%% Modified 3/99 by S. Sherwood.  Default 10pt (9pt not available, use \small
%% etc.)

%% 
%% This is file `article.cls', generated 
%% on <1995/1/27> with the docstrip utility (2.2i).
%% 
%% The original source files were:
%% 
%% classes.dtx  (with options: `article')
%% 
%% Copyright 1994 the LaTeX3 project and the individual authors. 
%% All rights reserved. For further copyright information see the file 
%% legal.txt, and any other copyright indicated in this file. 
%% 
%% This file is part of the LaTeX2e system. 
%% ---------------------------------------- 
%% 
%% This system is distributed in the hope that it will be useful, 
%% but WITHOUT ANY WARRANTY; without even the implied warranty of 
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 
%% 
%% 
%% IMPORTANT NOTICE: 
%% 
%% For error reports in case of UNCHANGED versions see bugs.txt. 
%% 
%% Please do not request updates from us directly. Distribution is 
%% done through Mail-Servers and TeX organizations. 
%% 
%% You are not allowed to change this file. 
%% 
%% You are allowed to distribute this file under the condition that 
%% it is distributed together with all files mentioned in manifest.txt. 
%% 
%% If you receive only some of these files from someone, complain! 
%% 
%% You are NOT ALLOWED to distribute this file alone. You are NOT 
%% ALLOWED to take money for the distribution or use of either this 
%% file or a changed version, except for a nominal charge for copying 
%% etc. 
%% \CharacterTable
%%  {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%%   Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%%   Digits        \0\1\2\3\4\5\6\7\8\9
%%   Exclamation   \!     Double quote  \"     Hash (number) \#
%%   Dollar        \$     Percent       \%     Ampersand     \&
%%   Acute accent  \'     Left paren    \(     Right paren   \)
%%   Asterisk      \*     Plus          \+     Comma         \,
%%   Minus         \-     Point         \.     Solidus       \/
%%   Colon         \:     Semicolon     \;     Less than     \<
%%   Equals        \=     Greater than  \>     Question mark \?
%%   Commercial at \@     Left bracket  \[     Backslash     \\
%%   Right bracket \]     Circumflex    \^     Underscore    \_
%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%%   Right brace   \}     Tilde         \~}
\NeedsTeXFormat{LaTeX2e}
\ProvidesClass{AMSabs}
              [1994/12/09 v1.2x
 Standard LaTeX document class, edited for AMS abstract volume.]
\newcommand{\@ptsize}{}
\newif\if@restonecol
\newif\if@titlepage
\@titlepagefalse
\newif\if@openbib
\@openbibfalse
\DeclareOption{a4paper}
   {\setlength\paperheight {297mm}%
    \setlength\paperwidth  {210mm}}
\DeclareOption{a5paper}
   {\setlength\paperheight {210mm}%
    \setlength\paperwidth  {148mm}}
\DeclareOption{b5paper}
   {\setlength\paperheight {250mm}%
    \setlength\paperwidth  {176mm}}
\DeclareOption{letterpaper}
   {\setlength\paperheight {11in}%
    \setlength\paperwidth  {8.5in}}
\DeclareOption{legalpaper}
