%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% ws-jnmp.cls: 2-Oct-09
%% The content, structure, format and layout of this style file is the
%% property of World Scientific Publishing Co. Pte. Ltd.
%% Copyright 2009 by World Scientific Publishing Co.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%% Article FM %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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  \vspace*{-3.76cm}\baselineskip=11pt
 {\hfill{\raisebox{-.5in}{\fbox{\large\sc\the\arttype}\hspace*{-3.4pt}}}} %Article%%%%%%changed as per mail dated 26/05/09
%  \hbox to 7.03truein{\hfill{\fbox{\ \large\sc\the\arttype\ }}} %Article
 \vspace*{-.5in}%%%%%%changed as per mail dated 26/05/09
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%
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%
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\def\http#1{\it http://#1\par}
\def\uurl#1{\it #1\par}
\def\received#1{Received~#1\par}
\def\revised#1{Revised~#1\par}
\def\accepted#1{Accepted~#1\par}
\def\comby#1{\par\addvspace{1\baselineskip}Communicated\ by~#1\par}
%
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\vspace*{44pt}
%\includegraphics[scale=.43]{\clsdir/wlogo.eps}\hfill\includegraphics[scale=.80]{\clsdir/atlantis.eps}\par
\includegraphics[scale=.43]{wlogo.eps}\hfill\includegraphics[scale=.80]{atlantis.eps}\par
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%
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%
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%
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%
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%
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%
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}{%
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%
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%
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%
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%
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%
%%%%%%%%%%%%%%%%%%%%%%%% Table of Contents %%%%%%%%%%%%%%%%%%%%%%%
%
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%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Lists %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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%
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%
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%
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%
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%
\def\@enumerate[#1]{\ifnum \@enumdepth >3 \@toodeep\else
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      {\csname label\@enumctr\endcsname}{\usecounter
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%
\let\Item\item
\newenvironment{enumeroman}{%
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  \def\labelenumi{(\theenumi)}\def\labelenumii{(\theenumii)}%
        \let\item\Item
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}{%
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%
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  \def\theenumi{\alph{enumi}}\def\theenumii{\alph{enumii}}%
  \def\labelenumi{(\theenumi)}\def\labelenumii{(\theenumii)}%
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}{%
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%
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    \def\labelenumi{\theenumi.}\def\labelenumii{(\theenumii)}%
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    \end{enumerate}}
%
\newenvironment{romanlist}{%
    \def\theenumi{\roman{enumi}}\def\theenumii{\roman{enumii}}
    \def\labelenumi{(\theenumi)}\def\labelenumii{(\theenumii)}%
    \let\item\Item
    \begin{enumerate}
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    \end{enumerate}}
%
\newenvironment{itemlist}{%
    \def\labelenumi{\labelitemi}
    \let\item\Item
    \begin{enumerate}
    }{%
    \end{enumerate}}
%
\newenvironment{description}
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               {\endlist}
\newcommand*\descriptionlabel[1]{\hspace\labelsep
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%
\newenvironment{unnumlist}{%
    \let\item\Item
    \leftmargini2pc
    \ifnum \@enumdepth >3 \@toodeep\else
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   \fi
}{%
  \endlist}
%
%%%%%%%%%%%%%%%%%%%%%%%%%% Poetry %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newenvironment{verse}
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                \list{}{\itemsep      \z@
                        \itemindent   -1.5em%
                        \listparindent\itemindent
                        \rightmargin  \leftmargin
                        \advance\leftmargin 1.5em}%
                \item\relax}
               {\endlist}
\let\poetry\verse
\let\endpoetry\endverse
%
%%%%%%%%%%%%%%%%%%%%%%%% Extract %%%%%%%%%%%%%%%%%%%%%%%
%
\newenvironment{quotation}
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                        \itemindent    \listparindent
                        \rightmargin   \leftmargin
                        \parsep        \z@ \@plus\p@}%
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               {\endlist}
\newenvironment{quote}
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                \item\relax}
               {\endlist}
%
\let\extract\quotation
\let\endextract\endquotation
%
\def\source#1{\par\hspace*{\fill}{\it#1}\par}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Maths %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\renewcommand\theequation{\thesection.\arabic{equation}}
\@addtoreset{equation}{section}
%
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\def\tstrut{\vrule width0pt height10pt}
\jot=3pt
%
%
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%

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%\renewenvironment{equation}{\@equation}{\end@equation}

