%%
%% This is file `elsart.cls',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% esl.dtx (with options: `package,elsart,ONECOL,DEEPLIST')
%%
%% elsart.cls Copyright (C) 1994-2007 Elsevier Science
%%
%% This file may be distributed and/or modified under the
%% conditions of the LaTeX Project Public License, either version 1.2
%% of this license or (at your option) any later version.
%% The latest version of this license is in
%% http://www.latex-project.org/lppl.txt
%% and version 1.2 or later is part of all distributions of LaTeX
%% version 1999/12/01 or later.
%%
\def\readRCS$#1: #2 #3 #4 #5${%
\def\RCSfile{#2}%
\def\RCSversion{#3}%
\def\RCSdate{#4}%
}
\def\@shortjnl{\relax}
\def\esp@fileversion{2.20}
\def\esp@filedate{2007/08/16}
\def\@journal{Elsevier} \def\@company{Elsevier}
\def\@issn{000-0000}
\def\@shortjid{elsart}
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
\ProvidesClass{\@shortjid}[\esp@filedate, \esp@fileversion: \@journal]
\newif\if@TwoColumn
\newif\if@seceqn
\newif\if@secthm
\newif\if@nameyear
\newif\if@Elproofing
\@Elproofingfalse
\DeclareOption{12pt}{}
\DeclareOption{11pt}{}
\DeclareOption{10pt}{}
\DeclareOption{oneside}{\@twosidefalse \@mparswitchfalse}
\DeclareOption{twoside}{\@twosidetrue \@mparswitchtrue}
\@twocolumnfalse
\DeclareOption{onecolumn}{\@TwoColumnfalse}
\DeclareOption{twocolumn}{\@TwoColumntrue}
\newif\if@narrowdisplay
\@narrowdisplayfalse
\DeclareOption{narrowdisplay}{\@narrowdisplaytrue}
\newif\if@draft\@draftfalse
\DeclareOption{draft}{%
\@drafttrue
\overfullrule 5\p@ % to indicate overfull boxes
}
\DeclareOption{final}{%
\@draftfalse
\overfullrule \z@
}
\let\snm\relax \let\cty\relax \let\cny\relax\let\jr\relax
\newif\if@ussrhead \@ussrheadfalse
\DeclareOption{ussrhead}{\@ussrheadtrue}
\@seceqnfalse % Default: equation numbering is not
\DeclareOption{seceqn}{\@seceqntrue} % reset at beginning of each section
\@secthmfalse
\DeclareOption{secthm}{\@secthmtrue}
\@nameyearfalse
\DeclareOption{nameyear}{\@nameyeartrue}
\def\@blstr{1}
\DeclareOption{doublespacing}{\def\@blstr{1.7}}
\DeclareOption{reviewcopy}{\def\@blstr{1.7}}
\newif\if@symbold\@symboldfalse
\DeclareOption{symbold}{\@symboldtrue}
\newif\if@amsthm\@amsthmfalse
\DeclareOption{amsthm}{\@amsthmtrue}
\ExecuteOptions{oneside}
\ExecuteOptions{onecolumn,final}
\ProcessOptions
\if@TwoColumn\@narrowdisplayfalse\fi
\if@draft\else\@narrowdisplayfalse\fi
\def\@pagenumprefix{}
\def\author@font{}
\def\partname{Part}
\def\appendixname{Appendix}
\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@
\normallineskip 1\p@
\def\baselinestretch{1}
\frenchspacing
