% warticle.sty  12-Oct-87
 
\typeout{Document Style `warticle' <12 Oct 87>.
Modified by Charles Wells 24 April 1988.}
 
% Note: the following have been modified to allow the specification
% of both digits of the point size.  Compare the definitions in
% article.sty.
\def\@ptsize{10} \@namedef{ds@11pt}{\def\@ptsize{11}}
\@namedef{ds@12pt}{\def\@ptsize{12}}
\@namedef{ds@14pt}{\def\@ptsize{14}}
\@namedef{ds@17pt}{\def\@ptsize{17}}
\@namedef{ds@20pt}{\def\@ptsize{20}}
\def\ds@twoside{\@twosidetrue \@mparswitchtrue} \def\ds@draft{\overfullrule
5pt}
\@options
\input wart\@ptsize.sty\relax
 
 
\def\labelenumi{\arabic{enumi}.}
\def\theenumi{\arabic{enumi}}
\def\labelenumii{(\alph{enumii})}
\def\theenumii{\alph{enumii}}
\def\p@enumii{\theenumi}
\def\labelenumiii{\roman{enumiii}.}
\def\theenumiii{\roman{enumiii}}
\def\p@enumiii{\theenumi(\theenumii)}
\def\labelenumiv{\Alph{enumiv}.}
\def\theenumiv{\Alph{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
 
 
\def\theequation{\arabic{equation}}
 
 
\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
 
\newcounter{part}
\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]
\newcounter {subparagraph}[paragraph]
 
\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\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{3}
 
\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
 {\large \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 #1\hfil \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\thebibliography#1{\section*{References\@mkboth
 {REFERENCES}{REFERENCES}}\list
 {[\arabic{enumi}]}{\settowidth\labelwidth{[#1]}\leftmargin\labelwidth
 \advance\leftmargin\labelsep
 \usecounter{enumi}}
 \def\newblock{\hskip .11em plus .33em minus .07em}
 \sloppy\clubpenalty4000\widowpenalty4000
 \sfcode`\.=1000\relax}
\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 .4\columnwidth
 \kern 2.6\p@}
 
\long\def\@makefntext#1{\parindent 1em\noindent
 \hbox to 1.8em{\hss$^{\@thefnmark}$}#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}
 
\long\def\@makecaption#1#2{
 \vskip 10pt
 \setbox\@tempboxa\hbox{#1: #2}
 \ifdim \wd\@tempboxa >\hsize #1: #2\par \else \hbox
to\hsize{\hfil\box\@tempboxa\hfil}
 \fi}
 
\newcounter{figure}
\def\thefigure{\@arabic\c@figure}
\def\fps@figure{tbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{Figure \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{tbp}
\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}
 
 \mathsurround=1pt
 
 \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\kern1em}\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\setbox0=\hbox{#8}%
 \hskip #3\@svsec \ifdim\wd0>\z@ \box0.\else \kern-1em
 \fi\csname #1mark\endcsname
                       {#7}\addcontentsline
                            {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                              \protect\numberline{\csname the#1\endcsname}\fi
                        #7}}\fi
      \@xsect{#5}}
 
\def\maketitle{\par
 \begingroup
 \def\thefootnote{\fnsymbol{footnote}}
 \def\@makefnmark{\hbox
 to 0pt{$^{\@thefnmark}$\hss}}
 \if@twocolumn
 \twocolumn[\@maketitle]
 \else \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{\newpage
 \null
 \vskip 1em \begin{center}
 {\LARGE \@title \par} \vskip .75em {\large \lineskip .5em
\begin{tabular}[t]{c}\@author
 \end{tabular}\par}
 \vskip .5em {\normalsize \@date} \end{center}
 \par
 \vskip .75em}
\def\abstract{\if@twocolumn
\section*{Abstract}
\else \small
\begin{center}
{\bf Abstract\vspace{-.5em}\vspace{0pt}}
\end{center}
\quotation
\fi}
\def\endabstract{\if@twocolumn\else\endquotation\fi}
 
%\mark{{}{}}
 
\if@twoside
\def\ps@headings{\let\@mkboth\markboth
\def\@oddfoot{}\def\@evenfoot{}\def\@evenhead{\rm \thepage\hfil \sl
\leftmark}\def\@oddhead{\hbox{}\sl \rightmark \hfil
\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 {}\sl \rightmark \hfil
\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{}\sl\rightmark \hfil
\rm\thepage}\def\@oddfoot{}\def\@evenhead{\rm \thepage\hfil\sl\leftmark\hbox
{}}\def\@evenfoot{}\def\sectionmark##1{}\def\subsectionmark##1{}}
 
