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-
-
-This file constitutes the full distribution for SIAM Proceedings
-Series LaTeX version macros. The files included here are:
-
-ltexproc.tex    (An example file, also containing documentation)
-
-ltexproc.sty    (The style file)
-
-siamproc.bst    (for BiBTeX users)
-
-To use these macros, separate the files at the indicated cut lines.
-
-%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% This is ltexproc.tex, an example file for use with the SIAM LaTeX
-% Proceedings Series macros. 
-% Please take the time to read the following comments, as they describe
-% how to use these macros. This file can be composed and printed out for
-% use as sample output.
-
-% 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. There are no new tags.  Existing LaTeX tags have been formatted to
-%%     match the Proceedings series style.    
-%%
-%%  2. You must use \cite in the text to mark your reference citations and 
-%%     \bibitem in the listing of references at the end of your chapter. See
-%%     the examples in the following file. The file siamproc.bst has been 
-%%     included for use with BiBTeX. Please be sure to include the appropriate
-%%     .bib file with BiBTeX submissions. You may also submit the .bbl file
-%%     instead of the .bib file.
-%% 
-%%  3. Unless otherwise stated by your editor, do your chapter as if it
-%%     is Chapter 1. The appropriate chapter number will be included during
-%%     the production of the proceedings.
-%%
-%%  4. This macro is set up for three levels of headings (\section, 
-%%     \subsection, and \subsubsection). The macro will automatically number 
-%%     the headings for you.
-%%
-%%  5. The running heads are indicated by the \markboth command. Please 
-%%     define the running heads by placing the authors last names in the 
-%%     first field and the title of the paper in the second field.
-%%     They should be typed initial cap and lower case. Please see the example.
-%%     Neither field can contain more than 50 characters including spaces, 
-%%     so please use a  shortened version of the title if necessary. For 
-%%     papers with multiple authors please follow these rules; for 
-%%     two authors type {Author 1 and Author 2}; for more that two authors type 
-%%     {Author 1 et al.}.
-%% 
-%%  6. 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. The macro will 
-%%     automatically do the numbering for you.
-%%
-%%  7. Proofs are handled with the commands \begin{proof}\end{proof}.
-%%     If you wish to use an end of proof box, use \qed preceding \end{proof}.
-%%     The example uses one. It is not required.
-%%
-%%  8. Figures, equations, and tables must be single-numbered. All equation
-%%     numbers are to be on the left. Figure captions should be placed under
-%%     the figures they pertain to. Table captions should be placed above 
-%%     the tables. Use existing LaTeX tags for these elements. Numbering of 
-%%     these elements will be done automatically. 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.
-%%   
-%%  9. Grant information and author affiliations.
-%%     This information is included in the file with the two commands,
-%%     \thanks and \footnotemark []. (See example). The \thanks command 
-%%     produces a footnote for the title or author, and places the 
-%%     appropriate footnote symbol with the title or author and at the
-%%     bottom of the page. The \footnotemark [] command allows the use of
-%%     duplicate footnote symbols. This macro follows the normal LaTeX order 
-%%     of footnote symbols. Below is a list of these symbols, and their 
-%%     corresponding footnotemark:
-%%
-%%      asterisk                \footnotemark[1]
-%%      single-dagger           \footnotemark[2]
-%%      double-dagger           \footnotemark[3]
-%%      section sign            \footnotemark[4]
-%%      paragraph               \footnotemark[5]
-%%      parallel                \footnotemark[6]
-%%      double asterisk         \footnotemark[7]
-%%      double single-dagger    \footnotemark[8]
-%%      double double-dagger    \footnotemark[9]   
-%%
-%%    The following general rules for grants and affiliations apply:
-%%      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, include the grant information
-%%         with each author's 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.
-%%      d) For authors sharing the same affiliation, use \thanks for the
-%%         first author with that affiliation and the appropriate
-%%         \footnotemark[] (from the list above) for all subsequent authors
-%%         with that affiliation.
-%%
-%% 10. 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}. These macros are not yet
-%%     updated to make use of the New Font Selection Scheme (NFSS) of
-%%     Mittelbach and Schopf. To make these macros compatible with NFSS, use 
-%%     the oldlfont style option. 
-%%
-%% 11. 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 it.
-%%     
-%%
-%%
-%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%-
-%%%
-
-
-\documentstyle[leqno,twoside,11pt,ltexproc]{article} %You must set up your
-                                              %\documentstyle line like this.