\def\cropwidth{297mm}
\def\cropheight{210mm}
\def\cropleft{0mm}
\def\croptop{0mm}
\def\FullCopyrightText{}
\def\copyrightholder#1{\def\@copyrightholder{#1}}
\newdimen\@frontmatterwidth
\def\@overtitleskip{69\p@}
\def\@overhistoryskip{\z@}
\def\@undertitleskip{\z@}
\def\@overkeywordskip{12\p@}
\def\@overabstractskip{8\p@}
\def\@overcaptionskip{8\p@}
\def\@preabstractskip{24\p@ \@plus 6\p@ \@minus 3\p@}
\def\@belowfmskip{18\p@}
\def\@bibliosize{\small}
\def\@historysize{\small}
\def\@keywordsize{\small}
\def\@overaddressskip{2pt}
\def\@titlesize{\Large\bfseries}
\def\@bibitemsep{0.3\@bls \@plus 0.1\@bls \@minus 0.1\@bls}
\def\@authorsize{\large}
\def\@keywordheading{{\it Key words: \ }}
\def\@addressstyle{\small\itshape}
\def\@captionsize{\small}
\def\@tablecaptionsize{\@captionsize}
\def\@figurecaptionsize{\@captionsize}
\def\@tablesize{\small}
\def\@keywordwidth{.8\textwidth}
\def\@abstractwidth{.8\textwidth}
\def\@fignumfont#1{#1}
\def\@secnumfont#1{\upshape}
\def\@catchlinesize{\footnotesize}
\def\@runheadsize{\normalsize}
\def\@narrowdisplaywidth{259pt}
\def\etal{et al.}
\def\AND{\&}
\def\@Colofonheight{1cm}
\def\@abstractsize{\fontsize{\@ixpt}{11pt}\selectfont}
\def\@articletypesize{\fontsize{\@xiiipt}{13pt}\selectfont}
\def\normalsize{\@setfontsize\normalsize\@xiipt{14.5}%
\def\@ptsize{2}
\abovedisplayskip 12\p@ \@plus 2\p@ \@minus 2\p@%
\belowdisplayskip \abovedisplayskip
\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 \parsep
\topsep 9\p@ \@plus3\p@ minus5\p@}}
\let\footnotesize=\small
\let\@xviiipt\@xviipt
\def\scriptsize{\@setfontsize\scriptsize\@viiipt{9.5}}
\def\tiny{\@setfontsize\tiny\@vipt{7}}
\def\large{\@setfontsize\large\@xivpt{18}}
\def\Large{\@setfontsize\Large\@xviipt{22}}
\def\LARGE{\@setfontsize\LARGE\@xxpt{22}}
\def\huge{\@setfontsize\huge\@xxvpt{27}}
\let\Huge=\huge
\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 20\p@ % Left margin on odd-numbered pages.
\evensidemargin 20\p@ % Left margin on even-numbered pages.
\marginparwidth 10\p@ % \@Width of marginal notes.
\else % Values for one-sided printing:
\oddsidemargin 20\p@ % Left margin on odd-numbered pages.
\evensidemargin 20\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
\@tempdima=651pt \advance\@tempdima -\topskip \@tempcnta=\@tempdima
\@tempdimb=\@blstr\@bls \@tempcntb=\@tempdimb
\divide\@tempcnta\@tempcntb
\textheight\@tempdimb \multiply\textheight\@tempcnta
\advance\textheight\topskip
\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 1pc \@plus 1\p@ % Extra vertical space between paragraphs.
\parindent \z@ % Indentation of each paragraph.
