diff options
Diffstat (limited to 'Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath')
29 files changed, 1004 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/WARNINGS b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/WARNINGS new file mode 100644 index 00000000000..9d1d9f764ee --- /dev/null +++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/WARNINGS @@ -0,0 +1,2 @@ + +redefining command \d diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/images.pl b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/images.pl new file mode 100644 index 00000000000..a319f5c597b --- /dev/null +++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/images.pl @@ -0,0 +1,132 @@ +# LaTeX2HTML 99.1 release (March 30, 1999) +# Associate images original text with physical files. + + +$key = q/displaystylefrac{epsilon-bar{epsilon}}{xi}-gamma'-beta^2-lnfrac{xi}{E_{{rm{max}};MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="185" HEIGHT="51" ALIGN="MIDDLE" BORDER="0" + SRC="img5.gif" + ALT="$\displaystyle \frac{\epsilon -\bar{\epsilon} }{\xi} +- \gamma' - \beta^2 - \ln \frac{\xi} {E_{\rm max}}$">|; + +$key = q/a^2+b^2=c^2;MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="88" HEIGHT="33" ALIGN="MIDDLE" BORDER="0" + SRC="img15.gif" + ALT="$a^2+b^2=c^2$">|; + +$key = q/n>2;MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="43" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" + SRC="img17.gif" + ALT="$n>2$">|; + +$key = q/y=B(x);MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" + SRC="img14.gif" + ALT="$y=B(x)$">|; + +$key = q/mathcal{N}(A)=mathcal{R}(B);MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="104" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" + SRC="img13.gif" + ALT="$\mathcal{N}(A) = \mathcal{R}(B)$">|; + +$key = q/displaystylelambda;MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="13" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img4.gif" + ALT="$\displaystyle \lambda$">|; + +$key = q/displaystyle0.577215dotsmathrm{hspace{5mm}(Euler'sconstant)};MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="235" HEIGHT="33" ALIGN="MIDDLE" BORDER="0" + SRC="img7.gif" + ALT="$\displaystyle 0.577215\dots \mathrm{\hspace{5mm}(Euler's\ constant)}$">|; + +$key = q/displaystylegamma;MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="13" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" + SRC="img6.gif" + ALT="$\displaystyle \gamma$">|; + +$key = q/displaystylefrac{1}{2pii}int^{c+iinfty}_{c-iinfty}expleft(ulnu+lambdauright)duhspace{1cm}mbox{for}cgeq0;MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="325" HEIGHT="58" ALIGN="MIDDLE" BORDER="0" + SRC="img3.gif" + ALT="$\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$">|; + +$key = q/displaystylembox{actualslashaverageenergyloss};MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="187" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" + SRC="img11.gif" + ALT="$\displaystyle \mbox{actual/average energy loss}$">|; + +$key = q/displaystyleleft<sum_iM_imathbf{V}_imathbf{V}_i+sum_isum_{j>i}mathbf{R}_{ij}mathbf{F}_{ij}right>;MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="233" HEIGHT="63" ALIGN="MIDDLE" BORDER="0" + SRC="img19.gif" + ALT="$\displaystyle \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i ++ \sum_i \sum_{j>i} \mathbf{R}_{ij} \mathbf{F}_{ij}\right>$">|; + +$key = q/displaystylegamma';MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="18" HEIGHT="33" ALIGN="MIDDLE" BORDER="0" + SRC="img8.gif" + ALT="$\displaystyle \gamma'$">|; + +$key = q/a^n+b^n=c^n;MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="93" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img16.gif" + ALT="$a^n+b^n=c^n$">|; + +$key = q/textstyle=;MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" + SRC="img2.gif" + ALT="$\textstyle =$">|; + +$key = q/displaystyleepsilon,bar{epsilon};MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="24" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" + SRC="img10.gif" + ALT="$\displaystyle \epsilon , \bar{\epsilon}$">|; + +$key = q/displaystyleleft<sum_iM_imathbf{V}_imathbf{V}_i+sum_{i}sum_{j>i}sum_alphasum_betalphajbeta}-sum_isum_alphamathbf{p}_{ialpha}mathbf{f}_{ialpha}right>;MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="418" HEIGHT="63" ALIGN="MIDDLE" BORDER="0" + SRC="img20.gif" + ALT="$\displaystyle \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i ++ \sum_{i}\sum_{j>i}\... +... j\beta} +- \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} \right>$">|; + +$key = q/deltamathbf{c};MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img12.gif" + ALT="$\delta\mathbf{c}$">|; + +$key = q/displaystyle0.422784dots=1-gamma;MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="143" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" + SRC="img9.gif" + ALT="$\displaystyle 