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+%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% This is proc2e.sty.
+% This file may be freely distributed but may not be altered in any way.
+% Any comments or questions regarding these macros should be directed to:
+
+% Corey Gray
+% SIAM
+% 3600 University City Science Center
+% Philadelphia, PA 19104-2688
+% USA
+% Telephone: (215) 382-9800
+% Fax: (215) 386-7999
+% e-mail: gray@siam.org
+
+% This is a file of macros and definitions for creating a chapter for
+% publication in the SIAM Proceedings series using LaTeX2e.
+
+% Report the version.
+\message{*** SIAM LaTeX2e Proceedings Series macro package, version 1.1,
+October 28, 1996 ***}
+
+\pretolerance=800
+\tolerance=10000
+\sloppy
+
+
+\vsize=56pc
+\hsize=36pc
+\baselineskip=13pt
+\hoffset -.5in
+\voffset -.5in
+\footskip=18pt
+\topmargin 24pt
+\headheight 12pt
+\headsep 15pt
+\textheight 53.5pc \advance\textheight by \topskip
+\textwidth 36pc
+\parskip 0pt
+\parindent 18pt
+\def\topfraction{.9}
+\def\textfraction{.1}
+\def\topnumber{2}
+%% footnotes to be set 8/10
+\def\footnotesize{\@setsize\footnotesize{11pt}\ixpt\@ixpt
+ % \indent
+ \abovedisplayskip \z@
+ \belowdisplayskip\z@
+ \abovedisplayshortskip\abovedisplayskip
+ \belowdisplayshortskip\belowdisplayshortskip
+\def\@listi{\leftmargin\leftmargini \topsep 3pt plus 1pt minus 1pt
+ \parsep 2pt plus 1pt minus 1pt
+ \itemsep \parsep}}
+
+\let\referencesize\footnotesize
+
+\footnotesep 0pt
+
+\skip\footins 12pt plus 12pt
+
+\def\footnoterule{\kern3\p@ \hrule width 3em\vspace{3pt}} % the \hrule is .4pt high
+
+
+\def\ps@plain{\let\@mkboth\@gobbletwo
+ \def\@oddfoot{{\hfil\small\thepage\hfil}}%
+ \def\@oddhead{}
+ \def\@evenhead{}\def\@evenfoot{}}
+
+
+
+\def\ps@headings{\let\@mkboth\markboth
+ \def\@oddfoot{}\def\@evenfoot{}%
+ \def\@evenhead{{\rm\thepage}\hspace*{2pc}{\sc\leftmark}\hfil}%
+ \def\@oddhead{\hfil{\noindent\sc\rightmark}\hspace*{2pc}{\rm\thepage}}%
+
+
+
+\def\ps@myheadings{\let\@mkboth\@gobbletwo
+ \def\@oddfoot{}\def\@evenfoot{}%
+ \def\@oddhead{\hfil{\sc\rightmark}\hspace*{2pc}{\normalsize\rm\thepage}}%
+ \def\@evenhead{{\normalsize\rm\thepage}\hspace*{2pc}{\sc\leftmark}\hfil}%
+% \def\chaptermark##1{}%
+ % \def\sectionmark##1{}\def\subsectionmark##1{}}
+}}
+
+
+
+\def\theequation{\arabic{equation}}
+
+\def\abstract{\if@twocolumn
+\section*{Abstract}
+\else \small
+\begin{center}
+{\bf Abstract\vspace{-.5em}\vspace{3pt}}
+\end{center}
+\quotation
+\fi}
+\def\endabstract{\if@twocolumn\else\endquotation\fi}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% THEOREMS, PROOFS, ALGORITHMS %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%% defined proof environment by theorem model (took out counter)
+
+\def\qed{{\qquad \vbox{\hrule\hbox{%
+ \vrule height1.3ex\hskip0.8ex\vrule}\hrule
+ }}\par}
+
+\def\newproof#1{\@nprf{#1}}
+
+\def\@nprf#1#2{\@xnprf{#1}{#2}}
+
+\def\@xnprf#1#2{\expandafter\@ifdefinable\csname #1\endcsname
+\global\@namedef{#1}{\@prf{#1}{#2}}\global\@namedef{end#1}{\@endproof}}
+
+\def\@prf#1#2{\@xprf{#1}{#2}}
+
+\def\@xprf#1#2{\@beginproof{#2}{\csname the#1\endcsname}\ignorespaces}
+
+
+
+%%% defined algorithm environment by theorem model
+
+\def\newalgorithm#1{\@ifnextchar[{\@oalg{#1}}{\@nalg{#1}}}
+
+\def\@nalg#1#2{%
+\@ifnextchar[{\@xnalg{#1}{#2}}{\@ynalg{#1}{#2}}}