-
-
-\begin{document}
-\cleardoublepage
-\pagestyle{myheadings}
-
-\title{Chapter 1\\
-SIAM Proceedings Series Macros\\
- for Use With LaTeX\thanks{Any information regarding grants should be placed 
-here.}}
-\author{J. Corey Gray\thanks{Production Manager, Society for Industrial and Applied 
-Mathematics, Philadelphia, PA.}
-\and 
-Tricia Manning\thanks{Publications Specialist, Society for Industrial and Applied
-Mathematics, Philadelphia, PA.}
-\and
-Vickie Kearn\thanks{Publisher, Society for Industrial and Applied Mathematics,
-Philadelphia, PA.}\\
-\and
-Nancy Abbott\thanks{Design Supervisor, Society for Industrial and Applied 
-Mathematics, Philadelphia, PA}
-\and 
-Sue Ciambrano\thanks{Acquisitions Editor, Society for Industrial and Applied 
-Mathematics, Philadelphia, PA}
-\and
-Paul Duggan\thanks{Composition Specialist, Society for Industrial and Applied 
-Mathematics, Philadelphia, PA}
-\and
-Robbi Anne Albert\thanks{Production Assistant, Society for Industrial and Applied 
-Mathematics, Philadelphia, PA}
-\and 
-Jean Anderson\thanks{Composition Coordinator, Society for Industrial and Applied 
-Mathematics, Philadelphia, PA}
-}
-\date{}
-\maketitle
-\markboth{Gray et al.}{SIAM Proceedings Series Macros} % See section 5 above
-                                                       % for explanation.
-\pagenumbering{arabic}
-
-\begin{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. \end{abstract}
-\section{Problem Specification}In this paper, we consider the solution of the $N \times
-N$ linear
-system
-\begin{equation} \label{e1.1}
-\cos \sin A x = b
-\end{equation}
-where $A$ is large, sparse, symmetric, and positive definite.  We consider
-the direct solution of (\ref{e1.1}) by means of general sparse Gaussian
-elimination.  In such a procedure, we find a permutation matrix $P$, and
-compute the decomposition
-\[
-P A P^{t} = L D L^{t}
-\]
-where $L$ is unit lower triangular and $D$ is diagonal.  
-
- 
-\section{Design Considerations}Several good ordering algorithms (nested dissection and
-minimum degree)
-are available for computing $P$  \cite{GEORGELIU}, \cite{ROSE72}.
-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 $P$.
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in  \cite{BANKSMITH}.
-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.
-
-\begin{theorem} 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.\end{theorem} 
-
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$  \cite{GEORGELIU}, \cite{ROSE72}.
-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 $P$.
-
-
-\begin{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 in each of the three
-independent variables and then ignoring the intermediate
-grids; this artifice simplifies coding considerably.\qed
-\end{proof}
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in  \cite{BANKSMITH}.
-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.
-
-\begin{Definition}{\rm We describe the two methods in \S 1.2. In \S\ 1.3. we
-discuss
-some remaining details.}
-\end{Definition}
-
-\begin{figure}
-\vspace*{24pc}
-\caption{This is  figure 1.}
-\end{figure}
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in  \cite{BANKSMITH}.
-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.  
-
-\begin{lemma} 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 $G_{z}^k$.
-\end{lemma}
- 
-This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-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
-\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76},  \cite{SCHREIBER}.
-
-\subsection{Robustness} 
-We do not
-attempt to present an overview
-here, but rather attempt to focus on those results that
-are relevant to our particular algorithm.
-This section assumes prior knowledge of the role of graph theory
-in sparse Gaussian elimination; surveys of this role are
-available in \cite{ROSE72} and \cite{GEORGELIU}. More general
-discussions of elimination trees are given in
-\cite{LAW} - \cite{LIU2}, \cite{SCHREIBER}.
-Thus, at the $k$th stage, the bordering algorithm consists of
-solving the lower triangular system
-\begin{equation} \label{1.2}
- L_{k-1}v = c
-\end{equation}
-and setting
-\begin{eqnarray} 
-\ell &=& D^{-1}_{k-1}v , \\
-\delta &=& \alpha - \ell^{t} v .
-\end{eqnarray}
-
-\subsubsection{Versatility.} We do not
-attempt to present an overview
-here, but rather attempt to focus on those results that
-are relevant to our particular algorithm.
- 
-\section{Conclusions}  The special
-structure of this problem allows us to make exact estimates of
-the 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
-\cite{GEORGELIU}, \cite{ROSEWHITTEN}.  For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$. 
-
-\begin{thebibliography}{99}
-
-
-\bibitem{BANKSMITH}
-R.~E. Bank and R.~K. Smith, {\em General sparse elimination requires no
-  permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987),
-  pp.~574--584.
-
-\bibitem{EISENSTAT}
-S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\em
-  Algorithms and data structures for sparse symmetric gaussian elimination},
-  SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.
-
-\bibitem{GEORGELIU}
-A.~George and J.~Liu, {\em Computer Solution of Large Sparse Positive
-  Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.
