

This file constitutes the full distribution of SIAM Proceedings Series
Plain TeX macros. The files are:

ptexproc.tex    (An example file, also containing documentation)

ptexproc.sty    (the style file)

To use these macros, separate at the indicated cut lines.

%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% This is ptexproc.tex, an example file for use with the SIAM Plain TeX
% Proceedings Series macros. Comments are placed at the beginning and 
% throughout this file. Please take the time to read them as they document
% how to use these macros. This file can be composed and printed out for
% use as sample output. Please ignore the underfull \vbox on page 3.

% Any comments or questions regarding these macros should be directed to:
%
%                 Corey Gray
%                 SIAM
%                 3600 University City Science Center
%                 Philadelphia, PA 19104-2688
%                 USA
%                 Telephone: (215) 382-9800
%                 Fax: (215) 386-7999
%                 e-mail: gray@siam.org


% This file is to be used as an example for style only. It should not be read
% for content.

%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%%

%%  1. You must use the numbered reference style([1],[2]), listing the 
%%     references at the end of the chapter either by order of citation
%%     or alphabetically.
%% 
%%  2. This macro is set up for three levels of headings. Use the commands
%%     \headone, \headtwo, and \headthree. The macro will automatically
%%     number the headings.
%%
%%  3. Theorems, Lemmas, Definitions, etc. are to be double-numbered, 
%%     indicating the section and the occurrence of that element
%%     within that section. (For example, the first theorem in the second
%%     section would be numbered 2.1.) This numbering must
%%     be done manually. 
%%
%%  4. Proofs are handled by \prf\endprf. If you want to use an end-of-proof
%%     box, insert \qed right before the \endprf command.
%%
%%  5. Figures and equations must be manually single-numbered. Use \leqno 
%%     for equation numbering. The macro provides the \fig for including 
%%     figures. This command consists of three fields. The first field is
%%     used for inserting the appropriate space for the figure. The second 
%%     field is the figure number. The third field is the caption. See the 
%%     example included in this file. SIAM supports the use of psfig for 
%%     including Postscript figures. All Postscript figures should be sent 
%%     as separate files. A hardcopy version of all Postscript figures is 
%%     also required. See note regarding this under How to Submit Your Paper.
%%
%%  6. Use of \title\endtitle and \lasttitle\endlastitle.
%%     This macro package provides two possible commands for handling the 
%%     title of your paper. The commands \title\endtitle should be used for
%%     all lines except the last line of multiple line titles. The commands 
%%     \lasttitle\endlasttitle should be used for the last line of multiple 
%%     line titles. In the case of a single line title, \lasttitle\endlasttitle
%%     should be used.
%%
%%  7. Use of \author\endauthor and \lastauthor\endlastauthor.
%%     As in the title macro, two possible commands are provided for the 
%%     author. The commands \author\endauthor should be used for the first
%%     line of authors if there are more than one line. The commands
%%     \lastauthor\endlastauthor should be used for the last line
%%     of multiple lines of authors. In the case of a single line of authors,
%%     \lastauthor\endlastauthor should be used. A maximum of four authors 
%%     should be placed on any one line. The appropriate space must also be
%%     hard coded between authors on the same line. The spacing is as follows:
%%       
%%       If 2 authors; \hskip4pc between
%%       If 3 authors; \hskip3pc between
%%       If 4 authors; \hskip2pc between
%%
%% 8. Grant information and author affiliations.
%%     This information is included by using the \footnote command and the 
%%     appropriate footnote symbol. SIAM uses footnote symbols in a 
%%     particular order. Below is a list of these symbols:
%%
%%      asterisk                
%%      single-dagger           
%%      double-dagger           
%%      section sign            
%%      paragraph               
%%      parallel                
%%      double asterisk         
%%      double single-dagger    
%%      double double-dagger    
%%
%%     For illustrative purposes, all footnote symbols have been used in the
%%     example file.
%%
%%     A note regarding \footnote. This command seems to leave extra white
%%     space between footnotes. This is quite evident in the example file. If
%%     any user of these macros has a solution to this problem, I would 
%%     appreciate hearing from you. Send your comments to: gray@siam.org.
%%
%%    The following general rules apply for including grants and affiliations:
%%      a) If there is a single grant for the paper, then the grant 
%%         information should be footnoted to the title.
%%      b) If there is more than one grant, included the grant information
%%         with each authors affiliation.
%%      c) If there are different grants for the paper but the authors share
%%         the same affiliation, footnote the grant information to the title.
%%         For example, The work of the first author was supported by xyz.
%%         The work of the second author was supported by abc. And so on.
%%
%%
%% 9. Special fonts.
%%     SIAM supports the use of AMS-TeX fonts version 2.0 and later. As 
%%     described in the manual for these fonts, they can be included by
%%     \input{amssym.def} and \input{amssym.tex}. 
%%
%% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\input ptexproc.sty

