% File modified 3/92 by G. W. Stewart to handle conference proceedings
% for the Institute for Mathematics and Its Applications.
% The basic modifications are to add a contribution environment
% (in ima10.sty).  The references and citation labels for
% each contribution are supplemented by a user-supplied
% identifier to make them unique.  Provisions are made
% for global references.

% Modifications Copyright 1992 by G. W. Stewart. All rights reserved.


%
%The following .sty file was used with the LaTeX source file.
%
% siam.sty 11 Feb 88, based on article.sty 5 Feb 88
% Changed to hardwire the right headings for publications
% Christian Bischof, 22January1990
\typeout{Document Style 'siam'. Released 11 February 1988}
\def\myoddhead{ }
\def\myevenhead{ }

\def\@ptsize{0} \@namedef{ds@11pt}{\def\@ptsize{1}}
\@namedef{ds@12pt}{\def\@ptsize{2}} 
\def\ds@twoside{\@twosidetrue \@mparswitchtrue} \def\ds@draft{\overfullrule
5pt} 
\@options
%\input /ima/smith/conf/jan92/ima1\@ptsize.sty\relax
\input ima10.sty

% Enumerate labels arabic all the way down
\def\labelenumi{\arabic{enumi}.}
\def\theenumi{\arabic{enumi}}
\def\labelenumii{\arabic{enumii}.}
\def\theenumii{\arabic{enumii}}
\def\p@enumii{\theenumi.}
\def\labelenumiii{\arabic{enumiii}.}
\def\theenumiii{\arabic{enumiii}}
\def\p@enumiii{\theenumi.\theenumii.}
\def\labelenumiv{\arabic{enumiv}.}
\def\theenumiv{\arabic{enumiv}}
\def\p@enumiv{\p@enumiii.\theenumiii}

\def\labelitemi{$\bullet$}
\def\labelitemii{\bf --}
\def\labelitemiii{$\ast$}
\def\labelitemiv{$\cdot$}

\def\verse{\let\\=\@centercr 
 \list{}{\itemsep\z@ \itemindent -1.5em\listparindent \itemindent 
 \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}
\let\endverse\endlist
\def\quotation{\list{}{\listparindent 1.5em
 \itemindent\listparindent
 \rightmargin\leftmargin \parsep 0pt plus 1pt}\item[]}
\let\endquotation=\endlist
\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

\def\descriptionlabel#1{\hspace \labelsep \bf #1}
\def\description{\list{}{\labelwidth\z@ \itemindent -\leftmargin
\let\makelabel\descriptionlabel}}
\let\enddescription\endlist

\newcounter{part}
\newcounter{section}
\newcounter{subsection}[section]
\newcounter{subsubsection}[subsection]
\newcounter{paragraph}[subsubsection]
\newcounter{subparagraph}[paragraph]
\newcounter{sectn}

\def\thefigure{\thesection.\arabic{figure}}
\def\thetable{\thesection.\arabic{table}}

\def\@begintheorem#1#2{\par\bgroup{\sc #1\ #2. }\it\ignorespaces}
\def\@opargbegintheorem#1#2#3{\par\bgroup{\sc #1\ #2\ (#3). }\it\ignorespaces}
\def\@endtheorem{\egroup\par}
\def\proof{\par{\it Proof}. \ignorespaces}
\def\endproof{{\hfill \vbox{\hrule\hbox{%
   \vrule height1.3ex\hskip0.8ex\vrule}\hrule
  }}\par}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{corollary}{Corollary}[section]
\newtheorem{proposition}{Proposition}[section]
%%Kaye added
\newtheorem{definition}{Definition}[section]

\def\theequation{\arabic{equation}}
\def\@eqnnum{\hbox to .01pt{}\rlap{\rm \hskip -\displaywidth(\theequation)}}


\newif\ifnumbysec

\@addtoreset{equation}{section}
\@addtoreset{figure}{section}
\@addtoreset{table}{section}

\def\numberbysection{\numbysectrue
                     \renewcommand{\thesection}{\arabic{section}}
                     \renewcommand{\theequation}{\thesection.\arabic{equation}}
                     \renewcommand{\thetheorem}{\thesection.\arabic{theorem}}
                     \renewcommand{\thefigure}{\thesection.\arabic{figure}}
                     \renewcommand{\thetable}{\thesection.\arabic{table}}}