\newskip\eqntopsep % Extra vertical space, in addition to
\eqntopsep 12\p@ \@plus 2\p@ \@minus 2\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\subsection{\@startsection{subsection}{2}{\z@}{\@bls
\@plus .3\@bls \@minus .1\@bls}{\@bls}{\normalsize\itshape}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{\@bls
\@plus .2\@bls}{0.0001pt}{\normalsize\itshape}}
\def\paragraph{\@startsection{paragraph}{4}{\z@}{3.25ex \@plus
2ex \@minus 0.2ex}{-1em}{\normalsize\bfseries}}
\setcounter{secnumdepth}{4}
\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@format#1#2{#2}
\def\head@style{\interlinepenalty\@M
\hyphenpenalty\@M \exhyphenpenalty\@M
\rightskip \z@ \@plus 0.5\hsize \relax
}
\def\app@number#1{\setcounter{#1}{0}%
\@addtoreset{#1}{section}%
\@namedef{the#1}{\thesection.\arabic{#1}}}
\def\appendix{\@ifstar{\appendix@star}{\appendix@nostar}}
\def\appendix@nostar{%
\def\lb@section{\appendixname\ \thesection.\half@em}
\def\lb@empty@section{\appendixname\ \thesection}
\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\appendix@star{%
\def\lb@section{\appendixname}\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*{Acknowledgements}%
\addtocontents{toc}{\protect\vspace{6pt}}%
\addcontentsline{toc}{section}{Acknowledgements}%
}
\@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
\leftmarginiii\labelwidthiii \advance\leftmarginiii\labelsep
\leftmarginiv\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 \z@ \partopsep\z@ \parsep\z@ \itemsep\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\right@label#1{\hss\llap{#1}}
\def\thick@label#1{\hspace\labelsep #1}
\newcount\@maxlistdepth
\@maxlistdepth=4
\def\labelitemi{$\bullet$} \def\labelitemii{$\cdot$}
\def\labelenumi{(\theenumi)} \def\theenumi{\arabic{enumi}}
\def\labelenumii{(\alph{enumii})} \def\theenumii{\theenumi\alph{enumii}}
\def\labelenumiii{(\roman{enumiii})}\def\theenumiii{\theenumii.\roman{enumiii}}
\def\labelenumiv{(\Alph{enumiv})} \def\theenumiv{\theenumiii.\Alph{enumiv}}
\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=\right@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\right@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
\if@narrowdisplay
\def\calcmathindent{%
\mathindent\linewidth\relax
\advance\mathindent-\@narrowdisplaywidth}
\else
\let\calcmathindent\relax
\fi
\def\[{\relax\ifmmode\@badmath
\else%\bgroup removed on request from BW (1993-05-17)
\@beginparpenalty\predisplaypenalty
\@endparpenalty\postdisplaypenalty
\calcmathindent
\begin{trivlist}\@topsep \eqntopsep % used by first \item
\@topsepadd \eqntopsep % used by \@endparenv
\item[]\leavevmode
\hbox to\linewidth\bgroup$ \displaystyle
\hskip\mathindent\bgroup\fi}
\def\]{\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
\calcmathindent
\item[]\leavevmode
\hbox to\linewidth\bgroup $ \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
\calcmathindent
\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.
\newdimen\rulepreskip \newdimen\rulepostskip
\rulepreskip=4\p@ \rulepostskip=6\p@
\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{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\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
\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}
\RequirePackage{latexsym}
\def\qed{\relax\ifmmode\hskip2em \Box\else\unskip\nobreak\hskip1em $\Box$\fi}
