% Style file for Electronic Notes in Discrete Mathematics.
% Adopted from document-style for journals published by Elsevier.
%
% Version: 1.01
% Date:    1 November 2004
%
% Copyright (C) 2004. All rights reserved.
%
% IMPORTANT NOTICE:
%
% You are NOT ALLOWED to change this file. You may however copy this file
% to a file with a different name and then change the copy.
%
% You are NOT ALLOWED to distribute this file alone. You are NOT ALLOWED
% to take money for the distribution or use of this file (or a changed
% version) except for a nominal charge for copying etc.
%
% You are allowed to distribute this file under the condition that it is
% distributed together with all the files mentioned in "README.FIRST".
%
% If you receive only some of these files from someone, complain!
%
%
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\def\esp@filedate{1994/01/12}
\def\@shortjnl{\relax}
 \def\@journal{Elsevier Preprint} \def\@company{}
  \def\@shortjid{endm}
 \NeedsTeXFormat{LaTeX2e}
 \ProvidesClass{\@shortjid}
 [\esp@filedate, \esp@fileversion: \@journal]
\RequirePackage{newlfont}
\RequirePackage{amssymb}
\RequirePackage{latexsym}
% \RequirePackage{ifpdf}
% \ifpdf\RequirePackage[raiselinks=false,colorlinks=true,citecolor=blue,urlcolor=blue,linkcolor=blue,bookmarksopen=true,pdftex]{hyperref}\else
\RequirePackage[raiselinks=false,colorlinks=true,citecolor=blue,urlcolor=blue,linkcolor=blue,bookmarksopen=true,dvips]{hyperref}
\input{leqno.clo}
\DeclareOption{12pt}{}
\DeclareOption{11pt}{}
\DeclareOption{10pt}{}
\DeclareOption{oneside}{\@twosidefalse \@mparswitchfalse}
\DeclareOption{twoside}{\@twosidetrue  \@mparswitchtrue}
\@twocolumnfalse
\newif\if@TwoColumn
\DeclareOption{onecolumn}{\@twocolumnfalse\@TwoColumnfalse}
\DeclareOption{twocolumn}{\@twocolumntrue\@TwoColumntrue}
\def\@docty{XX}
\DeclareOption{letter}{%
 \def\@docty{SN}%
}
\DeclareOption{proc}{%
 \def\@docty{PP}%
}
\DeclareOption{erratum}{%
 \def\@docty{EN}\gdef\@articletype{Erratum}%
}
\newif\if@draft
\DeclareOption{draft}{%
  \@drafttrue
  \def\query{\marginpar{???}}%       % mark author queries in proof
  \overfullrule 5\p@                 % to indicate overfull boxes
}
\DeclareOption{final}{%
  \@draftfalse
  \def\query{}%
  \overfullrule \z@
}
\let\snm\relax \let\cty\relax \let\cny\relax
\DeclareOption{capcas}{\typeout {* `capcas' option ignored *}}
\newif\if@ussrhead \@ussrheadfalse
\DeclareOption{ussrhead}{\@ussrheadtrue}
\newif\if@debug \@debugfalse
\DeclareOption{debug}{\typeout{* Debugging is on *}\@debugtrue
              \errorcontextlines=1000}
\newif\if@seceqn
\@seceqnfalse                          % Default: equation numbering is not
\DeclareOption{seceqn}{\@seceqntrue}   % reset at beginning of each section
\newif\if@secthm
\@secthmfalse
\DeclareOption{secthm}{\@secthmtrue}
\newif\if@nameyear
\@nameyearfalse
\DeclareOption{nameyear}{\@nameyeartrue}
 \ExecuteOptions{oneside}
 \ExecuteOptions{onecolumn,final}
\ProcessOptions
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\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
\def\partname{Part}
\def\contentsname{Contents}
\def\listfigurename{List of Figures}
\def\listtablename{List of Tables}
\def\refname{References}
\def\indexname{Index}
\def\figurename{Fig.}
\def\tablename{Table}
\def\abstractname{Abstract}
\lineskip 1\p@
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\def\baselinestretch{1}
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\def\@overtitleskip{69pt}
\def\@bibliosize{\frenchspacing\small}
\def\@historysize{\small}
\def\@keywordsize{\small}
\def\@titlesize{\Large}
\def\@authorsize{\large}
\def\@keywordheading{{\it Keywords: \ }}
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\abovedisplayskip 12\p@ \@plus 2\p@ \@minus 2\p@%
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\abovedisplayshortskip \z@ \@plus 2\p@%
\belowdisplayshortskip 3.5\p@ \@plus 2\p@ \@minus 2\p@
\let\@listi\@listI}
\def\small{\@setfontsize\small\@xipt{13.6}%
\abovedisplayskip 11\p@ plus3\p@ minus6\p@
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip  \z@ plus3\p@
\belowdisplayshortskip  6.5\p@ plus3.5\p@ minus3\p@
\def\@listi{\leftmargin\leftmargini
 \parsep 4.5\p@ plus2\p@ minus\p@ \itemsep 5\p@%\parsep
            \topsep 9\p@ plus3\p@ minus5\p@}}
%\let\footnotesize=\small
\def\footnotesize{\@setsize\footnotesize{12\p@}\xpt\@xpt}
\def\scriptsize{\@setfontsize\scriptsize\@viiipt{9.5}}
\def\tiny{\@setfontsize\tiny\@vipt{7}}
\def\large{\@setfontsize\large\@xivpt{18}}
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\def\huge{\@setfontsize\huge\@xxvpt{27}}
\let\Huge=\huge
\def\baselinestretch{1}
\normalsize                                % Choose the normalsize font.
\newdimen\@bls                             % Several dimensions are
\@bls=\baselineskip                        % expressed in terms of this.
\if@twoside                  % Values for two-sided printing:
   \oddsidemargin   50\p@    %   Left margin on odd-numbered pages.
   \evensidemargin  10\p@    %   Left margin on even-numbered pages.
   \marginparwidth  10\p@    %   \@Width of marginal notes.
\else                        % Values for one-sided printing:
   \oddsidemargin   35\p@    %   Left margin on odd-numbered pages.
   \evensidemargin  35\p@    %   Left margin on even-numbered pages.
   \marginparwidth   2pc
\fi
\marginparsep 20\p@          % Horizontal space between outer margin and
                             % marginal note
\topmargin \z@           %    Nominal distance from top of page to top of
                         %    box containing running head.
\headheight  \z@         %    \@Height of box containing running head.
\headsep     \z@         %    Space between running head and text.
 \footskip 40\p@
\bigskipamount=\@bls \@plus 0.3\@bls \@minus 0.3\@bls % 1/1 line
\medskipamount=0.5\bigskipamount                  % 1/2 line
\smallskipamount=0.25\bigskipamount               % 1/4 line
\textheight 42\baselineskip  %44? \@Height of text (including footnotes and 
\advance\textheight\topskip  % figures, excluding running head and foot).
\textwidth 33pc              % \@Width of text line.
                             % For two-column mode:
\columnsep 2pc               %   Space between columns
\columnseprule \z@           %   \@Width of rule between columns.
 \footnotesep 8.4\p@
\skip\footins 12\p@ \@plus  8\p@      % Space between last line of text and
                                      % top of first footnote.
\floatsep 8\p@ \@plus 4\p@ \@minus 2\p@ % Space between adjacent floats moved
                                        % to top or bottom of text page.
\textfloatsep 8\p@ \@plus 4\p@\@minus 2\p@ % Space between main text and 
                                           % floats at top or bottom of page.