-
-\bibitem{LAW}
-K.~H. Law and S.~J. Fenves, {\em A node addition model for symbolic
-  factorization}, ACM TOMS, 12 (1986), pp.~37--50.
-
-\bibitem{LIU}
-J.~W.~H. Liu, {\em A compact row storage scheme for cholesky factors
-  using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.
-
-\bibitem{LIU2}
-\sameauthor , {\em The role of
-  elimination trees in sparse factorization}, Tech. Report CS-87-12,Department
-  of Computer Science, York University, Ontario, Canada, 1987.
-
-\bibitem{ROSE72}
-D.~J. Rose, {\em A graph theoretic study of the numeric solution of
-  sparse positive definite systems}, in Graph Theory and Computing, Academic  Press, New
-York, 1972.
-
-\bibitem{ROSE76}
-D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\em Algorithmic aspects of
-  vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.
-
-\bibitem{ROSEWHITTEN}
-D.~J. Rose and G.~F. Whitten, {\em A recursive analysis of disection
-  strategies}, in Sparse Matrix Computations, Academic Press, New York, 1976.
-
-\bibitem{SCHREIBER}
-R.~Schreiber, {\em A new implementation of sparse gaussian elimination},
-  ACM TOMS, 8 (1982), pp.~256--276.
-
-\end{thebibliography}
-
-\end{document}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%   This is ltexproc.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 LaTeX.
-
-%   Report the version.
-\message{*** SIAM LaTeX Proceedings Series macro package, version 1.0,
-November 6, 1992 ***} 
-
-\pretolerance=800 
-\tolerance=10000 
-\sloppy 
- 
- 
-\vsize=56pc 
-\hsize=36pc 
-\baselineskip=13pt 
-\hoffset -.5in
-\voffset -.5in
-\footskip=18pt 
-\topmargin 24pt  
-\headheight 12pt  
-\headsep 15pt  
-\textheight 53.5pc  \advance\textheight by \topskip 
-\textwidth 36pc  
-\parskip 0pt
-\parindent 18pt
-\def\topfraction{.9}
-\def\textfraction{.1}
-\def\topnumber{2}
-%% footnotes  to be set 8/10 
-\def\footnotesize{\@setsize\footnotesize{11pt}\ixpt\@ixpt 
-   %  \indent 
-       \abovedisplayskip \z@ 
-      \belowdisplayskip\z@ 
-     \abovedisplayshortskip\abovedisplayskip 
-    \belowdisplayshortskip\belowdisplayshortskip 
-\def\@listi{\leftmargin\leftmargini \topsep 3pt plus 1pt minus 1pt 
-     \parsep 2pt plus 1pt minus 1pt 
-    \itemsep \parsep}} 
- 
-\let\referencesize\footnotesize 
- 
-\footnotesep 0pt  
- 
-\skip\footins 12pt plus 12pt  
- 
-\def\footnoterule{\kern3\p@  \hrule width 3em\vspace{3pt}} % the \hrule is .4pt high 
- 
- 
-\def\ps@plain{\let\@mkboth\@gobbletwo 
-     \def\@oddfoot{{\hfil\small\thepage\hfil}}% 
-     \def\@oddhead{} 
-      \def\@evenhead{}\def\@evenfoot{}} 
- 
- 
- 
-\def\ps@headings{\let\@mkboth\markboth 
-        \def\@oddfoot{}\def\@evenfoot{}% 
-        \def\@evenhead{{\rm\thepage}\hspace*{2pc}{\sc\leftmark}\hfil}%
-        \def\@oddhead{\hfil{\noindent\sc\rightmark}\hspace*{2pc}{\rm\thepage}}%
-
- 
- 
-\def\ps@myheadings{\let\@mkboth\@gobbletwo 
- \def\@oddfoot{}\def\@evenfoot{}% 
- \def\@oddhead{\hfil{\sc\rightmark}\hspace*{2pc}{\normalsize\rm\thepage}}% 
- \def\@evenhead{{\normalsize\rm\thepage}\hspace*{2pc}{\sc\leftmark}\hfil}% 
-%        \def\chaptermark##1{}% 
- %       \def\sectionmark##1{}\def\subsectionmark##1{}} 
-}} 
- 
- 
- 
-\def\theequation{\arabic{equation}} 
- 
-\def\abstract{\if@twocolumn
-\section*{Abstract}
-\else \small 
-\begin{center}
-{\bf Abstract\vspace{-.5em}\vspace{3pt}} 
-\end{center}
-\quotation 
-\fi}
-\def\endabstract{\if@twocolumn\else\endquotation\fi}
- 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-%                                         % 
-%     THEOREMS, PROOFS, ALGORITHMS        % 
-%                                         % 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
- 
-%%% defined proof environment by theorem model (took out counter) 
-
-\def\qed{{\qquad \vbox{\hrule\hbox{%
-   \vrule height1.3ex\hskip0.8ex\vrule}\hrule
-  }}\par}   
