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<title>MathJax Example</title> |
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tex: { |
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inlineMath: [['$', '$'], ['\(', '\)']] |
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<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> |
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<body> |
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<p> $c_{j}=\epsilon_{2}$ </p> |
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<p> $\{e_{1},e_{2}\}$ </p> |
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<p> $\Delta_{2}({\text{MARK\_LEFT}})=(c_{1})\times X+(1-c_{1})\times X$ </p> |
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<p> $A$ </p> |
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<p> $S$ </p> |
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<p> $\alpha\geq 1$ </p> |
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<p> $|w_{3}+w^{*}+w_{4}-w_{3}-w_{4}|=w^{*}$ </p> |
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<p> $\displaystyle\pi_{v_{i},u_{j}}$ </p> |
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<p> $\{v^{\prime}_{4},v^{\prime}_{5},v^{\prime}_{6}\}$ </p> |
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<p> $x=w_{0}$ </p> |
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<p> $v_{n_{1}+1}$ </p> |
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<p> $\displaystyle=$ </p> |
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<p> $e^{*},$ </p> |
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<p> ${n_{L}}{n_{R}}\times(({\mathcal{L}}-i-1)({\mathcal{R}}-j)-({\mathcal{L}}-i)({% |
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\mathcal{R}}-j))={n_{L}}{n_{R}}\times({\mathcal{L}}{\mathcal{R}}-{\mathcal{L}}% |
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j-i{\mathcal{R}}+ij-{\mathcal{R}}+j-{\mathcal{L}}{\mathcal{R}}+{\mathcal{L}}j+% |
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i{\mathcal{R}}-ij)={n_{L}}{n_{R}}\times(j-{\mathcal{R}})$ </p> |
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<p> ${R}_{j}$ </p> |
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<p> $-2\times R_{i}\times(S_{RM}-R_{i})$ </p> |
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<p> $V_{m}=\{v|v,u\in V,\exists e=(u,v)\in E_{m}\}$ </p> |
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<p> $v_{2}$ </p> |
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<p> $\Delta_{v_{i},u_{j}}=\mathcal{E}^{v_{i},u_{j}}_{2}-\mathcal{E}^{v_{i},u_{j}}_{% |
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1}=\left|w^{*}_{k}\right|-\left|\mathcal{W}^{\prime}(E^{(v_{i},u_{j})})-% |
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\mathcal{W}^{*}(E^{(v_{i},u_{j})})\right|\leq\left|w^{*}_{k}-\mathcal{W}^{% |
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\prime}(E^{(v_{i},u_{j})})+\mathcal{W}^{*}(E^{(v_{i},u_{j})})\right|$ </p> |
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<p> $k$ </p> |
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<p> $w^{\prime}(e_{i})=w(e_{i})+\epsilon_{i},\epsilon_{i}\in\{0,w^{*}\}$ </p> |
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<p> $c_{1}$ </p> |
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<p> $n_{R}=3$ </p> |
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<p> $\displaystyle=n_{L}\times(w_{0}-x+w_{0}+w_{1}-x+\dots+w_{0}+w_{1}+\dots+w_{k}-% |
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x)=n_{L}\times\big{(}\big{(}\sum_{j=0}^{k}(k+1-j)w_{j}\big{)}-(k+1)\times x% |
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\big{)}$ </p> |
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<p> $\mathcal{C}(v)=k$ </p> |
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<p> $\{v_{1},v_{2}\}$ </p> |
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<p> $\mathcal{E}_{L}^{(\frac{k}{2})}$ </p> |
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<p> $k^{\prime}$ </p> |
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<p> $c_{i}+c_{j}\leq 1$ </p> |
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<p> $S_{L}-L_{i}-S_{R}\leq 0$ </p> |
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<p> $\{v^{\prime}_{1},v^{\prime}_{2},v^{\prime}_{3}\}$ </p> |
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<p> $E^{\prime}\subset E$ </p> |
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<p> $v_{1},v_{3}\in\overline{V_{m}}$ </p> |
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<p> $w^{*}_{1},w^{*}_{2},\dots,w^{*}_{k}$ </p> |
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<p> $\mathcal{F}$ </p> |
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<p> $x<0$ </p> |
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<p> $C\leq x\leq B+C$ </p> |
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<p> $T_{j}^{L}$ </p> |
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<p> $\mathcal{E}(M_{L}^{*})\leq\mathcal{E}(M_{R}^{*})\xrightarrow[]{}\sum_{e_{i}\in |
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E% |
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_{L}}L_{i}\times w^{*}\times(S_{L}-L_{i}-S_{R})\leq\sum_{e_{i}\in E_{R}}R_{i}% |
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\times w^{*}\times(S_{R}-R_{i}-S_{L})$ </p> |
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<p> $x\geq A+B$ </p> |
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<p> $\mathcal{E}_{LR}$ </p> |
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<p> $\displaystyle\geq\mathcal{E}(M_{0})+\sum_{e_{i}\in E_{L}}L_{i}\times w^{*}% |
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\times(S_{L}-L_{i}-S_{R})=\mathcal{E}(M_{L}^{*})$ </p> |