\intextsep 8\p@ \@plus 4\p@ \@minus 2\p@ %Space between in-text figures and
                                         % text.
\dblfloatsep 8\p@ \@plus 4\p@ \@minus 4\p@ %Same as \floatsep for double-column
                                         % figures in two-column mode.
\dbltextfloatsep 12\p@ \@plus 4\p@ \@minus 4\p@ %\textfloatsep for double-column
                                         % floats.
\@fptop \z@ \@plus 1fil  % Stretch at top of float page/column. (Must be
                         % \z@ \@plus ...)
\@fpsep 8\p@ \@plus 2fil % Space between floats on float page/column.
\@fpbot \z@ \@plus 1fil  % Stretch at bottom of float page/column. (Must be
                         % \z@ \@plus ... )
\@dblfptop \z@ \@plus 1fil %Stretch at top of float page. (Must be \z@ \@plus ...)
\@dblfpsep 8\p@ \@plus 2fil % Space between floats on float page.
\@dblfpbot \z@ \@plus 1fil % Stretch at bottom of float page. (Must be
                           % \z@ \@plus ... )
\marginparpush 5\p@        % Minimum vertical separation between two marginal
                           % notes.
\parskip 1pt % 1pc \@plus 1\p@   % Extra vertical space between paragraphs.
\parindent 1.5em                 % Indentation of each paragraph.
\newskip\eqntopsep                   % Extra vertical space, in addition to
 \eqntopsep 4pt plus 1\p@ minus 1\p@ % \parskip, added above and below
\newdimen\eqnarraycolsep             % Half the space between columns
\eqnarraycolsep 1\p@                 % in an \eqnarray.
\@lowpenalty   51      % Produced by \nopagebreak[1] or \nolinebreak[1]
\@medpenalty  151      % Produced by \nopagebreak[2] or \nolinebreak[2]
\@highpenalty 301      % Produced by \nopagebreak[3] or \nolinebreak[3]
\@beginparpenalty -\@lowpenalty    % Before a list or paragraph environment.
\@endparpenalty   -\@lowpenalty    % After a list or paragraph environment.
\@itempenalty     -\@lowpenalty    % Between list items.
% \def\section{\@startsection{section}{1}{\z@}{1.5\@bls
%   \@plus .4\@bls \@minus .1\@bls}{\@bls}{\normalsize\bfseries}}
\def\section{\@startsection{section}{1}{\z@}%
        {-3ex plus -1ex minus -.2ex}%
        {2ex plus .2ex}{\large\bfseries}}
% \def\subsection{\@startsection{subsection}{2}{\z@}{\@bls
%   \@plus .3\@bls \@minus .1\@bls}{\@bls}{\normalsize\itshape}}
\def\subsection{\@startsection{subsection}{2}{\z@}%
        {-3ex plus -1ex minus -.2ex}%
        {1.3ex plus .2ex}{\normalsize\itshape}}
% \def\subsubsection{\@startsection{subsubsection}{3}{\z@}{\@bls
%   \@plus .2\@bls}{0.0001pt}{\normalsize\itshape}}
\def\subsubsection{\@startsection{subsubsection}{3}{-\lastskip}{-\@bls plus
-.2\@bls}{0.0001pt}{\normalsize\itshape}}
\def\paragraph{\@startsection{paragraph}{4}{\z@}{3.25ex plus
  2ex \@minus 0.2ex}{0.0001pt}{\normalsize\bfseries}} %was -1em
\setcounter{secnumdepth}{3}
\def\half@em{\hskip 0.5em} \def\lb@part{PART \thepart.\half@em}
\def\lb@empty@part{PART \thepart}
\def\lb@section{\thesection.\half@em}
\def\lb@empty@section{\thesection}
\def\lb@subsection{\thesubsection.\half@em}
\def\lb@empty@subsection{\thesubsection}
\def\lb@subsubsection{\thesubsubsection.\half@em}
\def\lb@empty@subsubsection{\thesubsubsection}
\def\lb@paragraph{\theparagraph.\half@em}
\def\lb@empty@paragraph{\theparagraph}
\def\lb@subparagraph{\thesubparagraph.\half@em}
\def\lb@empty@subparagraph{\thesubparagraph}
\def\head@style{\interlinepenalty\@M \hyphenpenalty\@M
  \exhyphenpenalty\@M \rightskip 0pt plus 0.5\hsize \relax}
\def\app@number#1{\setcounter{#1}{0}%
  \@addtoreset{#1}{section}%
  \@namedef{the#1}{\thesection.\arabic{#1}}}
\def\appendix{%
  \renewcommand*{\theHsection}{\Alph{section}}
  \@ifstar{\appendix@star}{\appendix@nostar}}
\def\appendix@nostar{%
  \def\lb@section{Appendix \thesection.\half@em}
  \def\lb@empty@section{Appendix \thesection}%
  \setcounter{section}{0}%
  \setcounter{subsection}{0}%
  \setcounter{subsubsection}{0}%
  \setcounter{paragraph}{0}%
  \def\thesection{\Alph{section}}
  \app@number{equation}\app@number{figure}
  \app@number{table}}
\def\appendix@star{%
  \def\lb@section{Appendix}\let\lb@empty@section\lb@section
  \setcounter{section}{0}\def\thesection{\Alph{section}}%
  \setcounter{subsection}{0}%
  \setcounter{subsubsection}{0}%
  \setcounter{paragraph}{0}%
  \app@number{equation}\app@number{figure}\app@number{table}}
\def\ack{\section*{%
Acknowledgement
  }
  \addtocontents{toc}{\protect\vspace{6pt}}%
  \addcontentsline{toc}{section}{%
Acknowledgement
}}
\@namedef{ack*}{\par\vskip 3.0ex \@plus 1.0ex \@minus 1.0ex}
\let\endack\par
\@namedef{endack*}{\par}
\newdimen\labelwidthi
\newdimen\labelwidthii
\newdimen\labelwidthiii
\newdimen\labelwidthiv
\def\normal@labelsep{0.5em}
\labelsep\normal@labelsep
\settowidth{\labelwidthi}{(iii)}
\settowidth{\labelwidthii}{(d)}
\settowidth{\labelwidthiii}{(iii)}
\settowidth{\labelwidthiv}{(M)}
\leftmargini\labelwidthi    \advance\leftmargini\labelsep
\leftmarginii\labelwidthii  \advance\leftmarginii\labelsep
\leftmarginii\labelwidthiii \advance\leftmarginiii\labelsep
\leftmarginii\labelwidthiv  \advance\leftmarginiv\labelsep
\def\setleftmargin#1#2{\settowidth{\@tempdima}{#2}\labelsep\normal@labelsep
  \csname labelwidth#1\endcsname\@tempdima
  \@tempdimb\@tempdima \advance\@tempdimb\labelsep
  \csname leftmargin#1\endcsname\@tempdimb}
\def\@listI{\leftmargin\leftmargini
  \labelwidth\labelwidthi \labelsep\normal@labelsep
  \topsep .35pc%\z@
\partopsep\z@ \parsep\z@ \itemsep .3pc%5\p@%2\parsep%\z@
  \listparindent 1em}