\def\proof@headerfont{\upshape\bfseries}
\if@amsthm
\RequirePackage{amsthm}%
\def\th@plain{%
\thm@preskip\parskip
\thm@postskip\z@
\itshape % body font
}
\def\th@definition{%
\thm@preskip\parskip
\thm@postskip\z@
\normalfont % body font
}
\def\th@remark{%
\thm@headfont{\itshape}%
\normalfont % body font
\thm@preskip\parskip \divide\thm@preskip\tw@
\thm@postskip\z@
}
\else\let\theoremstyle\@gobble\fi
\newenvironment{pf}%
{\par\addvspace{\@bls \@plus 0.5\@bls \@minus 0.1\@bls}\noindent
{\bfseries\Elproofname}\enspace\ignorespaces}%
{\par\addvspace{\@bls \@plus 0.5\@bls \@minus 0.1\@bls}}
\def\Elproofname{PROOF.}
\@namedef{pf*}#1{\par\begingroup\def\Elproofname{#1}\pf\endgroup\ignorespaces}
\expandafter\let\csname endpf*\endcsname=\endpf
\theoremstyle{plain}
\if@secthm
\newtheorem{thm}{Theorem}[section]
\@addtoreset{thm}{section}
\else
\newtheorem{thm}{Theorem}
\fi
\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}
\theoremstyle{definition}
\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}}
\def\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}
\newcommand\listoffigures{%
\section*{\listfigurename
\@mkboth{\MakeUppercase\listfigurename}%
{\MakeUppercase\listfigurename}}%
\@starttoc{lof}%
}
\newcommand*\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
\newcommand\listoftables{%
\section*{\listtablename
\@mkboth{%
\MakeUppercase\listtablename}{\MakeUppercase\listtablename}}%
\@starttoc{lot}%
}
\let\l@table\l@figure
\def\tableofcontents{%
\begin{small}
\leftline {{\bfseries \contentsname\/}}
\setcounter{secnumdepth}{4}%
\setcounter{tocdepth}{2}%
{\@starttoc{toc}}%
\end{small}
}
\newcommand*\l@section{\@dottedtocline{1}{1.5em}{2.3em}}
\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}}
\def\@dotsep{2000}
\def\thebibliography{%
\@startsection{section}{1}{\z@}{20\p@ \@plus 8\p@ \@minus 4pt}
{\@bls}{\normalsize\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\@bibitemsep
\usecounter{enumiv}\let\p@enumiv\@empty
\def\theenumiv{\arabic{enumiv}}}%
\tolerance\@M
\hyphenpenalty\@M
\hbadness5000 \sfcode`\.=1000\relax}
\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em}
\if@nameyear
\def\@biblabel#1{}
\else
\def\@biblabel#1{[#1]\hskip \z@ \@plus 1filll}
\fi
\let\make@bb@error\relax
\def\@mkbberr{\def\bibitem{\ClassError{elsart}%
{Bibitem after note}%
{You are using a bibitem after a note in a subbibitems
environment;\MessageBreak
note should the last item in a subbibitems environment}}}
\def\@itemnote{\make@bb@error\item[]}
\def\mk@noitemnote{\ifx\@tempa\note \let\note\@noitemnote \fi}
\def\@noitemnote{\let\note\@itemnote}
\AtBeginDocument{%
\let\nopeek@bibitem\@bibitem
\let\nopeek@lbibitem\@lbibitem
\def\@bibitem#1{\let\note\@itemnote\nopeek@bibitem{#1}%
\futurelet\@tempa\mk@noitemnote}
\def\@lbibitem[#1]#2{\let\note\@itemnote\nopeek@lbibitem[#1]{#2}%
\futurelet\@tempa\mk@noitemnote}
}
\newif\if@natbibloaded\@natbibloadedfalse
\AtBeginDocument{\@ifpackageloaded{natbib}{\@natbibloadedtrue}{}}
\newenvironment{subbibitems}[1]{%
\if@natbibloaded\def\bib@ctr{NAT@ctr}\else\def\bib@ctr{enumiv}\fi
\if@filesw {\let \protect \noexpand \immediate \write \@auxout
{\string \nocollapse@cites}%
\global\let\nocollapse@cites\relax}\fi
\def\@itemslabel{#1}%
\stepcounter{\bib@ctr}%
\edef\main@bibnum{\the\value{\bib@ctr}}%
\setcounter{\bib@ctr}{0}%
\def\thebib@ctr{\main@bibnum\alph{\bib@ctr}}%
\if@natbibloaded