\def\leftrh{}
\def\rightrh{}

\startchapter %Place this command at the beginning of the file immediately
              %after the \input command.



\title SIAM Proceedings Series Macros\endtitle
\lasttitle for Use with Plain TeX\footnote*{Any information 
regarding grants should be placed here.}\endlasttitle

\author J. Corey Gray\footnote{$^{\dag}$}{Production Manager, Society for
Industrial and Applied Mathematics, Philadelphia, PA.}
\hskip2truepc Tricia Manning\footnote{$^{\ddag}$}{Publications 
Specialist, Society for Industrial and Applied Mathematics, Philadelphia, 
PA.}
\hskip2truepc Vickie Kearn\footnote{$^{\S}$}{Publisher, Society for Industrial
and Applied Mathematics, Philadelphia, PA.}
\hskip2truepc Nancy Abbott\footnote{$^{\P}$}{Design Supervisor, Society for
Industrial and Applied Mathematics, Philadelphia, PA.}
\endauthor
\lastauthor Sue Ciambrano\footnote{$^{\parallel}$}{Acquisition Editor, Society for
Industrial and Applied Mathematics, Philadelphia, PA.}
\hskip2truepc Paul Duggan\footnote{$^{**}$}{Composition 
Specialist, Society for Industrial and Applied Mathematics, Philadelphia, 
PA.}
\hskip2truepc Robbi Anne Albert\footnote{$^{\dagger\dagger}$}{Production, 
Assistant, Society for Industrial
and Applied Mathematics, Philadelphia, PA.}
\hskip2truepc Jean Anderson\footnote{$^{\ddag\ddag}$}{Composition Coordinator, Society for
Industrial and Applied Mathematics, Philadelphia, PA.}
\endlastauthor

% Use \headone for the first level headings. The macro will automatically
% number the headings.

\centerline{\bf Abstract}
\abstract An equivalence is shown between realizability of input/output (i/o) operators by
rational control systems and high-order algebraic differential equations for
i/o pairs.  This generalizes, to nonlinear systems, the equivalence
between autoregressive representations and finite dimensional linear
realizability.\endabstract


\headone{Problem Specification}
In this paper, we consider the solution of the $N \times N$ linear
system
$$A x = b\leqno (1)$$
where $A$ is large, sparse, symmetric, and positive definite.  We consider
the direct solution of by means of general sparse Gaussian
elimination.  In such a procedure, we find a permutation matrix $P$, and
compute the decomposition
$$
P A P^{t} = L D L^{t}
\leqno (2)$$

\noindent where $L$ is unit lower triangular and $D$ is diagonal.  


\headone{Design Considerations}
Several good ordering algorithms (nested dissection and minimum degree)
are available for computing $P$  [1], [2].
Since our interest here does not
focus directly on the ordering, we assume for convenience that $P=I$,
or that $A$ has been preordered to reflect an appropriate choice of $P$.