%
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%
\def\@equation{\let\topsep\abovedisplayskip\@beginparpenalty\predisplaypenalty\@endparpenalty\postdisplaypenalty
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     \trivlist \item[]\leavevmode
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\def\end@equation{$\hfill\eqnnum\egroup\endtrivlist}
%
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   \stepcounter{equation}%
   \def\@currentlabel{\p@equation\theequation}%
   \global\@eqnswtrue
   \m@th
   \global\@eqcnt\z@
   \tabskip\@centering
   \let\\\@eqncr
   $$\everycr{}\halign to\displaywidth\bgroup
       \hskip\@centering$\displaystyle\tabskip\z@skip{##}$\@eqnsel
      &\global\@eqcnt\@ne\hskip \tw@\arraycolsep \hfil${##}$\hfil
      &\global\@eqcnt\tw@ \hskip \tw@\arraycolsep
         $\displaystyle{##}$\hfil\tabskip\@centering
      &\global\@eqcnt\thr@@ \hb@xt@\z@\bgroup\hss##\egroup
         \tabskip\z@skip
      \cr}
        {%
      \@@eqncr
      \egroup
      \global\advance\c@equation\m@ne
   $$\global\@ignoretrue
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Floats %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\FigName{figure}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\figurename{Fig.}
\newcounter{figure}
\renewcommand\thefigure{\@arabic\c@figure}
\def\fps@figure{tbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{\figurename~\thefigure}
\newenvironment{figure}
               {\@float{figure}}
               {\end@float}
\newenvironment{figure*}
               {\@dblfloat{figure}}
               {\end@dblfloat}
%
\InputIfFileExists{psfig.sty}{\typeout{^^Jpsfig.sty inputed...ok}}{\typeout{^^JWarning: psfig.sty could be be found.^^J}}
\InputIfFileExists{epsfsafe.tex}{\typeout{^^Jepsfsafe.tex inputed...ok}}
            {\typeout{^^JWarning: epsfsafe.tex could not be found.^^J}}
\InputIfFileExists{epsfig.sty}{\typeout{^^Jepsfig.sty inputed...ok}}{\typeout{^^JWarning: epsfig.sty could not be found.^^J}}
\InputIfFileExists{epsf.sty}{\typeout{^^Jepsf.sty inputed...ok}}{\typeout{^^JWarning: epsf.sty could not be found.^^J}}%
%
\def\ArtDir{\jobname/}
%
\def\figurebox#1#2#3{%
        \def\arg{#3}%
        \ifx\arg\empty
        {\hfill\vbox{\hsize#2\hrule\hbox to #2{%
                \vrule\hfill\vbox to #1{\hsize#2\vfill}\vrule}\hrule}\hfill}%
        \else
        \hbox to \hsize{\hfill\epsfbox{\ArtDir#3.eps}\hfill}
        \fi}
%
\def\PSFIG#1#2#3{\par
  {\hbox to \hsize{%
    \hfill{\psfig{file=\ArtDir#1.eps,width=#2,angle=#3}}\hfill}\par}}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%% Tables %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newcounter{table}
\def\tablename{Table}
\renewcommand\thetable{\@arabic\c@table}
\def\fps@table{tbp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{\tablename~\thetable}
\newenvironment{table}
               {\@float{table}}
               {\end@float}
\newenvironment{table*}
               {\@dblfloat{table}}
               {\end@dblfloat}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\tableformat#1{\centerline{#1}}
\newdimen\tabledim
\long\def\tbl#1#2{%
\global\setbox\tempbox\hbox{\tablefont #2}%
 \global\tabledim\wd\tempbox
 \tableformat{\vbox{\hsize\tabledim
                   \caption{#1}
                   \box\tempbox}}%
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\long\def\ttbl#1#2#3{%
%   \parindent\z@
%   \noindent
%   \tablecaptionfont
%   \caption{#2}%
%   \tablewd\hsize
%   \advance\tablewd-#1
%   \global\divide\tablewd\tw@
%   \ifdim \wd\captionbox<#1
%   \centerline{\unhbox\captionbox}
%   \else
%   {\leftskip\tablewd% plus1fill{}
%   \rightskip\tablewd% plus1fill{}
%   \unhbox\captionbox\par}
%   \fi
%   \vskip-8pt
%   \centerline{#3}
%}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newenvironment{InTextTable}{%
    \par\addvspace{16pt plus6pt minus6pt}%
    \begin{center}
    \tablecaptionfont\noindent\ignorespaces
}{%
    \end{center}
    \par\addvspace{17pt plus6pt minus6pt}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\tabnotehead{Note}
\def\tabsourcehead{Source}
\newenvironment{tabnote}{%
   \par\addvspace{2pt}
   \setbox\tempbox\vbox\bgroup\hsize\tabledim\parindent12pt
   \tabnotefont
   \@ifnextchar[{\@tabnote}{\@tabnote[\tabnotehead]}%
}{%
        \par\egroup
   \tableformat{\box\tempbox}}
%
\def\@tabnote[#1]{\vskip6pt\noindent\def\@Tempa{#1}\ifx\@Tempa\@empty\hskip0pt\else{\it#1}:\hskip5pt\ignorespaces\fi}
%
%%
\newenvironment{tabfootnote}{%
   \par\addvspace{2pt}
   \setbox\tempbox\vbox\bgroup\hsize\tabledim\parindent12pt
   \tabnotefont
}{%
        \par\egroup
   \tableformat{\box\tempbox}}
%
%%
\def\tabmark#1{\noindent\hbox{\normalsize$\m@th^{#1}$}\ignorespaces}
%
\newenvironment{tabsource}{%
   \let\tabnotehead\tabsourcehead
   \begin{tabnote}
}{%
   \end{tabnote}
}
%
\def\Hline{%
  \noalign{\ifnum0=`}\fi\hrule \@height 2\arrayrulewidth \futurelet
   \@tempa\@xhline}
%
\def\x{@{\extracolsep{\fill}}}
\def\toprule{\Hline\\[-7.5pt]}
\def\colrule{\\[-7.5pt]\hline\\[-7.5pt]}
\def\TMcolrule{\\[-9.5pt]\hline\\[-9.5pt]}
\def\botrule{\\[-9pt]\Hline}
\def\crule#1{\\[-10pt]#1\\[-6pt]}
%
%%%%%%%%%%%%%%%%%%%%%%%% Caption %%%%%%%%%%%%%%%%%%%%%%%
%
\newlength\abovecaptionskip
\newlength\belowcaptionskip
\setlength\abovecaptionskip{10\p@}
%\setlength\belowcaptionskip{0\p@}
\setlength\belowcaptionskip{4\p@}
\long\def\@makecaption#1#2{%
  \figurecaptionfont
  \vskip\abovecaptionskip
  \sbox\@tempboxa{#1. #2}%
  \ifdim \wd\@tempboxa >\hsize
    #1. #2\par
  \else
    \global \@minipagefalse
    \hbox to \hsize{\hfil\box\@tempboxa\hfil}%
  \fi
  \vskip\belowcaptionskip}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Footnote %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\renewcommand\footnoterule{%
  \kern-3\p@
  \hrule depth0pt height0pt \@width.2\columnwidth
  \kern2.6\p@}
\newcommand\@makefntext[1]{%
    \parindent 1em%
    \noindent
     \@makefnmark#1}
%
\def\@fnsymbol#1{\ensuremath{\ifcase#1\or *\or \dagger\or \ddagger\or
    \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger
    \or \ddagger\ddagger \else\@ctrerr\fi}}
%
\def\thefootnote{\alph{footnote}}
\def\@makefnmark{{$^{\rm \@thefnmark}$}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Page Style %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\mark{{}{}}
%
\def\ps@plain{%
     \let\@mkboth\@gobbletwo
     \let\@oddhead\@empty
%    \def\@oddfoot{\hfill\mbox{\lower12pt\hbox{\foliofont\thepage}}\hfill}%
     \def\@oddfoot{\hfill\mbox{\hbox{\foliofont\thepage}}\hfill}%
     \let\@evenhead\@empty
     \let\@evenfoot\@oddfoot}
%
\def\RightMark{}
%
\def\ps@headings{%
    \let\@oddfoot\@empty
    \let\@evenfoot\@empty
    \def\@evenhead{\rhfont{\upshape{\thepage}}\hskip1em\leftmark\hfill}%
    \def\@oddhead{\hfill\rhfont\rightmark\hskip1em{\upshape{\thepage}}}%
    \let\@mkboth\markboth
    \def\authormark##1{\markboth{##1}{\RightMark}}%
    \def\chaptermark##1{\gdef\RightMark{##1}\markright{##1}}}%
    %\def\sectionmark##1{\gdef\RightMark{##1}\markright{##1}}}%
%
\def\ps@myheadings{%
    \let\@oddfoot\@empty\let\@evenfoot\@empty
    \def\@evenhead{\rlap{\foliofont \thepage}\hfill{\rhfont\leftmark}\hfill}%
    \def\@oddhead{\hfill{\rhfont\rightmark}\hfill{\foliofont\thepage}}%
    \let\@mkboth\@gobbletwo
    \let\chaptermark\@gobble
    \let\sectionmark\@gobble}
%
\def\ps@pblind{%
    \let\@mkboth\@gobbletwo
    \def\@evenhead{}%
    \def\@oddhead{}
    \def\@oddfoot{\hfill\mbox{\lower8pc\hbox{}}\hfill}
   \let\@evenfoot\@oddfoot}
%