-
-\def\newproof#1{\@nprf{#1}} 
- 
-\def\@nprf#1#2{\@xnprf{#1}{#2}} 
- 
-\def\@xnprf#1#2{\expandafter\@ifdefinable\csname #1\endcsname 
-\global\@namedef{#1}{\@prf{#1}{#2}}\global\@namedef{end#1}{\@endproof}} 
- 
-\def\@prf#1#2{\@xprf{#1}{#2}} 
- 
-\def\@xprf#1#2{\@beginproof{#2}{\csname the#1\endcsname}\ignorespaces} 
- 
- 
- 
-%%% defined algorithm environment by theorem model 
- 
-\def\newalgorithm#1{\@ifnextchar[{\@oalg{#1}}{\@nalg{#1}}} 
- 
-\def\@nalg#1#2{% 
-\@ifnextchar[{\@xnalg{#1}{#2}}{\@ynalg{#1}{#2}}} 
- 
-\def\@xnalg#1#2[#3]{\expandafter\@ifdefinable\csname #1\endcsname 
-{\@definecounter{#1}\@addtoreset{#1}{#3}% 
-\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand 
-  \csname the#3\endcsname \@thmcountersep \@thmcounter{#1}}% 
-\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}} 
- 
-\def\@ynalg#1#2{\expandafter\@ifdefinable\csname #1\endcsname 
-{\@definecounter{#1}% 
-\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% 
-\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}} 
- 
-\def\@oalg#1[#2]#3{\expandafter\@ifdefinable\csname #1\endcsname 
-  {\global\@namedef{the#1}{\@nameuse{the#2}}% 
-\global\@namedef{#1}{\@alg{#2}{#3}}% 
-\global\@namedef{end#1}{\@endalgorithm}}} 
- 
-\def\@alg#1#2{\refstepcounter 
-    {#1}\@ifnextchar[{\@yalg{#1}{#2}}{\@xalg{#1}{#2}}} 
- 
-\def\@xalg#1#2{\@beginalgorithm{#2}{\csname the#1\endcsname}\ignorespaces} 
-\def\@yalg#1#2[#3]{\@opargbeginalgorithm{#2}{\csname 
-       the#1\endcsname}{#3}\ignorespaces} 
- 
- 
- 
- 
-\def\@beginproof#1{\rm {\it #1.\ }} 
-\def\@endproof{\outerparskip 0pt\endtrivlist} 
- 
-\def\@begintheorem#1#2{\it {\sc #1\ #2.\ }} 
-\def\@opargbegintheorem#1#2#3{\it 
-      {\sc #1\ #2\ (#3).\ }} 
-\def\@endtheorem{\outerparskip 0pt\endtrivlist} 
-
-%\def\@begindefinition#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]} 
-%\def\@opargbegindefinition#1#2#3{\rm \trivlist 
-%      \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} 
-%\def\@enddefinition{\outerparskip 0pt\endtrivlist} 
-
- 
-\def\@beginalgorithm#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]} 
-\def\@opargbeginalgorithm#1#2#3{\rm \trivlist 
-      \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} 
-\def\@endalgorithm{\outerparskip 6pt\endtrivlist} 
- 
- 
-\newskip\outerparskip 
- 
-\def\trivlist{\parsep\outerparskip 
-  \@trivlist \labelwidth\z@ \leftmargin\z@ 
-  \itemindent\parindent \def\makelabel##1{##1}} 
- 
-\def\@trivlist{\topsep=0pt\@topsepadd\topsep 
-  \if@noskipsec \leavevmode \fi 
-  \ifvmode \advance\@topsepadd\partopsep \else \unskip\par\fi 
-  \if@inlabel \@noparitemtrue \@noparlisttrue  
-    \else \@noparlistfalse \@topsep\@topsepadd \fi 
-    \advance\@topsep \parskip 
-  \leftskip\z@\rightskip\@rightskip \parfillskip\@flushglue 
-  \@setpar{\if@newlist\else{\@@par}\fi}% 
-  \global\@newlisttrue \@outerparskip\parskip} 
- 
- 
-\def\endtrivlist{\if@newlist\@noitemerr\fi  
-   \if@inlabel\indent\fi  
-   \ifhmode\unskip \par\fi  
-   \if@noparlist \else 
-      \ifdim\lastskip >\z@ \@tempskipa\lastskip \vskip -\lastskip 
-         \advance\@tempskipa\parskip \advance\@tempskipa -\@outerparskip  
-         \vskip\@tempskipa 
-   \fi\@endparenv\fi 
-   \vskip\outerparskip} 
- 
- 
-
- \newproof{@proof}{Proof} 
- \newenvironment{proof}{\begin{@proof}}{\end{@proof}} 
- 
- \newtheorem{@theorem}{Theorem}[section] 
- \newenvironment{theorem}{\begin{@theorem}}{\end{@theorem}} 
- 
-% \newalgorithm{@algorithm}{Algorithm}[section] 
-% \newenvironment{algorithm}{\begin{@algorithm}}{\end{@algorithm}} 
- 
- 
- 
-\newtheorem{lemma}{Lemma}[section] 
-\newtheorem{fact}{Fact}[section] 
-\newtheorem{corollary}{Corollary}[section] 
-\newtheorem{axiom}{Axiom}[section] 
-\newtheorem{cond}{Condition}[section] 
-\newtheorem{property}{Property}[section]  
-\newtheorem{proposition}{Proposition}[section] 