\def\@listii{\leftmargin\leftmarginii
  \labelwidth\labelwidthii \labelsep\normal@labelsep
  \topsep\z@ \partopsep\z@ \parsep\z@ \itemsep \z@
  \listparindent 1em}
\def\@listiii{\leftmargin\leftmarginiii
  \labelwidth\labelwidthiii \labelsep\normal@labelsep
  \topsep\z@ \partopsep\z@ \parsep\z@ \itemsep \z@
  \listparindent 1em}
\def\@listiv{\leftmargin\leftmarginiv
  \labelwidth\labelwidthiv \labelsep\normal@labelsep
  \topsep\z@ \partopsep\z@ \parsep\z@ \itemsep \z@
  \listparindent 1em}
\let\@listi\@listI
\@listi
\def\left@label#1{{#1}\hss}
\def\rechts@label#1{\hss\llap{#1}}
\def\thick@label#1{\hspace\labelsep #1}
\newcount\@maxlistdepth
\@maxlistdepth=2
\def\labelitemi{\lower.5ex\hbox{$^\bullet$}} %originally -- changed  8-6-95
\def\labelitemii{$\cdot$}           %originally \cdot changed 8-6-95
\def\labelenumi{(\theenumi)}        \def\theenumi{\roman{enumi}}
\def\labelenumii{(\theenumii)}      \def\theenumii{\alph{enumii}}
\def\enumerate{%
  \ifnum \@enumdepth >\@maxlistdepth
    \@toodeep
  \else
    \advance\@enumdepth \@ne
    \edef\@enumctr{enum\romannumeral\the\@enumdepth}%
    \list{\csname label\@enumctr\endcsname}%
       {\usecounter{\@enumctr}
       \let\makelabel=\rechts@label}
  \fi}
\def\itemize{%
  \ifnum \@itemdepth >\@maxlistdepth
    \@toodeep
  \else
    \advance\@itemdepth \@ne
    \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
     \setleftmargin{i}{--}%
     \setleftmargin{ii}{$\cdot$}%
    \list{\csname\@itemitem\endcsname}%
       {\let\makelabel\rechts@label}
  \fi}
\def\verse{\let\\=\@centercr
  \list{}{\itemsep\z@
  \itemindent \z@
  \listparindent\z@
  \rightmargin 1em
  \leftmargin \rightmargin}\item[]}
\let\endverse\endlist
\def\quotation{\list{}{\itemindent\z@
 \leftmargin 1em \rightmargin \z@
  \parsep \z@ \@plus 1pt}\item[]}
\let\endquotation=\endlist
\def\quote{\list{}{\itemindent\z@
   \leftmargin 1em \rightmargin \z@}%
\item[]}
\let\endquote=\endlist
\def\descriptionlabel#1{\hspace\labelsep \bfseries #1}
\def\description{\list{}{\labelwidth\z@
  \leftmargin 1em \itemindent-\leftmargin
  \let\makelabel\descriptionlabel}}
\let\enddescription\endlist
\def\@atfmtname{atlplain}
\ifx\fmtname\@atfmtname
 \def\neq{\not\nobreak\mkern -2mu =}%
 \let\ne\neq
\fi
\def\operatorname#1{\mathop{\mathrm{#1}}\nolimits}
\def\lefteqn#1{\hbox to\z@{$\displaystyle {#1}$\hss}}
\newskip\eqnbaselineskip % Standard interline spacing in an {eqnarray}
\jot=2\p@
\newskip\eqnlineskip     % Minimal space between the bottom of
                         % a line and the top of the next line.
\eqnbaselineskip=14\p@  \eqnlineskip=2\p@
\newdimen\mathindent
\if@TwoColumn
  \mathindent 0em
\else
  \mathindent 2em
\fi
\def\[{\relax\ifmmode\@badmath
  \else  %\bgroup removed on request from BW (1993-05-17)
  \@beginparpenalty\predisplaypenalty
  \@endparpenalty\postdisplaypenalty
  \begin{trivlist}\@topsep \eqntopsep       % used by first \item
   \@topsepadd \eqntopsep                   % used by \@endparenv
  \item[]\leavevmode
   \hbox to\linewidth\bgroup\hfil $ \displaystyle
  \hskip\mathindent\bgroup\fi}
\def\]{\relax\ifmmode \egroup $\hfil \egroup
  \end{trivlist}    % \egroup removed on request from BW (1993-05-17)
  \else \@badmath \fi}
\def\equation{\@beginparpenalty\predisplaypenalty
  \@endparpenalty\postdisplaypenalty
\refstepcounter{equation}\trivlist
   \@topsep \eqntopsep                      % used by first \item
   \@topsepadd \eqntopsep                   % used by \@endparenv
   \item[]\leavevmode
   \hbox to\linewidth\bgroup \hfil $ \displaystyle \hskip\mathindent\bgroup}
\def\endequation{\egroup$\hfil \displaywidth\linewidth
  \@eqnnum\egroup \endtrivlist}
\def\eqnarray{%
  \par                                               %BW
  \noindent                                          %BW
  \baselineskip\eqnbaselineskip\lineskip\eqnlineskip %BW
  \lineskiplimit\eqnlineskip                         %BW
  \stepcounter{equation}%
  \let\@currentlabel=\theequation
  \global\@eqnswtrue
  \global\@eqcnt\z@ \tabskip\mathindent \let\\=\@eqncr
  \abovedisplayskip\eqntopsep\ifvmode\advance\abovedisplayskip\partopsep\fi
  \belowdisplayskip\abovedisplayskip
  \belowdisplayshortskip\abovedisplayskip
  \abovedisplayshortskip\abovedisplayskip
  $$\halign to \displaywidth\bgroup\@eqnsel
    \pre@coli$\displaystyle\tabskip\z@{##}$\post@coli
    &\global\@eqcnt\@ne
    \pre@colii$\displaystyle{##}$\post@colii
    &\global\@eqcnt\tw@
    \pre@coliii $\displaystyle\tabskip\z@{##}$\post@coliii
    \tabskip\@centering&\llap{##}\tabskip\z@\cr}
\def\endeqnarray{\@@eqncr\egroup
 \global\advance\c@equation\m@ne$$\global\@ignoretrue }
\def\pre@coli{\hskip\@centering}              \def\post@coli{}
\def\pre@colii{\hskip 2\eqnarraycolsep \hfil} \def\post@colii{\hfil}
\def\pre@coliii{\hskip 2\eqnarraycolsep}      \def\post@coliii{\hfil}
\arraycolsep 2\p@      % Half the space between columns in array environment.
\tabcolsep 6\p@        % idem in tabular environment.
\def\arraystretch{1.5} % More vertical space in tables
\arrayrulewidth 0.4\p@ % \@Width of rules and space between adjacent
\doublerulesep 2\p@    % rules in any of these two environments.
\tabbingsep \labelsep  % Space used by the \' command.  (See LaTeX{} manual.)
\skip\@mpfootins = 6\p@ \@plus 2\p@  % Space between last line of text and
                                     % top of first footnote.
\fboxsep = 7\p@    % Space left between box and text by \fbox and \framebox.
\fboxrule = 0.4\p@ % \@Width of rules in box made by \fbox and \framebox.
