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diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/index.html b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/index.html deleted file mode 100644 index 47104a5ce76..00000000000 --- a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/index.html +++ /dev/null @@ -1,235 +0,0 @@ -<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> - -<!--Converted with LaTeX2HTML 99.1 release (March 30, 1999) -original version by: Nikos Drakos, CBLU, University of Leeds -* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan -* with significant contributions from: - Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -<HTML> -<HEAD> -<TITLE>sampleMath</TITLE> -<META NAME="description" CONTENT="sampleMath"> -<META NAME="keywords" CONTENT="sampleMath"> -<META NAME="resource-type" CONTENT="document"> -<META NAME="distribution" CONTENT="global"> - -<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"> -<META NAME="Generator" CONTENT="LaTeX2HTML v99.1 release"> -<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css"> - -<LINK REL="STYLESHEET" HREF="sampleMath.css"> - -<LINK REL="next" HREF="node1.html"> -<LINK REL="next" HREF="node1.html"> -</HEAD> - -<BODY > -<!--Navigation Panel--> -<A NAME="tex2html9" - HREF="node1.html"> -<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" - SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/next_motif.gif"></A> -<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" - SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/up_motif_gr.gif"> -<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" - SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/previous_motif_gr.gif"> -<BR> -<B> Next:</B> <A NAME="tex2html10" - HREF="node1.html">About this document ...</A> -<BR> -<BR> -<!--End of Navigation Panel--> -<P> -<H2 ALIGN="center"><A NAME="SECTION00000000000000000000"> -Math examples</A> -</H2> -<BR> -<DIV ALIGN="CENTER"><A NAME="xiEmax"></A> - -<!-- MATH - \begin{eqnarray} -\phi(\lambda) & = & \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\infty} - \exp \left( u \ln u + \lambda u \right ) du \hspace{1cm}\mbox{for } c \geq 0 \\ - \lambda & = & \frac{\epsilon -\bar{\epsilon} }{\xi} - - \gamma' - \beta^2 - \ln \frac{\xi} {E_{\rm max}}\\ - \gamma & = & 0.577215\dots \mathrm{\hspace{5mm}(Euler's\ constant)} \\ - \gamma' & = & 0.422784\dots = 1 - \gamma \\ - \epsilon , \bar{\epsilon} & = & \mbox{actual/average energy loss} -\end{eqnarray} - --> - -<TABLE ALIGN="CENTER" CELLPADDING="0" WIDTH="100%"> -<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG - WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" - SRC="img1.gif" - ALT="$\displaystyle \phi(\lambda)$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="325" HEIGHT="58" ALIGN="MIDDLE" BORDER="0" - SRC="img3.gif" - ALT="$\displaystyle \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\infty} -\exp \left( u \ln u + \lambda u \right ) du \hspace{1cm}\mbox{for } c \geq 0$"></TD> -<TD WIDTH=10 ALIGN="RIGHT"> -(1)</TD></TR> -<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG - WIDTH="13" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" - SRC="img4.gif" - ALT="$\displaystyle \lambda$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="185" HEIGHT="51" ALIGN="MIDDLE" BORDER="0" - SRC="img5.gif" - ALT="$\displaystyle \frac{\epsilon -\bar{\epsilon} }{\xi} -- \gamma' - \beta^2 - \ln \frac{\xi} {E_{\rm max}}$"></TD> -<TD WIDTH=10 ALIGN="RIGHT"> -(2)</TD></TR> -<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG - WIDTH="13" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img6.gif" - ALT="$\displaystyle \gamma$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="235" HEIGHT="33" ALIGN="MIDDLE" BORDER="0" - SRC="img7.gif" - ALT="$\displaystyle 0.577215\dots \mathrm{\hspace{5mm}(Euler's\ constant)}$"></TD> -<TD WIDTH=10 ALIGN="RIGHT"> -(3)</TD></TR> -<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG - WIDTH="18" HEIGHT="33" ALIGN="MIDDLE" BORDER="0" - SRC="img8.gif" - ALT="$\displaystyle \gamma'$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="143" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img9.gif" - ALT="$\displaystyle 0.422784\dots = 1 - \gamma$"></TD> -<TD WIDTH=10 ALIGN="RIGHT"> -(4)</TD></TR> -<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG - WIDTH="24" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img10.gif" - ALT="$\displaystyle \epsilon , \bar{\epsilon}$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="187" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" - SRC="img11.gif" - ALT="$\displaystyle \mbox{actual/average energy loss}$"></TD> -<TD WIDTH=10 ALIGN="RIGHT"> -(5)</TD></TR> -</TABLE></DIV> -<BR CLEAR="ALL"><P></P> - -<P> -Since <A HREF="sampleMath.html#xiEmax">2</A> and <A HREF="sampleMath.html#eqn:stress-sr">6</A> hold for arbitrary -<!-- MATH - $\delta\mathbf{c}$ - --> -<IMG - WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" - SRC="img12.gif" - ALT="$\delta\mathbf{c}$">-vectors, -it is clear that -<!-- MATH - $\mathcal{N}(A) = \mathcal{R}(B)$ - --> -<IMG - WIDTH="104" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" - SRC="img13.gif" - ALT="$\mathcal{N}(A) = \mathcal{R}(B)$"> and that when <IMG - WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" - SRC="img14.gif" - ALT="$y=B(x)$"> one has... -<BR> -...the <A NAME="tex2html4" - HREF="http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pythagoras.html">Pythagorians</A> knew infinitely many solutions in integers to <IMG - WIDTH="88" HEIGHT="33" ALIGN="MIDDLE" BORDER="0" - SRC="img15.gif" - ALT="$a^2+b^2=c^2$">. -That no non-trivial integer solutions exist for <IMG - WIDTH="93" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" - SRC="img16.gif" - ALT="$a^n+b^n=c^n$"> with integers <IMG - WIDTH="43" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img17.gif" - ALT="$n>2$"> has long -been suspected (<A NAME="tex2html5" - HREF="http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.html">Fermat, c.1637</A>). Only during the current decade has this been proved (<A NAME="tex2html6" - HREF="http://www.pbs.org:80/wgbh/nova/proof">Wiles, 1995</A>). - -<P> -<BR> -<DIV ALIGN="CENTER"><A NAME="eqn:stress-sr"></A> - -<!-- MATH - \begin{eqnarray} -V \mathbf{\pi}^{sr} & = & \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i - + \sum_i \sum_{j>i} \mathbf{R}_{ij} \mathbf{F}_{ij}\right> \\\nonumber - & = & \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i - + \sum_{i}\sum_{j>i}\sum_\alpha\sum_\beta \mathbf{r}_{i\alpha j\beta}\mathbf{f}_{i\alpha j\beta} - - \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} \right> -\end{eqnarray} - --> - -<TABLE ALIGN="CENTER" CELLPADDING="0" WIDTH="100%"> -<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG - WIDTH="40" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" - SRC="img18.gif" - ALT="$\displaystyle V \mathbf{\pi}^{sr}$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="233" HEIGHT="63" ALIGN="MIDDLE" BORDER="0" - SRC="img19.gif" - ALT="$\displaystyle \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i -+ \sum_i \sum_{j>i} \mathbf{R}_{ij} \mathbf{F}_{ij}\right>$"></TD> -<TD WIDTH=10 ALIGN="RIGHT"> -(6)</TD></TR> -<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"> </TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="418" HEIGHT="63" ALIGN="MIDDLE" BORDER="0" - SRC="img20.gif" - ALT="$\displaystyle \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i -+ \sum_{i}\sum_{j>i}\... -... j\beta} -- \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} \right>$"></TD> -<TD WIDTH=10 ALIGN="RIGHT"> - </TD></TR> -</TABLE></DIV> -<BR CLEAR="ALL"><P></P> -<BR><HR> -<!--Table of Child-Links--> -<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A> - -<UL> -<LI><A NAME="tex2html11" - HREF="node1.html">About this document ...</A> -</UL> -<!--End of Table of Child-Links--> -<BR><HR> -<ADDRESS> -<I>Michel Goossens</I> -<BR><I>1999-03-30</I> -</ADDRESS> -</BODY> -</HTML> |