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I can't make pdf I type this :

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$‎E(‎\frac{1}{2}‎\Phi ‎+‎\frac{1}{2}‎\Phi‎‎\prime ‎,‎\frac{1}{2}‎\Psi ‎+‎\frac{1}{2}‎\Psi‎‎\prime‎)\leq ‎‎\frac{1}{2}E(‎\Phi , ‎‎‎‎\Psi‎‎\prime‎)+‎\frac{1}{2}E(‎\Phi‎‎\prime ‎,‎\Psi‎).‎‎$‎

\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}‎‎‎ 

please help me

Joseph Wright
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1 Answers1

3

Something like this, although it is still a little wide for the page

Note that you had one "hidden" error in addition to the general syntax errors, each of your \sum_ is the unicode sequence

  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

The two left-to-right mark characters meant that the subscript was not seen as a subscript of the summation sign, but of an empty math atom to the right.

\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}
David Carlisle
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