\def\bibitem{\@ifnextchar [{\@lbibitem }{\global \NAT@stdbsttrue
\stepcounter {\bib@ctr}\@lbibitem [\thebib@ctr]}}%
\else
\def\@bibitem##1{\stepcounter{\bib@ctr}\@lbibitem[\thebib@ctr]{##1}}%
\fi
\let\make@bb@error\@mkbberr
}{%
\if@filesw {%
\if@natbibloaded{%
\let\protect\noexpand
\immediate\write\@auxout {\string\bibcite{\@itemslabel}%
{{\main@bibnum a--\alph {\bib@ctr}}{}{{}}{{}}}}%
\immediate\write\@auxout {\string\bibcite{\@itemslabel :s}%
{{\main@bibnum}{}{{}}{{}}}}%
}\else{%
\let\protect\noexpand
\immediate\write\@auxout {\string\bibcite{\@itemslabel}%
{\main@bibnum a--\alph{\bib@ctr}}}%
\immediate\write\@auxout {\string\bibcite{\@itemslabel :s}%
{\main@bibnum}}%
}\fi
}\fi
\setcounter{\bib@ctr}{\main@bibnum}%
}
\let\nocollapse@citex\@citex
\newcount\@tempcntc
\def\collapse@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi
\@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do
{\edef\@citeb{\expandafter\@firstofone\@citeb\@empty}%
\@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}}
\let\@citex\collapse@citex
\def\nocollapse@cites{%
\@ifpackageloaded{hyperref}{}{\global\let\@citex\nocollapse@citex}%
\global\let\nocollapse@cites\relax}
\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}\protected@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{\,\hbox{$^{\mathrm{\@thefnmark}}$}}
\long\def\@mpmakefntext#1{\noindent
\hbox{$^{\mathrm{\@thefnmark}}$} #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{$^{\fn@presym\mathrm{\@thefnmark}}$}\,}
\def\patched@end@dblfloat{%
\if@twocolumn
\par\vskip\z@skip %% \par\vskip\z@ added 15 Dec 87
\global\@minipagefalse
\outer@nobreak
\egroup %% end of vbox
\color@endbox
\ifnum\@floatpenalty <\z@
\@largefloatcheck
\@cons\@dbldeferlist\@currbox
\fi
\ifnum \@floatpenalty =-\@Mii \@Esphack\fi
\else
\end@float
\fi
}
\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{\@tablecaptionsize
\global \@minipagefalse
\hbox to \hsize{\parbox[t]{\hsize}{#1 \\ #2}}}
\long\def\@makefigurecaption#1#2{\@figurecaptionsize
\vskip \@overcaptionskip
\setbox\@tempboxa\hbox{#1. #2}
\ifdim \wd\@tempboxa >\hsize % IF longer than one line THEN
\unhbox\@tempboxa\par % set as justified paragraph
\else % ELSE
\global \@minipagefalse
\hbox to\hsize{\hfil\box\@tempboxa\hfil}% center single line.
\fi}
\def\@makecaption{\@makefigurecaption}
\def\conttablecaption{\par \begingroup \@parboxrestore \normalsize
\@makecaption{\fnum@table\,---\,continued}{}\par
\vskip-1pc \endgroup}
\def\contfigurecaption{\vskip-1pc \par \begingroup \@parboxrestore
\@captionsize
\@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}}
\def\endfigure{\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}
\let\old@floatboxreset\@floatboxreset
\def\table{%
\let\@makecaption\@maketablecaption
\def\@floatboxreset{%
\old@floatboxreset
\@tablesize
}%
\let\footnoterule\relax
\let\contcaption\conttablecaption \@float{table}}
\def\endtable{\end@float}
\@namedef{table*}{%
\let\@makecaption\@maketablecaption
\def\@floatboxreset{%
\old@floatboxreset
\@tablesize
}%
\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
\newtoks\corauth@text
\newtoks\email@text
\newtoks\url@text
\newcounter{corauth}
\newcounter{author} % Author counter
\newcount\n@author % Total number of authors
\def\n@author@{1} % 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
\def\theHaddress{\arabic{address}}% for hyperref