\newcounter{part}
\newcounter{section}
\newcounter{subsection}[section]
\newcounter{subsubsection}[subsection]
\newcounter{paragraph}[subsubsection]
\newcounter{subparagraph}[paragraph]
\if@seceqn
 \@addtoreset{equation}{section}
 \def\theequation{\arabic{section}.\arabic{equation}}
\else
  \def\theequation{\arabic{equation}}
\fi
\def\thepart         {\arabic{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}}
\@addtoreset{section}{part} % reset section numbers at beginning of part
%\def\qed{\relax\ifmmode\hskip2em \Box\else\unskip\nobreak\hskip1em $\Box$\fi}
\def\qed{\relax\ifmmode\hfill \Box\else\unskip\nobreak\hfill $\Box$\fi}

\def\proof@headerfont{\upshape\bfseries}
\gdef\theorem@headerfont{\itshape}
\gdef\th@plain{\upshape
  \def\@begintheorem##1##2{\item[\hskip\labelsep
    {\theorem@headerfont ##1\ ##2.}]}%
  \def\@opargbegintheorem##1##2##3{\item[\hskip\labelsep
    {\theorem@headerfont ##1\ ##2.}\ {\upshape (##3).}]}}
\gdef\th@definition{\upshape
  \def\@begintheorem##1##2{\item[\hskip\labelsep
    {\theorem@headerfont ##1\ ##2.}]}%
  \def\@opargbegintheorem##1##2##3{\item[\hskip\labelsep
    {\theorem@headerfont ##1\ ##2.}\ {\upshape (##3).}]}}

\newenvironment{pf}%
  {\par\addvspace{.6pc plus .2pc minus .1pc}
   \noindent
   {\textbf\proofname}\enspace\ignorespaces}%
  {\par\addvspace{.6pc plus .2pc minus .1pc}}
\def\proofname{Proof.}
\@namedef{pf*}#1{\par\begingroup\def\proofname{#1}\pf\endgroup\ignorespaces}
\expandafter\let\csname endpf*\endcsname=\endpf
\newtheorem{thm}{Theorem}[section]
\newtheorem{cor}[thm]{Corollary}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{claim}[thm]{Claim}
\newtheorem{axiom}[thm]{Axiom}
\newtheorem{conj}[thm]{Conjecture}
\newtheorem{fact}[thm]{Fact}
\newtheorem{hypo}[thm]{Hypothesis}
\newtheorem{assum}[thm]{Assumption}
\newtheorem{prop}[thm]{Proposition}
\newtheorem{crit}[thm]{Criterion}
\newtheorem{defn}[thm]{Definition}
\newtheorem{exmp}[thm]{Example}
\newtheorem{rem}[thm]{Remark}
\newtheorem{prob}[thm]{Problem}
\newtheorem{prin}[thm]{Principle}
\newtheorem{alg}{Algorithm}
\long\def\@makealgocaption#1#2{\vskip 2ex \small
  \hbox to \hsize{\parbox[t]{\hsize}{{\bfseries #1.} #2}}}
\newcounter{algorithm}
\def\thealgorithm{\@arabic\c@algorithm}
\def\fps@algorithm{tbp}
\def\ftype@algorithm{4}
\def\ext@algorithm{lof}
\def\fnum@algorithm{Algorithm \thealgorithm}
\def\algorithm{\let\@makecaption\@makealgocaption\@float{algorithm}}
\let\endalgorithm\end@float
\newtheorem{note}{Note}
\newtheorem{summ}{Summary}
\newtheorem{case}{Case}
\def\@pnumwidth{2.55em}
\def\@tocrmarg{2.55em \@plus 5em}
\def\@dotsep{-2.5}
\setcounter{tocdepth}{2}
\def\tableofcontents{%
  \section*{\contentsname}%
  \@starttoc{toc}}
\def\l@section{\@dottedtocline{1}{0.0em}{1.40em}}
\def\l@subsection{\@dottedtocline{2}{1.40em}{2.24em}}
\def\l@subsubsection{\@dottedtocline{3}{2.24em}{3.09em}}
\def\thebibliography{%
  \@startsection{section}{1}{\z@}{20\p@ \@plus 8\p@ \@minus 4pt}
  {\@bls}{\large\bfseries}*{\refname}%
  \addcontentsline{toc}{section}{\refname}%
  \@thebibliography}
\let\endthebibliography=\endlist
\def\@thebibliography#1{\@bibliosize
  \list{\@biblabel{\arabic{enumiv}}}{\settowidth\labelwidth{\@biblabel{#1}}
  \if@nameyear
    \labelwidth\z@ \labelsep\z@ \leftmargin\parindent
    \itemindent-\parindent
  \else
    \labelsep 3\p@ \itemindent\z@
    \leftmargin\labelwidth \advance\leftmargin\labelsep
\fi
     \itemsep 0.3\@bls \@plus 0.1\@bls \@minus 0.1\@bls
    \usecounter{enumiv}\let\p@enumiv\@empty
    \def\theenumiv{\arabic{enumiv}}}%
    \def\newblock{\hskip 0.11em \@plus 0.33em \@minus -0.07em}
    \tolerance\@M \hyphenpenalty\@M \hbadness5000 \sfcode`\.=1000\relax}
\if@nameyear
  \def\@biblabel#1{}
\else
  \def\@biblabel#1{\hskip \z@ \@plus 1filll[#1]}
\fi
\newcount\@tempcntc
\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi
 \@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do
  {\@ifundefined
   {b@\@citeb}{\@citeo\@tempcntb\m@ne\@citea\def\@citea{,}{\bfseries ?}\@warning
   {Citation `\@citeb' on page \thepage \space undefined}}%
  {\setbox\z@\hbox{\global\@tempcntc0\csname b@\@citeb\endcsname\relax}%
   \ifnum\@tempcntc=\z@ \@citeo\@tempcntb\m@ne
    \@citea\def\@citea{,}\hbox{\csname b@\@citeb\endcsname}%
   \else
    \advance\@tempcntb\@ne
    \ifnum\@tempcntb=\@tempcntc
    \else\advance\@tempcntb\m@ne\@citeo
    \@tempcnta\@tempcntc\@tempcntb\@tempcntc\fi\fi}}\@citeo}{#1}}
\def\@citeo{\ifnum\@tempcnta>\@tempcntb\else\@citea\def\@citea{,}%
 \ifnum\@tempcnta=\@tempcntb\the\@tempcnta\else
  {\advance\@tempcnta\@ne\ifnum\@tempcnta=\@tempcntb \else \def\@citea{--}\fi
   \advance\@tempcnta\m@ne\the\@tempcnta\@citea\the\@tempcntb}\fi\fi}
\@namedef{cv*}{\section*{Curriculum Vitae}\cv}
 \def\cv{\hangindent=7pc \hangafter=-12 \parskip\bigskipamount \small}
\def\footnote{\@ifnextchar[{\@xfootnote}{\refstepcounter
   {\@mpfn}\xdef\@thefnmark{\thempfn}\@footnotemark\@footnotetext}}
\def\footnotemark{\@ifnextchar[{\@xfootnotemark
    }{\refstepcounter{footnote}\xdef\@thefnmark{\thefootnote}\@footnotemark}}
\def\footnoterule{\kern-3\p@
  \hrule \@width 3pc           % The \hrule has default \@height of 0.4pt.