\def\ignoresections{\numbysecfalse
                    \renewcommand{\thesection}{\arabic{sectn}}
                    \renewcommand{\thesectn}{\arabic{sectn}}
                    \renewcommand{\theequation}{\arabic{equation}}
                    \renewcommand{\thetheorem}{\arabic{theorem}}
                    \renewcommand{\thefigure}{\arabic{figure}}
                    \renewcommand{\thetable}{\arabic{table}}}
\numberbysection



\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
 \else \newpage \fi \thispagestyle{empty}\c@page\z@}
\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}

\arraycolsep 5pt \tabcolsep 6pt \arrayrulewidth .4pt \doublerulesep 2pt 
\tabbingsep \labelsep 

\skip\@mpfootins = \skip\footins
\fboxsep = 3pt \fboxrule = .4pt 


\def\thepart{\Roman{part}} \def\thesection {\arabic{section}}
\def\thesubsection {\thesection.\arabic{subsection}}
\def\thesubsubsection {\thesubsection .\arabic{subsubsection}}
\def\theparagraph {\thesubsubsection.\arabic{paragraph}}
\def\thesubparagraph {\theparagraph.\arabic{subparagraph}}
\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
     \def\@svsec{}\else \ifnumbysec\refstepcounter{#1}
        \else\ifnum #2>1 \refstepcounter{#1}
        \else\refstepcounter{sectn}
             \setcounter{subsection}{0}
             \setcounter{subsubsection}{0}
             \setcounter{paragraph}{0}
             \setcounter{subparagraph}{0}
        \fi\fi
     \edef\@svsec{\csname the#1\endcsname.\hskip .5em }\fi
     \@tempskipa #5\relax
      \ifdim \@tempskipa>\z@ 
        \begingroup #6\relax
          \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}
        \endgroup
       \csname #1mark\endcsname{#7}\addcontentsline
         {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                      \protect\numberline{\csname the#1\endcsname}\fi
                    #7}\else
        \def\@svsechd{#6\hskip #3\@svsec #8.\csname #1mark\endcsname
                      {#7}\addcontentsline
                           {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                             \protect\numberline{\csname the#1\endcsname}\fi
                       #7}}\fi
     \@xsect{#5}}
\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax
   \ifdim \@tempskipa>\z@
     \begingroup #4\@hangfrom{\hskip #1}{\interlinepenalty \@M
#5.\par}\endgroup
   \else \def\@svsechd{#4\hskip #1\relax #5.}\fi
    \@xsect{#3}}


\def\ref#1{\imaref{#1\@cid}}
\def\imaref#1{\@ifundefined{r@#1}{{\bf ??}\@warning
   {Reference `#1' on page \thepage \space
    undefined}}{\edef\@tempa{\@nameuse{r@#1}}\expandafter
    \@car\@tempa \@nil\null}}

\def\pageref#1{\imapageref{#1\@cid}}
\def\imapageref#1{\@ifundefined{r@#1}{{\bf ??}\@warning
   {Reference `#1' on page \thepage \space
    undefined}}{\edef\@tempa{\@nameuse{r@#1}}\expandafter
    \@cdr\@tempa\@nil\null}}

\def\label#1{\imalabel{#1\@cid}}
\def\imalabel#1{\@bsphack\if@filesw {\let\thepage\relax
   \xdef\@gtempa{\write\@auxout{\string
      \newlabel{#1}{{\@currentlabel}{\thepage}}}}}\@gtempa
   \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack}

\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{0}

\def\tableofcontents{\section*{Contents\@mkboth{CONTENTS}{CONTENTS}}
 \@starttoc{toc}}
\def\l@part#1#2{\addpenalty{\@secpenalty}
 \addvspace{2.25em plus 1pt} \begingroup
 \@tempdima 3em \parindent \z@ \rightskip \@pnumwidth \parfillskip
-\@pnumwidth 
 {\bf \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}}\par
 \nobreak \endgroup}
\def\l@section#1#2{\addpenalty{\@secpenalty} \addvspace{1.0em plus 1pt}
\@tempdima 1.5em \begingroup
 \parindent \z@ \rightskip \@pnumwidth 
 \parfillskip -\@pnumwidth 
 \bf \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip #1\nobreak\hfil
\nobreak\hbox to\@pnumwidth{\hss #2}\par
 \endgroup}
\def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
\def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
\def\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
\def\l@subparagraph{\@dottedtocline{5}{10em}{5em}}
\def\listoffigures{\section*{List of Figures\@mkboth
 {LIST OF FIGURES}{LIST OF FIGURES}}\@starttoc{lof}}
\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
\def\listoftables{\section*{List of Tables\@mkboth
 {LIST OF TABLES}{LIST OF TABLES}}\@starttoc{lot}}
\let\l@table\l@figure

