbar und es gilt $$\int\limits_C \vec F \cdot d\vec r = \int\limits_a^b F_1(\vec r(t)) \cdot x_1'(t) + F_2(\vec r(t)) \cdot x_2' + F_3(\vec r(t))\cdot x_3'\; dt$$ wobei $\vec r(t) = (x_1(t),\,x_2(t),\,x_3(t))^T$. \subsubsection{Bemerkung} \index{Zirkulation} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Für ein Kurvenintegral längs einer \emph{geschlossenen} Kurve (d.h. $\vec r(a) = \vec r(b)$) schreibt man auch \begin{center} $\displaystyle\oint_C\vec F\,d\vec r$ \qquad (\emph{Zirkulation} von $\vec F$ längs $C$) \end{center} \item Auch die folgende Schreibweise ist üblich: $$C:\vec r(t) = (x(t),\,y(t),\,z(t)), \quad \vec F = (F_x,\, F_y,\,F_z) \quad \textnormal{(keine part. Abl.!)}$$ \begin{eqnarray} \int\limits_C\! \vec F \cdot d\vec r & = & \int\limits_C\! F_x(x,y,z)\,dx + F_y(x,y,z)\,dy + F_z(x,y,z)\,dz\\ & = & \int\limits_a^b\! F_x \cdot \dot x + F_y \cdot \dot y + F_z \cdot \dot z\; dt \end{eqnarray} \item Wird der Integrationsweg in umgekehrter Richtung durchlaufen, so tritt beim Integral ein Vorzeichenwechsel ein. \item Analog definiert man das Kurvenintegral für ein ebenes Vektorfeld $\vec F = (F_x,\,F_y)^T$ längs einer bestimmten Kurve $C : \vec r(t) = (x(t),\,y(t))^T$. Es gilt: $$\int\limits_C\! \vec F\cdot d\vec r = \int\limits_C \! F_x(x,y)\,dx + F_y(x,y)\,dy = \int\limits_a^b F_x\cdot\dot x + F_y \cdot \dot y\; dt$$ \end{enumerate} \subsection{Beispiel} \begin{minipage}{245pt} Vektorfeld: $F(x,y) = (xy^2,\,xy)^T$ \begin{eqnarray} I &=& \int\limits_C (xy^2,\,xy)^T\,d\vec r = \int\limits_C xy^2\,dx + xy\,dy =\\ & = & \int\limits_a^b x(t) \cdot y(t)^2 \cdot \dot x(t) + x(t) \cdot y(t) \cdot \dot y(t) \; dt \end{eqnarray} \end{minipage} \begin{minipage}{110pt} \flushright \begin{picture}(100,95) \put(0,40){$C_3^$} \put(34,76){$C_3^{*}$} \put(30,48){$C_1$} \put(57,28){$C_2$} \put(15,10){\vector(0,1){85}} \put(10,15){\vector(1,0){90}} \put(70,13){\line(0,1){4}} \put(13,70){\line(1,0){4}} \put(5,66.5){$1$} \put(68,3){$1$} \put(90,5){$x$} \put(6,85){$y$} \put(70,70){\circle{2}} \put(73,73){$P$} \thicklines \put(15,15){\vector(1,1){33}} \put(15,15){\line(1,1){55}} \qbezier(15,15)(50,15)(70,70) \put(56.5,41){\vector(2,3){0}} \put(15,15){\line(0,1){55}} \put(15,70){\line(1,0){55}} \put(15,15){\vector(0,1){33}} \put(15,70){\vector(1,0){33}} \vspace{0.5cm} \end{picture} \end{minipage} \paragraph{Integrationsweg $C_1$:} $x = t$, $\dot x = 1$, \quad $y = t$, $\dot y = 1$ \qquad $(0\leq t \leq 1)$ $$I = \int\limits_0^1\! t^3 + t^2 \, dt = \frac{1}{4} t^4 + \frac{1}{3}t^3\bigg\|_0^1 = \frac{7}{12}$$ \paragraph{Integrationsweg $C_2$:} $x = t$, $\dot x = 1$, \quad $y = t^3$, $\dot y = 3t^2$ \qquad $(0\leq t \leq 1)$ $$I = \int\limits_0^1 t^7+3t^6\,dt = \frac{1}{8}t^8 + \frac{3}{7}t^7\bigg\|_0^1 = \frac{31}{36}$$ \subsubsection{Integrationsweg $C_3 = C_3^* \land C_3^{*}$} \paragraph{Teilweg $C_3^$:} $x = 0$, $\dot x = 0$, \quad $y = t$, $\dot y = 1$ \qquad $(0\leq t \leq 1)$ $$I = \int\limits_0^1 0\,dt = 0$$ \paragraph{Teilweg $C_3^{*}$:} $x = t$, $\dot x = 1$, \quad $y = 1$, $\dot y = 0$ \qquad $(0\leq t \leq 1)$ $$I = \int\limits_0^1 t\,dt = \frac{1}{2}t^2\bigg\|_0^1 = \frac{1}{2}$$ \subsection{Satz} Es sei $\vec F$ ein stetig partiell differentierbares Vektorfeld in einem \emph{einfach--zusammenhängendem} Bereich. Dann sind die folgenden Eigenschaften gleichwertig: \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item Das Kurvenintegral $\int_C \vec F \cdot d\vec r$ ist längs einer Kurve $C$, die zwei beliebige Punkte $P$ und $Q$ verbindet, ist unabhängig vom eingeschlagenen Verbindungsweg (der im Bereich liegt). \item Das Kurvenintegral längs einer im Bereich liegenden geschlossenen Kurve hat stets den Wert $0$. \item $\vec F$ ist als Gradient einer Skalaren Funktion $\varphi$ (\emph{Potential}) darstellbar: $\vec F = \mathrm{grad}\,\varphi$. Für $\varphi$ gilt dann $\int\limits_C\vec F d\vec r = \varphi(Q) - \varphi(P)$. \item $\vec F$ ist wirbelfrei; $\mathrm{rot}\,\vec F = 0$. \end{enumerate} $\vec F$ heißt \emph{konservativ}, wenn eine dieser Bedingungen (dann auch alle) erfüllt ist. \index{konservativ (Vektorfeld)} \bigskip Ein Bereich heißt \emph{einfach--zusammenhängend}, wenn sich jede im Bereich liegende geschlossene Kurve auf einen Punkt zusammenziehen lässt. \index{einfach--zus.hängender Bereich} \section{Oberflächenintegral} \index{Oberflächenintegral} Wir betrachten eine Flüssigkeitsströmung mit der Geschwindigkeit $\vec v(P)$ (räumliches Vektorfeld). Wir interessieren uns für die Flüssigkeitsmenge, die pro Zeiteinheit durch ein bestimmtes Flächenstück $A$ hindurchströmt. \paragraph{Spezialfall:} $\vec v$ ist konstant, $A$ ist ein Rechteck \smallskip \begin{minipage}{240pt} Wir nehmen an, daß $\vec n_1 = \vec r \times \vec s$ "`zur selben Seite"' zeigt wie $\vec r$. \smallskip (Vereinbarung; \emph{orientierte Fläche}). \index{orientierte Fläche} \index{Fläche, orientiert} \bigskip Die gesuchte Flüssigkeit ist dann gleich dem Volumen des Spates, das durch $\vec r$, $\vec s$, und $\vec v$ aufgespannt wird: \end{minipage} \begin{minipage}{115pt} \flushright \begin{picture}(100,100) \thicklines \put(15,25){\vector(0,1){50}} \put(15,25){\vector(2,1){30}} \put(15,25){\vector(1,0){50}} \put(15,25){\vector(3,-1){30}} \thinlines \qbezier(15,35)(26,35)(25,22) \qbezier(23,29)(33,28)(25,22) \put(20,29){\circle{2}} \put(24,25.5){\circle{2}} \put(15,75){\line(2,1){30}} \put(45,40){\line(0,1){50}} \put(15,75){\line(1,0){50}} \multiput(45,40)(0,50){2}{\line(1,0){50}} \multiput(65,25)(0,50){2}{\line(2,1){30}} \multiput(65,25)(30,15){2}{\line(0,1){50}} \put(5,65){$\vec s$} \put(35,39){$\vec r$} \put(25,52){$A$} \put(57,15){$\vec v$} \put(41,5){$\vec n_1$} \end{picture} \end{minipage} $$V = \underbrace{[r,\,s,\,v]}_{\textnormal{\tiny Spatprodukt}} = \vec v \cdot (\vec r \times \vec s) = \vec v \cdot \vec n_1 = \vec v\cdot \vec n \cdot \textnormal{Flächeninhalt } A$$ \begin{center} \fbox{$\displaystyle \quad \vec n = \frac{\vec n_1}{\|\vec n_1\|} = \frac{\vec n_1}{\|\vec r \times \vec s\|} \quad $} \quad $\|\vec r \times \vec s\| =$ Flächeninhalt von $A$ \end{center} \paragraph{Der allgemeine Fall:} $A$ sei eine sogenannte \emph{orientierte Fläche}. Eine Fläche hat 2 Seiten. Sie heißt \emph{orientiert}, wenn eine Vereinbarung getroffen wurde, die Flächennormale $\vec n$, $\|\vec n\| = 1$ auf einer bestimmten Seite anzuheften. Bei einer geschlossenen Fläche, z.B. der Oberfläche einer Kugel, zeigt $\vec n$ vereinbarungsgemäß nach außen. \begin{itemize} \item Wir wählen eine Zerlegung $Z$ von $A$ in $n$ Teilflächen $A_1,\ldots,A_n$. $\Delta (Z)$ : der maximale Durchmesser (\emph{Feinheit} der Zerlegung) \item Aus jeder Teilfläche $A_k$ wählen wir einen Punkt $P_k$. Sei $\vec n(P_k)$ die Flächennormale im Punkt $P_k$ (Länge $1$). \item Wir bilden die Zwischensumme ($\|A_k\|$ : Flächeneinhalt) $$S(Z) = \sum\limits_{k=1}^n \vec v(P_k) \cdot \vec n(P_k) \cdot \|A_k\|$$ \end{itemize} \subsection{Definition} Existiert der Grenzwert $\lim\limits_{\Delta (Z) \to 0} S(Z)$, so wird er \emph{Oberflächenintegral} des Vektorfeldes $\vec v$ über die orientierte Fläche $A$ genannt und durch $$\iint_{(A)} \vec v \cdot \vec n \,dA$$ bezeichnet (\emph{Flußintegral}, \emph{Fluß des Vektorfeldes} $\vec v$ durch $A$). \index{Flußintegral} \subsubsection{Bemerkungen} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Das Oberflächenintegral über eine geschlossene Fläche wird mit $\oiint\limits_{(A)} \vec v \vec n \, dA$ bezeichnet (\emph{Hüllenintegral}).\index{Hüllenintegral} \item Setzt man speziell $\vec v = \vec n$, dann ist das Integral $\iint\limits_{(A)} 1\,dA$ und ist gleich dem Flächeninhalt von $A$. \end{enumerate} \subsection{Berechnung eines Oberflächenintegrals} Sei $\vec F$ ein Vektorfeld, die Fläche $A$ sei in Parameterdarstellung durch $\vec r(u,v)$, $(a \leq u \leq b,\, c \leq v \leq d)$ gegeben. Dann ist $\vec r_u(u_0,v_0) \times \vec r_v(u_0,v_0)$ ein Normalenvektor für die Fläche (für die Tangetialebene) im Punkt $(u_0,v_0)$. Für die Flächennormale $\vec n(u,v)$ wählen wir den Vektor $\vec n = \frac{\vec r_u \times \vec r_v}{\|\vec r_u \times \vec r_v\|}$. \bigskip Existiert das Integral $\iint\limits_{(A)} \vec F \cdot \vec n \,dA$, so gilt $$\iint\limits_{(A)} \vec F \cdot \vec n \, dA = \int\limits_a^b\! \int\limits_c^d \! \vec F(u,v) \cdot \left[\vec r_u(u,v) \times \vec r_v(u,v)\right]\, dv\,du$$ \paragraph{Spezialfall:} $\vec F = \vec n$ : Flächeninhalt von $A$: $$\int\limits_a^b\! \int\limits_c^d \! \|\vec r_u(u,v) \times \vec r_v(u,v)\|\, dv\,du$$ \subsection{Beispiel} Wir berechnen den Fluß des Vektorfeldes $\vec F(x,y,z) = (y,x,z^2)^T$ durch die Mantelfläche des folgenden Zylinders. \begin{minipage}[c]{100pt} \begin{picture}(100,110) \put(70,20){\vector(1,0){30}} \multiput(50,20)(4,0){5}{\line(1,0){2}} \put(50,70){\vector(0,1){30}} \multiput(50,20)(0,4){15}{\line(0,1){2}} \put(45,15){\vector(-1,-1){15}} \qbezier(46.5,16.5)(46.5,16.5)(48,18) \put(92,11){$y$} \put(73,42){$h$} \put(53,93){$z$} \put(22,0){$x$} \put(50,70){\line(1,0){20}} \put(55,76){$R$} \multiput(50,20)(0,50){2}{\circle{2}} \qbezier(70,70)(70,75)(50,75) \qbezier(70,70)(70,65)(50,65) \qbezier(30,70)(30,75)(50,75) \qbezier(30,70)(30,65)(50,65) \qbezier(70,20)(70,15)(50,15) \qbezier(30,20)(30,15)(50,15) \multiput(30,20)(40,0){2}{\line(0,1){50}} \put(0,-20){\qbezier(30,40)(30.5,42)(32,42.8) \qbezier(35,43.7)(36,44)(37,44.2) \qbezier(40,44.6)(41,44.7)(42,44.8) \qbezier(45,44.9)(46,44.9)(47,45) \qbezier(70,40)(69.5,42)(68,42.8) \qbezier(65,43.7)(64,44)(63,44.2) \qbezier(60,44.6)(59,44.7)(58,44.8) \put(49,45.2){\line(1,0){2}} \qbezier(55,44.9)(54,44.9)(53,45)} \end{picture} \end{minipage} \begin{minipage}[c]{255pt} Parameterdarstellung der Mantelfläche mit Zylinderkoordinaten ($R = 5$, $h = 10$): $$\vec r(\varphi,z) = (5\cdot \cos \varphi,\, 5\cdot \sin\varphi, z)^T$$ $$0 \leq z \leq 10 \qquad 0 \leq \varphi \leq 2\pi$$ \end{minipage} \bigskip Das Vektorfeld in Zylinderkoordinaten: $$\vec F(x,y,z) = (y,x,z^2)^T = (5\cdot \sin\varphi, 5\cdot \cos \varphi , z^2)^T$$ Berechnung des Normalenvektors: \begin{eqnarray} \vec r_{\varphi} \times \vec r_z &=&\! \!(-5 \cdot \sin \varphi, 5\cdot \cos \varphi, 0)^T\! \times\! (0,0,1)^T = \left\|\begin{array}{ccc}\vec e_1 & \vec e_2 & \vec e_3 \\\! - 5\cdot \sin\varphi \!& \!5\cdot \cos \varphi \! & 0 \\ 0 & 0 & 1\end{array}\right\|\\ & = & \!\!(5\cdot \cos\varphi, 5\cdot \sin\varphi,0)^T \end{eqnarray} Berechnung des Integranden: $$\vec F \cdot [\vec r_{\varphi} \times \vec r_z] = 50\cdot \sin\varphi \cdot \cos\varphi = 25 \cdot \sin2\varphi$$ Integration: $$\iint\limits_{(A)} \vec F \cdot \vec n \, dA = \int\limits_{0}^{2\pi}\!\int\limits_0^{10} \! 25 \cdot \sin 2\varphi \, dz \, d\varphi \stackrel{[\ldots]}{=} 0$$ \section{Integralsätze von Gauß und Stoke}\index{Integralsätze, Gauß, Stokes} \subsection{Satz (Gaußscher Integralsatz im Raum)}\index{Gaußscher Integralsatz} Es sei $\vec F$ ein stetig partiell differenzierbares Vektorfeld, $V$ ein räumlicher Bereich mit der geschlossenen Oberfläche $A$ und $\vec n$ die nach außen gerichtete Flächennormale. Dann gilt: $$\iiint_{V} \mathrm{div}\,\vec F\,dV = \oiint_{(A)}\vec F \cdot \vec n \; dA$$ \subsubsection{Anmerkungen} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Im Strömungsmodell hat $F$ die Bedeutung des Geschwindigkeitsfeldes einer strömenden Flüssigkeit: \bigskip \begin{tabular}{lcp{8cm}} $\oiint\limits_{(A)} \vec F \cdot \vec n \,dA$ & :& Flüssigkeitsmenge, die in der Zeiteinheit durch $A$ fließt.\\ $\iiint\limits_{V} \mathrm{div}\,\vec F\,dV$ &: &im Gesamtvolumen $V$ in der Zeiteinheit erzeugte oder vernichtete Flüssigkeitsmenge \end{tabular} \item Bei einem quellfreien Feld ($\mathrm{div}\,\vec F = 0$) ist der Gesamtfluß durch die geschlossene Oberfläche gleich $0$. \end{enumerate} \paragraph{Eine typische Anwendung:} Bestimmung des elektrischen Feldes $\vec E$ eines homogen geladenen Zylinders. \begin{description} \item[Maxwell:] $\mathrm{div}\,\vec E =\displaystyle \frac{\varrho_{el}}{\varepsilon_0} = \frac{\textnormal{Ladungsdichte}}{\textnormal{el. Feldkonstante}}$ \item[Gauß:] Integralsatz für den Zylinder mit Radius $R$ (sehr lang). Vollständige Rechnung siehe Papula Band 3, 9.3.1. \bigskip \begin{minipage}{6cm} $\displaystyle E(\varrho) = \left\{\begin{array}{ll}\displaystyle\frac{\varrho_{el}}{2\varepsilon_0}\cdot \varrho & \varrho \leq R\\ \\ \displaystyle \frac{\varrho_{el} \cdot R^2}{2\varepsilon_0} \cdot \varrho & \varrho \geq R\end{array} \right.$ \end{minipage} \begin{minipage}{5.5cm} \center \begin{picture}(110,50) \put(40,25){\circle{40}} \put(60,25){\vector(1,0){30}} \put(40,25){\circle{2}} \put(40,25){\line(1,1){14}} \put(80,30){$\vec E$} \put(40,35){$\varrho$} \end{picture} Querschnitt des Zylinders \end{minipage} \end{description} \subsection{Satz (Stoke'scher Integralsatz)}\index{Stoke'scher Integralsatz} Es sei $F$ ein stetig partiell differenzierbares Vektorfeld und $C$ eine \emph{einfach geschlossene} Kurve. Dann ist das Kurvenintegral von $\vec F$ längs $C$ gleich dem Oberflächenintegral der Rotation von $F$ über eine beliebige Fläche $A$, die durch $C$ berandet wird. $$\oint_{C}\vec F\,dr = \iint_{(A)} \mathrm{rot}\,\vec F \cdot \vec n \, dA$$ \begin{minipage}{9.8cm} Dabei wird die Umlaufrichtung für $C$ wie folgt festgelegt: Ein Beobachter, der in die Richtung von $\vec n$ schaut, durchläuft $C$ so, daß $A$ links liegen bleibt. \end{minipage} \begin{minipage}{2.5cm} \center \begin{picture}(50,55) \setlength{\unitlength}{0.5pt} \qbezier(15,80)(40,115)(65,75) \qbezier(15,80)(0,55)(20,35) \qbezier(20,35)(25,30)(20,25) \qbezier(20,25)(5,12)(30,4) \qbezier(30,4)(110,-8)(65,75) \put(1,85){$C$} \put(35,39){$A$} \put(60,74){\vector(1,3){10}} \put(63,107){$\vec n$} \put(33,96){\vector(-1,0){0}} \put(09,55){\vector(0,-1){0}} \put(55,2.5){\vector(1,0){0}} \put(73.5,58){\vector(-1,2){0}} \end{picture} \end{minipage} \subsubsection{Anmerkungen} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})}\index{Wirbelfluß}\index{Fluß, Wirbel--} \item $\oiint\limits_A \mathrm{rot}\,\vec F\,\vec n\,dA$ wird auch als \emph{Wirbelfluß} bezeichnet. Satz von Strokes: Der Wirbelfluß durch eine Fläche ist gleich der Zirkulation längs der Randkurve dieser Fläche. \item Der Wirbelfluß ist für alle Flächen, die von der gleichen Kurve berandet werden, gleich groß. \item Der Wirbelfluß durch eine geschlossene Fläche ist 0. Nach dem Gaußschen Integralsatz gilt nämlich (mit $\mathrm{rot}\,\vec F$ anstelle von $\vec F$): $$\iint\limits_{(A)} \mathrm{rot}\,\vec F\cdot \vec n \cdot dA = \iiint\limits_V \underbrace{\mathrm{div}(\mathrm{rot}\,\vec F)}_{0}\,dV = 0$$ \item Eine stetige Kurve $C : (x(t), y(t), z(t))$, $a \leq t \leq b$ heißt \emph{einfach geschlossen}, wenn $(x(a),y(a),z(a)) = (x(b),y(b),z(b))$ und $(x(t_1),y(t_1),$ $z(t_1))\ne (x(t_2),y(t_2),z(t_2))$, wenn $a\leq t_1 < t_2 < b$. \index{einfach geschlossene Kurve} \end{enumerate} \paragraph{Eine typische Anwendung:} Bestimmung des Magnetfeldes $\vec H$ eines \newline stromduchflossenen linearen Leiters. \begin{description} \item[Maxwell:] $\mathrm{rot}\, \vec H = \vec i$ \qquad (Stromdichte) \item[Stokes:] $C$: Kreisförmige magnetische Feldlinien, $A$: Kreisfläche \end{description} \begin{minipage}{2.5cm} \begin{picture}(63,90) \put(30,0){\line(0,1){80}} \put(30,40){\circle{40}} \put(35,67){$\vec i$} \put(53,35){$\vec H$} \put(30,73){\vector(0,1){0}} \put(50,42){\vector(0,1){0}} \put(30,40){\line(-1,1){14}} \put(15,43){$\varrho$} \put(33,9){$C$} \put(35,33){$A$} \end{picture} \end{minipage} \begin{minipage}{9.0cm} \center $$H(\varrho) = \frac{1}{2\pi} \cdot \frac{1}{\varrho} \qquad (\varrho > 0)$$ (siehe Papula, Band 3, 9.3.2.) \end{minipage} \chapter{Unendliche Reihen} \section{Zahlenreihen}\index{Zahlenreihen} \index{Partialsumme} \index{unendliche Reihe} \index{Reihe, unendliche} \subsection{Definition} Gegeben sei eine Folge $\{a_n\}\big._{n=1}^{\infty}$. Bezeichnen wir die Summe der ersten $n$ Glieder mit $s_n$, also $s_1 = a_1$, $s_2 = a_1 + a_2$, \ldots , $s_n = a_1 + a_2 + \cdots + a_n = \sum\limits_{k=1}^n a_k$, so erhalten wir eine neue Folge $\{s_n\}\big._1^{\infty}$, die Folge der \emph{Partialsummen} von $\{a_n\}$. Diese Folge heißt die zu $\{a_n\}$ gehörende \emph{unendliche Reihe}. \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})}\index{geometrische Reihe} \index{Reihe, geometrische} \item Geometrische Reihe: Es sei $a_1$, $q \in \mathbb{R} \smallsetminus 1$ geometrische Folge $a_k = a_1 \cdot q^{k-1}$ zugehörige geometrische Reihe: $s_n = \sum\limits_{k=1}^{n} a_1 \cdot q^{k-1} = a_1 + a_1 \cdot q + a_2 \cdot q^2 + \cdots + a_1 \cdot q^{n-1} = a_1 \frac{1-q^n}{1-q}$ \item Harmonische Reihe: $a_k = \frac{1}{k}$\index{harmonische Reihe} \index{Reihe, harmonische} $s_n = \sum\limits_{k=1}^n \frac{1}{k} = 1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n}$. z.B. $s_1 = 1$, $s_2 = 1,\!5$, $s_{50} = 5,\!18$ \end{enumerate} \subsection{Definition: Konvergenz} \index{Konvergenz (Reihen)} Konvergiert die Folge $\{s_n\}$ gegen eine Zahl $s$, so sagen wir, die unendliche Reihe sei \emph{konvergent} und besitze die \emph{Summe} $s$. Schreibweise: $$s = \sum\limits_{k=1}^{\infty} a_k = \lim\limits_{n \to \infty} \sum\limits_{k=1}^n a_k = a_1 + a_2 + a_3 + \cdots $$ Existiert der Grenzwert nicht, so heißt die Reihe \emph{divergent}.\index{Divergenz (Reihen)} \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Die geometrische Reihe mit $\|q\| < 1$ ist konvergent. $$\sum_{k=1}^{\infty} a_1 \cdot q^{k-1} = \lim\limits_{k \to \infty} a_1 \frac{1-q^n}{1-q} = \frac{a_1}{1-q}$$ \item $\displaystyle \sum\limits_{n=1}^{\infty} \frac{1}{n\cdot(n+1)} =$ ? \qquad $\displaystyle \frac{1}{n\cdot (n+1)} = \frac{1}{n} - \frac{1}{n+1}$ \begin{eqnarray} s_n &=& \sum\limits_{k=1}^n \left(\frac{1}{k} - \frac{1}{k+1}\right)\\ & =& \left(\frac{1}{1} - \frac{1}{2}\right) +\left(\frac{1}{2} - \frac{1}{3}\right) +\left(\frac{1}{3} - \frac{1}{4}\right) + \cdots + \left(\frac{1}{n} - \frac{1}{n+1}\right)\\ & = & 1 - \frac{1}{n+1} \qquad \Rightarrow \lim\limits_{n\to \infty} s_n = 1 \end{eqnarray} Bemerkung: $\sum\limits_{n=1}^{\infty} \frac{1}{n^2}= \frac{\pi}{6}$ (schwierig!) \item Die harmonische Reihe ist divergent: $\displaystyle \sum\limits_{n=1}^{\infty} = \infty$. $s_n = 1 + \frac{1}{2} + \bigg(\!\underbrace{\frac{1}{3} + \frac{1}{4}}_{> 2 \cdot \frac{1}{4} = \frac{1}{2}}\!\bigg) + \bigg(\!\underbrace{\frac{1}{5} + \cdots +\frac{1}{8}}_{> 4 \cdot \frac{1}{8} = \frac{1}{2}}\!\bigg) + \bigg(\! \underbrace{\frac{1}{9} + \cdots +\frac{1}{16}}_{> 8 \cdot{1}{16} = \frac{1}{2}}\!\bigg) +$ \hfill $+ \bigg(\!\underbrace{\frac{1}{2^k+1} + \cdots +\frac{1}{2^{k+1}}}_{> 2^k \cdot \frac{1}{2^{k+1}} = \frac{1}{2}}\!\bigg)$ \smallskip $\displaystyle \Rightarrow \lim\limits_{n\to \infty} s_n = \infty = \sum\limits_{n=1}^{\infty} \frac{1}{n}$ \end{enumerate} \subsection{Satz} Wenn $\sum\limits_{n=1}^{\infty} a_n$ und $\sum\limits_{n=1}^{\infty} b_n$ konvergente Reihen mit den Summen $a$ und $b$ sind und $\alpha,\; \beta \in \mathbb{R}$, dann gilt: $$\sum\limits_{n=1}^{\infty}(\alpha\cdot a_n + \beta \cdot b_n) = \alpha \cdot \sum\limits_{n=1}^{\infty} a_n + \beta \cdot \sum\limits_{n=1}^{\infty} b_n = \alpha \cdot a + \beta \cdot b$$ \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $\displaystyle\sum\limits_{n=1}^{\infty} \frac{3^{n+1} - 2^{n+1}}{6^n} = \sum\limits_{n=1}^{\infty} \frac{3^{n+1}}{6^n} - \sum\limits_{n=1}^{\infty}\frac{2^{n+1}}{6^n} = 3 \cdot \underbrace{\sum\limits_{n=1}^{\infty}\left(\frac{1}{2}\right)^n}_{\textnormal{\scriptsize geom. Reihe}} - 2 \cdot \underbrace{\sum\limits_{n=1}^{\infty}\left(\frac{1}{3}\right)^n}_{\textnormal{\scriptsize geom. Reihe}}$ $\displaystyle = 3 \cdot \frac{\frac{1}{2}}{1 - \frac{1}{2}} - 2 \cdot \frac{\frac{1}{3}}{1 - \frac{1}{3}} = 3 - 1 = 2$ \item $A$, $B$: Fahrradfahrer, $F$: Fliege \begin{minipage}{135pt} \begin{picture}(125,60) \put(5,5){\vector(1,0){110}} \put(115,5){\vector(-1,0){110}} \put(51,8){$20\,\mathrm{km}$} \multiput(5,35)(110,0){2}{\line(0,1){5}} \put(5,37.5){\line(1,0){110}} \put(0,23){$A\!\! \longrightarrow \! \raisebox{0.7pt}{$\scriptstyle 10\,\mathrm{\frac{km}{h}}$}$} \put(69,23){$\raisebox{0.7pt}{$\scriptstyle 10\,\mathrm{\frac{km}{h}}$} \! \longleftarrow \!\! B$ } \put(0,45){$F\!\! \longrightarrow \raisebox{0.7pt}{$\scriptstyle 20\,\mathrm{\frac{km}{h}}$}$} \end{picture} \end{minipage} \begin{minipage}{195pt} $A$, $B$, $F$ starten zusammen. $F$ fliegt, bis sie $B$ trifft, dann wendet sie und fliegt bis sie $A$ trifft, usw. Man berechne die Länge der Strecke, die $F$ bis zum Treffen von $A$ und $B$ zurücklegt hat. \end{minipage} \begin{eqnarray} s &=& \frac{2}{3} \cdot 20 + \frac{1}{3} \cdot \frac{2}{3} \cdot 20 + \frac{1}{3^2} \cdot \frac{2}{3} \cdot 20 + \cdots\\ & = & \frac{2}{3} \cdot 20 \cdot \left(1 + \frac{1}{3} + \frac{1}{3^2} + \cdots \right) \vphantom{\int\limits_a^b} \\ & = & \frac{2}{3}\cdot 20 \cdot \frac{1}{1-\frac{1}{3}} = 20 \end{eqnarray} Einfachere Lösung: $A$ und $B$ treffen sich nach einer Stunde $\rightarrow 20\,\mathrm{km}$ \end{enumerate} \subsection{Satz} \index{Konvergenz, notwendige Bed.} Wenn die Reihe $\sum\limits_{n=1}^{\infty} a_n$ konvergent ist, so ist $\lim\limits_{n \to \infty} a_n = 0$ \paragraph{Bemerkung:} Diese Bedingung ist nur notwendig aber nicht hinreichend für die Konvergenz (z.B. $\sum\limits_{n=1}^{\infty} \frac 1 n$ ist divergent obwohl $\lim\limits_{n \to \infty} \frac{1}{n} = 0$) \subsection{Satz: Majoranten-- und Minorantenkriterium}\index{Majorantenkriterium} \index{Minorantenkriterium} Gegeben sei die Reihe $\sum\limits_{n=1}^{\infty} a_n$. \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item Majorantenkriterium: Gibt es eine konvergente Reihe $\sum\limits_{n=1}^{\infty} c_n$, so daß $\|a_n\| \leq c_n$, $(n \in \mathbb{N})$, dann ist die Reihe $\sum\limits_{n=1}^{\infty} a_n$ konvergent. \item Minorantenkriterium: Gibt es eine Reihe $\sum\limits_{n=1}^{\infty} d_n$ mit $a_n \geq d_n$, $(n \in \mathbb{N})$, und $\sum\limits_{n=1}^{\infty} d_n = \infty$, dann ist $\sum\limits_{n=1}^{\infty} a_n = \infty$. \end{enumerate} \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Ist $\sum\limits_{n=1}^{\infty} \frac{1}{(n+1)^2}$ konvergent? Wir wissen $\sum\limits_{n=1}^{\infty} \frac{1}{n(n+1)}$ ist konvergent, und $\frac{1}{(n+1)^2} < \frac{1}{n(n+1)}$. $\Rightarrow$ Die Folge ist konvergent! \item Ist $\sum\limits_{n=1}^{\infty} \frac{1}{n^{\frac 1 3}}$ konvergent? \quad $\frac{1}{n^{\frac 1 3}} \geq \frac 1 n$, $\sum\limits_{n=1}^{\infty} \frac 1 n= \infty \quad \Rightarrow \quad \sum\limits_{n=1}^{\infty}\frac{1}{n^{\frac 1 3}} = \infty$ \end{enumerate} \subsection{Satz (Leibnitz)}\index{Satz von Leibnitz (Reihen)} \index{Leibnitz, Satz von (Reihen)} Ist $\{a_n\}$ eine Nullfolge (d.h. $\lim\limits_{n \to \infty} a_n = 0$) mit $a_1 > a_2 > a_3 > \cdots > 0$, so ist die Reihe $a_1 - a_2 + a_3 - a_4 + \cdots = \sum\limits_{n=1}^{\infty} (-1)^{n+1} \cdot a_n$ konvergent. \subsection{Definition: Absolute Konvergenz}\index{Konvergenz, absolute} \index{absolute Konvergenz} Eine Reihe $\sum\limits_{n=1}^{\infty} a_n$ heißt \emph{absolut konvergent}, wenn die Reihe $\sum\limits_{n=1}^{\infty} \|a_n\|$ konvergiert. \subsubsection{Bemerkungen} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $1 - \frac{1}{2} + \frac 1 3 - \frac 1 4 + \cdots$ ist konvergent nach Satz (13.1.10), aber nicht absolut konvergent, da $1 + \frac 1 2 + \frac 1 3 + \frac 1 4 + \cdots = \infty$. \item Konvergente Reihen, die nur nichtnegative Glieder besitzen, sind absolut konvergent. \item Jede absolut konvergente Reihe ist konvergent (folgt aus dem Majorantenkriterium). \end{enumerate} \subsection{Satz (Wurzelkriterium)} \index{Wurzelkriterium (Reihen)} Gegeben sei die Reihe $\sum\limits_{n=1}^{\infty} a_n$. Ist die Folge $\left\{\sqrt[n]{\|a_n\|}\right\}^{\infty}_{n=1}$ konvergent gegen den Grenzwert $a$, so gilt: \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Ist $a < 1$, so ist die Reihe konvergent \item Ist $a > 1$, so ist die Reihe divergent \end{enumerate} \subsection{Beispiel} $\sum\limits_{n=1}^{\infty} \left(\sqrt[n]{2} - 1\right)^n$ ist konvergent, da $\sqrt[n]{\|a_n\|} = \sqrt[n]{2} -1 \stackrel{n \to \infty}{-\!\!\!-\!\!\!-\!\!\!\longrightarrow} 0$ (wegen 7.1.6.ii). \subsection{Satz (Quotientenkriterium)} \index{Quotientenkriterium (Reihen)} Gegeben sei die Reihe $\sum\limits_{n=1}^{\infty} a_n$ mit $a_n \ne 0$. Ist die Folge $\left\{\|\frac{a_{n+1}}{a_n}\|\right\}_1^{\infty}$ konvergent gegen $a$, so gilt: \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Ist $a < 1$, so ist die Reihe konvergent \item Ist $a > 1$, so ist die Reihe divergent \end{enumerate} \subsection{Beispiel} $\sum\limits_{n=0}^{\infty} \frac{1}{n!}$ ist konvergent, da $\left\|\frac{a_{n+1}}{a_n}\right\| = \frac{\frac{1}{(n+1)!}}{\frac{1}{n!}} = \frac{n!}{(n+1)!} = \frac{1}{n+1} \stackrel{n \to \infty}{-\!\!\!-\!\!\!-\!\!\!\longrightarrow} 0 < 1$ (Man kann zeigen: $\sum\limits_{n=1}^{\infty} \frac{1}{n!} = e$) \subsection{Einige "`berühmte"' Reihen} $1 + \frac 1 2 + \frac 1 3 + \frac 1 4 + \cdots = \infty$ \quad harmonische Reihe \bigskip $\lim\limits_{n\to\infty} \left(1 + \frac 1 2 + \frac 1 3 + \cdots + \frac 1 n - \log_e 2\right) = 0,\!577215\ldots$ \quad (Eulersche Konstante) \bigskip $1 - \frac 1 2 + \frac 1 3 - \frac 1 4 + \cdots = \log_e 2 \approx 0,\!693$ \bigskip $\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \cdots = \frac{\pi^2}{6}$ \quad (Euler, 1736) \bigskip $\frac{1}{p_1} + \frac{1}{p_2} + \frac{1}{p_3} + \cdots = \infty$ \quad (Es gibt "`mehr"' Primzahlen als Quadratzahlen) $\frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \cdots = e$ \quad (Eulersche Zahl) \paragraph{allgemein:} $\frac{x^0}{0!} + \frac{x^1}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots = e^x \qquad (x \in \mathbb{R})$ \section{Potenzreihen} \index{Potenzreihe} \subsection{Definiton} Unter einer \emph{Potenzreihe} versteht man eine unendliche Reihe der Form $$P(x) = \sum\limits_{n=0}^{\infty} a_n \cdot (x-x_0)^n = a_0 \cdot (x-x_0)^0 + a_1 \cdot (x-x_0)^1 + a_2 \cdot (x - x_0)^2 + \cdots$$ (alle Zahlen reell). Die Menge aller Zahlen $x$, für die die Reihe konvergiert heißt \emph{Konvergenzbereich} der Potenzreihe. $a_n$ : \emph{Koeffizienten} der Potenzreihe, $x_0$ : \emph{Entwicklungspunkt}.\index{Konvergenzbereich (Potenzreihe)} \index{Koeffizienten (Potenzreihe)} \index{Entw.punkt (Potenzreihe)} \paragraph{Beispiel:} $P(x) = \sum\limits_{n=0}^{\infty} x^n = 1 + x + x^2 + x^3 + \cdots$ (geom. Reihe, $x_0 = 0$) Diese Reihe konvergiert genau dann, wenn $\|x\| < 1$ (siehe (13.1.4)). Der Konvergenzbereich ist also ein Intervall: $(-1,\,1)$, in diesem Intervall gilt: $P(x) = \frac{1}{1-x}$. \subsection{Satz} Zu jeder Potenzreihe $\sum\limits_{n=0}^{\infty} a_n \cdot (x-x_0)^n$ gibt es eine reelle Zahl $r$, \emph{Konvergenzradius} genannt, mit den folgenden Eigenschaften:\index{Konvergenzrad. (Potenzreihe)} \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item Die Potenzreihe konvergiert im Intervall $\|x - x_0\| < r$ \item Die Potenzreihe divergiert, wenn $\|x - x_0\| > r$ \item In den Randpunkten des Konvergenzbereiches kann die Reihe i.A. konvergieren oder divergieren \item Existiert der Grenzwert $\lim\limits_{n\to \infty} \left\|\frac{a_n}{a_{n+1}}\right\|$, so ist er gleich $r$ \end{enumerate} \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Für die geometrische Reihe ist $a_n = 1$, $r = \lim\limits_{n\to\infty}\left\|\frac{a_n}{a_{n+1}}\right\| = 1$. Divergenz in den Randpunkten $+1$ und $-1$: \begin{description} \item[$\mathbf{+1:}$]$ 1 + 1 + 1 + 1 + \cdots = \infty$ \item[$\mathbf{-1:}$]$ 1 - 1 + 1 - 1 + \cdots$, $s_n\! =\! \left\{\!\!\!\begin{array}{ll}1 & n \textnormal{ gerade}\\ 0 & n \textnormal{ ungerade}\end{array}\right.\! \Rightarrow\! \lim\limits_{n\to\infty} s_n$ existiert nicht \end{description} \item $\sum\limits_{n=0}^{\infty} \frac{x^n}{n!} \quad (x_0 = 0)$ Konvergenzradius: $r = \lim\limits_{n \to \infty}\left\|\frac{a_n}{a_{n+1}}\right\| = \lim\limits_{n \to \infty}\left\|\frac{(n+1)!}{n!}\right\| = \lim\limits_{n \to \infty} (n+1) = \infty$ \smallskip $r = \infty \Rightarrow$ Die Reihe konvergiert für alle $x \in \mathbb{R} =$ Konvergenzbereich \item Der Konvergenzradius der Potenzreihe $\sum\limits_{n=0}^{\infty} n! \cdot x^n$ $r = \lim\limits_{n \to \infty} \|\frac{a_n}{a_{n+1}}\| = \lim\limits_{n \to \infty} \frac{n!}{(n+1)!} = \lim\limits_{n\to \infty} \frac{1}{n+1} = 0$ Die Reihe ist konvergent für $x= 0$. \item $\sum\limits_{n=1}^{\infty} \frac{x^n}{n} \quad (x_0 = 0) \qquad r = \lim\limits_{n \to \infty} \frac{n+1}{n} = 1$ Randpunkte: \begin{description} \item[$\mathbf{x=1}$:] $1 + \frac 1 2 + \frac 1 3 + \cdots = \infty$ \item[$\mathbf{x=-1}$:] $1 - \frac 1 2 + \frac 1 3 - \cdots$ konvergiert nach Satz von Leibnitz \end{description} \end{enumerate} \subsection{Eigenschaften von Potenzreihen} \begin{itemize} \item Eine Potenzreihe ist im Innern ihres Konvergenzradius absolut konvergent \item Eine Potenzreihe darf im Innern ihres Konvergenzradius gliedweise differenziert und integriert werden. Die neuen Potenzreihen besitzen dabei denselben Konvergenzradius wie die ursprüngliche Reihe. Beispiel: $\frac{d}{dx} e^x = \frac{d}{dx}\sum\limits_{n=0}^{\infty}\frac{x^n}{n!} = \sum\limits_{n=0}^{\infty} \frac{d}{dx} \frac{x^n}{n!} = \sum\limits_{n=1}^{\infty} \frac{nx^{n-1}}{n!} = \sum\limits_{n=1}\frac{n^{n-1}}{(n-1)!} = \sum\limits_{n=0}^{\infty} \frac{x^n}{n!} = e^x$ \item Zwei Potenzreihen dürfen im gemeinsamen Konvergenzbereich gliedweise addiert und subtrahiert werden. Die neuen Potenzreihen konvergieren dann mindestens im gemeinsamen Konvergenzbereich \end{itemize} \subsection{Definition: Taylor--Reihe} \index{Taylor--Reihe} $f$ sei eine auf $(a,\,b)$ beliebig oft differenzierbare Funktion und $x_0 \in (a,\,b)$. Dann heißt $$\sum\limits_{k=0}^{\infty} \frac{f^{(k)}(x_0)}{k!} (x-x_0)^k$$ die \emph{Taylor--Reihe} von $f$ im Punkt $x$. Es gibt drei Möglichkeiten: \begin{itemize} \item die Reihe konvergiert für alle $x \in\mathbb{R}$ \item die Reihe besitzt einen positiven Konvergenzradius \item die Reihe konvergiert nur für $x =x_0$ \end{itemize} Nach dem Satz von Taylor (8.4) gilt für jedes $n$ ($t$ zwischen $x_0$ und $x$): $$f(x) = \sum\limits_{k=0}^{n} \frac{f^{(k)}(x_0)}{k!} \cdot (x-x_0)^k + \frac{f^{(n+1)}(t)}{(n+1)!} \cdot (x-x_0)^{n+1}$$ Deshalb konvergiert die Taylor--Reihe in $x$ genau dann gegen $f(x)$. wemm dort das Restglied gegen 0 konvergiert. \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $f(x) = e^x, \quad x_0 = 0, \quad f^{(k)}(x) = e^x$ $f^{(k)} = 0$ $(\forall k)$ : Restglied $\frac{f^{(n+1)}(t)}{(n+1)!} x^{n+1} \stackrel{n\to\infty}{\longrightarrow} 0$ ($t$ zwischen $x_0$ und $x$) \smallskip $\lim\limits_{n\to\infty} \frac{x^{n+1}}{(n+1)!} = 0$\qquad für alle $x \in \mathbb{R}$ $f^{(n+1)}(t) = e^t \Rightarrow e^x = \sum\limits_{n=0}^{\infty} \frac{x^n}{n!} = 1 + x + \frac{1}{2}x + \frac{1}{6}x + \cdots$ \item Weitere Beispiele: \begin{tabular}{llll} $\sin x$ & = & $x - \frac{1}{3!} \cdot x^3 + \frac{1}{5!}\cdot x^5 - \frac{1}{7!}\cdot x^7 + \cdots$ & $(x \in \mathbb{R})$ \vspace{0.2cm}\\ $\sinh x$ & = & $x + \frac{1}{3!} \cdot x^3 - \frac{1}{5!}\cdot x^5 + \frac{1}{7!}\cdot x^7 - \cdots$ & $(x \in \mathbb{R})$ \vspace{0.2cm}\\ $\cos x$ & = & $x - \frac{1}{2!} \cdot x^2 + \frac{1}{4!}\cdot x^4 - \frac{1}{6!}\cdot x^6 + \cdots$ & $(x \in \mathbb{R}) \vspace{0.2cm}$ \end{tabular} \item $f(x) = \ln (1+x)$ \smallskip $f'(x) = \frac{1}{1+x}, \quad f''(x) = - \frac{1}{(1-x)^2}, \quad f^{(n)} = (-1)^{n-1}\cdot (n-1)! \quad (n \geq 1)$ \smallskip $f^{(n)}(0) = (-1)^{n-1}\cdot (n-1)!$ Taylor--Reihe für $f$: $\sum\limits_{n=1}^{\infty} \frac{(-1)^{n-1}}{n} \cdot x^n = \ln (1+x) \qquad (-1 < x <1)$ Konvergenzradius: $\lim\limits_{n \to \infty}\left\|\frac{a_n}{a_{n+1}}\right\| = 1$ \item Wir definieren die Funktion $f$ durch $f(x) = e^{-\frac{1}{x^2}}$, wenn $x \ne 0$ und $f(0) = 0$. \begin{minipage}{115pt} \begin{picture}(100,60) \put(0,10){\vector(1,0){100}} \put(50,0){\vector(0,1){50}} \put(53,43){$y$} \put(92,1){$x$} \put(48.5,38){\line(1,0){3}} \put(40,35){$1$} \qbezier(5,38)(25,38)(30,25) \qbezier(30,25)(35,10)(50,10) \qbezier(95,38)(75,38)(70,25) \qbezier(70,25)(65,10)(50,10) \end{picture} \end{minipage} \begin{minipage}{215pt} Man kann zeigen, daß $f$ beliebig oft differenzierbar ist und $f^{(k)}(0) = 0$ für alle $k = 1,\,2,\,3,\, \ldots$ \end{minipage} $\Rightarrow$ Die Taylor--Reihe ist die Nullfunktion und stellt $f$ somit nur im Punkt $x=0$ dar. \end{enumerate} \section{Fourier--Reihen} \index{Fourier--Reihe} \subsection{Einleitung} In einfachen Fällen läßt sich ein periodischer Vorgang (z.B. Wechselspannung) durch eine sogenannte \emph{harmonische Schwingung} \[y(t) = A \cdot \sin (\omega \cdot t + \varphi) \quad \textnormal{ oder } \quad y(t) = A\cdot \cos (\omega \cdot t + \varphi)\] beschrieben. \begin{minipage}{170pt} \begin{picture}(150,75) \put(0,30){\vector(1,0){145}} \multiput(5,30)(60,0){2}{\qbezier(0,0)(15,30)(30,0)\qbezier(30,0)(45,-30)(60,0) \put(45,-20){\line(0,1){5}} } \put(50,12.5){\vector(1,0){60}} \put(110,12.5){\vector(-1,0){60}} \put(62,0){$T = \frac{2\pi}{\omega}$} \put(5,25){\vector(1,0){10}} \put(15,25){\vector(-1,0){10}} \multiput(5,22.5)(10,0){2}{\line(0,1){5}} \put(15,0){\vector(0,1){60}} \put(6,12){$\frac{\varphi}{\omega}$} \put(13.5,45){\line(1,0){3}} \put(2,42){$A$} \put(132,21){$t$} \put(18,55){$y$} \end{picture} \end{minipage} \begin{minipage}{150pt} \vspace{0.4cm} \begin{tabular}{l@{ }l@{ }l} $\omega$ &:& \emph{Kreisfrequenz} \vspace{0.2cm}\\ $\|A\|$ &:& \emph{Amplitute} \vspace{0.2cm}\\ $T$ &:& \emph{Schwingungsdauer} \end{tabular} \end{minipage} \newpage Nicht sinusförmige aber periodische Vorgänge: \begin{itemize} \item Kippschwingung (Sägezahn) \item Sinusimpuls (nur positive/negative Halbwellen) \end{itemize} \paragraph{Frage:} Läßt sich eine nichtsinusförmige Schwingung aus harmonischen Schwingungen zusammensetzen? \subsection{Definition: Trigonometrische Reihe} \index{trigonometrische Reihe} \index{Reihe, trigonometrische} \index{Kosinusreihe} \index{Sinusreihe} Man nennt eine Reihe der Form \[\frac{a_0}{2} + \sum\limits_{n=1}^{\infty} \left[a_n \cdot \cos (n\cdot \omega \cdot x) + b_n \cdot \sin (n\cdot \omega \cdot x)\right]\] eine \emph{trigonometrische Reihe}. Sind alle $a_n$ (alle $b_n$) gleich 0, so spricht man von einer \emph{Sinusreihe} (\emph{Kosinusreihe}). Im Weiteren betrachten wir den Spezialfall $\omega = 1$, der allgemeine Fall läßt sich auf diesen zurückführen. \subsubsection{Bemerkungen} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $\sin (n\cdot x)$ und $\cos (n\cdot x)$ sind periodisch mit der Periode $2\pi$ \item Die Menge aller $x$, für die die obige Reihe konvergiert, läßt sich nicht so einfach beschreiben wie bei Potenzreihen \end{enumerate} \subsection{Satz} Wenn $\sum\limits_{n=1}^{\infty} \|a_n\| < \infty$ und $\sum\limits_{n=1}^{\infty} \|b_n\| < \infty$, dann konvergiert die trigonometrische Reihe \[f(x) = \frac{a_0}{2} + \sum\limits_{n=1}^{\infty} \left[a_n \cdot \cos (n\cdot x) + b_n \cdot \sin (n\cdot x)\right]\] für jedes $x \in \mathbb{R}$. Die Funktion $f$ ist stetig und periodisch mit der Periode $2\pi$. \paragraph{Bemerkung:} Die Bedingungen des Satzes sind nur hinreichend aber nicht notwendig für die Konvergenz. So konvergiert z.B. die Reihe $\sum\limits_{n=1}^{\infty}\frac{\sin(nx)}{n}$ für jedes $x \in \mathbb{R}$, obwohl $\sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty$. \subsection{Definition} \index{Fourier--Koeffizienten} \index{Koeffizienten (Fourier)} Es sei $f$ über $[0,\,2\pi]$ integrierbar. Dann heißen die Zahlen \[a_n = \frac{1}{\pi} \cdot \int\limits_{0}^{2\pi} f(x) \cdot \cos (n\cdot x) \,dx \qquad (n = 0,1,2,\ldots)\] \[b_n = \frac{1}{\pi} \cdot \int\limits_{0}^{2\pi} f(x) \cdot \sin (n\cdot x) \,dx \qquad (n = 1,2,3,\ldots)\] die \emph{Fourier--Koeffizienten} der Funktion $f$. Die mit diesen Zahlen gebildete Reihe \[\frac{a_0}{2} + \sum\limits_{n=1}^{\infty} \left[a_n \cdot \cos (n\cdot x) + b_n \cdot \sin (n\cdot x)\right]\] heißt die \emph{Fourier--Reihe} von $f$. \subsubsection{Bemerkungen} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item In den Integralen kann man $\int\limits_0^{2\pi}$ durch $\int\limits_{-\pi}^{\pi}$ ersetzen \item Ist $f$ eine gerade Funktion, so ist $b_n = 0$, ist $f$ eine ungerade Funktion, so gilt $a_n = 0$ für alle $n$ \end{enumerate} Eine Funktion heißt \emph{stückweise glatt} auf $[a,b]$, wenn $f'$ bis auf endlich viele Punkte in $[a,b]$ existiert und $f'$ stückweise stetig ist. \subsection{Satz} Es sei $f$ eine $2\pi$--periodische Funktion auf $\mathbb{R}$, die auf $[0,2\pi]$ stückweise glatt ist. Dann konvergiert die zu $f$ gehörende Fourier--Reihe $s(x)$ für alle $x \in \mathbb R$ und es gilt: \[s(x) = \frac{f(x+0) + f(x-0)}{2}\] ($+0$, $-0$ : Grenzwerte von links bzw. rechts). Ist $x$ eine Stetigkeitsstelle, so ist $s(x) = f(x)$. \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Rechteckkurve $f$ mit $f(x) = 1$, $0 \leq x \leq \pi$ und $f(x) = -1$, $\pi < x < 2\pi$ \smallskip $f$ ist ungerade $\Rightarrow a_n = 0$ $b_n = \frac{1}{\pi}\int\limits_0^{2\pi} f(x) \cdot \sin(n\cdot x) \, dx = \frac{1}{\pi} \int\limits_0^{\pi} 1\cdot \sin (n\cdot x) \,dx + \int\limits_{\pi}^{2\pi}(-1)\cdot \sin(n \cdot x)\,dx$ $\phantom{b_n} = \frac{1}{\pi}\left[-\frac 1 n \cdot \cos (n \cdot x)\right]_0^{\pi} - \left[-\frac 1 n \cdot \cos (n \cdot x)\right]_{\pi}^{2\pi} = \frac{2}{n \cdot \pi} (1-\cos(n\cdot \pi))$ \newpage $\Rightarrow b_n = 0$, falls $n=2k$ gerade ist und $b_n = b_{2k-1} = \frac{4}{\pi} \cdot \frac{1}{2k-1}$, falls $n$ ungerade ist. Wir erhalten: $f(x) = \frac{4}{\pi} \cdot \sum\limits_{k=1}^{\infty} \frac{\sin(2k-1)\cdot x}{2k-1} = \frac{4}{\pi}\left[\sin x + \frac{1}{3} \sin 2x + \frac 1 5 \sin 5x + \cdots\right]$ \item Sägezahn--Funktion: $f(t) = \frac{A}{2\pi} \cdot t - \frac A 2, \quad 0 < t < 2\pi, \quad f(0) = 0$ \smallskip \begin{minipage}{130pt} \begin{picture}(130,100) \put(0,40){\vector(1,0){120}} \put(40,0){\vector(0,1){90}} \multiput(10,38.5)(30,0){4}{\line(0,1){3}} \put(0,30){$-\pi$} \put(67,30){$\pi$} \put(94,30){$2\pi$} \put(10,40){\line(1,1){30}} \put(40,10){\line(1,1){60}} \multiput(40,40)(60,0){2}{\circle{2}} \multiput(38.5,10)(0,60){2}{\line(1,0){3}} \put(20,7){$-\frac{A}{2}$} \put(43,67){$\frac{A}{2}$} \put(31,82){$y$} \put(113,30){$x$} \end{picture} \end{minipage} \begin{minipage}{200pt} $f(t)$ ist ungerade $\Rightarrow a_n = 0$ \begin{eqnarray} b_n &=&\frac{1}{\pi} \int\limits_0^{2\pi}\left(\frac{A}{2\pi} - \frac{A}{2}\right)\cdot\sin(nt)\,dt\\ & = & \ldots \:\: = - \frac{A}{n\cdot \pi} \end{eqnarray} \end{minipage} \smallskip $f(t) = - \frac{A}{\pi} \cdot \sum\limits_{n=1}^{\infty} \frac{1}{n} \cdot \sin (nt) = - \frac{A}{\pi} \left(\sin t + \frac 1 2 \sin(2t) + \frac 1 3 \sin (3t)+ \cdots \right)$ \smallskip $t = \frac{\pi}{2} \Rightarrow f(\frac{2}{\pi}) = \frac{A}{2\pi} \cdot \frac{\pi}{2} - \frac{A}{2} = -\frac{A}{4} = \sum\limits_{l=0}^{\infty} \frac{1}{(2l+1)}(-1)^l$ $\Rightarrow \sum\limits_{l=0}^{\infty} \frac{1}{(2l+1)} (-1)^l = \frac{A}{4}$ \end{enumerate} \chapter{Gewöhnliche Differentialgleichungen}\index{Differentialgleichungen} \section{Grundlegende Begriffe} Mathematische Beschreibung physikalischer Probleme. \subsection{Beispiel: Schwingende Feder} Eine Kugel der Masse $m$ hänge an einer Feder mit Federkonstante $k$. Zur Zeit $t=0$ werde die Feder um $x_0$ gedehnt und dann losgelassen. \paragraph{Aufgabe:} Beschreibe die Bewegung \smallskip \begin{minipage}{70pt} \begin{picture}(60,110) \put(0,100){\line(1,0){50}} \multiput(25,100)(0,-50){2}{\line(0,-1){5}} \multiput(20,87.5)(0,-10){4}{\qbezier(0,0)(10,-5)(10,-5)} \multiput(20,87.5)(0,-10){4}{\qbezier(0,0)(10,5)(10,5)} \qbezier(30,92.5)(30,92.5)(25,95) \qbezier(30,52.5)(30,52.5)(25,50) \multiput(25,41)(0,-21){2}{\circle{8}} \multiput(25,40)(0,-4){5}{\line(0,-1){2}} \put(10,41){\vector(0,1){20}} \put(10,41){\vector(0,-1){20}} \put(40,100){\vector(0,-1){100}} \multiput(38.5,41)(0,-21){2}{\line(1,0){3}} \put(45,37){$0$} \put(45,17){$x_0$} \end{picture} \end{minipage} \begin{minipage}{285pt} Nach unten zeigende Bewegungsrichtung. Nullpunkt: Mittelpunkt der Kugel in Ruhelage. \smallskip $x(t)$: Lage des Mittelpunktes der Kugel zur Zeit $t$ \begin{description} \item[Grundgesetz der Mechanik:] $m \cdot a = m \cdot x'' = \sum F$ \item[Federkraft:] $-k\cdot x(t)$, $(k > 0)$ \end{description} \end{minipage} \vspace{0.5cm} Daraus folgt für die Bewegung: \begin{equation} m\cdot x''(t) = -k\cdot x(t) \end{equation} \subsection{Definition}\index{Ordnung (DGL)} \index{Differentialgleichungen!gewöhnlich} \index{Differentialgleichungen!partiell} Eine Gleichung zur Bestimmung einer Funktion heißt \emph{Differentialgleicheung}, wenn sie mindestens eine Ableitung der gesuchten Funktion enthält. Die Ordnung der in der Differentialgleichung vorkommenden höchsten Ableitung der gesuchten Funktion heißt \emph{Ordnung der Differentialgleichung}. Hängt die gesuchte Funktion von nur einer Veränderlichen ab, so nennt man die Differentialgleichung \emph{gewöhnlich}. Enthält die Differentialgleichung partielle Ableitungen, so heißt sie \emph{partiell}. \subsubsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Die Gleichung (14.1) ist eine gewöhnliche Differentialgleichung der Ordnung 2 für die Funktion $x(t)$. \item $y'''(x) + 2y'(x) + 3y(x) = \sin x$ ist eine gewöhnliche Differentialgleichung dritter Ordnung für $y(x)$. \item $\frac{\partial u(x,y)}{\partial x} = \frac{\partial u(x,y)}{\partial y}$ ist eine partielle Differentialgleichung der Ordnung 1 für die Funktion $u(x,y)$ \end{enumerate} \index{implizite Form (DGL)} \index{explizite Form (DGL)} Eine gewöhnliche Differentialgleichung der Ordnung $n$ hat die \emph{implizite Form} \[F\left(x,y,y',y'',\ldots,y^{(n)}\right) = 0\] falls die Auflösung nach der höchsten Ableitung möglich ist, \emph{explizite Form} \[y^{(n)} = f\left(x,y,y',y'',\ldots,y^{(n-1)}\right)\] \paragraph{Beispiel:} $y' = x \Rightarrow y(x) = \frac{x^2}{2}+c, \quad c \in\mathbb{R}$ \bigskip Die Menge aller Lösungen einer Differentialgleichung heißt deren \emph{allgemeine Lösung} oder \emph{allgemeines Integral}. \index{Integral, allgemeines (DGL)} \index{allgemeines Integral (DGL)} \paragraph{Beispiel:} Die allgemeine Lösung der DGL (14.1) mit $m=1$, $k=1$ \[X=\{x:x(t) = c_1 \cdot \cos t + c_2 \cdot \sin t, \: c_1, c_2 \in \mathbb R\}\] Probe durch Einsetzen der Lösung in die DGL: \[-1 \cdot x''(t) = - 1 \cdot x(t)\] Beweis später. \bigskip Es ist üblich auch $x(t) = c_1 \cdot \cos t + c_2 \cdot \sin t$, $c_1,c_2 \in \mathbb R$ als allgemeine Lösung zu bezeichnen. Die allgemeine Lösung enthält Konstanten: \emph{Integrationskonstanten}. \bigskip \emph{Spezielle} oder \emph{partikuläre} Lösung: spezielle Wahl aller Konstanten in der allgemeinen Lösung. \index{spezielle Lösung (DGL)} \index{partikuläre Lösung (DGL)} \bigskip Gegeben sei die Differentialgleichung \index{Anfangswertproblem (DGL)} \[y^{(n)} = f\left(x,y',y'',y''',\ldots,y^{(n-1)}\right)\] sowie $x_0,\, y_0,\, y_1,\, \ldots\, , y_{n-1} \in \mathbb R$ : \emph{Anfangswertproblem}: Die Aufgabe, eine Funktion zu finden, die der Differentialgleichung genügt und die Bedingungen \begin{equation} y(x_0)=y_0, \; y'(x_0) = y_1, \; y''(x_0) = y_2,\; \ldots,\; y^{(n-1)}(x_0) = y_{n-1} \end{equation} $y_0,\,y_1,\,y_2,\,\ldots,\,y_{n-1}$: \emph{Anfangswerte}, \quad (14.2): \emph{Anfangsbedingungen} \paragraph{Beispiel:} Im Beispiel (14.1.1) sei der Anfangswert $x_0$ und der Anfangszeitpunkt $t=0$. \smallskip Anfangsbedingungen: $x(0) = 0$ und $x'(0) = 0$ \begin{eqnarray} x(t) & = & c_1\cdot \cos t + c_2 \cdot\sin t\qquad c_1,\,c_2 = \mathbb R\\ x'(t) & = & -c_1 \cdot\sin t + c_2 \cdot\cos t \end{eqnarray} Einsetzen der Randbedingungen: \begin{eqnarray} x_0 & = & x\phantom{'}(0) = \phantom{-} c_1 \cdot \cos (0) + c_2 \cdot \sin(0) \qquad \Rightarrow c_1 = x_0\\ 0 & = & x'(0) = -c_1 \cdot \sin (0) + c_2 \cdot \cos(0) \qquad \Rightarrow c_2 = 0 \end{eqnarray} Die gesuchte Funktion lautet also $x(t) = x_0 \cdot \cos t$ \section{Differentialgleichung 1. Ordnung} \index{Differentialgleichungen!1. Ordnung} Spezielle Lösungsmethoden \subsection{Trennung der Veränderlichen}\index{Trennung d. Veränderl. (DGL)} Eine Differentialgleichung der Form $y' = f(x) \cdot g(y)$ heißt \emph{separabel}.