%%%%%%%%%%%%%%%%%%%%%%%%% THEOREM ENVIRONMENTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\def\@xthm#1#2{\@begintheorem{#2}{\csname the#1\endcsname}{}\ignorespaces}
%\def\@ythm#1#2[#3]{\@begintheorem{}{\csname the#1\endcsname}{#3}\ignorespaces}
%

%
\def\@xthm#1#2{\@begintheorem{#2}{\csname the#1\endcsname}{}\ignorespaces}
%

%%%%%%%%%%%%%%%%%%%%%% UPDATED BY SOORAN - 6-6-2001 %%%%%%%%%%%%%%%%%%%%%%%
%
\def\@ythm#1#2[#3]{\@opargbegintheorem{#2}{\csname
       the#1\endcsname}{#3}\ignorespaces}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%

\let\Definitionfont\upshape%
\let\Theoremfont\itshape
\let\Corollaryfont\itshape
\let\Propositionfont\itshape
\let\Lemmafont\itshape
\let\Examplefont\upshape
\let\Theoremheadfont\bfseries
\let\Corollaryheadfont\bfseries
\let\Propositionheadfont\bfseries
\let\Lemmaheadfont\bfseries
\let\Definitionheadfont\bfseries
\let\Remarkfont\upshape
\def\Exampleheadfont{\bfseries}
\def\Remarkheadfont{\bfseries}

\def\Questionheadfont{\bfseries}
\let\Questionfont\itshape

\def\Conjectureheadfont{\bfseries}
\let\Conjecturefont\itshape

\def\Problemheadfont{\bfseries}
\let\Problemfont\itshape

\def\hypothesisheadfont{\bfseries}
\let\hypothesisfont\upshape

%%
\def\@begintheorem#1#2#3{\par\addvspace{8pt plus3pt minus2pt}%
              \noindent{\csname#1headfont\endcsname#1\ \ignorespaces#3 #2.}%
              \csname#1font\endcsname\hskip.5em\ignorespaces}
\def\@endtheorem{\par\addvspace{8pt plus3pt minus2pt}\@endparenv}
%

%%%%%%%%%%%%%%%%%%%%%% UPDATED BY SOORAN - 6-6-2001 %%%%%%%%%%%%%%%%%%%%%%%
%
\def\@opargbegintheorem#1#2#3{\par\addvspace{6pt plus3pt minus2pt}%
    \def\@tempa{#3}%
    \noindent{\bf #1 #2 \ifx\@tempa\empty\unskip\else\unskip\ (#3).\fi\hskip.5em}\csname#1font\endcsname\ignorespaces
%   \noindent{\bf #2 \ifx\@tempa\empty\unskip\else\unskip: #3\fi\hskip1em}\it
\ignorespaces}