\def\@lbibitem[#1]#2{\imabibitem[#1]{#2\@cid}}
\def\@bibitem#1{\imabibitem{#1\@cid}}
\def\imabibitem{\@ifnextchar[{\@imalbibitem}{\@imabibitem}}

\def\@imalbibitem[#1]#2{\item[\@biblabel{#1}]\if@filesw
      { \def\protect##1{\string ##1\space}\immediate
        \write\@auxout{\string\bibcite{#2}{#1}}\fi\ignorespaces}}

\def\@imabibitem#1{\item\if@filesw \immediate\write\@auxout
       {\string\bibcite{#1}{\the\c@enumi}}\fi\ignorespaces}

\def\imacite{{\let\@cid=\relax\ifnextchar[{\@lcite}{\@nlcite}}}
\def\@lcite[#1]#2{\cite[#1]{#2}}
\def\@nlcite[#1]#2{\cite{#1}}

\def\@citex[#1]#2{\if@filesw\@for\@citeb:=#2\do
        {\immediate\write\@auxout{\string\citation{`\@citeb\@cid'}}}\fi
  \def\@citea{}\@cite{\@for\@citeb:=#2\do
    {\@citea\def\@citea{,}\@ifundefined
       {b@\@citeb\@cid}{{\bf ?}\@warning
       {Citation `\@citeb\@cid' on page \thepage \space undefined}}%
\hbox{\csname b@\@citeb\@cid\endcsname}}}{#1}}


\def\thebibliography#1{\par\addvspace{.25in}%
\begin{center}\small REFERENCES\end{center}\@mkboth
 {REFERENCES}{REFERENCES}\addvspace{.15in}\nopagebreak\list
 {[\arabic{enumi}]}{\settowidth\labelwidth{[#1]}\leftmargin\labelwidth
 \advance\leftmargin\labelsep \advance\leftmargin 16pt \itemindent -16pt
 \usecounter{enumi}}
 \def\newblock{\hskip .11em plus .33em minus .07em}
 \sloppy\clubpenalty4000\widowpenalty4000
 \sfcode`\.=1000\relax\footnotesize}
\let\endthebibliography=\endlist
 

\newif\if@restonecol
\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi
\columnseprule \z@
\columnsep 35pt\twocolumn[\section*{Index}]






\@mkboth{INDEX}{INDEX}\thispagestyle{plain}\parindent\z@
 \parskip\z@ plus .3pt\relax\let\item\@idxitem}
\def\@idxitem{\par\hangindent 40pt}
\def\subitem{\par\hangindent 40pt \hspace*{20pt}}
\def\subsubitem{\par\hangindent 40pt \hspace*{30pt}}
\def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi}
\def\indexspace{\par \vskip 10pt plus 5pt minus 3pt\relax}

\def\footnoterule{\kern-3\p@ 
 \hrule width .5in 
 \kern 2.6\p@} 

\long\def\@makefntext#1{\parindent .25in\noindent 
 \hbox to .25in{\hss$^{\@thefnmark}$\kern 3pt}#1}


\setcounter{topnumber}{2}
\def\topfraction{.7}
\setcounter{bottomnumber}{1}
\def\bottomfraction{.3}
\setcounter{totalnumber}{3}
\def\textfraction{.2}
\def\floatpagefraction{.5}
\setcounter{dbltopnumber}{2}
\def\dbltopfraction{.7}
\def\dblfloatpagefraction{.5}

\def\@figtxt{figure}
\long\def\@makecaption#1#2{\footnotesize
 \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}


\newcounter{figure}
\def\thefigure{\@arabic\c@figure}
\def\fps@figure{tp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{Fig.\ \thefigure}
\def\figure{\@float{figure}}
\let\endfigure\end@float
\@namedef{figure*}{\@dblfloat{figure}}
\@namedef{endfigure*}{\end@dblfloat}
\newcounter{table}
\def\thetable{\@arabic\c@table}
\def\fps@table{tp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{Table \thetable}
\def\table{\@float{table}}
\let\endtable\end@float
\@namedef{table*}{\@dblfloat{table}}
\@namedef{endtable*}{\end@dblfloat}