+
+\def\@xnalg#1#2[#3]{\expandafter\@ifdefinable\csname #1\endcsname
+{\@definecounter{#1}\@addtoreset{#1}{#3}%
+\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand
+ \csname the#3\endcsname \@thmcountersep \@thmcounter{#1}}%
+\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}}
+
+\def\@ynalg#1#2{\expandafter\@ifdefinable\csname #1\endcsname
+{\@definecounter{#1}%
+\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
+\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}}
+
+\def\@oalg#1[#2]#3{\expandafter\@ifdefinable\csname #1\endcsname
+ {\global\@namedef{the#1}{\@nameuse{the#2}}%
+\global\@namedef{#1}{\@alg{#2}{#3}}%
+\global\@namedef{end#1}{\@endalgorithm}}}
+
+\def\@alg#1#2{\refstepcounter
+ {#1}\@ifnextchar[{\@yalg{#1}{#2}}{\@xalg{#1}{#2}}}
+
+\def\@xalg#1#2{\@beginalgorithm{#2}{\csname the#1\endcsname}\ignorespaces}
+\def\@yalg#1#2[#3]{\@opargbeginalgorithm{#2}{\csname
+ the#1\endcsname}{#3}\ignorespaces}
+
+
+
+
+\def\@beginproof#1{\rm {\it #1.\ }}
+\def\@endproof{\outerparskip 0pt\endtrivlist}
+
+\def\@begintheorem#1#2{\it {\sc #1\ #2.\ }}
+\def\@opargbegintheorem#1#2#3{\it
+ {\sc #1\ #2\ (#3).\ }}
+\def\@endtheorem{\outerparskip 0pt\endtrivlist}
+
+%\def\@begindefinition#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]}
+%\def\@opargbegindefinition#1#2#3{\rm \trivlist
+% \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]}
+%\def\@enddefinition{\outerparskip 0pt\endtrivlist}
+
+
+\def\@beginalgorithm#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]}
+\def\@opargbeginalgorithm#1#2#3{\rm \trivlist
+ \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]}
+\def\@endalgorithm{\outerparskip 6pt\endtrivlist}
+
+
+\newskip\outerparskip
+
+%\def\trivlist{\parsep\outerparskip
+% \@trivlist \labelwidth\z@ \leftmargin\z@
+% \itemindent\parindent \def\makelabel##1{##1}}
+%
+%\def\@trivlist{\topsep=0pt\@topsepadd\topsep
+% \if@noskipsec \leavevmode \fi
+% \ifvmode \advance\@topsepadd\partopsep \else \unskip\par\fi
+% \if@inlabel \@noparitemtrue \@noparlisttrue
+% \else \@noparlistfalse \@topsep\@topsepadd \fi
+% \advance\@topsep \parskip
+% \leftskip\z@\rightskip\@rightskip \parfillskip\@flushglue
+% \@setpar{\if@newlist\else{\@@par}\fi}%
+% \global\@newlisttrue \@outerparskip\parskip}
+%
+%
+%\def\endtrivlist{\if@newlist\@noitemerr\fi
+% \if@inlabel\indent\fi
+% \ifhmode\unskip \par\fi
+% \if@noparlist \else
+% \ifdim\lastskip >\z@ \@tempskipa\lastskip \vskip -\lastskip
+% \advance\@tempskipa\parskip \advance\@tempskipa -\@outerparskip
+% \vskip\@tempskipa
+% \fi\@endparenv\fi
+% \vskip\outerparskip}
+
+
+
+ \newproof{@proof}{Proof}
+ \newenvironment{proof}{\begin{@proof}}{\end{@proof}}
+
+ \newtheorem{@theorem}{Theorem}[section]
+ \newenvironment{theorem}{\begin{@theorem}}{\end{@theorem}}
+
+% \newalgorithm{@algorithm}{Algorithm}[section]
+% \newenvironment{algorithm}{\begin{@algorithm}}{\end{@algorithm}}
+
+
+
+\newtheorem{lemma}{Lemma}[section]
+\newtheorem{fact}{Fact}[section]
+\newtheorem{corollary}{Corollary}[section]
+\newtheorem{axiom}{Axiom}[section]
+\newtheorem{cond}{Condition}[section]
+\newtheorem{property}{Property}[section]
+\newtheorem{proposition}{Proposition}[section]
+
+\newtheorem{Conjecture}{Conjecture}[section]
+\newtheorem{Definition}{Definition}[section]
+\newtheorem{Lemma}{Lemma}[section]
