%%%%%%%%%%%%%%%%%%%%%%%%%%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 