  \kern 2.6\p@}
\def\thempfootnote{\alph{mpfootnote}}
\def\mpfootnotemark{%
  \@ifnextchar[{\@xmpfootnotemark}{\stepcounter{mpfootnote}%
  \begingroup
    \let\protect\noexpand
    \xdef\@thefnmark{\thempfootnote}%
  \endgroup
  \@footnotemark}}
\def\@xmpfootnotemark[#1]{%
  \begingroup
    \c@mpfootnote #1\relax
    \let\protect\noexpand
    \xdef\@thefnmark{\thempfootnote}%
  \endgroup
  \@footnotemark}
\def\@mpmakefnmark{$\,^{\mathrm{\@thefnmark}}$}
\long\def\@mpmakefntext#1{\noindent
                     {$^{\mathrm{\@thefnmark}}$ #1}}
\def\@iiiminipage#1#2[#3]#4{%
  \leavevmode
  \@pboxswfalse
  \setlength\@tempdima{#4}%
  \def\@mpargs{{#1}{#2}[#3]{#4}}%
  \setbox\@tempboxa\vbox\bgroup
    \color@begingroup
      \hsize\@tempdima
      \textwidth\hsize \columnwidth\hsize
      \@parboxrestore
      \def\@mpfn{mpfootnote}\def\thempfn{\thempfootnote}\c@mpfootnote\z@
      \let\@footnotetext\@mpfootnotetext
      \let\@makefntext\@mpmakefntext
      \let\@makefnmark\@mpmakefnmark
      \let\@listdepth\@mplistdepth \@mplistdepth\z@
      \@minipagerestore\global\@minipagetrue  %% \global added 24 May 89
      \everypar{\global\@minipagefalse\everypar{}}}
\def\fn@presym{}
\long\def\@makefntext#1{\noindent\hbox to 1em
  {$^{\fn@presym\mathrm{\@thefnmark}}$\hss}#1}
\def\@makefnmark{\,\hbox{$^{\fn@presym\mathrm{\@thefnmark}}$}\,}
\setcounter{topnumber}{5}
\def\topfraction{0.99}
\def\textfraction{0.05}
\def\floatpagefraction{0.9}
\setcounter{bottomnumber}{5}
\def\bottomfraction{0.99}
\setcounter{totalnumber}{10}
\def\dbltopfraction{0.99}
\def\dblfloatpagefraction{0.8}
\setcounter{dbltopnumber}{5}
\long\def\@maketablecaption#1#2{\@captionsize
  \hbox to \hsize{\parbox[t]{\hsize}{\begin{center}#1 \\ #2\end{center}}}}
\long\def\@makefigurecaption#1#2{\@captionsize
  \vskip 8\p@
  \setbox\@tempboxa\hbox{#1. #2}
  \ifdim \wd\@tempboxa >\hsize              % IF longer than one line THEN
    \unhbox\@tempboxa\par                   % set as justified paragraph
  \else                                     % ELSE
    \hbox to\hsize{\hfil\box\@tempboxa\hfil}%   center single line.
  \fi}
\def\conttablecaption{\par \begingroup \@parboxrestore \normalsize
  \@makecaption{\fnum@table\,---\,continued}{}\par
  \vskip-1pc \endgroup}
\def\contfigurecaption{\vskip-1pc \par \begingroup \@parboxrestore \normalsize
  \@makecaption{\fnum@figure\,---\,continued}{}\par
  \endgroup}
\newcounter{figure}
\def\thefigure{\@arabic\c@figure}
\def\fps@figure{tbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{\figurename~\thefigure}
\def\figure{%
\let\@makecaption\@makefigurecaption
  \let\contcaption\contfigurecaption \@float{figure}}
% \let\endfigure\end@float
\def\endfigure{\addvspace{.2pc plus .2pc minus .1pc}\end@float}
\@namedef{figure*}{%
\let\@makecaption\@makefigurecaption
  \let\contcaption\contfigurecaption \@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{\tablename~\thetable}
\def\table{%
\let\@makecaption\@maketablecaption
\small
  \let\footnoterule\relax
  \let\contcaption\conttablecaption \@float{table}}
%\let\endtable\end@float
\def\endtable{\addvspace{.2pc plus .2pc minus .1pc}\end@float}
\@namedef{table*}{%
\let\@makecaption\@maketablecaption
\small
  \let\footnoterule\relax
  \let\contcaption\conttablecaption \@dblfloat{table}}
\@namedef{endtable*}{\end@dblfloat}
\newtoks\t@glob@notes             % List of all notes
\newtoks\t@loc@notes              % List of notes for one element
\newcount\note@cnt                % Number of notes per element
\newcounter{author}               % Author counter
\newcount\n@author                % Total number of authors
\def\n@author@{}                  % idem, read from .aux file
\newcounter{collab}               % Collaboration counter
\newcount\n@collab                % Total number of collaborations
\def\n@collab@{}                  % idem, read from .aux file
\newcounter{address}              % Address counter
\newdimen\sv@mathsurround         % Dimen register to save \mathsurround
\newcount\sv@hyphenpenalty        % Count register to save \hyphenpenalty
\newcount\prev@elem \prev@elem=0  % Variables to keep track of
\newcount\cur@elem  \cur@elem=0   % types of elements that are processed
\chardef\e@title=1
\chardef\e@subtitle=1
\chardef\e@author=2
\chardef\e@collab=3
\chardef\e@address=4
\newif\if@newelem                 % Switch to new type of element?
\newif\if@firstauthor             % First author or collaboration?
\newif\if@preface                 % If preface: omit history and abstract
\newif\if@hasabstract             % If abstract / keywords: do not omit rules
\newbox\fm@box                    % Box for collected front matter
\newdimen\fm@size                 % Total height of \fm@box
\newbox\t@abstract                % Box for abstract
\newbox\t@keyword                 % Box for keyword abstract
 \let\report@elt\@gobble
\def\add@tok#1#2{\global#1\expandafter{\the#1#2}}
\def\add@xtok#1#2{\begingroup
  \no@harm
  \xdef\@act{\global\noexpand#1{\the#1#2}}\@act
\endgroup}
\def\beg@elem{\global\t@loc@notes={}\global\note@cnt\z@}
\def\@xnamedef#1{\expandafter\xdef\csname #1\endcsname}
\def\no@harm{%
  \let\\=\relax  \let\rm\relax
  \let\ss=\relax \let\ae=\relax \let\oe=\relax
  \let\AE=\relax \let\OE=\relax
  \let\o=\relax  \let\O=\relax
  \let\i=\relax  \let\j=\relax
  \let\aa=\relax \let\AA=\relax
  \let\l=\relax  \let\L=\relax
  \let\d=\relax  \let\b=\relax \let\c=\relax
  \let\bar=\relax
  \def\protect{\noexpand\protect\noexpand}}
\def\proc@elem#1#2{
  \begingroup
    \no@harm                             % make a few instructions harmless
    \let\thanksref\@gobble               % remove \thanksref from element
    \@xnamedef{@#1}{#2}%                 % and store as \@#1
  \endgroup
  \prev@elem=\cur@elem                   % keep track of type of previous
  \cur@elem=\csname e@#1\endcsname       % and current element
  \expandafter\elem@nothanksref#2\thanksref\relax}
\def\elem@nothanksref#1\thanksref{\futurelet\@peektok\elem@thanksref}
\def\elem@thanksref{\ifx\@peektok\relax  % No more \thanksref, so now exit
  \else \expandafter\elem@morethanksref \fi}
\def\elem@morethanksref#1{\add@thanksref{#1}\elem@nothanksref}
\def\add@thanksref#1{\global\advance\note@cnt\@ne
  \ifnum\note@cnt>\@ne \add@xtok\t@loc@notes{\note@sep}\fi
  \add@tok\t@loc@notes{\ref{#1}}}
\def\note@sep{,}
\def\thanks{\@ifnextchar[{\@tempswatrue
  \thanks@optarg}{\@tempswafalse\thanks@optarg[]}}
\def\thanks@optarg[#1]#2{\refstepcounter{footnote}\if@tempswa
  \label{#1}\else\relax\fi
  \add@tok\t@glob@notes{\footnotetext}%
  \add@xtok\t@glob@notes{[\the\c@footnote]}%
  \add@tok\t@glob@notes{{#2}}}
%\def\footnote{\@ifnextchar[{\@xfootnote}{\refstepcounter%
%   {\@mpfn}\xdef\@thefnmark{\thempfn}\@footnotemark\@footnotetext}}
%\def\footnotemark{\@ifnextchar[{\@xfootnotemark%
%    }{\refstepcounter{footnote}\xdef\@thefnmark{\thefootnote}\@footnotemark}}
%\def\footnoterule{\kern-3\p@\hrule \@width 3pc% The \hrule has default \@height of 0.4pt.