+\newtheorem{Remark}{Remark}[section]
+
+\newproof{Example}{Example}
+\newproof{Method}{Method}
+\newproof{Exercise}{Exercise}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% TABLE AND FIGURE CAPTIONS %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \def\@figtxt{figure}
+\long\def\@makecaption#1#2{\small
+\setlength{\parindent}{18pt}
+\baselineskip 14pt
+ \ifx\@captype\@figtxt
+ \vskip 10pt
+ \setbox\@tempboxa\hbox{{\sc #1} {\it #2}}
+ \ifdim \wd\@tempboxa >\hsize {\sc #1} {\it #2}\par \else \hbox
+to\hsize{\hfil\box\@tempboxa\hfil}%
+ \fi\else\hbox to\hsize{\hfil{\sc #1}\hfil}%
+ \setbox\@tempboxa\hbox{{\it #2}}%
+ \ifdim \wd\@tempboxa >\hsize {\it #2}\par \else
+ \hbox to \hsize{\hfil\box\@tempboxa\hfil}\fi
+ \vskip 10pt
+ \fi}
+
+
+%\newif\iftable \global\tablefalse
+
+
+%\long\def\@makecaption#1#2{%
+%\setlength{\parindent}{18pt}
+% \vskip 12pt
+% \iftable
+ % \hbox to \hsize{\hfil\sc #1\hfil}
+ % \hbox to \hsize{\hfil\it #2\hfil}
+ % \global\tablefalse
+ % \else
+ % \setbox\@tempboxa\hbox{{\small#1} {\small\it#2}}
+ % \ifdim \wd\@tempboxa >\hsize
+ % \indent{\small#1}{\small\it#2}\par
+ % \else
+ % \hbox to\hsize{\hfil\box\@tempboxa\hfil}\fi
+ % \fi}
+% \vskip 6pt}
+
+
+
+%\def\figure{\global\tablefalse\@float{figure}}
+\def\fnum@figure{\par\sc Fig. \thefigure.\ }
+%\def\fnum@figure{\par\sc Fig. \thefigure\ }
+
+%\def\table{\global\tabletrue\@float{table}}
+\def\fnum@table{\small \sc Table \thetable}
+
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% SECTIONS %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\def\section{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus
+ -.2ex}%{2.3ex plus .2ex}
+{2pt}{\large\bf}}
+\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus -1ex minus
+ -.2ex}%{1.5ex plus .2ex}
+{2pt}{\large\bf}}
+\def\subsubsection{\@startsection {subsubsection}{3}{\z@}{1.3ex plus .5ex minus
+ .2ex}{-.5em plus -.1em}{\normalsize\bf}}
+
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% %%
+%% BIBLIOGRAPHY %%
+%% %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+\def\thebibliography#1{%
+%\cleardoublepage
+\parindent 0em
+\vspace{9pt}
+\begin{flushleft}\large\bf {References}\end{flushleft}
+\addvspace{3pt}\nopagebreak\list
+ %% default is no labels, for those not using \cite or BibTeX
+{[\arabic{enumi}]} {\settowidth\labelwidth{[#1]}
+%%{[\arabic{enumi}]}{\settowidth\labelwidth{mm}
+\leftmargin\labelwidth
+\leftmargin=17pt
+ \advance\leftmargin\labelsep
+ \usecounter{enumi}\@bibsetup}
+\def\newblock{\hskip .11em plus .33em minus -.07em}
+ \sloppy\clubpenalty4000\widowpenalty4000
+ \sfcode`\.=1000\relax}
+
+
+
+%% setup 8/10 type
+\def\@bibsetup{%\itemindent=0pt
+\itemsep=0pt \parsep=0pt
+\small}
+
+\def\sameauthor{\leavevmode\vrule height 2pt depth -1.6pt width 23pt}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% INDEX %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%makeindex.sty official version 6.4
+%The second line came from /usr/misc/lib/tex82/report.sty.
+
+\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi
+\columnseprule \z@
+\columnsep 35pt\twocolumn[\chapter*{Index}]
+ \parskip\z@ plus .3pt\relax\let\item\@idxitem}
+
+
+\def\printindex{\cleardoublepage\markboth{INDEX}{INDEX}
+\addcontentsline{toc}{chapter}{Index}\@input{\jobname.ind}}
+
+\ps@headings
+
+
+%%% end of style file