- 
-\newtheorem{Conjecture}{Conjecture}[section] 
-\newtheorem{Definition}{Definition}[section] 
-\newtheorem{Lemma}{Lemma}[section] 
-\newtheorem{Remark}{Remark}[section] 
- 
-\newproof{Example}{Example} 
-\newproof{Method}{Method} 
-\newproof{Exercise}{Exercise} 
- 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-%                                         % 
-%        TABLE AND FIGURE CAPTIONS        % 
-%                                         % 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
- \def\@figtxt{figure}
-\long\def\@makecaption#1#2{\small
-\setlength{\parindent}{18pt}
-\baselineskip 14pt
- \ifx\@captype\@figtxt
- \vskip 10pt 
- \setbox\@tempboxa\hbox{{\sc #1} {\it #2}}
- \ifdim \wd\@tempboxa >\hsize {\sc #1} {\it #2}\par \else \hbox
-to\hsize{\hfil\box\@tempboxa\hfil}%
- \fi\else\hbox to\hsize{\hfil{\sc #1}\hfil}%
- \setbox\@tempboxa\hbox{{\it #2}}%
- \ifdim \wd\@tempboxa >\hsize {\it #2}\par \else
- \hbox to \hsize{\hfil\box\@tempboxa\hfil}\fi
- \vskip 10pt
- \fi}
-
- 
-%\newif\iftable  \global\tablefalse 
- 
- 
-%\long\def\@makecaption#1#2{% 
-%\setlength{\parindent}{18pt}
-% \vskip 12pt  
-%    \iftable 
- %              \hbox to \hsize{\hfil\sc #1\hfil} 
- %              \hbox to \hsize{\hfil\it #2\hfil} 
- %              \global\tablefalse 
- %    \else 
- %      \setbox\@tempboxa\hbox{{\small#1} {\small\it#2}} 
- %        \ifdim \wd\@tempboxa >\hsize  
- %           \indent{\small#1}{\small\it#2}\par  
- %               \else  
- %                \hbox to\hsize{\hfil\box\@tempboxa\hfil}\fi 
- % \fi} 
-% \vskip 6pt} 
- 
- 
- 
-%\def\figure{\global\tablefalse\@float{figure}} 
-\def\fnum@figure{\par\sc Fig. \thefigure.\ } 
-%\def\fnum@figure{\par\sc Fig. \thefigure\ } 
- 
-%\def\table{\global\tabletrue\@float{table}} 
-\def\fnum@table{\small \sc Table \thetable} 
- 
- 
- 
-
- 
- 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-%                                         % 
-%             SECTIONS                    % 
-%                                         % 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-\def\section{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus 
- -.2ex}%{2.3ex plus .2ex}
-{2pt}{\large\bf}}
-\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus -1ex minus 
- -.2ex}%{1.5ex plus .2ex}
-{2pt}{\large\bf}}
-\def\subsubsection{\@startsection {subsubsection}{3}{\z@}{1.3ex plus .5ex minus 
-    .2ex}{-.5em plus -.1em}{\normalsize\bf}}
-
-
-
-
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-%%                                          %% 
-%%            BIBLIOGRAPHY                  %% 
-%%                                          %% 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
- 
-\def\thebibliography#1{% 
-%\cleardoublepage 
-\parindent 0em
-\vspace{9pt}
-\begin{flushleft}\large\bf {References}\end{flushleft}
-\addvspace{3pt}\nopagebreak\list 
- %% default is no labels, for those not using \cite or BibTeX 
-{[\arabic{enumi}]} {\settowidth\labelwidth{[#1]} 
-%%{[\arabic{enumi}]}{\settowidth\labelwidth{mm} 
-\leftmargin\labelwidth 
-\leftmargin=17pt
- \advance\leftmargin\labelsep 
- \usecounter{enumi}\@bibsetup} 
-\def\newblock{\hskip .11em plus .33em minus -.07em} 
- \sloppy\clubpenalty4000\widowpenalty4000 
- \sfcode`\.=1000\relax} 
-
-
- 
-%% setup 8/10 type 
-\def\@bibsetup{%\itemindent=0pt
-\itemsep=0pt \parsep=0pt
-\small} 
- 
-\def\sameauthor{\leavevmode\vrule height 2pt depth -1.6pt width 23pt} 
- 
-  
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-%                                         % 
-%                INDEX                    % 
-%                                         % 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
- 
- 
-%makeindex.sty        official version 6.4  
-%The second line came from /usr/misc/lib/tex82/report.sty. 