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<p> $x<w_{0}$ </p> |
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<p> $S_{RM}>0$ </p> |
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<p> $\mathcal{E}(M)<\mathcal{E}(M^{\prime})$ </p> |
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<p> ${L}_{i}$ </p> |
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<p> ${n_{R}}$ </p> |
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<p> $e_{1}=(v_{1},v_{3})$ </p> |
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<p> ${\mathcal{L}}\xleftarrow[]{}|E_{L}|$ </p> |
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<p> $\mathcal{E}_{L}$ </p> |
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<p> $\mathcal{E}(M^{\prime\prime})\leq\mathcal{E}(M)$ </p> |
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<p> $w^{*}$ </p> |
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<p> $0<\epsilon<w_{\frac{k}{2}+1}$ </p> |
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<p> $|\sum_{k=i}^{n_{1}}\epsilon_{k}|$ </p> |
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<p> $|\Delta E|$ </p> |
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<p> $-R_{i}\times S_{LM}$ </p> |
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<p> $w^{\prime}(e)=w(e)+w(e^{*})$ </p> |
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<p> $u_{1}\in T_{i}^{L},u_{2}\in T_{j}^{R}$ </p> |
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<p> $S_{RM}=0$ </p> |
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<p> $\Delta({\text{MARK\_LEFT}})\leq 0$ </p> |
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<p> $C_{R}$ </p> |
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<p> $-L_{i}\times(S_{LM})+L_{i}\times(S_{LU}-L_{i})$ </p> |
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<p> $c_{0},c_{1},\dots,c_{i}$ </p> |
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<p> $k+1-j$ </p> |
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<p> $|\Delta E|\geq(n-2)B=|\overline{V_{m}}|B$ </p> |
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<p> $B\times k^{\prime}\times(n-(k+k^{\prime}))=B\times(n-2)$ </p> |
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<p> $P^{\prime}$ </p> |
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<p> $|\Delta E|^{\prime}\geq w^{*}$ </p> |
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<p> $C$ </p> |
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<p> $|y-C|+|y-B-C|$ </p> |
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<p> $E_{m}\subset E$ </p> |
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<p> $j<i+1$ </p> |
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<p> $\overline{V_{m}}=V-V_{m}$ </p> |
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<p> $v_{i}\in V_{L},v_{i}\neq v_{n_{1}+1}$ </p> |
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<p> ${\mathcal{L}}$ </p> |
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<p> $e^{*}=(v_{1},v_{2})$ </p> |
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<p> $y=C$ </p> |
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<p> $\mathcal{E}(M_{L}^{*})\leq\mathcal{E}(M_{R}^{*})$ </p> |
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<p> $u\in T_{2}^{L}$ </p> |
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<p> $\Delta({\text{UNMARK\_RIGHT}})$ </p> |
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<p> $v_{i},v_{j}\in V_{L}\;(i<j,\;j\neq n_{1}+1)$ </p> |
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<p> $c_{i}=1$ </p> |
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<p> ${n^{2}_{R}}\times((j-1)({\mathcal{R}}-j+1)-j({\mathcal{R}}-j))={n^{2}_{R}}% |
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\times(j{\mathcal{R}}-j^{2}+j-{\mathcal{R}}+j-1-j{\mathcal{R}}+j^{2})={n^{2}_{% |
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R}}\times(2j-{\mathcal{R}}-1)$ </p> |
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<p> $\mathcal{C}(u)=k^{\prime}$ </p> |
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<p> $E^{\prime}$ </p> |
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<p> $0.4$ </p> |
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<p> $\Delta({\text{UNMARK\_RIGHT}})=0$ </p> |
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<p> ${n_{L}}{n_{R}}((i+1)j-ij)={n_{L}}{n_{R}}\times j$ </p> |
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<p> $-\left|w^{*}-\sum_{k=i}^{n_{1}}\epsilon_{k}\right|$ </p> |
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<p> $c_{i}<c_{j}$ </p> |
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<p> $e\in E^{\prime}$ </p> |
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<p> $k-k^{\prime}\geq 0$ </p> |
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<p> $-R_{i}\times(S_{RU})+R_{i}\times(S_{RM}-R_{i})$ </p> |
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<p> $w^{*}_{k}$ </p> |
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<p> $\operatorname{CONTRACTION}(\pi)$ </p> |
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<p> $T-\{v_{1},v_{2}\}$ </p> |
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<p> $V_{R}$ </p> |
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<p> $\begin{array}[]{cc}\Delta&=R_{i}\times\bigg{(}\underbrace{-(S_{RM}-R_{i})}_{<0% |
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}-S_{RU}\underbrace{-S_{LM}}_{<0}+S_{LU}\bigg{)}<R_{i}(\underbrace{-S_{RU}+S_{% |
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LU}}_{\leq 0})<0\end{array}$ </p> |
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<p> $G=P_{n}$ </p> |
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<p> $\triangleright$ </p> |
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