\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
\newif\if@haskeywords % 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
\let\corauthref\@gobble
\@xnamedef{@#1}{#2}% % and store as \@#1
\let\thanksref\add@thanksref
\let\corauthref\add@thanksref
\setbox\@tempboxa\hbox{#2}%
\endgroup
\prev@elem=\cur@elem % keep track of type of previous
\cur@elem=\csname e@#1\endcsname % and current element
}
\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}}%
\ignorespaces}
\def\corauth{\@ifnextchar[{\@tempswatrue
\corauth@optarg}{\@tempswafalse\corauth@optarg[]}}
\def\corauth@optarg[#1]#2{\refstepcounter{corauth}%
\if@tempswa\label{#1}\else\relax\fi
\add@tok\corauth@text{\footnotetext}%
\add@xtok\corauth@text{[\the\c@corauth]}%
\add@tok\corauth@text{{#2}}\ignorespaces}
\newcommand\ead[1][email]{%
\add@eadcomma{#1}%
\expandafter\ifcase\csname has@ead@#1\endcsname
\expandafter\global\expandafter\chardef
\csname has@ead@#1\endcsname=1\relax\else
\expandafter\global\expandafter\chardef
\csname has@ead@#1\endcsname=2\relax\fi
\add@ead{#1}%
}
\def\add@ead#1#2{%
\expandafter\add@tok\csname #1@text\endcsname{\texttt{#2}\ead@au}%
\expandafter\add@xtok\csname #1@text\endcsname{{\@author}}%
\ignorespaces
}
\def\add@eadcomma#1{%
\expandafter\ifcase\csname has@ead@#1\endcsname\else
\expandafter\add@tok\csname #1@text\endcsname{, }\fi
}
\let\@ead@au\@empty
\def\ead@newau{\ifx\@ead@au\@empty\else\ead@addau\@ead@au
\let\@ead@au\@empty\fi}
\let\ead@endau\ead@newau
\def\ead@addau#1{ (#1)}
\def\ead@au#1{\def\@ead@au{#1}}
\def\email@name{Email address}
\def\emails@name{Email addresses}
\chardef\has@ead@email=0
\def\url@name{URL}
\def\urls@name{URLs}
\chardef\has@ead@url=0
\let\real@refstepcounter\refstepcounter
\def\footnote{\@ifnextchar[{\@xfootnote}{\real@refstepcounter
{\@mpfn}\protected@xdef\@thefnmark{\thempfn}\@footnotemark\@footnotetext}}
\def\footnotemark{\@ifnextchar[{\@xfootnotemark
}{\real@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
\newenvironment{NoHyper}{}{}
\def\frontmatter{%
\newif\if@hastoc\@hastocfalse
\let\ltx@tableofcontents\tableofcontents
\def\tableofcontents{\global\@hastoctrue}
\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\@haskeywordsfalse % Default: no abstract or keywords
\global\@prefacefalse % not preface
\ifnum\c@firstpage=\c@lastpage
\gdef\@pagerange{\@pagenumprefix\ESpagenumber{firstpage}}
\else
\gdef\@pagerange{\@pagenumprefix
\ESpagenumber{firstpage}--\@pagenumprefix\ESpagenumber{lastpage}}%
\fi
\parskip 4\p@
\open@fm \ignorespaces}
\def\preface{\@prefacetrue}
\def\endfrontmatter{%
\ifx\@runauthor\relax
\global\let\@runauthor\@runningauthor
\fi
\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
\vskip \@overhistoryskip
\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 \@preabstractskip % Space above rule
\hrule height 0.4\p@ % Rule above abstract/keywords
\vskip 8\p@
\unvbox\t@abstract % print abstract, if any
\fi
\if@haskeywords % IF keywords THEN
\vskip \@overkeywordskip
\unvbox\t@keyword % Keyword abstract, if any
\fi % FI
\if@hastoc % IF keywords THEN
\vskip \@overkeywordskip
\ltx@tableofcontents % Keyword abstract, if any
\fi % FI
\vskip 10\p@
\hrule height 0.4\p@ % rule below abstract/keywords
\dedicated@fmt % print dedication
\vskip \@belowfmskip % Vertical space below frontmatter
\fi % FI
\close@fm % Close front matter material.
