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<title>MathJax Example</title> |
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<script> |
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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> $\alpha_{2}=|y-C|+|y-B-C|$ </p> |
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<p> $v_{j}\in V_{R}$ </p> |
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<p> $\displaystyle{n^{2}_{L}}\times{\mathcal{L}}({\mathcal{L}}-1)-{n^{2}_{R}}\times% |
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{\mathcal{R}}({\mathcal{R}}-1)$ </p> |
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<p> $u_{6}$ </p> |
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<p> $\alpha_{2}=B$ </p> |
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<p> $w_{1}+w_{2}=\sum_{k=1}^{2}w_{k}$ </p> |
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<p> $R_{i}$ </p> |
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<p> $k+1$ </p> |
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<p> $\mathcal{E}_{L}^{(\frac{k}{2})}+(\frac{k}{2}+1)\;\epsilon-(\frac{k}{2})\;% |
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\epsilon>\mathcal{E}_{L}^{(\frac{k}{2})}$ </p> |
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<p> $w^{\prime}(e)=w(e)$ </p> |
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<p> $i<{\mathcal{L}}$ </p> |
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<p> $\mathcal{C},\;\mathcal{C}:V_{s}\rightarrow\mathbb{N},$ </p> |
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<p> $v_{6}$ </p> |
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<p> $\Delta_{1}({\text{UNMARK\_LEFT}})\geq 0$ </p> |
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<p> $L_{1}\times R_{1}\times w^{*}$ </p> |
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<p> $v_{4}$ </p> |
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<p> $\mathcal{W}(E^{(v_{1},u_{5})})=w_{1}+w_{2}+w_{3}+w_{4}$ </p> |
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<p> $k=k^{\prime}=1$ </p> |
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<p> $n_{L}=0$ </p> |
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<p> $w(e_{i})$ </p> |
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<p> $\Delta(\text{UNMARK\_RIGHT})\leq 0$ </p> |
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<p> $\Delta({\text{MARK\_LEFT}})=L_{i}\times\bigg{(}S_{LM}+(S_{LU}-L_{i})+S_{RM}-S_% |
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{RU}\bigg{)}$ </p> |
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<p> $\alpha_{1}=A-x+A+B-x<B\xrightarrow{}A<x$ </p> |
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<p> $c_{1}+c_{2}<1+\epsilon=c_{1}+c_{2}$ </p> |
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<p> $M^{*}$ </p> |
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<p> $\mathcal{E}(M)$ </p> |
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<p> $n_{L}+n_{R}=n-(k+k^{\prime})$ </p> |
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<p> $\mathcal{O}(|V|)$ </p> |
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<p> $e^{\prime}$ </p> |
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<p> $S_{L}-S_{R}\leq L_{i}$ </p> |
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<p> $B\times k^{\prime}\times(n-(k+k^{\prime}))$ </p> |
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<p> $e\in S$ </p> |
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<p> $1\leq i\leq{\mathcal{L}}$ </p> |
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<p> $e_{2}$ </p> |
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<p> $\mathcal{E}(M^{\prime})\leq\mathcal{E}(M)$ </p> |
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<p> $-S_{L}+L_{i}+S_{R}\geq 0\xrightarrow{}L_{i}\geq S_{L}-S_{R}$ </p> |
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<p> $\displaystyle n_{L}\times k^{\prime}\times B$ </p> |
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<p> $e_{j}$ </p> |
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<p> $\frac{{\mathcal{L}}}{2}+\frac{{n_{R}}(1-{\mathcal{R}})}{2{n_{L}}}-i=\frac{{% |
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\mathcal{L}}{n_{L}}+{n_{R}}(1-{\mathcal{R}})}{2{n_{L}}}-i$ </p> |
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<p> $\displaystyle\pi^{\prime}_{v_{i},u_{j}}$ </p> |
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<p> $w^{\prime}\left(e_{i}\right)=w\left(e_{i}\right)+c_{i}w\left(e^{*}\right)$ </p> |
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<p> $i<j$ </p> |
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<p> $w^{\prime}$ </p> |
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<p> $u_{1}$ </p> |
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<p> $u,v\in V,$ </p> |
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<p> $E_{m}$ </p> |
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<p> $\displaystyle(k-k^{\prime})\times n_{L}\times|x-A|+n_{L}\times k^{\prime}% |
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\times\big{(}|x-A|+|x-A-B|\big{)}$ </p> |
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<p> $\displaystyle\underbrace{|w_{2}-(w_{2}+\epsilon_{2})|}_{\text{between }u\text{% |
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and }v_{1}}+\underbrace{|w_{2}+w^{*}-(w_{2}+\epsilon_{2})|}_{\text{between }u% |
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\text{ and }v_{2}}=|\epsilon_{2}|+|w^{*}-\epsilon_{2}|=|\epsilon_{2}|+|% |
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\epsilon_{2}-w^{*}|$ </p> |
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<p> $n_{1}=n_{L}$ </p> |
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<p> $T^{L}_{1}$ </p> |
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<p> $-\epsilon\times w^{*}$ </p> |
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<p> $V_{m}$ </p> |