\index{separabel (DGL)} \index{Differentialgleichungen!separabel} \subsubsection{Lösungsmethode für separable Differentialgleichungen} Beispiel: $y' = y \cdot \cos x$ \begin{enumerate} \item $\frac{dy}{dx} = y \cdot \cos (x) \qquad / \cdot dx, \; \cdot \frac{1}{y}$ \item $\frac{1}{y} \cdot dy = \cos (x) \cdot dx$ \item $\int\frac 1 y \cdot dy = \int\cos (x) \cdot dx$ \item $\ln\|y\| = \sin(x) + c$ \item $\|y\| = e^{\sin(x)} \cdot e^c = e^{\sin(x)} \cdot c_1 \qquad (c_1 = e^c > 0)$ \item $y = c_1 \cdot e^{\sin (x)}$ oder $y = -c_1 \cdot e^{\sin (x)}$ \end{enumerate} \smallskip $\Rightarrow y=c_1 \cdot e^{\sin(x)}$ für $c_1 \in \mathbb R$ \subsection{Substitution eines linearen Terms} Die Differentialgleichung $y' = f(ax + by + c)$, $(a,b,c \in \mathbb R)$ kann durch Substitution $z=ax + by + c$ in eine separable Differentialgleichung überführt werden: \[z'=a-b\cdot y' = a-b\cdot f(z)\] $z'=a-b\cdot f(z) \cdot 1$ ist separabel. \paragraph{Beispiel:} $y' = (x+y)^2, \quad z = x+y \Rightarrow z' = 1+y' = 1+z^2$ \begin{enumerate} \item $\frac{dz}{dx} = 1 + z^2$ \item $\frac{1}{1+z^2} \cdot dz = 1 \cdot dx$ \item $\int\frac{1}{1+z^2}\cdot dz = \int 1 \cdot dx$ \item $\arctan z = x + c \qquad \frac{-\pi}{2} \leq x+c \leq \frac{\pi}{2}$ \item $z = \tan(x+c)$ \item $x+y = \tan (x+c)$ \qquad für $\frac{-\pi}{2} + c \leq x \leq \frac{\pi}{2} + c$ \end{enumerate} $\Rightarrow y = -x+\tan(x+c)$ \subsection{Gleichgradige Differentialgleichungen}\index{gleichgradige DGL} \index{Differentialgleichungen!gleichgradig}\index{Ähnlichkeits--DGL}\index{Differentialgleichungen!Ähnlichkeits--} Die Differentialgleichung $y' = f\left(\frac y x\right)$ heißt \emph{gleichgradige Differentialgleichung} oder \emph{Ähnlichkeitsdifferentialgleichung}. Substitution: \[z = \frac y x \Rightarrow y = x \cdot z \Rightarrow y' = 1 \cdot z + x \cdot z' = f(z) \Rightarrow z' = \frac 1 x (f(z) - z)\] Diese Differentialgleichung ist separabel. \paragraph{Beispiel:} $(x^2 + y^2) \cdot y' = x\cdot y$ \[y' = \frac{x\cdot y}{x^2+y^2} = \frac{\frac y x}{1 + (\frac y x)^2}\] Mit Substitution: $z = \frac y x$, $y' = x\cdot z + z$ ergibt sich ($x,y \ne 0$) \[x\cdot z' + z = \frac{z}{1+z^2} \Rightarrow x\cdot z' = \frac{z}{1+z^2} - \frac{z(1+z^2)}{1+z^2} = \frac{-z^3}{1+z^2}\] \[\Rightarrow \frac{1+z^2}{z^3} \cdot \frac{dz}{dx} = -\frac 1 x \Rightarrow \int\left(\frac{1}{z^3} + \frac{1}{z}\right) \,dz = - \int\frac{1}{x}\,dx\] \[\frac{z^{-2}}{2} + \ln \|z\| = - \ln\|x\| + c\] Rücksubstitution: Setzt man $z = \frac y x$ ein, so folgt: \[-\frac 1 2 \frac{x^2}{y^2} + \ln\left\|\frac y x\right\| = - \ln\|x\| + c\] \[-\frac 1 2 \frac{x^2}{y^2} + \ln\left\|y\right\| = c \Rightarrow x^2 = 2\cdot(\ln\|y\| - c)\cdot y^2\] Lösung in expliziter Form, $y=0$ ist auch Lösung. \subsection{Lineare Differentialgleichung erster Ordnung}\index{lineare DGL. 1. Ordnung} \index{Differentialgleichungen!linear 1. Ordnung} Die Differentialgleichung $y' + f(x) \cdot y = g(x)$ heißt \emph{lineare Differentialgleichung erster Ordnung}. Man nennt sie \emph{homogen}, wenn $g=0$. $g$ heißt \emph{Störglied}.\index{Störglied (DGL)}\index{homogene DGL} \index{Differentialgleichungen!homogen} \paragraph{Satz:} Es sei $Y_h$ die Menge aller Lösungen der homogenen Differentialgleichung $y' + y \cdot f(x) = 0$ und $y_p$ eine spezielle Lösung der inhomogenen Differentialgleichung $y' + f(x) \cdot y = g(x)$. Dann ist $Y = \{y : y= y_h + y_p,\; y_h \in Y_h\}$ die allgemeine Lösung der inhomogenen Differentialgleichung. \subparagraph{Probe:} $y' = {y_h}' + {y_p}'$ einsetzen: ${y_h}' + {y_p}' + f(x)(y_h + y_p) = 0 + g(x)$ \paragraph{Lösungsmethode:} Erläuterung an dem Beispiel $y' + 2xy = x$ \begin{enumerate} \renewcommand{\labelenumi}{\Roman{enumi}.} \item Lösung der homogenen Gleichung $y' + 2xy = 0$ $\Rightarrow \frac{dy}{dx} + 2xy = 0 \Rightarrow \frac{dy}{y} = -2x \cdot dx \Rightarrow \ln\|y\| = -2\frac{x^2}{2} + c$ \smallskip $\Rightarrow \|y\| = k_1 \cdot e^{-x^2} \Rightarrow y_h = k \cdot e^{-x^2} \quad (k \in \mathbb R)$ \item Bestimmung einer speziellen Lösung der inhomogenen Gleichung. Methode: \emph{Variation der Konstanten}. Wir ersetzen in der Lösung der homogenen Gleichung die Konstante $k$ durch $k(x)$:\index{Variation der Konstanten (DGL)} \[y_p = k(x) \cdot e^{-x^2} \Rightarrow {y_p}' = k'(x) \cdot e^{-x^2} + k(x) \cdot e^{-x^2}\cdot (-2x)\] Einsetzen der speziellen Lösung $y_p$ in $y' + 2xy = x$: \[ k'(x) \cdot e^{-x^2} + k(x) \cdot e^{-x^2}\cdot (-2x) + 2x \cdot k(x)\cdot e^{-x^2} = x \Rightarrow k'(x) \cdot e^{-x^2} = x\] \[k'(x) \cdot (x) = x \cdot e^{x^2} \Rightarrow k(x) = \int x\cdot e^{x^2} \,dx = \frac{e^{x^2}}{2} + c\] Wir setzen $\displaystyle c=0 \Rightarrow k(x) = \frac{e^{x^2}}{2} \Rightarrow y_p = \frac 1 2$. \bigskip Allgemeine Lösung: $\displaystyle y = k \cdot e^{-x^2} + \frac 1 2$ \quad $(k \in \mathbb R)$ \end{enumerate} \paragraph{Beispiel:} Ladevorgang eines Kondensators \begin{minipage}{125pt} \center \begin{picture}(105,110) \put(0,30){\line(1,0){60}} \multiput(60,30)(20,0){2}{\circle{2}} \put(60,30){\line(2,1){20}} \put(80,30){\line(1,0){20}} \multiput(0,30)(100,0){2}{\line(0,1){50}} \put(0,80){\line(1,0){15}} \multiput(15,75)(20,0){2}{\line(0,1){10}} \multiput(15,75)(0,10){2}{\line(1,0){20}} \put(25,30){\circle{20}} \put(35,80){\line(1,0){38.5}} \put(76.5,80){\line(1,0){23.5}} \thicklines\multiput(73.5,73)(3,0){2}{\line(0,1){14}}\thinlines \multiput(40,73)(50,0){2}{\vector(2,1){0}} \put(21,88){$R$} \put(71,90){$C$} \put(19,62){$u_R$} \put(69,62){$u_C$} \multiput(0,0)(50,0){2}{\qbezier(10,73)(25,66)(40,73)} \qbezier(10,20)(25,13)(40,20) \put(10,20){\vector(-2,1){0}} \put(10,5){$u = U_0$} \end{picture} \end{minipage} \begin{minipage}{230pt} Maschensatz: $u_R + u_C = u = U_0$ \bigskip $u_R = R \cdot i = R \cdot \frac{dq}{dt} = R \cdot \frac{d}{dt}(C\cdot u_C) = R \cdot C \cdot \dot U_C$ \bigskip $\Rightarrow \underbrace{RC}_{\displaystyle \tau} \cdot \dot u_c + u_c = U_0$ \end{minipage} \smallskip homogene Differentialgleichung: $\displaystyle \dot u_C = - \frac{1}{\tau} \cdot u_C$ \begin{enumerate} \renewcommand{\labelenumi}{\Roman{enumi}.} \item Trennung der Veränderlichen $\int\frac{du_C}{u_C} = - \frac{1}{\tau} \int dt \quad \Rightarrow \quad \ln\|u_C\| = - \frac{1}{\tau} \cdot t + c \quad \Rightarrow \quad u_C = e^{-\frac{1}{\tau} \cdot t} \cdot c_1$ \item Variation der Konstanten $u_{Cp} = e^{-\frac{1}{\tau} \cdot t} \cdot c_1(t) \Rightarrow \dot u_{Cp} = e^{-\frac{1}{\tau} \cdot t} \cdot \left(-\frac{1}{\tau}\right) \cdot c_1(t) + {c_1}'(t) \cdot e^{-\frac{1}{\tau} \cdot t}$ Einsetzen: $U_0 = \tau\cdot\left(\frac{e^{-\frac{1}{\tau} \cdot t}\cdot c_1(t)}{-\tau} + {c_1}'(t) \cdot e^{-\frac{1}{\tau} \cdot t}\right) + e^{-\frac{1}{\tau} \cdot t} \cdot {c_1}(t)$ \smallskip $\Rightarrow \tau \cdot {c_1}'(t) \cdot e^{-\frac{1}{\tau} \cdot t} = U_0 \Rightarrow \tau \cdot {c_1}'(t) = U_0 \cdot e^{\frac{t}{\tau}}$ \smallskip $\Rightarrow c_1(t) = U_0 \cdot e^{\frac{t}{\tau}}$ \end{enumerate} Allgemeine Lösung: $\displaystyle u_C = c \cdot e^{-\frac{t}{\tau}} + U_0$ \paragraph{Anfangswertaufgabe:} $u_C(0) = 0$ \begin{minipage}{220pt} \begin{eqnarray} u_C &=& c \cdot e^{-\frac{t}{\tau}} + U_0\\ 0 & = & c \cdot 1 + U_0 \Rightarrow c = -U_0\\ \Rightarrow u_C & = & (-U_0) \cdot e^{-\frac{t}{\tau}} + U_0 \end{eqnarray} \end{minipage} \begin{minipage}{135pt} \begin{picture}(120,100) \put(15,10){\vector(0,1){70}} \put(10,15){\vector(1,0){110}} \put(3,70){$u_c$} \put(0,50){$U_0$} \multiput(14,53)(4,0){25}{\line(1,0){2}} \qbezier(15,15)(15,50)(100,52) \put(115,5){$t$} \end{picture} \end{minipage} \subsection{Satz} Die allgemeine Lösung der inhomogenen Differentialgleichung $y' + f(x) \cdot y = g(x)$ ist \[y = e^{-\int f(x)\,dx} \cdot \left(k + \int \! g(x) \cdot e^{\int f(x)\,dx} \, dx\right) \qquad (k \in \mathbb R)\] \subsection{Geometrische Deutung, Isoklinen}\index{Isoklinen (DGL)} Wir betrachten die Differentialgleichung $y' = f(x,y)$ \begin{enumerate} \renewcommand{\labelenumi}{(\Alph{enumi})} \item \textbf{Voraussetzung:} Das zu $y(x_0) = y_0$ gehörige Anfangswertproblem besitzt eine eindeutige Lösung. In jedem Punkt $P(x_0,y_0)$ ist ein Funktionswert $f(x_0,y_0)$ gegeben. Wegen $y' = f(x_0,y_0)$ ist dieser Wert der Anstieg der durch $P(x_0,y_0)$ gehenden Lösungskurve an dieser Stelle. Annäherung der Lösungskurve in einer Umgebung von $P$ durch ein kleines Tangentenstück, \emph{Richtungselement}. \bigskip \begin{minipage}{200pt} \paragraph{Methode:} Wir wählen eine Länge des Richtungselementes mit dem Mittelpunkt $(x_0,y_0)$. Sei $(x_1,y_1)$ der rechte Eckpunkt. $y_1$ ist dann eine Näherung für die gesuchte Lösung an der Stelle $x_1$. Wir konstruieren ein weiteres Richtungselement mit dem Mittelpunkt $(x_1,y_1)$, usw. \end{minipage} \begin{minipage}{130pt} \begin{picture}(130,100) \put(25,10){\vector(0,1){80}} \put(20,15){\vector(1,0){105}} \put(118,6){$x$} \put(15,84){$y$} \multiput(45,14)(0,4){6}{\line(0,1){2}} \multiput(24,35)(4,0){6}{\line(1,0){2}} \multiput(55,14)(0,4){8}{\line(0,1){2}} \multiput(24,45)(4,0){8}{\line(1,0){2}} \multiput(67.5,14)(0,4){10}{\line(0,1){2}} \multiput(24,52)(4,0){11}{\line(1,0){2}} \put(41.5,8){$\scriptstyle x_0$} \put(14,33.5){$\scriptstyle y_0$} \put(52,8){$\scriptstyle x_1$} \put(14,44){$\scriptstyle y_1$} \put(64.5,8){$\scriptstyle x_2$} \put(14,51){$\scriptstyle y_2$} \put(35,25){\line(1,1){20}} \put(42.5,39){\line(2,1){25}} \end{picture} \end{minipage} \item\textbf{Isoklinenverfahren:} Definition: Gegeben sei die Differentialgleichung $y'\! =\! f(x,y)$. Jede durch die Gleichung $f(x,y) = c$ bestimmte Kurve heißt Isokline der Differentialgleichung zum Wert $c$. Mit Hilfe der Isoklinen wollen wir geometrisch Näherungslösungen skizzieren: \begin{enumerate} \renewcommand{\labelenumii}{(\arabic{enumii})} \item Zeichnung einiger Isoklinen \item Wir tragen auf ihnen einige Richtungselemente ein \item Die Näherungen für die Lösungskurven sind dann so zu ziehen, daß sie in den Schnittpunkten mit den Isokliden parallel zu den zugehörigen Richtungselementen verlaufen \end{enumerate} \end{enumerate} \paragraph{Beispiel:} $y' = x^2 + y^2$ \smallskip Die Isoklinen $f(x,y) = c$ sind Kreise mit dem Radius $\sqrt{c}$. \bigskip \begin{minipage}{150pt} \begin{picture}(140,120) \put(70,0){\vector(0,1){120}} \put(0,60){\vector(1,0){140}} \qbezier(115,60)(115,78.639612)(101.819806,91.819806) \qbezier(70,105)(88.639612,105)(101.819806,91.819806) \qbezier(25,60)(25,41.360388)(38.180194,28.180194) \qbezier(70,15)(51.360388,15)(38.180194,28.180194) \qbezier(25,60)(25,78.639612)(38.180194,91.819806) \qbezier(70,105)(51.360388,105)(38.180194,91.819806) \qbezier(115,60)(115,41.360388)(101.819806,28.180194) \qbezier(70,15)(88.639612,15)(101.819806,28.180194) \qbezier(92.5,60)(92.5,69.319806)(85.909903,75.909903) \qbezier(70,82.5)(79.319806,82.5)(85.909903,75.909903) \qbezier(47.5,60)(47.5,50.680194)(54.090097,44.090097) \qbezier(70,37.5)(60.680194,37.5)(54.090097,44.090097) \qbezier(47.5,60)(47.5,69.319806)(54.090097,75.909903) \qbezier(70,82.5)(60.680194,82.5)(54.090097,75.909903) \qbezier(92.5,60)(92.5,50.680194)(85.909903,44.090097) \qbezier(70,37.5)(79.319806,37.5)(85.909903,44.090097) \qbezier(81.25,60)(81.25,64.659903)(77.9549515,67.9549515) \qbezier(70,71.25)(74.659903,71.25)(77.9549515,67.9549515) \qbezier(58.75,60)(58.75,55.340097)(62.0450485,52.0450485) \qbezier(70,48.75)(65.340097,48.75)(62.0450485,52.0450485) \qbezier(58.75,60)(58.75,64.659903)(62.0450485,67.9549515) \qbezier(70,71.25)(65.340097,71.25)(62.0450485,67.9549515) \qbezier(81.25,60)(81.25,55.340097)(77.9549515,52.0450485) \qbezier(70,48.75)(74.659903,48.75)(77.9549515,52.0450485) \multiput(42.5,55)(45,0){2}{\line(1,1){10}} \multiput(0,0)(0,-17.2){2}{\multiput(44.2,63.6)(41.6,0){2}{\line(1,1){10}}} \multiput(0,0)(0,-31.8){2}{\multiput(49.1,70.9)(31.8,0){2}{\line(1,1){10}}} \multiput(0,0)(0,-41.6){2}{\multiput(56.4,75.8)(17.2,0){2}{\line(1,1){10}}} \multiput(65,77.5)(0,-45){2}{\line(1,1){10}} \multiput(23.3,53.2)(90,0){2}{\line(1,4){3.4}} \multiput(0,0)(0,-17.6){2}{\multiput(24.2,62)(88.3,0){2}{\line(1,4){3.4}}} \multiput(0,0)(0,-34.4){2}{\multiput(26.7,70.4)(83.1,0){2}{\line(1,4){3.4}}} \multiput(0,0)(0,-50){2}{\multiput(30.9,78.2)(74.8,0){2}{\line(1,4){3.4}}} \multiput(0,0)(0,-63.6){2}{\multiput(36.5,85.0)(63.6,0){2}{\line(1,4){3.4}}} \multiput(0,0)(0,-74.8){2}{\multiput(43.3,90.6)(50.0,0){2}{\line(1,4){3.4}}} \multiput(0,0)(0,-83.1){2}{\multiput(51.1,94.8)(34.4,0){2}{\line(1,4){3.4}}} \multiput(0,0)(0,-88.3){2}{\multiput(59.5,97.3)(17.6,0){2}{\line(1,4){3.4}}} \multiput(68.3,98.2)(0,-90){2}{\line(1,4){3.4}} \multiput(52,58.3)(22.5,0){2}{\line(4,1){13.6}} \multiput(0,0)(0,-16){2}{\multiput(55.3,66.3)(16,0){2}{\line(4,1){13.6}}} \multiput(63.2,69.6)(0,-22.5){2}{\line(4,1){13.6}} \put(134,51){$x$} \put(61,114){$y$} \end{picture} \end{minipage} \begin{minipage}{205pt} Isoklinen und dazugehörige Richtungselemente für $c = 4 \Rightarrow \sqrt c = 2$, $c = 1 \Rightarrow \sqrt{c} = 1$, $c = 0,\!25 \Rightarrow \sqrt{c} = \frac{1}{2}$ \end{minipage} \subsection{Definition: Exakte Differentialgleichungen}\index{Differentialgleichungen!exakte} \index{exakte DGLn} Mit \begin{equation} P(x,y)\,dx + Q(x,y)\,dy = 0 \end{equation} meint man die Aufgabe, bei konstanten Funktionen $P$ und $Q$, entweder Funktionen $y=y(x)$ zu bestimmen, die der Differentialgleichung $P(x,y) + Q(x,y)\cdot y' = 0$ genügen (Division durch $dx$), oder die Aufgabe, Funktionen $x = x(y)$ zu ermitteln, die der Differentialgleichung $P(x,y)\cdot x' + Q(x,y) = 0$ geügen (Division durch $dy$). Die Differentialgleichung (14.3) heißt \emph{exakt}, falls es eine Funktion $U(x,y)$ mit \[\frac{\partial U}{\partial x}(x,y) = P(x,y) \qquad \textnormal{ und } \qquad \frac{\partial U}{\partial y} (x,y) = Q(x,y)\] gibt. \paragraph{Bemerkung:} (14.3) ist genau dann exakt, wenn der Ausdruck $P(x,y)\,dx + Q(x,y)\,dx$ ein vollständiges Differential ist (siehe Def. 6.5.5). Aus Satz (6.5.6) folgt: Die Differentialgleichung ist genau dann exakt, wenn \[\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x}\] \paragraph{Beispiel:} Die Differentialgleichung \[e^{-y} + (1+x\cdot e^{-y}) \cdot \underbrace{y'}_{\frac{dy}{dx}} = 0 \longrightarrow \underbrace{e^{-y}}_{P}\,dx + \underbrace{(1-x\cdot e^{-y})}_{Q} \,dy = 0\] ist exakt: $P_y = -e^{-y} = Q_x = - e^{-y}$ \subsection{Satz} Ist die Differentialgleichung (14.3) exakt, so werden die Lösungen $y=y(x)$ bzw. $x=x(y)$ durch \[U(x,y) = c \qquad (c \in \mathbb R)\] \emph{implizit} dargestellt. \subsection{Beispiel} $e^{-y}\,dx + (1-x\cdot e^{-y})\,dy = 0$ ist exakt, deshalb existiert eine Funktion $U$ mit $U_x = e^{-y}$ und $U_y = 1 - x \cdot e^{-y}$. \smallskip $U_x$ nach $x$ integrieren ($y$ als Konstante betrachten): $U_y(x,y) = x\cdot e^{-y} + C(y)$. Dieses Ergebnis wird abgeleitet und in $U_y$ eingesetzt: \[\underbrace{-x\cdot e^{-y} + C'(y)}_{U_y'(x,y)} = 1 + x \cdot e^{-y} \Rightarrow C'(y) = 1 \Rightarrow C(y) = y + K\] (wir wählen $K =0$, da nur eine $U$ benötigt wird) $\Rightarrow U = x \cdot e^{-y} + y$ \newpage Implizite Angabe der Lösungen: \[U(x,y) = x \cdot e^{-y} + y = c \qquad (x \in \mathbb{R})\] \subsection{Integrierender Faktor}\index{integrierender Faktor (DGL)}\index{äquivalente DGL} \index{Differentialgleichungen!äquivalente} Ist die Differentialgleichung \[P(x,y)\,dx + Q(x,y)\,dy = 0\] nicht exakt, so versucht man mit einem \emph{integrierenden Faktor} (oder \emph{Multiplikator}) $v = v(x,y)$ eine \emph{äquivalente Differentialgleichung} (d.h. mit den selben Lösungen) zu erhalten, die exakt ist. Man betrachte dazu den Ansatz \[\underbrace{v(x,y) \cdot P(x,y)\,dx}_{\hat P(x,y)} + \underbrace{v(x,y) \cdot Q(x,y)\,dy}_{\hat Q(x,y)} = 0\] Dabei ist $v(x,y) \ne 0$ so zu bestimmen, daß $\hat P_y = \hat Q_x$ gilt. Mitunter existieren Multiplikatoren, die nur von $x$ oder von $y$ allein abhängen. \begin{enumerate} \item Nehmen wir an, daß $\frac{P_y - Q_x}{Q} = h(x)$, also die linke Seite unabhängig von $y$ ist. Dann existiert ein Multiplikator $v=v(x)$, der aus der homogenen linearen Differentialgleichung $v'(x) - h(x) \cdot v(x) = 0$ bestimmt werden kann. \item Ist $\frac{P_y - Q_x}{Q} = h(y)$, also die linke Seite unabhängig von $x$, so existiert ein Multiplikator $v = v(y)$, der aus der Gleichung $v'(y) + h(y) \cdot v(y) = 0$ bestimmt wird. \end{enumerate} \subsection{Beispiel} \[\underbrace{y\cdot(2y-3x)}_{P}\, dx + \underbrace{x\cdot(2y -x)}_{Q}\, dy = 0\] $P_y - Q_x = 2y - x$ \bigskip $\displaystyle\frac{P_y-Q_x}{Q} = \frac{2y-x}{x\cdot (2y-x)} = \frac 1 x$ \quad hängt nur von $x$ ab $\Rightarrow v(x)$ \bigskip $\displaystyle v'(x) - \frac 1 x \cdot v(x) = 0 \Rightarrow \frac{dv}{v} = \frac{dx}{x}$ \quad (separabel) \bigskip $\Rightarrow \ln\|v\| = \ln\|x\| + c \quad \stackrel{c=0}{\longrightarrow} \quad v(x) = x$ \qquad ist ein Multiplikator \[\underbrace{xy\cdot(2y-3x)}_{\hat P}\, dx + \underbrace{x^2\cdot(2y -x)}_{\hat Q}\, dy = 0 \qquad \textnormal{ist exakt}\] \subsubsection{Bestimmung von U} $U_x = \hat P = xy\cdot (2y +3x) \longrightarrow U = \int xy\cdot (2y + 3x)\,dx = x^2y^2 - x^2y + c(x)$ $U_y = \hat Q = x^2 \cdot (2y - x)$ $U_y = 2x^2\cdot y - x^3 + c'(y) = 2x^2y - x^3 \quad \Rightarrow c' = 0 \Rightarrow c(y) = k$ \bigskip Sei $k = 0$: $U = x^2 y^2 - x^3y$ \bigskip Die allgemeine Lösung: $U(x,y) = x^2 y^2 - x^3 y = c \qquad (c \in \mathbb R)$ \section{Physikalische Anwendungen} \subsection{Freier Fall aus großer Höhe (Fall ohne Reibung)} \begin{tabular}{lll} $K$ & : & Körper\\ $m$ & : & Masse von $K$\\ $s(t)$ &:& Entfernung von $K$ vom Erdmittelpunkt zur Zeit $t$\\ $v(t)$ & : & Fallgeschwindigkeit von $K$\\ $R$ & : & Erdradius ($\approx 6370\,\mathrm{km}$)\\ $g$ & : & Erdbeschleunigung ($\approx 9,\!81\,\frac{\mathrm m}{\mathrm s^2}$) \end{tabular} \begin{description} \item[Gravitationskraft:] $\displaystyle F = - g \cdot m \cdot \frac{R^2}{s^2}$ \item[Grundgesetz der Mechanik:] $\displaystyle F = m \cdot a = m \cdot \frac{dv}{dt}$ \end{description} Daraus ergibt sich für die Bewegung die Gleichung: \[\quad m \cdot \frac{dv}{dt} = - g \cdot m \cdot \frac{R^2}{s^2}\] Nach der Kettenregel ist: $\displaystyle \frac{dv}{dt} = \frac{dv}{ds}\frac{ds}{dt}=\frac{dv}{ds} \cdot v$ \bigskip $\displaystyle \Rightarrow \quad v \cdot \frac{dv}{ds} = - g \cdot \frac{R^2}{s^2}$ \quad (wobei wir $v$ in Abhängigkeit von $s$ betrachten) \bigskip Diese Differentialgleichung ist separabel. Lösung: \begin{equation} v^2 = \frac{2\cdot g \cdot R^2}{s} + 2\cdot k \qquad (k \in \mathbb R) \end{equation} \subsubsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Ein Körper falle aus einer Höhe von $10\,\mathrm{km}$ auf die Erde. Man berechne die Geschwindigkeit, mit der er an der Erdoberfläche ankommt. $v_0 = v (6370 + 10) = 0 \quad \Rightarrow \quad s = 6380 \textnormal{ in (14.4)}$ \bigskip $\displaystyle 2\cdot k= \frac{2\cdot g \cdot R^2}{6380}$ \bigskip $v^2 = 2 \cdot 9,\!81 \cdot 1000 \cdot 6370 \cdot \left(1-\frac{6370}{6380}\right) \quad \Rightarrow \quad v = 1593\,\mathrm{\frac{km}{h}}$ \item Fordern wir $\lim\limits_{s\to \infty} v(s) = 0$, so ist $k = 0$ und \[v^2(s) = \frac{2\cdot g\cdot R^2}{s} \quad \textrm{und} \quad v(R) = \sqrt{2\cdot g\cdot R} = 11,\!8\,\mathrm{\frac{km}{s}}\] Mit dieser Geschwindigkeit würde ein Körper (beliebiger Masse) aus dem "`Unendlichen kommend"' auf der Erdoberfläche auftreffen. Umgekehrt müsste ein Körper (beliebige Masse) diese Geschwindigkeit mindestens haben, wenn er den Anziehungsbereich der Erde verlassen soll (\emph{Fluchtgeschwindigkeit}). \end{enumerate} \subsection{Radioaktiver Zerfall} Beim radioaktiven Zerfall ist die Geschwindigkeit des Zerfalls proportional zu der vorhandenen Menge des Stoffes. \smallskip $n(t)$ : die Menge zur Zeit $t$ \smallskip $n'(t) = - \lambda \cdot n(t), \qquad (\lambda > 0) \qquad (n'(t) \textrm{ ist negativ, DGL separabel})$ \paragraph{Lösung:} $n(t) = k \cdot e^{-\lambda \cdot t} \qquad (k\in\mathbb R)$ \bigskip Für $t=0: \quad n(0) = k \Rightarrow n(t) = n(0) \cdot e^{-\lambda t}$ \subsection{Newtonsches Abkühlungsgesetz} Die Abkühlungsgeschwindigkeit eines Körpers in bewegter Luft ist proportional zu der Temperaturdifferenz zwischen der Temperatur des Körpers und der Temperatur der Luft. \smallskip $T(t)$ : Temperatur des Körpers zur Zeit $t$ \smallskip $T_L$ : Temperatur der Luft \[T'(t) = - \alpha \cdot (T(t) - T_L) \qquad (a > 0)\] Diese Differentialgleichung ist separabel. Lösung: \[T(t) = T_L + k \cdot e^{-\alpha t} \qquad (k \in \mathbb{R})\] \paragraph{Beispiel:} Ein Körper kühle sich in 10 Minuten von $300^{\circ}\mathrm{C}$ auf $200^{\circ}\mathrm{C}$ ab, wobei die Temperatur der Luft $30^{\circ}\mathrm{C}$ beträgt. Wann hat sich dieser Körper auf $100^{\circ}\mathrm{C}$ abgekühlt? \begin{eqnarray} T(t) & = & 30 + k \cdot e^{-\alpha t}\\ T(0) & = & 300 = 30 + k\cdot e^{-\alpha \cdot 0} = 30 + k \quad \Rightarrow \quad k=270\\ T(10) & = & 200 = 30 + 270 \cdot e^{-\alpha \cdot 10} \hspace{1.46cm} \Rightarrow \quad \alpha \approx 0,\!0463\\ T(t) & \approx & 30 + 270 \cdot e^{-0,0463 \cdot t} \end{eqnarray} Gesucht: $T(t) = 100 \quad \Rightarrow \quad t \approx 29,\!16$ \subsection{Bewegung mit Reibung} An einem Massepunkt der Masse $m$ greife die äußere Kraft $F$ an, der Bewegung wirke dabei die zur Geschwindigkeit proportionale Reibungskraft $F_r = - r \cdot v(t), \quad (r > 0)$ entgegen. \smallskip $r$ : \emph{Reibungskoeffizient}, \quad $v(t)$ : Geschwindigkeit \paragraph{Grundgesetz der Mechanik:} $\displaystyle m \cdot v'(t) = F - r \cdot v(t) \Rightarrow v + \frac{m}{r} \cdot \frac{dV}{dt} = \frac{F}{r}$ \smallskip Lineare Differentialgleichung erster Ordnung. Lösung: \[v(t) = k \cdot e^{-\frac{m}{r}\cdot t} + \frac F r\] ist z.B. $v=0$ zur Zeit $t=0$, so folgt $k = - \frac{F}{r}$. \[v(t) = \frac{F}{r} \cdot \left(1-e^{-\frac m r \cdot t}\right), \qquad \lim\limits_{t\to \infty} = \frac F r\] \section{Differentialgleichungen zweiter Ordnung}\index{Differentialgleichungen!2. Ordnung} \emph{Lineare Differentialgleichungen} zweiter Ordnung mit \emph{konstanten Koeffizienten}: \[y'' + a_1 \cdot y' + a_0 \cdot y = f(x) \qquad (a_0,\,a_1 \in \mathbb R)\] Ist $f = 0$, so heißt die Differentialgleichung \emph{homogen}, sonst \emph{inhomogen}. $f$: \emph{Störfunktion}, \emph{Störglied} \subsection{Satz} Ist $Y_h$ die Menge aller Lösungen der homogenen Differentialgleichung \[y'' + a_1 \cdot y' + a_0 \cdot y = 0\] und $y_p$ eine spezielle Lösung der inhomogenen Gleichung \[y'' + a_1 \cdot y' + a_0 \cdot y = f(x)\] so ist $Y = \{y: y=y_h + y_p \textrm{ mit } y_h \in Y_h\}$ die allgemeine Lösung der inhomogenen Gleichung. \paragraph{Lösungsweg:} Man bestimmt \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item alle Lösungen der homogenen Differentialgleichung \item eine Lösung der inhomogenen Differentialgleichung (Ansatz) \end{enumerate} \subsection{Die homogene Differentialgleichung}\index{charakteristisches Polynom} \index{Polynom, charakteristisches} Das Polynom $p(\lambda) = \lambda^2 + a_1 \cdot \lambda + a_0$ heißt \emph{charakteristisches Polynom} der Differentialgleichung, die Gleichung $p(\lambda) = 0$ heißt \emph{charakteristische Gleichung}. $p(\lambda) = 0$ hat zwei Lösungen, $\lambda_{1/2} = - \frac{a_1}{2} \pm \sqrt{\left(\frac{a}{2}\right)^2 - a_0}$. \subsection{Satz} Es seien $\lambda_1$ und $\lambda_2$ die Lösungen der charakteristischen Gleichung der Differentialgleichung $y'' + a_1 \cdot y' + a_0 \cdot y = 0$. Dann ist die allgemeine Lösung dieser Differentialgleichung: \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item $y=A_1 \cdot e^{\lambda_1 x} + A_2 \cdot e^{\lambda_2 x}, \quad (A_1,\,A_2 \in\mathrm R) \quad$ falls $\lambda_1,\,\lambda_2 \in \mathbb R$ und $\lambda_1 \ne \lambda_2$ \item $y = (A_1 + A_2 \cdot x) \cdot e^{\lambda_1 x}, \quad (A_1,\,A_2 \in \mathbb R) \quad$ falls $\lambda_1 = \lambda_2 \in \mathbb R$ \item $y=(A_1 \cdot \cos (\beta x) + A_2 \sin (\beta x)) \cdot e^{\alpha x} \quad$ falls $\lambda_1,\,\lambda_2 = \alpha \pm i\,\beta$ mit $\beta \ne 0$ \end{enumerate} \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $y'' + 4y' - 5y = 0$, char. Gleichung: $\lambda^2 + 4\lambda - 5 = 0 \Rightarrow \lambda_1 = 1,\,\lambda_2 = -5$ allgemeine Lösung: $y_H = A_1 \cdot e^x + A_2 \cdot e^{-5x}$ \item $y'' + 4y' + 4y = 0$, char. Gleichung: $\lambda^2 + 4\lambda + 4 = 0 \Rightarrow \lambda_1 = \lambda_2 = -2$ allgemeine Lösung: $y_H = (A_1 + A_2 \cdot x) \cdot e^{-2x}$ \item $y'' + 4y' + 13y = 0$, char. Gleichung: $\lambda^2 + 4\lambda + 13 = 0 \Rightarrow \lambda_{1/2} = -2\pm 3i$ allgemeine Lösung: $y_H = (A_1 \cdot \cos (3x) + A_2 \cdot \sin(3x)) \cdot e^{-2x}$ \end{enumerate} \subsection{Die inhomogene Differentialgleichung} Bestimmung einer speziellen Lösung, wenn die rechte Seite eine spezielle Form hat. \subsection{Satz} Gegeben sei die Definition \[y'' + a_1 \cdot y' + a_0 \cdot y = p_n(x) \cdot e^{bx}\] wobei $p_n$ ein Polynom vom Grade $n$ ist. Dann gibt es ein Polynom $q_n$, vom Grade $n$, so daß \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item falls $b$ nicht Nullstelle des charakteristischen Polynoms ist, die Funktion $y_p = q_n(x) \cdot e^{bx}$ \item falls $b$ einfache Nullstelle des charakteristischen Polynoms ist, die Funktion $y_p = x \cdot q_n(x) \cdot e^{bx}$ \item falls $b$ zweifache Nullstelle des charakteristischen Polynoms ist, die Funktion $y_p = x^2 \cdot q_n(x) \cdot e^{bx}$ \end{enumerate} eine Lösung der Differentialgleichung ist. \paragraph{Bemerkung:} Im Falle (ii) spricht man von \emph{einfacher Resonanz}, im Falle (iii) von \emph{zweifacher Resonanz}.\index{Resonanz (DGL)} \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Man bestimme eine spezielle Lösung der Differentialgleichung $Y'' + y' - 2y = x^2$, $b = 0$, $n=2$. Charakteristische Gleichung: $\lambda^2 + \lambda - 2 = 0$, $b=0$ ist keine Nullstelle. $\Rightarrow$ Ansatz: $y_p = q_2(x) = Ax^2 + Bx + C$. Bestimmung von $A$, $B$, $C$ durch Einsetzen in Differentialgleichung: ${y_p}' = 2Ax + B$, ${y_p}'' = 2A, \Rightarrow -2Ax^2 + (2A-2B)x+(2A+B-2C) = x^2$ Koeffizientenvergleich: $\left.\begin{array}{ll}-2A = 1 & \Rightarrow A = - \frac 1 2\\ 2A - 2B = 0 & \Rightarrow B = - \frac 1 2 \vphantom{\Big\|}\\ 2A+B-2C=0 & \Rightarrow C = -\frac 3 4 \end{array}\right\} \displaystyle y_p = - \frac 1 2 x^2 - \frac 12 x - \frac 34$ \item $y'' + y' = x^2$, $b=0$, $n=2$ $\lambda^2 + \lambda = \lambda\cdot (\lambda + 1) \Rightarrow \lambda_1 = 0,\; \lambda_2 = -1$ $b$ ist eine einfache Nullstelle (einfache Resonanz) Ansatz: $y_p = x \cdot (Ax^2 + Bx + C) \Rightarrow (6Ax + 2B) + (3Ax^2 + 2Bx + C) = x^2$, Koeffizientenvergleich: $3A = 1$, $6A+2B = 0$, $2B + C = 0$ $\Rightarrow A = \frac 13$, $B = -1$, $C = 2 \quad \Rightarrow \quad y_p = \frac 13 x^3 - x^2 + 2x$ \item $y'' + y' - 2y = x \cdot e^{3x}$, $b=3$, $n=1$ $\lambda^2 + \lambda - 2 = 0$, $\lambda_1 = 1$, $\lambda_2 = -2 \Rightarrow$ keine Resonanz Ansatz: $y_p = (Ax + B) \cdot e^{3x}$ Ableitungen: ${y_p}' = (3Ax + 3B +A) \cdot e^{3x}$, ${y_p}'' = (9Ax + 9B + 6A)\cdot e^{3x}$ Einsetzen: $(10Ax + 7A + 10B) \cdot e^{3x} = x \cdot e^{3x}$ Koeffizientenvergleich: $10A = 1$, $7A + 10B = 0 \Rightarrow A = \frac{1}{10}$, $B = \frac{-7}{100}$ $\displaystyle \Rightarrow y_p = \left(\frac{1}{10} x - \frac{7}{100}\right) \cdot e^{3x}$ \item $y'' + y' - 2y = x \cdot e^{x}$, $\lambda_1 = 1$, $\lambda_2 = -2$, $b=1$ (einfache Resonanz) Ansatz: $y_p = x (Ax + B) \cdot e^x$, [\ldots] $\Rightarrow \displaystyle y_p = \left(\frac 1 6 x^2 - \frac 1 9 x\right) \cdot e^x$ \item $y'' - 2y' + y = x \cdot e^{x}$, $b=1$, $\lambda_1 = \lambda_2 = 1$ (zweifache Resonanz) Ansatz: $y_p = \frac 1 6 x^3 \cdot e^x$ \end{enumerate} \subsection{Satz} Gegeben sei die Differentialgleichung \[y'' + a_1 \cdot y' + a_0 \cdot y = (p_n(x) \cdot \cos (cx) + q_n(x) \cdot \sin(cx))\cdot e^{bx}\] wobei $p_n$ und $q_n$ Polynome vom Grade $\leq n$ sind und $c \ne 0$. Dann gibt es Polynome $r_n$ und $s_n$ vom Grade $\leq n$, so daß \begin{enumerate} \renewcommand{\labelenumi}{(\roman{enumi})} \item falls $b+ci$ nicht Nullstelle des charakteristischen Polynoms ist, die Funktion $y_p = (r_n (x) \cdot \cos (cx) + s_n (x) \cdot \sin(cx)) \cdot e^{bx}$ \item falls $b+ci$ einfache Nullstelle des charakteristischen Polynoms ist, die Funktion $y_p = x \cdot (r_n (x) \cdot \cos (cx) + s_n (x) \cdot \sin(cx)) \cdot e^{bx}$ \end{enumerate} eine Lösung der Differentialgleichung ist. \paragraph{Bemerkung:} Im Falle (ii) spricht man von \emph{einfacher Resonanz} (zweifache Resonanz kann hier nicht auftreten). \subsection{Satz: Superpositionsprinzip}\index{Differentialgleichungen!Superspositionsprinzip} \index{Superpositionsprinzip (DGL)} Ist $y_1$ eine spezielle Lösung der Differentialgleichung $y'' + a_1 \cdot y' + a_0 \cdot y = f_1(x)$ und $y_2$ eine spezielle Lösung der Differentialgleichung $y'' + a_1 \cdot y' + a_0 \cdot y = f_2(x)$, so ist $y_1 + y_2$ eine spezielle Lösung der Differentialgleichung $f_1(x) + f_2(x)$. \subsection{Beispiel} $y'' + 2y' - 3y = \underbrace{e^x}_{f_1(x)} - \underbrace{x^2+4x-5}_{f_2(x)}$ \begin{enumerate} \item spezielle Lösung von $y'' + 2y' - 3y = e^x$: $y_1 = \frac x 4 e^x$ (nach 14.4.4) \item spezielle Lösung von $y'' + 2y' - 3y = -x^2 + 4x -5$: $y_2 = - \frac 1 3 x^2 - \frac{16}{9} x + \frac{7}{24}$ \item $\Rightarrow y_p = y_1 + y_2 = \frac x 4 \cdot e^x - \frac 1 3 x^2 - \frac{16}{9} x + \frac{7}{24}$ \end{enumerate} \subsection{Energiemethode}\index{Energiemethode (DGL)} \index{Differentialgleichungen!Energiemethode} Zu lösen sei die Differentialgleichung $y'' = f(y)$. Jede Lösung dieser Gleichung erfüllt die Differentialgleichung \[\frac 1 2 (y')^2 = \int f(y)\,dy\] die separabel und von erster Ordnung ist. \paragraph{Beispiel:} $y'' = 2y^3$ (keine lineare DGL!). Anfangsbedingungen $y(-2) = 1,\; y'(-2) = -1$ \smallskip Integration: $\frac 1 2 (y'(x))^2 = \int 2y(x)^3\, dy = \frac{y(x)^4}{2} + C$ \smallskip $x=-2$ einsetzen: $\frac 1 2 \cdot 1 = \frac 1 2 \cdot 1 + C \Rightarrow C = 0$ \smallskip $\frac 1 2 (y')^2 = \frac 1 2 y^4 \Rightarrow y' = \pm y^2$ \bigskip Wegen $y'(-2) = -1$ ist $y' = -y^2$ (separable DGL). \bigskip $\frac{dy}{dx} = -y^2 \Leftrightarrow \frac{1}{y^2}\, dy = -1\,dx$ \smallskip Integration: $-\frac 1 y = - x + C_1$. Wegen $y(-2) = 1$ ist $C_1 = -3$ \smallskip $\Rightarrow y= \frac{1}{x+3}$ \section{Lineare Differentialgleichung n-ter Ordnung}\index{lin. DGL n--ter Ordnung} \index{Differentialgleichungen!lin., n--ter Ordnung} \begin{equation} y^{(n)} + a_{n-1}(x) \cdot y^{n-1} + \cdots + a_1 (x) \cdot y^1 + a_0(x) = f(x) \end{equation} bezeichnet man als lineare Differentialgleichung $n$--ter Ordnung. Ist $f=0$, so heißt sie \emph{homogen}, sonst \emph{inhomogen}. $f$ heißt\emph{Störfunktion} oder \emph{Störglied}. Sind die Funktionen $a_j$ konstant, so spricht man von einer \emph{linearen Differentialgleichung $n$--ter Ordnung mit konstanten Koeffizientzen}. \subsection{Satz} Ist $Y_h$ die Menge aller Lösungen der homogenen Differentialgleichung \[y^{(n)} + a_{n-1} \cdot y^{(n-1)} + \cdots + a_0 \cdot y = 0\] und $y_p$ eine spezielle Lösung der Gleichung (14.5), so ist \[Y = \{y:y=y_h + y_p \textrm{ mit } y_n \in Y_h\}\] die allgemeine Lösung der inhomogenen Differentialgleichung. \subsection{Struktur der Lösung im homogenen Fall} \subsection{Definition} Die Funktionen $y_1,\ldots,y_n$ heißen \emph{linear unabhängig}, wenn aus \[c_1 \cdot y_1(x) + c_2 \cdot y_2(x) + \cdots + c_n\cdot y_n(x) = 0 \qquad (x \in D)\] $c_1 = \cdots = c_n = 0$ folgt. ($D$ bezeichnet den gemeinsamen Definitionsbereich, $D \ne \emptyset$, offene Menge) \subsection{Satz}\index{Wronski'sche Determinante} Sind die Funktionen $y_1,\ldots,y_n$ $(n-1)$--mal differenzierbar und ist die \emph{Wronski'sche Determinante} \[W(x) = \left\|\begin{array}{ccc}y_1(x) & y_2(x) & y_3(x)\\{y_1}'(x) & {y_2}'(x) &{y_3}'(x)\\ \vdots & & \vdots \\ {y_1}^{(n-1)} & {y_2}^{(n-1)} & {y_3}^{(n-1)}\end{array}\right\|\] in $D$ überall ungleich $0$, so sind die Funktionen $y_1,\ldots,y_n$ linear unabhängig. $W(x)$ ist entweder überall gleich Null oder überall ungleich Null in $D$. \subsection{Beispiel} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Sind $f_1(x) = 1,\, f_2(x) = x,\, f_3(x) = x^2,\, f_4(x) = x^3 \: (D \in \mathbb R)$ linear unabhängig? \[W(x) = \left\|\begin{array}{cccc}1&x&x^2&x^3\\0&1&2x&3x^2\\0&0&2&6x\\0&0&0&6\end{array}\right\| = 1 \cdot 1 \cdot 1 \cdot 2 \cdot 6 = 12 \ne 0\] $\Rightarrow$ linear unabhängig \item Die Funktionen $f_1(x) = 1,\, f_2(x) = x$ und $f_3(x) = 2x + 3$ sind linear abhängig, da $3 \cdot f_1(x) + 2 \cdot f_2(x) = f_3(x) = 0 \; (\forall x \in \mathbb R)$. Die Wronski'sche Determinante ist \[W(x) = \left\|\begin{array}{ccc}1&x&2x+3\\0&1&2\\0&0&0\end{array}\right\| = 0\] \end{enumerate} \subsection{Satz} Die allgemeine Lösung der homogenen linearen Differentialgleichung $n$--ter Ordnung kann in der Gestalt \[y_h(x) = C_1 \cdot y_1(x) + C_2 \cdot y_2(x) + \cdots + C_n \cdot y_n(x)\] angegeben werden, wobei $y_1(x), \ldots , y_n(x)$ linear unabhängige Lösungen und $C_1, \ldots , C_n$ beliebige Konstanten sind. \subsection{Lineare homogene Differentialgleichung mit konstanten Koeffizienten} \subsection{Definition: Charakteristische Gleichung} Die Gleichung \[\lambda^n + a_{n-1} \cdot \lambda^{(n-1)} + \cdots + a_1 \cdot \lambda + a_0 = 0\] heißt \emph{charakteristische Gleichung der Differentialgleichung}\index{charakteris. Gleichung (DGL)} \index{Differentialgleichungen!charakt. Gleichung} \begin{equation} y^{(n)} + a_{n-1} \cdot y^{(n-1)} + \cdots + a_1 \cdot y' + a_0 \cdot y = 0 \end{equation} \subsection{\hspace{-2pt}Die allgemeine Lösung der Differentialgleichung (14.6)} %% pfui! Eine $r$-fache reelle Lösung $\lambda$ der charakteristischen Gleichung führt zu dem folgenden Beitrag in der allgemeine Lösung: \[(C_0 + C_1\cdot x + C_2 \cdot x^2 + \cdots + C_{r-1}x^{r-1})\cdot e^{\lambda \cdot x}\] Eine $r$--fache komplexe Nullstelle $\alpha \pm i\omega$ ($\omega \ne 0$) führt zu dem folgenden Beitrag in der allgemeinen Lösung: \[(P(x) \cdot \cos(\omega \cdot x) + Q(x) \cdot \sin(\omega \cdot x)) \cdot e^{\alpha \cdot x}\] wobei $P(x) = C_0 + C_1 \cdot x + \cdots + C_{r-1} \cdot x^{r-1}$ und $Q(x) = D_0 + D_1 \cdot x + \cdots + D_{r-1} \cdot x^{r-1}$. Um die allgemeine Lösung zu erhalten, werden alle diese Beiträge addiert. \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item $y''' - 4y'' - y' + 4y = 0$ char. Gleichung: $\lambda^4 - 4\lambda^2 - \lambda + 4 =0 \Rightarrow \lambda_1 = -1,\, \lambda_2 = 1,\,\lambda_3 = 4$ Allgemeine Lösung: $y = A \cdot e^{-x} + B \cdot e^x + C \cdot e^{4x}$ ($A$, $B$, $C$ beliebig) \item $y^{(4)} - 6y''' + 12 y'' - 10y' + 3y = 0$ $\lambda^4 - 6\lambda^3 + 12 \lambda^2 - 10\lambda + 3 = 0 \quad \Rightarrow \quad \lambda_{1,2,3} = 1,\, \lambda_4 = 3$ Allgemeine Lösung: $y = (C_0 + C_1 \cdot x + C_2 \cdot x^2) \cdot e^x + B \cdot e^x$ \item $y^{(4)} + 3y'' - 4y = 0$ $\lambda^4 + 3\lambda^2 - 4 = 0 \quad \Rightarrow \quad \lambda_1 = -1,\, \lambda_2 = 1,\,\lambda_{3,4} = \pm 2i$ Allgemeine Lösung: $y = A \cdot e^{-x} + B \cdot e^{x} + C \cdot \cos (2x) + D \cdot \sin(2x)$ \quad ($\alpha = 0,\, e^{\alpha} = 1$) \end{enumerate} \subsection{Lineare inhomogene Differentialgleichungen mit konstanten Koeffizienten} \[y^{(n)} + a_{n-1} \cdot y^{n-1} + \cdots + a_1 \cdot y' + a_0 \cdot y = f(x)\] Lösungsansatz für eine spezielle Lösung in Abhängigkeit von $f$, ähnlich wie in (14.4.4) und (14.4.6), siehe Formelsammlungen. \section{Systeme linearer Differentialgleichungen}\index{Differentialgleichungen!Systeme} \index{Systeme lin. DGLn} \subsection{Beispiel} \begin{center} \begin{picture}(220,80) \put(0,27){$u=U(t) \Big\downarrow$} \multiput(55,0)(0,35){2}{\line(0,1){25}} \multiput(55,26)(0,8){2}{\circle{2}} \put(55,0){\line(1,0){120}} \multiput(115,0)(60,0){2}{ \multiput(0,0)(0,40){2}{\line(0,1){20}} \multiput(-5,20)(10,0){2}{\line(0,1){20}} \multiput(-5,20)(0,20){2}{\line(1,0){10}} } \multiput(55,60)(100,0){2}{\line(1,0){20}} \put(95,60){\line(1,0){40}} \multiput(75,60)(60,0){2}{\multiput(0,0)(5,0){4}{\qbezier(0,0)(0,5)(2.5,5)\qbezier(2.5,5)(5,5)(5,0)}} \multiput(82,68)(60,0){2}{$L$} \multiput(98,27)(60,0){2}{$R$} \multiput(80,30)(60,0){2}{\circle{20}} \multiput(77.5,20)(60,0){2}{\vector(-1,0){0}} \put(77,27){$i_1$} \put(137,27){$i_2$} \put(115,20){\vector(0,-1){12}} \put(118,9){$\scriptstyle i_1 -i_2$} \multiput(115,0)(0,60){2}{\circle{2}} \end{picture} \end{center} Zwei gleiche Widerstände, zwei gleiche Induktivitäten, Spannung $U = U(t)$ bekannt. \begin{description} \item[Maschenregel:] In jeder Masche ist die Summe der Spannungen gleich 0. \end{description} \begin{enumerate} \renewcommand{\labelenumi}{$\circlearrowright$ \arabic{enumi}:} \item $L \cdot \frac{di_1}{dt} +R \cdot (i_1 - i_2) - u = 0 \quad \Rightarrow \quad \frac{di_1}{dt} = \frac R L \cdot i_1 + \frac R L \cdot i_2 + \frac u L$ \item $L \cdot \frac{di_2}{dt} + R \cdot (i_1 - i_2) + R\cdot i_2 = 0 \quad \Rightarrow \quad \frac{di_2}{dt} = \frac R L \cdot i_1 - \frac{2R} L \cdot i_2$ \end{enumerate} Beide Stromgrößen treten in beiden Gleichungen auf. Man spricht daher von miteinander \emph{gekoppelten Differentialgleichungen}. Sind die Werte der beiden Ströme z.B. zur Zeit $t=0$ vorgegeben (d.h. $i_1(0)$ und $i_2(0)$, so handelt es sich um ein \emph{Anfangsproblem}.\index{gekoppelte DGL} \index{Differentialgleichungen!gekoppelte} \subsection{Definition} Ein (explizites) \emph{System von linearen Gleichungen erster Ordnung} für die Funktionen $y_1, \ldots , y_n$ hat die Form: \newpage \begin{eqnarray} {y_1}'(x) & = & a_{11}(x) \cdot y_1(x) + \cdots + a_{1n} \cdot y_n(x) + f_1(x)\\ {y_2}'(x) & = & a_{21}(x) \cdot y_1(x) + \cdots + a_{2n} \cdot y_n(x) + f_2(x)\\ & \vdots & \hspace{2.85cm} \vdots\\ {y_k}'(x) & = & a_{k1}(x) \cdot y_1(x) + \cdots + a_{kn} \cdot y_n(x) + f_k(x) \end{eqnarray} Sind die Funktionen $a_{ij}$ konstant, so spricht man von einem System mit \emph{konstanten Koeffizienten}, sind die Funktionen $f_j$ alle gleich $0$, so heißt das System \emph{homogen}. \bigskip Im Weiteren werden wir immer $k=n$ voraussetzen. Ein solches System läßt sich auch in \emph{Matrizenform} schreiben als\index{Matrizenform (DGL)} \[y'(x) = A(x) \cdot y(x) + f(x)\] wobei: \begin{minipage}{165pt} \begin{eqnarray} y(x) &=& (y_1(x), \ldots , y_n(x))^T\\ y'(x) &=& ({y_1}'(x), \ldots , {y_n}'(x))^T \vphantom{\Big\|}\\ f(x) &=& (f_1(x), \ldots , f_n(x))^T \end{eqnarray} \end{minipage} \begin{minipage}{185pt} \[A = \left[\begin{array}{cccc} a_{11}(x) & a_{12}(x) & \cdots & a_{1n}(x)\\ a_{21}(x) & a_{22}(x) & \cdots & a_{2n}(x)\\ \vdots & & \vdots \\ a_{n1}(x) & a_{n2}(x) & \cdots & a_{nn}(x)\end{array}\right]\] \end{minipage} \paragraph{Beispiel:} Für das System aus (14.6.1) \begin{minipage}{165pt} \begin{eqnarray} y(t) &=& (i_1(t), i_2(t))^T\\ y'(t) &=& ({i_1}'(t), {i_2}'(t))^T \vphantom{\Big\|}\\ f(t) &=& \left(\frac{U(t)}{L}, 0\right)^T \end{eqnarray} \end{minipage} \begin{minipage}{185pt} \[A = \left[\begin{array}{cc} -1 & 1 \\ 1 -2\end{array}\right]\] \end{minipage} \subsection{Satz} Die allgemeine Lösung des Systems $y'(x) = A(x) \cdot y(x) + f(x)$ setzt sich zusammen aus der allgemeinen Lösung $y_h$ des homogenen Systems $y'(x) = A(x) \cdot y(x)$ und einer speziellen Lösung $y_p$ des inhomogenen Systems. Ist $A$ eine Diagonalmatrix, so hat das System die Form: \begin{eqnarray} {y_1}'(x) & = & a_{11}(x) \cdot y_1(x) + f_1(x)\\ {y_2}'(x) & = & a_{22}(x) \cdot y_2(x) + f_2(x)\\ & \vdots \\ {y_n}'(x) & = & a_{nn}(x) \cdot y_n(x) + f_n(x) \end{eqnarray} \smallskip (sogenanntes \emph{entkoppeltes System})\index{entkoppeltes System (DGL)} In diesem Fall können die Gleichungen unabhängig von einander gelöst werden. Einige Systeme lassen sich entkoppeln. \subsection{Satz} Besitzt eine $n\times n$--Matrix $A$ $n$ linear unabhängige Eigenvektoren $r_1,\ldots, r_n$, dann ist die Matrix $T=[r_1,\ldots,r_n]$ invertierbar und $T^{-1} \cdot A \cdot T$ ist eine Diagonalmatrix mit den Eigenwerten $\lambda_1 , \ldots , \lambda_n$ von $A$ in der Hauptdiagonale: \[T^{-1} \cdot A \cdot T = \mathrm{diag}\,(\lambda_1 , \ldots , \lambda_n)\] \paragraph{Bemerkung:} (bereits bekannt aus erstem Semester) Die Eigenwerte von $A$ sind die Lösungen der Gleichung $\det(A - \lambda\cdot E) = 0$ (die sogenannten charakteristischen Gleichungen). Die zugehörigen Eigenvektoren bestimmt man aus $(A - \lambda \cdot E) \cdot r = 0$ (lineares Gleichungssystem). \subsection{Beispiel} Gegeben sei $A = \left[\begin{array}{rr}2 & 1 \\ 4 & -1\end{array}\right]$ \begin{description} \item[Eigenwerte:] $\det(A - \lambda \cdot E) = \left\|\begin{array}{cc}(2-\lambda) & 1 \\ 4 & (-1-\lambda)\end{array}\right\| = 0$ \smallskip $\Rightarrow \lambda_1 = 3, \quad \lambda_2 = -2$ \item[Eigenvektoren:] $(A - 3E) \cdot \left[\begin{array}{l}r_1^1\\r_1^2\end{array}\right] = 0 \Rightarrow r_1 = (1,1)^T$ $(A + 2E) \cdot \left[\begin{array}{l}r_2^1\\r_2^2\end{array}\right] = 0 \Rightarrow r_1 = (1,-4)^T$ \smallskip $\Rightarrow T = \left[\begin{array}{rr}1 & 1 \\ 1 & -4\end{array}\right]$, \qquad $T^{-1} \cdot A \cdot T = \left[\begin{array}{rr}3 & 0 \\ 0 & -2\end{array}\right] = \mathrm{diag}\,(3,-2)$ \end{description} \subsection{Satz (Lösungsverfahren durch Diagonalisierung)}\index{Diagonalisierung (DGL)} Gegeben sei das homogene System von linearen Differentialgleichungen mit konstanten Koeffizienten $y'(x) = A \cdot y(x)$. Nehmen wir an, daß die Matrix $A$ $n$ linear unabhängige Eigenvektoren $r_1, \ldots, r_n \in \mathbb R^n$ mit den zugehörigen Eigenwerten $\lambda_1 , \ldots , \lambda_n \in \mathbb R$ besitzt und sei $T = [r_1, \ldots , r_n]$ und $u = T^{-1} \cdot y$. Dann erfüllt $u$ die (entkoppelte) Gleichung \[u' = T^{-1} \cdot A \cdot T \cdot u = \mathrm{diag}\,(\lambda_1, \ldots , \lambda_n) \cdot u\] welche \[u_h = C_1 e^{\lambda_1 x} \cdot (1,0,\ldots,0)^T + C_2 e^{\lambda_2 x} \cdot (0,1,\ldots,0)^T + \cdots + C_n e^{\lambda_n x} \cdot (0,0,\ldots,1)^T\] als allgemeine Lösung besitzt. Die allgemeine Lösung des ursprünglichen Systems lautet: \[y_h = T \cdot u_h = C_1 \cdot r_1 \cdot e^{\lambda_1 \cdot x} + \cdots + C_n \cdot r_n \cdot e^{\lambda_n \cdot x} \qquad (C_1,\ldots,C_2 \in \mathbb R)\] \paragraph{Beweis:} $y' = A \cdot y, \quad u = T^{-1} \cdot y$ \smallskip $\Rightarrow \left.\begin{array}{ll}y = T \cdot u\\y' = T \cdot u'\end{array}\right\} T \cdot u' = A \cdot T \cdot u \qquad \| \cdot T$ \smallskip \hspace{3.5cm}$u' = \underbrace{T^{-1} \cdot A \cdot T}_{=\mathrm{diag}\,(\lambda_1,\ldots,\lambda_n)} \cdot u$ \subsection{Beispiel} Zu lösen: ${y_1}' = -y_1 + y_2$, ${y_2}' = y_1 - y_2$, d.h. $y' = A \cdot y = \left[\begin{array}{rr}-1&1\\1&-1\end{array}\right] \cdot y$ \begin{description} \item[Eigenwerte und Eigenvektoren:] \quad $\lambda_1 = -2$, $\lambda_2 = 0$ $r_1 = (1,-1)^T$, $r_2 = (1,1)^T$ (linear unabhängig) \item[Lösung des entkoppelten Systems:] \quad $u_h = C_1 \cdot e^{-2x} \cdot (1,0)^T + C_2 \cdot e^0 \cdot (0,1)^T = (C_1 \cdot e^{-2x}, C_2)^T$ \smallskip mit $C_1,\, C_2 \in \mathbb R$, beliebig \item[Lösung des ursprünglichen Systems:] \quad $y_h = T \cdot u_h = \left[\begin{array}{rr}1 & 1 \\ -1 & 1\end{array}\right] \cdot \left[\begin{array}{c}C_1 \cdot e^{2x}\\ C_2\end{array}\right] = \left[\begin{array}{r}C_1 \cdot e^{-2x} + C_2\\-C_1 \cdot e^{-2x} + C_2\end{array}\right] = \left[\begin{array}{r}y_1\\y_2\end{array}\right]$ \end{description} \subsection{Satz (Lösungsverfahren mit \emph{Exponentialansatz})}\index{Exponentialansatz (DGL)} Gegeben sei das homogene System von linearen Differentialgleichungen mit konstanten Koeffizienten $y'(x) = A \cdot y(x)$. Dann gilt: Die allgemeine Lösung $y_h$ ergibt sich als Linearkombination des Exponentialansätze. \[\left[\begin{array}{c} C_{1,0} + C_{1,1} \cdot x + \cdots + C_{1,k-1} \cdot x^{k_j-1}\\ C_{2,0} + C_{2,1} \cdot x + \cdots + C_{2,k-1} \cdot x^{k_j-1}\\ \vdots\\ C_{n,0} + C_{n,1} \cdot x + \cdots + C_{n,k-1} \cdot x^{k_j-1} \end{array}\right] \cdot e^{\lambda_j \cdot x}\] Wobei $\lambda_j$ die Eigenwerte von $A$ mit der Vielfachheit $k_j$ bedeuten. \subsubsection{Bemerkungen} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item Die Konstanten in dem Ansatz werden durch Einsetzen in die Gleichung $y' = A \cdot y$ bestimmt. \item Falls Eigenwerte komplex sind, so erhält man auch komplexe Lösungsfunktionen $y_j$. Durch Aufspaltung in Real-- und Imaginärteil ergeben sich dann die zugehörigen Lösungsfunktionen ($e^{x+iy} = e^x \cdot e^{iy} = e^x(\cos y + \sin y)$). \item Der Fall $n=2$ ${y_1}' = a_{11} \cdot y_1 + a_{12} \cdot y_2 \qquad (a_{12} \ne 0)$ ${y_2}' = a_{21} \cdot y_2 + a_{22} \cdot y_2$ \smallskip Man macht zuerst den Exponentialansatz für $y_1$ (d.h. die erste Komponente des Lösungsvektors). Dieser Ansatz wird dann in die erste Gleichung eingesetzt und diese Gleichung nach $y_2$ aufgelöst: \begin{equation} y_2 = \frac{1}{a_{12}} \cdot ({y_1}' - a_{11} \cdot y_1) \end{equation} \begin{enumerate} \renewcommand{\labelenumii}{(\arabic{enumii})} \item $\lambda_1 \ne \lambda_2$, reell. Ansatz für $y_1$: \[y_1 = C_1 \cdot e^{\lambda_1 \cdot x} + C_2 \cdot e^{\lambda_2 \cdot x}\] \item $\lambda_1 = \lambda_2 = \alpha$, reell. Ansatz für $y_1$: \[y_1 = (C_1 + C_2\cdot x) \cdot e^{\alpha \cdot x}\] \item $\lambda_{1/2} = \alpha \pm i\omega$, konjugiert komplex. Ansatz: \[y_1 = (C_1 \cdot \sin(\omega \cdot x) + C_2 \cdot \cos(\omega \cdot x)) \cdot e^{\alpha \cdot x} \] \end{enumerate} \end{enumerate} \subsection{Beispiele} \begin{enumerate} \renewcommand{\labelenumi}{(\alph{enumi})} \item ${y_1}' = y_1 + y_2, \quad {y_2}' = - y_1 + y_2 \quad \Rightarrow y' = \left[\begin{array}{l}{y_1}'\\{y_2}'\end{array}\right] = \underbrace{\bigg[\begin{array}{rr}1&1\\-1&1\end{array}\bigg]}_{A} \cdot \left[\begin{array}{l}{y_1}\\{y_2}\end{array}\right]$ Eigenvektoren von $A$: $\left\|\begin{array}{rr}1-\lambda & 1\\-1&1-\lambda\end{array}\right\| = 0 = (1-\lambda)^2 + 1, \quad \lambda_{1,2} = 1 \pm i$ Ansatz: $y_1 = (C_1 \cdot \sin(\omega \cdot x) + C_2 \cdot \cos(\omega \cdot x)) \cdot e^{\alpha \cdot x}$ \smallskip In (14.7) einsetzen: $y_2 = e^x \cdot (C_1 \cdot \cos x - C_2 \cdot \sin x)$ \smallskip $\Rightarrow$ allgemeine Lösung: $y_1 = e^x\cdot(C_1 \cdot \sin x + C_2 \cdot \cos x)$ $y_2 = e^x\cdot(C_1 \cdot \cos x + C_2 \cdot \sin x)$ \item ${y_1}' = 4\cdot y_1 - 3 \cdot y_2 \qquad$ Anfangswerte: $y_1(0) = 1$ ${y_2}' = 3 \cdot y_1 - 2 \cdot y_2$ \hspace{3.17cm} $y_2(0) = 0$ \smallskip Eigenwerte: $\left\|\begin{array}{rr}4-\lambda &-3\\3&-2-\lambda\end{array}\right\| = 0 = (\lambda-1)^2 \Rightarrow \lambda_{1,2} = 1$ (zweif. NST) \newpage Ansatz: $y_1 = (C_1 + C_2 \cdot x) \cdot e^x$ in (14.7) einsetzen: \hspace{1.28cm} $y_2 = (C_1 - \frac 1 3 C_2 + C_2 \cdot x) \cdot e^x$ \smallskip Anfangswerte: $y_1(0) = 1 \Rightarrow C_1 = 1$ \hspace{2.5cm}$y_2(0) = 0 \Rightarrow C_1 - \frac 1 3 C_2 = 0 \Rightarrow C_2 = 3$ \[\Rightarrow y_1 = (1+3\cdot x) \cdot e^x \qquad \textrm{und} \qquad y_2 = 3\cdot x \cdot e^x\] \end{enumerate} \subsection[Bestimmung einer speziellen Lösung der Gleichung\ldots]{Bestimmung einer speziellen Lösung der\\ Gleichung $y'(x) = A \cdot y(x) + f(x)$} Wir wissen bereits: Die allgemeine Lösung setzt sich zusammen aus der allgemeinen Lösung $y_h$ des homogenen Systems $y'(x) = A \cdot y(x)$ und einer beliebigen speziellen Lösung $y_p$ des inhomogenen Systems. \subsubsection{(a) Lösungsansatz in Abhängigkeit von $f$} Ähnlich wie in (14.4.4) und (14.4.6), siehe auch Formelsammlungen. Zu beachten ist jedoch: Beim Lösungsansatz sind in \textbf{allen} Komponenten jeweils \textbf{alle} Komponenten des Störgliedes zu berücksichtigen. \smallskip Erläuterung an einem Beispiel: \smallskip \begin{minipage}{177pt} ${y_1}' = - y_1 + 3 \cdot y_2 + x$ ${y_2}' = 2\cdot y_1 - 2 \cdot y_2 + e^{-x}$ \end{minipage} \begin{minipage}{177pt} allg. Lösung des homogenen Systems: $y_1 = _1 \cdot e^{-4x} + C_2 \cdot e^{x}$ $y_2 = -C_1 \cdot e^{-4x} + \frac 2 3 C_2 \cdot e^{x}$ \end{minipage} \paragraph{Ansatz für eine spezielle Lösung:} \quad $y_{1,p} = a\cdot x + b + c \cdot e^{-x}$ \qquad \quad\raisebox{-6pt}{einsetzen in das inhomogene System} %% bahpfui! $y_{2,p} = A\cdot x + B + C \cdot e^{-x}$ \begin{eqnarray} a - c \cdot e^{-x} &=& (-b + 3B) + (-a + 3A + 1) \cdot x + (-c + 3C) \cdot e^{-x}\\ A-C\cdot e^{-x} & = & (2b - 2B) + (-2a - 2A) \cdot x + /2c - 2C +1) \cdot e^{-x} \end{eqnarray} Koeffizientenvergleich: \smallskip $\begin{array}{lll} a & = & -b + 3B\\ 0 & = & -a + 3A +1\\ -c & = & -c + 3C\\ & \ldots \end{array}$ \smallskip $\Rightarrow$ 6 Gleichungen, 6 Unbekannte \smallskip $y_{1,p} = - \frac 5 8 - \frac 1 2 x - \frac 1 2 e^{-x}$ $y_{2,p} = -\frac 3 8 - \frac 1 2 x$ \printindex \end{document}