   {\setlength\paperheight {14in}%
    \setlength\paperwidth  {8.5in}}
\DeclareOption{executivepaper}
   {\setlength\paperheight {10.5in}%
    \setlength\paperwidth  {7.25in}}
\DeclareOption{landscape}
   {\setlength\@tempdima   {\paperheight}%
    \setlength\paperheight {\paperwidth}%
    \setlength\paperwidth  {\@tempdima}}
\DeclareOption{10pt}{\renewcommand{\@ptsize}{10}}
\DeclareOption{11pt}{\renewcommand{\@ptsize}{11}}
\DeclareOption{12pt}{\renewcommand{\@ptsize}{12}}
\DeclareOption{oneside}{\@twosidefalse \@mparswitchfalse}
\DeclareOption{twoside}{\@twosidetrue  \@mparswitchtrue}
\DeclareOption{draft}{\setlength\overfullrule{5pt}}
\DeclareOption{final}{\setlength\overfullrule{0pt}}
\DeclareOption{titlepage}{\@titlepagetrue}
\DeclareOption{notitlepage}{\@titlepagefalse}
\DeclareOption{onecolumn}{\@twocolumnfalse}
\DeclareOption{twocolumn}{\@twocolumntrue}
\DeclareOption{leqno}{\input{leqno.clo}}
\DeclareOption{fleqn}{\input{fleqn.clo}}
\DeclareOption{openbib}{\@openbibtrue}
\ExecuteOptions{letterpaper,10pt,oneside,twocolumn,final}
\ProcessOptions
\input{size\@ptsize.clo}
\setlength\lineskip{1\p@}
\setlength\normallineskip{1\p@}
\renewcommand{\baselinestretch}{}
\setlength\parskip{0\p@ \@plus \p@}
\@lowpenalty   51
\@medpenalty  151
\@highpenalty 301

%% Added to make 9pt the default size (SS 2000)
\renewcommand\normalsize{%
   \@setfontsize\normalsize\@ixpt{11}
   \abovedisplayskip 8.5\p@ \@plus2\p@ \@minus4\p@
   \abovedisplayshortskip \z@ \@plus3\p@
   \belowdisplayshortskip 4\p@ \@plus2\p@ \@minus2\p@
   \belowdisplayskip \abovedisplayskip
   \let\@listi\@listI}
\normalsize

\renewcommand\small{%
   \@setfontsize\small\@viiipt{9.5}%
   \abovedisplayskip 6\p@ \@plus2\p@ \@minus4\p@
   \abovedisplayshortskip \z@ \@plus\p@
   \belowdisplayshortskip 3\p@ \@plus\p@ \@minus2\p@
   \def\@listi{\leftmargin\leftmargini
               \topsep 3\p@ \@plus\p@ \@minus\p@
               \parsep 2\p@ \@plus\p@ \@minus\p@
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip
}
\renewcommand\footnotesize{%
   \@setfontsize\footnotesize\@viiipt\@ixpt
   \abovedisplayskip 4\p@ \@plus2\p@ \@minus2\p@
   \abovedisplayshortskip \z@ \@plus\p@
   \belowdisplayshortskip 2\p@ \@plus\p@ \@minus2\p@
   \def\@listi{\leftmargin\leftmargini
               \topsep 2\p@ \@plus\p@ \@minus\p@
               \parsep 2\p@ \@plus\p@ \@minus\p@
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip
}
\renewcommand\scriptsize{\@setfontsize\scriptsize\@vpt\@vipt}
\renewcommand\large{\@setfontsize\large\@xpt{12}}
\renewcommand\Large{\@setfontsize\Large\@xiipt{14}}
\renewcommand\LARGE{\@setfontsize\LARGE\@xivpt{18}}
\renewcommand\huge{\@setfontsize\huge\@xviipt{22}}
\renewcommand\Huge{\@setfontsize\Huge\@xxpt{25}}

\setcounter{topnumber}{1}
\renewcommand{\topfraction}{.7}
\setcounter{bottomnumber}{1}
\renewcommand{\bottomfraction}{.3}
\setcounter{totalnumber}{2}
\renewcommand{\textfraction}{.2}
\renewcommand{\floatpagefraction}{.5}
\setcounter{dbltopnumber}{1}
\renewcommand{\dbltopfraction}{.7}