\output@glob@notes % Put notes at bottom of 1st page
\endNoHyper
\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
\let\nolinenumbers\relax
\def\open@fm{\global\setbox\fm@box=\vbox\bgroup\nolinenumbers
\hsize=\@frontmatterwidth % Front matter is page-wide by default
\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}{\global\def\@runtitle{#1}}{}%
\vspace*{12pt} % Vertical space above title
{\@titlesize #1\,\hbox{$^{#2}$}\par}%
\vskip\@undertitleskip
\vskip24\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
\add@tok\email@text{\ead@newau}%
\add@tok\url@text{\ead@newau}%
\@for\@tempa:=#1\do{\expandafter\add@thanksref\expandafter{\@tempa}}%
\report@elt{author}\proc@elem{author}{#2}%
\ifnum0\n@collab@=\z@ \runningauthor@fmt \fi
\author@fmt{\the\c@author}{\the\t@loc@notes}{\@author}%
}
\def\runningauthor@fmt{%
\begingroup\no@harm
\if@firstauthor
\ifnum0\n@author@ > 2
\global\edef\@runningauthor{\@author\ et al.}%
\else
\global\let\@runningauthor\@author%
\fi
\else % \c@author > 1
\ifnum0\n@author@ = 2
\global\edef\@runningauthor{\@runningauthor\ \& \noexpand\@author}%
\fi
\fi
\endgroup
}
\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
\corauth@mark@fmt
\add@tok\t@glob@notes
{\output@corauth@text
\output@ead@text{email}%
\output@ead@text{url}%
\author@note@fmt}%
}%
\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@author \global\@firstauthorfalse \fi
\gdef\@runningauthor{#1}%
\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
\edef\@tempb{#2}\ifx\@tempb\@empty
{\@authorsize #3}\else
{\@authorsize #3\,$^{\mathrm{#2}}$}%
\fi}
\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\corauth@mark@fmt{\def\thecorauth{\astsymbol{corauth}}}
\def\output@corauth@text{\def\thefootnote{\astsymbol{footnote}}%
\the\corauth@text}
\def\output@ead@text#1{%
\expandafter\add@tok\csname #1@text\endcsname{\ead@endau}%
\expandafter\ifcase\csname has@ead@#1\endcsname\else
{\let\thefootnote\relax
\footnotetext[0]{\raggedright\textit{%
\expandafter\ifcase\csname has@ead@#1\endcsname\or
\csname #1@name\endcsname\else
\csname #1s@name\endcsname\fi
: }%
\expandafter\the\csname #1@text\endcsname.}}%
\fi}
\def\xarabic#1{%
\expandafter\expandafter\expandafter\ifnum\expandafter\the\@nameuse{c@#1}<0
*\else\arabic{#1} \fi}
\def\xalph#1{%
\expandafter\expandafter\expandafter\ifnum\expandafter\the\@nameuse{c@#1}<0
*\else\alph{#1} \fi}
\def\xfnsymbol#1{%
\expandafter\expandafter\expandafter\ifnum\expandafter\the\@nameuse{c@#1}<0
*\else\fnsymbol{#1} \fi}
\def\address{\@ifstar{\address@star}%
{\@ifnextchar[{\address@optarg}{\address@noptarg}}}
\def\address@optarg[#1]#2{\real@refstepcounter{address}%
\beg@elem
\report@elt{address}\proc@elem{address}{#2}%
\address@fmt{\c@address}{\the\t@loc@notes}{\@address}{#1}%
\if@Elproofing\else\label{#1}\fi
\ignorespaces}
\def\address@noptarg#1{\real@refstepcounter{address}%
\beg@elem
\proc@elem{address}{#1}%
\address@fmt{\z@}{\the\t@loc@notes}{\@address}{\theaddress}%
\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#4{\@newelemtrue
\if@Elproofing\def\@eltag{#4}\else\def\@eltag{\theaddress}\fi
\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
$^{\phantom{\mathrm{\@eltag}}}$\space #3\,$^{\mathrm{#2}}$%
\else
$^{\mathrm{\@eltag}}\space$#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
\leftskip\z@
\@rightskip\z@ \rightskip\@rightskip \parfillskip\@flushglue
\small
\parindent 1em % \parindent in abstract
\noindent {\bfseries\abstractname} % caption `Abstract' (bold)
\vskip 0.5\@bls % half a line of space below
\noindent\ignorespaces
}
\def\endabstract{\par \egroup}
\def\keyword{%
\global\@haskeywordstrue % 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