%  \kern 2.6\p@} \let\report@elt\@gobble
\def\frontmatter{%
  \label{FirstPage}
  \NoHyper
  \let\@corresp@note\relax
  \global\t@glob@notes={}\global\c@author\z@
  \global\c@collab\z@ \global\c@address\z@
  \sv@mathsurround\mathsurround \m@th
  \global\n@author=0\n@author@\relax
  \global\n@collab=0\n@collab@\relax
  \global\advance\n@author\m@ne   % In comparisons later on we need
  \global\advance\n@collab\m@ne   % n@author-1 and n@collab-1
  \global\@firstauthortrue        % set to false by first \author or \collab
  \global\@hasabstractfalse       % Default:  no abstract or keywords
  \global\@prefacefalse           %           not preface
  \@ifundefined{RIfM@}{}{\undo@AMS}%
 \parskip 4\p@
 \open@fm \ignorespaces}
\def\preface{\@prefacetrue}
\def\endfrontmatter{%
  \global\n@author=\c@author
  \global\n@collab=\c@collab \@writecount
  \global\@topnum\z@
  \thispagestyle{copyright}%            % Format rest of front matter:
  \if@preface \else                     % IF not preface THEN
  \history@fmt                          % print history (received, ...)
  \newcount\c@sv@footnote
  \global\c@sv@footnote=\c@footnote     % save current footnote number
  \if@hasabstract                       % IF abstract/ keywords THEN
   \vskip 24\p@ \@plus 6\p@ \@minus 3\p@ % Space above rule
    \hrule height 0.4pt
    \vskip 8\p@
    \unvbox\t@abstract                  % print abstract, if any
    \unvbox\t@keyword                   % Keyword abstract, if any
    \vskip 10\p@
    \hrule height 0.4pt
  \fi                                   % FI
  \dedicated@fmt                        % print dedication
  \vskip 8\p@                          % Vertical space below frontmatter
  \fi                                   % FI
  \close@fm                             % Close front matter material.
  \endNoHyper
  \output@glob@notes                   % Put notes at bottom of 1st page
  \global\c@footnote=\c@sv@footnote     % restore footnote number
  \global\@prefacefalse
  \global\leftskip\z@                   % Restore the normal values of
  \global\@rightskip\z@                 % \leftskip,
  \global\rightskip\@rightskip          % \rightskip and
  \global\mathsurround\sv@mathsurround  % \mathsurround.
  \let\title\relax       \let\author\relax
  \let\collab\relax      \let\address\relax
  \let\frontmatter\relax \let\endfrontmatter\relax
  \let\@maketitle\relax  \let\@@maketitle\relax
  \normal@text}
\let\maketitle\relax
\newdimen\t@xtheight
\t@xtheight\textheight \advance\t@xtheight-\splittopskip
\def\open@fm{\global\setbox\fm@box=\vbox\bgroup
  \hsize=\textwidth                         % Front matter is page-wide
  \centering                                % and centered
  \sv@hyphenpenalty\hyphenpenalty           % (save \hyphenpenalty)
  \hyphenpenalty\@M}                        % and not hyphenated
\def\close@fm{\egroup                       % close \vbox (\fm@box)
  \fm@size=\dp\fm@box \advance\fm@size by \ht\fm@box
  \@whiledim\fm@size>\t@xtheight \do{%
    \global\setbox\@tempboxa=\vsplit\fm@box to \t@xtheight
    \unvbox\@tempboxa \newpage
    \fm@size=\dp\fm@box \advance\fm@size by \ht\fm@box}
  \if@TwoColumn
    \emergencystretch=1pc \twocolumn[\unvbox\fm@box]
  \else
    \unvbox\fm@box
  \fi}
\def\output@glob@notes{\bgroup
  \the\t@glob@notes
  \egroup}
\def\justify@off{\let\\=\@normalcr
  \leftskip\z@ \@rightskip\@flushglue \rightskip\@rightskip}
\def\justify@on{\let\\=\@normalcr
  \leftskip\z@ \@rightskip\z@ \rightskip\@rightskip}
\def\normal@text{\global\let\\=\@normalcr
  \global\leftskip\z@ \global\@rightskip\z@ \global\rightskip\@rightskip
  \global\parfillskip\@flushglue}
\def\@writecount{\write\@mainaux{\string\global
  \string\@namedef{n@author@}{\the\n@author}}%
  \write\@mainaux{\string\global\string
  \@namedef{n@collab@}{\the\n@collab}}}
\def\title#1{%
  \beg@elem
  \title@note@fmt                      % formatting instruction
  \add@tok\t@glob@notes                % for \thanks commands
    {\title@note@fmt}%
  \proc@elem{title}{#1}%
  \def\title@notes{\the\t@loc@notes}%  % store the notes of the title,
  \title@fmt{\@title}{\title@notes}%   % print the title
  \ignorespaces}
\def\subtitle#1{%
  \beg@elem
  \proc@elem{subtitle}{#1}%
  \def\title@notes{\the\t@loc@notes}%     % store the notes of the title,
  \subtitle@fmt{\@subtitle}{\title@notes} % print the title
  \ignorespaces}
\newdimen \@logoheight \@logoheight 5pc
\def\@Lhook{\vrule \@height \@logoheight \@width \z@ \vrule \@height 10\p@
\@width 0.2\p@ \vrule \@height 0.2\p@ \@width 10pt}
\def\@Rhook{\vrule \@height 0.2\p@ \@width 10\p@ \vrule \@height 10\p@
\@width 0.2\p@ \vrule \@height \@logoheight \@width \z@}
\def\title@fmt#1#2{%
\@ifundefined{@runtitle}{\gdef\@runtitle{#1}}{}%
 \vspace*{16pt}                         % Vertical space above title
  {\LARGE #1\,\hbox{$^{#2}$}\par}%
 \vskip 24\p@                           % Vertical space below title
  }
\def\subtitle@fmt#1#2{%                 % No vertical space above sub-title
  {\@titlesize #1\,\hbox{$^{#2}$}}\par}
\def\title@note@fmt{\def\thefootnote{\fnstar{footnote}}}
\def\author{\@ifnextchar[{\author@optarg}{\author@optarg[]}}
\def\author@optarg[#1]#2{\stepcounter{author}%
  \beg@elem
  \@for\@tempa:=#1\do{\expandafter\add@thanksref\expandafter{\@tempa}}%
  \report@elt{author}\proc@elem{author}{#2}%
  \author@fmt{\the\c@author}{\the\t@loc@notes}{\@author}} % removed by SP
\ignorespaces
\def\author@fmt#1#2#3{\@newelemtrue
  \if@firstauthor
  \first@author \global\@firstauthorfalse \fi
  \ifnum\prev@elem=\e@author \global\@newelemfalse \fi
  \if@newelem \author@fmt@init \fi
  \edef\@tempb{#2}\ifx\@tempb\@empty
    \hbox{{\author@font #3}}\else