\def\maketitle{\par
 \begingroup
 \def\thefootnote{\fnsymbol{footnote}}
 \def\@makefnmark{\hbox 
 to 0pt{$^{\@thefnmark}$\hss}} 
 \if@twocolumn 
 \twocolumn[\@maketitle] 
 \else %%%% commented out for \newpage
 \global\@topnum\z@ \@maketitle \fi\thispagestyle{plain}\@thanks
 \endgroup
 \setcounter{footnote}{0}
% \let\maketitle\relax
% \let\@maketitle\relax
 \gdef\@thanks{}\gdef\@author{}\gdef\@title{}
%\let\thanks\relax
}
\def\@maketitle{%%% commented out\newpage
 \null
 \begin{center}
  {\bf\@ucnothanks\@title\par}\vskip .075in
  {\footnotesize\spaceskip=1.5\fontdimen2\the\font
  \@tempswafalse\expandafter\@doauth\@author\and\relax}
 \end{center}
 \par \vskip .11in}
\def\@ucnothanks#1{\expandafter\@ucnt#1\thanks\relax}
\def\@ucnt#1\thanks{\uppercase{#1}\futurelet\@tempa\@ucnta}
\def\@ucnta{\ifx\@tempa\relax\else\@ucntb\fi}
\def\@ucntb#1\thanks\relax{\thanks{#1}}
\def\@doauth#1\and{\let\@nextdoa=\@doauth
 \def\@tempc{\@ucnothanks{#1}}
 \futurelet\@tempa\@doautha}
\def\@doautha{\ifx\@tempa\relax
  \if@tempswa {\ \scriptsize AND }\fi
  \let\@nextdoa=\relax
 \else
  \if@tempswa , \fi
 \fi
 \@tempc\unskip\@tempswatrue\@nextdoa}
\let\and=\relax
\def\@abssec#1{\vspace{.05in}\footnotesize \parindent .2in
{\bf #1. }\ignorespaces}
\def\abstract{\@abssec{Abstract}}
\def\keywords{\@abssec{Key words}}
\def\AMSMOS{\@abssec{AMS(MOS) subject classifications}}

\def\endabstract{\par\vspace{.1in}}
\let\endkeywords\endabstract
\let\endAMSMOS\endabstract

\mark{{}{}} 

\def\ps@plain{\let\@mkboth\@gobbletwo
     \def\@oddhead{}\def\@oddfoot{\footnotesize\rm\hfil\thepage
     \hfil}\def\@evenhead{}\let\@evenfoot\@oddfoot}
\if@twoside \def\ps@headings{\let\@mkboth\markboth
\def\@oddfoot{}\def\@evenfoot{}\def\@evenhead{
\rm\rlap{\thepage}\footnotesize\rm
\hfil \leftmark\hfil}\def\@oddhead{\hbox{}\hfil
{\footnotesize\rm\rightmark \hfil}\llap{\rm\thepage}}
\def\sectionmark##1{\markboth {\uppercase{\ifnum \c@secnumdepth
>\z@
 \thesection.\hskip 1em\relax \fi ##1}}{}}\def\subsectionmark##1{\markright
{\ifnum \c@secnumdepth >\@ne
 \thesubsection.\hskip 1em\relax \fi ##1}}}
\else \def\ps@headings{\let\@mkboth\markboth\def\@oddfoot{}\def\@evenfoot{}%
\def\@oddhead{\hbox{}\hfil{\footnotesize\rm \rightmark}\hfil
\llap{\rm\thepage}}\def\sectionmark##1{\markright
{\uppercase{\ifnum \c@secnumdepth >\z@
 \thesection.\hskip 1em\relax \fi ##1}}}}
\fi
\def\ps@myheadings{\let\@mkboth\@gobbletwo
\def\@oddhead{\hbox{}\hfil{\footnotesize\rm {\scriptsize \myoddhead}
\rightmark}\hfil
\llap{\rm\thepage}}\def\@oddfoot{}%
\def\@evenhead{\rm\rlap{\thepage}\footnotesize\rm
\hfil \leftmark {\scriptsize \myevenhead}
\hfil\hbox{}}\def\@evenfoot{}\def\sectionmark##1{}%
\def\subsectionmark##1{}}


\def\today{\ifcase\month\or
 January\or February\or March\or April\or May\or June\or
 July\or August\or September\or October\or November\or December\fi
 \space\number\day, \number\year}

\ps@plain \pagenumbering{arabic} \onecolumn \if@twoside\else\raggedbottom\fi 



%%%%%%% Set up for Black Board Bold (\Bbb) font
% N.B. \Bbb works only in math mode
\input amssym.def
\input amssym
%\font\tenmsy=msym10
%\font\sevenmsy=msym7
%\font\fivemsy=msym5
%\newfam\msyfam
%\textfont\msyfam=\tenmsy
%\scriptfont\msyfam=\sevenmsy
%\scriptscriptfont\msyfam=\fivemsy
%\def\Bbb{\fam\msyfam}