0.422784\dots = 1 - \gamma$">|; + +$key = q/displaystylephi(lambda);MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" + SRC="img1.gif" + ALT="$\displaystyle \phi(\lambda)$">|; + +$key = q/displaystyleVmathbf{pi}^{sr};MSF=1.6;AAT/; +$cached_env_img{$key} = q|<IMG + WIDTH="40" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" + SRC="img18.gif" + ALT="$\displaystyle V \mathbf{\pi}^{sr}$">|; + +1; + diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/images.tex b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/images.tex new file mode 100644 index 00000000000..9b738e34b59 --- /dev/null +++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/images.tex @@ -0,0 +1,254 @@ +\batchmode +\documentclass[a4paper,twoside]{article} + +\usepackage{html} + +% +\renewcommand{\d}{\partial}% +\providecommand{\bm}[1]{\mathbf{#1}}% +\providecommand{\Range}{\mathcal{R}}% +\providecommand{\Ker}{\mathcal{N}}% +\providecommand{\Quat}{\vec{\mathbf{Q}}} +% +\providecommand{\StAndrews}{\htmlurl{http://www-groups.dcs.st-and.ac.uk/~history}}%% +\providecommand{\Pythagorians}{\htmladdnormallink + {Pythagorians}{\htmlurl{http://www-groups.dcs.st-and.ac.uk/~history}/Mathematicians/Pythagoras.html}}% +\providecommand{\Fermat}{\htmladdnormallink + {Fermat, c.1637}{\htmlurl{http://www-groups.dcs.st-and.ac.uk/~history}/HistTopics/Fermat's_last_theorem.html}}% +\providecommand{\Wiles}{\htmladdnormallink + {Wiles, 1995}{\htmlurl{http://www.pbs.org:80/wgbh/nova/proof}}} + +\usepackage[dvips]{color} +\pagecolor[gray]{.7} + + + +\makeatletter + +\makeatletter +\count@=\the\catcode`\_ \catcode`\_=8 +\newenvironment{tex2html_wrap}{}{} \catcode`\_=\count@ +\newcommand{\renewedcommand}[1]{\expandafter\renewcommand\csname #1\endcsname}% +\makeatother +\let\mathon=$ +\let\mathoff=$ +\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi +\newbox\sizebox +\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt} +\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt} +\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt} +\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt} +\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt} +\setlength{\textwidth}{349pt} +\newwrite\lthtmlwrite +\makeatletter +\let\realnormalsize=\normalsize +\global\topskip=2sp +\def\preveqno{}\let\real@float=\@float \let\realend@float=\end@float +\def\@float{\let\@savefreelist\@freelist\real@float} +\def\end@float{\realend@float\global\let\@freelist\@savefreelist} +\let\real@dbflt=\@dbflt \let\end@dblfloat=\end@float +\let\@largefloatcheck=\relax +\let\if@boxedmulticols=\iftrue +\def\@dbflt{\let\@savefreelist\@freelist\real@dbflt} +\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize + \parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}% + \def\phantompar{\csname par\endcsname}\normalsize}% +\def\lthtmltypeout#1{{\let\protect\string\immediate\write\lthtmlwrite{#1}}}% +\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup\kern.05em }% +\newcommand\lthtmlhboxmathB{\adjustnormalsize\setbox\sizebox=\hbox to\hsize\bgroup\hfill }% +\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup % + \let\ifinner=\iffalse }% +\newcommand\lthtmlboxmathZ{\@next\next\@currlist{}{\def\next{\voidb@x}}% + \expandafter\box\next\egroup}% +\newcommand\lthtmlmathtype[1]{\def\lthtmlmathenv{#1}}% +\newcommand\lthtmllogmath{\lthtmltypeout{l2hSize % +:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}% +\newcommand\lthtmlfigureA[1]{\let\@savefreelist\@freelist + \lthtmlmathtype{#1}\lthtmlvboxmathA}% +\newcommand\lthtmlpictureA[1]{\let\@savefreelist\@freelist + \lthtmlmathtype{#1}\lthtmlhboxmathB}% +\newcommand\lthtmlpictureZ[1]{\hfill\lthtmlfigureZ}% +\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox + \global\let\@freelist\@savefreelist}% +\newcommand\lthtmldisplayA[1]{\lthtmlmathtype{#1}\lthtmlvboxmathA}% +\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}% + \lthtmldisplayA{#1}\let\@eqnnum\relax}% +\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}% +\newcommand\lthtmlinlinemathA[1]{\lthtmlmathtype{#1}\lthtmlhboxmathA + \vrule height1.5ex width0pt }% +\newcommand\lthtmlinlineA[1]{\lthtmlmathtype{#1}\lthtmlhboxmathA}% +\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt % + \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline} +\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt % + \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath} +\newcommand\lthtmlindisplaymathZ{\egroup % + \centerinlinemath\lthtmllogmath\lthtmlsetmath} +\def\lthtmlsetinline{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{% + \kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi + \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}} +\def\lthtmlsetmath{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{% + \kern.1em\kern0.8 