% deproc.sty 24-Apr-86, by Barbara Beeton, AMS

\typeout{Document Style Option 'deproc' -- Released 24 April 1986}
\input article.sty

\oddsidemargin -2.5pc \evensidemargin -2.5pc
\topmargin -3pc \headheight 0pt \headsep 0pt
%\footheight 0pt \footskip 0pt
\footheight 1pc \footskip 2pc
\textheight 58pc \textwidth 44pc \columnsep 2pc \columnseprule 0pt

\def\@oddhead{}\def\@evenhead{}
%  For debugging, keep running footers.
%\def\@oddfoot{}
%\def\@oddfoot{\rm\rightmark \hfil Page \thepage}
\def\@oddfoot{\hfil \tiny\thepage \hfil}
\def\@evenfoot{\@oddfoot}










\def\maketitle{\par
 \begingroup
 \def\@makefnmark{\hbox to 0pt{$^{\@thefnmark}$\hss}}
 \twocolumn[\@maketitle]
 \@thanks
 \endgroup
 \let\maketitle\relax
 \let\@maketitle\relax
 \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\let\thanks\relax
 \@afterheading}

\def\@maketitle{\vbox{\hsize\textwidth
 \linewidth\hsize \vskip\baselineskip \centering
 {\large\bf \@title \par} \vskip 2em
 {%\let\@endline=\\\def\\{\@endline\rm}%
  \def\and{\unskip\enspace{\rm and}\enspace}%
  \def\And{\unskip\\\null\\\bf}%
  \begin{tabular}[t]{c}\bf\@author \end{tabular}\par} \vskip 3\baselineskip
 \unvbox\@abstractbox}}

%\def\copyrightspace{\footnotetext[0]{\mbox{}\vrule height 97pt width 0pt}}

\newbox\@abstractbox
\long\def\abstract{\def\endabstract{\ifhmode\unskip\strut\endgraf\fi
                         \vskip 3\baselineskip \egroup}%
        \global\setbox\@abstractbox=\vbox\bgroup \hsize=\textwidth
                \leftskip=1.25in \rightskip=\leftskip
                \centerline{\bf Abstract}%
                \vskip.5\baselineskip
                \noindent\strut\ignorespaces }


%  Allow more space above a narrower footnote rule.
%  Footnotes not quite so far apart.
\footnotesep=10pt
\skip\footins=12pt              % full blank line
\def\footnoterule{\kern-8pt
  \hrule width 5pc \kern 7.6pt } % the \hrule is .4pt high


%  Force footnotes to bottom of page, regardless of ragged bottom.
\def\@makecol{\ifvoid\footins \setbox\@outputbox\box\@cclv
   \else\setbox\@outputbox
     \vbox to\@colht{\unvbox\@cclv\vfill\relax
          \vskip\skip\footins\footnoterule\unvbox\footins}\fi
     \xdef\@freelist{\@freelist\@midlist}\gdef\@midlist{}\@combinefloats
     \setbox\@outputbox\vbox to\@colht{\boxmaxdepth\maxdepth
        \@texttop\unvbox\@outputbox \@textbottom}\global\maxdepth\@maxdepth}


%  All footnotes are numbered; no other symbols.
\setcounter{footnote}{0}











%  Section headings differ from those in ARTICLE.STY.
%  Omit section numbers (just suppress printing), use different fonts.

\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
     \def\@svsec{}\else
     \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname\hskip 1em }\fi
     \@tempskipa #5\relax
      \ifdim \@tempskipa>\z@
        \begingroup #6\relax
          \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\section{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex
 minus -.2ex}{2.3ex plus .2ex}{\centering\normalsize\bf}}
\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus -1ex
 minus -.2ex}{1.5ex plus .2ex}{\parindent=\z@\normalsize\bf}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-3.25ex plus -1ex
 minus -.2ex}{1.5ex plus .2ex}{\parindent=\z@\normalsize\sl}}

%  Change the default item labels after the first.