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<p> $B$ </p> |
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<p> $V$ </p> |
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<p> $|\Delta E|\geq B(n-2)+n_{L}n_{R}|x+y-A-B-C|\geq B(n-2)=|\overline{V_{m}}|B$ </p> |
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<p> $e^{*}=(u_{1},v_{1})$ </p> |
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<p> $e=(u,w_{2})$ </p> |
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<p> $A\leq x\leq A+B$ </p> |
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<p> $T=(V,E)$ </p> |
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<p> $\epsilon_{1}$ </p> |
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<p> $|V|$ </p> |
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<p> $\mathcal{E}_{L}^{(i)}$ </p> |
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<p> $c^{\prime}_{i}=c_{i}+\epsilon$ </p> |
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<p> $R_{1}\times R_{2}\times w^{*}$ </p> |
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<p> $e^{*}=(u_{1},v_{1}),w^{*}=w(e^{*})$ </p> |
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<p> $|z|-|x|\leq|z-x|$ </p> |
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<p> $|x|=-x$ </p> |
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<p> ${\mathcal{R}}\xleftarrow[]{}|E_{R}|$ </p> |
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<p> $V_{L}=\{v_{3},v_{4}\}$ </p> |
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<p> $\displaystyle|\Delta E|=\underbrace{n_{L}\times|x-A|\times k}_{\text{between % |
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the subpath of }w_{1}\text{ and the vertices in }v}+\underbrace{n_{L}\times|x-% |
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A-B|\times k^{\prime}}_{\text{between the subpath of }w_{1}\text{ and the % |
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vertices in }u}+$ </p> |
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<p> $\displaystyle\frac{{\mathcal{L}}{n_{L}}-{n_{R}}(1-{\mathcal{R}})}{2{n_{L}}}({n% |
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^{2}_{L}}\times({\mathcal{L}}-1)+{n_{L}}{n_{R}}(-{\mathcal{R}}))$ </p> |
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<p> $|w^{*}|-\left|w^{*}-\sum_{k=n_{1}+1}^{j-2}\epsilon_{k}\right|\leq\left|\sum_{k% |
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=n_{1}+1}^{j-2}\epsilon_{k}\right|$ </p> |
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<p> $\left|w^{*}-\sum_{k=i}^{n_{1}}\epsilon_{k}\right|$ </p> |
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<p> $0\leq j\leq k$ </p> |
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<p> $e^{*}=(v_{n_{1}+1},v_{n_{1}+2}$ </p> |
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<p> $L_{i}\times L_{j}\times 2w^{*}$ </p> |
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<p> $i=\{1,\dots,{\mathcal{R}}\}$ </p> |
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<p> $e_{i}\in\overline{E_{m}}=E-E_{m}$ </p> |
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<p> $R_{i}\times S_{LU}$ </p> |
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<p> $\overline{V_{m}}$ </p> |
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<p> $c_{j}$ </p> |
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<p> $R_{1}$ </p> |
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<p> ${n^{2}_{L}}\times 2\bigg{(}{i+1\choose 2}-{i\choose 2}\bigg{)}={n^{2}_{L}}% |
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\times 2i$ </p> |
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<p> $i=\frac{{\mathcal{L}}{n_{L}}+{n_{R}}(1-{\mathcal{R}})}{2{n_{L}}}$ </p> |
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<p> $\begin{array}[]{cc}\Delta({\text{MARK\_LEFT}})\leq 0\xrightarrow[]{}{n^{2}_{L}% |
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}\times({\mathcal{L}}-1)+{n_{L}}{n_{R}}(2j-{\mathcal{R}})&\leq 0\\ |
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\end{array}$ </p> |
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<p> $\displaystyle n_{L}\times\big{(}\sum_{j=0}^{i+1}j\;w_{j}+\sum_{j=i+2}^{k}(k+1-% |
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j)\;w_{j}\big{)}$ </p> |
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<p> $\{e_{1},\dots,e_{k}\}$ </p> |
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<p> $e^{\prime}\neq e^{*}$ </p> |
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<p> $w_{1}+\epsilon_{1}+w_{2}+\epsilon_{2}=\sum_{k=1}^{2}(w_{k}+\epsilon_{k})$ </p> |
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<p> $e^{*}_{k}=(u_{j},u_{j+1})\in E_{m}$ </p> |
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<p> $n_{L}=n_{R}$ </p> |
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<p> $\Delta(\text{MARK\_LEFT})\leq 0$ </p> |
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<p> $e^{*}_{j}$ </p> |
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<p> $\alpha_{1}<B$ </p> |
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<p> $|w^{*}|-\left|\sum_{k=i}^{n_{1}}\epsilon_{k}\right|$ </p> |
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<p> $i+1$ </p> |
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<p> $\Delta_{v_{i},u_{j+1}}=\mathcal{E}^{v_{i},u_{j+1}}_{2}-\mathcal{E}^{v_{i},u_{j% |
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+1}}_{1}=-\left|w^{*}_{k}+\mathcal{W}^{*}(E^{(v_{i},u_{j})})-\mathcal{W}^{% |
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\prime}(E^{(v_{i},u_{j})})\right|$ </p> |
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<p> $v_{i},v_{j}\in V_{L}(i<j)$ </p> |
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<p> $w^{\prime}:E\rightarrow\mathbb{R}_{\geq 0}$ </p> |
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<p> $x=\epsilon+\sum_{j=0}^{\frac{k}{2}}w_{j}$ </p> |
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