pt\hbox{\hglue.17em\copy\sizebox\hglue0.8 pt}}\kern.3pt% + \ifdim\dp\sizebox>0pt\kern.1em\fi \kern0.8 pt% + \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}} +\def\centerinlinemath{% + \dimen1=\ifdim\ht\sizebox<\dp\sizebox \dp\sizebox\else\ht\sizebox\fi + \advance\dimen1by.5pt \vrule width0pt height\dimen1 depth\dimen1 + \dp\sizebox=\dimen1\ht\sizebox=\dimen1\relax} + +\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize + \ifdim\wd\sizebox<\hsize\expandafter\hfill\fi \expandafter\vfill + \else\expandafter\vss\fi}% +\providecommand{\selectlanguage}[1]{}% +\makeatletter \tracingstats = 1 + + +\begin{document} +\pagestyle{empty}\thispagestyle{empty}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength hsize=\the\hsize}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength vsize=\the\vsize}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength voffset=\the\voffset}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength topskip=\the\topskip}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength headheight=\the\headheight}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength headsep=\the\headsep}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength parskip=\the\parskip}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength oddsidemargin=\the\oddsidemargin}\lthtmltypeout{}% +\makeatletter +\if@twoside\lthtmltypeout{latex2htmlLength evensidemargin=\the\evensidemargin}% +\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi% +\lthtmltypeout{}% +\makeatother +\setcounter{page}{1} +\onecolumn + +% !!! IMAGES START HERE !!! + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay173}% +$\displaystyle \phi(\lambda)$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay174}% +$\textstyle =$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay175}% +$\displaystyle \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\infty} +\exp \left( u \ln u + \lambda u \right ) du \hspace{1cm}\mbox{for } c \geq 0$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay176}% +$\displaystyle \lambda$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay178}% +$\displaystyle \frac{\epsilon -\bar{\epsilon} }{\xi} +- \gamma' - \beta^2 - \ln \frac{\xi} {E_{\rm max}}$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay179}% +$\displaystyle \gamma$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay181}% +$\displaystyle 0.577215\dots \mathrm{\hspace{5mm}(Euler's\ constant)}$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay182}% +$\displaystyle \gamma'$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay184}% +$\displaystyle 0.422784\dots = 1 - \gamma$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay185}% +$\displaystyle \epsilon , \bar{\epsilon}$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay187}% +$\displaystyle \mbox{actual/average energy loss}$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline112}% +$\delta\mathbf{c}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline114}% +$\mathcal{N}(A) = \mathcal{R}(B)$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline116}% +$y=B(x)$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline118}% +$a^2+b^2=c^2$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline120}% +$a^n+b^n=c^n$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline122}% +$n>2$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay195}% +$\displaystyle V \mathbf{\pi}^{sr}$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay197}% +$\displaystyle \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i ++ \sum_i \sum_{j>i} \mathbf{R}_{ij} \mathbf{F}_{ij}\right>$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_indisplay199}% +$\displaystyle \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i ++ \sum_{i}\sum_{j>i}\sum_\alpha\sum_\beta \mathbf{r}_{i\alpha j\beta}\mathbf{f}_{i\alpha j\beta} +- \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} \right>$% +\lthtmlindisplaymathZ +\lthtmlcheckvsize\clearpage} + + +\end{document} diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/img1.gif b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/img1.gif Binary files differnew file mode 100644 index 00000000000..5916d47b1f4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/img1.gif diff --git 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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> diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/internals.pl b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/internals.pl new file mode 100644 index 00000000000..129a18c5241 --- /dev/null +++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/internals.pl @@ -0,0 +1,14 @@ +# LaTeX2HTML 99.1 release (March 30, 1999) +# Associate internals original text with physical files. + + +$key = q/xiEmax/; +$ref_files{$key} = "$dir".q|sampleMath.html|; +$noresave{$key} = "$nosave"; + +$key = q/eqn:stress-sr/; +$ref_files{$key} = "$dir".q|sampleMath.html|; +$noresave{$key} = "$nosave"; + +1; + diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/labels.pl b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/labels.pl new file mode 100644 index 00000000000..47f50cc587b --- /dev/null +++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/labels.pl @@ -0,0 +1,29 @@ +# LaTeX2HTML 99.1 release (March 30, 1999) +# Associate labels original text with physical files. + + +$key = q/xiEmax/; +$external_labels{$key} = "$URL/" . q|sampleMath.html|; +$noresave{$key} = "$nosave"; + +$key = q/eqn:stress-sr/; +$external_labels{$key} = "$URL/" . q|sampleMath.html|; +$noresave{$key} = "$nosave"; + +1; + + +# LaTeX2HTML 99.1 release (March 30, 1999) +# labels from external_latex_labels array. + + +$key = q/xiEmax/; +$external_latex_labels{$key} = q|2|; +$noresave{$key} = "$nosave"; + +$key = q/eqn:stress-sr/; +$external_latex_labels{$key} = q|6|; +$noresave{$key} = "$nosave"; + +1; + diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/node1.html b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/node1.html new file mode 100644 index 00000000000..35ab2f29258 --- /dev/null +++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/node1.html @@ -0,0 +1,72 @@ +<!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>About this document ...</TITLE> +<META NAME="description" CONTENT="About this document ..."> +<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="previous" HREF="sampleMath.html"> +<LINK REL="up" HREF="sampleMath.html"> +</HEAD> + +<BODY > +<!--Navigation Panel--> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" + SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/next_motif_gr.gif"> +<A NAME="tex2html16" + HREF="sampleMath.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" + SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/up_motif.gif"></A> +<A NAME="tex2html12" + HREF="sampleMath.html"> +<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" + SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/previous_motif.gif"></A> +<BR> +<B> Up:</B> <A NAME="tex2html17" + HREF="sampleMath.html">sampleMath</A> +<B> Previous:</B> <A NAME="tex2html13" + HREF="sampleMath.html">sampleMath</A> +<BR> +<BR> +<!--End of Navigation Panel--> + +<H1><A NAME="SECTION00010000000000000000"> +About this document ...</A> +</H1> + <P> +This document was generated using the +<A HREF="http://www-dsed.llnl.gov/files/programs/unix/latex2html/manual/"><STRONG>LaTeX</STRONG>2<tt>HTML</tt></A> translator Version 99.1 release (March 30, 1999) +<P> +Copyright © 1993, 1994, 1995, 1996, +<A HREF="http://cbl.leeds.ac.uk/nikos/personal.html">Nikos Drakos</A>, +Computer Based Learning Unit, University of Leeds. +<BR> +Copyright © 1997, 1998, 1999, +<A HREF="http://www.maths.mq.edu.au/~ross/">Ross Moore</A>, +Mathematics Department, Macquarie University, Sydney. +<P> +The command line arguments were: <BR> + <STRONG>latex2html</STRONG> <TT>sampleMath</TT> +<P> +The translation was initiated by Michel Goossens on 1999-03-30 +<BR><HR> +<ADDRESS> +<I>Michel Goossens</I> +<BR><I>1999-03-30</I> +</ADDRESS> +</BODY> +</HTML> diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/sampleMath.css b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/sampleMath.css new file mode 100644 index 00000000000..1993b851311 --- /dev/null +++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/sampleMath.css @@ -0,0 +1,31 @@ + +/* Century Schoolbook font is very similar to Computer Modern Math: cmmi */ +.MATH { font-family: "Century Schoolbook", serif; } +.MATH I { font-family: "Century Schoolbook", serif; font-shape: italic } +.BOLDMATH { font-family: "Century Schoolbook", serif; font-weight: bold } + +/* implement both fixed-size and relative sizes */ +SMALL.XTINY { font-size : xx-small } +SMALL.TINY { font-size : x-small } +SMALL.SCRIPTSIZE { font-size : smaller } +SMALL.FOOTNOTESIZE { font-size : small } +SMALL.SMALL { } +BIG.LARGE { } +BIG.XLARGE { font-size : large } +BIG.XXLARGE { font-size : x-large } +BIG.HUGE { font-size : larger } +BIG.XHUGE { font-size : xx-large } + +/* heading styles */ +H1 { } +H2 { } +H3 { } +H4 { } +H5 { } + +/* mathematics styles */ +DIV.displaymath { } /* math displays */ +TD.eqno { } /* equation-number cells */ + + +/* document-specific styles come next */ diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/sampleMath.html b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/sampleMath.html new file mode 100644 index 00000000000..47104a5ce76 --- /dev/null +++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/sampleMath.html @@ -0,0 +1,235 @@ +<!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> |