\renewcommand{\dblfloatpagefraction}{.5}
\if@twoside
  \def\ps@headings{%
      \let\@oddfoot\@empty\let\@evenfoot\@empty
      \def\@evenhead{\thepage\hfil\slshape\leftmark}%
      \def\@oddhead{{\slshape\rightmark}\hfil\thepage}%
      \let\@mkboth\markboth
    \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\@oddfoot\@empty
    \def\@oddhead{{\slshape\rightmark}\hfil\thepage}%
    \let\@mkboth\markboth
    \def\sectionmark##1{%
      \markright {\uppercase{%
        \ifnum \c@secnumdepth >\m@ne
          \thesection \hskip 1em\relax
        \fi
        ##1}}}}
\fi
\def\ps@myheadings{%
    \let\@oddfoot\@empty\let\@evenfoot\@empty
    \def\@evenhead{\thepage\hfil\slshape\leftmark}%
    \def\@oddhead{{\slshape\rightmark}\hfil\thepage}%
    \let\@mkboth\@gobbletwo
    \let\sectionmark\@gobble
    \let\subsectionmark\@gobble
    }
\if@titlepage
  \newcommand{\maketitle}{\begin{titlepage}%
  \let\footnotesize\small
  \let\footnoterule\relax
  \null\vfil
  \vskip 60\p@
  \papernumber
  \begin{center}%
    {\large \@title \par}%
    \vskip 3em%
    {\normalsize
     \lineskip .75em%
      \begin{tabular}[t]{c}%
        \@author
      \end{tabular}\par}%
%      \vskip 1.5em%
%    {\large \@date \par}%       % Set date in \large size.--> No date.
  \end{center}\par
  \@thanks
  \vfil\null
  \end{titlepage}%
  \setcounter{footnote}{0}%
  \let\thanks\relax\let\maketitle\relax
  \gdef\@thanks{}\gdef\@author{}\gdef\@title{}}
\else
\newcommand{\maketitle}{\par
  \begingroup
    \renewcommand{\thefootnote}{\fnsymbol{footnote}}%
    \def\@makefnmark{\hbox to\z@{$\m@th^{\@thefnmark}$\hss}}%
    \long\def\@makefntext##1{\parindent 1em\noindent
            \hbox to1.8em{\hss$\m@th^{\@thefnmark}$}##1}%
    \if@twocolumn
      \ifnum \col@number=\@ne
        \@maketitle
      \else
        \twocolumn[\@maketitle]%
      \fi
    \else
      \newpage
      \global\@topnum\z@   % Prevents figures from going at top of page.
      \@maketitle
    \fi
         \@thanks
  \endgroup
  \setcounter{footnote}{0}%
  \let\thanks\relax
  \let\maketitle\relax\let\@maketitle\relax
  \gdef\@thanks{}\gdef\@author{}\gdef\@title{}}
\def\@maketitle{%
  \newpage
  \null
  {\bfseries \papernumber}%
  \vspace*{-2.15 em}
  \begin{center}%
    {\large \@title \par}%
    \vskip 1.5em%
    {\normalsize
      \lineskip .5em%
      \begin{tabular}[t]{c}%
        \@author
      \end{tabular}\par}%
    \vskip 1em%
%    {\large \@date}%
  \end{center}%
  \par
  \vskip 1.5em}
\fi
\setcounter{secnumdepth}{3}
\newcounter {part}
\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]
\newcounter {subparagraph}[paragraph]
\renewcommand{\thepart}         {\Roman{part}}
\renewcommand{\thesection}      {\arabic{section}}
\renewcommand{\thesubsection}   {\thesection.\arabic{subsection}}
\renewcommand{\thesubsubsection}{\thesubsection.\arabic{subsubsection}}
\renewcommand{\theparagraph} {\thesubsubsection.\arabic{paragraph}}
\renewcommand{\thesubparagraph} {\theparagraph.\arabic{subparagraph}}

% Use helvetica.