%
\def\@endtheorem{\par\addvspace{6pt plus3pt minus2pt}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{proposition}{Proposition}[section]
\newtheorem{definition}{Definition}[section]
\newtheorem{example}{Example}[section]
\newtheorem{remark}{Remark}[section]
\newtheorem{question}{Question}[section]
\newtheorem{conjecture}{Conjecture}[section]
\newtheorem{hypothesis}{Hypothesis}[section]
\newtheorem{problem}{Problem}[section]
%
\DeclareRobustCommand{\qed}{%
  \ifmmode \mathqed
  \else
    \leavevmode\unskip\penalty9999 \hbox{}\nobreak\hfill
    \quad\hbox{\qedsymbol}%
  \fi
}
\let\QED@stack\@empty
\let\qed@elt\relax
\newcommand{\pushQED}[1]{%
  \toks@{\qed@elt{#1}}\@temptokena\expandafter{\QED@stack}%
  \xdef\QED@stack{\the\toks@\the\@temptokena}%
}
\newcommand{\popQED}{%
  \begingroup\let\qed@elt\popQED@elt \QED@stack\relax\relax\endgroup
}
\def\popQED@elt#1#2\relax{#1\gdef\QED@stack{#2}}
\newcommand{\qedhere}{%
  \begingroup \let\mathqed\math@qedhere
    \let\qed@elt\setQED@elt \QED@stack\relax\relax \endgroup
}
\newif\ifmeasuring@
\newif\iffirstchoice@ \firstchoice@true
\def\setQED@elt#1#2\relax{%
  \ifmeasuring@
  \else \iffirstchoice@ \gdef\QED@stack{\qed@elt{}#2}\fi
  \fi
  #1%
}
\def\qed@warning{%
  \PackageWarning{amsthm}{The \@nx\qedhere command may not work
    correctly here}%
}
\newcommand{\mathqed}{\quad\hbox{\qedsymbol}}
\def\linebox@qed{\hfil\hbox{\qedsymbol}\hfilneg}
\@ifpackageloaded{amsmath}{%
  \def\math@qedhere{%
    \@ifundefined{\@currenvir @qed}{%
      \qed@warning\quad\hbox{\qedsymbol}%
    }{%
      \@xp\aftergroup\csname\@currenvir @qed\endcsname
    }%
  }
  \def\displaymath@qed{%
    \relax
    \ifmmode
      \ifinner \aftergroup\linebox@qed
      \else
        \eqno
        \let\eqno\relax \let\leqno\relax \let\veqno\relax
        \hbox{\qedsymbol}%
      \fi
    \else
       \aftergroup\linebox@qed
    \fi
  }
  \@xp\let\csname equation*@qed\endcsname\displaymath@qed
  \def\equation@qed{%
    \iftagsleft@
      \hbox{\phantom{\quad\qedsymbol}}%
      \gdef\alt@tag{%
        \rlap{\hbox to\displaywidth{\hfil\qedsymbol}}%
        \global\let\alt@tag\@empty
      }%
    \else
      \gdef\alt@tag{%
        \global\let\alt@tag\@empty
        \vtop{\ialign{\hfil####\cr
                \tagform@\theequation\cr
                \qedsymbol\cr}}%
        \setbox\z@
      }%
    \fi
  }
  \def\qed@tag{%
    \global\tag@true \nonumber
    &\omit\setboxz@h {\strut@ \qedsymbol}\tagsleft@false
    \place@tag@gather
    \kern-\tabskip
    \ifst@rred \else \global\@eqnswtrue \fi \global\advance\row@\@ne \cr
  }
  \def\split@qed{%
    \def\endsplit{\crcr\egroup \egroup \ctagsplit@false \rendsplit@
      \aftergroup\align@qed
    }%
  }
  \def\align@qed{%
    \ifmeasuring@ \tag*{\qedsymbol}%
    \else \let\math@cr@@@\qed@tag
    \fi
  }
  \@xp\let\csname align*@qed\endcsname\align@qed
  \@xp\let\csname gather*@qed\endcsname\align@qed
%% Needs some patching up for amsmath 1.2
}{% end of amsmath branch, start plain LaTeX branch
  \def\math@qedhere{%
    \@ifundefined{\@currenvir @qed}{%
      \qed@warning \aftergroup\displaymath@qed
    }{%
      \@xp\aftergroup\csname\@currenvir @qed\endcsname
    }%
  }
  \def\displaymath@qed{%
    \relax
    \ifmmode
      \ifinner \aftergroup\aftergroup\aftergroup\linebox@qed
      \else
        \eqno \def\@badmath{$$}%
        \let\eqno\relax \let\leqno\relax \let\veqno\relax
        \hbox{\qedsymbol}%
      \fi
    \else
       \aftergroup\linebox@qed
    \fi
  }
  \@ifundefined{ver@leqno.clo}{%
    \def\equation@qed{\displaymath@qed \quad}%
  }{%
    \def\equation@qed{\displaymath@qed}%
  }
  \def\@tempa#1$#2#3\@nil{%
    \def\[{#1$#2\def\@currenvir{displaymath}#3}%
  }%
  \expandafter\@tempa\[\@nil
}
\@ifpackageloaded{amstex}{%
  \def\@tempa{TT}%
}{%
  \@ifpackageloaded{amsmath}{%
    \def\@tempb#1 v#2.#3\@nil{#2}%
    \ifnum\@xp\@xp\@xp\@tempb\csname ver@amsmath.sty\endcsname v0.0\@nil
       <\tw@
      \def\@tempa{TT}%
    \else
      \def\@tempa{TF}%
    \fi
  }{%
    \def\@tempa{TF}
  }%
}
\if\@tempa
  \renewcommand{\math@qedhere}{\quad\hbox{\qedsymbol}}%
\fi