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https://docs.qore.org/qore-0.9.2/lang/latex/group__functional__domain__constants.tex	qore.org	CC-MAIN-2021-39	application/octet-stream	application/x-tex	crawl-data/CC-MAIN-2021-39/segments/1631780057524.58/warc/CC-MAIN-20210924110455-20210924140455-00489.warc.gz	265,649,126	3,902	\hypertarget{group__functional__domain__constants}{}\section{Functional Domain Constants} \label{group__functional__domain__constants}\index{Functional Domain Constants@{Functional Domain Constants}} \subsection*{Variables} \begin{DoxyCompactItemize} \item const \mbox{\hyperlink{group__functional__domain__constants_ga13575102458aeb4a1c4d8b79ce887561}{Qore\+::\+D\+O\+M\+\_\+\+D\+A\+T\+A\+B\+A\+SE}} = Q\+D\+O\+M\+\_\+\+D\+A\+T\+A\+B\+A\+SE \begin{DoxyCompactList}\small\item\em provides access to databases \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_ga2f13313c2aa21817850133f99b44c2fa}{Qore\+::\+D\+O\+M\+\_\+\+D\+E\+B\+U\+G\+G\+ER}} = Q\+D\+O\+M\+\_\+\+D\+E\+B\+U\+G\+G\+ER \begin{DoxyCompactList}\small\item\em provides debugging functionality \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_ga945741abd74f2121fa9a2fb89d8c6b4c}{Qore\+::\+D\+O\+M\+\_\+\+E\+M\+B\+E\+D\+D\+E\+D\+\_\+\+L\+O\+G\+IC}} = Q\+D\+O\+M\+\_\+\+E\+M\+B\+E\+D\+D\+E\+D\+\_\+\+L\+O\+G\+IC \begin{DoxyCompactList}\small\item\em provides dynamic parsing functionality \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_ga86d8ac6c1ca9050fe51107a97ea5b9fd}{Qore\+::\+D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+I\+N\+FO}} = Q\+D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+I\+N\+FO \begin{DoxyCompactList}\small\item\em provides access to external information (ex\+: hostname, pid, process uid, etc) \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_ga2492eb49a7b137acb574a98a18176d22}{Qore\+::\+D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+P\+R\+O\+C\+E\+SS}} = Q\+D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+P\+R\+O\+C\+E\+SS \begin{DoxyCompactList}\small\item\em provides external process control functionality (can affect) start) or stop external processes) \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_gaed32c700f988d21a2a3c55ccf36f451c}{Qore\+::\+D\+O\+M\+\_\+\+F\+I\+L\+E\+S\+Y\+S\+T\+EM}} = Q\+D\+O\+M\+\_\+\+F\+I\+L\+E\+S\+Y\+S\+T\+EM \begin{DoxyCompactList}\small\item\em provides access to the filesystem \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_gaac43540fdce157e8f8df0ad26bbf7437}{Qore\+::\+D\+O\+M\+\_\+\+G\+UI}} = Q\+D\+O\+M\+\_\+\+G\+UI \begin{DoxyCompactList}\small\item\em provides G\+UI functionality \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_ga122e9d3fcaf41d9fecd53f24be496568}{Qore\+::\+D\+O\+M\+\_\+\+I\+N\+J\+E\+C\+T\+I\+ON}} = Q\+D\+O\+M\+\_\+\+I\+N\+J\+E\+C\+T\+I\+ON \begin{DoxyCompactList}\small\item\em provides functionality related to code / dependency injection \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_gaaf4c9194f22ca56bd3b95caa436214c3}{Qore\+::\+D\+O\+M\+\_\+\+L\+O\+C\+A\+L\+E\+\_\+\+C\+O\+N\+T\+R\+OL}} = Q\+D\+O\+M\+\_\+\+L\+O\+C\+A\+L\+E\+\_\+\+C\+O\+N\+T\+R\+OL \begin{DoxyCompactList}\small\item\em provides access to functionality that changes locale information \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_ga233b03c196dcaa21187f359e87c48ac8}{Qore\+::\+D\+O\+M\+\_\+\+M\+O\+D\+U\+LE}} = Q\+D\+O\+M\+\_\+\+M\+O\+D\+U\+L\+ES \begin{DoxyCompactList}\small\item\em provides access to external modules \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_ga0b0bb2cc8627c910e5445bf004a8a46b}{Qore\+::\+D\+O\+M\+\_\+\+N\+E\+T\+W\+O\+RK}} = Q\+D\+O\+M\+\_\+\+N\+E\+T\+W\+O\+RK \begin{DoxyCompactList}\small\item\em provides network functionality \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_ga51bbde061f74c08025b1d7c18184f773}{Qore\+::\+D\+O\+M\+\_\+\+P\+R\+O\+C\+E\+S\+S\+\_\+\+C\+O\+N\+T\+R\+OL}} = Q\+D\+O\+M\+\_\+\+P\+R\+O\+C\+E\+SS \begin{DoxyCompactList}\small\item\em provides process control functionality (can affect or stop the current process) \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_gaad785fc289011722fb8a3c6c9ab53790}{Qore\+::\+D\+O\+M\+\_\+\+R\+E\+F\+L\+E\+C\+T\+I\+ON}} = Q\+D\+O\+M\+\_\+\+R\+E\+F\+L\+E\+C\+T\+I\+ON \begin{DoxyCompactList}\small\item\em provides reflection functionality \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_ga27d39c32f12097d84a446f06e3c7978d}{Qore\+::\+D\+O\+M\+\_\+\+T\+E\+R\+M\+I\+N\+A\+L\+\_\+\+IO}} = Q\+D\+O\+M\+\_\+\+T\+E\+R\+M\+I\+N\+A\+L\+\_\+\+IO \begin{DoxyCompactList}\small\item\em provides terminal I/O functionality \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_ga8cb18f231d451bed11c5fb81f9124f6c}{Qore\+::\+D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+L\+A\+SS}} = Q\+D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+L\+A\+SS \begin{DoxyCompactList}\small\item\em provides thread control functionality \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_gaf63c9d233d9365eb6d12a48b444485a5}{Qore\+::\+D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+O\+N\+T\+R\+OL}} = Q\+D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+O\+N\+T\+R\+OL \begin{DoxyCompactList}\small\item\em provides the ability to check or manipulate threads (including starting new threads) \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_gaddd830f869f2a077097683f84f409f2e}{Qore\+::\+D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+I\+N\+FO}} = Q\+D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+I\+N\+FO \begin{DoxyCompactList}\small\item\em provides access to information regarding threading (tid, active threads, etc) \end{DoxyCompactList}\item const \mbox{\hyperlink{group__functional__domain__constants_gaa643a322407977526fadc2a08d636916}{Qore\+::\+D\+O\+M\+\_\+\+U\+N\+C\+O\+N\+T\+R\+O\+L\+L\+E\+D\+\_\+\+A\+PI}} = Q\+D\+O\+M\+\_\+\+U\+N\+C\+O\+N\+T\+R\+O\+L\+L\+E\+D\+\_\+\+A\+PI \begin{DoxyCompactList}\small\item\em provides unchecked access to system functionality that could bypass \mbox{\hyperlink{namespace_qore}{Qore}}\textquotesingle{}s sandboxing controls \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Detailed Description} Constants providing values for functional domains; each constant is a unique element of a bitfield \begin{DoxySince}{Since} Qore 0.\+9 \end{DoxySince} \subsection{Variable Documentation} \mbox{\Hypertarget{group__functional__domain__constants_ga13575102458aeb4a1c4d8b79ce887561}\label{group__functional__domain__constants_ga13575102458aeb4a1c4d8b79ce887561}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+D\+A\+T\+A\+B\+A\+SE@{D\+O\+M\+\_\+\+D\+A\+T\+A\+B\+A\+SE}} \index{D\+O\+M\+\_\+\+D\+A\+T\+A\+B\+A\+SE@{D\+O\+M\+\_\+\+D\+A\+T\+A\+B\+A\+SE}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+D\+A\+T\+A\+B\+A\+SE}{DOM\_DATABASE}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+D\+A\+T\+A\+B\+A\+SE = Q\+D\+O\+M\+\_\+\+D\+A\+T\+A\+B\+A\+SE} provides access to databases \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_gac496a9d9bcf9d5c626c8c267c73a83bc}{P\+O\+\_\+\+N\+O\+\_\+\+D\+A\+T\+A\+B\+A\+SE}} \item \mbox{\hyperlink{parse_directives_no-database}{no-\/database}} \end{DoxyItemize} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_ga2f13313c2aa21817850133f99b44c2fa}\label{group__functional__domain__constants_ga2f13313c2aa21817850133f99b44c2fa}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+D\+E\+B\+U\+G\+G\+ER@{D\+O\+M\+\_\+\+D\+E\+B\+U\+G\+G\+ER}} \index{D\+O\+M\+\_\+\+D\+E\+B\+U\+G\+G\+ER@{D\+O\+M\+\_\+\+D\+E\+B\+U\+G\+G\+ER}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+D\+E\+B\+U\+G\+G\+ER}{DOM\_DEBUGGER}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+D\+E\+B\+U\+G\+G\+ER = Q\+D\+O\+M\+\_\+\+D\+E\+B\+U\+G\+G\+ER} provides debugging functionality \begin{DoxySeeAlso}{See also} \mbox{\hyperlink{group__parse__options_gad0d38cd46f08bf4210d4010204269cc9}{P\+O\+\_\+\+A\+L\+L\+O\+W\+\_\+\+D\+E\+B\+U\+G\+G\+ER}} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_ga945741abd74f2121fa9a2fb89d8c6b4c}\label{group__functional__domain__constants_ga945741abd74f2121fa9a2fb89d8c6b4c}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+E\+M\+B\+E\+D\+D\+E\+D\+\_\+\+L\+O\+G\+IC@{D\+O\+M\+\_\+\+E\+M\+B\+E\+D\+D\+E\+D\+\_\+\+L\+O\+G\+IC}} \index{D\+O\+M\+\_\+\+E\+M\+B\+E\+D\+D\+E\+D\+\_\+\+L\+O\+G\+IC@{D\+O\+M\+\_\+\+E\+M\+B\+E\+D\+D\+E\+D\+\_\+\+L\+O\+G\+IC}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+E\+M\+B\+E\+D\+D\+E\+D\+\_\+\+L\+O\+G\+IC}{DOM\_EMBEDDED\_LOGIC}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+E\+M\+B\+E\+D\+D\+E\+D\+\_\+\+L\+O\+G\+IC = Q\+D\+O\+M\+\_\+\+E\+M\+B\+E\+D\+D\+E\+D\+\_\+\+L\+O\+G\+IC} provides dynamic parsing functionality \begin{DoxySeeAlso}{See also} \mbox{\hyperlink{group__parse__options_gab1337f461ab4a90df9b39a7f1b6cc2b0}{P\+O\+\_\+\+N\+O\+\_\+\+E\+M\+B\+E\+D\+D\+E\+D\+\_\+\+L\+O\+G\+IC}} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_ga86d8ac6c1ca9050fe51107a97ea5b9fd}\label{group__functional__domain__constants_ga86d8ac6c1ca9050fe51107a97ea5b9fd}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+I\+N\+FO@{D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+I\+N\+FO}} \index{D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+I\+N\+FO@{D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+I\+N\+FO}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+I\+N\+FO}{DOM\_EXTERNAL\_INFO}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+I\+N\+FO = Q\+D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+I\+N\+FO} provides access to external information (ex\+: hostname, pid, process uid, etc) \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_ga213aab826b55076c29ffeecebbaea237}{P\+O\+\_\+\+N\+O\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+I\+N\+FO}} \item \mbox{\hyperlink{parse_directives_no-external-info}{no-\/external-\/info}} \end{DoxyItemize} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_ga2492eb49a7b137acb574a98a18176d22}\label{group__functional__domain__constants_ga2492eb49a7b137acb574a98a18176d22}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+P\+R\+O\+C\+E\+SS@{D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+P\+R\+O\+C\+E\+SS}} \index{D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+P\+R\+O\+C\+E\+SS@{D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+P\+R\+O\+C\+E\+SS}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+P\+R\+O\+C\+E\+SS}{DOM\_EXTERNAL\_PROCESS}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+P\+R\+O\+C\+E\+SS = Q\+D\+O\+M\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+P\+R\+O\+C\+E\+SS} provides external process control functionality (can affect) start) or stop external processes) \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_gaab2d8faa88f066837e100152187e6368}{P\+O\+\_\+\+N\+O\+\_\+\+E\+X\+T\+E\+R\+N\+A\+L\+\_\+\+P\+R\+O\+C\+E\+SS}} \item \mbox{\hyperlink{parse_directives_no-external-process}{no-\/external-\/process}} \end{DoxyItemize} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_gaed32c700f988d21a2a3c55ccf36f451c}\label{group__functional__domain__constants_gaed32c700f988d21a2a3c55ccf36f451c}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+F\+I\+L\+E\+S\+Y\+S\+T\+EM@{D\+O\+M\+\_\+\+F\+I\+L\+E\+S\+Y\+S\+T\+EM}} \index{D\+O\+M\+\_\+\+F\+I\+L\+E\+S\+Y\+S\+T\+EM@{D\+O\+M\+\_\+\+F\+I\+L\+E\+S\+Y\+S\+T\+EM}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+F\+I\+L\+E\+S\+Y\+S\+T\+EM}{DOM\_FILESYSTEM}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+F\+I\+L\+E\+S\+Y\+S\+T\+EM = Q\+D\+O\+M\+\_\+\+F\+I\+L\+E\+S\+Y\+S\+T\+EM} provides access to the filesystem \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_ga5e466ed886222f0b57b0a399b455be71}{P\+O\+\_\+\+N\+O\+\_\+\+F\+I\+L\+E\+S\+Y\+S\+T\+EM}} \item \mbox{\hyperlink{parse_directives_no-filesystem}{no-\/filesystem}} \end{DoxyItemize} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_gaac43540fdce157e8f8df0ad26bbf7437}\label{group__functional__domain__constants_gaac43540fdce157e8f8df0ad26bbf7437}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+G\+UI@{D\+O\+M\+\_\+\+G\+UI}} \index{D\+O\+M\+\_\+\+G\+UI@{D\+O\+M\+\_\+\+G\+UI}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+G\+UI}{DOM\_GUI}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+G\+UI = Q\+D\+O\+M\+\_\+\+G\+UI} provides G\+UI functionality \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_ga005117c783de66a8635beead079f52bd}{P\+O\+\_\+\+N\+O\+\_\+\+G\+UI}} \item \mbox{\hyperlink{parse_directives_no-gui}{no-\/gui}} \end{DoxyItemize} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_ga122e9d3fcaf41d9fecd53f24be496568}\label{group__functional__domain__constants_ga122e9d3fcaf41d9fecd53f24be496568}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+I\+N\+J\+E\+C\+T\+I\+ON@{D\+O\+M\+\_\+\+I\+N\+J\+E\+C\+T\+I\+ON}} \index{D\+O\+M\+\_\+\+I\+N\+J\+E\+C\+T\+I\+ON@{D\+O\+M\+\_\+\+I\+N\+J\+E\+C\+T\+I\+ON}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+I\+N\+J\+E\+C\+T\+I\+ON}{DOM\_INJECTION}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+I\+N\+J\+E\+C\+T\+I\+ON = Q\+D\+O\+M\+\_\+\+I\+N\+J\+E\+C\+T\+I\+ON} provides functionality related to code / dependency injection \begin{DoxySeeAlso}{See also} \mbox{\hyperlink{group__parse__options_ga1c78ca9bda4b8f5b2ad669c48fe0368d}{P\+O\+\_\+\+A\+L\+L\+O\+W\+\_\+\+I\+N\+J\+E\+C\+T\+I\+ON}} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_gaaf4c9194f22ca56bd3b95caa436214c3}\label{group__functional__domain__constants_gaaf4c9194f22ca56bd3b95caa436214c3}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+L\+O\+C\+A\+L\+E\+\_\+\+C\+O\+N\+T\+R\+OL@{D\+O\+M\+\_\+\+L\+O\+C\+A\+L\+E\+\_\+\+C\+O\+N\+T\+R\+OL}} \index{D\+O\+M\+\_\+\+L\+O\+C\+A\+L\+E\+\_\+\+C\+O\+N\+T\+R\+OL@{D\+O\+M\+\_\+\+L\+O\+C\+A\+L\+E\+\_\+\+C\+O\+N\+T\+R\+OL}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+L\+O\+C\+A\+L\+E\+\_\+\+C\+O\+N\+T\+R\+OL}{DOM\_LOCALE\_CONTROL}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+L\+O\+C\+A\+L\+E\+\_\+\+C\+O\+N\+T\+R\+OL = Q\+D\+O\+M\+\_\+\+L\+O\+C\+A\+L\+E\+\_\+\+C\+O\+N\+T\+R\+OL} provides access to functionality that changes locale information \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_ga99046cc8285fb26438508cdf29b5771e}{P\+O\+\_\+\+N\+O\+\_\+\+L\+O\+C\+A\+L\+E\+\_\+\+C\+O\+N\+T\+R\+OL}} \item \mbox{\hyperlink{parse_directives_no-locale-control}{no-\/locale-\/control}} \end{DoxyItemize} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_ga233b03c196dcaa21187f359e87c48ac8}\label{group__functional__domain__constants_ga233b03c196dcaa21187f359e87c48ac8}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+M\+O\+D\+U\+LE@{D\+O\+M\+\_\+\+M\+O\+D\+U\+LE}} \index{D\+O\+M\+\_\+\+M\+O\+D\+U\+LE@{D\+O\+M\+\_\+\+M\+O\+D\+U\+LE}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+M\+O\+D\+U\+LE}{DOM\_MODULE}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+M\+O\+D\+U\+LE = Q\+D\+O\+M\+\_\+\+M\+O\+D\+U\+L\+ES} provides access to external modules \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_gaccf9af08f7acb25e66b777dcb4c4563b}{P\+O\+\_\+\+N\+O\+\_\+\+M\+O\+D\+U\+L\+ES}} \item \mbox{\hyperlink{parse_directives_no-modules}{no-\/modules}} \end{DoxyItemize} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_ga0b0bb2cc8627c910e5445bf004a8a46b}\label{group__functional__domain__constants_ga0b0bb2cc8627c910e5445bf004a8a46b}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+N\+E\+T\+W\+O\+RK@{D\+O\+M\+\_\+\+N\+E\+T\+W\+O\+RK}} \index{D\+O\+M\+\_\+\+N\+E\+T\+W\+O\+RK@{D\+O\+M\+\_\+\+N\+E\+T\+W\+O\+RK}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+N\+E\+T\+W\+O\+RK}{DOM\_NETWORK}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+N\+E\+T\+W\+O\+RK = Q\+D\+O\+M\+\_\+\+N\+E\+T\+W\+O\+RK} provides network functionality \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_ga20400e83c6271a294a48b15a8f952efa}{P\+O\+\_\+\+N\+O\+\_\+\+N\+E\+T\+W\+O\+RK}} \item \mbox{\hyperlink{parse_directives_no-network}{no-\/network}} \end{DoxyItemize} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_ga51bbde061f74c08025b1d7c18184f773}\label{group__functional__domain__constants_ga51bbde061f74c08025b1d7c18184f773}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+P\+R\+O\+C\+E\+S\+S\+\_\+\+C\+O\+N\+T\+R\+OL@{D\+O\+M\+\_\+\+P\+R\+O\+C\+E\+S\+S\+\_\+\+C\+O\+N\+T\+R\+OL}} \index{D\+O\+M\+\_\+\+P\+R\+O\+C\+E\+S\+S\+\_\+\+C\+O\+N\+T\+R\+OL@{D\+O\+M\+\_\+\+P\+R\+O\+C\+E\+S\+S\+\_\+\+C\+O\+N\+T\+R\+OL}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+P\+R\+O\+C\+E\+S\+S\+\_\+\+C\+O\+N\+T\+R\+OL}{DOM\_PROCESS\_CONTROL}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+P\+R\+O\+C\+E\+S\+S\+\_\+\+C\+O\+N\+T\+R\+OL = Q\+D\+O\+M\+\_\+\+P\+R\+O\+C\+E\+SS} provides process control functionality (can affect or stop the current process) \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_ga10d8e3f76c427b0f974529de572dd0ec}{P\+O\+\_\+\+N\+O\+\_\+\+P\+R\+O\+C\+E\+S\+S\+\_\+\+C\+O\+N\+T\+R\+OL}} \item \mbox{\hyperlink{parse_directives_no-process-control}{no-\/process-\/control}} \end{DoxyItemize} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_gaad785fc289011722fb8a3c6c9ab53790}\label{group__functional__domain__constants_gaad785fc289011722fb8a3c6c9ab53790}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+R\+E\+F\+L\+E\+C\+T\+I\+ON@{D\+O\+M\+\_\+\+R\+E\+F\+L\+E\+C\+T\+I\+ON}} \index{D\+O\+M\+\_\+\+R\+E\+F\+L\+E\+C\+T\+I\+ON@{D\+O\+M\+\_\+\+R\+E\+F\+L\+E\+C\+T\+I\+ON}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+R\+E\+F\+L\+E\+C\+T\+I\+ON}{DOM\_REFLECTION}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+R\+E\+F\+L\+E\+C\+T\+I\+ON = Q\+D\+O\+M\+\_\+\+R\+E\+F\+L\+E\+C\+T\+I\+ON} provides reflection functionality \begin{DoxySeeAlso}{See also} \mbox{\hyperlink{group__parse__options_ga454fabf3a392b8fec9ee587e97a2d8e8}{P\+O\+\_\+\+N\+O\+\_\+\+R\+E\+F\+L\+E\+C\+T\+I\+ON}} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_ga27d39c32f12097d84a446f06e3c7978d}\label{group__functional__domain__constants_ga27d39c32f12097d84a446f06e3c7978d}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+T\+E\+R\+M\+I\+N\+A\+L\+\_\+\+IO@{D\+O\+M\+\_\+\+T\+E\+R\+M\+I\+N\+A\+L\+\_\+\+IO}} \index{D\+O\+M\+\_\+\+T\+E\+R\+M\+I\+N\+A\+L\+\_\+\+IO@{D\+O\+M\+\_\+\+T\+E\+R\+M\+I\+N\+A\+L\+\_\+\+IO}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+T\+E\+R\+M\+I\+N\+A\+L\+\_\+\+IO}{DOM\_TERMINAL\_IO}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+T\+E\+R\+M\+I\+N\+A\+L\+\_\+\+IO = Q\+D\+O\+M\+\_\+\+T\+E\+R\+M\+I\+N\+A\+L\+\_\+\+IO} provides terminal I/O functionality \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_gaa92bf6eafb76a4ccf1a0d0df45b13363}{P\+O\+\_\+\+N\+O\+\_\+\+T\+E\+R\+M\+I\+N\+A\+L\+\_\+\+IO}} \item \mbox{\hyperlink{parse_directives_no-terminal-io}{no-\/terminal-\/io}} \end{DoxyItemize} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_ga8cb18f231d451bed11c5fb81f9124f6c}\label{group__functional__domain__constants_ga8cb18f231d451bed11c5fb81f9124f6c}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+L\+A\+SS@{D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+L\+A\+SS}} \index{D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+L\+A\+SS@{D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+L\+A\+SS}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+L\+A\+SS}{DOM\_THREAD\_CLASS}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+L\+A\+SS = Q\+D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+L\+A\+SS} provides thread control functionality \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_gade963e1fbbd1f5b2c777df7221512a1b}{P\+O\+\_\+\+N\+O\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+L\+A\+S\+S\+ES}} \item \mbox{\hyperlink{parse_directives_no-thread-classes}{no-\/thread-\/classes}} \end{DoxyItemize} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_gaf63c9d233d9365eb6d12a48b444485a5}\label{group__functional__domain__constants_gaf63c9d233d9365eb6d12a48b444485a5}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+O\+N\+T\+R\+OL@{D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+O\+N\+T\+R\+OL}} \index{D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+O\+N\+T\+R\+OL@{D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+O\+N\+T\+R\+OL}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+O\+N\+T\+R\+OL}{DOM\_THREAD\_CONTROL}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+O\+N\+T\+R\+OL = Q\+D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+O\+N\+T\+R\+OL} provides the ability to check or manipulate threads (including starting new threads) \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_ga16d8c2b85171b6673b60b5f7d0eaf5eb}{P\+O\+\_\+\+N\+O\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+C\+O\+N\+T\+R\+OL}} \item \mbox{\hyperlink{parse_directives_no-thread-control}{no-\/thread-\/control}} \end{DoxyItemize} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_gaddd830f869f2a077097683f84f409f2e}\label{group__functional__domain__constants_gaddd830f869f2a077097683f84f409f2e}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+I\+N\+FO@{D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+I\+N\+FO}} \index{D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+I\+N\+FO@{D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+I\+N\+FO}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+I\+N\+FO}{DOM\_THREAD\_INFO}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+I\+N\+FO = Q\+D\+O\+M\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+I\+N\+FO} provides access to information regarding threading (tid, active threads, etc) \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_gac379d98e62c57231c2efb7ea87c75a3a}{P\+O\+\_\+\+N\+O\+\_\+\+T\+H\+R\+E\+A\+D\+\_\+\+I\+N\+FO}} \item \mbox{\hyperlink{parse_directives_no-thread-info}{no-\/thread-\/info}} \end{DoxyItemize} \end{DoxySeeAlso} \mbox{\Hypertarget{group__functional__domain__constants_gaa643a322407977526fadc2a08d636916}\label{group__functional__domain__constants_gaa643a322407977526fadc2a08d636916}} \index{Functional Domain Constants@{Functional Domain Constants}!D\+O\+M\+\_\+\+U\+N\+C\+O\+N\+T\+R\+O\+L\+L\+E\+D\+\_\+\+A\+PI@{D\+O\+M\+\_\+\+U\+N\+C\+O\+N\+T\+R\+O\+L\+L\+E\+D\+\_\+\+A\+PI}} \index{D\+O\+M\+\_\+\+U\+N\+C\+O\+N\+T\+R\+O\+L\+L\+E\+D\+\_\+\+A\+PI@{D\+O\+M\+\_\+\+U\+N\+C\+O\+N\+T\+R\+O\+L\+L\+E\+D\+\_\+\+A\+PI}!Functional Domain Constants@{Functional Domain Constants}} \subsubsection{\texorpdfstring{D\+O\+M\+\_\+\+U\+N\+C\+O\+N\+T\+R\+O\+L\+L\+E\+D\+\_\+\+A\+PI}{DOM\_UNCONTROLLED\_API}} {\footnotesize\ttfamily const Qore\+::\+D\+O\+M\+\_\+\+U\+N\+C\+O\+N\+T\+R\+O\+L\+L\+E\+D\+\_\+\+A\+PI = Q\+D\+O\+M\+\_\+\+U\+N\+C\+O\+N\+T\+R\+O\+L\+L\+E\+D\+\_\+\+A\+PI} provides unchecked access to system functionality that could bypass \mbox{\hyperlink{namespace_qore}{Qore}}\textquotesingle{}s sandboxing controls \begin{DoxySeeAlso}{See also} \begin{DoxyItemize} \item \mbox{\hyperlink{group__parse__options_ga88a927479c495b99209a6397ef67c240}{P\+O\+\_\+\+N\+O\+\_\+\+U\+N\+C\+O\+N\+T\+R\+O\+L\+L\+E\+D\+\_\+\+A\+P\+IS}} \item \mbox{\hyperlink{parse_directives_no-uncontrolled-apis}{no-\/uncontrolled-\/apis}} \end{DoxyItemize} \end{DoxySeeAlso}
https://mirror.las.iastate.edu/tex-archive/graphics/mcf2graph/mcf_manual.tex	iastate.edu	CC-MAIN-2022-49	application/x-tex	text/x-matlab	crawl-data/CC-MAIN-2022-49/segments/1669446710924.83/warc/CC-MAIN-20221203043643-20221203073643-00213.warc.gz	420,489,727	13,131	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Molecular Coding Format manual by Akira Yamaji 2022.11.12 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \documentclass[a4paper]{article} %%%\usepackage{graphicx} %%%\usepackage{hyperref} \usepackage[pdftex]{graphicx} \usepackage[pdftex]{hyperref} %%%\usepackage[dvipdfmx]{graphicx} %%%\usepackage[dvipdfmx]{hyperref} \usepackage{makeidx} \makeindex \hypersetup{colorlinks=true,linkcolor=blue} \usepackage{mcf_setup} \edef\MCFjobname{mcf_man_soc}% %---------------------------------------------------------------------------- \edef\fext{mps}% \topmargin=-18mm \textheight=254mm \textwidth=168mm \oddsidemargin=0mm %%%%\oddsidemargin=7mm %%%%\evensidemargin=-7mm \unitlength=1mm% %---------------------------------------------------------------------------- \newcount \fnum% \newdimen \htman% \newdimen \wdman% \newdimen \htmans% \newbox \fbox% %---------------------------------------------------------------------------- \htman=45mm% \wdman=94mm% \htmans=42mm% \fnum=1% %---------------------------------------------------------------------------- \makeatletter %---------------------------------------------------------------------------- \def\MCFgraph{% \edef\file@name{\MCFjobname-\z@num\fnum.\fext}% \includegraphics{\file@name}% \global\advance\fnum\@ne\relax% }% %---------------------------------------------------------------------------- \def\put@char{% \begin{picture}(75,100)% \put(0,95){\bf [\NO]\EN}% \put(5,90){\small\tt FM:\fm{ }MW:\mw}% \put(5,0){\MCFgraph}% \end{picture}% }% %---------------------------------------------------------------------------- \begin{document} \title{\Huge\sf Molecular Coding Format manual} \author{Akira Yamaji} \date{\today} \maketitle \begin{center} Located at http://www.ctan.org/pkg/mcf2graph \end{center} \begin{center} Suggestion or request mail to: [email protected] \end{center} %----------------------------------------------------------------------------- \thispagestyle{empty} \vspace{5mm}% \MCFgraph\MCFgraph\MCFgraph\MCFgraph\\ \MCFgraph\MCFgraph\MCFgraph\MCFgraph\\ \MCFgraph\MCFgraph\MCFgraph\MCFgraph\\ \MCFgraph\MCFgraph\MCFgraph\MCFgraph\\ \MCFgraph\MCFgraph\MCFgraph\MCFgraph\\ \MCFgraph\MCFgraph\MCFgraph\MCFgraph\\ \MCFgraph\MCFgraph\MCFgraph\MCFgraph %----------------------------------------------------------------------------- \twocolumn \thispagestyle{empty} \tableofcontents %----------------------------------------------------------------------------- \linethickness{0.08mm}% %---------------------------------------------------------------------------- \newpage \twocolumn \section{Introduction} Molecular Coding Format(MCF) is new linear notation represent chemical structure diagrams. This Coding is named from programing technique such as operator, array, scope, macro, adressing, etc. mcf2graph convert from MCF to PNG, SVG, EPS, MOL file. It is also able to calculate molecular weight, exact mass, molecular formula. %----------------------------------------------------------------------------- \section{MCF syntax} \subsection{Make bond} \subsubsection{Chain} \begin{verbatim} real number plus (+): counterclockwize real number minus(-): clockwize $n (0<=n<360): absolute angle <10,-30,45,-45,60,$300,$0 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Chain use !,!n} \index{"!}% \begin{verbatim} ! : take value 60 or -60 depend on current angle and environment !6 : !,!,!,!,!,! <-30,!6 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Jump to atom} \index{"@}% \begin{verbatim} @n : Jump to An ** An: atom number(-999<=n<=4095) <-30,!6,@3,0,!,@5,-30 \end{verbatim} \MCFgraph %------------------------------------ \subsubsection{Branch bond} \index{\textbackslash}% \begin{verbatim} \ : 0 <-30,!6,@3,\,! \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Branch modified bond} \index{\textbackslash}% \index{\textbackslash}% \index{\textbackslash\textbackslash}% \index{\textbackslash}% \begin{verbatim} \ : 0 \ : 0~wf \ : 0~zf \\ : 0~dm \ : 0~wv <30,!8, @2,\,!,@4,\,!,@6,\,!,@8,\\,!,@10,\,! \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \index{\textasciicircum}% ^ \index{\textasciitilde}% ~ \index{`}% \begin{verbatim} <30,!6, \~dr,!, : 0~dr,! \`1.5,-90 : 0`1.5,-90 \^15,-60 : 0^15,-60 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Connect atom} \index{\&}% \begin{verbatim} &n : Connect to An <-30,!6,@3,\,!3,&6~bd,@9,&4~bz \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Ring} \index{?}% \begin{verbatim} ?n : n membered ring(3<=n<=20) ?6 : <-120,60,60,60,60,60,&1 ?6 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Rotate current angle} \index{\textgreater}% \begin{verbatim} <angle : rotate current angle 0,0,<90,0,<-90,0,<$315,0,<$90,0,<$0,0 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Change bond type} \subsubsection{Double,triple,wedge,vector} \index{\textasciitilde}% \index{\textasciitilde\textasciitilde}% \index{"!"!}% \index{"!"!"!}% \index{dm}% \index{dl}% \index{dr}% \index{db}% \index{tm}% \begin{verbatim} (Double,triple) a~type : ~~type,a dm : double middle dl : double left side dr : double right side db : double left or right side tm : triple !! : !~db / !!! : !~tm <-30,!~dm,!,!~dl,!,!~dr,!~db,!~db,!,!~tm <-30,!~dm,!,!~dl,!,!~dr,!! ,!! ,!,!!! \end{verbatim} \MCFgraph \vspace{-3mm}% %----------------------------------------------------------------------------- %%\subsubsection{Wedge} \index{wf}% \index{wb}% \index{zf}% \index{zb}% \index{vf}% \index{vb}% \begin{verbatim} (Wedge,Vector) wf: wedge forward wb: wedge backward zf: hashed(zebra stripe) wedge foward zb: hashed(zebra stripe) wedge backward vf:vector forward vb:vector backward <-30, !~wf,!,!~wb,!,!~zf,!,!~zb,!,!~vf,!~vb \end{verbatim} \MCFgraph \vspace{-3mm}% %----------------------------------------------------------------------------- %%\subsubsection{Dotted,wave} \index{dt}% \index{wv}% \index{bd}% \index{bz}% \begin{verbatim} (Dotted,wave) Bn=bond type : change bond type at Bn dt : dotted / wv : wave bd : broad / bz : broad dotted <-30,!7,1=dt,3=wv,5=bd,7=bz \end{verbatim} \MCFgraph \vspace{-3mm}% %----------------------------------------------------------------------------- \subsubsection{Over line} \index{si\_}% \index{wf\_}% \index{wb\_}% \index{zf\_}% \index{zb\_}% \index{bd\_}% \index{dl\_}% \index{dr\_}% \index{dm\_}% \begin{verbatim} si_ : single over line wf_ : wedge forward over line wb_ : wedge backward over line zf_ : hashed wedge forward over line zb_ : hashed wedge backward over line bd_ : broad over line dl_ : duble left over line dr_ : duble right over line dm_ : duble over line <30,!8,!,60,90`18, {2~si_,4~wf_,6~wb_,8~zf_,10~zb_, 12~bd_,14~dl_,16~dr_,18~dm_}:/_`2 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Steric ring} \index{wf\_r}% \index{wb\_r}% \index{bd\_r}% \begin{verbatim} wf_r : wedge foward (half width) bd_r : broad (half width, rounded) wb_r : wedge backward (half width) #1.25,-30~wf_r,30~bd_r`1,30~wb_r, 120,O,30,&1,##,#.5,6^$90:/!OH, {1^$-90,2^$90,3^$-90,4^$90}:/OH, \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Change multiple bond type} \index{vf}% \begin{verbatim} {2,4,6,8'}=dl : 2=dl,4=dl,6=dl,8=dr <30,!7,{2,4,6,8'}=dl \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Change bond length} \subsubsection{Chain length} \index{`}% \begin{verbatim} (!,!n)`length : change length of !,!n <-30,!2,!4`1.2,!2 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \index{\#}% \index{\#\#}% \begin{verbatim} #n : bond length=n ## : reset bond length <-30,!2,#1.2,!4,##,!2 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Ring length} \begin{verbatim} ?n`length : change ring length ?6,@4,\,?6`1.2 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Change atom} \subsubsection{Insert atom} \begin{verbatim} Insert hetero atom <-30,!2,O,!2,N,!2 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Addressed atom} \index{:}% \begin{verbatim} 2:O : change A2 C to O {3,4}:N : change A3,A4 C to N <30,!4,2:O,{3,4}:N \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Brock address} \index{\textbar}% \| \begin{verbatim} \| : divide brock ?6,@4,\,\|,?6,2:O \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Reset brock address} \index{\textbar\textbar}% \|\| \begin{verbatim} \|\| : reset brock adress ?6,@4,\,\|,?6,\|\|,2:N \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Absolute address} \index{\$}% $ \begin{verbatim} $2:N : change A$2 C to N 1<=n<=3095 ?6,@4,\,\|,?6,$2:N \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Relative address} \begin{verbatim} -2:N : change A(-2) C to N -999<=n<=-1 ?6,@4,\,?6,-2:N \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Charged atom} \begin{verbatim} p_ : positive / n_ : negative <-30,!2,N,??,p_,!2,S,n_^180, !6,7:N,7:??,9:S,7:n_,9:n_^180 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \newpage %----------------------------------------------------------------------------- \subsection{Fuse ring} %%%\subsubsection{Attached 1 bond} \begin{verbatim} (Attached 1 bond) ?6,3=?6 : fuse ?6 at B3 Bn(n:-999<=n<=4095): bond number ?6,3=?6 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \begin{verbatim} fused ring size depend on attached bond length ?6,@4,\,?6`1.2,5=?6,11=?6 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \begin{verbatim} ?6,3=?6[13] : fuse ?6[13] at B3 ?6[13]: 6 membered ring scaled 13/10 ** ?m[n] (5<=m<=8,11<=n<=15) ?6,3=?6[13] \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \begin{verbatim} ?6,{-3,-4,-4,-2,-2,-4,-4}=?6 ?6,{4,8,13,20,25,28,33}=?6 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- %%%\subsubsection{Attached 2 bond} \index{--}% \begin{verbatim} (Attached 2 bond) 4--11=?6 : fuse 4/6 ring to B11..B4 4--11=?5 : fuse 3/5 ring to B11..B4 4--11=?4 : fuse 2/4 ring to B11..B4 1:<30,?6,3=?6,11--4=?6 2:<30,?6,3=?6,11--4=?5 3:<30,?6,3=?6,11--4=?4 \end{verbatim} \MCFgraph \vspace{-3mm}% \begin{verbatim} \end{verbatim} %----------------------------------------------------------------------------- %%%\subsubsection{Attached 3 bond} \index{---}% \begin{verbatim} (Attached 3 bond) 16---4=?6 : fuse 3/6 ring to B16..B4 16---4=?5 : fuse 2/5 ring to B16..B4 1:?6,{3,10,16---4}=?6 2:?6,{3,10}=?6,16---4=?5 \end{verbatim} \MCFgraph \vspace{-3mm}% \begin{verbatim} \end{verbatim} %----------------------------------------------------------------------------- %%%%\subsubsection{Attached 4 bond} \index{----}% \begin{verbatim} (Attached 4 bond) 21----4=?6 : fuse 2/6 ring to B21..B4 <-30,?6,{3,10,15,21----4}=?6 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Spiro ring} \begin{verbatim} @4,?5 : add ?5 at A4 <30,!6,@4,?5 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Group} \subsubsection{Insert group} \index{/}% \index{Ph}% \begin{verbatim} / : group start single bond /_ : methyl /! : ethyl /!2 : propyl /?! : isopropyl /??! : tert-butyl /Ph : phenyl <30,!,/_,!2,/!,!2,/!2,!4,/?!, !4,/??!,!2,/Ph^-60,! \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Insert modified group} \index{//}% \index{/}% \index{/}% \index{/}% \index{*}% \begin{verbatim} // : double (double middle) / : wedge forward /* : hashed wedge forward / : wave ** : direct <30,!,//O,!2,/H,!2,/H,!2,/H,!2,*?3,! \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \index{\textasciicircum}% ^ \index{\textasciitilde}% ~ \index{`}% \index{\textless}% \begin{verbatim} ~ : change type ^ : change angle ` : change length > : change environment <-30,``1,!, /_`2^30,!2,/!2>lr,!2,/!2>rl,!) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Add group} \begin{verbatim} <30,!17,2:/_,3:/!,4:/!2,7:/iPr, 8:/tBu,10:/'(Ph`0.6)^-15, {11,12,13'}:/_,{15,16,17'}:/_ \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Add modified group} \begin{verbatim} ~,^,` : change type,angle,length <30,!6,{2~wf,4~zf,6^-30,8^$120}:/_ \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \begin{verbatim} ^,`,> : change angle,length,environment <-30,!7`1,3:/_`2^30,5:/!2>lr,7:/!2>rl \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \newpage %----------------------------------------------------------------------------- \subsection{Chain environment} \subsubsection{Horizontal,vertical} \index{hz}% \index{vt}% \index{"'}% \begin{verbatim} >hz : horizontal environment (default) >vt : vertical environment ?4, {3^-90,3^-30,3^90}:/!3>hz, {1^-60,1,1^60}:/!3>vt \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Left-right,right-left} \index{lr}% \index{rl}% \begin{verbatim} >lr : left-right environment >rl : right-left environment <-30,!6, {3^-30,3,3^30}:/!3>lr, {5^-30,5,5^30}:/!3>rl \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Fixed rotate angle} \index{\textgreater}% \begin{verbatim} >n : rotate n <30,!4, 2:/!6>30, % 2:\,30,30,30,30,30,30 4:/!4>-45 % 4:\,-45,-45,-45,-45 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Multiple rotate angle} \begin{verbatim} >'(90,-90,...) : rotate 90,-90,... <30,!6,6>'(90,-90,90,-90,90):/!5 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \newpage \subsection{Miscellaneous} %----------------------------------------------------------------------------- \subsubsection{Abbreviated parts} \index{NH}% \index{N"!}% \index{N"!2}% \index{SO}% \index{SOO}% \begin{verbatim} NH : N,/H~nl N! : N,/_ N!2 : N,/! SO : S,//O SOO : S,//O^35,//^-35 <-30,!2,NH,!2,N!,!2,N!2,SO,!2,SOO,! \end{verbatim} \MCFgraph \index{?"!}% \index{??}% \index{??"!}% \index{N?"!