- 
-\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi 
-\columnseprule \z@ 
-\columnsep 35pt\twocolumn[\chapter*{Index}] 
- \parskip\z@ plus .3pt\relax\let\item\@idxitem} 
- 
- 
-\def\printindex{\cleardoublepage\markboth{INDEX}{INDEX} 
-\addcontentsline{toc}{chapter}{Index}\@input{\jobname.ind}} 
- 
-\ps@headings  
- 
- 
-%%% end of style file 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% This is siamproc.bst
-% SIAM bibliography style (29-Jan-88 version)
-%    numeric labels, alphabetic order, Mathematical Reviews abbreviations,
-%    names in \sc, titles in italics, book titles mixed upper-lower and article
-%    titles lowercase, commas separate all fields except before "notes".
-%
-%   History
-%    1/30/86	(HWT)	Original version, by Howard Trickey.
-%    6/15/87	(HWT)	Fix format.editors---Martin Costabel.
-%    1/29/88	(OP&HWT) Updated for BibTeX version 0.99a, Oren Patashnik;
-%			THIS `siam' VERSION DOES NOT WORK WITH BIBTEX 0.98i.
-
-ENTRY
-  { address
-    author
-    booktitle
-    chapter
-    edition
-    editor
-    howpublished
-    institution
-    journal
-    key
-    month
-    note
-    number
-    organization
-    pages
-    publisher
-    school
-    series
-    title
-    type
-    volume
-    year
-  }
-  {}
-  { label }
-
-INTEGERS { output.state before.all mid.sentence after.block }
-
-FUNCTION {init.state.consts}
-{ #0 'before.all :=
-  #1 'mid.sentence :=
-  #2 'after.block :=
-}
-
-STRINGS { s t }
-
-FUNCTION {output.nonnull}
-{ 's :=
-  output.state mid.sentence =
-    { ", " * write$ }
-    { output.state after.block =
-	{ add.period$ write$
-	  newline$
-	  "\newblock " write$
-	}
-	'write$
-      if$
-      mid.sentence 'output.state :=
-    }
-  if$
-  s
-}
-
-FUNCTION {output}
-{ duplicate$ empty$
-    'pop$
-    'output.nonnull
-  if$
-}
-
-FUNCTION {output.check}
-{ 't :=
-  duplicate$ empty$
-    { pop$ "empty " t * " in " * cite$ * warning$ }
-    'output.nonnull
-  if$
-}
-
-FUNCTION {output.bibitem}
-{ newline$
-  "\bibitem{" write$
-  cite$ write$
-  "}" write$
-  newline$
-  ""
-  before.all 'output.state :=
-}
-
-FUNCTION {fin.entry}
-{ add.period$
-  write$
-  newline$
-}
-
-FUNCTION {new.block}
-{ output.state before.all =
-    'skip$
-    { after.block 'output.state := }
-  if$
-}
-
-FUNCTION {not}
-{   { #0 }
-    { #1 }
-  if$
-}
-
-FUNCTION {and}
-{   'skip$
-    { pop$ #0 }
-  if$
-}
-
-FUNCTION {or}
-{   { pop$ #1 }
-    'skip$
-  if$
-}
-
-FUNCTION {new.block.checka}
-{ empty$
-    'skip$
-    'new.block
-  if$
-}
-
-FUNCTION {field.or.null}
-{ duplicate$ empty$
-    { pop$ "" }
-    'skip$
-  if$
-}
-
-FUNCTION {emphasize}
-{ duplicate$ empty$
-    { pop$ "" }
-    { "{\em " swap$ * "}" * }
-  if$
-}
-
-FUNCTION {scapify}
-{ duplicate$ empty$
-    { pop$ "" }
-    { "{\sc " swap$ * "}" * }
-  if$
-}
-
-INTEGERS { nameptr namesleft numnames }
-
-FUNCTION {format.names}
-{ 's :=
-  #1 'nameptr :=
-  s num.names$ 'numnames :=
-  numnames 'namesleft :=
-    { namesleft #0 > }
-    { s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ 't :=
-      nameptr #1 >
-	{ namesleft #1 >
-	    { ", " * t * }
-	    { numnames #2 >
-		{ "," * }
-		'skip$
-	      if$
-	      t "others" =
-		{ " et~al." * }
-		{ " and " * t * }
-	      if$
-	    }
-	  if$
-	}
-	't
-      if$
-      nameptr #1 + 'nameptr :=
-      namesleft #1 - 'namesleft :=
-    }
-  while$
-}
-
-STRINGS { last.authors }
-
-FUNCTION {init.last.authors}
-{ "" 'last.authors :=
-}
-
-FUNCTION {format.authors}
-{ author empty$