% Use \thm and \endthm for theorems. They must be numbered manually.
% Lemmas (\lem \endlem), corollaries (\cor \endcor), and 
% propositions (\prop \endprop) are coded the same as theorems and must
% also be numbered manually.

\thm{Theorem 2.1.} The method  was extended to three
dimensions. For the standard multigrid
coarsening
(in which, for a given grid, the next coarser grid has $1/8$
as many points), anisotropic problems require plane
relaxation to
obtain a good smoothing factor.\endthm 

Several good ordering algorithms (nested dissection and minimum degree)
are available for computing $P$  [1], [2].
Since our interest here does not
focus directly on the ordering, we assume for convenience that $P=I$,
or that $A$ has been preordered to reflect an appropriate choice of $P$.
Several good ordering algorithms (nested dissection and minimum degree)
are available for computing $P$  [1], [2].
Since our interest here does not
focus directly on the ordering, we assume for convenience that $P=I$,
or that $A$ has been preordered to reflect an appropriate choice of $P$.

% Use \prf and \endprf to begin and end a proof.
% The use of \qed will produce an end-of-proof box.

\prf{Proof} In this paper we consider two methods. The first method
is
basically the method considered with two differences:
first, we perform plane relaxation by a two-dimensional
multigrid method, and second, we use a slightly different
choice of
interpolation operator, which improves performance
for nearly singular problems. In the second method coarsening
is done by successively coarsening each.\qed\endprf

% Use \dfn and \enddfn to begin and end definitions.

\dfn{Definition 2.1.}We describe the two methods in \S\ 1.2. This is a 
definition in the plain tex macro.\enddfn 

This is accomplished by exploiting the m-tree,
a particular spanning tree for the graph of the filled-in matrix.
Our purpose here is to examine the nonnumerical complexity of the
sparse elimination algorithm given in  [3].
As was shown there, a general sparse elimination scheme based on the
bordering algorithm requires less storage for pointers and
row/column indices than more traditional implementations of general
sparse elimination. This is accomplished by exploiting the m-tree,
a particular spanning tree for the graph of the filled-in matrix.


Our purpose here is to examine the nonnumerical complexity of the
sparse elimination algorithm given in  [3].
As was shown there, a general sparse elimination scheme based on the
bordering algorithm requires less storage for pointers and
row/column indices than more traditional implementations of general
sparse elimination. This is accomplished by exploiting the m-tree,
a particular spanning tree for the graph of the filled-in matrix.
Since our interest here does not
focus directly on the ordering, we assume for convenience that $P=I$,
or that $A$ has been preordered to reflect an appropriate choice of $P$.

% Use \lem and \endlem to begin and end lemmas.

\lem{Lemma 2.1.}We discuss first the choice for $I_{k-1}^k$
which is a generalization. We assume that $G^{k-1}$ is
obtained
from $G^k$
by standard coarsening; that is, if $G^k$ is a tensor product
grid $G_{x}^k \times G_{y}^k \times G_{z}^k$,
$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$,
where $G_{x}^{k-1}$ is obtained by deleting every other grid
point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$.
\endlem

% Use \fig to insert space for figures .

\fig{10pc}{Fig. 1}{This is the caption for figure one.}

To our knowledge, the m-tree previously has not been applied in this
fashion to the numerical factorization, but it has been used,
directly or indirectly, in several optimal order algorithms for
computing the fill-in during the symbolic factorization phase
[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
approaches to the intersection problem for the special case of
an $n \times n$ grid ordered by nested dissection. The special
structure of this problem allows us to make exact estimates of
the complexity. To our knowledge, the m-tree previously has not been applied in this
fashion to the numerical factorization, but it has been used,
directly or indirectly, in several optimal order algorithms for
computing the fill-in during the symbolic factorization phase
[4] - [10], [5], [6].

% Use \headtwo for second level headings. They will be numbered automatically.