}% \begin{verbatim} ?! : /_,! ?? : /_^35,/_-35 /?! : isopropyl /??! : tert-butyl /N?! : dimethylamino <30,!9`1,?!,!,??,!,2:??,4:/??,6:/??!,8:/N?! \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Parts definition} \begin{verbatim} '(..) : user defined parts iBuOH:='(!,/_,!,OH); MC(<30,?6,{4,6}:/iBuOH) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Parts inline definition} \begin{verbatim} <30,!8,{2,6}:/'(!,/_,!,OH) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Move position} \index{"@()}% \begin{verbatim} @(x,y) : Move l(x,y) from current position @$(x,y): Move l(x,y) from origin(@1) * l=bond length of ring <30,?6,@3,!4,//O,!,O,n_^60,@$(6,1),H,p_^15 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Serial number} \index{\-\-}% \begin{verbatim} 6:10 : 6,7,8,9,10 <30,!14,{2,6:10,14}:/_~bd_r`0.5 \end{verbatim} \MCFgraph \newpage %----------------------------------------------------------------------------- \subsubsection{Change color} \index{red}% \index{blue}% \index{green}% \begin{verbatim} beginfigm() MC( <30,Ph,{2,5}:N,3:/NH2,4:/COOH, %--------------------- 2:red, % red A2 5:blue, % blue A5 3=green % green B3 %--------------------- ) endfigm \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Change font} \index{atomfont}% \begin{verbatim} beginfigm() %---------------- atomfont:="cmr8"; %---------------- MC(<30,Ph,{2,5}:N,3:/NH2,4:/COOH) endfigm \end{verbatim} \MCFgraph %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Option parameter} %------------------------------------------------------------------------------ \subsection{Angle parameter} \index{mangle}% \begin{verbatim} mangle=0 default MCat(0.2,0.5)(Ph) mangle:=30; MCat(0.8,0.5)(Ph) \end{verbatim} \MCFgraph %------------------------------------------------------------------------------ \subsection{Size/Ratio parameter} %----------------------------------------------------------------------------- \subsubsection{Bond length} \index{blength}% \begin{verbatim} (fit to figure size) blength=0 default \end{verbatim} \MCFgraph %----------------------------------------- \begin{verbatim} (ratio bond/figure width) blength=0.1 ** (0<blength<=1) blength=60mm(width)0.1=6mm \end{verbatim} \MCFgraph %----------------------------------------- \begin{verbatim} (bond length) blength=9mm * (blength>1) ignore msize(w,h) \end{verbatim} \MCFgraph %------------------------------------------------------------------------------ \subsubsection{Molecular size} \index{msize}% \begin{verbatim} msize=(1,1) ** default \end{verbatim} \MCFgraph %----------------------------------------------------------- \begin{verbatim} msize=(0.25,1) msize=40mm-4mm0.25=9mm \end{verbatim} \MCFgraph %----------------------------------------------------------- \begin{verbatim} msize=(11mm,11mm) \end{verbatim} \MCFgraph %------------------------------------------------------------------------------ \subsubsection{Molecular position} \index{mposition}% \begin{verbatim} mposition=(0.5,0.5) * default \end{verbatim} \MCFgraph %-------------------------------------------------------------- \begin{verbatim} mposition=(1,0) \end{verbatim} \MCFgraph %-------------------------------------------------------------- \begin{verbatim} mposition=(10mm,4mm) \end{verbatim} \MCFgraph %------------------------------------------------------------------------------ \subsection{Size parameter} %----------------------------------------------------------------------------- \subsubsection{Figure size} \index{fsize}% \begin{verbatim} fsize=(figure width,figure height) default: (30mm,20mm) fsize=(40mm,15mm) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Figure margin} \index{fmargin}% \begin{verbatim} fmargin=(margin left rigth,top bottom) default: (0.4mm,0.4mm) fmargin=(10mm,2mm) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Offset thickness of bond} \index{offset\_thickness}% \begin{verbatim} default: offset_thickness=0.2pt \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Offset of double bond gap} \index{offset\_bond\_gap}% \begin{verbatim} default: offset_bond_gap=0.3pt \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Offset of atom width} \index{offset\_atom}% \begin{verbatim} default: offset_atom=0.8pt \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Offset of wedge width} \index{offset\_wedge}% \begin{verbatim} default: offset_wedge=0.4pt \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Max bond length} \index{max\_blength}% \begin{verbatim} default: max_blength=10mm \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Ratio parameter} %----------------------------------------------------------------------------- \subsubsection{Thickness/bond length} \index{ratio\_thickness\_bond}% \begin{verbatim} default: ratio_thickness_bond=0.015 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Char/bond thickness} \index{ratio\_char\_bond}% \begin{verbatim} default: ratio_char_bond=1.5 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Bond gap/bond length} \index{ratio\_bondgap\_bond}% \begin{verbatim} default: ratio_bondgap_bond= 0.15 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Atom/bond length} \index{ratio\_atom\_bond}% \begin{verbatim} default: ratio_atom_bond= 0.36 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Wedge/bond length} \index{ratio\_wedge\_bond}% \begin{verbatim} default: ratio_wedge_bond=0.12 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Figure atom gap/atom length} \index{ratio\_atomgap\_atom}% \begin{verbatim} default: ratio_atomgap_atom= 0.050 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Chain/ring length} \index{ratio\_chain\_ring}% \begin{verbatim} default: ratio_chain_ring= 0.66 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Hash gap/bond length} \index{ratio\_hashgap\_bond}% \begin{verbatim} default: ratio_hashgap_bond=0.12 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- %%%%\newpage %----------------------------------------------------------------------------- \subsection{Drawing mode} %----------------------------------------------------------------------------- \subsubsection{Numbering atom} \index{sw\_numbering}% \index{Atom}% \index{numbering\_start}% \index{numbering\_end}% \begin{verbatim} sw_numbering=Atom numbering_start:=3; numbering_end:=8; default: sw_numbering=0 sw_numbering:=Atom; MC(<-30,!9) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Numbering bond} \index{numbering\_start}% \index{numbering\_end}% \index{Bond}% \begin{verbatim} sw_numbering=Bond numbering_start:=3; numbering_end:=8; default: sw_numbering=0 sw_numbering:=Bond; MC(<-30,!9) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Trimming mode} \index{sw\_trimming}% \begin{verbatim} sw_trimming:=0; default msize:=(1,0.7); MCat(0.2,0.3)(Ph) MCat(0.8,0.7)(Ph) \end{verbatim} \MCFgraph \begin{verbatim} sw_trimming:=1; MCat(0.2,0.3)(Ph) MCat(0.8,0.7)(Ph) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Expand mode} \index{sw\_expand}% \begin{verbatim} MCat(0, .5)(<30,Ph,4:/COOH,3:/NH2) sw_expand:=1; MCat(1, .5)(<30,Ph,4:/COOH,3:/NH2) default: sw_expand=0 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Abbreviate group} \index{Group}% \index{sw\_abbreviate}% \begin{verbatim} default: sw_abbreviate=Group \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Abbreviate bond type} \index{Bond}% \index{sw\_abbreviate}% \begin{verbatim} default: sw_abbreviate=Bond \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Frame} %----------------------------------------------------------------------------- \subsubsection{Figure frame} \index{sw\_frame}% \index{Bothside}% \index{Inside}% \index{Outside}% \begin{verbatim} default:sw_frame=0 (Draw figure frame) fmargin:=(5mm,2mm); sw_frame=Outside \end{verbatim} \MCFgraph \begin{verbatim} (Frame inside margin) sw_frame=Inside \end{verbatim} \MCFgraph \begin{verbatim} (Draw both frame) sw_frame=Bothside=Inside+Outside \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Molecular frame} \index{Mol}% \begin{verbatim} sw_frame=Mol default:sw_frame=0 \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Atom frame} \index{Atom}% \begin{verbatim} sw_frame=Atom default: sw_frame=0 MC(<30,COOH,!,COOH) \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Parameter setting} \subsubsection{Local parameter setting} \index{beginfigm()}% \index{endfigm}% \begin{verbatim} beginfigm() MC(Ph) endfigm beginfigm() %-------------------------- ratio_thickness_bond:=0.05; %-------------------------- MC(Ph) endfigm beginfigm() MC(Ph) endfigm \end{verbatim} \MCFgraph\MCFgraph\MCFgraph %----------------------------------------------------------------------------- \subsubsection{Global parameter setting} \begin{verbatim} beginfigm() MC(Ph) endfigm %-------------------------- ratio_thickness_bond:=0.05; %-------------------------- beginfigm() MC(Ph) endfigm beginfigm() MC(Ph) endfigm \end{verbatim} \MCFgraph\MCFgraph\MCFgraph %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Function} %----------------------------------------------------------------------------- \subsection{Function MC()} \index{MC()}% \begin{verbatim} (Draw molecule) msize=(a,b) default (1,1) mposition=(c,d) default (0.5,0.5) a: ratio molecular width/figure width b: ratio molecular hight/figure hight c: x axis position d: y axis position beginfigm() MC(<30,Ph,3:/F,4:/Cl) endfigm \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Function MCat()} \index{MCat()}% \begin{verbatim} (Draw molecule at mposition) MCat(c,d)(....) : mposition:=(c,d); MC(....) c: x axis position d: y axis position defaultsize:=5bp; fsize:=(60mm,40mm); fmargin:=(3mm,3mm); blength:=0.07; sw_frame:=Outside; mangle:=0; for i=1 step -0.5 until 0: for j=0 step 0.33 until 1: MCat(j,i)(Ph,4:N) add(drawarrow((A1+A1upaw)..A1); label(decimal(mangle), p0+(0.5w,0.5h)); ) mangle:=mangle+30; endfor endfor \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Function mc\_check()} \index{mc\_check()}% \begin{verbatim} (immediately compile) beginfigm("EN:Pyridine") MC(<30,Ph,2:N) endfigm (check mcf and compile) mc_check(mc) : error count beginfigm("EN:Pyridine", ":<30,Ph,}2:N") % extra '}' if mc_check(mc)=0: MC(scantokens(mc)) fi endfigm \end{verbatim} \MCFgraph\hspace{22mm}\MCFgraph \begin{verbatim} mc_check(mc)=0 mc_check(mc)>=1 \end{verbatim} %=============================================================================== \newpage \subsection{Function add()} \index{add()}% \index{plus}% \index{minus}% \index{lonepair}% \index{lonepairdiam}% \index{lonepairspace}% \index{circlediam}% \index{circlepen}% \index{w}% \index{h}% \index{aw}% \index{em}% \index{p0}% \index{l}% \index{/}% \index{}% \index{\textgreater\textgreater}% \index{An}% \index{A[]}% \index{A[]ang}% \index{A[]up}% \index{A[]left}% \index{A[]right}% \index{A[]down}% \index{Bn}% \index{B[]}% \index{B[]s}% \index{B[]m}% \index{B[]e}% \index{B[]ang}% \index{B[]up}% \index{B[]left}% \index{B[]right}% \index{B[]down}% \index{defaultscale}% \index{labeloffset}% \begin{verbatim} (Add label to molecule) w: molecular width h: molecular height aw: atom font size em: label font size p0: origin of molecular structure l: bond length An: atom number A[m]: atom position A[m]ang: branch angle of A[m] A[m]up: dir A[m]ang A[m]left: dir A[m]ang+90 A[m]right: dir A[m]ang-90 A[m]down: dir A[m]ang+180 Bn: bond number B[m]: bond(path) B[m]s: bond start position B[m]m: bond middle position B[m]e: bond end position B[m]ang: bond angle B[m]up: dir B[m]ang B[m]left: dir B[m]ang+90 B[m]right: dir B[m]ang-90 B[m]down: dir B[m]ang+180 plus : '+' circled minus : '-' circled circlediam = 0.6aw (default) circlepen = 0.2bp (default) lonepair r: ':' rotated r lonepairdiam = 0.3aw (default) lonepairspace = 0.7aw (default) * : scaled << : rotated a /* b : point b of a beginfigm("EN:add() 1") fsize:=(70mm,40mm); sw_frame:=Bothside; max_blength:=10mm; msize:=(.91,.9); MCat(.5,.85)(<30,?6,{2,5}:O) add( defaultscale:=.8; labeloffset:=.3aw; dotlabel.lft("p0",p0); dotlabel.rt( "p0+(w,h)",p0+(w,h)); dotlabel.ulft("A1",A1); drawarrow A1..A1+__l<<A1ang; dotlabel.lrt( "B3s",B3s); dotlabel.rt("B3m",B3m); drawarrow B3m..B3m+__l<<(B3ang+90); dotlabel.ulft("A6",A6); drawarrow A1{A1down}..A6; dotlabel.urt( "B3e",B3e); label.rt( "An="&decimal(An)& " Bn="&decimal(Bn)& " aw="&decimal(aw)& " em="&decimal(em), p0+(-9em,-1.5em)); label.rt( "w="&decimal(w)& " h="&decimal(h)& " l="&decimal(l), p0+(-9em,-3em)); ) endfigm \end{verbatim} \MCFgraph \begin{verbatim} beginfigm("EN:add() 2") fsize:=(60mm,20mm); msize:=(1,0.85); %--------------------------------------- MCat(0,0)(<30,Ph,3=dl,4:/NH2) %--------------------------------------- add( labeloffset:=.7aw; label.top(lone_pair 90,A7); drawarrow (A7+up*1.2aw){A7left} ..{B7right}B7/0.3; drawarrow B3m..A3+B2up1.5aw..{A3down}A3; ) %--------------------------------------- MCat(1,0)(<30,?6,{1,5}=dl,4://NH2) %--------------------------------------- add( labeloffset:=.7aw; label.top(plus,A7); label.urt(minus,A3); label(lonepair A3ang,A3+A3up.7aw); ) %--------------------------------------- ext(drawdblarrow (.4w,.4h)..(.55w,.4h);) %--------------------------------------- endfigm \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \newpage \subsection{Function ext()} \index{ext()}% \index{w0}% \index{h0}% \index{aw}% \index{em}% \index{n}% \index{ratio\_thickness\_char}% \index{defaultscale}% \begin{verbatim} (Extra label to figure) w: figure width h: figure height w0: figure width-2xpart(fmargin) h0: figure height-2ypart(fmargin) aw: atom font size em: label font size p0: fmargin n: molecular number p[m]: molecular origin position w[m]: molecular width h[m]: molecular height ratio_thickness_char: pen thickness / char width %---------------------------------------- beginfigm() fsize:=(70mm,30mm;); blength:=0.065; %--------------------------------------- MCat(0.1,0.5)( <-210,60`1,60`1,60`1,{1,3}=dl, 1:/R1,4:/R2^-60 ) add( defaultscale:=0.6; label.bot("Diene",p0+(0.5w,0)); ) MCat(0.4,0.5)( <-30,-60`1,1=dl,1:/R3,2:/R4^60) add(defaultscale:=0.6; label.bot("Dienophile",p0+(.5w,0)); ) MCat(0.9,0.5)( <30,?6,6=dl,2:/R2,3:/R4,4:/R3,5:/R1 ) %--------------------------------------- ext( drawarrow (.52w,.5h)..(.6w,.5h); defaultscale:=0.7; label("+",(0.25w,0.5h)); ratio_thickness_char:=0.125; label.bot("Diels-Alder Reaction", (.5w,h)); ) %--------------------------------------- endfigm \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsubsection{Local ext() setting} \begin{verbatim} beginfigm("EN:?3") fsize:=(12mm,15mm); MCat(0.5,1)(<30,?3) endfigm beginfigm("EN:?4") fsize:=(12mm,15mm); MCat(0.5,1)(?4) %------------------------------- ext(label.top(inf_EN,(0.5w,0));) %------------------------------- endfigm beginfigm("EN:?5") fsize:=(12mm,15mm); MCat(0.5,1)(?5) endfigm beginfigm("EN:?5") fsize:=(12mm,15mm); MCat(0.5,1)(?6) endfigm \end{verbatim} \MCFgraph\MCFgraph\MCFgraph\MCFgraph \subsubsection{Global ext() setting} \index{ext\_clear}% \begin{verbatim} ext_clear: reset global ext() beginfigm("EN:?3") fsize:=(12mm,15mm); MCat(0.5,1)(<30,?3) endfigm %------------------------------- ext(label.top(inf_EN,(0.5w,0));) %------------------------------- beginfigm("EN:?4") fsize:=(12mm,15mm); MCat(0.5,1)(?4) endfigm beginfigm("EN:?5") fsize:=(12mm,15mm); MCat(0.5,1)(?5) endfigm %--------- ext_clear; %--------- beginfigm("EN:?6") fsize:=(12mm,15mm); MCat(0.5,1)(?6) endfigm \end{verbatim} \MCFgraph\MCFgraph\MCFgraph\MCFgraph %----------------------------------------------------------------------------- \newpage %----------------------------------------------------------------------------- \section{MCF example} %----------------------------------------------------------------------------- \subsection{Luciferin} \index{mc\_check()}% \begin{verbatim} (use library file 'mcf_library') beginfigm("f:mcf_library", "t:EN","v:Luciferin") fsize:=(50mm,15mm); if mc_check(mc)=0: MC(scantokens(mc)) fi endfigm \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Colchicine} \begin{verbatim} beginfigm("EN:Colchicine","MW:385.41", %------------------------------------- ": <30,Ph,{1,2,6}:/O!,{-4,-5}=?7, ", ": {-1,-4,-6}=dl,-2://O,-3:/O!, ", ": @9,\,NH,!,//O,! ") %------------------------------------- fsize:=(50mm,20mm); if mc_check(mc)=0: MC(scantokens(mc)) fi endfigm \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Paclitaxel} \begin{verbatim} beginfigm("EN:Paclitaxel","MW:853.91", %------------------------------------ ": ?6,5=dl,@3,#1,36,45,45,45,45,##, ", ": &5", ", ": -4=?6,-4=?4,-1=wb,-3=wf,-1:O,\|\|, ", ": 4:??,6:/_,{3^-60,15}:/OH, ", ": 8:/H^-60,", ", ": 9:/_^60,10://O, ", ": @1,\,O,!,//O,!,/OH,!,/Ph,60~wf, ", ": NH,-60,//O,60,Ph, ", ": @7,\,O,-45,//O,60,Ph, ", ": @11,\,O,-60,//O,60, ", ": @12,\^-15,O,60,//O,-60 ") %------------------------------------ fsize:=(50mm,25mm); if mc_check(mc)=0: MC(scantokens(mc)) fi endfigm \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Maltose} \index{arc\_lb} \index{arc\_br} \begin{verbatim} (bond type for glycan) arc_lb : arc left > bottom arc_br : arc bottom right beginfigm("EN:Maltose","MW:342.3", %----------------------------------------- ": #1.25,-30~wf_r,30~bd_r`1,30~wb_r, ", ": 120,O,30,&1,##, ", ": #.5,{1^$-90,2^$90,3^$-90}:/OH, ", ": 6^$90:/!OH, ", ": @4,$-50~arc_lb`1,O,$50~arc_br`1,<$0, ", ": \|,#1.25,-30~wf_r,30~bd_r`1,30~wb_r, ", ": 120,O,30,&1,##, ", ": #.5,{2^$90,3^$-90,4^$-90}:/OH, ", ": 6^$90:/!OH ") %----------------------------------------- fsize:=(50mm,20mm); if mc_check(mc)=0: MC(scantokens(mc)) fi endfigm \end{verbatim} \MCFgraph %----------------------------------------------------------------------------- \subsection{Cellobiose} \index{arc\_lbr} \index{arc\_ltr} \begin{verbatim} (bond type for glycan) arc_lbr : arc left > bottom > right arc_ltr : arc left > top > right beginfigm("EN:Cellobiose","MW:342.3", %----------------------------------------- ": #1.25,-30~wf_r,30~bd_r`1,30~wb_r, ", ": 120,O,30,&1,##, ", ": #.5,{1^$-90,2^$90,3^$-90}:/OH, ", ": 6^$90:/!OH, ", ": @4,$0~arc_ltr,O,$0~arc_lbr, ", ": \|,#1.25,-30~wf_r,30~bd_r`1,30~wb_r, ", ": 120,O,30,&1,##, ", ": #.5,{2^$90,3^$-90,4^$-90}:/OH, ", ": 6^$90:/!OH ") %----------------------------------------- fsize:=(50mm,20mm); if mc_check(mc)=0: MC(scantokens(mc)) fi endfigm \end{verbatim} \MCFgraph %------------------------------------------------------------------------ \onecolumn \section{Example to use mcf2graph} \subsection{MetaPost souce file} \index{mcf2graph.mp}% \index{sw\_output}% \index{tag}% \index{var}% \begin{verbatim} %------------------------------------------------------------------------- input mcf2graph; > input main macro %------------------------------------------------------------------------- sw_output:=Info; % aux(information) file output on > global setting %%%% sw_output:=Report; > report output %%%% sw_output:=MOL2k; > MOL file output fsize:=(60mm,40mm); % (figure width,figure height) > tag1:="J"; > jobname tag2:="C"; > char No tag3:="mw"; % calculated molecular weight > tag4:="fm"; % calculated molecular formula > outputformat:="png"; hppp:=vppp:=0.1; > PNG output outputtemplate:="c%3c-%{EN_}.png"; > %------------------------------------------------------------------------- beginfigm("EN:Ampicillin","MW:349.405") > information MC(<45,?4,-3=?5,2:N,7:S, > immediately compile 3^45:/H,1://O^15,5:/COOH^-18,6:??, > @4,\^15,NH,!,//O,!,/NH2,!,Ph) > endfigm > %------------------------------------------------------------------------ beginfigm("EN:Cholesterol","MW:386.65", >information %---------------------------------------- > ": <30,?6,{-4,-2}=?6,-4=?5,7=dl, ", > mc1 ": 10:/H^180,11:/H^-60,17:/H^-54, ", > mc2 ": {4,12}:/_^60, ", > mc3 ": @-1,18,/_,-60,!3,?! ") > mc4 %---------------------------------------- > if mc_check(mc)=0: MC(scantokens(mc)) fi > mc=mc1 - mc4 endfigm > %------------------------------------------------------------------------------ beginfigm("f:mcf_library.mcf","t:EN","v:Adenine") > from mcf_library.mcf if mc_check(mc)=0: MC(scantokens(mc)) fi > select EN="Adenine" endfigm > %------------------------------------------------------------------------------ beginfigm("t:EN","v:Guanine") > select EN="Guanine" if mc_check(mc)=0: MC(scantokens(mc)) fi endfigm %------------------------------------------------------------------------------ beginfigm("t:EN","v:Cytosine") > select EN="Cytosine" if mc_check(mc)=0: MC(scantokens(mc)) fi > endfigm > %------------------------------------------------------------------------------ beginfigm("t:n","v+:4") > v+:4 = select No.4 if mc_check(mc)=0: MC(scantokens(mc)) fi > keep file open endfigm > %------------------------------------------------------------------------------ forever: %%%%%%%%%% beginfigm("f:mcf_library","v+:") > select all beginfigm("f:mcf_library","t:EXA","v+:1") > 'v+:1'= select EXA=1 if f_EOF=0: if mc_check(mc)=0: MC(scantokens(mc)) fi fi > keep file open endfigm > exitif f_EOF=1; > exit if file end endfor %------------------------------------------------------------------------------ bye \end{verbatim} %------------------------------------------------------------------------ \noindent% \newpage \subsection{Molecular library file} \begin{verbatim} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % molecular library file mcf_library.mcf by Akira Yamaji 2022.10.10 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % tag1:var1;tag2:var2;tag3:var3 ..... % first character of line "%" comment out % first character of line ":" start MCF % first character of line ";" stop MCF % first character of line "=" start parameter setting % first character of line "" start ext(...) % first character of line "+" start add(...) % Cat = Category,EN = Name,MW = Molecular weight %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Cat:Category;EN:Example;MW:100.00;EXA:% = sw_frame:=Atom; : <30,?6,3=?5,{1,3,5,9}=dl,{2,6,9}:N,5:/NH2,7:NH * defaultscale:=.5; label.bot(decimal(fig_num)&":"&inf_EN,(.5w,0)); + defaultscale:=.3; label.bot("A2",A2) withcolor red; label.top("A6",A6) withcolor red; label.top("A9",A9) withcolor red; ; %============================================================================== Cat:biological;EN:Adenine;MW:135.13;EXA:1 : <30,?6,3=?5,{1,3,5,9}=dl,{2,6,9}:N,5:/NH2,7:NH ; %------------------------------------------------------------------------------ Cat:biological;EN:Guanine;MW:151.13;EXA:1 : <30,?6,3=?5,{1,3,9}=dl,{2,9}:N,{6,7}:NH,5://O,1:/NH2 ; %------------------------------------------------------------------------------ Cat:biological;EN:Cytosine;MW:111.10;EXA:1 : <30,?6,{4,6}=dl,4:N,3://O,2:NH,5:/NH2 ; %------------------------------------------------------------------------------ Cat:biological;EN:Thymine;MW:126.11;EXA:1 : <30,?6,3=dl,{2,6}:NH,{1,5}://O,4:/_ ; %------------------------------------------------------------------------------ Cat:biological;EN:Uracil;MW:112.09;EXA:1 : <30,?6,6=dl,{3,5}://O,{2,4}:NH ; %== Amino acid ================================================================ Cat:biological;EN:Glycine;MW:75.07;EXA:- : <30,NH2,!2,COOH ; %------------------------------------------------------------------------------ \end{verbatim} %------------------------------------------------------------------------------ \noindent% \newpage \subsection{Function mc\_query()} \index{mc\_query()}% \paragraph{(Example)} \begin{verbatim} %-------------------------------------------------------------- % mc_query() % % "f:filename" : input file name (default "mcf_library.mcf") % "o:filename" : output file name (default "temp.mcf") % % "a:sort-key" : sort by sort-key ascending % "d:sort-key" : sort by sort-key descending % % operator : = , <> , <= , >= , < , > % % filter 1 : Cat=biological % filter 2 : MW>=285 % filter 3 : MW<=295 % %-------------------------------------------------------------- mc_query("Cat=biological","MW>=285","MW<=290","a:EN"); %-------------------------------------------------------------- \end{verbatim} %--------------------------------------------------------------- \paragraph{(output)} \begin{verbatim} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Input : mcf_library.mcf [506] % Output : temp.mcf [5] % Filter(1): Cat =biological % Filter(2): MW >= 285 % Filter(3): MW <= 290 % Sort key : EN (ascending) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Cat:biological;EN:Atoropin;MW:289.375;EXA:1 : <30,O,!,//O,!2,Ph,@$1,\~zb^-60,\|,?7`1.1,@6,\^190`1.25,N!,&3~wb,$3:/!OH~wv ; Cat:biological;EN:Luteolin;MW:286.24;EXA:- : <30,Ph,3=?6,9=dl,10:O,7://O,@9,\,Ph,{2,6,14,15}:/OH ; Cat:biological;EN:Lycorine;MW:287.315;EXA:1 : <30,Ph,{-4,-2}=?6,{6,(9,12)}=?5,13=dl,8:N,{15,17}:O, {9'^180,10^60}:/H,{13,14'}:/OH ; Cat:biological;EN:Morphine;MW:285.343;EXA:1 : <30,Ph,{2,-4}=?6,(1,12)=?5[2],-1:O,-1=zb, @7,60~wf`0.75,70~si_`1.3,45,N!,&9~wb,15=dl,6:/OH,8^180:/H,12:/OH ; Cat:biological;EN:Piperine;MW:285.343;EXA:1 : <30,Ph,-1=?5,{-1,-3}:O,@4,\,!!,!,!!,!,//O,!,?6,-6:N ; \end{verbatim} %------------------------------------------------------------------------------ \noindent% \newpage \subsection{Information aux file output} \paragraph{(Option parameter setting)} \index{J}% \index{C}% \index{NO}% \index{MW}% \index{MI}% \index{EN}% \index{JN}% \index{FM}% \index{USE}% \index{mw}% \index{fm}% \index{mi}% \index{w}% \index{h}% \index{Info}% \index{Table}% \index{Temp}% \begin{verbatim} sw_output:=Info; %% tag1:var1;tag2:var2 sw_output:=Info+Table; %% tag1;tag2 var1;var2 \end{verbatim} \paragraph{(Command line)} \begin{verbatim} >mpost -s ahlength=1 FILENAME (sw_output=Info) >mpost -s ahlength=2 FILENAME (sw_output=Info+Table) \end{verbatim} \paragraph{(Sourse)} \begin{verbatim} beginfigm("EN:Ampicillin") .... endfigm beginfigm("EN:Cholesterol") .... endfigm beginfigm("EN:Limonin") .... endfigm beginfigm("EN:beta-Carotene") .... endfigm \end{verbatim} \paragraph{(Setting)} \begin{verbatim} tag1:="J"; tag2:="C"; tag3:="mw"; tag4:="fm"; tag5:="EN"; \end{verbatim} \paragraph{(Output)} \index{aux\_delimiter}% \begin{verbatim} (sw_output=Info) F:mcf_man_soc;C:1;mw:349.40462;fm:C16H19N3O4S;EN:Ampicillin F:mcf_man_soc;C:2;mw:386.6532;fm:C27H46O;EN:Cholesterol F:mcf_exa_soc;C:3;mw:470.5113;fm:C26H30O8;EN:Limonin F:mcf_exa_soc;C:4;mw:536.8722;fm:C40H56;EN:beta-Carotene (sw_output=Info+Table) F;C;mw;fm mcf_man_soc;1;349.40462;C16H19N3O4S;Ampicillin mcf_man_soc;2;386.6532;C27H46O;Cholesterol mcf_exa_soc;3;470.5113;C26H30O8;Limonin mcf_exa_soc;4;536.8722;C40H56;beta-Carotene (aux_delimiter="/") F:mcf_man_soc/C:1/mw:349.40462/fm:C16H19N3O4S/EN:Ampicillin F:mcf_man_soc/C:2/mw:386.6532/fm:C27H46O/EN:Cholesterol F:mcf_exa_soc/C:3/mw:470.5113/fm:C26H30O8/EN:Limonin F:mcf_exa_soc/C:4/mw:536.8722/fm:C40H56/EN:beta-Carotene \end{verbatim} \paragraph{(Tag)} \begin{verbatim} J : jobname C : char number NO : serial number EN : english name JN : japanese name FM : formula from literature data MW : molecular weight from literature data MI : monoisotopic mass from literature data USE : the use mw : molecular weight calculated mi : monoisotopic mass calculated fm : molecular formula calculated w : figure width h : figure height \end{verbatim} %------------------------------------------------------------------------ \noindent% \newpage \subsection{MCF aux file output} \paragraph{(Option parameter setting)} \index{Mcode}% \index{Temp}% \begin{verbatim} sw_output:=Mcode; %% output 'temp-mc.aux' \end{verbatim} \paragraph{(Command line)} \begin{verbatim} >mpost -s ahlength=3 FILENAME (sw_output=Info+Mcode) \end{verbatim} \paragraph{(Output mcf file)} \begin{verbatim} sw_output=Mcode %% file name = 'temp-mc.aux' (result) <30,?6,3=?5,{1,3,5,9}=dl,{2,6,9}:N,5:/NH2,7:NH \end{verbatim} \paragraph{(Output library file)} \begin{verbatim} sw_output=Info+Mcode %% file name = 'jobname-lib.aux' (result) Cat:biological;EN:Adenine;MW:135.13;EXA:1 + <30,?6,3=?5,{1,3,5,9}=dl,{2,6,9}:N,5:/NH2,7:NH +-------------------------------------------------- \end{verbatim} %------------------------------------------------------------------------ \paragraph{(LuaLaTeX example)} %----------------------------------------------------------------------- \begin{verbatim} %----------------------------------------------------------------------- \begin{mplibcode} beginfigm("t:EN","v:Vancomycin") sw_output:=Mcode; %%%% output temp-mc.aux %%%% endfigm; \end{mplibcode} %----------------------------------------------------------------------- \verbatiminput{temp-mc.aux} %----------------------------------------------------------------------- \end{verbatim} %----------------------------------------------------------------------- \begin{verbatim} (result) file name = 'temp-mc.aux' <30,?6,@4,?6,@-4,\,!3,<-12,?5,@-3,<-12,?6,-3=?6,@-3,\,!3, ?6,@-4,?6,@6,\,!,/Me^-40,/OH^20,!,//O,!1,OH, 3=wb,11=dl,15=dr,17=wf,19=wf,38=wb,{5,7,16,24,25,33,42}:O, 32:/H^60,10:/Me,{12,31}:/_,27://_,37:/_,28:/OH,{3,29}:/OH \end{verbatim} %------------------------------------------------------------------------ \newpage \noindent% \subsection{Report output} \paragraph{(Option parameter setting)} \index{sw\_output}% \index{Report}% \begin{verbatim} sw_output:=Report; %% file name = 'jobname-report.aux' \end{verbatim} \paragraph{(Command line)} \begin{verbatim} >mpost -s ahlength=7 FILENAME \end{verbatim} \paragraph{(Output)} \begin{verbatim} =========================================================================== No[3],Name<Cytosine>,Category<biological>,File<mcf_library.mcf> --------------------------------------------------------------------------- <30,?6,{4,6}=dl,4:N,3://O,2:NH,5:/NH2 --------------------------------------------------------------------------- Row[1],Length[37],Commands[7],&Code[59],Warning[0] --------------------------------------------------------------------------- =[1]({}=[1]), :[4]({}:[0]), '()[0] @[0],&[0],<[1],~[0],^[0],`[0],>[0],\|[0],\|\|[0],#[0],##[0] --------------------------------------------------------------------------- Width[30.92432],Height[42.36536], Shift x[0],Shift y[-12.99213] Bond length[11.33856],Atom size[4.8819] --------------------------------------------------------------------------- Atom[9],Bond[9],Ring[1],Hide H[2] < NO. ><atom(s) >( x axis , y axis )<bond><hideH><chg> A1 C ( 0 , 0 ) 3 1 A2 N ( 1 , 0 ) 3 A3 C ( 2 , 0 ) 4 A4 N ( 2 , 1 ) 3 A5 C ( 1 , 2 ) 4 A6 C ( 0 , 1 ) 3 1 A7 O ( 3 , 0 ) 2 A8 H ( 1 , -1 ) 1 A9 NH2 ( 1 , 2 ) 1 --------------------------------------------------------------------------- < NO. >< bond (sdt)><angle +( +- )><length ( pt )> B1 1 -> 2 ( 1) 330 ( -30) 1 ( 11) B2 2 -> 3 ( 1) 30 ( 30) 1 ( 11) B3 3 -> 4 ( 1) 90 ( 90) 1 ( 11) B4 4 -> 5 ( 2) 150 ( 150) 1 ( 11) B5 5 -> 6 ( 1) 210 ( -150) 1 ( 11) B6 6 -> 1 ( 2) 270 ( -90) 1 ( 11) B7 3 -> 7 ( 2) 330 ( -30) 0.66 ( 7) B8 2 -> 8 ( 1) 270 ( -90) 0.36 ( 4) B9 5 -> 9 ( 1) 90 ( 90) 0.66 ( 7) --------------------------------------------------------------------------- <atom>( atom wt )[ mi wt ] < cnt > < sum wt >[ sum mi wt ] C ( 12.0107)[ 12] * 4 48.04279[ 48] H ( 1.00793)[ 1.00783] * 5 5.03967[ 5.03914] N ( 14.0067)[ 14.00307] * 3 42.0201[ 42.0092] O ( 15.9994)[ 15.99492] * 1 15.9994[ 15.99492] Molecular Weight [Mono Isotopic] = 111.1019[ 111.04326] --------------------------------------------------------------------------- Weight Calc: 111.1019 / Input: 111.10 / weight gap= 0.00195 Fomula Calc: C4H5N3O / Input: =========================================================================== \end{verbatim}% \newpage %------------------------------------------------------------------------ \noindent% \subsection{MOL file output} \paragraph{(Option parameter setting)} \index{sw\_output}% \index{MOL2k}% \index{MOL3k}% \begin{verbatim} sw_output:=MOL2k; % MOL(V2000) sw_output:=MOL3k; % MOL(V3000) \end{verbatim} \paragraph{(Command line)} \begin{verbatim} >mpost -s ahlength=5 FILENAME % MOL(V2000) >mpost -s ahlength=6 FILENAME % MOL(V3000) \end{verbatim} \paragraph{(Output)} \begin{verbatim} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -MCFtoMOL- EN:Caffeine 14 15 0 0 0 0 0 0 0 0999 V2000 0 0 0 C 0 0 0 0 0.86603 -0.5 0 N 0 0 0 0 1.73206 0 0 C 0 0 0 0 1.73206 1 0 C 0 0 0 0 0.86603 1.5 0 C 0 0 0 0 0 1 0 N 0 0 0 0 2.6831 -0.30902 0 N 0 0 0 0 3.27089 0.5 0 C 0 0 0 0 2.6831 1.30902 0 N 0 0 0 0 0.86603 -1.36383 0 C 0 0 0 0 -0.76894 1.44394 0 C 0 0 0 0 -0.76894 -0.44394 0 O 0 0 0 0 0.86603 2.36383 0 O 0 0 0 0 2.95299 2.1396 0 C 0 0 0 0 1 2 1 0 0 0 2 3 1 0 0 0 3 4 2 0 0 0 4 5 1 0 0 0 5 6 1 0 0 0 6 1 1 0 0 0 3 7 1 0 0 0 7 8 2 0 0 0 8 9 1 0 0 0 9 4 1 0 0 0 2 10 1 0 0 0 6 11 1 0 0 0 1 12 2 0 0 0 5 13 2 0 0 0 9 14 1 0 0 0 M END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{verbatim}% %---------------------------------------------------------------------------- \newpage \subsection{LuaTeX file example} \index{Fig}% %############################################################################ \begin{verbatim} \documentclass{article} \usepackage{luamplib}% \usepackage[T1]{fontenc}% \usepackage{textcomp}% \mplibcodeinherit{enable}% \mplibverbatim{enable}% \mplibnumbersystem{double}% \everymplib{% if unknown Ph1: input mcf2graph; fi sw_output:=Fig; max_blength:=4.5mm; defaultfont:="uhvr8r"; defaultsize:=8bp; defaultscale:=1; }% \begin{document} \noindent% %-------------------------------------------------------------------- \begin{mplibcode} fsize:=(50mm,50mm); beginfigm("NO:1","EN:Limonin","MW:470.51", %---------------------------------------- ": <30,?6,{-3,-4}=?6, ", ": -5=?3,-2=wf,-1=wb,6=?5,-4=?6,-5=wf, ", ": {13,15,17,20}:O,{3,12,21}://O, ", ": {4~wf^60,8~zf^60,18^35,18^-35}:/_, ", ": {1^60,5^180,16^60}:/H, ", ": @14,\,\|,?5,{1,4}=dl,3:O ") %---------------------------------------- if mc_check(mc)=0: MC(scantokens(mc)) fi endfigm \end{mplibcode}\\ %-------------------------------------------------------------------- \begin{mplibcode} fsize:=(80mm,50mm); beginfigm("NO:2","EN:beta-carotene","MW:536.87", %------------------------------------------ ": <30,?6,3=dl,{3,5^35,5^-35}:/_, ", ": @4,\,\|,!18,{1,3,5,7,9,11,13,15,17}=dr, ", ": {3,7,12,16}:/_, ", ": \|,?6,6=dl,{6,2^35,2^-35}:/_ ") %------------------------------------------ if mc_check(mc)=0: MC(scantokens(mc)) fi endfigm \end{mplibcode}\\ %-------------------------------------------------------------------- \begin{mplibcode} fsize:=(50mm,50mm); beginfigm("NO:3","EN:Gibberellin A3","MW:346.37", %------------------------------------ ": <18,?5,3=?7,5=?6[12], ", ": @8,160`1.3,&3,13=dl,6=wf,8=wb, ", ": @5,40~zf`1,O,60,//O^180,&14~zb, ", ": 2:/COOH,7://_,13:/OH,8:/OH, ", ": 14:/_,{1^60,4^60}:/H ") %------------------------------------ if mc_check(mc)=0: MC(scantokens(mc)) fi endfigm; %-------------------------------------------------------------------- \end{mplibcode}\\ \end{document} \end{verbatim}% %############################################################################ %------------------------------------------------------------------------ \texttt{\printindex} %------------------------------------------------------------------------ \end{document}
http://dlmf.nist.gov/28.23.E13.tex	nist.gov	CC-MAIN-2014-10	application/x-tex	null	crawl-data/CC-MAIN-2014-10/segments/1393999671474/warc/CC-MAIN-20140305060751-00064-ip-10-183-142-35.ec2.internal.warc.gz	52,613,955	725	\[\mathop{{\mathrm{Ms}^{{(j)}}_{{2m+2}}}\/}\nolimits\!\left(z,h\right)=(-1)^{{m+% 1}}\left({\mathop{\mathrm{se}_{{2m+2}}\/}\nolimits^{{\prime}}}\!\left(\tfrac{1% }{2}\pi,h^{2}\right)\right)^{{-1}}\mathop{\coth\/}\nolimits z\sum_{{\ell=0}}^{% {\infty}}(2\ell+2)B_{{2\ell+2}}^{{2m+2}}(h^{2}){\cal C}_{{2\ell+2}}^{{(j)}}(2h% \mathop{\sinh\/}\nolimits z).\]
https://authorea.com/users/391117/articles/505294/download_latex	authorea.com	CC-MAIN-2021-17	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2021-17/segments/1618038887646.69/warc/CC-MAIN-20210419142428-20210419172428-00252.warc.gz	222,807,983	2,852	\documentclass[10pt]{article} \usepackage{fullpage} \usepackage{setspace} \usepackage{parskip} \usepackage{titlesec} \usepackage[section]{placeins} \usepackage{xcolor} \usepackage{breakcites} \usepackage{lineno} \usepackage{hyphenat} \PassOptionsToPackage{hyphens}{url} \usepackage[colorlinks = true, linkcolor = blue, urlcolor = blue, citecolor = blue, anchorcolor = blue]{hyperref} \usepackage{etoolbox} \makeatletter \patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{% \errmessage{\noexpand\@combinedblfloats could not be patched}% }% \makeatother \usepackage{natbib} \renewenvironment{abstract} {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize} {\bigskip} \titlespacing{\section}{0pt}{3}{1} \titlespacing{\subsection}{0pt}{2}{0.5} \titlespacing{\subsubsection}{0pt}{*1.5}{0pt} \usepackage{authblk} \usepackage{graphicx} \usepackage[space]{grffile} \usepackage{latexsym} \usepackage{textcomp} \usepackage{longtable} \usepackage{tabulary} \usepackage{booktabs,array,multirow} \usepackage{amsfonts,amsmath,amssymb} \providecommand\citet{\cite} \providecommand\citep{\cite} \providecommand\citealt{\cite} % You can conditionalize code for latexml or normal latex using this. \newif\iflatexml\latexmlfalse \providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}% \AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}} \usepackage[utf8]{inputenc} \usepackage[english]{babel} \usepackage{float} \begin{document} \title{Interlayer Dural Split Technique for Chiari I Malformation Treatment in Adult -- Technical Note} \author[1]{Ioan Alexandru Florian}% \author[2]{Mihaela Maria Pop}% \author[1]{Teodora Larisa Timis}% \author[1]{Ioan Stefan Florian}% \affil[1]{Iuliu Hagieganu University of Medicine and Pharmacy Faculty of Medicine}% \affil[2]{Spitalul Clinic Judetean de Urgenta Cluj-Napoca}% \vspace{-1em} \date{\today} \begingroup \let\center\flushleft \let\endcenter\endflushleft \maketitle \endgroup \selectlanguage{english} \begin{abstract} Objective: To present an alternative surgical technique in treating cases of Chiari I Malformation with mild-to-moderate syringomyelia after decompressive suboccipital craniectomy: incising only the outer layer of the dura mater, then dissecting it from the inner layer without opening the latter. Methods and Results: We utilized this technique in a short series of three cases who were admitted in our department for mild symptoms such as intermittent headache and dissociated sensory loss in the upper limbs, caused by a Chiari Malformation Type I. The patients were placed in the sitting position. We performed a reduced median suboccipital craniectomy and resection of the posterior arch of C1 adapted to the level of tonsil descent, from a limited superior half to a complete resection. Afterwards, we incised the outer dural layer, while sparing the inner one. Using a fine dissector, we then split apart the outer and inner layers to the margin of the craniectomy. Through the transparency of the inner layer and the arachnoid, the cerebellum and the medulla were visible and pulsating. An autologous fascia duraplasty was then performed. The postoperative course was favorable in all cases, patients being discharged without any deficits and with complete symptom resolution. Conclusions: Interlayer dural split technique can be used effectively in treating symptomatic cases of type I Chiari malformation in adults, with mild-to-moderate syringomyelia. It is less invasive than opening the dura and possibly more effective than decompressive craniectomy and C1 laminectomy alone. This technique must be validated in a larger case-control series.% \end{abstract}% \sloppy \textbf{Hosted file} \verb`Interlayer.pdf` available at \url{https://authorea.com/users/391117/articles/505294-interlayer-dural-split-technique-for-chiari-i-malformation-treatment-in-adult-technical-note}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Fig-1/Fig-1} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Fig-2/Fig-2} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Fig-3/Fig-3} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Fig-4/Fig-4} \end{center} \end{figure} \selectlanguage{english} \FloatBarrier \end{document}
http://rpi.edu/dept/arc/training/latex/resumes/let3.tex	rpi.edu	CC-MAIN-2019-30	application/x-tex	text/x-matlab	crawl-data/CC-MAIN-2019-30/segments/1563195526237.47/warc/CC-MAIN-20190719115720-20190719141720-00162.warc.gz	135,033,713	2,041	% Cover letter using letter.cls \documentclass[11pt]{letter} % default is 10 pt %\usepackage{helvetica} % uses helvetica postscript font (download helvetica.sty) \usepackage{newcent} % uses new century schoolbook postscript font % the following commands control the margins: \topmargin=-1in % Make letterhead start about 1 inch from top of page \textheight=8.5in % text height can be bigger for a longer letter \oddsidemargin=0pt % leftmargin is 1 inch \textwidth=6.5in % textwidth of 6.5in leaves 1 inch for right margin \begin{document} \signature{Andrew Malone} % name for signature \longindentation=0pt % needed to get closing flush left \let\raggedleft\raggedright % needed to get date flush left \begin{letter}{Ms. Terri Roberts \\ Senior Staff Recruiter \\ XYZ Corporation \\ Rt. 56 \\ Anytown, New Jersey 05867} \begin{center} \large\bf ANDREW J. MALONE \\ 739 Mill Grove Drive \\ Audubon, PA 19403 \\ (215) 555-2216 \end{center} \vfill % forces letterhead to top of page \opening{Dear Ms. Roberts:} \noindent PARAGRAPH ONE: State reason for letter, name the position or type of work you are applying for and identify source from which you learned of the opening. (i.e. Career Development Center, newspaper, employment service, personal contact). \noindent PARAGRAPH TWO: Indicate why you are interested in the position, the company, its products, services - above all, stress what you can do for the employer. If you are a recent graduate, explain how your academic background makes you a qualified candidate for the position. If you have practical work experience, point out specific achievements or unique qualifications. Try not to repeat the same information the reader will find in the resume. Refer the reader to the enclosed resume or application which summarizes your qualifications, training, and experiences. The purpose of this section is to strengthen your resume by providing details which bring your experiences to life. \noindent PARAGRAPH THREE: Request a personal interview and indicate your flexibility as to the time and place. Repeat your phone number in the letter and offer assistance to help in a speedy response. For example, state that you will be in the city where the company is located on a certain date and would like to set up an interview. Or, state that you will call on a certain date to set up an interview. End the letter by thanking the employer for taking time to consider your credentials. \closing{Sincerely yours,} \encl{} % Enclosures \end{letter} \end{document}