 
\def\ps@underline{\let\@mkboth\markboth
\def\@oddfoot{}\def\@evenfoot{}\def\@evenhead{%
\begin{minipage}{\textwidth}%
\thepage\hfill heading \\[-4pt] \rule{\textwidth}{1pt}\end{minipage}}
\def\@oddhead{\@evenhead}}
 
\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
\def\ps@canada{\let\@mkboth\@gobbletwo
     \def\@oddhead{\rm\hfil\thepage}\def\@oddfoot{\addtocounter{page}1%
     \hfil($\ldots$\thepage)\addtocounter{page}{-1}}
     \let\@evenhead\@oddhead\let\@evenfoot\@oddfoot}
\def\ps@canadafoot{\let\@mkboth\@gobbletwo
     \def\@oddhead{}\def\@oddfoot{\addtocounter{page}1%
     \hfil($\ldots$\thepage)\addtocounter{page}{-1}}
     \let\@evenhead\@oddhead\let\@evenfoot\@oddfoot}
 
\def\eqnarray{\stepcounter{equation}\let\@currentlabel=\theequation
\global\@eqnswtrue
\global\@eqcnt\z@\tabskip\@centering\let\\=\@eqncr
$$\halign to \displaywidth\bgroup\@eqnsel\hskip\@centering
  $\displaystyle\tabskip\z@{##}$&\global\@eqcnt\@ne
 $\mskip \thickmuskip \hfil {##}$\hfil
  &\global\@eqcnt\tw@ $\mskip \thickmuskip \displaystyle\tabskip\z@{##}$\hfil
   \tabskip\@centering&\llap{##}\tabskip\z@\cr}
 
   \def\@endpbox{\unskip\strut\par\egroup\hfil}
   \let\@@endpbox=\@endpbox
 
%Slight changes in spacing
\fontdimen2\twlrm=4.1pt% space instead of 3.91663
\fontdimen3\twlrm=2.0pt%stretch instead of 1.95831
\fontdimen4\twlrm=1.0pt%shrink instead of 1.30554
 
\def\proclamation{\@startsection{subsection}{2}{\z@}{-\medskipamount
}{-1em plus 1em minus .4em}{\normalsize\bf}}
\def\theorem{\proclamation{Theorem}\begingroup\em}
\def\proposition{\proclamation{Proposition}\begingroup\em}
\def\corollary{\proclamation{Corollary}\begingroup\em}
\def\lemma{\proclamation{Lemma}\begingroup\em}
\def\example{\proclamation{Example}}
\def\endtheorem{\endgroup \par\addvspace{\medskipamount}}
\def\pr@@f[#1]{\par\addvspace{\medskipamount}\noindent Proof#1.\enskip}
\def\proof{\@ifnextchar[{\pr@@f}{\pr@@f[]}}
\def\Box{\vbox{\hrule\hbox{\vrule\kern.5ex
   \vbox{\kern1ex}\kern.5ex\vrule}\hrule}}
\def\endproof{~\hfill$\Box$\par\addvspace{\medskipamount}}
 
\def\addtotextheight#1{\advance\textheight by #1 \advance\@colht by #1
   \advance\@colroom by @1 \advance\vsize by #1}
\def\ps@footings{\let\@mkboth\@gobbletwo
     \def\@oddhead{}\def\@oddfoot{\rm\hfil\thepage}
     \def\@evenhead{}\def\@evenfoot{\rm\thepage\hfil}}
\def\ps@tick{\let\@mkboth\@gobbletwo
\def\@oddhead{\smash{\kern-.8in\lower2.7in \hbox{-}}\hfil}%
\def\@oddfoot{}\def\@evenhead{}\def\@evenfoot{}}
 
% Added to reduce extra space in \eqnarray
\def\eqnarray{\stepcounter{equation}\let\@currentlabel=\theequation
\global\@eqnswtrue
\global\@eqcnt\z@\tabskip\@centering\let\\=\@eqncr
$$\halign to \displaywidth\bgroup\@eqnsel
  $\displaystyle\tabskip\z@{##}$&\global\@eqcnt\@ne
  \hfil${{}##{}}$\hfil
  &\global\@eqcnt\tw@  $\displaystyle\tabskip\z@{##}$\hfil
   \tabskip\@centering&\llap{##}\tabskip\z@\cr}
\let\@eqnsel = \hfil
 
\def\lefteqn#1{\hbox to 4\arraycolsep{$\displaystyle #1$\hss}}