-    { "" 'last.authors :=
-      ""
-    }
-    { author last.authors =
-        { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" }
-        { author format.names }% scapify }
-      if$
-      author 'last.authors :=
-    }
-  if$
-}
-
-FUNCTION {format.organization}
-{ organization empty$
-    { "" 'last.authors :=
-      ""
-    }
-    { organization last.authors =
-        { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" }
-        { organization scapify }
-      if$
-      organization 'last.authors :=
-    }
-  if$
-}
-
-FUNCTION {format.editors}
-{ editor empty$
-    { "" 'last.authors :=
-      ""
-    }
-    { editor last.authors =
-        { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" }
-	{ editor format.names scapify }
-      if$
-      editor num.names$ #1 >
-        { ", eds." * }
-	{ ", ed." * }
-      if$
-      editor 'last.authors :=
-    }
-  if$
-}
-
-FUNCTION {format.ineditors}
-{ editor empty$
-    { "" }
-    { editor format.names
-      editor num.names$ #1 >
-	{ ", eds." * }
-	{ ", ed." * }
-      if$
-    }
-  if$
-}
-
-FUNCTION {format.title}
-{ title empty$
-    { "" }
-    { title "t" change.case$ emphasize }
-  if$
-}
-
-FUNCTION {n.dashify}
-{ 't :=
-  ""
-    { t empty$ not }
-    { t #1 #1 substring$ "-" =
-	{ t #1 #2 substring$ "--" = not
-	    { "--" *
-	      t #2 global.max$ substring$ 't :=
-	    }
-	    {   { t #1 #1 substring$ "-" = }
-		{ "-" *
-		  t #2 global.max$ substring$ 't :=
-		}
-	      while$
-	    }
-	  if$
-	}
-	{ t #1 #1 substring$ *
-	  t #2 global.max$ substring$ 't :=
-	}
-      if$
-    }
-  while$
-}
-
-FUNCTION {format.date}
-{ year empty$
-    { month empty$
-	{ "" }
-	{ "there's a month but no year in " cite$ * warning$
-	  month
-	}
-      if$
-    }
-    { month empty$
-	'year
-	{ month " " * year * }
-      if$
-    }
-  if$
-}
-
-FUNCTION {format.btitle}
-{ title emphasize
-}
-
-FUNCTION {tie.or.space.connect}
-{ duplicate$ text.length$ #3 <
-    { "~" }
-    { " " }
-  if$
-  swap$ * *
-}
-
-FUNCTION {either.or.check}
-{ empty$
-    'pop$
-    { "can't use both " swap$ * " fields in " * cite$ * warning$ }
-  if$
-}
-
-FUNCTION {format.bvolume}
-{ volume empty$
-    { "" }
-    { "vol.~" volume *
-      series empty$
-	'skip$
-	{ " of " * series * }
-      if$
-      "volume and number" number either.or.check
-    }
-  if$
-}
-
-FUNCTION {format.number.series}
-{ volume empty$
-    { number empty$
-	{ series field.or.null }
-	{ "no.~" number *
-	  series empty$
-	    { "there's a number but no series in " cite$ * warning$ }
-	    { " in " * series * }
-	  if$
-	}
-      if$
-    }
-    { "" }
-  if$
-}
-
-FUNCTION {format.edition}
-{ edition empty$
-    { "" }
-    { edition "l" change.case$ "~ed." * }
-  if$
-}
-
-INTEGERS { multiresult }
-
-FUNCTION {multi.page.check}
-{ 't :=
-  #0 'multiresult :=
-    { multiresult not
-      t empty$ not
-      and
-    }
-    { t #1 #1 substring$
-      duplicate$ "-" =
-      swap$ duplicate$ "," =
-      swap$ "+" =
-      or or
-	{ #1 'multiresult := }
-	{ t #2 global.max$ substring$ 't := }
-      if$
-    }
-  while$
-  multiresult
-}
-
-FUNCTION {format.pages}
-{ pages empty$
-    { "" }
-    { pages multi.page.check
-	{ "pp.~" pages n.dashify * }
-	{ "p.~" pages * }
-      if$
-    }
-  if$
-}
-
-FUNCTION {format.vol.year}
-{ volume field.or.null
-  year empty$
-    { "empty year in " cite$ * warning$ }
-    { " (" year * ")" * * }
-  if$
-}
-
-FUNCTION {format.chapter.pages}
-{ chapter empty$
-    'format.pages
-    { type empty$