    \hbox{{\author@font #3}\,$^{\mathrm{#2}}$}%
  \fi}
\def\first@author{\author@note@fmt  % re-define \thefootnote as
                                    % appropriate for author/address
  \add@tok\t@glob@notes
    {\author@note@fmt\@corresp@note}}%
\def\author@fmt@init{%
  \par
  \vskip 8\p@ \@plus 4\p@ \@minus 2\p@
  \@authorsize
  \leavevmode}                        % Vertical space above author list
 \def\and{\unskip~and~}
\def\collab{\@ifstar{\collab@arg}{\collab@arg}}
\let\collaboration=\collab
\def\collab@arg#1{\stepcounter{collab}%
  \if@firstauthor \first@collab \global\@firstauthorfalse \fi
  \beg@elem
  \proc@elem{collab}{#1}%
  \collab@fmt{\the\c@collab}{\the\t@loc@notes}{\@collab}%
  \ignorespaces}
\def\collab@fmt#1#2#3{\@newelemtrue
  \ifnum\prev@elem=\e@collab \global\@newelemfalse \fi
  \if@newelem \collab@fmt@init \fi
  \par                                 % Start new paragraph
  {\large #3\,$^{\mathrm{#2}}$}}
\def\first@collab{
  \collab@note@fmt                     % re-define \thefootnote as
  \add@tok\t@glob@notes                % appropriate for collab/address
    {\collab@note@fmt}}%
\def\collab@fmt@init{\vskip 1em}       % Vertical space above list
\def\author@note@fmt{\setcounter{footnote}{0}%
  \def\thefootnote{\xarabic{footnote}}}
\let\collab@note@fmt=\author@note@fmt
\def\xarabic#1{%
\expandafter\expandafter\expandafter\ifnum\expandafter\the\@nameuse{c@#1}<0
  *\else\arabic{#1} \fi}
\def\address{\@ifstar{\address@star}%
  {\@ifnextchar[{\address@optarg}{\address@noptarg}}}
\def\address@optarg[#1]#2{\refstepcounter{address}%
  \beg@elem
  \report@elt{address}\proc@elem{address}{#2}%
  \address@fmt{\the\c@address}{\the\t@loc@notes}{\@address}\label{#1}%
  \ignorespaces}
\def\address@noptarg#1{\refstepcounter{address}%
  \beg@elem
  \proc@elem{address}{#1}%
  \address@fmt{\z@}{\the\t@loc@notes}{\@address}%
  \ignorespaces}
\def\address@star#1{%
  \beg@elem
  \proc@elem{address}{#1}%
  \address@fmt{\m@ne}{\the\t@loc@notes}{\@address}%
  \ignorespaces}
\def\theaddress{\alph{address}}
\def\address@fmt#1#2#3{\@newelemtrue
  \ifnum\prev@elem=\e@address \@newelemfalse \fi
  \if@newelem \address@fmt@init \fi
  \noindent \bgroup \@addressstyle
  \ifnum#1=\z@
    #3\,$^{\mathrm{#2}}$\space%
  \else
    \ifnum#1=\m@ne
      $^{\phantom{\mathrm{\theaddress}}}$\space #3\,$^{\mathrm{#2}}$%
    \else
      $^{\mathrm{\theaddress}}$\space #3\,$^{\mathrm{#2}}$%
    \fi
  \fi
  \par \egroup}
\def\address@fmt@init{%
  \par                                % Start new paragraph
   \vskip 6\p@ \@plus 3\p@ \@minus 1.5pt}
\def\abstract{\@ifnextchar[{\@abstract}{\@abstract[]}}
% \def\@abstract[#1]{%
%   \global\@hasabstracttrue
%   \hyphenpenalty\sv@hyphenpenalty     % restore \hyphenpenalty
%   \global\setbox\t@abstract=\vbox\bgroup
%    \small
%    \hbox to \textwidth\bgroup\hfill\begin{minipage}{.8\textwidth}
%  \abstractname
%   \ignorespaces}
%  \def\endabstract{\end{minipage}\hfill\egroup\egroup}
\def\@abstract[#1]{%
  \global\@hasabstracttrue
  \hyphenpenalty\sv@hyphenpenalty
  \global\setbox\t@abstract=\vbox\bgroup
  \leftskip\z@%
  \@rightskip\z@ \rightskip\@rightskip \parfillskip\@flushglue
  \small
  \parindent 1em
  \noindent {\bf\abstractname}
  \par\noindent
  \ignorespaces}
\def\endabstract{\par \egroup}
\def\keyword{%
  \global\@hasabstracttrue             % Implies rules are to be printed
  \hyphenpenalty\sv@hyphenpenalty      % restore \hyphenpenalty
  \def\sep{\unskip, }                  % separator for multiple keywords
  \def\MSC{\par\leavevmode\hbox {\it 1991 MSC:\ }}%
  \def\PACS{\par\leavevmode\hbox {\it PACS:\ }}%
  \global\setbox\t@keyword=\vbox\bgroup
   \hbox to \textwidth\bgroup\hfill\begin{minipage}{1.0\textwidth}
  \@keywordsize
  \parskip\z@
  \vskip 10\p@ \@plus 2\p@ \@minus 2\p@  % One line of space above keywords.
  \noindent \@keywordheading
  \justify@off                         % Keywords are not justified.
  \ignorespaces}
\def\endkeyword{\end{minipage}\hfill\egroup\egroup}
\def\runtitle#1{\gdef\@runtitle{#1}}
\def\runauthor#1{\gdef\@runauthor{#1}} \def\@runauthor{}
\def\journal#1{\gdef\@journal{#1}}
\def\volume#1{\gdef\@volume{#1}}       \def\@volume{0}
\def\issue#1{\gdef\@issue{#1}}         \def\@issue{0}
\newcount\@pubyear
\newcount\@copyear
\@pubyear=\number\year
\@copyear\@pubyear \advance\@copyear-1900
\def\pubyear#1{\global\@pubyear#1
  \global\@copyear\@pubyear \global\advance\@copyear-1900
  \ignorespaces}
\def\firstpage#1{\def\@tempa{#1}\ifx\@tempa\@empty\else
  \gdef\@firstpage{#1}%
  \global\c@page=#1 \ignorespaces\fi}
\def\@firstpage{1}
\def\@lastpage{\@ifundefined{r@LastPage}{0}{\pageref{LastPage}}}
\def\lastpage#1{\def\@tempa{#1}\ifx\@tempa\@empty\else
  \gdef\@lastpage{#1}\ignorespaces\fi
  }
\AtEndDocument{%
   \clearpage
   \addtocounter{page}{-1}%
   \immediate\write\@auxout{\string
   \newlabel{LastPage}{{}{\thepage}{\relax }{}{}}}%
   \addtocounter{page}{1}%
}
\def\date#1{\gdef\@date{#1}}                  
\def\@date{\today}
\def\aid#1{}
\def\ssdi#1#2{}
\def\received#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@received{#1}\fi}
  \def\@received{\relax}
\def\revised#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@revised{#1}\fi}
  \def\@revised{\relax}
\def\accepted#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@accepted{#1}\fi}
  \def\@accepted{\relax}
\def\communicated#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@communicated{#1}\fi}
  \def\@communicated{\relax}
\def\dedicated#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@dedicated{#1}\fi}
  \def\@dedicated{\relax}
\def\presented#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@presented{#1}\fi}
  \def\@presented{\relax}