https://www.tinc-vpn.org/git/browse?p=tinc;a=blob_plain;f=doc/tinc.texi;hb=5a28aa7b8b0ab6237c2eab5f8b11253ea3ec5a05	tinc-vpn.org	CC-MAIN-2021-17	application/x-texinfo	application/x-tex	crawl-data/CC-MAIN-2021-17/segments/1618039601956.95/warc/CC-MAIN-20210423041014-20210423071014-00564.warc.gz	1,123,401,826	28,305	\input texinfo @c --texinfo-- @c %start of header @setfilename tinc.info @settitle tinc Manual @setchapternewpage odd @c %end of header @include tincinclude.texi @ifinfo @dircategory Networking tools @direntry * tinc: (tinc). The tinc Manual. @end direntry This is the info manual for @value{PACKAGE} version @value{VERSION}, a Virtual Private Network daemon. Copyright @copyright{} 1998-2011 Ivo Timmermans, Guus Sliepen <guus@@tinc-vpn.org> and Wessel Dankers <wsl@@tinc-vpn.org>. Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies. Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. @end ifinfo @titlepage @title tinc Manual @subtitle Setting up a Virtual Private Network with tinc @author Ivo Timmermans and Guus Sliepen @page @vskip 0pt plus 1filll This is the info manual for @value{PACKAGE} version @value{VERSION}, a Virtual Private Network daemon. Copyright @copyright{} 1998-2011 Ivo Timmermans, Guus Sliepen <guus@@tinc-vpn.org> and Wessel Dankers <wsl@@tinc-vpn.org>. Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies. Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. @end titlepage @ifnottex @c ================================================================== @node Top @top Top @menu * Introduction:: * Preparations:: * Installation:: * Configuration:: * Running tinc:: * Technical information:: * Platform specific information:: * About us:: * Concept Index:: All used terms explained @end menu @end ifnottex @c ================================================================== @node Introduction @chapter Introduction @cindex tinc Tinc is a Virtual Private Network (VPN) daemon that uses tunneling and encryption to create a secure private network between hosts on the Internet. Because the tunnel appears to the IP level network code as a normal network device, there is no need to adapt any existing software. The encrypted tunnels allows VPN sites to share information with each other over the Internet without exposing any information to others. This document is the manual for tinc. Included are chapters on how to configure your computer to use tinc, as well as the configuration process of tinc itself. @menu * Virtual Private Networks:: * tinc:: About tinc * Supported platforms:: @end menu @c ================================================================== @node Virtual Private Networks @section Virtual Private Networks @cindex VPN A Virtual Private Network or VPN is a network that can only be accessed by a few elected computers that participate. This goal is achievable in more than just one way. @cindex private Private networks can consist of a single stand-alone Ethernet LAN. Or even two computers hooked up using a null-modem cable. In these cases, it is obvious that the network is @emph{private}, no one can access it from the outside. But if your computers are linked to the Internet, the network is not private anymore, unless one uses firewalls to block all private traffic. But then, there is no way to send private data to trusted computers on the other end of the Internet. @cindex virtual This problem can be solved by using @emph{virtual} networks. Virtual networks can live on top of other networks, but they use encapsulation to keep using their private address space so they do not interfere with the Internet. Mostly, virtual networks appear like a single LAN, even though they can span the entire world. But virtual networks can't be secured by using firewalls, because the traffic that flows through it has to go through the Internet, where other people can look at it. As is the case with either type of VPN, anybody could eavesdrop. Or worse, alter data. Hence it's probably advisable to encrypt the data that flows over the network. When one introduces encryption, we can form a true VPN. Other people may see encrypted traffic, but if they don't know how to decipher it (they need to know the key for that), they cannot read the information that flows through the VPN. This is what tinc was made for. @c ================================================================== @node tinc @section tinc @cindex vpnd I really don't quite remember what got us started, but it must have been Guus' idea. He wrote a simple implementation (about 50 lines of C) that used the ethertap device that Linux knows of since somewhere about kernel 2.1.60. It didn't work immediately and he improved it a bit. At this stage, the project was still simply called "vpnd". Since then, a lot has changed---to say the least. @cindex tincd Tinc now supports encryption, it consists of a single daemon (tincd) for both the receiving and sending end, it has become largely runtime-configurable---in short, it has become a full-fledged professional package. @cindex traditional VPNs @cindex scalability Tinc also allows more than two sites to connect to eachother and form a single VPN. Traditionally VPNs are created by making tunnels, which only have two endpoints. Larger VPNs with more sites are created by adding more tunnels. Tinc takes another approach: only endpoints are specified, the software itself will take care of creating the tunnels. This allows for easier configuration and improved scalability. A lot can---and will be---changed. We have a number of things that we would like to see in the future releases of tinc. Not everything will be available in the near future. Our first objective is to make tinc work perfectly as it stands, and then add more advanced features. Meanwhile, we're always open-minded towards new ideas. And we're available too. @c ================================================================== @node Supported platforms @section Supported platforms @cindex platforms Tinc has been verified to work under Linux, FreeBSD, OpenBSD, NetBSD, MacOS/X (Darwin), Solaris, and Windows (both natively and in a Cygwin environment), with various hardware architectures. These are some of the platforms that are supported by the universal tun/tap device driver or other virtual network device drivers. Without such a driver, tinc will most likely compile and run, but it will not be able to send or receive data packets. @cindex release For an up to date list of supported platforms, please check the list on our website: @uref{http://www.tinc-vpn.org/platforms}. @c @c @c @c @c @c @c Preparing your system @c @c @c @c @c @c ================================================================== @node Preparations @chapter Preparations This chapter contains information on how to prepare your system to support tinc. @menu * Configuring the kernel:: * Libraries:: @end menu @c ================================================================== @node Configuring the kernel @section Configuring the kernel @menu * Configuration of Linux kernels:: * Configuration of FreeBSD kernels:: * Configuration of OpenBSD kernels:: * Configuration of NetBSD kernels:: * Configuration of Solaris kernels:: * Configuration of Darwin (MacOS/X) kernels:: * Configuration of Windows:: @end menu @c ================================================================== @node Configuration of Linux kernels @subsection Configuration of Linux kernels @cindex Universal tun/tap For tinc to work, you need a kernel that supports the Universal tun/tap device. Most distributions come with kernels that already support this. Here are the options you have to turn on when configuring a new kernel: @example Code maturity level options [] Prompt for development and/or incomplete code/drivers Network device support <M> Universal tun/tap device driver support @end example It's not necessary to compile this driver as a module, even if you are going to run more than one instance of tinc. If you decide to build the tun/tap driver as a kernel module, add these lines to @file{/etc/modules.conf}: @example alias char-major-10-200 tun @end example @c ================================================================== @node Configuration of FreeBSD kernels @subsection Configuration of FreeBSD kernels For FreeBSD version 4.1 and higher, tun and tap drivers are included in the default kernel configuration. Using tap devices is recommended. @c ================================================================== @node Configuration of OpenBSD kernels @subsection Configuration of OpenBSD kernels For OpenBSD version 2.9 and higher, the tun driver is included in the default kernel configuration. There is also a kernel patch from @uref{http://diehard.n-r-g.com/stuff/openbsd/} which adds a tap device to OpenBSD which should work with tinc, but with recent versions of OpenBSD, a tun device can act as a tap device by setting the link0 option with ifconfig. @c ================================================================== @node Configuration of NetBSD kernels @subsection Configuration of NetBSD kernels For NetBSD version 1.5.2 and higher, the tun driver is included in the default kernel configuration. Tunneling IPv6 may not work on NetBSD's tun device. @c ================================================================== @node Configuration of Solaris kernels @subsection Configuration of Solaris kernels For Solaris 8 (SunOS 5.8) and higher, the tun driver may or may not be included in the default kernel configuration. If it isn't, the source can be downloaded from @uref{http://vtun.sourceforge.net/tun/}. For x86 and sparc64 architectures, precompiled versions can be found at @uref{http://www.monkey.org/~dugsong/fragroute/}. If the @file{net/if_tun.h} header file is missing, install it from the source package. @c ================================================================== @node Configuration of Darwin (MacOS/X) kernels @subsection Configuration of Darwin (MacOS/X) kernels Tinc on Darwin relies on a tunnel driver for its data acquisition from the kernel. Tinc supports either the driver from @uref{http://tuntaposx.sourceforge.net/}, which supports both tun and tap style devices, and also the driver from from @uref{http://chrisp.de/en/projects/tunnel.html}. The former driver is recommended. The tunnel driver must be loaded before starting tinc with the following command: @example kmodload tunnel @end example @c ================================================================== @node Configuration of Windows @subsection Configuration of Windows You will need to install the latest TAP-Win32 driver from OpenVPN. You can download it from @uref{http://openvpn.sourceforge.net}. Using the Network Connections control panel, configure the TAP-Win32 network interface in the same way as you would do from the tinc-up script, as explained in the rest of the documentation. @c ================================================================== @node Libraries @section Libraries @cindex requirements @cindex libraries Before you can configure or build tinc, you need to have the OpenSSL, zlib and lzo libraries installed on your system. If you try to configure tinc without having them installed, configure will give you an error message, and stop. @menu OpenSSL:: * zlib:: * lzo:: @end menu @c ================================================================== @node OpenSSL @subsection OpenSSL @cindex OpenSSL For all cryptography-related functions, tinc uses the functions provided by the OpenSSL library. If this library is not installed, you wil get an error when configuring tinc for build. Support for running tinc without having OpenSSL installed @emph{may} be added in the future. You can use your operating system's package manager to install this if available. Make sure you install the development AND runtime versions of this package. If you have to install OpenSSL manually, you can get the source code from @url{http://www.openssl.org/}. Instructions on how to configure, build and install this package are included within the package. Please make sure you build development and runtime libraries (which is the default). If you installed the OpenSSL libraries from source, it may be necessary to let configure know where they are, by passing configure one of the --with-openssl-* parameters. @example --with-openssl=DIR OpenSSL library and headers prefix --with-openssl-include=DIR OpenSSL headers directory (Default is OPENSSL_DIR/include) --with-openssl-lib=DIR OpenSSL library directory (Default is OPENSSL_DIR/lib) @end example @subsubheading License @cindex license The complete source code of tinc is covered by the GNU GPL version 2. Since the license under which OpenSSL is distributed is not directly compatible with the terms of the GNU GPL @uref{http://www.openssl.org/support/faq.html#LEGAL2}, we include an exemption to the GPL (see also the file COPYING.README) to allow everyone to create a statically or dynamically linked executable: @quotation This program is released under the GPL with the additional exemption that compiling, linking, and/or using OpenSSL is allowed. You may provide binary packages linked to the OpenSSL libraries, provided that all other requirements of the GPL are met. @end quotation Since the LZO library used by tinc is also covered by the GPL, we also present the following exemption: @quotation Hereby I grant a special exception to the tinc VPN project (http://www.tinc-vpn.org/) to link the LZO library with the OpenSSL library (http://www.openssl.org). Markus F.X.J. Oberhumer @end quotation @c ================================================================== @node zlib @subsection zlib @cindex zlib For the optional compression of UDP packets, tinc uses the functions provided by the zlib library. If this library is not installed, you wil get an error when configuring tinc for build. Support for running tinc without having zlib installed @emph{may} be added in the future. You can use your operating system's package manager to install this if available. Make sure you install the development AND runtime versions of this package. If you have to install zlib manually, you can get the source code from @url{http://www.gzip.org/zlib/}. Instructions on how to configure, build and install this package are included within the package. Please make sure you build development and runtime libraries (which is the default). @c ================================================================== @node lzo @subsection lzo @cindex lzo Another form of compression is offered using the lzo library. If this library is not installed, you wil get an error when configuring tinc for build. Support for running tinc without having lzo installed @emph{may} be added in the future. You can use your operating system's package manager to install this if available. Make sure you install the development AND runtime versions of this package. If you have to install lzo manually, you can get the source code from @url{http://www.oberhumer.com/opensource/lzo/}. Instructions on how to configure, build and install this package are included within the package. Please make sure you build development and runtime libraries (which is the default). @c @c @c @c Installing tinc @c @c @c @c @c ================================================================== @node Installation @chapter Installation If you use Debian, you may want to install one of the precompiled packages for your system. These packages are equipped with system startup scripts and sample configurations. If you cannot use one of the precompiled packages, or you want to compile tinc for yourself, you can use the source. The source is distributed under the GNU General Public License (GPL). Download the source from the @uref{http://www.tinc-vpn.org/download, download page}, which has the checksums of these files listed; you may wish to check these with md5sum before continuing. Tinc comes in a convenient autoconf/automake package, which you can just treat the same as any other package. Which is just untar it, type `./configure' and then `make'. More detailed instructions are in the file @file{INSTALL}, which is included in the source distribution. @menu * Building and installing tinc:: * System files:: @end menu @c ================================================================== @node Building and installing tinc @section Building and installing tinc Detailed instructions on configuring the source, building tinc and installing tinc can be found in the file called @file{INSTALL}. @cindex binary package If you happen to have a binary package for tinc for your distribution, you can use the package management tools of that distribution to install tinc. The documentation that comes along with your distribution will tell you how to do that. @menu * Darwin (MacOS/X) build environment:: * Cygwin (Windows) build environment:: * MinGW (Windows) build environment:: @end menu @c ================================================================== @node Darwin (MacOS/X) build environment @subsection Darwin (MacOS/X) build environment In order to build tinc on Darwin, you need to install the MacOS/X Developer Tools from @uref{http://developer.apple.com/tools/macosxtools.html} and a recent version of Fink from @uref{http://fink.sourceforge.net/}. After installation use fink to download and install the following packages: autoconf25, automake, dlcompat, m4, openssl, zlib and lzo. @c ================================================================== @node Cygwin (Windows) build environment @subsection Cygwin (Windows) build environment If Cygwin hasn't already been installed, install it directly from @uref{http://www.cygwin.com/}. When tinc is compiled in a Cygwin environment, it can only be run in this environment, but all programs, including those started outside the Cygwin environment, will be able to use the VPN. It will also support all features. @c ================================================================== @node MinGW (Windows) build environment @subsection MinGW (Windows) build environment You will need to install the MinGW environment from @uref{http://www.mingw.org}. When tinc is compiled using MinGW it runs natively under Windows, it is not necessary to keep MinGW installed. When detaching, tinc will install itself as a service, which will be restarted automatically after reboots. @c ================================================================== @node System files @section System files Before you can run tinc, you must make sure you have all the needed files on your system. @menu * Device files:: * Other files:: @end menu @c ================================================================== @node Device files @subsection Device files @cindex device files Most operating systems nowadays come with the necessary device files by default, or they have a mechanism to create them on demand. If you use Linux and do not have udev installed, you may need to create the following device file if it does not exist: @example mknod -m 600 /dev/net/tun c 10 200 @end example @c ================================================================== @node Other files @subsection Other files @subsubheading @file{/etc/networks} You may add a line to @file{/etc/networks} so that your VPN will get a symbolic name. For example: @example myvpn 10.0.0.0 @end example @subsubheading @file{/etc/services} @cindex port numbers You may add this line to @file{/etc/services}. The effect is that you may supply a @samp{tinc} as a valid port number to some programs. The number 655 is registered with the IANA. @example tinc 655/tcp TINC tinc 655/udp TINC # Ivo Timmermans <ivo@@tinc-vpn.org> @end example @c @c @c @c @c Configuring tinc @c @c @c @c @c ================================================================== @node Configuration @chapter Configuration @menu * Configuration introduction:: * Multiple networks:: * How connections work:: * Configuration files:: * Generating keypairs:: * Network interfaces:: * Example configuration:: @end menu @c ================================================================== @node Configuration introduction @section Configuration introduction Before actually starting to configure tinc and editing files, make sure you have read this entire section so you know what to expect. Then, make it clear to yourself how you want to organize your VPN: What are the nodes (computers running tinc)? What IP addresses/subnets do they have? What is the network mask of the entire VPN? Do you need special firewall rules? Do you have to set up masquerading or forwarding rules? Do you want to run tinc in router mode or switch mode? These questions can only be answered by yourself, you will not find the answers in this documentation. Make sure you have an adequate understanding of networks in general. @cindex Network Administrators Guide A good resource on networking is the @uref{http://www.linuxdoc.org/LDP/nag2/, Linux Network Administrators Guide}. If you have everything clearly pictured in your mind, proceed in the following order: First, generate the configuration files (@file{tinc.conf}, your host configuration file, @file{tinc-up} and perhaps @file{tinc-down}). Then generate the keypairs. Finally, distribute the host configuration files. These steps are described in the subsections below. @c ================================================================== @node Multiple networks @section Multiple networks @cindex multiple networks @cindex netname In order to allow you to run more than one tinc daemon on one computer, for instance if your computer is part of more than one VPN, you can assign a @var{netname} to your VPN. It is not required if you only run one tinc daemon, it doesn't even have to be the same on all the sites of your VPN, but it is recommended that you choose one anyway. We will asume you use a netname throughout this document. This means that you call tincd with the -n argument, which will assign a netname to this daemon. The effect of this is that the daemon will set its configuration root to @file{@value{sysconfdir}/tinc/@var{netname}/}, where @var{netname} is your argument to the -n option. You'll notice that it appears in syslog as @file{tinc.@var{netname}}. However, it is not strictly necessary that you call tinc with the -n option. In this case, the network name would just be empty, and it will be used as such. tinc now looks for files in @file{@value{sysconfdir}/tinc/}, instead of @file{@value{sysconfdir}/tinc/@var{netname}/}; the configuration file should be @file{@value{sysconfdir}/tinc/tinc.conf}, and the host configuration files are now expected to be in @file{@value{sysconfdir}/tinc/hosts/}. But it is highly recommended that you use this feature of tinc, because it will be so much clearer whom your daemon talks to. Hence, we will assume that you use it. @c ================================================================== @node How connections work @section How connections work When tinc starts up, it parses the command-line options and then reads in the configuration file tinc.conf. If it sees one or more `ConnectTo' values pointing to other tinc daemons in that file, it will try to connect to those other daemons. Whether this succeeds or not and whether `ConnectTo' is specified or not, tinc will listen for incoming connection from other deamons. If you did specify a `ConnectTo' value and the other side is not responding, tinc will keep retrying. This means that once started, tinc will stay running until you tell it to stop, and failures to connect to other tinc daemons will not stop your tinc daemon for trying again later. This means you don't have to intervene if there are temporary network problems. @cindex client @cindex server There is no real distinction between a server and a client in tinc. If you wish, you can view a tinc daemon without a `ConnectTo' value as a server, and one which does specify such a value as a client. It does not matter if two tinc daemons have a `ConnectTo' value pointing to each other however. @c ================================================================== @node Configuration files @section Configuration files The actual configuration of the daemon is done in the file @file{@value{sysconfdir}/tinc/@var{netname}/tinc.conf} and at least one other file in the directory @file{@value{sysconfdir}/tinc/@var{netname}/hosts/}. These file consists of comments (lines started with a #) or assignments in the form of @example Variable = Value. @end example The variable names are case insensitive, and any spaces, tabs, newlines and carriage returns are ignored. Note: it is not required that you put in the `=' sign, but doing so improves readability. If you leave it out, remember to replace it with at least one space character. The server configuration is complemented with host specific configuration (see the next section). Although all host configuration options for the local node listed in this document can also be put in @file{@value{sysconfdir}/tinc/@var{netname}/tinc.conf}, it is recommended to put host specific configuration options in the host configuration file, as this makes it easy to exchange with other nodes. In this section all valid variables are listed in alphabetical order. The default value is given between parentheses, other comments are between square brackets. @menu * Main configuration variables:: * Host configuration variables:: * Scripts:: * How to configure:: @end menu @c ================================================================== @node Main configuration variables @subsection Main configuration variables @table @asis @cindex AddressFamily @item AddressFamily = <ipv4\|ipv6\|any> (any) This option affects the address family of listening and outgoing sockets. If any is selected, then depending on the operating system both IPv4 and IPv6 or just IPv6 listening sockets will be created. @cindex BindToAddress @item BindToAddress = <@var{address}> [experimental] If your computer has more than one IPv4 or IPv6 address, tinc will by default listen on all of them for incoming connections. Multiple BindToAddress variables may be specified, in which case listening sockets for each specified address are made. This option may not work on all platforms. @cindex BindToInterface @item BindToInterface = <@var{interface}> [experimental] If you have more than one network interface in your computer, tinc will by default listen on all of them for incoming connections. It is possible to bind tinc to a single interface like eth0 or ppp0 with this variable. This option may not work on all platforms. @cindex Broadcast @item Broadcast = <yes \| no> (yes) [experimental] When disabled, tinc will drop all broadcast and multicast packets, in both router and switch mode. @cindex ConnectTo @item ConnectTo = <@var{name}> Specifies which other tinc daemon to connect to on startup. Multiple ConnectTo variables may be specified, in which case outgoing connections to each specified tinc daemon are made. The names should be known to this tinc daemon (i.e., there should be a host configuration file for the name on the ConnectTo line). If you don't specify a host with ConnectTo, tinc won't try to connect to other daemons at all, and will instead just listen for incoming connections. @cindex DecrementTTL @item DecrementTTL = <yes \| no> (yes) When enabled, tinc will decrement the Time To Live field in IPv4 packets, or the Hop Limit field in IPv6 packets, before forwarding a received packet to the virtual network device or to another node, and will drop packets that have a TTL value of zero, in which case it will send an ICMP Time Exceeded packet back. @cindex Device @item Device = <@var{device}> (@file{/dev/tap0}, @file{/dev/net/tun} or other depending on platform) The virtual network device to use. Tinc will automatically detect what kind of device it is. Note that you can only use one device per daemon. Under Windows, use @var{Interface} instead of @var{Device}. Note that you can only use one device per daemon. See also @ref{Device files}. @cindex DeviceType @item DeviceType = <@var{type}> (platform dependent) The type of the virtual network device. Tinc will normally automatically select the right type of tun/tap interface, and this option should not be used. However, this option can be used to select one of the special interface types, if support for them is compiled in. @table @asis @cindex dummy @item dummy Use a dummy interface. No packets are ever read or written to a virtual network device. Useful for testing, or when setting up a node that only forwards packets for other nodes. @cindex raw_socket @item raw_socket Open a raw socket, and bind it to a pre-existing @var{Interface} (eth0 by default). All packets are read from this interface. Packets received for the local node are written to the raw socket. However, at least on Linux, the operating system does not process IP packets destined for the local host. @cindex UML @item uml (not compiled in by default) Create a UNIX socket with the filename specified by @var{Device}, or @file{@value{localstatedir}/run/@var{netname}.umlsocket} if not specified. Tinc will wait for a User Mode Linux instance to connect to this socket. @cindex VDE @item vde (not compiled in by default) Uses the libvdeplug library to connect to a Virtual Distributed Ethernet switch, using the UNIX socket specified by @var{Device}, or @file{@value{localstatedir}/run/vde.ctl} if not specified. @end table Also, in case tinc does not seem to correctly interpret packets received from the virtual network device, it can be used to change the way packets are interpreted: @table @asis @item tun (BSD and Linux) Set type to tun. Depending on the platform, this can either be with or without an address family header (see below). @cindex tunnohead @item tunnohead (BSD) Set type to tun without an address family header. Tinc will expect packets read from the virtual network device to start with an IP header. On some platforms IPv6 packets cannot be read from or written to the device in this mode. @cindex tunifhead @item tunifhead (BSD) Set type to tun with an address family header. Tinc will expect packets read from the virtual network device to start with a four byte header containing the address family, followed by an IP header. This mode should support both IPv4 and IPv6 packets. @item tap (BSD and Linux) Set type to tap. Tinc will expect packets read from the virtual network device to start with an Ethernet header. @end table @cindex DirectOnly @item DirectOnly = <yes\|no> (no) [experimental] When this option is enabled, packets that cannot be sent directly to the destination node, but which would have to be forwarded by an intermediate node, are dropped instead. When combined with the IndirectData option, packets for nodes for which we do not have a meta connection with are also dropped. @cindex Forwarding @item Forwarding = <off\|internal\|kernel> (internal) [experimental] This option selects the way indirect packets are forwarded. @table @asis @item off Incoming packets that are not meant for the local node, but which should be forwarded to another node, are dropped. @item internal Incoming packets that are meant for another node are forwarded by tinc internally. This is the default mode, and unless you really know you need another forwarding mode, don't change it. @item kernel Incoming packets are always sent to the TUN/TAP device, even if the packets are not for the local node. This is less efficient, but allows the kernel to apply its routing and firewall rules on them, and can also help debugging. @end table @cindex GraphDumpFile @item GraphDumpFile = <@var{filename}> [experimental] If this option is present, tinc will dump the current network graph to the file @var{filename} every minute, unless there were no changes to the graph. The file is in a format that can be read by graphviz tools. If @var{filename} starts with a pipe symbol \|, then the rest of the filename is interpreted as a shell command that is executed, the graph is then sent to stdin. @cindex Hostnames @item Hostnames = <yes\|no> (no) This option selects whether IP addresses (both real and on the VPN) should be resolved. Since DNS lookups are blocking, it might affect tinc's efficiency, even stopping the daemon for a few seconds everytime it does a lookup if your DNS server is not responding. This does not affect resolving hostnames to IP addresses from the configuration file. @cindex Interface @item Interface = <@var{interface}> Defines the name of the interface corresponding to the virtual network device. Depending on the operating system and the type of device this may or may not actually set the name of the interface. Under Windows, this variable is used to select which network interface will be used. If you specified a Device, this variable is almost always already correctly set. @cindex LocalDiscovery @item LocalDiscovery = <yes \| no> (no) [experimental] When enabled, tinc will try to detect peers that are on the same local network. This will allow direct communication using LAN addresses, even if both peers are behind a NAT and they only ConnectTo a third node outside the NAT, which normally would prevent the peers from learning each other's LAN address. Currently, local discovery is implemented by sending broadcast packets to the LAN during path MTU discovery. This feature may not work in all possible situations. @cindex Mode @item Mode = <router\|switch\|hub> (router) This option selects the way packets are routed to other daemons. @table @asis @cindex router @item router In this mode Subnet variables in the host configuration files will be used to form a routing table. Only unicast packets of routable protocols (IPv4 and IPv6) are supported in this mode. This is the default mode, and unless you really know you need another mode, don't change it. @cindex switch @item switch In this mode the MAC addresses of the packets on the VPN will be used to dynamically create a routing table just like an Ethernet switch does. Unicast, multicast and broadcast packets of every protocol that runs over Ethernet are supported in this mode at the cost of frequent broadcast ARP requests and routing table updates. This mode is primarily useful if you want to bridge Ethernet segments. @cindex hub @item hub This mode is almost the same as the switch mode, but instead every packet will be broadcast to the other daemons while no routing table is managed. @end table @cindex KeyExpire @item KeyExpire = <@var{seconds}> (3600) This option controls the time the encryption keys used to encrypt the data are valid. It is common practice to change keys at regular intervals to make it even harder for crackers, even though it is thought to be nearly impossible to crack a single key. @cindex MACExpire @item MACExpire = <@var{seconds}> (600) This option controls the amount of time MAC addresses are kept before they are removed. This only has effect when Mode is set to "switch". @cindex Name @item Name = <@var{name}> [required] This is a symbolic name for this connection. The name should consist only of alfanumeric and underscore characters (a-z, A-Z, 0-9 and _). @cindex PingInterval @item PingInterval = <@var{seconds}> (60) The number of seconds of inactivity that tinc will wait before sending a probe to the other end. @cindex PingTimeout @item PingTimeout = <@var{seconds}> (5) The number of seconds to wait for a response to pings or to allow meta connections to block. If the other end doesn't respond within this time, the connection is terminated, and the others will be notified of this. @cindex PriorityInheritance @item PriorityInheritance = <yes\|no> (no) [experimental] When this option is enabled the value of the TOS field of tunneled IPv4 packets will be inherited by the UDP packets that are sent out. @cindex PrivateKey @item PrivateKey = <@var{key}> [obsolete] This is the RSA private key for tinc. However, for safety reasons it is advised to store private keys of any kind in separate files. This prevents accidental eavesdropping if you are editting the configuration file. @cindex PrivateKeyFile @item PrivateKeyFile = <@var{path}> (@file{@value{sysconfdir}/tinc/@var{netname}/rsa_key.priv}) This is the full path name of the RSA private key file that was generated by @samp{tincd --generate-keys}. It must be a full path, not a relative directory. Note that there must be exactly one of PrivateKey or PrivateKeyFile specified in the configuration file. @cindex ProcessPriority @item ProcessPriority = <low\|normal\|high> When this option is used the priority of the tincd process will be adjusted. Increasing the priority may help to reduce latency and packet loss on the VPN. @cindex ReplayWindow @item ReplayWindow = <bytes> (16) This is the size of the replay tracking window for each remote node, in bytes. The window is a bitfield which tracks 1 packet per bit, so for example the default setting of 16 will track up to 128 packets in the window. In high bandwidth scenarios, setting this to a higher value can reduce packet loss from the interaction of replay tracking with underlying real packet loss and/or reordering. Setting this to zero will disable replay tracking completely and pass all traffic, but leaves tinc vulnerable to replay-based attacks on your traffic. @cindex StrictSubnets @item StrictSubnets <yes\|no> (no) [experimental] When this option is enabled tinc will only use Subnet statements which are present in the host config files in the local @file{@value{sysconfdir}/tinc/@var{netname}/hosts/} directory. @cindex TunnelServer @item TunnelServer = <yes\|no> (no) [experimental] When this option is enabled tinc will no longer forward information between other tinc daemons, and will only allow connections with nodes for which host config files are present in the local @file{@value{sysconfdir}/tinc/@var{netname}/hosts/} directory. Setting this options also implicitly sets StrictSubnets. @cindex UDPRcvBuf @item UDPRcvBuf = <bytes> (OS default) Sets the socket receive buffer size for the UDP socket, in bytes. If unset, the default buffer size will be used by the operating system. @cindex UDPSndBuf @item UDPSndBuf = <bytes> Pq OS default Sets the socket send buffer size for the UDP socket, in bytes. If unset, the default buffer size will be used by the operating system. @end table @c ================================================================== @node Host configuration variables @subsection Host configuration variables @table @asis @cindex Address @item Address = <@var{IP address}\|@var{hostname}> [<port>] [recommended] This variable is only required if you want to connect to this host. It must resolve to the external IP address where the host can be reached, not the one that is internal to the VPN. If no port is specified, the default Port is used. @cindex Cipher @item Cipher = <@var{cipher}> (blowfish) The symmetric cipher algorithm used to encrypt UDP packets. Any cipher supported by OpenSSL is recognized. Furthermore, specifying "none" will turn off packet encryption. It is best to use only those ciphers which support CBC mode. @cindex ClampMSS @item ClampMSS = <yes\|no> (yes) This option specifies whether tinc should clamp the maximum segment size (MSS) of TCP packets to the path MTU. This helps in situations where ICMP Fragmentation Needed or Packet too Big messages are dropped by firewalls. @cindex Compression @item Compression = <@var{level}> (0) This option sets the level of compression used for UDP packets. Possible values are 0 (off), 1 (fast zlib) and any integer up to 9 (best zlib), 10 (fast lzo) and 11 (best lzo). @cindex Digest @item Digest = <@var{digest}> (sha1) The digest algorithm used to authenticate UDP packets. Any digest supported by OpenSSL is recognized. Furthermore, specifying "none" will turn off packet authentication. @cindex IndirectData @item IndirectData = <yes\|no> (no) This option specifies whether other tinc daemons besides the one you specified with ConnectTo can make a direct connection to you. This is especially useful if you are behind a firewall and it is impossible to make a connection from the outside to your tinc daemon. Otherwise, it is best to leave this option out or set it to no. @cindex MACLength @item MACLength = <@var{bytes}> (4) The length of the message authentication code used to authenticate UDP packets. Can be anything from 0 up to the length of the digest produced by the digest algorithm. @cindex PMTU @item PMTU = <@var{mtu}> (1514) This option controls the initial path MTU to this node. @cindex PMTUDiscovery @item PMTUDiscovery = <yes\|no> (yes) When this option is enabled, tinc will try to discover the path MTU to this node. After the path MTU has been discovered, it will be enforced on the VPN. @cindex Port @item Port = <@var{port}> (655) This is the port this tinc daemon listens on. You can use decimal portnumbers or symbolic names (as listed in @file{/etc/services}). @cindex PublicKey @item PublicKey = <@var{key}> [obsolete] This is the RSA public key for this host. @cindex PublicKeyFile @item PublicKeyFile = <@var{path}> [obsolete] This is the full path name of the RSA public key file that was generated by @samp{tincd --generate-keys}. It must be a full path, not a relative directory. @cindex PEM format From version 1.0pre4 on tinc will store the public key directly into the host configuration file in PEM format, the above two options then are not necessary. Either the PEM format is used, or exactly @strong{one of the above two options} must be specified in each host configuration file, if you want to be able to establish a connection with that host. @cindex Subnet @item Subnet = <@var{address}[/@var{prefixlength}[#@var{weight}]]> The subnet which this tinc daemon will serve. Tinc tries to look up which other daemon it should send a packet to by searching the appropiate subnet. If the packet matches a subnet, it will be sent to the daemon who has this subnet in his host configuration file. Multiple subnet lines can be specified for each daemon. Subnets can either be single MAC, IPv4 or IPv6 addresses, in which case a subnet consisting of only that single address is assumed, or they can be a IPv4 or IPv6 network address with a prefixlength. Shorthand notations are not supported. For example, IPv4 subnets must be in a form like 192.168.1.0/24, where 192.168.1.0 is the network address and 24 is the number of bits set in the netmask. Note that subnets like 192.168.1.1/24 are invalid! Read a networking HOWTO/FAQ/guide if you don't understand this. IPv6 subnets are notated like fec0:0:0:1:0:0:0:0/64. MAC addresses are notated like 0:1a:2b:3c:4d:5e. @cindex CIDR notation Prefixlength is the number of bits set to 1 in the netmask part; for example: netmask 255.255.255.0 would become /24, 255.255.252.0 becomes /22. This conforms to standard CIDR notation as described in @uref{ftp://ftp.isi.edu/in-notes/rfc1519.txt, RFC1519} @cindex Subnet weight A Subnet can be given a weight to indicate its priority over identical Subnets owned by different nodes. The default weight is 10. Lower values indicate higher priority. Packets will be sent to the node with the highest priority, unless that node is not reachable, in which case the node with the next highest priority will be tried, and so on. @cindex TCPonly @item TCPonly = <yes\|no> (no) [deprecated] If this variable is set to yes, then the packets are tunnelled over a TCP connection instead of a UDP connection. This is especially useful for those who want to run a tinc daemon from behind a masquerading firewall, or if UDP packet routing is disabled somehow. Setting this options also implicitly sets IndirectData. Since version 1.0.10, tinc will automatically detect whether communication via UDP is possible or not. @end table @c ================================================================== @node Scripts @subsection Scripts @cindex scripts Apart from reading the server and host configuration files, tinc can also run scripts at certain moments. Under Windows (not Cygwin), the scripts should have the extension .bat. @table @file @cindex tinc-up @item @value{sysconfdir}/tinc/@var{netname}/tinc-up This is the most important script. If it is present it will be executed right after the tinc daemon has been started and has connected to the virtual network device. It should be used to set up the corresponding network interface, but can also be used to start other things. Under Windows you can use the Network Connections control panel instead of creating this script. @cindex tinc-down @item @value{sysconfdir}/tinc/@var{netname}/tinc-down This script is started right before the tinc daemon quits. @item @value{sysconfdir}/tinc/@var{netname}/hosts/@var{host}-up This script is started when the tinc daemon with name @var{host} becomes reachable. @item @value{sysconfdir}/tinc/@var{netname}/hosts/@var{host}-down This script is started when the tinc daemon with name @var{host} becomes unreachable. @item @value{sysconfdir}/tinc/@var{netname}/host-up This script is started when any host becomes reachable. @item @value{sysconfdir}/tinc/@var{netname}/host-down This script is started when any host becomes unreachable. @item @value{sysconfdir}/tinc/@var{netname}/subnet-up This script is started when a Subnet becomes reachable. The Subnet and the node it belongs to are passed in environment variables. @item @value{sysconfdir}/tinc/@var{netname}/subnet-down This script is started when a Subnet becomes unreachable. @end table @cindex environment variables The scripts are started without command line arguments, but can make use of certain environment variables. Under UNIX like operating systems the names of environment variables must be preceded by a $ in scripts. Under Windows, in @file{.bat} files, they have to be put between % signs. @table @env @cindex NETNAME @item NETNAME If a netname was specified, this environment variable contains it. @cindex NAME @item NAME Contains the name of this tinc daemon. @cindex DEVICE @item DEVICE Contains the name of the virtual network device that tinc uses. @cindex INTERFACE @item INTERFACE Contains the name of the virtual network interface that tinc uses. This should be used for commands like ifconfig. @cindex NODE @item NODE When a host becomes (un)reachable, this is set to its name. If a subnet becomes (un)reachable, this is set to the owner of that subnet. @cindex REMOTEADDRESS @item REMOTEADDRESS When a host becomes (un)reachable, this is set to its real address. @cindex REMOTEPORT @item REMOTEPORT When a host becomes (un)reachable, this is set to the port number it uses for communication with other tinc daemons. @cindex SUBNET @item SUBNET When a subnet becomes (un)reachable, this is set to the subnet. @cindex WEIGHT @item WEIGHT When a subnet becomes (un)reachable, this is set to the subnet weight. @end table @c ================================================================== @node How to configure @subsection How to configure @subsubheading Step 1. Creating the main configuration file The main configuration file will be called @file{@value{sysconfdir}/tinc/@var{netname}/tinc.conf}. Adapt the following example to create a basic configuration file: @example Name = @var{yourname} Device = @file{/dev/tap0} @end example Then, if you know to which other tinc daemon(s) yours is going to connect, add `ConnectTo' values. @subsubheading Step 2. Creating your host configuration file If you added a line containing `Name = yourname' in the main configuarion file, you will need to create a host configuration file @file{@value{sysconfdir}/tinc/@var{netname}/hosts/yourname}. Adapt the following example to create a host configuration file: @example Address = your.real.hostname.org Subnet = 192.168.1.0/24 @end example You can also use an IP address instead of a hostname. The `Subnet' specifies the address range that is local for @emph{your part of the VPN only}. If you have multiple address ranges you can specify more than one `Subnet'. You might also need to add a `Port' if you want your tinc daemon to run on a different port number than the default (655). @c ================================================================== @node Generating keypairs @section Generating keypairs @cindex key generation Now that you have already created the main configuration file and your host configuration file, you can easily create a public/private keypair by entering the following command: @example tincd -n @var{netname} -K @end example Tinc will generate a public and a private key and ask you where to put them. Just press enter to accept the defaults. @c ================================================================== @node Network interfaces @section Network interfaces Before tinc can start transmitting data over the tunnel, it must set up the virtual network interface. First, decide which IP addresses you want to have associated with these devices, and what network mask they must have. Tinc will open a virtual network device (@file{/dev/tun}, @file{/dev/tap0} or similar), which will also create a network interface called something like @samp{tun0}, @samp{tap0}. If you are using the Linux tun/tap driver, the network interface will by default have the same name as the @var{netname}. Under Windows you can change the name of the network interface from the Network Connections control panel. @cindex tinc-up You can configure the network interface by putting ordinary ifconfig, route, and other commands to a script named @file{@value{sysconfdir}/tinc/@var{netname}/tinc-up}. When tinc starts, this script will be executed. When tinc exits, it will execute the script named @file{@value{sysconfdir}/tinc/@var{netname}/tinc-down}, but normally you don't need to create that script. An example @file{tinc-up} script: @example #!