我无法制作 pdf 我输入以下内容:
$E(\frac{1}{2}\Phi +\frac{1}{2}\Phi\prime ,\frac{1}{2}\Psi +\frac{1}{2}\Psi\prime)\leq \frac{1}{2}E(\Phi , \Psi\prime)+\frac{1}{2}E(\Phi\prime ,\Psi).$
\begin{eqmarray}
$\sum_{u\in\Sigma(0,\Gamma) }\frac{1}{|\Gamma_u | }E_{u,\Phi}(\Psi(u)) $
$~&=&\sum_{u\in \Sigma(0,\Gamma) }\frac{1}{|\Gamma_u| }\sum\underline{v\in\Sigma_u(0) }m((u,v))f(d(\Psi(u),\Phi(v)))$
$~&=&\sum\_{u\in\Sigma(0,\Gamma) }\frac{1}{|\Gamma_u| }\sum_{\eta\in\Sigma(1),u\subset\eta }\frac{m(\eta)}{2}f(d(\Psi(u),\Phi(\eta -u))),$
$~&=&\sum_{\eta\in\Sigma(1,\Gamma) }\frac{m(\eta }{2|\Gamma_\eta | }\sum_{u\in\Sigma(0),u\subset\eta }f(d(\Psi(u),\Phi(\eta -u)))$
$~&=&\sum_{(u,v)\in\Sigma(1,\Gamma) }\frac{m((u,v))}{2|\Gamma_(u,v)| }(f(d(\Psi(u),\Phi(v)))+f(d(\Psi(v),\Phi(u)))$
$~&=&\sum_{(u,v)\in\Sigma(1,\Gamma) }\frac{m((u,v))}{|\Gamma_(u,v) }f(d(\Psi(u),\Phi(v)))$
$~&=&E(\Phi ,\Psi).$
\end{eqmarray}
请帮我
答案1
类似这样,虽然对于页面来说还是有点宽
请注意,除了一般的语法错误之外,还有一个“隐藏”错误,每个错误\sum_
都是unicode序列
U+005c REVERSE SOLIDUS
U+0073 LATIN SMALL LETTER S
U+0075 LATIN SMALL LETTER U
U+006d LATIN SMALL LETTER M
U+200e LEFT-TO-RIGHT MARK
U+200e LEFT-TO-RIGHT MARK
U+005f LOW LINE
两个从左到右的标记字符意味着下标不被视为求和符号的下标,而是右边的空数学原子的下标。
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
E(\frac{1}{2}\Phi +\frac{1}{2}\Phi' ,\frac{1}{2}\Psi +\frac{1}{2}\Psi')\leq \frac{1}{2}E(\Phi , \Psi')+\frac{1}{2}E(\Phi' ,\Psi)
\]
\begin{align*}
\sum_{u\in\Sigma(0,\Gamma)}\frac{1}{|\Gamma_u | }E_{u,\Phi}(\Psi(u)) \\
&=\sum_{u\in \Sigma(0,\Gamma) }\frac{1}{|\Gamma_u| }\sum\underline{v\in\Sigma_u(0) }m((u,v))f(d(\Psi(u),\Phi(v)))\\
&=\sum_{u\in\Sigma(0,\Gamma) }\frac{1}{|\Gamma_u| }\sum_{\eta\in\Sigma(1),u\subset\eta }\frac{m(\eta)}{2}f(d(\Psi(u),\Phi(\eta -u))),\\
&=\sum_{\eta\in\Sigma(1,\Gamma) }\frac{m(\eta }{2|\Gamma_\eta | }\sum_{u\in\Sigma(0),u\subset\eta }f(d(\Psi(u),\Phi(\eta -u)))\\
&=\sum_{(u,v)\in\Sigma(1,\Gamma) }\frac{m((u,v))}{2|\Gamma_{(u,v)}| }(f(d(\Psi(u),\Phi(v)))+f(d(\Psi(v),\Phi(u)))\\
&=\sum_{(u,v)\in\Sigma(1,\Gamma) }\frac{m((u,v))}{|\Gamma_{(u,v)}|}f(d(\Psi(u),\Phi(v)))\\
&=E(\Phi ,\Psi).
\end{align*}
\end{document}