\newcommand{\openbox}{\leavevmode
  \hbox to.77778em{%
  \hfil\vrule
  \vbox to.675em{\hrule width.6em\vfil\hrule}%
  \vrule\hfil}}
\DeclareRobustCommand{\textsquare}{%
  \begingroup \usefont{U}{msa}{m}{n}\thr@@\endgroup
}
\providecommand{\qedsymbol}{\openbox}
\newenvironment{proof}[1][\proofname]{\par
  \pushQED{\qed}%
  \normalfont \topsep6\p@\@plus6\p@\relax
  \trivlist
  \item[\hskip\labelsep
        \bf
    #1\@addpunct{.}]\ignorespaces
}{%
  \popQED\endtrivlist\@endpefalse
}
\providecommand{\proofname}{Proof}
%
%%%%%%%%%%%%%%%%%%%%%%%%% THEOREM ENVIRONMENTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Appendix %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newcounter{appendix}
\newcommand\appendix{\par
    \refstepcounter{appendix}
    \setcounter{section}{0}%
        \setcounter{lemma}{0}
        \setcounter{theorem}{0}
    \setcounter{definition}{0}
        \setcounter{corollary}{0}
    \setcounter{equation}{0}
    \@addtoreset{equation}{section}
\renewcommand\thesection{\appendixname\ \Alph{section}}
\renewcommand\thesubsection{\Alph{section}.\arabic{subsection}}%
\renewcommand\theequation{\Alph{section}.\arabic{equation}}}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%For contents pages %%%%%%%%%%%%%%%%%%%%%%%%
%
\def\journalname{\uppercase{Group 1 Journals}}
\def\No{No.}
\def\chead#1#2#3{\par
\thispagestyle{empty}
{\centering{%
{\titlefont\journalname}\par
{\sl Vol.~#1, \No~#2 (#3)}\par
\vspace*{34pt}
\noindent CONTENTS\par}}
\vspace*{14pt}}
\def\leaderfill{\leaders\hbox to 1em{\hss.\hss}\hfill}
\def\centry#1#2#3{\par
    {\foliofont
    \setbox\tempbox\hbox{#3}
    {\rightskip3.5pc plus1fil
    \noindent{\uppercase{#1}}\par}
    {\leftskip12pt{\rightskip1pc plus1fil
    \ignorespaces\noindent#2\leaderfill\hspace*{2pt}\hskip\wd\tempbox\par}\par}\par
    \vskip-\lastskip
    \vskip-\baselineskip
    \hbox to \hsize{\hfill#3}\par}
    \addvspace{8pt plus1pt minus1pt}\par}
%%
\def\cent#1#2#3{\par{\foliofont
    {\rightskip2pc plus1fil
    \noindent\par}
    {\noindent{\uppercase{#1}}\ignorespaces#2\leaderfill\hspace*{2pt}#3\par}}\par
    \addvspace{8pt plus1pt minus1pt}\par
    }
%
\def\ehead#1#2#3{\par
    \addvspace{12pt plus1pt minus1pt}
    {\foliofont\rightskip4pc plus1fil
    \noindent{\bf #1{#2}{#3}\par}
    \vspace*{4pt}}\par}
%
\def\eehead#1#2#3{\par
    \addvspace{12pt plus1pt minus1pt}
    {\foliofont\rightskip4pc plus1fil
    \noindent{\bf #1{#2}{#3}\par}
    \vspace*{4pt}}\par}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Trim Marks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newcommand\today{\ifcase\month\or
  January\or February\or March\or April\or May\or June\or
  July\or August\or September\or October\or November\or December\fi
    \space\number\day, \number\year}
\newcount\minute
\newcount\hour
\def\currenttime{%
    \minute\time
    \hour\minute
    \divide\hour60
    \the\hour:\multiply\hour60\advance\minute-\hour\the\minute}
%
%
% \def\draftnote{\today\quad\currenttime\quad WSPC/INSTRUCTION FILE
% \qquad\jobname}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\cropmarks{\nointerlineskip%
     \vbox to 0pt{\vskip-8.6pt
    \parindent0pt\hspace*{6pt} % \draftnote
     \par\advance\trimheight by 2pc
     \vbox to \trimheight{\offinterlineskip\parindent0pt\vskip-2pc
     \hbox to \trimwidth{\raise2.6pc\hbox{\vrule height2pc width0.3pt}\raisebox{2pc}
   {\hspace*{-2.6pc}\vrule width2pc height0.3pt}\hfill\raisebox{2pc}
   {\vrule width2pc height0.3pt}\hspace*{-2.6pc}\raise2.6pc\hbox{\vrule height2pc width0.3pt}}\vfill
     \hbox to \trimwidth{\lower1.2pc\hbox{\vrule height2pc width0.3pt}\raisebox{1.4pc}
        {\hspace*{-2.6pc}\vrule width2pc height0.3pt}\hfill
    \lower1.2pc\hbox{\vrule height2pc width0.3pt}\rlap{\hspace*{0.6pc}\raisebox{1.4pc}{\vrule width2pc height0.3pt}}}}}
     \vbox to 0pt{\offinterlineskip\parindent0pt\vskip\topmargin%\vskip1.3pt
     \tempdimen\normaltextheight
     \advance\tempdimen24pt
     \moveright\@themargin
     \vbox to \tempdimen{\hrule height\draftrule
     \vbox to 0pt{\vskip\headheight\vskip\headsep%\vskip3pt
                \vrule height\draftrule width\textwidth}%