\def\articletype#1{\gdef\@articletype{#1}}
  \@ifundefined{@articletype}{\def\@articletype{}}{}
\def\received@prefix{Received~}
\def\revised@prefix{; revised~}
\def\accepted@prefix{; accepted~}
\def\communicated@prefix{; communicated~by~}
\def\history@prefix{}
\def\received@postfix{}
\def\revised@postfix{}
\def\accepted@postfix{}
\def\communicated@postfix{}
\def\history@postfix{}
\def\empty@data{\relax}
\def\history@fmt{%
  \bgroup
  \@historysize
  \vskip 6\p@ \@plus 2\p@ \@minus 1\p@      % Vertical space above history
  \ifx\@received\empty@data \else           % If there is no \received, do not print anything
    \leavevmode
    \history@prefix
    \received@prefix\@received \received@postfix%
    \ifx\@revised\empty@data \else
      \revised@prefix\@revised \revised@postfix%
    \fi
    \ifx\@accepted\empty@data \else
      \accepted@prefix\@accepted \accepted@postfix%
    \fi
    \ifx\@communicated\empty@data \else
      \communicated@prefix\@communicated \communicated@postfix%
    \fi
    \history@postfix
  \fi
  \par \egroup}
\def\dedicated@fmt{%
  \ifx\@dedicated\empty@data \else
    \vskip 4\p@ \@plus 3\p@
    \normalsize\it\centering \@dedicated
    \fi}
\def\@ialph#1{\ifcase#1\or \or \or \or \or e\or f\or g\or h\or i\or j\or
  k\or \ell\or m\or n\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x\or
  y\or z\or aa\or ab\or ac\or ad\or ae\or af\or ag\or ah\or ai\or aj\or
  ak\or a\ell\or am\or an\or ao\or ap\or aq\or ar\or as\or at\or au\or av\or
  aw\or ay\or az\or ba\or bb\or bc\or bd\or be\or bf\or bg\or bh\or bi\or
  bj\or bk\or b\ell\or bm\or bn\or bo\or bp\or bq\or br\or bs\or bt\or
  bu\or bw\or bx\or by\or bz\or ca\or cb\or cc\or cd\or ce\or cf\or cg\or
  ch\or ci\or cj\or ck\or c\ell\or cm\or cn\or co\or cp\or cq\or cr\or
  cs\or ct\or cu\or cw\or cx\or cy\or cz\else\@ctrerr\fi}
\def\fnstar#1{\@fnstar{\@nameuse{c@#1}}}
\def\@fnstar#1{\ifcase#1\or
    \hbox{$\star$}\or
    \hbox{$\star\star$}\or
    \hbox{$\star\star\star$}\or
    \hbox{$\star\star\star\star$}\or
    \hbox{$\star\star\star\star\star$}\or
    \hbox{$\star\star\star\star\star\star$}
  \else
    \@ctrerr
  \fi
  \relax}
\mark{{}{}}   % Initializes TeX's marks
\def\rightheadline{}
\def\leftheadline{}
\def\annum{\the\@pubyear}
\def\firstheadline{}
\def\firstfootline{}
\def\ps@plain{\let\@mkboth\@gobbletwo
 \def\@oddhead{\rightheadline}%
 \def\@evenhead{\leftheadline}%
 \def\@oddfoot{\hfil {\rmfamily\thepage} \hfil}%
 \let\@evenfoot\@oddfoot}
\def\@copyright{\the\@copyear/ $\copyright$\ \the\@pubyear\
  Elsevier B.V. \@company{} All  rights reserved}
\def\@jou@vol@pag{\@journal\ \@volume\ (\the\@pubyear)\ }
\def\sectionmark#1{}
\def\subsectionmark#1{}
\let\@j@v@p\@jou@vol@pag    % long journal title appears in reprint line
\let\@@j@v@p\@jou@vol@pag   % long journal title appears in running headline
\def\sectionmark#1{}
\def\subsectionmark#1{}
\def\ps@copyright{\let\@mkboth\@gobbletwo
  \def\@oddhead{\ifnum\value{page}=1\firstheadline
              \else\rightheadline\fi}
        \def\@evenhead{\ifnum\value{page}=1\firstheadline
              \else\leftheadline\fi}
  \def\@oddfoot{\small\slshape
    \def\@tempa{0}
    \ifx\@volume\@tempa
      Preprint submitted to \@journal\hfil\@date\/%
    \else
      \firstfootline\fi}%
  \let\@evenfoot\@oddfoot
}
\let\ps@headings\ps@plain
\def\today{\number\day\space\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\year}
\def\nuc#1#2{\relax\ifmmode{}^{#1}{\protect\text{#2}}\else${}^{#1}$#2\fi}
\def\itnuc#1#2{\setbox\@tempboxa=\hbox{\scriptsize\it #1}
  \def\@tempa{{}^{\box\@tempboxa}\!\protect\text{\it #2}}\relax
  \ifmmode \@tempa \else $\@tempa$\fi}
\let\old@vec\vec % save old definition of \vec
\def\pol#1{\old@vec{#1}}
\def\@bfvec#1{\boldsymbol{#1}}
\def\@pmbfvec#1{\pmb{#1}}
\def\undo@AMS{\global\let\vec\@bfvec}
\def\half{{\textstyle {1\over2}}}
\def\threehalf{{\textstyle {3\over2}}}
\def\quart{{\textstyle {1\over4}}}
\def\d{\,\mathrm{d}}
\def\e{\mathop{\mathrm{e}}\nolimits}
\def\int{\intop}
\def\oint{\ointop}
\newbox\slashbox \setbox\slashbox=\hbox{$/$}
\newbox\Slashbox \setbox\Slashbox=\hbox{\large$/$}
\def\pFMslash#1{\setbox\@tempboxa=\hbox{$#1$}
  \@tempdima=0.5\wd\slashbox \advance\@tempdima 0.5\wd\@tempboxa
  \copy\slashbox \kern-\@tempdima \box\@tempboxa}
\def\pFMSlash#1{\setbox\@tempboxa=\hbox{$#1$}
  \@tempdima=0.5\wd\Slashbox \advance\@tempdima 0.5\wd\@tempboxa
  \copy\Slashbox \kern-\@tempdima \box\@tempboxa}
\def\FMslash{\protect\pFMslash}
\def\FMSlash{\protect\pFMSlash}
\mathchardef\Gamma="0000
\mathchardef\Delta="0001
\mathchardef\Theta="0002
\mathchardef\Lambda="0003
\mathchardef\Xi="0004
\mathchardef\Pi="0005
\mathchardef\Sigma="0006
\mathchardef\Upsilon="0007
\mathchardef\Phi="0008
\mathchardef\Psi="0009
\mathchardef\Omega="000A
\mathchardef\varGamma="0100
\mathchardef\varDelta="0101
\mathchardef\varTheta="0102
\mathchardef\varLambda="0103
\mathchardef\varXi="0104
\mathchardef\varPi="0105
\mathchardef\varSigma="0106
\mathchardef\varUpsilon="0107
\mathchardef\varPhi="0108
\mathchardef\varPsi="0109
\mathchardef\varOmega="010A
  \def\Cset{\Bbb{C}}
  \def\Hset{\Bbb{H}}
  \def\Nset{\Bbb{N}}
  \def\Qset{\Bbb{Q}}
  \def\Rset{\Bbb{R}}
  \def\Zset{\Bbb{Z}}
\if@TwoColumn
  \adjdemerits=100
  \linepenalty=100
  \doublehyphendemerits=5000        % experimental (1993-12-14)
  \emergencystretch=1.6pc
  \spaceskip=0.3em \@plus 0.17em \@minus 0.12em
\fi
\ps@headings                                % 'headings' page style
\pagenumbering{arabic}                      % Arabic page numbers
\def\thepage{\@pagenumprefix\arabic{page}}  % preceded by \@pagenumprefix
\InputIfFileExists{\@shortjid.cfg}{}{}
\endinput
%%
%% End of file `endm.cls'.