\headtwo{Robustness}In \S 1.2, we review the bordering algorithm, and introduce
the sorting and intersection problems that arise in the
sparse formulation of the algorithm.  

\headtwo{Versatility} In \S 1.3., we analyze the complexity of the old and new
approaches to the intersection problem for the special case of
an $n \times n$ grid ordered by nested dissection. The special
structure of this problem allows us to make exact estimates of
the complexity. To our knowledge, the m-tree previously has not been applied in this
fashion to the numerical factorization, but it has been used,
directly or indirectly, in several optimal order algorithms for
computing the fill-in during the symbolic factorization phase
[4] - [10], [5], [6].


% Use \headthree for third level headings.

\headthree{Complexity.}For the old approach, we show that the
complexity of the intersection problem is $O(n^{3})$, the same
as the complexity of the numerical computations.  For the
new approach, the complexity of the second part is reduced to
$O(n^{2} (\log n)^{2})$.  

% The command \Refs sets the word Reference as a heading and allows the proper
% amount of space before the start of the references. Each reference must
% begin with \ref\\. The article or title of the reference should be in 
% italic. Use the \it command within brackets. End each reference with
% \endref and allow two returns between references. Use the command
% \sameauthor (see reference 8)  when the same author or group of authors
% is listed consecutively.

\Refs

\ref 1\\R.~E. Bank, {\it PLTMG  users' guide, edition 5.0}, tech. report,
  Department of Mathematics, University of California, San Diego, CA, 1988.\endref

\ref 2\\R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\it The hierarchical basis
  multigrid method}, Numer. Math., 52 (1988), pp.~427--458.\endref

\ref 3\\R.~E. Bank and R.~K. Smith, {\it General sparse elimination requires no
  permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987),
  pp.~574--584.\endref

\ref 4\\S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\it
  Algorithms and data structures for sparse symmetric gaussian elimination},
  SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.\endref

\ref 5\\A.~George and J.~Liu, {\it Computer Solution of Large Sparse Positive
  Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.\endref

\ref 6\\K.~H. Law and S.~J. Fenves, {\it A node addition model for symbolic
  factorization}, ACM TOMS, 12 (1986), pp.~37--50.\endref

\ref 7\\J.~W.~H. Liu, {\it A compact row storage scheme for cholesky factors
  using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.\endref

\ref 8\\\sameauthor , {\it The role of
  elimination trees in sparse factorization}, Tech. Report CS-87-12,Department
  of Computer Science, York University, Ontario, Canada, 1987.\endref

\ref 9\\D.~J. Rose, {\it A graph theoretic study of the numeric solution of
  sparse positive definite systems}, in Graph Theory and Computing, 
  Academic Press, New York, 1972.\endref

\ref 10\\D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\it Algorithmic aspects of
  vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.\endref


\bye

%end of example file
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% This is ptexproc.sty
% This file may be freely distributed but may not be altered in any way. 
% Any comments or questions regarding these macros should be directed to: 
 
%                 Corey Gray 
%                 SIAM 
%                 3600 University City Science Center 
%                 Philadelphia, PA 19104-2688 
%                 USA 
%                 Telephone: (215) 382-9800 
%                 Fax: (215) 386-7999 
%                 e-mail: gray@siam.org 
 
% 
%       This is a file of macros and definitions for creating a chapter 
%       for publication in the SIAM Proceedings Series using Plain TeX. 
 
%    Report the version. 
\message{*** SIAM Plain TeX Proceedings Series macro package, version 1.0, 
November 6, 1992.***} 
 
% Make the @ sign a letter for internal control sequences. 
\catcode`\@=11 
% 
% 
% 
 
\overfullrule=0pt
\baselineskip=14truept 
 
 
%%%  DIMENSIONS  %%% 
 
\hsize=36truepc 
\vsize=55truepc 
%\hoffset=.5in 
\parindent=18truept 
\def\firstpar{\parindent=0pt\global\everypar{\parindent=18truept}} 
\parskip=0pt 
 