      \hbox to \textwidth{\vrule width\draftrule \hfill\vrule height\tempdimen width\draftrule}%
           \hrule height\draftrule}}}%%
\def\xcropmarks{\nointerlineskip%
     \vbox to 0pt{\vskip-8.6pt
    \parindent0pt\hspace*{6pt} % \draftnote
     \par\advance\trimheight by 2pc
     \vbox to \trimheight{\offinterlineskip\parindent0pt\vskip-2pc
     \hbox to \trimwidth{\raise2.6pc\hbox{\vrule height2pc width0.3pt}\raisebox{2pc}
   {\hspace*{-2.6pc}\vrule width2pc height0.3pt}\hfill\raisebox{2pc}
   {\vrule width2pc height0.3pt}\hspace*{-2.6pc}\raise2.6pc\hbox{\vrule height2pc width0.3pt}}\vfill
     \hbox to \trimwidth{\lower1.2pc\hbox{\vrule height2pc width0.3pt}\raisebox{1.4pc}
        {\hspace*{-2.6pc}\vrule width2pc height0.3pt}\hfill
    \lower1.2pc\hbox{\vrule height2pc width0.3pt}\rlap{\hspace*{0.6pc}\raisebox{1.4pc}{\vrule width2pc height0.3pt}}}}}
     \vbox to 0pt{\offinterlineskip\parindent0pt\vskip\topmargin%\vskip1.3pt
     \tempdimen\normaltextheight
     \advance\tempdimen27pt
     \moveright\@themargin
     \vbox to \tempdimen{\hrule height\draftrule
     \vbox to 0pt{\vskip\headheight\vskip\headsep%\vskip3pt
                \vrule height\draftrule width\textwidth}%
      \hbox to \textwidth{\vrule width\draftrule \hfill\vrule height\tempdimen width\draftrule}%
           \hrule height\draftrule}}}%%
%
\let\trimmarks\cropmarks
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% Output Routine %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\@outputpage{%
\begingroup           % the \endgroup is put in by \aftergroup
  \let \protect \noexpand
  \@resetactivechars
  \let\-\@dischyph
  \let\'\@acci\let\`\@accii\let\=\@acciii
  \let\\\@normalcr
  \let\par\@@par          %% 15 Sep 87
  \shipout \vbox{%
    \set@typeset@protect
    \aftergroup \endgroup
    \aftergroup \set@typeset@protect
                                % correct? or just restore by ending
                                % the group?
  \if@specialpage
    \global\@specialpagefalse\@nameuse{ps@\@specialstyle}%
  \fi
  \if@twoside
    \ifodd\count\z@ \let\@thehead\@oddhead \let\@thefoot\@oddfoot
         \let\@themargin\oddsidemargin
    \else \let\@thehead\@evenhead
       \let\@thefoot\@evenfoot \let\@themargin\evensidemargin
    \fi
  \fi
  \reset@font
  \normalsize
  \baselineskip\z@skip \lineskip\z@skip \lineskiplimit\z@
    \@begindvi\trimmarks
    \vskip \topmargin
    \moveright\@themargin \vbox {%
      \setbox\@tempboxa \vbox to\headheight{%
        \vfil
        \color@hbox
          \normalcolor
          \hb@xt@\textwidth {%
            \let \label \@gobble
            \let \index \@gobble
            \let \glossary \@gobble %% 21 Jun 91
            \@thehead
            }%
        \color@endbox
        }%                        %% 22 Feb 87
      \dp\@tempboxa \z@
      \box\@tempboxa
      \vskip \headsep
      \box\@outputbox
      \baselineskip \footskip
      \color@hbox
        \normalcolor
        \hb@xt@\textwidth{%
          \let \label \@gobble
          \let \index \@gobble      %% 22 Feb 87
          \let \glossary \@gobble   %% 21 Jun 91
          \@thefoot
          }%
      \color@endbox
      }%
    }%
\global \@colht \textheight
\stepcounter{page}%
\let\firstmark\botmark
}
%
\def\enddocument{%
   \label{eof}
   \@enddocumenthook
   \@checkend{document}%
   \clearpage
   \begingroup
     \if@filesw
       \immediate\closeout\@mainaux
       \let\@setckpt\@gobbletwo
       \let\@newl@bel\@testdef
       \@tempswafalse
       \makeatletter \input\jobname.aux
     \fi
     \@dofilelist
     \ifdim \font@submax >\fontsubfuzz\relax
       \@font@warning{Size substitutions with differences\MessageBreak
                  up to \font@submax\space have occured.\@gobbletwo}%
     \fi
     \@defaultsubs
     \@refundefined
     \if@filesw
       \ifx \@multiplelabels \relax
         \if@tempswa
           \@latex@warning@no@line{Label(s) may have changed.
               Rerun to get cross-references right}%
         \fi
       \else
         \@multiplelabels
       \fi
     \fi
   \endgroup
   \deadcycles\z@\@@end}