\renewcommand{\rmdefault}{phv}
\renewcommand{\sfdefault}{phv}

\newcommand{\part}{\par
   \addvspace{4ex}%
   \@afterindentfalse
   \secdef\@part\@spart}

\def\@part[#1]#2{%
    \ifnum \c@secnumdepth >\m@ne
      \refstepcounter{part}%
      \addcontentsline{toc}{part}{\thepart\hspace{1em}#1}%
    \else
      \addcontentsline{toc}{part}{#1}%
    \fi
    {\parindent \z@ \raggedright
     \interlinepenalty \@M
     \reset@font
     \ifnum \c@secnumdepth >\m@ne
       \Large\bfseries \partname~\thepart
       \par\nobreak
     \fi
     \huge \bfseries #2%
     \markboth{}{}\par}%
    \nobreak
    \vskip 3ex
    \@afterheading}
\def\@spart#1{%
    {\parindent \z@ \raggedright
     \interlinepenalty \@M
     \reset@font
     \huge \bfseries #1\par}%
     \nobreak
     \vskip 3ex
     \@afterheading}
\def\@endpart{\vfil\newpage
              \if@twoside
                \hbox{}%
                \thispagestyle{empty}%
                \newpage
              \fi
              \if@tempswa
                \twocolumn
              \fi}

% Added 3/99 to correct section number punctuation.
\def\@sect#1#2#3#4#5#6[#7]#8{
  \ifnum #2>\c@secnumdepth
    \let\@svsec\@empty
  \else
    \refstepcounter{#1}
    \ifnum #2< 2 
       \edef\@svsec{\csname  the#1\endcsname.\ \ } \fi
    \ifnum #2> 1 
       \edef\@svsec{\csname  the#1\endcsname\ \ } \fi
  \fi%
     %
 \@tempskipa #5\relax
  \ifdim \@tempskipa>\z@
    \begingroup
      #6{%
        \@hangfrom{\hskip #3\relax\upshape\@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\relax
      \@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}}

% These lengths have been shortened for AMS.
\newcommand{\section}{\@startsection {section}{1}{\z@}%
                                   {-2.0ex \@plus -1ex \@minus -.2ex}%
                                   {1.5ex \@plus.2ex}%
                                   {\reset@font\bfseries}}
\newcommand{\subsection}{\@startsection{subsection}{2}{\z@}%
                                     {-1.5ex\@plus -1ex \@minus -.2ex}%
                                     {1.5ex \@plus .2ex}%
{\reset@font\bfseries\slshape}}
\newcommand{\subsubsection}{\@startsection{subsubsection}{3}{\z@}%
                                     {-1.5ex\@plus -1ex \@minus -.2ex}%
                                     {1.5ex \@plus .2ex}%
                                     {\reset@font\scshape \hskip 1em}}
\newcommand{\paragraph}{\@startsection{paragraph}{4}{\z@}%
                                    {1.5ex \@plus1ex \@minus.2ex}%
                                    {-1em}%
{\reset@font\normalsize\bfseries}}
\newcommand{\subparagraph}{\@startsection{subparagraph}{5}{\parindent}%
                                       {1.5ex \@plus1ex \@minus .2ex}%
                                       {-1em}%
{\reset@font\normalsize\bfseries}}
\if@twocolumn
  \setlength\leftmargini  {2em}
\else
  \setlength\leftmargini  {2.5em}
\fi
\setlength\leftmarginii  {2.2em}
\setlength\leftmarginiii {1.87em}
\setlength\leftmarginiv  {1.7em}
\if@twocolumn
  \setlength\leftmarginv  {.5em}
  \setlength\leftmarginvi {.5em}
\else
  \setlength\leftmarginv  {1em}
  \setlength\leftmarginvi {1em}
\fi
\setlength\leftmargin    {\leftmargini}
\setlength  \labelsep  {.5em}