 
%%%  FONTS  %%% 
 
\font\tenrm=cmr10 
\font\tenbf=cmbx10 
\font\tenit=cmti10                   
\font\tensmc=cmcsc10 
\def\tenpoint{% 
   \def\rm{\tenrm}\def\bf{\tenbf}% 
   \def\it{\tenit}\def\smc{\tensmc} 
        \textfont0=\tenrm \scriptfont0=\sevenrm 
        \textfont1=\teni \scriptfont1=\seveni 
        \textfont2=\tensy \scriptfont2=\sevensy 
        \textfont3=\tenex \scriptfont3=\tenex 
\baselineskip=12pt\rm}% 
 
\font\ninerm=cmr9 
\font\ninebf=cmbx9 
\font\nineit=cmti9 
\def\ninepoint{% 
   \def\rm{\ninerm}\def\bf{\ninebf}% 
   \def\it{\nineit}\baselineskip=11pt\rm}% 
 
\font\eightrm=cmr8 
\font\eightbf=cmbx8 
\font\eightit=cmti8         
\font\eighti=cmmi8 
\font\eightsy=cmsy8 
\def\eightpoint{% 
   \def\rm{\eightrm}\def\bf{\eightbf}% 
   \def\it{\eightit}\def\smc{\eightrm}\baselineskip=10pt\rm% 
        \textfont0=\eightrm \scriptfont0=\sixrm 
        \textfont1=\eighti \scriptfont1=\sixi 
        \textfont2=\eightsy \scriptfont2=\sixsy 
        \textfont3=\tenex \scriptfont3=\tenex 
} 
 
\font\sixrm=cmr6 
\font\sixbf=cmbx6 
\font\sixi=cmmi6         
\font\sixsmc=cmr5 
\font\sixsy=cmsy6 
\def\sixpoint{% 
   \def\rm{\sixrm}\def\bf{\sixbf}% 
   \def\smc{\sixsmc}\baselineskip=8pt\rm}% 
 
\fontdimen13\tensy=2.6pt 
\fontdimen14\tensy=2.6pt 
\fontdimen15\tensy=2.6pt 
\fontdimen16\tensy=1.2pt 
\fontdimen17\tensy=1.2pt 
\fontdimen18\tensy=1.2pt               
 
\font\eightrm=cmr8 
\font\ninerm=cmr9 
\font\elevenrm=cmr10 scaled\magstephalf
\font\fourteenrm=cmr10 scaled\magstep 1
\font\eighteenrm=cmr10 scaled\magstep 3
\font\twelvebf=cmbx10 scaled\magstep 1
\font\elevenbf=cmbx10 scaled\magstephalf
\font\elevenit=cmti10 scaled\magstephalf
\font\elevensc=cmcsc10 scaled\magstephalf

\def\theoremfont{\elevensc}
\def\textfont{\elevenrm}
\def\itfont{\elevenit}
\def\headfont{\twelvebf}
\def\smallheadfont{\elevenbf}
\def\titlefont{\eighteenrm} 
\def\chapterfont{\fourteenrm} 
\def\authorfont{\fourteenrm} 
\def\rheadfont{\tenrm} 
\def\abstractfont{\tenrm}
\def\smc{\tensmc} 
\font\eightsmc=cmcsc8 
 
\def\footnote#1{\baselineskip=11truept\edef\@sf{\spacefactor\the\spacefactor}#1\@sf
  \insert\footins\bgroup\ninepoint\hsize=36pc
  \interlinepenalty10000 \let\par=\endgraf
   \leftskip=0pt \rightskip=0pt
   \splittopskip=10pt plus 1pt minus 1pt \floatingpenalty=20000
\smallskip   
\item{#1}\bgroup\baselineskip=10pt\strut
\aftergroup\@foot\let\next}
\skip\footins=12pt plus 2pt minus 4pt
\dimen\footins=36pc