%
%%%%%%%%%%%%%%%%%%%%% Local Defs. %%%%%%%%%%%%%%%%%%%%%%
%
\def\mtb{\fboxsep=0pt\fbox{\phantom{e}}}
\def\breakhere{\par\vskip-\lastskip
            \pagebreak}
\def\forcebreak{\vadjust{\pagebreak}}
%
\def\and{\hbox{\lowercase{and }}}
\def\aand{\\[10pt]{\upshape{and}}\\[-3pt]}
%

%%%%%%%%%%%%%%%%%%%% CITATIONS  & BIBLIOGRAPHY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newif\if@cghi
\def\cite{\@cghitrue\@ifnextchar [{\@tempswatrue\@citex}{\@tempswafalse\@citex[]}}
\def\@citex[#1]#2{%
  \let\@citea\@empty
  \@cite{\@for\@citeb:=#2\do
    {\@citea\def\@citea{,\penalty\@m}%
     \edef\@citeb{\expandafter\@firstofone\@citeb}%
     \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
     \@ifundefined{b@\@citeb}{\mbox{\reset@font\bfseries ?}%
       \G@refundefinedtrue\@latex@warning
       {Citation `\@citeb' on page \thepage \space undefined}}%
     {\hbox{\csname b@\@citeb\endcsname}}}}{#1}}
%
%
\def\@refcitex[#1]#2{\if@filesw\immediate\write\@auxout
    {\string\citation{#2}}\fi
\def\@citea{}\@refcite{\@for\@citeb:=#2\do
    {\@citea\def\@citea{, }\@ifundefined
    {b@\@citeb}{{\bf ?}\@warning
    {Citation `\@citeb' on page \thepage \space undefined}}
    \hbox{\csname b@\@citeb\endcsname}}}{#1}}
 \def\@refcite#1#2{{#1\if@tempswa\typeout
        {WSPC warning: optional citation argument
    ignored: `#2'} \fi}}
 \def\refcite{\@ifnextchar[{\@tempswatrue
    \@refcitex}{\@tempswafalse\@refcitex[]}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newdimen\bibindent
\bibindent=2em
\def\@biblabel#1{[#1]}
\newenvironment{thebibliography}[1]
     {\section*{\bibname}\bibfont%
      \list{\@biblabel{\arabic{enumiv}}}%
           {\settowidth\labelwidth{\@biblabel{#1}}%
            \leftmargin\labelwidth
        \labelsep6pt%.33em
            \advance\leftmargin\labelsep
        \itemsep0pt\parsep0pt
            \usecounter{enumiv}%
            \renewcommand\theenumiv{\arabic{enumiv}}}%
      \sloppy\clubpenalty4000\widowpenalty4000%
      \sfcode`\.=\@m}
     {\def\@noitemerr
       {\@latex@warning{Empty `thebibliography' environment}}%
      \endlist}
\newcommand\newblock{}
%
%\def\dfrac#1#2{{\displaystyle{#1\over#2}}}
%\def\tfrac#1#2{{\textstyle{#1\over#2}}}
%
%%%%%%%%%%%%%%%%%%%% CITATIONS  & BIBLIOGRAPHY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Process Options %%%%%%%%%%%%%%%%%%%%%%%%%
%