\def\bull{\vrule height .9ex width .8ex depth -.1ex } % square bullet

\def\labelitemii{$\circ$}
\def\labelitemiii{\bull}
\def\labelitemiv{$\ast$}











%  Indent verbatim blocks
\def\verbatim{\@totalleftmargin\parindent
   \@verbatim \frenchspacing\@vobeyspaces \@xverbatim}

%  Figure and table caption labels boldface
\long\def\@makecaption#1#2{
  \vskip 10pt
  \setbox\@tempboxa\hbox{{\bf#1:}\enspace#2}
  \ifdim \wd\@tempboxa >\hsize \unhbox\@tempboxa\par \else \hbox
    to\hsize{\hfil\box\@tempboxa\hfil}
  \fi}

%  Reference list varies from standard by permitting labels to be omitted.

\newif\ifomit@biblabels         \omit@biblabelsfalse
\def\omit{\global\omit@biblabelstrue}

\def\thebibliography#1{\setbox0=\hbox{#1}\section*{References\markboth
  {REFERENCES}{REFERENCES}}\list
  {\ifomit@biblabels \else [\arabic{enumi}]\fi}{\ifomit@biblabels
  \setlength{\labelwidth}{0pt}\setlength{\labelsep}{0pt}\else
  \settowidth\labelwidth{[#1]}\fi\leftmargin\labelwidth
  \advance\leftmargin\labelsep
  \ifomit@biblabels\else\usecounter{enumi}\fi}}

\newlength{\n@rmal@parindent}   % set below after \parindent set
\def\no@biblabelindent{\ifomit@biblabels\leavevmode\kern\n@rmal@parindent\fi}

\def\@lbibitem[#1]#2{\item[\@biblabel{#1}]\if@filesw
      { \def\protect##1{\string ##1\space}\immediate
        \write\@auxout{\string\bibcite{#2}{#1}}\fi
    \no@biblabelindent\ignorespaces}}
\def\@bibitem#1{\item\if@filesw \immediate\write\@auxout
      {\string\bibcite{#1}{\the\c@enumi}}\fi\no@biblabelindent\ignorespaces}











%  Abbreviations (same list as in DEPROC.TeX).

\def \careof{\leavevmode\hbox{\raise.75ex\hbox{c}\kern-.15em
                /\kern-.125em\smash{\lower.3ex\hbox{o}}} }  % ends with space

%  This is \frac in DEPROC.TeX, but that conflicts with LaTeX \frac .
\def \sfrac#1/#2{\leavevmode\kern.1em
        \raise.5ex\hbox{\the\scriptfont0 #1}\kern-.1em
        /\kern-.15em\lower.25ex\hbox{\the\scriptfont0 #2}}

\def \d@sh#1{\nobreak\thinspace#1\penalty0\thinspace}
\def \dash{\d@sh{--}}
\def \Dash{\d@sh{---}}

\def \DECUS{Digital Equipment Computer Users Society}
\def \TeX{\leavevmode\hbox{T\kern-.1667em\lower.424ex\hbox{E}\kern-.125emX}}
\def \AMSTeX{\leavevmode\hbox{$\cal A\kern-.2em\lower.376ex
        \hbox{$\cal M$}\kern-.2em\cal S$-\TeX}}
%  The following definition of \LaTeX does not depend on the presence
%  of a small caps font to match every type style.
%\newcount\TestCount
%\def\LaTeX{\TestCount=\the\fam
%       \leavevmode L\raise.4ex
%       \hbox{$\fam\TestCount\scriptstyle\kern-.3em A$}\kern-.15em\TeX}
%  Unfortunately, standard LaTeX does not provide scriptstyle \bf, \sl
%  or \sf fonts, so a definition comparable to that used in LaTeX.TeX
%  is kept; the definition used in LaTeX version 2.08 (the most recent
%  available at AMS) does not incorporate the definitive TeX logo, so
%  an adjusted version is given here.
\def \LaTeX{{\rm L\kern-.36em\raise.3ex\hbox{\sc a}\kern-.15em\TeX}}
\def \MF{{\logo META}\-{\logo FONT}}
\def \WEB{{\tt WEB}}












\twocolumn
\sloppy
\parindent 20pt
\setlength{\n@rmal@parindent}{\parindent}
\leftmargini 2em
\leftmargin\leftmargini
\leftmarginv .5em
\leftmarginvi .5em
%\flushbottom

\endinput