%%%  CHAPTER OPENING MACROS  %%% 
 
\def\startchapter{\topinsert\vglue54pt\endinsert} 

\def\title#1\endtitle{\titlefont\centerline{#1}\vglue5pt}%\vskip40truept\tenrm} 
\def\lasttitle#1\endlasttitle{\titlefont\centerline{#1}\vskip1.32truepc}
\def\author#1\endauthor{\authorfont\centerline{#1}\vglue8pt\textfont} 
\def\lastauthor#1\endlastauthor{\authorfont\centerline{#1}\vglue2.56pc\textfont} 
\def\abstract#1\endabstract{\baselineskip=12pt\leftskip=2.25pc
     \rightskip=2.25pc\abstractfont{#1}\textfont} 

%%%  COUNTERS FOR HEADINGS  %%% 
 
\newcount\headcount 
\headcount=1 
\newcount\seccount 
\seccount=1 
\newcount\subseccount 
\subseccount=1 
\def\secreset{\global\seccount=1} 
 \def\subsecreset{\global\subseccount=1}
 
%%%  HEADINGS  %%% 
 
\def\headone#1{\baselineskip=14pt\leftskip=0pt\rightskip=0pt\vskip17truept\parindent=0pt
{\headfont\the\headcount\hskip14truept #1}
\par\nobreak\firstpar\global\advance\headcount by 0 
   \global\advance\headcount by 1\secreset\vskip2truept\textfont} 

\def\headtwo#1{\advance\headcount by -1% 
   \vskip17truept\parindent=0pt{\headfont\the\headcount.% 
   \the\seccount\hskip14truept #1}%\enspace\ignorespaces\firstpar 
   \global\advance\headcount by 1\global\advance\seccount by 1 
   \global\advance\subseccount by 1\subsecreset\vskip2pt\textfont} 
 
 \def\headthree#1{\advance\headcount by -1\advance\seccount by -1
%   \advance\subseccount by -1% 
   \vskip17truept\parindent=0pt{\smallheadfont\the\headcount.% 
   \the\seccount.\the\subseccount\hskip11truept #1}\hskip6pt\ignorespaces 
   \firstpar\global\advance\headcount by 1\global\advance\seccount by 1 
   \global\advance\subseccount by 1\textfont} 
 
%%%  THEOREMS, PROOFS, DEFINITIONS, etc.  %%% 
 
\def\thm#1{{\theoremfont 
#1\enspace} 
\hskip-5pt\begingroup\itfont\ignorespaces} 
 
\let\lem=\thm 
\let\cor=\thm 
\let\prop=\thm 
 
\def\endthm{\endgroup\textfont} 
\let\endlem=\endthm 
\let\endcor=\endthm 
\let\endprop=\endthm 
 
\def\prf#1{{\itfont #1.}\textfont\enspace\ignorespaces} 
\let\rem=\prf 
\let\case=\prf 
 
\def\endprf{\textfont} 
\let\endrem=\endprf 
\let\endcase=\endprf 

\def\qed{{\qquad \vbox{\hrule\hbox{%
   \vrule height1.3ex\hskip0.8ex\vrule}\hrule
  }}\par}  
 
\def\dfn#1{{\theoremfont
#1\enspace} 
\textfont\ignorespaces} 
 
\let\fact=\dfn 
 
\def\enddfn{\textfont} 
 
\let\endfact=\enddfn 

%%%  FIGURES AND CAPTIONS  %%% 


\newcount\figcount
\figcount=1


%\newcount\tablenumber
%\tablenumber=1

\def\\{\hfill\break}

\newbox\TestBox
\newdimen\setwd
\newskip\belowcaptionskip
\belowcaptionskip=6pt plus 1pt