/bin/sh ifconfig $INTERFACE 192.168.1.1 netmask 255.255.0.0 @end example This script gives the interface an IP address and a netmask. The kernel will also automatically add a route to this interface, so normally you don't need to add route commands to the @file{tinc-up} script. The kernel will also bring the interface up after this command. @cindex netmask The netmask is the mask of the @emph{entire} VPN network, not just your own subnet. The exact syntax of the ifconfig and route commands differs from platform to platform. You can look up the commands for setting addresses and adding routes in @ref{Platform specific information}, but it is best to consult the manpages of those utilities on your platform. @c ================================================================== @node Example configuration @section Example configuration @cindex example Imagine the following situation. Branch A of our example `company' wants to connect three branch offices in B, C and D using the Internet. All four offices have a 24/7 connection to the Internet. A is going to serve as the center of the network. B and C will connect to A, and D will connect to C. Each office will be assigned their own IP network, 10.x.0.0. @example A: net 10.1.0.0 mask 255.255.0.0 gateway 10.1.54.1 internet IP 1.2.3.4 B: net 10.2.0.0 mask 255.255.0.0 gateway 10.2.1.12 internet IP 2.3.4.5 C: net 10.3.0.0 mask 255.255.0.0 gateway 10.3.69.254 internet IP 3.4.5.6 D: net 10.4.0.0 mask 255.255.0.0 gateway 10.4.3.32 internet IP 4.5.6.7 @end example Here, ``gateway'' is the VPN IP address of the machine that is running the tincd, and ``internet IP'' is the IP address of the firewall, which does not need to run tincd, but it must do a port forwarding of TCP and UDP on port 655 (unless otherwise configured). In this example, it is assumed that eth0 is the interface that points to the inner (physical) LAN of the office, although this could also be the same as the interface that leads to the Internet. The configuration of the real interface is also shown as a comment, to give you an idea of how these example host is set up. All branches use the netname `company' for this particular VPN. @subsubheading For Branch A @emph{BranchA} would be configured like this: In @file{@value{sysconfdir}/tinc/company/tinc-up}: @example # Real interface of internal network: # ifconfig eth0 10.1.54.1 netmask 255.255.0.0 ifconfig $INTERFACE 10.1.54.1 netmask 255.0.0.0 @end example and in @file{@value{sysconfdir}/tinc/company/tinc.conf}: @example Name = BranchA Device = /dev/tap0 @end example On all hosts, @file{@value{sysconfdir}/tinc/company/hosts/BranchA} contains: @example Subnet = 10.1.0.0/16 Address = 1.2.3.4 -----BEGIN RSA PUBLIC KEY----- ... -----END RSA PUBLIC KEY----- @end example Note that the IP addresses of eth0 and tap0 are the same. This is quite possible, if you make sure that the netmasks of the interfaces are different. It is in fact recommended to give both real internal network interfaces and tap interfaces the same IP address, since that will make things a lot easier to remember and set up. @subsubheading For Branch B In @file{@value{sysconfdir}/tinc/company/tinc-up}: @example # Real interface of internal network: # ifconfig eth0 10.2.43.8 netmask 255.255.0.0 ifconfig $INTERFACE 10.2.1.12 netmask 255.0.0.0 @end example and in @file{@value{sysconfdir}/tinc/company/tinc.conf}: @example Name = BranchB ConnectTo = BranchA @end example Note here that the internal address (on eth0) doesn't have to be the same as on the tap0 device. Also, ConnectTo is given so that this node will always try to connect to BranchA. On all hosts, in @file{@value{sysconfdir}/tinc/company/hosts/BranchB}: @example Subnet = 10.2.0.0/16 Address = 2.3.4.5 -----BEGIN RSA PUBLIC KEY----- ... -----END RSA PUBLIC KEY----- @end example @subsubheading For Branch C In @file{@value{sysconfdir}/tinc/company/tinc-up}: @example # Real interface of internal network: # ifconfig eth0 10.3.69.254 netmask 255.255.0.0 ifconfig $INTERFACE 10.3.69.254 netmask 255.0.0.0 @end example and in @file{@value{sysconfdir}/tinc/company/tinc.conf}: @example Name = BranchC ConnectTo = BranchA Device = /dev/tap1 @end example C already has another daemon that runs on port 655, so they have to reserve another port for tinc. It knows the portnumber it has to listen on from it's own host configuration file. On all hosts, in @file{@value{sysconfdir}/tinc/company/hosts/BranchC}: @example Address = 3.4.5.6 Subnet = 10.3.0.0/16 Port = 2000 -----BEGIN RSA PUBLIC KEY----- ... -----END RSA PUBLIC KEY----- @end example @subsubheading For Branch D In @file{@value{sysconfdir}/tinc/company/tinc-up}: @example # Real interface of internal network: # ifconfig eth0 10.4.3.32 netmask 255.255.0.0 ifconfig $INTERFACE 10.4.3.32 netmask 255.0.0.0 @end example and in @file{@value{sysconfdir}/tinc/company/tinc.conf}: @example Name = BranchD ConnectTo = BranchC Device = /dev/net/tun @end example D will be connecting to C, which has a tincd running for this network on port 2000. It knows the port number from the host configuration file. Also note that since D uses the tun/tap driver, the network interface will not be called `tun' or `tap0' or something like that, but will have the same name as netname. On all hosts, in @file{@value{sysconfdir}/tinc/company/hosts/BranchD}: @example Subnet = 10.4.0.0/16 Address = 4.5.6.7 -----BEGIN RSA PUBLIC KEY----- ... -----END RSA PUBLIC KEY----- @end example @subsubheading Key files A, B, C and D all have generated a public/private keypair with the following command: @example tincd -n company -K @end example The private key is stored in @file{@value{sysconfdir}/tinc/company/rsa_key.priv}, the public key is put into the host configuration file in the @file{@value{sysconfdir}/tinc/company/hosts/} directory. During key generation, tinc automatically guesses the right filenames based on the -n option and the Name directive in the @file{tinc.conf} file (if it is available). @subsubheading Starting After each branch has finished configuration and they have distributed the host configuration files amongst them, they can start their tinc daemons. They don't necessarily have to wait for the other branches to have started their daemons, tinc will try connecting until they are available. @c ================================================================== @node Running tinc @chapter Running tinc If everything else is done, you can start tinc by typing the following command: @example tincd -n @var{netname} @end example @cindex daemon Tinc will detach from the terminal and continue to run in the background like a good daemon. If there are any problems however you can try to increase the debug level and look in the syslog to find out what the problems are. @menu * Runtime options:: * Signals:: * Debug levels:: * Solving problems:: * Error messages:: * Sending bug reports:: @end menu @c ================================================================== @node Runtime options @section Runtime options Besides the settings in the configuration file, tinc also accepts some command line options. @cindex command line @cindex runtime options @cindex options @c from the manpage @table @option @item -c, --config=@var{path} Read configuration options from the directory @var{path}. The default is @file{@value{sysconfdir}/tinc/@var{netname}/}. @item -D, --no-detach Don't fork and detach. This will also disable the automatic restart mechanism for fatal errors. @cindex debug level @item -d, --debug=@var{level} Set debug level to @var{level}. The higher the debug level, the more gets logged. Everything goes via syslog. @item -k, --kill[=@var{signal}] Attempt to kill a running tincd (optionally with the specified @var{signal} instead of SIGTERM) and exit. Use it in conjunction with the -n option to make sure you kill the right tinc daemon. Under native Windows the optional argument is ignored, the service will always be stopped and removed. @item -n, --net=@var{netname} Use configuration for net @var{netname}. This will let tinc read all configuration files from @file{@value{sysconfdir}/tinc/@var{netname}/}. Specifying . for @var{netname} is the same as not specifying any @var{netname}. @xref{Multiple networks}. @item -K, --generate-keys[=@var{bits}] Generate public/private keypair of @var{bits} length. If @var{bits} is not specified, 2048 is the default. tinc will ask where you want to store the files, but will default to the configuration directory (you can use the -c or -n option in combination with -K). After that, tinc will quit. @item -o, --option=[@var{HOST}.]@var{KEY}=@var{VALUE} Without specifying a @var{HOST}, this will set server configuration variable @var{KEY} to @var{VALUE}. If specified as @var{HOST}.@var{KEY}=@var{VALUE}, this will set the host configuration variable @var{KEY} of the host named @var{HOST} to @var{VALUE}. This option can be used more than once to specify multiple configuration variables. @item -L, --mlock Lock tinc into main memory. This will prevent sensitive data like shared private keys to be written to the system swap files/partitions. @item --logfile[=@var{file}] Write log entries to a file instead of to the system logging facility. If @var{file} is omitted, the default is @file{@value{localstatedir}/log/tinc.@var{netname}.log}. @item --pidfile=@var{file} Write PID to @var{file} instead of @file{@value{localstatedir}/run/tinc.@var{netname}.pid}. @item --bypass-security Disables encryption and authentication. Only useful for debugging. @item -R, --chroot Change process root directory to the directory where the config file is located (@file{@value{sysconfdir}/tinc/@var{netname}/} as determined by -n/--net option or as given by -c/--config option), for added security. The chroot is performed after all the initialization is done, after writing pid files and opening network sockets. Note that this option alone does not do any good without -U/--user, below. Note also that tinc can't run scripts anymore (such as tinc-down or host-up), unless it's setup to be runnable inside chroot environment. @item -U, --user=@var{user} Switch to the given @var{user} after initialization, at the same time as chroot is performed (see --chroot above). With this option tinc drops privileges, for added security. @item --help Display a short reminder of these runtime options and terminate. @item --version Output version information and exit. @end table @c ================================================================== @node Signals @section Signals @cindex signals You can also send the following signals to a running tincd process: @c from the manpage @table @samp @item ALRM Forces tinc to try to connect to all uplinks immediately. Usually tinc attempts to do this itself, but increases the time it waits between the attempts each time it failed, and if tinc didn't succeed to connect to an uplink the first time after it started, it defaults to the maximum time of 15 minutes. @item HUP Partially rereads configuration files. Connections to hosts whose host config file are removed are closed. New outgoing connections specified in @file{tinc.conf} will be made. If the --logfile option is used, this will also close and reopen the log file, useful when log rotation is used. @item INT Temporarily increases debug level to 5. Send this signal again to revert to the original level. @item USR1 Dumps the connection list to syslog. @item USR2 Dumps virtual network device statistics, all known nodes, edges and subnets to syslog. @item WINCH Purges all information remembered about unreachable nodes. @end table @c ================================================================== @node Debug levels @section Debug levels @cindex debug levels The tinc daemon can send a lot of messages to the syslog. The higher the debug level, the more messages it will log. Each level inherits all messages of the previous level: @c from the manpage @table @samp @item 0 This will log a message indicating tinc has started along with a version number. It will also log any serious error. @item 1 This will log all connections that are made with other tinc daemons. @item 2 This will log status and error messages from scripts and other tinc daemons. @item 3 This will log all requests that are exchanged with other tinc daemons. These include authentication, key exchange and connection list updates. @item 4 This will log a copy of everything received on the meta socket. @item 5 This will log all network traffic over the virtual private network. @end table @c ================================================================== @node Solving problems @section Solving problems If tinc starts without problems, but if the VPN doesn't work, you will have to find the cause of the problem. The first thing to do is to start tinc with a high debug level in the foreground, so you can directly see everything tinc logs: @example tincd -n @var{netname} -d5 -D @end example If tinc does not log any error messages, then you might want to check the following things: @itemize @item @file{tinc-up} script Does this script contain the right commands? Normally you must give the interface the address of this host on the VPN, and the netmask must be big enough so that the entire VPN is covered. @item Subnet Does the Subnet (or Subnets) in the host configuration file of this host match the portion of the VPN that belongs to this host? @item Firewalls and NATs Do you have a firewall or a NAT device (a masquerading firewall or perhaps an ADSL router that performs masquerading)? If so, check that it allows TCP and UDP traffic on port 655. If it masquerades and the host running tinc is behind it, make sure that it forwards TCP and UDP traffic to port 655 to the host running tinc. You can add @samp{TCPOnly = yes} to your host config file to force tinc to only use a single TCP connection, this works through most firewalls and NATs. Since version 1.0.10, tinc will automatically fall back to TCP if direct communication via UDP is not possible. @end itemize @c ================================================================== @node Error messages @section Error messages What follows is a list of the most common error messages you might find in the logs. Some of them will only be visible if the debug level is high enough. @table @samp @item Could not open /dev/tap0: No such device @itemize @item You forgot to `modprobe netlink_dev' or `modprobe ethertap'. @item You forgot to compile `Netlink device emulation' in the kernel. @end itemize @item Can't write to /dev/net/tun: No such device @itemize @item You forgot to `modprobe tun'. @item You forgot to compile `Universal TUN/TAP driver' in the kernel. @item The tun device is located somewhere else in @file{/dev/}. @end itemize @item Network address and prefix length do not match! @itemize @item The Subnet field must contain a @emph{network} address, trailing bits should be 0. @item If you only want to use one IP address, set the netmask to /32. @end itemize @item Error reading RSA key file `rsa_key.priv': No such file or directory @itemize @item You forgot to create a public/private keypair. @item Specify the complete pathname to the private key file with the @samp{PrivateKeyFile} option. @end itemize @item Warning: insecure file permissions for RSA private key file `rsa_key.priv'! @itemize @item The private key file is readable by users other than root. Use chmod to correct the file permissions. @end itemize @item Creating metasocket failed: Address family not supported @itemize @item By default tinc tries to create both IPv4 and IPv6 sockets. On some platforms this might not be implemented. If the logs show @samp{Ready} later on, then at least one metasocket was created, and you can ignore this message. You can add @samp{AddressFamily = ipv4} to @file{tinc.conf} to prevent this from happening. @end itemize @item Cannot route packet: unknown IPv4 destination 1.2.3.4 @itemize @item You try to send traffic to a host on the VPN for which no Subnet is known. @item If it is a broadcast address (ending in .255), it probably is a samba server or a Windows host sending broadcast packets. You can ignore it. @end itemize @item Cannot route packet: ARP request for unknown address 1.2.3.4 @itemize @item You try to send traffic to a host on the VPN for which no Subnet is known. @end itemize @item Packet with destination 1.2.3.4 is looping back to us! @itemize @item Something is not configured right. Packets are being sent out to the virtual network device, but according to the Subnet directives in your host configuration file, those packets should go to your own host. Most common mistake is that you have a Subnet line in your host configuration file with a prefix length which is just as large as the prefix of the virtual network interface. The latter should in almost all cases be larger. Rethink your configuration. Note that you will only see this message if you specified a debug level of 5 or higher! @item Chances are that a @samp{Subnet = ...} line in the host configuration file of this tinc daemon is wrong. Change it to a subnet that is accepted locally by another interface, or if that is not the case, try changing the prefix length into /32. @end itemize @item Node foo (1.2.3.4) is not reachable @itemize @item Node foo does not have a connection anymore, its tinc daemon is not running or its connection to the Internet is broken. @end itemize @item Received UDP packet from unknown source 1.2.3.4 (port 12345) @itemize @item If you see this only sporadically, it is harmless and caused by a node sending packets using an old key. @end itemize @item Got bad/bogus/unauthorized REQUEST from foo (1.2.3.4 port 12345) @itemize @item Node foo does not have the right public/private keypair. Generate new keypairs and distribute them again. @item An attacker tries to gain access to your VPN. @item A network error caused corruption of metadata sent from foo. @end itemize @end table @c ================================================================== @node Sending bug reports @section Sending bug reports If you really can't find the cause of a problem, or if you suspect tinc is not working right, you can send us a bugreport, see @ref{Contact information}. Be sure to include the following information in your bugreport: @itemize @item A clear description of what you are trying to achieve and what the problem is. @item What platform (operating system, version, hardware architecture) and which version of tinc you use. @item If compiling tinc fails, a copy of @file{config.log} and the error messages you get. @item Otherwise, a copy of @file{tinc.conf}, @file{tinc-up} and all files in the @file{hosts/} directory. @item The output of the commands @samp{ifconfig -a} and @samp{route -n} (or @samp{netstat -rn} if that doesn't work). @item The output of any command that fails to work as it should (like ping or traceroute). @end itemize @c ================================================================== @node Technical information @chapter Technical information @menu * The connection:: * The meta-protocol:: * Security:: @end menu @c ================================================================== @node The connection @section The connection @cindex connection Tinc is a daemon that takes VPN data and transmit that to another host computer over the existing Internet infrastructure. @menu * The UDP tunnel:: * The meta-connection:: @end menu @c ================================================================== @node The UDP tunnel @subsection The UDP tunnel @cindex virtual network device @cindex frame type The data itself is read from a character device file, the so-called @emph{virtual network device}. This device is associated with a network interface. Any data sent to this interface can be read from the device, and any data written to the device gets sent from the interface. There are two possible types of virtual network devices: `tun' style, which are point-to-point devices which can only handle IPv4 and/or IPv6 packets, and `tap' style, which are Ethernet devices and handle complete Ethernet frames. So when tinc reads an Ethernet frame from the device, it determines its type. When tinc is in it's default routing mode, it can handle IPv4 and IPv6 packets. Depending on the Subnet lines, it will send the packets off to their destination IP address. In the `switch' and `hub' mode, tinc will use broadcasts and MAC address discovery to deduce the destination of the packets. Since the latter modes only depend on the link layer information, any protocol that runs over Ethernet is supported (for instance IPX and Appletalk). However, only `tap' style devices provide this information. After the destination has been determined, the packet will be compressed (optionally), a sequence number will be added to the packet, the packet will then be encrypted and a message authentication code will be appended. @cindex encapsulating @cindex UDP When that is done, time has come to actually transport the packet to the destination computer. We do this by sending the packet over an UDP connection to the destination host. This is called @emph{encapsulating}, the VPN packet (though now encrypted) is encapsulated in another IP datagram. When the destination receives this packet, the same thing happens, only in reverse. So it checks the message authentication code, decrypts the contents of the UDP datagram, checks the sequence number and writes the decrypted information to its own virtual network device. If the virtual network device is a `tun' device (a point-to-point tunnel), there is no problem for the kernel to accept a packet. However, if it is a `tap' device (this is the only available type on FreeBSD), the destination MAC address must match that of the virtual network interface. If tinc is in it's default routing mode, ARP does not work, so the correct destination MAC can not be known by the sending host. Tinc solves this by letting the receiving end detect the MAC address of its own virtual network interface and overwriting the destination MAC address of the received packet. In switch or hub modes ARP does work so the sender already knows the correct destination MAC address. In those modes every interface should have a unique MAC address, so make sure they are not the same. Because switch and hub modes rely on MAC addresses to function correctly, these modes cannot be used on the following operating systems which don't have a `tap' style virtual network device: OpenBSD, NetBSD, Darwin and Solaris. @c ================================================================== @node The meta-connection @subsection The meta-connection Having only a UDP connection available is not enough. Though suitable for transmitting data, we want to be able to reliably send other information, such as routing and session key information to somebody. @cindex TCP TCP is a better alternative, because it already contains protection against information being lost, unlike UDP. So we establish two connections. One for the encrypted VPN data, and one for other information, the meta-data. Hence, we call the second connection the meta-connection. We can now be sure that the meta-information doesn't get lost on the way to another computer. @cindex data-protocol @cindex meta-protocol Like with any communication, we must have a protocol, so that everybody knows what everything stands for, and how she should react. Because we have two connections, we also have two protocols. The protocol used for the UDP data is the ``data-protocol,'' the other one is the ``meta-protocol.'' The reason we don't use TCP for both protocols is that UDP is much better for encapsulation, even while it is less reliable. The real problem is that when TCP would be used to encapsulate a TCP stream that's on the private network, for every packet sent there would be three ACKs sent instead of just one. Furthermore, if there would be a timeout, both TCP streams would sense the timeout, and both would start re-sending packets. @c ================================================================== @node The meta-protocol @section The meta-protocol The meta protocol is used to tie all tinc daemons together, and exchange information about which tinc daemon serves which virtual subnet. The meta protocol consists of requests that can be sent to the other side. Each request has a unique number and several parameters. All requests are represented in the standard ASCII character set. It is possible to use tools such as telnet or netcat to connect to a tinc daemon started with the --bypass-security option and to read and write requests by hand, provided that one understands the numeric codes sent. The authentication scheme is described in @ref{Authentication protocol}. After a successful authentication, the server and the client will exchange all the information about other tinc daemons and subnets they know of, so that both sides (and all the other tinc daemons behind them) have their information synchronised. @cindex ADD_EDGE @cindex ADD_SUBNET @example message ------------------------------------------------------------------ ADD_EDGE node1 node2 21.32.43.54 655 222 0 \| \| \| \| \| +-> options \| \| \| \| +----> weight \| \| \| +--------> UDP port of node2 \| \| +----------------> real address of node2 \| +-------------------------> name of destination node +-------------------------------> name of source node ADD_SUBNET node 192.168.1.0/24 \| \| +--> prefixlength \| +--------> network address +------------------> owner of this subnet ------------------------------------------------------------------ @end example The ADD_EDGE messages are to inform other tinc daemons that a connection between two nodes exist. The address of the destination node is available so that VPN packets can be sent directly to that node. The ADD_SUBNET messages inform other tinc daemons that certain subnets belong to certain nodes. tinc will use it to determine to which node a VPN packet has to be sent. @cindex DEL_EDGE @cindex DEL_SUBNET @example message ------------------------------------------------------------------ DEL_EDGE node1 node2 \| +----> name of destination node +----------> name of source node DEL_SUBNET node 192.168.1.0/24 \| \| +--> prefixlength \| +--------> network address +------------------> owner of this subnet ------------------------------------------------------------------ @end example In case a connection between two daemons is closed or broken, DEL_EDGE messages are sent to inform the other daemons of that fact. Each daemon will calculate a new route to the the daemons, or mark them unreachable if there isn't any. @cindex REQ_KEY @cindex ANS_KEY @cindex KEY_CHANGED @example message ------------------------------------------------------------------ REQ_KEY origin destination \| +--> name of the tinc daemon it wants the key from +----------> name of the daemon that wants the key ANS_KEY origin destination 4ae0b0a82d6e0078 91 64 4 \| \| \______________/ \| \| +--> MAC length \| \| \| \| +-----> digest algorithm \| \| \| +--------> cipher algorithm \| \| +--> 128 bits key \| +--> name of the daemon that wants the key +----------> name of the daemon that uses this key KEY_CHANGED origin +--> daemon that has changed it's packet key ------------------------------------------------------------------ @end example The keys used to encrypt VPN packets are not sent out directly. This is because it would generate a lot of traffic on VPNs with many daemons, and chances are that not every tinc daemon will ever send a packet to every other daemon. Instead, if a daemon needs a key it sends a request for it via the meta connection of the nearest hop in the direction of the destination. @cindex PING @cindex PONG @example daemon message ------------------------------------------------------------------ origin PING dest. PONG ------------------------------------------------------------------ @end example There is also a mechanism to check if hosts are still alive. Since network failures or a crash can cause a daemon to be killed without properly shutting down the TCP connection, this is necessary to keep an up to date connection list. PINGs are sent at regular intervals, except when there is also some other traffic. A little bit of salt (random data) is added with each PING and PONG message, to make sure that long sequences of PING/PONG messages without any other traffic won't result in known plaintext. This basically covers what is sent over the meta connection by tinc. @c ================================================================== @node Security @section Security @cindex TINC @cindex Cabal Tinc got its name from ``TINC,'' short for @emph{There Is No Cabal}; the alleged Cabal was/is an organisation that was said to keep an eye on the entire Internet. As this is exactly what you @emph{don't} want, we named the tinc project after TINC. @cindex SVPN But in order to be ``immune'' to eavesdropping, you'll have to encrypt your data. Because tinc is a @emph{Secure} VPN (SVPN) daemon, it does exactly that: encrypt. Tinc by default uses blowfish encryption with 128 bit keys in CBC mode, 32 bit sequence numbers and 4 byte long message authentication codes to make sure eavesdroppers cannot get and cannot change any information at all from the packets they can intercept. The encryption algorithm and message authentication algorithm can be changed in the configuration. The length of the message authentication codes is also adjustable. The length of the key for the encryption algorithm is always the default length used by OpenSSL. @menu * Authentication protocol:: * Encryption of network packets:: * Security issues:: @end menu @c ================================================================== @node Authentication protocol @subsection Authentication protocol @cindex authentication A new scheme for authentication in tinc has been devised, which offers some improvements over the protocol used in 1.0pre2 and 1.0pre3. Explanation is below. @cindex ID @cindex META_KEY @cindex CHALLENGE @cindex CHAL_REPLY @cindex ACK @example daemon message -------------------------------------------------------------------------- client <attempts connection> server <accepts connection> client ID client 12 \| +---> version +-------> name of tinc daemon server ID server 12 \| +---> version +-------> name of tinc daemon client META_KEY 5f0823a93e35b69e...7086ec7866ce582b \_________________________________/ +-> RSAKEYLEN bits totally random string S1, encrypted with server's public RSA key server META_KEY 6ab9c1640388f8f0...45d1a07f8a672630 \_________________________________/ +-> RSAKEYLEN bits totally random string S2, encrypted with client's public RSA key From now on: - the client will symmetrically encrypt outgoing traffic using S1 - the server will symmetrically encrypt outgoing traffic using S2 client CHALLENGE da02add1817c1920989ba6ae2a49cecbda0 \_________________________________/ +-> CHALLEN bits totally random string H1 server CHALLENGE 57fb4b2ccd70d6bb35a64c142f47e61d57f \_________________________________/ +-> CHALLEN bits totally random string H2 client CHAL_REPLY 816a86 +-> 160 bits SHA1 of H2 server CHAL_REPLY 928ffe +-> 160 bits SHA1 of H1 After the correct challenge replies are received, both ends have proved their identity. Further information is exchanged. client ACK 655 123 0 \| \| +-> options \| +----> estimated weight +--------> listening port of client server ACK 655 321 0 \| \| +-> options \| +----> estimated weight +--------> listening port of server -------------------------------------------------------------------------- @end example This new scheme has several improvements, both in efficiency and security. First of all, the server sends exactly the same kind of messages over the wire as the client. The previous versions of tinc first authenticated the client, and then the server. This scheme even allows both sides to send their messages simultaneously, there is no need to wait for the other to send something first. This means that any calculations that need to be done upon sending or receiving a message can also be done in parallel. This is especially important when doing RSA encryption/decryption. Given that these calculations are the main part of the CPU time spent for the authentication, speed is improved by a factor 2. Second, only one RSA encrypted message is sent instead of two. This reduces the amount of information attackers can see (and thus use for a cryptographic attack). It also improves speed by a factor two, making the total speedup a factor 4. Third, and most important: The symmetric cipher keys are exchanged first, the challenge is done afterwards. In the previous authentication scheme, because a man-in-the-middle could pass the challenge/chal_reply phase (by just copying the messages between the two real tinc daemons), but no information was exchanged that was really needed to read the rest of the messages, the challenge/chal_reply phase was of no real use. The man-in-the-middle was only stopped by the fact that only after the ACK messages were encrypted with the symmetric cipher. Potentially, it could even send it's own symmetric key to the server (if it knew the server's public key) and read some of the metadata the server would send it (it was impossible for the mitm to read actual network packets though). The new scheme however prevents this. This new scheme makes sure that first of all, symmetric keys are exchanged. The rest of the messages are then encrypted with the symmetric cipher. Then, each side can only read received messages if they have their private key. The challenge is there to let the other side know that the private key is really known, because a challenge reply can only be sent back if the challenge is decrypted correctly, and that can only be done with knowledge of the private key. Fourth: the first thing that is sent via the symmetric cipher encrypted connection is a totally random string, so that there is no known plaintext (for an attacker) in the beginning of the encrypted stream. @c ================================================================== @node Encryption of network packets @subsection Encryption of network packets @cindex encryption A data packet can only be sent if the encryption key is known to both parties, and the connection is activated. If the encryption key is not known, a request is sent to the destination using the meta connection to retrieve it. The packet is stored in a queue while waiting for the key to arrive. @cindex UDP The UDP packet containing the network packet from the VPN has the following layout: @example ... \| IP header \| UDP header \| seqno \| VPN packet \| MAC \| UDP trailer \___________________/\_____/ \| \| V +---> digest algorithm Encrypted with symmetric cipher @end example So, the entire VPN packet is encrypted using a symmetric cipher, including a 32 bits sequence number that is added in front of the actual VPN packet, to act as a unique IV for each packet and to prevent replay attacks. A message authentication code is added to the UDP packet to prevent alteration of packets. By default the first 4 bytes of the digest are used for this, but this can be changed using the MACLength configuration variable. @c ================================================================== @node Security issues @subsection Security issues In August 2000, we discovered the existence of a security hole in all versions of tinc up to and including 1.0pre2. This had to do with the way we exchanged keys. Since then, we have been working on a new authentication scheme to make tinc as secure as possible. The current version uses the OpenSSL library and uses strong authentication with RSA keys. On the 29th of December 2001, Jerome Etienne posted a security analysis of tinc 1.0pre4. Due to a lack of sequence numbers and a message authentication code for each packet, an attacker could possibly disrupt certain network services or launch a denial of service attack by replaying intercepted packets. The current version adds sequence numbers and message authentication codes to prevent such attacks. On the 15th of September 2003, Peter Gutmann posted a security analysis of tinc 1.0.1. He argues that the 32 bit sequence number used by tinc is not a good IV, that tinc's default length of 4 bytes for the MAC is too short, and he doesn't like tinc's use of RSA during authentication. We do not know of a security hole in this version of tinc, but tinc's security is not as strong as TLS or IPsec. We will address these issues in tinc 2.0. Cryptography is a hard thing to get right. We cannot make any guarantees. Time, review and feedback are the only things that can prove the security of any cryptographic product. If you wish to review tinc or give us feedback, you are stronly encouraged to do so. @c ================================================================== @node Platform specific information @chapter Platform specific information @menu * Interface configuration:: * Routes:: @end menu @c ================================================================== @node Interface configuration @section Interface configuration When configuring an interface, one normally assigns it an address and a netmask. The address uniquely identifies the host on the network attached to the interface. The netmask, combined with the address, forms a subnet. It is used to add a route to the routing table instructing the kernel to send all packets which fall into that subnet to that interface. Because all packets for the entire VPN should go to the virtual network interface used by tinc, the netmask should be such that it encompasses the entire VPN. For IPv4 addresses: @multitable {Darwin (MacOS/X)} {ifconfig route add -bla network address netmask netmask prefixlength interface} @item Linux @tab @code{ifconfig} @var{interface} @var{address} @code{netmask} @var{netmask} @item Linux iproute2 @tab @code{ip addr add} @var{address}@code{/}@var{prefixlength} @code{dev} @var{interface} @item FreeBSD @tab @code{ifconfig} @var{interface} @var{address} @code{netmask} @var{netmask} @item OpenBSD @tab @code{ifconfig} @var{interface} @var{address} @code{netmask} @var{netmask} @item NetBSD @tab @code{ifconfig} @var{interface} @var{address} @code{netmask} @var{netmask} @item Solaris @tab @code{ifconfig} @var{interface} @var{address} @code{netmask} @var{netmask} @item Darwin (MacOS/X) @tab @code{ifconfig} @var{interface} @var{address} @code{netmask} @var{netmask} @item Windows @tab @code{netsh interface ip set address} @var{interface} @code{static} @var{address} @var{netmask} @end multitable For IPv6 addresses: @multitable {Darwin (MacOS/X)} {ifconfig route add -bla network address netmask netmask prefixlength interface} @item Linux @tab @code{ifconfig} @var{interface} @code{add} @var{address}@code{/}@var{prefixlength} @item FreeBSD @tab @code{ifconfig} @var{interface} @code{inet6} @var{address} @code{prefixlen} @var{prefixlength} @item OpenBSD @tab @code{ifconfig} @var{interface} @code{inet6} @var{address} @code{prefixlen} @var{prefixlength} @item NetBSD @tab @code{ifconfig} @var{interface} @code{inet6} @var{address} @code{prefixlen} @var{prefixlength} @item Solaris @tab @code{ifconfig} @var{interface} @code{inet6 plumb up} @item @tab @code{ifconfig} @var{interface} @code{inet6 addif} @var{address} @var{address} @item Darwin (MacOS/X) @tab @code{ifconfig} @var{interface} @code{inet6} @var{address} @code{prefixlen} @var{prefixlength} @item Windows @tab @code{netsh interface ipv6 add address} @var{interface} @code{static} @var{address}/@var{prefixlength} @end multitable @c ================================================================== @node Routes @section Routes In some cases it might be necessary to add more routes to the virtual network interface. There are two ways to indicate which interface a packet should go to, one is to use the name of the interface itself, another way is to specify the (local) address that is assigned to that interface (@var{local_address}). The former way is unambiguous and therefore preferable, but not all platforms support this. Adding routes to IPv4 subnets: @multitable {Darwin (MacOS/X)} {ifconfig route add -bla network address netmask netmask prefixlength interface} @item Linux @tab @code{route add -net} @var{network_address} @code{netmask} @var{netmask} @var{interface} @item Linux iproute2 @tab @code{ip route add} @var{network_address}@code{/}@var{prefixlength} @code{dev} @var{interface} @item FreeBSD @tab @code{route add} @var{network_address}@code{/}@var{prefixlength} @var{local_address} @item OpenBSD @tab @code{route add} @var{network_address}@code{/}@var{prefixlength} @var{local_address} @item NetBSD @tab @code{route add} @var{network_address}@code{/}@var{prefixlength} @var{local_address} @item Solaris @tab @code{route add} @var{network_address}@code{/}@var{prefixlength} @var{local_address} @code{-interface} @item Darwin (MacOS/X) @tab @code{route add} @var{network_address}@code{/}@var{prefixlength} @var{local_address} @item Windows @tab @code{netsh routing ip add persistentroute} @var{network_address} @var{netmask} @var{interface} @var{local_address} @end multitable Adding routes to IPv6 subnets: @multitable {Darwin (MacOS/X)} {ifconfig route add -bla network address netmask netmask prefixlength interface} @item Linux @tab @code{route add -A inet6} @var{network_address}@code{/}@var{prefixlength} @var{interface} @item Linux iproute2 @tab @code{ip route add} @var{network_address}@code{/}@var{prefixlength} @code{dev} @var{interface} @item FreeBSD @tab @code{route add -inet6} @var{network_address}@code{/}@var{prefixlength} @var{local_address} @item OpenBSD @tab @code{route add -inet6} @var{network_address} @var{local_address} @code{-prefixlen} @var{prefixlength} @item NetBSD @tab @code{route add -inet6} @var{network_address} @var{local_address} @code{-prefixlen} @var{prefixlength} @item Solaris @tab @code{route add -inet6} @var{network_address}@code{/}@var{prefixlength} @var{local_address} @code{-interface} @item Darwin (MacOS/X) @tab ? @item Windows @tab @code{netsh interface ipv6 add route} @var{network address}/@var{prefixlength} @var{interface} @end multitable @c ================================================================== @node About us @chapter About us @menu * Contact information:: * Authors:: @end menu @c ================================================================== @node Contact information @section Contact information @cindex website Tinc's website is at @url{http://www.tinc-vpn.org/}, this server is located in the Netherlands. @cindex IRC We have an IRC channel on the FreeNode and OFTC IRC networks. Connect to @uref{http://www.freenode.net/, irc.freenode.net} or @uref{http://www.oftc.net/, irc.oftc.net} and join channel #tinc. @c ================================================================== @node Authors @section Authors @table @asis @item Ivo Timmermans (zarq) @item Guus Sliepen (guus) (@email{guus@@tinc-vpn.org}) @end table We have received a lot of valuable input from users. With their help, tinc has become the flexible and robust tool that it is today. We have composed a list of contributions, in the file called @file{THANKS} in the source distribution. @c ================================================================== @node Concept Index @unnumbered Concept Index @c ================================================================== @printindex cp @c ================================================================== @contents @bye
