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-
-
-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. The running heads are defined by the commands \def\leftrh{} and
-%% \def\rightrh{}. You must fill in the empty field of these commands
-%% with the appropriate information. The left running head should be the
-%% authors names. For papers with multiple authors, please follow these
-%% rules; for two authors type {Author 1 and Author 2}; for more than two
-%% authors type {Author 1 et al.}. The right running head is the title of
-%% the paper. If the title is more than 50 characters, including spaces,
-%% please provide a shortened version. All information should be typed
-%% initial cap and lower case.
-%%
-%% 5. 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.
-%%
-%% 6. Proofs are handled by \prf\endprf. If you want to use an end-of-proof
-%% box, insert \qed right before the \endprf command.
-%%
-%% 7. 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.
-%%
-%% 8. 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.
-%%
-%% 9. 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
-%%
-%% 10. 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.
-%%
-%%
-%% 11. 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}.
-%%
-%% 12. How to Submit Your Paper.
-%% The electronic version of your paper should be sent to proceed@siam.org.
-%% A hardcopy version should also be submitted. Instructions are included
-%% in your acceptance letter. Please be sure to send hardcopy
-%% versions of any Postscript figures you have submitted electronically.
-%% Be sure to return your signed Copyright Transfer Agreement. We cannot
-%% publish your paper without one.%%
-%%
-%%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\input ptexproc.sty
-
-\def\leftrh{Gray et al.}
-\def\rightrh{SIAM Proceedings Series Macros}
-
-\startchapter %Place this command at the beginning of the file immediately
- %after the \input command.
-
-
-
-\title Chapter 1\endtitle
-\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