\setlength  \labelwidth{\leftmargini}
\addtolength\labelwidth{-\labelsep}
\@beginparpenalty -\@lowpenalty
\@endparpenalty   -\@lowpenalty
\@itempenalty     -\@lowpenalty
\renewcommand{\theenumi}{\arabic{enumi}}
\renewcommand{\theenumii}{\alph{enumii}}
\renewcommand{\theenumiii}{\roman{enumiii}}
\renewcommand{\theenumiv}{\Alph{enumiv}}
\newcommand{\labelenumi}{\theenumi.}
\newcommand{\labelenumii}{(\theenumii)}
\newcommand{\labelenumiii}{\theenumiii.}
\newcommand{\labelenumiv}{\theenumiv.}
\renewcommand{\p@enumii}{\theenumi}
\renewcommand{\p@enumiii}{\theenumi(\theenumii)}
\renewcommand{\p@enumiv}{\p@enumiii\theenumiii}
\newcommand{\labelitemi}{$\m@th\bullet$}
\newcommand{\labelitemii}{\normalfont\bfseries --}
\newcommand{\labelitemiii}{$\m@th\ast$}
\newcommand{\labelitemiv}{$\m@th\cdot$}
\newenvironment{description}
               {\list{}{\labelwidth\z@ \itemindent-\leftmargin
                        \let\makelabel\descriptionlabel}}
               {\endlist}
\newcommand{\descriptionlabel}[1]{\hspace\labelsep
                                \normalfont\bfseries #1}
\if@titlepage
  \newenvironment{abstract}{%
      \titlepage
      \null\vfil
      \begin{center}
        \bfseries \abstractname
      \end{center}}
     {\par\vfil\null\endtitlepage}
\else
  \newenvironment{abstract}{%
      \if@twocolumn
        \section*{\abstractname}%
      \else
        \small
        \begin{center}%
          {\bfseries \abstractname\vspace{-.5em}\vspace{\z@}}%
        \end{center}%
        \quotation
      \fi}
      {\if@twocolumn\else\endquotation\fi}
\fi
\newenvironment{verse}
               {\let\\=\@centercr
                \list{}{\itemsep      \z@
                        \itemindent   -1.5em%
                        \listparindent\itemindent
                        \rightmargin  \leftmargin
                        \advance\leftmargin 1.5em}%
                \item[]}
               {\endlist}
\newenvironment{quotation}
               {\list{}{\listparindent 1.5em%
                        \itemindent    \listparindent
                        \rightmargin   \leftmargin
                        \parsep        \z@ \@plus\p@}%
                \item[]}
               {\endlist}
\newenvironment{quote}
               {\list{}{\rightmargin\leftmargin}%
                \item[]}
               {\endlist}
\newenvironment{titlepage}
    {%
      \if@twocolumn
        \@restonecoltrue\onecolumn
      \else
        \@restonecolfalse\newpage
      \fi
      \thispagestyle{empty}%
      \if@compatibility
        \setcounter{page}{0}
      \else
        \setcounter{page}{1}%
      \fi}%
    {\if@restonecol\twocolumn \else \newpage \fi
      \setcounter{page}{1}%
    }
\newcommand{\appendix}{\par
  \setcounter{section}{0}%
  \setcounter{subsection}{0}%
  \renewcommand{\thesection}{\Alph{section}}}
\setlength\arraycolsep{5\p@}
\setlength\tabcolsep{6\p@}
\setlength\arrayrulewidth{.4\p@}
\setlength\doublerulesep{2\p@}
\setlength\tabbingsep{\labelsep}
\skip\@mpfootins = \skip\footins
\setlength\fboxsep{3\p@}
\setlength\fboxrule{.4\p@}
\renewcommand{\theequation}{\arabic{equation}}
\newcounter{figure}
\renewcommand{\thefigure}{\@arabic\c@figure}
\def\fps@figure{tbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{\hspace*{2 ex}{\scshape\figurename}~\thefigure}