http://bryantheath.com/files/2016/11/NumberSense_AnswersTemplate.tex	bryantheath.com	CC-MAIN-2018-51	application/x-tex	text/x-matlab	crawl-data/CC-MAIN-2018-51/segments/1544376831933.96/warc/CC-MAIN-20181219090209-20181219112209-00544.warc.gz	52,544,112	1,508	%Need to learn fraction spacing % -- Answer: Use \dfrac{}{} %Need to learn how to custom question numbering % -- Answer: Use \renewcommand{\questionlabel}{*\thequestion}, where ** is the new format %Need to change margins % -- Answer: can use \extrawidth{} \documentclass[10pt]{exam} \usepackage{multicol} \usepackage{amsmath} \usepackage[none]{hyphenat} \setlength\columnsep{40pt} \extrawidth{1in} %Setting spacing between lines \linespread{1.5} %Setting question separation: %\renewcommand{\questionshook}{\setlength{\itemsep}{.5in}} %Changing default numbering scheme: \renewcommand{\questionlabel}{ (\thequestion)} \begin{document} \begin{multicols}{4}[\section{Number Sense Answer Key}] \begin{questions} \question $2188$ \question $10040$ \question $2\frac{23}{56}$ \question $\frac{35}{8}$ \question $-10.5, -\frac{21}{2}, -10\frac{1}{2}$ \question $\frac{3}{40}$ \question $420$ \question $10$ \question $529$ %Problem 10 \renewcommand{\questionlabel}{(\thequestion)} \question $19914-22010$ \renewcommand{\questionlabel}{ (\thequestion)} \question $13$ \question $6.6$ \question $\$5.00$ \question $376$ \question $1.3, \frac{13}{10}, 1\frac{3}{10}$ \question $\frac{8}{9}$ \question $0$ \question $8$ \question $1004$ %Problem 20 \renewcommand{\questionlabel}{(\thequestion)} \question -$219395 - $-$198499$ \renewcommand{\questionlabel}{ (\thequestion)} \question $28$ \question $\frac{40}{9}, 4\frac{4}{9}$ \question $\$125.00$ \question $.3125, \frac{5}{16}$ \question $75$ \question $15$ \question $13$ \question $2$ \question $1.25, \frac{5}{4}, 1\frac{1}{4}$ %Problem 30 \renewcommand{\questionlabel}{(\thequestion)} \question $11044 - 12206$ \renewcommand{\questionlabel}{ (\thequestion)} \question $22$ \question $2$ \question $104$ \question $4$ \question $79.04, \frac{1976}{25}, 79\frac{1}{25}$ \question $3$ \question $15$ \question $98$ \question $.2, \frac{1}{5}$ %Problem 40 \renewcommand{\questionlabel}{(\thequestion)} \question $1631 - 1802$ \renewcommand{\questionlabel}{ (\thequestion)} \question $36$ \question $3$ \question $65932$ \question $9$ \question $4275$ \question $7$ \question $960$ \question $20$ \question $21\frac{3}{7}$ %Problem 50 \renewcommand{\questionlabel}{(\thequestion)} \question $308 - 340$ \renewcommand{\questionlabel}{ (\thequestion)} \question $-7$ \question $48$ \question $-4$ \question $\frac{32}{261}$ \question $1.5, \frac{3}{2}, 1\frac{1}{2}$ \question $4225$ \question $3$ \question $20$ \question $47$ %Problem 60 \renewcommand{\questionlabel}{(\thequestion)} \question $315188 - 348364$ \renewcommand{\questionlabel}{ (\thequestion)} \question $75$ \question $9$ \question $11$ \question $-6$ \question $-.5, -\frac{1}{2}$ \question $12$ \question $6$ \question $667$ \question $3$ %Problem 70 \renewcommand{\questionlabel}{(\thequestion)} \question $5053 - 5584$ \renewcommand{\questionlabel}{ (\thequestion)} \question $-.125, \frac{1}{8}$ \question $-1.25, -\frac{5}{4}, -1\frac{1}{4}$ \question $3$ \question $9$ \question $-26$ \question $\frac{16}{3}, 5\frac{1}{3}$ \question $5$ \question $2997$ \question $\frac{2}{3}$ %Problem 80 \renewcommand{\questionlabel}{*(\thequestion)} \question $427 - 471$ \renewcommand{\questionlabel}{ (\thequestion)} \end{questions} \end{multicols} \end{document}
https://es.theanarchistlibrary.org/library/elisee-reclus-el-ideal-y-la-juventud.tex	theanarchistlibrary.org	CC-MAIN-2021-49	application/x-tex	application/x-tex	crawl-data/CC-MAIN-2021-49/segments/1637964362919.65/warc/CC-MAIN-20211203212721-20211204002721-00317.warc.gz	312,910,596	16,294	\documentclass[DIV=15,% BCOR=0mm,% headinclude=false,% footinclude=false,% fontsize=11pt,% twoside,% paper=a5]% {scrartcl} \usepackage{microtype} \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} \usepackage[shortlabels]{enumitem} \usepackage{tabularx} \usepackage[normalem]{ulem} \def\hsout{\bgroup \ULdepth=-.55ex \ULset} % https://tex.stackexchange.com/questions/22410/strikethrough-in-section-title % Unclear if \protect \hsout is needed. Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand{\forcelinebreak}{\strut\\{}} \newcommand{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand{\Slash}{\slash\hspace{0pt}} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} \usepackage{fontspec} \usepackage{polyglossia} \setmainlanguage{spanish} \setmainfont{LinLibertine_R.otf}[Script=Latin,% Path=/usr/share/fonts/opentype/linux-libertine/,% BoldFont=LinLibertine_RB.otf,% BoldItalicFont=LinLibertine_RBI.otf,% ItalicFont=LinLibertine_RI.otf] \setmonofont{cmuntt.ttf}[Script=Latin,% Scale=MatchLowercase,% Path=/usr/share/fonts/truetype/cmu/,% BoldFont=cmuntb.ttf,% BoldItalicFont=cmuntx.ttf,% ItalicFont=cmunit.ttf] \setsansfont{cmunss.ttf}[Script=Latin,% Scale=MatchLowercase,% Path=/usr/share/fonts/truetype/cmu/,% BoldFont=cmunsx.ttf,% BoldItalicFont=cmunso.ttf,% ItalicFont=cmunsi.ttf] \newfontfamily\spanishfont{LinLibertine_R.otf}[Script=Latin,% Path=/usr/share/fonts/opentype/linux-libertine/,% BoldFont=LinLibertine_RB.otf,% BoldItalicFont=LinLibertine_RBI.otf,% ItalicFont=LinLibertine_RI.otf] % footnote handling \usepackage[fragile]{bigfoot} \usepackage{perpage} \DeclareNewFootnote{default} \let\chapter\section % global style \pagestyle{plain} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand{\captionformat}{} \renewcommand{\figureformat}{} \renewcommand{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} \DeclareNewFootnote{B} \MakeSorted{footnoteB} \renewcommand\thefootnoteB{(\arabic{footnoteB})} \deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} \frenchspacing % avoid vertical glue \raggedbottom % this will generate overfull boxes, so we need to set a tolerance % \pretolerance=1000 % pretolerance is what is accepted for a paragraph without % hyphenation, so it makes sense to be strict here and let the user % accept tweak the tolerance instead. \tolerance=200 % Additional tolerance for bad paragraphs only \setlength{\emergencystretch}{30pt} % (try to) forbid widows/orphans \clubpenalty=10000 \widowpenalty=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{El ideal y la juventud} \date{1895} \author{Élisée Reclus} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={El ideal y la juventud},% pdfauthor={Élisée Reclus},% pdfsubject={},% pdfkeywords={Ideología}% } \begin{document} \thispagestyle{empty} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge El ideal y la juventud\par}}% \vskip 1em \vskip 2em {\usekomafont{author}{Élisée Reclus\par}}% \vskip 1.5em {\usekomafont{date}{1895\par}}% \end{center} \vskip 3em \par Si la palabra “Ideal” tiene realmente algún significado, significa mucho más que un vago anhelo de cosas mejores, una fatigosa búsqueda de la felicidad o un anhelo irregular y triste de un ambiente menos odioso que la sociedad de hoy; ah, sí, debemos darle al término un valor exacto, debemos resolver resueltamente e inteligentemente cuál es el final ostensible de nuestras incesantes aspiraciones. Investiguemos entonces ese Ideal. Para algunos, no sería más que un retorno a las edades del pasado, a la infancia de la humanidad; consistiría en la negación de la ciencia, en una postración humilde como en el pasado frente a un atronador Sinaí, y bajo el ojo de un Moisés que obra milagros, el autoritario traductor de la voluntad divina. A esa concepción de completa renuncia y obediencia, los anarquistas oponen otra, orgullosamente consistente con la libertad individual más plena y también con la acción voluntaria de la sociedad, la acción espontánea que se hace posible mediante la supresión del privilegio y de la autoridad arbitraria, mediante la abolición de la propiedad privada, por respeto mutuo, y por la cooperación inteligente con las leyes naturales. Entre esos dos ideales no hay compromiso posible: el conservadurismo y el moderatismo, el liberalismo, el progresismo e incluso el socialismo son solo un recurso político, diseñado para retrasar el buen momento, detener con unas pocas migajas de la libertad las bocas de aquellos que demandan pan completo Para liberarse de la agonía de la evolución, el hombre debe perderse en Dios o, como ser, erguido y libre, convertirse en su propio amo. Solo tome en consideración la última alternativa, hacia la cual todos los jóvenes, en quienes las gloriosas posibilidades de la vida están latentes, dirigen consciente o inconscientemente su pensamiento y esfuerzo. Lamentablemente, la mayoría actúa y piensa para este fin de forma inconsciente. Deambulan de aquí para allá, sin ningún propósito fijo, escépticos y pesimistas en teoría, aunque afortunadamente su acción es frecuentemente inconsistente con su profesión. Sobre todo, es importante tanto para ellos como para nosotros mismos deshacernos del lenguaje de la desesperación. ¿En qué tipo de futuro podríamos contar si fuera cierto que, a pesar de toda apariencia de lo contrario, no había nada nuevo bajo el sol, y que todas las luchas humanas eran meros conflictos de fuerza bruta, en el cual, por supuesto, el débil debe invariablemente ser conducido contra la pared? ¿De qué serviría en ese caso soñar y hablar de mejores entornos sociales en los que habría alimentos para todos, libertad y justicia para todos? Nuestras palabras serían solo un sonido pasajero, y el hombre sabio, como dijo Eclesiastés hace más de dos mil años y como los poetas y los rimadores han repetido repetidas veces y con frecuencia, estarían contentos de comer, beber y divertirse. Tomar la vida tal como viene sería una verdadera filosofía, y si debería estar cargada de demasiados problemas o demasiadas penas, lo mejor sería ponerle fin. Se jugaría una pequeña bola de plomo, una pequeña gota de veneno y la pobre farsa de la existencia. Aunque el suicidio es incuestionablemente raro entre los jóvenes, el modo de pensar que lo justifica es demasiado común; y además, hay muchas maneras de entrar a la muerte sin el vulgar derramamiento de sangre. Quizás lo más conveniente es dejar de vivir en cualquier sentido real, abandonar el uso de la mente, llegar a la conclusión de que no hay nada más que conocer, de derivar como una paja en el diluvio, tomar nuestras opiniones listo y repetirlos como un loro, para mirar desdeñosamente todos los esfuerzos independientes y la especulación; y aunque un retorno a la superstición del viejo mundo sea imposible, porque no podemos resucitar el pasado, estos muertos en la vida pretenden ser todavía del rebaño de los fieles, hablan de los artículos del credo y practican las payasadas prescritas por los sacerdotes. Sin fuerza de carácter o fuerza de voluntad para descubrir la verdad, se vuelven hipócritas cobardes, y pronto alcanzan el fin que han buscado, la aniquilación en sí de todas las cualidades humanas nobles. Esa es la verdadera muerte; deje que la cesación de la respiración sea rápida o lenta, solo hace que se coloque en un ataúd un objeto que hace mucho tiempo era un cadáver. Pero como decidieron no ver, no escuchar, como pueden ser pesimistas y hombres de placer, los peores, los pesimistas, ven que un cambio se cierne sobre el futuro cercano: como pasajeros en un barco cruzando un mar tormentoso sienten el temblor de las maderas, la vibración de la embarcación sobre la que viajan, y, a pesar de sí mismos, están asombrados por la posibilidad de un desastre inminente. La mañana lanza su molesta sombra al día: la “cuestión social”, o para usar su propio lenguaje, “las cuestiones sociales” se destacan en el primer plano de su punto de vista, y saben que los obstáculos y retrasos, como quiera que sean causados, son todo en vano para evitar una solución rápida. La nueva era está a la vuelta de la esquina, y el gran problema exige que se resuelva y todas las demás preguntas quedan relegadas. Entre los dichos, atribuidos al Cristo tradicional, hay uno que fanáticos piadosos y cómodos ruedan bajo su lengua con santo placer, y es este: “Tenéis al pobre siempre contigo”. Pero fuera de las profundidades ahora se escucha una voz que grita: “¿Por qué siempre?” Incluso últimamente algunos creían que la tierra no podía producir suficientes medios de existencia para aquellos que se aferraban a ella, y que para obtener una participación era necesario luchar con otros hombres en la necesidad similar, peleando como cerdos por la basura arrojada a sus abrevaderos Esa sigue siendo la doctrina de algunos economistas políticos, y aquellos que la enseñan la exponen con la mayor unción después de una buena cena. Pero ahora incluso los pobres se han cerciorado de que el mundo produce lo suficiente y de sobra para el pan, y que si los hombres fueran libres e iguales, las necesidades de todos podrían ser satisfechas. ¿Crees que después de que esta simple verdad haya sido dominada por la mente humana, la contienda continuará? No, en verdad, la sociedad se reorganizará: de acuerdo con los hechos. Ya no escucharemos esa voz incesante, triste y lastimosa que llama desde las profundidades: “¡Pan! ¡Pan!” haciendo que todo el trabajo sea un dolor, y robando la vida de cada gozo. Entonces llegamos al punto de inflexión de la historia. Todos los problemas sociales y revueltas de épocas pasadas han tenido, en mil fases diferentes, una causa fundamental: la falta de pan, y esa fuente continua de enemistad y odio está a punto de ser abolida. Ahora, por fin, el mundo girará en su propio eje, y los trabajadores del mundo tomarán sus asuntos en sus propias manos. Corto como puede ser el lapso de la vida humana en comparación con la evolución gradual de la humanidad, hay algunos de nosotros que pueden estar presentes cuando llega el gran cambio, y todos nosotros podemos abrir nuestros ojos para saludar el amanecer de la humanidad. Y en esta crisis, de verdad, leemos acerca de los jóvenes, descuidados de lo que depare el futuro, que están cansados de aburrimiento y que pretenden dar la bienvenida a la muerte con el dicho de que “la vida no vale la pena vivirla”. Sin embargo, parecería natural que los jóvenes de todo el mundo, con su impetuosidad característica, se apresuren a abrir las puertas a la nueva era, se pongan de puntillas para ver la llegada del futuro. Recordamos con qué entusiasmo los estudiantes alemanes se prepararon para la refriega cuando fue necesario derrocar la tiranía napoleónica, cuán espléndidamente los jóvenes de las universidades francesas tomaron parte del derecho contra el poder al final de la Restauración, y en los años inmediatamente precediendo a la Revolución de 1848. Los estudiantes de esa época eran mucho menos numerosos de lo que son hoy, pero desempeñaron un papel más destacado en la historia de su país. Se lanzaron a todas las luchas, románticas, republicanas y socialistas, de ese período fatídico, y negaron que ninguna clase en la nación fuera tan receptiva como ellos mismos a la nueva idea. Tampoco fue simplemente la licencia de los soñadores poéticos, la exuberancia de los espíritus animales o una exhibición teatral de desprecio por la burguesía. ¡Cuántos de ellos desafiaron el encarcelamiento e incluso la muerte por sus opiniones! ¡Cuántos de ellos, inspirados por el celo misionero, se convirtieron en los apóstoles de un altruismo revolucionario, arrojando fortuna, posición y ventaja monetaria! Cuando el santo simonismo y el fourierismo llevaron el pensamiento humano al punto de ebullición, fueron los estudiantes los que se alistaron valientemente en las filas de los rebeldes intelectuales, sin importar la calumnia, la persecución y el exilio. Aunque los estudiantes de la Europa moderna suman más de cien mil hombres, su influencia en el mundo de las ideas es mucho menor que la de sus predecesores. Hoy en día es por cientos y no por miles que contamos a los jóvenes de las universidades que han puesto sus intereses personales en el altar del progreso social y que, bajo diversos estandartes, están liderando la entrada a la tierra prometida. Incluso se dice, y no podría aventurarme llamarlo injuria, que la mayoría de nuestros jóvenes académicos están contentos con las cosas tal como son, y que su gran ambición es adoctrinar a la sociedad con conservadurismo, y sorprender a sus amigos con lo que llamar a la “moderación” de sus puntos de vista; a este respecto, afirman modestamente ser más sabios que sus padres, quienes no pueden negar haber compartido en sus días jóvenes el entusiasmo prevaleciente. Un fenómeno extraño es ver a hombres jóvenes que se jactan de sentirse cansados de la vida, como si la incapacidad de admirar, disfrutar y ser feliz fuera más un mérito que una desgracia. Pero es bastante cierto que de esta manera mueren los ociosos ricos. Sin lugar a dudas, nuestra juventud universitaria moderna, aunque naturalmente orgullosa de haber pasado por el molino de muchos exámenes, no podría resistir sus extravagantes pretensiones de enseñar a los obreros mucho en la esfera del estudio y el pensamiento. No, su tarea es ser alumnos, no dar instrucciones. En los grandes movimientos populares, como el de la Comuna, los estudiantes estuvieron muy poco representados, mientras que los obreros suministraron abundantes tendones y cerebros. No era la pregunta meramente de trabajo y salarios; los intereses en juego eran los de toda la nación, de hecho, de toda la humanidad. En la hora actual, cuando una nueva dispensación está a punto de ser introducida, cuando los jóvenes caballeros de la reforma se preparan para su tarea, no es en las avenidas de las escuelas que las cuestiones más importantes en las mentes de los hombres se discuten más inteligentemente y con la más aguda visión. El graduado no es necesariamente el filósofo, ni una memoria bien almacenada invariablemente acompaña una comprensión iluminada. A menudo, el escudriñador seco como el polvo es pobre en sabiduría junto al hombre astuto del mundo que ha reunido aquí y allá los innumerables hechos a partir de los cuales desarrolla una gran cantidad de ideas generales. Su hombre científico puede encerrarse en su laboratorio como en una prisión, y malinterpretar el gran mundo; pero las personas siempre forman una teoría consistente del universo, ya sea verdadera o falsa. Pero hace poco tiempo, los profesores de la universidad despreciaron la evolución, pero en las calles y detrás del arado, entre obreros y campesinos, la nueva verdad encontró un hogar tranquilo y una bienvenida entusiasta. Sería tonto hablar despectivamente de la ciencia. El descubrimiento de un ladrillo babilónico, o la observación de un estambre de flores rudimentario, bien puede alegrar nuestros corazones, cuando el científico relaciona el hecho aparentemente aislado con muchos otros y muestra el valor del descubrimiento. Todavía más en el ámbito de las ideas deberíamos valorar la enunciación de un pensamiento nuevo o la disposición de los datos mentales en su debida importancia y relativa orientación. A este respecto, el estudiante, a menudo ha sido observado, cegado por el polvo de la biblioteca, apenas percibe que hay una “pregunta social” al aire libre, mientras que el trabajador, por otro lado, lo considera el objeto más importante de estudio, y se encuentra, por lo tanto, muy por delante de su estudioso hermano. Esta observación es válida en otras tierras además de las lenguas latinas, aunque en estas la evolución intelectual o revolución, si prefiere la palabra, pueden haber progresado más, mucho más que en las escuelas alemanas de Alemania o entre los jóvenes alumnos de las universidades americanas. Los socialistas están contados por millones al este de la cordillera de los Vosgos [en Francia], pero en la Patria, dos o tres miserables pueden agruparse lejos de los bebedores de cerveza, unos pocos entre miles. En Harvard, la famosa universidad estadounidense, que cuenta con 3200 estudiantes, los reformadores son más numerosos, pero pocos se han atrevido a emanciparse de la superstición cristiana; en un censo reciente, solo dos de ellos declararon que no pertenecían a ninguna de las muchas sectas cuyo nombre figuraba en el cronograma. Es en la Inglaterra aristocrática, tal vez, que la mente humana disfruta de la mayor libertad. Bien, ¿cuáles son las causas de esta moderación conservadora entre los jóvenes, completamente fuera de contacto con el espíritu de la época? Incluso los profesores observan el fenómeno, pero tal es la esclavitud social de la vida universitaria moderna que el mal persiste con todas sus nefastas consecuencias. En general, se acepta que, desde su primer día en la escuela, la vida normal del niño es contraria a la naturaleza. ¿Qué se puede decir de una educación que organiza condiciones favorables para el desarrollo de la enfermedad de la columna vertebral, que a menudo daña permanentemente la visión, que controla los deseos naturales, que debilita o pervierte los instintos humanos? ¿No se opone a los grandes objetos de la educación tal como los entiende el sabio en todas las épocas: fuerza, gracia, belleza? Los indios americanos y los nativos de Australia, así como los griegos de la antigüedad, son unánimes en prescribir una vida fuera de la puerta como la mejor para los niños; mucho atletismo y ejercicio, calculado para desarrollar hombres fuertes, ágiles y sanos, elásticos con la vida y radiantes de energía. Entre nosotros, por desgracia, a menudo vemos que el joven que es nutrido de manera más cuidadosa y costosa resulta ser uno de los especímenes más deplorables de la humanidad muscular. Las estadísticas médicas nos permiten comprender que más de la mitad de los jóvenes académicos de las academias superiores de Europa continental han arruinado sus constituciones por autoindulgencia, por una vida de cansancio y monotonía; dos de cada tres son jóvenes débiles; y entre aquellos que han perdido su salud, hay muchos que han lesionado gravemente sus facultades mentales y que, al azotarlos y estimularlos en sus primeros años de vida, se ven obligados a utilizarlos con moderación en la edad adulta. Es cierto que podemos citar numerosos ejemplos de hombres que han mantenido su constitución robusta, sus extremidades ágiles y fuertes, su razón brillante y útil; pero estos casos son la excepción, no la regla, deben considerarse como causa no del currículum ordinario de la educación, sino casi siempre a los privilegios de la adolescencia adinerada y bien condicionada. Los jóvenes favoritos de la fortuna se agrupan naturalmente en dos clases: voluptuosos que agotan y no se capacitan por el libertinaje y el pesimismo, y unas pocas almas hermosas que aprecian un gran ideal, y se esfuerzan por estar a la altura. Si el entrenamiento de la familia y de la universidad educa al niño y al joven en detrimento de su naturaleza multifacética, al apartar de su visión los aspectos urbanos y rurales de la vida, excepto como se ve a través de agujeros, si se muere de hambre y lo empobrece físicamente, ¿qué significa eso para su persona? Por desgracia, hasta ahora, nuestras costumbres no nos han permitido respetar la individualidad del niño como la de un futuro igual, tal vez el de un superior en logros intelectuales y morales. Rara vez son los padres que ven en su hijo a un ser cuyas ideas y disposición tienen una inclinación propia, y rara vez se encuentran con el maestro que no trata de imbuir las mentes de sus alumnos con sus opiniones, su moralidad aceptada y quien no se esfuerza por facilitar su tarea al insistir en la obediencia estricta. Luego siga los exámenes de los cuales depende la carrera futura, y cada alumno, recibe su libro de texto como convicto con su cadena. El libro es el mismo para todos, y para todos el programa de estudio es el mismo. De ahora en adelante, toda originalidad en la investigación mental está prohibida, y la carga del compromiso diario con la memoria ocupa el lugar del pensamiento libre y la investigación espontánea; del mismo modo que el sacerdote debe saber de memoria su breviario, y el molino del budista tibetano gira incesantemente, mezclando su shibboleth perpetuo \emph{Oum mane padmi houm}. Al menos algunos de estos manuales están maravillosamente condensados y contienen un resumen extraordinario del conocimiento humano. Una emoción de reverencia y asombro nos alcanza frente a estas estupendas obras, de las cuales cada línea es volumen, embalsamando el trabajo de una larga sucesión de sabios. ¡Qué riqueza no contada, qué alegría indescriptible realmente haber dominado el contenido de estas revistas preñadas! Bien podríamos considerar con envidia al bendito examinado que responde con confianza todas las preguntas basadas en el libro de texto. ¿Pero él realmente sabe todas estas cosas? ¿Ha aprendido las razones por qué de todos los hechos? Si eso fuera así, podríamos orar con benevolencia que él pudiera devolver, como lo hicieron los invitados de Vitellias, toda la comida que le resultaba superflua de esa comida indigerible. Permita que olvide lo antes posible su examen para conocerse a sí mismo y para encontrarse en el dominio del estudio libre, en la perspectiva de descubrimientos inesperados como resultado de una investigación independiente. Pero si él ha incursionado en todas las ciencias sin gustarle, es probable que produzca un inventario ambulante, sin entusiasmo, sin ambición, profesantemente capaz sin preparación para la tarea más difícil. Suponiendo nuevamente que sea cierto que los testimonios y certificados de los profesores no son implícitamente confiables, que el favor especial de los maestros se otorga a menudo a los alumnos a quienes un amigo común les ha dicho una buena palabra. “Acostúmbrense como hombres”, dicen los maestros, ¡en vista de la distribución de premios! Pero no tomes esa llamada a la energía demasiado en serio. Con qué frecuencia, por el contrario, se debe interpretar como, “Sé complaciente, aprende a arrastrarte”. Además, a menudo se ha encontrado que los hombres que son geniales por genio pueden caer muy bajo a través de la flexibilidad del carácter. ¿No es bien sabido que los científicos a veces son lentos para respaldar una nueva opinión porque es inaceptable en lugares altos: “Tienes razón”, dicen ellos, “y nos complacería hablar bien de ti en público, pero el Emperador no está dispuesto ”. Ciertamente, la forma de educación es espantosa para los jóvenes, con sus competencias, sus exámenes, sus libros de texto y todo el atiborramiento científico sustituido por la ciencia: pero eso es solo una pequeña parte del mal. Con mucho, la fase más alarmante debe buscarse en la organización económica de la sociedad. ¿Cuál es el propósito final hacia el cual todos, jóvenes y viejos, son arrastrados por la corriente de las circunstancias? ¿Cuál es el ideal vulgar y común de los que nacen en la cima de la inundación? El viejo Guizot lo dio a conocer hace mucho tiempo, con su cinismo habitual: ¡hazte rico! ¡Hazte rico! “Ahora, desde la propia constitución de la sociedad, los estudiantes toman conciencia como un hecho preliminar de que acumularán dinero por medio de sus diplomas”. La ciencia significa dinero "bien pueden decir confidencialmente entre ellos, o incluso en voz alta cuando desafían la política de moderación. De sus filas se reclutan las clases dominantes, que son también las clases ricas. En la conversación de la familia se discuten sus perspectivas como hombres profesionales, pero sin eso están demasiado bien informados, con una matrícula inconfundible de juventud, en cuanto a la posición social y la fortuna que su trabajo les traerá. Más sabios que sus padres, que fueron neciamente contaminados por el republicanismo y el romance, pisan con los ojos abiertos y la mente autoconsciente los caminos tortuosos que conducen a una carrera brillante, a la fama y a la fortuna. Recientemente, el gran profesor Dubois-Reymond, en la recepción del emperador alemán a su regreso de la coronación en Versalles, ¡se esforzó por glorificar las universidades como el guardaespaldas de los Hohenzollerns! ¡Con el mismo espíritu, el ejército de estudiantes, sacerdotes y funcionarios podría presumir más sinceramente de que son el guardaespaldas de El Capital! Incluso en el santuario interior de la ciencia podemos leer estas palabras que Lamartine – pronunció innoble, “Comprado y Vendido”. Sin duda, la formación de la sociedad, construida sobre la propiedad privada como sobre una piedra angular, nos obliga a hacer lo que hacen los demás, las condiciones inevitables de éxito en la vida, pero debemos comprender a fondo la vergüenza de nuestros procedimientos forzados, y determinar poner fin a la desgracia, cada uno de acuerdo con su capacidad, trabajando para la realización de un mundo nuevo donde los resultados del trabajo común pertenecerán a todos sin una negociación preliminar. Cuanto más alto es un acto en la esfera intelectual y moral, más difícil y molesto es pedirle un salario: una vez más es la desmoralización de lo excelente lo que se convierte en lo horrible. ¿Qué se debe pensar, del cirujano que posee la vida de un hombre al final de su bisturí y quién comienza la operación estirando su mano por un poco de oro? ¿El poeta que se deleita en una nueva imagen, o el sabio que un nuevo descubrimiento transporta con alegría, espera una lista de precios o estudia la tasa de salarios de la unión comercial antes de publicar sus versos o proclamar la nueva verdad? Ante semejante cálculo, muchos miles de millones estaríamos en deuda con Bacon y Descartes por la ayuda que han dado al mundo científico. La antigüedad nos ha otorgado una historia significativa, la de Arquímedes, quien mientras tomaba un baño y notando el grado de inmersión de un flotador en madera y un corcho de aceite, de repente fue golpeado por un rayo por la idea de su ley el peso específico de los cuerpos. El descubrimiento fue hecho. ¿Pensó Arquímedes en el dinero que podría pedirle al tirano Hiero como recompensa de su genio? Saltó de la bañera, corrió por las calles de Siracusa y lloró a todos y cada uno, acuáticos, carreteros y peones: “Lo he encontrado, lo he encontrado”. El eco de ese grito de alegría se reduce a nuestros días. Los descubrimientos de la ciencia traen consigo felicidad tan exaltada que signfca que toda consideración debe degradarlos. Saber nos impone la obligación de enseñar. El hombre profesional de hoy en día se da cuenta de que puede vender al menor postor su conocimiento de segunda mano: el verdadero estudiante, digno de su nombre, investiga que se pueda difundir ampliamente la verdad. Además, ¿cómo podría un hombre semejante vivir a la altura de un ideal elevado si se le permite que su mente se vuelva insensible por la contemplación de intereses sobornables? La vieja fe religiosa que los supersticiosos aún nos predican está desapareciendo detrás de nosotros como una niebla. Hace lo mejor que puede para reconciliarse con el espíritu de la época en la beatificación de los que antes ardía, llamándose amigo de la evolución, del republicanismo, incluso del socialismo. No responde más a los requisitos de la humanidad; la cadena de milagros y de dogmas que arrastra retrasan su avance, y su moralidad, que es sustancialmente la de la resignación, del pesimismo atemperado por esperanzas lejanas, no puede entrar en rivalidad con éticas puramente humanas, lo que inculca el uso y desarrollo de nuestras energías en toda su plenitud. Así que la religión —y uso esa palabra en su más noble sentido, es decir, el amor y el éxtasis por un ideal sublime— se aleja cada vez más de la región del misterio y de lo desconocido, para dedicarse a los seres del mundo conocido, es decir, sobre la humanidad. ¿Crees que podría agotarse allí en profundidad, en intensidad, en poder de devoción? El que se sacrifica a sí mismo, sin esperanza de recompensa, ¿es inferior a aquel que macera su cuerpo o se dedica a la caridad para ganar la salvación? Los escritores antiguos nos han legado admirables tratados de ética y filosofía sobre la educación del ser humano, que puede encontrar sabiduría y, al mismo tiempo, felicidad al controlar sus pasiones, modelar su carácter, purificar sus pensamientos, reducir al mínimo sus necesidades. Tales palabras sobre este tema las de Lucrecio, Zenón, Epicteto, Séneca, incluso, Horacio, son palabras inmortales, que reverberarán de edad en edad, y que ayudarán constantemente a elevar el ideal humano y a elevar el valor del individuo. Pero ya no es en estos tiempos una mejora puramente personal, como en los días del heroísmo estoico, es una empresa hoy en día de ganar, por educación y unión, para toda la sociedad lo que nuestros antepasados reclamaban anteriormente para el individuo solitario. Debemos estudiar a la humanidad en la constitución de su conciencia moral y ver que encuentra su camino hacia la felicidad ante ella metódica y con energía, es decir, que alcanza la plena realización de su libertad. ¿No es esta estupenda tarea lo suficientemente grande como para emplear toda nuestra actividad, todos nuestros afectos, todo el poder intelectual y moral de cada uno de nosotros? Pero esta felicidad, ¿alguna vez podremos alcanzarla? Aquí es que el problema social nos confronta en toda su complejidad, porque para una mera comida feliz no es suficiente, también necesitan el libre desarrollo de su individualidad en condiciones de igualdad con otros hombres, sin restricciones y sin servidumbre. Tal es nuestro ideal anarquista, tal es también el ideal (estoy seguro de ello) que es apreciado de una manera más o menos consciente, por todas las personas benevolentes. Sin embargo, estamos sorprendidos de escuchar en ciertos círculos una opinión contraria. Algunos escritores incluso han sido conocidos por declarar que tal dicha no es algo que se desee. Para estos extraños idealistas, la guerra parece una bendición; se trata de despertar nuestra energía, nuestro coraje, restablecer el carácter que se ha avergonzado en los suaves abrazos de la paz. Odio mutuo entre las naciones, tal vez entre clases: tal es, si no su ética, al menos su esperanza. Para aquellos de nosotros que hemos experimentado las abominaciones de la guerra, tal idea parece monstruoso; sin embargo, mediante un ingenioso ejercicio de la inteligencia podemos comprender el residuo del sentimiento moral que se encuentra en el fondo de esta paradoja. La guerra es una condición de la actividad, y como tal es mejor, o al menos es menos una calamidad, que un estado de inercia flácida; podemos recuperarnos de ella, mientras que la inacción absoluta conduce inevitablemente a la muerte. Sí, la actividad es indispensable; cada fuerza debe ser probada antes de ser aplicada a un trabajo definido, pero, ¿deberían estos ensayos entrar en peligro, o no deberían emprenderse a la luz de la ciencia y con los métodos más aprobados? En este sentido, las personas a las que llamamos salvajes, y aún más notoriamente, los griegos, las civilizaciones más altamente civilizadas, nos dan dirección. Los hombres jóvenes no fueron admitidos a la ciudadanía y no se consideraron aptos para tomar su lugar al frente de una familia, o para realizar las tareas prescritas por el estado, antes de haber dado pruebas indudables de su destreza, su fuerza, su coraje y sus poderes de resistencia. No estaban sujetos a la complicidad, eran perfectamente libres de evitar la prueba, sin embargo, ninguno tomó ese curso, lo que habría implicado su deshonor. El respeto por la opinión pública era demasiado intenso como para que alguien quisiera retirarse de los juicios que lo pondrían en la categoría de los hombres. Entre las tribus más primitivas, una vez más, los héroes voluntarios, tanto niños como niñas, se sometieron alegremente a los sufrimientos más terribles, a auténticos dolores de tortura; soportaron el hambre y la sed durante varios días, se entregaron a las abrasadoras picaduras de las hormigas, se azotaron sin piedad entre sí, sufrieron mutilaciones temerosas, sin un grito, sin un murmullo. Con características sin problemas, sí, con una cara sonriente, se presentaron ante sus jueces: habían dado el precio de su futuro. No es de esta manera incivilizada en la que imaginamos que se aplicarán pruebas de valor, el futuro de los jóvenes en su admisión a la vida de hombres maduros, pero nos parece en armonía con la naturaleza humana que en el período de florecimiento de la adolescencia, fortaleza bien desarrollada y amor incalculable, los jóvenes pueden mostrar de manera brillante de qué material están hechos mediante actos de coraje, sacrificio y devoción. Si la opinión pública solo los alienta, ninguna acción parecerá demasiado difícil para su osadía. Apelemos solo a su naturaleza superior y todos responderán. Durante la guerra de los Estados Unidos, las jóvenes del Oberlin College dijeron a los jóvenes: “Ir, únanse al ejército”, y los cien mil estudiantes fueron a la guerra, no quedó nadie. ¿Qué no podríamos lograr con estas fuentes prodigiosas de fuerza, sustentadas por el entusiasmo? Cuando los jóvenes ya no tendrán el sucio lucro para corromper en su propia fuente su ambición de moverse libremente hacia su ideal, sin el disgusto de tener que despreciarse a sí mismos y despreciar su trabajo, cuando el aplauso general los alentará a la devoción, ¿Cuál será la empresa audaz de la cual se reducirán? ¿Les pedimos que vayan al polo antártico? Ellos irán. ¿Explorar el mar en buques submarinos y trazar un mapa de las profundidades? Lo harán. ¿Para transformar el Sahara en un jardín? Eso será para ellos un trabajo de amor. ¿Para servir a su aprendizaje de viajes, exploración, encontrar estudio? El trabajo será absorbido por el placer. ¿Pasar los años entre la juventud y el matrimonio en la educación de los niños, en la cura de los enfermos? Tendremos millones de maestros y enfermeras que ocuparán noblemente el lugar de los miles de soldados que ahora trabajan diligentemente para abrir sus brazos con el propósito de matarse unos a otros. Tal es el ideal que proponemos a la juventud. Al señalarle un futuro de solidaridad y altruismo, les prometemos nuestra palabra de que en ese futuro todo rastro de pesimismo habrá desaparecido de sus mentes. “Dense a ustedes mismos”. Pero “para darse a sí mismos, deben pertenecer a ustedes mismos”. % begin final page \clearpage % if we are on an odd page, add another one, otherwise when imposing % the page would be odd on an even one. \ifthispageodd{\strut\thispagestyle{empty}\clearpage}{} % new page for the colophon \thispagestyle{empty} \begin{center} Biblioteca anarquista \smallskip Anti-Copyright \bigskip \includegraphics[width=0.25\textwidth]{logo-en} \bigskip \end{center} \strut \vfill \begin{center} Élisée Reclus El ideal y la juventud 1895 \bigskip Recuperado el 13 de agosto de 2018 desde \href{https://pirateaydifunde.wordpress.com/2018/08/14/elisee-reclus-el-ideal-y-la-juventud-1895/}{https:\Slash{}\Slash{}pirateaydifunde.wordpress.com} Título Original: \emph{The Ideal and Youth} Publicado en \emph{Liberty Press}, London, 1895. Traducido por Piratea y Difunde. Texto en inglés recuperado de \href{http://dwardmac.pitzer.edu/anarchist\_archives/bright/reclus/idealandyouth.html}{http:\Slash{}\Slash{}dwardmac.pitzer.edu\Slash{}anarchist\_archives} \bigskip \textbf{es.theanarchistlibrary.org} \end{center} % end final page with colophon \end{document} % No format ID passed.