\def\endinsert{\egroup % finish the \vbox
  \if@mid \dimen@\ht\z@ \advance\dimen@\dp\z@
    \advance\dimen@12\p@ \advance\dimen@\pagetotal
    \ifdim\dimen@>\pagegoal\@midfalse\p@gefalse\fi\fi
   \if@mid\vskip\belowcaptionskip\box\z@\par \penalty-200\vskip\belowcaptionskip
  \else\insert\topins{\penalty100 % floating insertion
    \splittopskip\z@skip
    \splitmaxdepth\maxdimen \floatingpenalty\z@
    \ifp@ge \dimen@\dp\z@
    \vbox to\vsize{\unvbox\z@\kern-\dimen@}% depth is zero
    \else \box\z@\nobreak\vskip\belowcaptionskip\fi}\fi\endgroup}




\def\fig#1#2#3{%
       \setbox\TestBox=\hbox{\tenpoint #3.}\setwd=\wd\TestBox
        \topinsert
       \vskip #1
                \vskip 12pt
        \ifdim\setwd > 23pc
          {\tenit{\smc #2.}\ \ #3}
        \else
         \centerline{\tenit\noindent 
                {\smc #2.}\ \  #3}\fi%
               % \global\advance\figcount by 1
        \endinsert}


 
%%%  REFERENCES  %%% 
 
\newdimen\refindent@ 
\newdimen\refhangindent@ 
\newbox\refbox@ 
\setbox\refbox@=\hbox{\tenrm\baselineskip=11pt [00]}%   Default 2 digits 
\refindent@=\wd\refbox@ 
 
\def\resetrefindent#1{% 
        \setbox\refbox@=\hbox{\tenrm\baselineskip=11pt [#1]}% 
        \refindent@=\wd\refbox@} 
 
\def\Refs{% 
        \unskip\vskip1pc 
        \leftline{\noindent\headfont References}% 
        \penalty10000 
        \vskip4pt 
        \penalty10000 
        \refhangindent@=\refindent@ 
        \global\advance\refhangindent@ by .5em 
        \global\everypar{\hangindent\refhangindent@}% 
        \parindent=0pt\baselineskip=12pt\tenrm} 
                                       
\def\sameauthor{\leavevmode\vbox to 1ex{\vskip 0pt plus 100pt 
    \hbox to 2em{\leaders\hrule\hfil}\vskip 0pt plus 300pt}} 
     
\def\ref#1\\#2\endref{\leavevmode\hbox to \refindent@{\hfil[#1]}\enspace #2\par} 
 
 
%%%  OUTPUT  %%% 
 
\def\rightheadline{\hfill\tensmc\rightrh\hskip2pc\tenrm\folio} 
\def\leftheadline{\tenrm\folio\hskip2pc\tensmc\leftrh\hfill} 
 
\global\footline={\hss\tenrm\folio\hss}% first page 
 
\output{\plainoutput} 
\def\plainoutput{\shipout\vbox{\makeheadline\pagebody\makefootline}% 
  \advancepageno 
  \ifnum\pageno>1 
        \global\footline={\hfill}% 
  \fi      
  \ifodd\pageno 
        \global\headline={\rightheadline}% 
  \else 
        \global\headline={\leftheadline}% 
  \fi 
  \ifnum\outputpenalty>-\@MM \else\dosupereject\fi} 
\def\pagebody{\vbox to\vsize{\boxmaxdepth\maxdepth \pagecontents}} 
\def\makeheadline{\vbox to\z@{\vskip-22.5\p@ 
  \line{\vbox to8.5\p@{}\rheadfont\the\headline}\vss}% 
    \nointerlineskip} 
\def\makefootline{\baselineskip24\p@\vskip-6\p@\line{\the\footline}} 
\def\dosupereject{\ifnum\insertpenalties>\z@ % something is being held over 
  \line{}\kern-\topskip\nobreak\vfill\supereject\fi} 

\def\footnoterule{\vskip11pt\kern -4\p@\hrule width 3pc \kern 3.6\p@ } % rule = .4 pt high 

%       Turn off @ as being a letter. 
% 
\catcode`\@=13 
 
%end of style file 