\newenvironment{figure}
               {\@float{figure}}
               {\end@float}
\newenvironment{figure*}
               {\@dblfloat{figure}}
               {\end@dblfloat}
\newcounter{table}
\renewcommand{\thetable}{\@arabic\c@table}
\def\fps@table{tbp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{\tablename~\thetable}
\newenvironment{table}
               {\@float{table}}
               {\end@float}
\newenvironment{table*}
               {\@dblfloat{table}}
               {\end@dblfloat}
\newlength\abovecaptionskip
\newlength\belowcaptionskip
\setlength\abovecaptionskip{10\p@}
\setlength\belowcaptionskip{0\p@}
\long\def\@makecaption#1#2{%
  \vskip\abovecaptionskip
  \sbox\@tempboxa{#1: #2}%
  \ifdim \wd\@tempboxa >\hsize
    #1: #2\par
  \else
    \global \@minipagefalse
    \hbox to\hsize{\hfil\box\@tempboxa\hfil}%
  \fi
  \vskip\belowcaptionskip}
\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
\DeclareRobustCommand*{\cal}{\@fontswitch{\relax}{\mathcal}}
\DeclareRobustCommand*{\mit}{\@fontswitch{\relax}{\mathnormal}}
\newcommand{\@pnumwidth}{1.55em}
\newcommand{\@tocrmarg} {2.55em}
\newcommand{\@dotsep}{4.5}
\setcounter{tocdepth}{3}
\newcommand{\tableofcontents}{%
    \section*{\contentsname
\@mkboth{\uppercase{\contentsname}}{\uppercase{\contentsname}}}%
    \@starttoc{toc}%
    }
\newcommand*{\l@part}[2]{%
  \ifnum \c@tocdepth >-2\relax
    \addpenalty{\@secpenalty}%
    \addvspace{2.25em \@plus\p@}%
    \begingroup
      \setlength\@tempdima{3em}%
      \parindent \z@ \rightskip \@pnumwidth
      \parfillskip -\@pnumwidth
      {\leavevmode
       \large \bfseries #1\hfil \hbox to\@pnumwidth{\hss #2}}\par
       \nobreak
       \if@compatibility
         \global\@nobreaktrue
         \everypar{\global\@nobreakfalse\everypar{}}
      \fi
    \endgroup
  \fi}
\newcommand*{\l@section}[2]{%
  \ifnum \c@tocdepth >\z@
    \addpenalty{\@secpenalty}%
    \addvspace{1.0em \@plus\p@}%
    \setlength\@tempdima{1.5em}%
    \begingroup
      \parindent \z@ \rightskip \@pnumwidth
      \parfillskip -\@pnumwidth
      \leavevmode \bfseries
      \advance\leftskip\@tempdima
      \hskip -\leftskip
      #1\nobreak\hfil \nobreak\hbox to\@pnumwidth{\hss #2}\par
    \endgroup
  \fi}
\newcommand*{\l@subsection}   {\@dottedtocline{2}{1.5em}{2.3em}}
\newcommand*{\l@subsubsection}{\@dottedtocline{3}{3.8em}{3.2em}}
\newcommand*{\l@paragraph}    {\@dottedtocline{4}{7.0em}{4.1em}}
\newcommand*{\l@subparagraph} {\@dottedtocline{5}{10em}{5em}}
\newcommand{\listoffigures}{%
    \section*{\listfigurename
      \@mkboth{\uppercase{\listfigurename}}%
              {\uppercase{\listfigurename}}}%
    \@starttoc{lof}%
    }
\newcommand*{\l@figure}{\@dottedtocline{1}{1.5em}{2.3em}}
\newcommand{\listoftables}{%
    \section*{\listtablename
\@mkboth{\uppercase{\listtablename}}{\uppercase{\listtablename}}}%
    \@starttoc{lot}%
    }
\let\l@table\l@figure
\newdimen\bibindent
\bibindent=1.5em

%\def\thebibliography#1{\@startsection{section}{1}{\z@}
%{2.3ex plus 1ex minus .2ex}{1.5ex plus .2ex}{\large\bf}*{References} 
%\list{\null}{\leftmargin 1.2em\labelwidth\z@\labelsep\z@\itemindent -1.2em
%\usecounter{enumi}}
\newenvironment{thebibliography}[1]