http://kleine.mat.uniroma3.it/e/94-103.latex	uniroma3.it	CC-MAIN-2018-05	application/x-latex	application/x-latex	crawl-data/CC-MAIN-2018-05/segments/1516084887065.16/warc/CC-MAIN-20180118032119-20180118052119-00327.warc.gz	193,891,077	5,794	\documentstyle[defns,amssymbols,12pt]{article} \setlength{\textheight}{9.0truein} \setlength{\textwidth}{7truein} \setlength{\evensidemargin}{-0.10in} \setlength{\oddsidemargin}{-0.15in} \headheight 0truein \headsep .25in \topmargin -.50in \begin{document} \title{\bf Temperature Correlations of Quantum Spins} \author{\bf A.R. Its$^{1}$, A.G. Izergin$^{2,}$, V.E. Korepin$^3$, N.A. Slavnov$^{4}$} \date{ \ \ } \maketitle \vfill \begin{abstract} We consider isotropic XY model in the transverse magnetic field in one dimension. One can alternatively call this model Heisenberg XXO antiferromagnet. We solve the problem of evaluation of asymptotics of temperature correlations and explain the physical meaning of our result. To do this we represent quantum correlation function as a tau function of a completely integrable differential equation. This is the well-known Ablowitz-Ladik lattice nonlinear \s differential equation. \end{abstract} \vfill \noindent $^1$Department of Mathematics and Computer Science and the Institute for Nonlinear Studies Clarkson University Potsdam, New York 13699-5815, U.S.A. \noindent $^2$Laboratorie de Physique Th\'eorique ENSLAPP Ecole Normale, Superieure de Lyon, France \noindent $^3$Institute for Theoretical Physics State University of New York Stony Brook, NY 11794-3840, U.S.A. e-mail [email protected] \noindent $^{}$On leave of absence from St. Petersburg Branch (POMI) of Steklov Mathematical Institute of Russian Academy of Science Fontanka 27, 1191011 St. Petersburg, Russia \noindent $^{4}$V.A. Steklov Mathematical Institute of Russian Academy of Science Moscow, Russia \vfill \noindent {\bf PACS numbers: 75.10.Jm, 75.50Ee} \vfill \pagebreak \baselineskip 20pt XY model was introduced and studied by E. Lieb, T. Schultz and D. Mattis [1]. It describes interaction of spins 1/2 situated on 1-dimensional periodic lattice. The Hamiltonian of the model is $$ H =- \sum_n\left[\sigma^x_n \sigma^x_{n+1} + \sigma^y_n\sigma^y_{n+1} + h\sigma^z_n\right]. \eqno (1)$$ Here $\sigma$ are Pauli matrices, $h$ is transverse magnetic field, $n$ enumerate the cites of the lattice. At zero temperature the problem of evaluation of asymptotics of correlation functions was solved in [2,3]. Here we consider temperature correlation function $$ g(n,t) = \frac{Tr \{e^{-\frac{H}{T}}\sigma^+_{n_2}(t_2)\sigma^-_{n_1}(t_1)\}}{Tr e^{-\frac{H}{T}}}, \ \ \ \ n = n_2-n_1, \ \ \ \ t=t_2-t_1 \eqno (2) $$ for the infinite lattice. We consider finite temperature $0 < T < \infty$ and moderate magnetic field $0 \leq h < 2$. We evaluated asymptotics in cases where both space and time separation go to infinity $n \rightarrow \infty$, $t\rightarrow \infty$, in some direction $\varphi$ $$ \frac{n}{4t} = \cot \varphi, \ \ \ \ 0 \leq \varphi \leq \frac{\pi}{2}. \eqno (3)$$ In accordance with our calculations, correlation function $g(n,t)$ decays exponentially in any direction, but the rate of decay depends on the direction. In the space like direction $0 \leq \varphi < \frac{\pi}{4}$ asymptotics is $$ g(n,t) \rightarrow C \exp \left\{ \frac{n}{2\pi}\int^\pi_{-\pi}dp\ln \left\|\tanh (\frac{h-2\cos p}{T})\right\|\right\}. \eqno (4)$$ In the time like direction $\frac{\pi}{4} < \varphi \leq \frac{\pi}{2}$ asymptotics is different. $$ g(n,t) \rightarrow C t^{(2\nu^2_++2\nu^2_-)}\exp \left\{ \frac{1}{2\pi} \int^\pi_{-\pi}dp \left\|n-4t\sin p\right\|\ln\left\|\tanh(\frac{h-2\cos p}{T})\right\|\right\}. \eqno (5)$$ The values $\nu_\pm$, which define pre-exponent, are $$ \nu_+ = \frac{1}{2\pi}\ln\left\|\tanh \left( \frac{h-2\cos p_0}{T}\right)\right\|$$ $$ \nu_- = \frac{1}{2\pi}\ln\left\|\tanh \left( \frac{h+2\cos\rho_0}{T}\right)\right\|\eqno (6)$$ where $\frac{n}{4t} = \sin p_0$. Formula (5) is valid in the whole time like cone, with exception of one direction $h=2\cos p_0$. Higher asymptotic corrections will modify formulae by factor $(1+c(t,x))$, ($c$ decays exponentially in the space-like region and as $t^{-1/2}$ in the time-like region). Also, it should be mentioned that the constant factor $C$ in (4) does not depend on the direction $\varphi$, but it does depend on $\varphi$ in (5). We want to emphasize that for pure time direction $\varphi = \pi/2$ leading factor in asymptotics (exponent in (5)) was first obtained in [10]. To derive these formulae we went through few steps. The first step: The explicit expression for eigenfunctions of the Hamiltonian (1) (see [1]) was used to represent the correlation function as a determinant of an integral operator (of Fredholm type) [8]. In order to explain we need to introduce notations. Let us consider integral operator $\hat V$. Its kernel is equal to $$ V(\lambda\mu) = \frac{e_+(\lambda)e_-(\mu) - e_-(\lambda)e_+(\mu)}{\pi(\lambda - \mu)}. \eqno (8)$$ Here $\lambda$ and $\mu$ are complex variables, which go along the circle $\left\|\lambda\right\| = \left\|\mu\right\| = 1$ in a positive direction. Functions $e_\pm$ are $$ e_-(\lambda) = \lambda^{-n/2} \cdot e^{-it(\lambda+1/\lambda)} \sqrt{v(\lambda)} \eqno (9)$$ where $$ v(\lambda) = \left\{ 1 + \exp \left[ \frac{2h-2(\lambda + \frac{1}{\lambda})}{T}\right]\right\}^{-1} \eqno (10)$$ and $$ e_+(\lambda) = e_-(\lambda)E(x,t,\lambda). \eqno (11)$$ Here $E$ is defined as an integral $$ E(n,t,\lambda) = \frac{1}{\pi}v.p.\int\exp\{ 2it(\mu + \frac{1}{\mu})\} \cdot \frac{\mu^nd\mu}{\mu-\lambda}. \eqno (12)$$ It is convenient to define functions $f_\pm(\lambda)$ as solutions of the following integral equations: $$ (I + \hat V)f_k = e_k. \eqno (13)$$ Here $I$ is an identical operator and $k =\pm$. Next we define potentials $B_{kj} (k,j = \pm)$: $$ B_{kj}(n,t) = \frac{1}{2\pi i} \int f_k(\lambda) e_j(\lambda)\frac{d\lambda}{\lambda}. \eqno (14)$$ They depend on space and time variables $n,t$. These we shall use to define new potentials $b_{kj}$: $$ \begin{array}{ll} b_{--}(n,t) = B_{--}(n,t) \\ \\ b_{++}(n,t) = B_{++}(n,t) - 2iG(n,t)B_{+-}(n,t) - G(n,t). \end{array} \eqno (15)$$ \noindent Here we used function $$ G(n,t) = \frac{1}{2\pi i}\int \lambda^{n-1}\exp \{ 2it(\lambda + \frac{1}{\lambda})\} d\lambda. \eqno (16)$$ Now all the notation are ready to write determinant formula for the correlation function $g(n,t)$ (see (4)): $$ g(n,t) = e^{-2iht}b_{++}(n,t)\exp \{ \sigma(n,t)\}. \eqno (17)$$ Here $e^\sigma$ is a determinant of integral operator $$ \exp\{ \sigma(n,t)\} = \det(1+\hat V). \eqno (18)$$ Second step: Formulae (8)-(15) can be used to show that potentials $b_{++}$ and $b_{--}$ satisfy the system of nonlinear differential equations. $$ \frac{i}{2} \frac{\partial}{\partial t} b_{--}(n,t) = (1 + 4b_{--}(n,t)b_{++}(n,t))(b_{--}(n+1,t) + b_{--}(n-1,t)) $$ $$ -\frac{i}{2} \frac{\partial}{\partial t} b_{++}(n,t) = (1+4b_{--}(n,t)b_{++}(n,t))(b_{++}(n+1,t) + b_{++}(n-1,t)). \eqno (19)$$ Derivation of these equations is similar to [4,5,7]. Equations (19) are completely integrable differential equations. They were first discovered by Ablowitz and Ladik [9] as an integrable discretization of the Nonlinear \s equation. Logarithmic derivatives of $\sigma(x,t)$ (see (18)) can be expressed in terms of solutions of the system (19). $$ \begin{array}{ll} \frac{\partial^2\sigma(n,t)}{16\partial t^2} & = 2b_{--}(n,t)b_{++}(n,t) - b_{++}(n-1,t)b_{--}(n+1,t) - \\ \\ & -b_{--}(n-1,t)b_{++}(n+1,t) - 4b_{++}(n,t)b_{--}(n,t)[b_{++}(n-1,t)b_{--}(n+1,t) +\\ \\ & b_{--}(n-1,t)b_{++}(n+1,t)] \end{array} \eqno (20)$$ $$ \sigma(n+1,t) + \sigma(n-1,t) -2\sigma(n,t) = \ln[1+4b_{--}(n,t)b_{++}(n,t)] \eqno (21)$$ $$ \frac{\partial}{\partial t}[\sigma(n+1,t) - \sigma(n,t)] = 8i[b_{++}(n+1,t)b_{--}(n,t) - b_{++}(n,t)b_{--}(n+1,t)]. \eqno (22)$$ This shows that quantum correlation function $g$ (2) can be expressed in terms of solution of the system (19). The meaning of all these formulae is that correlation function of $XY$ model is the $\tau$ function of Ablowitz-Ladik's differential-difference equation. This is similar to quantum Nonlinear Shrodinger equation. In the papers [5,6,7] relation of $\tau$ function and quantum correlation functions is explained in more detail. Third step: In order to evaluate asymptotics one should solve Ablowitz-Ladik's differential equation. Initial data can be extracted from integral representations (8)-(18). We use Riemann-Hilbert problem in order to evaluate asymptotics of solution of equation (19). It is quite similar to the Nonlinear Shrodinger case [6,7]. Let us emphasize that it is quite remarkable that for the $XY$ model (like for Bose gas, [4-7] which is defined by quantum Nonlinear Shrodinger equation) quantum correlation function is the $\tau$ function of classical completely integrable differential equation. In the end let us explain the physical meaning of our asymptotic formula (4). We start from the expression for free energy [1]: $$ f(h)=-h-\frac{T}{2\pi}\int^\pi_{-\pi}dp \ln\left(1 + \exp[ \frac{4\cos p-2h}{T}]\right). \eqno (23)$$ We emphasize the dependence on the magnetic field $h$. The definition of $f(h)$ is standard: $$ Tre^{-\frac{H}{T}} = \exp\{ -\frac{L}{T}f(h)\}. \eqno (24)$$ Here $L$ is the length of the box. Let us use Jordan-Wigner transformation to transform correlator (2) (in the equal time case): $$ \sigma^+_{n_1}(0)\sigma^-_{n_1}(0) = \psi_{n_2}\exp \left\{ i\pi \sum^{n_2-1}_{k=n_1+1}\psi^+_k\psi_k\right\}\psi^+_{n_1}, \ \ \ \ \psi^+_k\psi_k=\frac{1}{2}(1- \sigma^z_k). \eqno (25)$$ Here $\psi_k$ is canonical Fermi field. We can say now that numerator in (2) differs from denominator by replacement of magnetic field $h\rightarrow h-i\pi T/2$ on the space interval $[n_1+1,n_2-1]$. This leads us to the following asymptotical expression for correlator $g(n,0)$ $$ g(n,0) \rightarrow \exp\left\{ Re \frac{n}{T} \left[ f(h)-f(h- \frac{i\pi T}{2})\right]\right\}. \eqno (26) $$ The reason why we wrote $Re$ is that $i\pi$ in (25) can be replaced by $-i\pi$. It is remarkable that (26) coincides with the correct answer (4). It is also worth mentioning that to go to exponent in (5) one should replace differential $d(np)$ by expression $\|d(np-t\varepsilon(p)\|$ where $\varepsilon(p) =-4\cos p+2h$ is the energy of the quasiparticle of the model. \vskip .2in \noindent{\Large Acknowledgements} This work was partially supported by NSF Grant No. PHY-9107261 and by NATO S.P. CRG 901098. One of the authors (A.G.I.) is grateful to the Laboratoire de Physique Theorique in Ecole Normale Superrieure de Lyon (France) for their warm hospitality. \begin{thebibliography}{5} \bibitem{1} E. Lieb, T. Schultz and D. Mattis, Ann. Phys. (N.Y.) {\bf 16}, 406 (1961). \bibitem{2} B.M. McCoy, J.H.H. Perk, R.E. Shrock, Nucl. Phys. B {\bf 220}, 269 (1983); Nucl. Phys. B {\bf 220}, 35 (1983). \bibitem{3} H.G. Vaidya, C.A. Tracy, Phys. Lett. A {\bf 68}, 378 (1978). \bibitem{4} A.R. Its, A.G. Izergin, V.E. Korepin, N.A. Slavnov, J. Mod. Phys. B. {\bf 4}, 1003 (1990). \bibitem{5} A.R. Its, A.G. Izergin, V.E. Korepin, N.A. Slavnov, in the book ``Important Developments in Soliton Theory, 1980-1990", eds. A.S. Fokas, V.E. Zakharov, Springer-Verlag, 1992. \bibitem{6} A.R. Its, A.G. Izergin, V.E. Korepin, G.G. Varzugin, Physica D, {\bf 54}, 351 (1992). \bibitem{7} V.E. Korepin, A.G. Izergin, N.M. Bogolinbov, ``Quantum Inverse Scattering Method, Correlation Functions and Algebraic Bethe Ansatz" Cambridge University Press, (1992). \bibitem{8} F. Colomo, A.G. Izergin, V.E. Korepin, V. Tognetti, ``Determinant Representation for Correlation Functions in the XXO Heisenberg Chain" preprint ITP-SB-92-12, accepted in Phys. Lett. \bibitem{9} M.J. Ablowitz, J.F. Ladik, Stud. Appl. Math. {\bf 55}, 213 (1976). \bibitem{10} P. Deift, X. Zhou, preprint, Courant Mathematical Institute (1992). \end{thebibliography} \pagebreak \noindent{\bf Suggested Referees} \begin{enumerate} \item C. Tracy, Mathematics Department, University of California, Davis, CA 95616-8633. \item R. Shrock, ITP, SUNY Stony Brook, Stony Brook, NY 11793-3840. \item M. Ablowitz, Program in Applied Mathematics, University of Colorado, Box 526, Boulder, CO 80309. \item H. Thacker, Physics Department, University of Virginia, Charlottesville, VA 22901. \item M. Fowler, Physics Department, University of Virginia, Charlottesville, VA 22901. \item A. Newell, Mathematics Department, University of Arizona, Tucson, AZ 85721. \item H. Flashka, Mathematics Department, University of Arizona, Tucson, AZ 85721. \item J. Palmer, Mathematics Department, University of Arizona, Tucson, AZ 85721. \item P. Deift, Courant Institute, New York University, 251 Mercer Street, NY, NY 10012. \end{enumerate} \end{document}
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Ağaçların içerisinden kapısına doğru ilerledikçe heyecanı doruğa varmasın. Bir yanda kocaman ağaçlar arasında çocuk salıncağı, diğer yanda toprağa saplanmış bel ve kürekle baharda sürülmeyi bekleyen bahçesi. İnanın, insanın her seferinde, içeriye girmeden önce şöyle bir tur atası geliyor\dots{} Hele ki içeride heyecan doruk noktasına varıyor ve kalbiniz gümbür gümbür atmaya başlıyor. Her an yanınızdan elinde piposuyla Bakunin geçebilir, Proudhon eski masanın üzerinde bir şeyler karalıyor olabilir ya da Malatesta‘nın İtalyanca aksanlı anarşist propagandalarını duyarsınız\dots{} Eski ve yeni kitap-dergi kokuları, eski siyah-beyaz mermer parkelerin arasındaki çizgilere öyle güzel sızmış ki, bir de üstüne ziyaretçilerin kendi ülkelerinden getirdikleri keklerin, böreklerin, şarapların kokuları karışmış, her yer merak, tarih, mücadelenin farklı boyutlarından gelen sıcak belgeler kokuyor. Raflardaki ve duvarlardaki afişler, yoldaşların konuşmalarıyla süslenmiş fotoğraflarının ve resimlerinin olduğu çerçeveler adeta içeride anarşinin olduğunu hissettiriyor size. 150 yıllık külliyatın büyük bir özenle korunmaya çalışıldığı, kitaplardan broşürlere, manifestolardan dergilere kadar dünyanın her yerinden gelen mektupların ve tarihe önem taşıyabilecek en ufak belgelerin büyük bir özenle saklandığı yerdeyim, CIRA‘da. -CENTRE INTERNATIONAL DE RECHERCHES SUR L'ANARCHISME (CIRA – Uluslararası Anarşist Arşiv Merkezi)- \bigskip Belçika‘dan gelen araştırmacı bir genç, görmek istediğim kişinin yani Marianne‘nin beni evde beklediğini söyledi. Marianne‘yle buluştuk; İsviçre’deki politik durumlardan İstanbul’a, Gezi direnişi ve sonrasına, Kürdistan’da yaşananlara değin hoş bir sohbet ettikten sonra kütüphaneye geçerek röportaja başladık. \section{\textbf{Meydan: Marianne bize CIRA’nın tarihini, nasıl oluştuğunu anlatabilir misin?}} \textbf{Marianne:} Aslında ben CIRA‘yla 1962 yılında “anarşist kütüphane” iken tanıştım. Benden önce 5 yılı daha var. Kurucumuz Pietro Ferrua savaş karşıtı bir vicdani retçiydi, bu yüzden ülkesinden sürgüne gelmişti ve İsviçre’de o zamanlar politik mülteciler sürgünler açıktan politika yapamazlardı, yasaktı. O İsviçre’de özgürlükçü bir kütüphane kurmayı düşündü. İsviçre’nin doküman toplama ve saklama açısından güvenli bir yer olduğuna karar verdi. Eski yoldaşlarının ve arkadaşlarının yardımıyla Cenevre‘de bir yer oluşturmaya başladılar. O zamanlar Cenevre‘de Luigi Bertoni çevresinde oluşan le Réveil-Il Risveglio [der Weck-ruf] (Kalk Çağrısı) adında anarşist bir grup vardı. Bertoni, 1900 yılından beri Fransızca ve İtalyanca olmak üzere, ayda iki kez haftalık gazete yayınlıyordu ve tabi ki 2. Dünya Savaşı zamanında. Bertoni 1947 yılında öldü ve ölümünden sonra her yıl arkadaşları düzenledikleri pikniklerde onu anıyorlardı. O zamanlar aktif değillerdi, hepsi yaşlı anarko-sendikalistler-di. Zamanla aralarına Fransa‘dan anti-militaristler, İtalya’dan ve Cezayir’den gelen savaş karşıtları ve genç yoldaşlar katılmaya başladı. Böylece de tekrar hareketlenmeye başladılar. Onlarla önce teyzem tanıştı ve des Service Civil International, des Internationalen Zivildienstes (Uluslararası Askerlik Yerine Sivil Hizmet Görenler) kurucusu Pierre Cerrosole ile evlendi. Pierre öldükten sonra teyzem daha da aktif şekilde mücadeleye devam etti. Yaşadığı küçük evde savaş karşıtı insanları ve arşivleri saklardı. Zamanla annem oraya gitti, okudu ve iş buldu. Ve ben yaşananlarla beraber anarşizmi keşfettim. \section{\textbf{O zamanları biraz anlatır mısın?}} Cezayir’deki savaş, Çin ve Sovyetlerdeki komünist partilerden bölünmeler, nükleer santral gibi birçok problemin yoğun yaşandığı zamanlar\dots{} O zamanlar okula gidiyordum ve sürekli insanlarla tartışıyorduk. Benimde politik kimliğimi ve anarşizmi keşfettiğim zamanlardı.Vicdani ret ve anti-militarist eylemler o zamanın koşullarında çok büyük rol oynuyordu. Aynı zamanda İspanya’da faşist Franco‘ya karşı mücadele yürüterek sürgün olanlarla dayanışma içindeydik. İspanya elçiliklerine karşı eylemler, yürüyüşler organize ediyorduk. İspanya’da hapiste bulunan, diğer taraftan Fransa, İtalya, Hollanda, İn-giltere, İsveç, Latin Amerika (Arjantin, Uruguay, Meksika) İspanya ve Bulgaristan gibi birçok ülkede sürgün anarşist yoldaşlara ilişkin de dayanışma kampanyalarımız oluyordu. CIRA o zamanlar Cenevre’deydi. Pietro Ferrua genç yoldaşlarla sürekli iletişimdeydi ve Cenevre’de bulunan İspanya Elçiliği’ne karşı küçük bir suikast eylemi gerçekleştirmişlerdi. Bombalama sonucunda sadece birkaç kapı yıkıldı ancak eylemcilere yine de dava açıldı. Bu eylemciler uzun yıllar hapiste kalmayacaklardı, fakat mülteciler İsviçre’den sınır dışı edileceklerdi. Ve biz yoldaşlarımızla toplandık. Annem de ben de kitapları çok seviyorduk ve dedik ki, evet, kitapları alacağız ve tekrar CIRA‘yı yaşatacağız. \bigskip \section{\textbf{Tam olarak hangi yıldı?}} 1963. 1964 yılında André Bernard ile birlikte şiddet karşıtı, anarşist bir gazete Anarchisme et Nonviolence‘yı çıkardık. Andre, aynı zamanda Cenevre’deki olaydan sora sürgün edilen ve ilk CIRA‘yı kuranlardandı. Fransa‘ya sürgün edilmişti ve geri döndükten sonra İsviçre’de bir şiddet karşıtı olarak vicdani ret eylemlerine başladı. Kampanyalar, toplantılar ve kurulan kamplar gibi hatırı sayılır işler yaptı. Örneğin, devlet gelip “Andre Bernard kim?” dediğinde, 10 kişi çıkıp benim diyordu, hiçbir belgeleri olmadığı için de 10 kişiyi birden tutukluyorlardı. Bu böyle, uzunca bir süre sürdü. Eylemlere katılanlar, Hristiyan veya ateist değişik gruplar veya kişiler olduğundan, anarşistler kendi iletişimlerini sağlamak için Anarschisme et Noviolence’yi kurdular. Sonrasında Andrea, Fransa’da yayın hayatını halen sürdürmekte olan anarşist gazete “La monde Libertaire”yi kurdu. CIRA, kitaplar, dokümanlar toplamaya; broşürlere, afişlere yani anarşiye dair ne varsa ulaşmaya çalıştı. 90’lı yıllarda “Réfractions”u çıkarmaya başladık. Teorik bir dergiye ihtiyacımız olduğunu düşünerek ve İtalya’da yayınlanan “Volonta”yi model olarak belirledik. lyon, Gronoble ve Toulouse de çeşitli toplantılar yaptık. \section{\textbf{Bizim oralardan CIRA’ya gelen giden oldu mu hiç?}} Yaklaşık 30 yıl kadar önce genç insanlarla tanıştık, kendilerini liberter Marksist ya da Marksizm’den kopmuş insanlar olarak adlandırıyorlardı. Anarşizmle tanıştıklarını ve ellerinde yeterince doküman olmadığını yazmışlardı. Bir şekilde bağlantıya geçtik ve onlara çeşitli dokümanlar yolladık. \section{\textbf{Sanıyorum annen Marie-Christine ile aynı zamanlara denk geliyor anarşist oluşunuz\dots{}}} Evet, beş çocuğu vardı ve yalnızdı. Politika ile uğraşmaya çok zaman bulamıyordu. Bunun üzerine çokça tartışıyorduk. Sonunda kabul etti, birçok kitap ödünç aldık ve okuduk. Beraberce bu gruba katıldık ve yaklaşık 40 yıl boyunca birlikte CIRA’da çalıştık. Tabi ki hiç kavgasız\Slash{}tartışmasız değil, bizim için gerçek bir maceraydı. \section{\textbf{Şu an CIRA nasıl işliyor?}} CIRA‘da şu an dünyanın birçok ülkesinden gelen, özellikle de İtalyanca, Fransızca, İngilizce, Almanca ve Rusça olan yaklaşık 20 bin kitap ve broşür, 5000 gazete-dergi (yaklaşık şu an 200 üzeri gazete yayınına devam ediyor ve yenileri eklendi), 100 üzeri belgesel film veya film, kartpostallar, afişler, fotoğraflar, resimler vs. muhafaza ediliyor. Yaklaşık 50 yıldır parasız veya çok çok küçük bütçeyle süren bir çalışmadır CIRA. Ayrıca belirtmek isterim ki CIRA sadece bir araştırma merkezi değildir, aynı zamanda bir kütüphanedir ve benim yaşamımdır. Kitapların ve arkadaşlarımın arasında çok güzel vakit geçirdiğim bir yerdir CIRA. Anarşist dayanışmanın da çok güzel örneklerinden biridir. CIRA’da düzenli olarak yaklaşık 6 çalışanımız var ve çok küçük bütçelerle çalışıyorlar. Çalışanlarımız da genelde yoldaşlarımız oluyor ve burada kendi küçük ütopyamız için faaliyet veriyoruz. Ayrıca İsviçre’de vicdani retçiler sosyal hizmet haklarını CIRA‘da da kullanabiliyorlar. Başvurular üzerine biz karar veriyoruz. Çünkü burada ciddi bir iş yapıyoruz ve burada sosyal hizmet yapmak isteyenlerin, kitaplara, dergilere ve arşivciliğe önem vermesi gerekiyor. \section{\textbf{Araştırmaları için gelenler burada aradıklarını nasıl buluyorlar?}} 150 yıla dayanan bir arşivimiz var ve birçok konuda yazılmış anarşist argümanlara burada ulaşmak mümkün. İnternet sitemizde de arşivimiz var ve her yıl bunu yeniliyoruz. Ama araştırmacıların da ne aradıklarını tam olarak bilmesi gerekiyor. Örneğin, mustafa kemal adına bir şeyler bulamaz ama Osmanlı dönemine ait belge ve kitaplardan aradıklarınızı bulabilirsiniz. Berlin‘de, Viyana‘da, İtalya‘da, Londra‘da, Fransa‘da birçok yerde böyle kütüphaneler var. Her kütüphane kendi ülkesindeki veya çevresindeki eski–yeni kitaplara veya gazetelere, eski mektuplara veya manifestolara ulaşmaya çalışıyor. Kütüphanelerle yaptığı-mız toplantılarda önemli gelişmeleri arşivimize ve birbirimize sunuyoruz. \section{\textbf{Genelde bu saydıklarınız anarşist kütüphaneler mi?}} İllaki anarşist olması gerekmiyor ve bizim çok dogma bir bakışımız yok. Otonomların, anti militaristlerin, ekolojistlerin ve bu gibi kişi ve grupların oluşturdukları kütüphanelerde de gerekli materyallere ulaşabiliyoruz. Ayrıca, uluslararası Liberter Dokümanlar Enstitü Merkezi (FICEDL) çatısı altında İtalya, Fransa, İspanya, Arjantin, Brezilya, Belçika, Rusya ve benzeri yerlerde küçük CIRA‘lar koordine etmeye çalışıyoruz. \section{\textbf{Sadece İsviçre’den mi veya Avrupa’dan mı gelenler oluyor?}} Dünyanın her yerinden gelenler var ve yolları çok uzun olanlar burada kalabiliyorlar böylece birçok diyaloğumuz oluyor. Öğrenciler, sanatçılar, aktivistler, öğretmenler, gazeteciler, gençler ve punk misafirlerimiz\dots{} Her yere ulaşmamız çok zor olduğu için genelde insanlar bize ulaşıp yayınlarını bırakıyor ya da yolluyorlar; kitaptan fanzine, dergiden küçük broşürlere kadar. \section{\textbf{CIRA’ya katkı ya da bağışlar oluyor mu?}} İnsanlar arşivlerini CIRA’ya bağışlayabiliyorlar. Tabi ki çok büyük yerlerimiz olmadığı için daha seçici davranarak önemli belgeleri alıp saklıyoruz. Bir de üyelik sistemimiz var. Üyelerimiz çok olmasa da yıllık 30 Euro’ya kadar destek-bağış yapabiliyorlar. \section{\textbf{İsviçre özel bir rol oynuyor mu anarşistler açısından, bunun tarihini biraz anlatabilir misin?}} Anarşist düşünce çok eskiye dayanır. Politik olarak anarşinin teorisi 19. yy'da keşfediliyor. Ama ilk anarşist hareket 1872 yılında İsviçre’nin şimdiki Jura kantonunun küçük bir köyü olan St.Imier’de kuruluyor. Den Haag’da yapılan (Hollanda)1. Enternasyonal buluşmasından sonra Michael Bakunin ve James Guillaume öncülüğünde İtalyan, Belçikalı, İspanyol ve sürgünde olan birçok anarşistin de katılımıyla birkaç yıl içerisinde Jura Federasyonu kuruluyor. Özellikle Jura Federasyonu’ndaki St.Imier Vadisi’nde, komşu köylerde ve kasabalarda bulunan yüzlerce işçi, isçi dernekleri, mesleki eğitim dernekleri, Paris Komünü’nden sürgün edilen devrimciler, orada önce Bakuninle, sonra da Kropotkin ve Reclusla buluşuyorlar. Sonrasında da saat fabrikalarında çalışan insanların doğrudan katıldıkları büyük eylemlilikler silsilesinde anarşist hareket doğuyor. \section{\textbf{Peki, Türkiye’deki ve Kürdistan’daki durumu takip ediyor musunuz?}} Tabi ki. Özellikle Gezi direnişi bizi burada çok mutlu etti, heyecanlandırdı. Yüzbinlerce insanın örgütlenerek böyle büyük eylemler yapması çok çok güzel. İspanya’daki gibi, Amerika’daki gibi çok büyük eylemler spontane gözükebilir ama bunlar katılımcıların da bir o kadar bilinçli olduğu eylemlerdir. İnsanların iradesi ve yaşamsal kararlarda kendilerini ateşin önüne atması, haksızlığa karsı durması, karşı konulamaz bir gerçekliktir. Bu noktada biri barikatta şiddet kullandı veya diğeri şiddetsiz veya farklılıkları olması tartışmalara mahal getirmemesi gereken şeyler. Orada şefler yoktu ve şefsiz insanlar bir şeyler yaptılar. Özellikle gençlerin bu eylemlere yoğun katılımları ve orada birçok kara bayrak görmek, eminim bizler gibi bir-çok yoldaşı da heyecanlandırmıştır. Sadece İstanbul’da da değil, Ankara ve Kürdistan’daki dergiler ve onların haberleri bizlere siz yoldaşlar sayesinde ulaşabiliyor. Anarşist örgütlenmelerin HES‘lerden tutun da, tutsaklarla olan dayanışma eylemlerine ve tabi ki Kürt meselesine duyarlı olmaları da çok önemli gelişmelerdir. \section{\textbf{Teşekkürler Marianne, her zaman için dayanışmayla\dots{}}} \bigskip % begin final page \clearpage % new page for the colophon \thispagestyle{empty} \begin{center} Anarşist Kütüphane \bigskip \includegraphics[width=0.25\textwidth]{logo-en.pdf} \bigskip \end{center} \strut \vfill \begin{center} Meydan Gazetesi Anarşizmin Arşivi CIRA 01.02.2014 \bigskip Bu yazı Meydan Gazetesi’nin 16. sayısında yayınlanmıştır. \bigskip \textbf{tr.anarchistlibraries.net} \end{center} % end final page with colophon \end{document} % No format ID passed.
https://isabelle.in.tum.de/repos/testboard/raw-diff/67d046de093e/doc-src/Ref/substitution.tex	tum.de	CC-MAIN-2022-40	text/plain	application/x-tex	crawl-data/CC-MAIN-2022-40/segments/1664030335004.95/warc/CC-MAIN-20220927100008-20220927130008-00592.warc.gz	358,756,539	986	diff -r e8d8fa0ddcef -r 67d046de093e doc-src/Ref/substitution.tex --- a/doc-src/Ref/substitution.tex Thu Nov 25 13:54:21 1993 +0100 +++ b/doc-src/Ref/substitution.tex Thu Nov 25 14:16:40 1993 +0100 @@ -143,7 +143,7 @@ \begin{ttbox} fun dest_eq (Const("Trueprop",_) $ (Const("op =",_)$t$u)) = (t,u); \end{ttbox} -Here {\tt Trueprop} is the coercion from type'~$o$ to type~$prop$, while +Here {\tt Trueprop} is the coercion from type~$o$ to type~$prop$, while \hbox{\tt op =} is the internal name of the infix operator~{\tt=}. Pattern-matching expresses the function concisely, using wildcards~({\tt_}) to hide the types.
http://dlmf.nist.gov/2.5.E20.tex	nist.gov	CC-MAIN-2017-17	application/x-tex	null	crawl-data/CC-MAIN-2017-17/segments/1492917123172.42/warc/CC-MAIN-20170423031203-00133-ip-10-145-167-34.ec2.internal.warc.gz	106,059,596	609	\[h(t)=\mathop{O\/}\nolimits\!\left(t^{c}\right),\]

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