summaryrefslogtreecommitdiff
path: root/texmf-dist/doc/latex/siam/ptexnec.all
diff options
context:
space:
mode:
Diffstat (limited to 'texmf-dist/doc/latex/siam/ptexnec.all')
-rw-r--r--texmf-dist/doc/latex/siam/ptexnec.all707
1 files changed, 707 insertions, 0 deletions
diff --git a/texmf-dist/doc/latex/siam/ptexnec.all b/texmf-dist/doc/latex/siam/ptexnec.all
new file mode 100644
index 00000000..2da4cfce
--- /dev/null
+++ b/texmf-dist/doc/latex/siam/ptexnec.all
@@ -0,0 +1,707 @@
+
+
+This file (ptexnec.all) constitutes the full distribution of NEC Proceedings Series
+Plain TeX macros. The files are:
+
+ptexnec.tex (An example file, also containing documentation)
+
+ptexnec.sty (the style file)
+
+To use these macros, separate at the indicated cut lines.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% This is ptexnec.tex, an example file for use with the NEC 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 ptexnec.sty
+
+\def\leftrh{Gray et al.}
+\def\rightrh{NEC Proceedings Series Macros}
+
+\startchapter %Place this command at the beginning of the file immediately
+ %after the \input command.
+
+
+
+\title Chapter 1\endtitle
+\title NEC 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
+
+\vfill\eject
+
+Extra page.
+\vfill
+\bye
+%%% End of example file
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% 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 NEC Proceedings Series using Plain TeX.
+
+% Report the version.
+\message{*** NEC Plain TeX Proceedings Series macro package, version 1.0,
+November 6, 1992.***}
+
+% Make the @ sign a letter for internal control sequences.
+\catcode`\@=11
+%
+%
+%
+
+
+\baselineskip=14truept
+
+
+%%% DIMENSIONS %%%
+
+\hsize=30truepc
+\vsize=49truepc
+%\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\tenrm\rightrh\hskip2pc\tenrm\folio}
+\def\leftheadline{\tenrm\folio\hskip2pc\tenrm\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
+