     {\section*{\refname
        \@mkboth{\uppercase{\refname}}{\uppercase{\refname}}}%
\list{\null}{\leftmargin .25in\labelwidth\z@\labelsep\z@\itemindent -.25in%%
%      \list{\@biblabel{\arabic{enumiv}}}%
%           {\settowidth\labelwidth{\@biblabel{#1}}%
%            \leftmargin\labelwidth
%            \advance\leftmargin\labelsep
%            \if@openbib
%              \advance\leftmargin\bibindent
%              \itemindent -\bibindent
%              \listparindent \itemindent
%              \parsep \z@
%            \fi
            \usecounter{enumiv}%
            \let\p@enumiv\@empty
            \renewcommand{\theenumiv}{\arabic{enumiv}}}%
      \if@openbib
        \renewcommand{\newblock}{\par}
      \else
        \renewcommand{\newblock}{\hskip .11em \@plus.33em \@minus.07em}%
      \fi
      \sloppy\clubpenalty4000\widowpenalty4000%
      \sfcode`\.=\@m}
     {\def\@noitemerr
       {\@latex@warning{Empty `thebibliography' environment}}%
      \endlist}
\newcommand{\newblock}{}
\newenvironment{theindex}
               {\if@twocolumn
                  \@restonecolfalse
                \else
                  \@restonecoltrue
                \fi
                \columnseprule \z@
                \columnsep 35\p@
                \twocolumn[\section*{\indexname}]%
                \@mkboth{\uppercase{\indexname}}%
                        {\uppercase{\indexname}}%
                \thispagestyle{plain}\parindent\z@
                \parskip\z@ \@plus .3\p@\relax
                \let\item\@idxitem}
               {\if@restonecol\onecolumn\else\clearpage\fi}
\newcommand{\@idxitem}  {\par\hangindent 40\p@}
\newcommand{\subitem}   {\par\hangindent 40\p@ \hspace*{20\p@}}
\newcommand{\subsubitem}{\par\hangindent 40\p@ \hspace*{30\p@}}
\newcommand{\indexspace}{\par \vskip 10\p@ \@plus5\p@ \@minus3\p@\relax}
\renewcommand{\footnoterule}{%
  \kern-3\p@
  \hrule width .4\columnwidth
  \kern 2.6\p@}
\long\def\@makefntext#1{%
    \parindent 1em%
    \noindent
    \hbox to 1.8em{\hss\@makefnmark}#1}
\newcommand{\contentsname}{Contents}
\newcommand{\listfigurename}{List of Figures}
\newcommand{\listtablename}{List of Tables}
\newcommand{\refname}{REFERENCES}
\newcommand{\indexname}{Index}
\newcommand{\figurename}{Fig.}
\newcommand{\tablename}{Table}
\newcommand{\partname}{Part}
\newcommand{\appendixname}{Appendix}
\newcommand{\abstractname}{Abstract}
\newcommand{\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}
%% For use below/above figures.
%\newcommand{\figrulew}{\hspace{.1 in}---------------------------------------------------------------}
%\newcommand{\dblfigrulew}{\hspace{.1 in}-----------------------------------------------------------------------------------------------------------------------------------------}
%%\setlength\columnsep{10\p@}
\setlength\columnsep{.25 in}
\setlength\columnseprule{0\p@}
\setlength\textheight{9 in}
\setlength\textwidth{6.5 in}
\setlength\topmargin{-.75 in}
\setlength\parindent{.25 in}
\setlength\footskip{.9 in}
\pagestyle{empty}
\pagenumbering{arabic}      % Arabic page numbers
\if@twoside
\else
  \raggedbottom
\fi
\if@twocolumn
  \twocolumn
  \sloppy
  \flushbottom
\else
  \onecolumn
\fi

\endinput


%% 
%% End of file `article.cls'.