\@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{\par \egroup}
\def\runtitle#1{\gdef\@runtitle{#1}}
\def\runauthor#1{\gdef\@runauthor{#1}}
\let\@runauthor\relax
\let\@runtitle\relax
\let\@runningauthor\relax
\def\RUNDATE{}
\def\RUNJNL{}
\def\RUNART{}
\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
\@pubyear=\number\year
\def\company#1{\def\@company{#1}}
\def\@copyrightyear{\number\year}
\def\@shortenyear#1#2#3#4\\{\global\def\@shortyear{#3#4}}
\expandafter\@shortenyear\the\@pubyear\\
\def\pubyear#1{\global\@pubyear#1
\expandafter\@shortenyear\the\@pubyear\\%
\ignorespaces}
\def\copyear#1{%
\gdef\@copyrightyear{#1}%
\ignorespaces}
\let\copyrightyear\copyear
\newcounter{firstpage}
\newcounter{lastpage}
\let\ESpagenumber\arabic
\def\firstpage#1{\def\@tempa{#1}\ifx\@tempa\@empty\else
\setcounter{firstpage}{#1}%
\global\c@page=#1 \ignorespaces\fi}
\setcounter{firstpage}{1}
\let\realpageref\pageref
\setcounter{lastpage}{0}
\def\lastpage#1{\def\@tempa{#1}\ifx\@tempa\@empty\else
\setcounter{lastpage}{#1}\ignorespaces\fi
}
\AtEndDocument{%
\clearpage
\addtocounter{page}{-1}%
\immediate\write\@auxout{%
\string\global\string\c@lastpage=\the\c@page}%
\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\@alph#1{\ifcase#1\or a\or b\or c\or d\or e\or f\or g\or h\or i\or
j\or k\or \ensuremath{\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\ensuremath{\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\ensuremath{\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\ensuremath{\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\or da\or db\or dc\or dd\or de\or df\or dg\or
dh\or di\or dj\or dk\or d\ensuremath{\ell}\or dm\or dn\or do\or dp\or
dq\or dr\or ds\or dt\or du\or dw\or dx\or dy\or dz\or ea\or eb\or ec\or
ed\or ee\or ef\or eg\or eh\or ei\or ej\or ek\or e\ensuremath{\ell}\or
em\or en\or eo\or ep\or eq\or er\or es\or et\or eu\or ew\or ex\or ey\or
ez\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}
\def\astsymbol#1{\@astsymbol{\@nameuse{c@#1}}}
\def\@astsymbol#1{\ifcase#1\or
\hbox{$\ast$}\or
\hbox{$\ast\ast$}\or
\hbox{$\ast\ast\ast$}\or
\hbox{$\ast\ast\ast\ast$}\or
\hbox{$\ast\ast\ast\ast\ast$}\or
\hbox{$\ast\ast\ast\ast\ast\ast$}%
\else
\@ctrerr
\fi
\relax}
\mark{{}{}} % Initializes TeX's marks
\def\ps@plain{\let\@mkboth\@gobbletwo
\def\@oddhead{}%
\def\@evenhead{}%
\def\@oddfoot{\hfil {\rmfamily\thepage} \hfil}%
\let\@evenfoot\@oddfoot}
\def\@copyright{\@issn/\@shortyear/\$\@price\ $\copyright$\ \the\@pubyear\
\@company{} All rights reserved}
\def\@jou@vol@pag{\@journal\ \@volume\ (\the\@pubyear)\ \@pagerange}
\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{}%
\let\@evenhead\@oddhead
\def\@oddfoot{\small\slshape
\def\@tempa{0}
\ifx\@volume\@tempa
Preprint submitted to \@journal\hfil\@date\/%
\else
Article published in \@jou@vol@pag\hfil\hbox{}\fi}%
\let\@evenfoot\@oddfoot
}
\let\ps@noissn\ps@empty
\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\half{{\textstyle\frac{1}{2}}}
\def\threehalf{{\textstyle\frac{3}{2}}}
\def\quart{{\textstyle\frac{1}{4}}}
\if@symbold\else\def\d{\,\mathrm{d}}\fi
\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}
\def\Cset{\mathbb{C}}
\def\Hset{\mathbb{H}}
\def\Nset{\mathbb{N}}
\def\Qset{\mathbb{Q}}
\def\Rset{\mathbb{R}}
\def\Zset{\mathbb{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
\@frontmatterwidth\textwidth
\ps@headings % 'headings' page style
\pagenumbering{arabic} % Arabic page numbers
\def\thepage{\@pagenumprefix\ESpagenumber{page}} % preceded by \@pagenumprefix
\let\baselinestretch\@blstr
\InputIfFileExists{\@shortjid.cfg}{}{}
\endinput
%%
%% End of file `elsart.cls'.