% Page break penalties
\@lowpenalty   51
\@medpenalty  151
\@highpenalty 301

% Disallow widows and orphans
\clubpenalty 10000
\widowpenalty 10000

% Disable page breaks before equations, allow pagebreaks after
% equations and discourage widow lines before equations.
\displaywidowpenalty 100
\predisplaypenalty   10000
\postdisplaypenalty  2500

% Allow breaking the page in the middle of a paragraph
\interlinepenalty 0

% Disallow breaking the page after a hyphenated line
\brokenpenalty 10000

%%%%%%%modified by Chand for new server

\DeclareTextCommandDefault{\textregistered}{\textcircled{\scshape r}}

% Hyphenation; don't split words into less than three characters
\lefthyphenmin=3
\righthyphenmin=3

\pagestyle{headings}
\pagenumbering{arabic}
\onecolumn
\frenchspacing
\flushbottom
\def\sloppy{\tolerance=100000\hfuzz=\maxdimen \vfuzz=\maxdimen}
\sloppy
\vbadness=12000
\hbadness=12000
\usepackage{amsfonts,amssymb,amsmath}
\usepackage[figuresright]{rotating}
\usepackage{url}
\usepackage{cite}
\endinput
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%End of file%%%%%%%%%%%%%%%%%%%%%%%%%%%%