-	{ "ch.~" chapter * }
-	{ type "l" change.case$ chapter tie.or.space.connect }
-      if$
-      pages empty$
-	'skip$
-	{ ", " * format.pages * }
-      if$
-    }
-  if$
-}
-
-FUNCTION {format.in.ed.booktitle}
-{ booktitle empty$
-    { "" }
-    { editor empty$
-	{ "in " booktitle * }
-	{ "in " booktitle * ", " * format.ineditors * }
-      if$
-    }
-  if$
-}
-
-FUNCTION {empty.misc.check}
-{ author empty$ title empty$ howpublished empty$
-  month empty$ year empty$ note empty$
-  and and and and and
-  key empty$ not and
-    { "all relevant fields are empty in " cite$ * warning$ }
-    'skip$
-  if$
-}
-
-FUNCTION {format.thesis.type}
-{ type empty$
-    'skip$
-    { pop$
-      type "l" change.case$
-    }
-  if$
-}
-
-FUNCTION {format.tr.number}
-{ type empty$
-    { "Tech. Rep." }
-    'type
-  if$
-  number empty$
-    { "l" change.case$ }
-    { number tie.or.space.connect }
-  if$
-}
-
-FUNCTION {format.article.crossref}
-{ key empty$
-    { journal empty$
-	{ "need key or journal for " cite$ * " to crossref " * crossref *
-	  warning$
-	  ""
-	}
-	{ "in " journal * }
-      if$
-    }
-    { "in " key * }
-  if$
-  " \cite{" * crossref * "}" *
-}
-
-FUNCTION {format.crossref.editor}
-{ editor #1 "{vv~}{ll}" format.name$
-  editor num.names$ duplicate$
-  #2 >
-    { pop$ " et~al." * }
-    { #2 <
-	'skip$
-	{ editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
-	    { " et~al." * }
-	    { " and " * editor #2 "{vv~}{ll}" format.name$ * }
-	  if$
-	}
-      if$
-    }
-  if$
-}
-
-FUNCTION {format.book.crossref}
-{ volume empty$
-    { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
-      "in "
-    }
-    { "vol.~" volume *
-      " of " *
-    }
-  if$
-  editor empty$
-  editor field.or.null author field.or.null =
-  or
-    { key empty$
-	{ series empty$
-	    { "need editor, key, or series for " cite$ * " to crossref " *
-	      crossref * warning$
-	      "" *
-	    }
-	    { series * }
-	  if$
-	}
-	{ key * }
-      if$
-    }
-    { format.crossref.editor * }
-  if$
-  " \cite{" * crossref * "}" *
-}
-
-FUNCTION {format.incoll.inproc.crossref}
-{ editor empty$
-  editor field.or.null author field.or.null =
-  or
-    { key empty$
-	{ booktitle empty$
-	    { "need editor, key, or booktitle for " cite$ * " to crossref " *
-	      crossref * warning$
-	      ""
-	    }
-	    { "in " booktitle * }
-	  if$
-	}
-	{ "in " key * }
-      if$
-    }
-    { "in " format.crossref.editor * }
-  if$
-  " \cite{" * crossref * "}" *
-}
-
-FUNCTION {article}
-{ output.bibitem
-  format.authors "author" output.check
-  format.title "title" output.check
-  crossref missing$
-    { journal "journal" output.check
-      format.vol.year output
-    }
-    { format.article.crossref output.nonnull }
-  if$
-  format.pages output
-  new.block
-  note output
-  fin.entry
-}
-
-FUNCTION {book}
-{ output.bibitem
-  author empty$
-    { format.editors "author and editor" output.check }
-    { format.authors output.nonnull
-      crossref missing$
-	{ "author and editor" editor either.or.check }
-	'skip$
-      if$
-    }
-  if$
-  format.btitle "title" output.check
-  crossref missing$
-    { format.bvolume output
-      format.number.series output
-      publisher "publisher" output.check
-      address output
-    }
-    { format.book.crossref output.nonnull }
-  if$
-  format.edition output
-  format.date "year" output.check
-  new.block
-  note output
-  fin.entry
-}
-
-FUNCTION {booklet}
-{ output.bibitem
-  format.authors output
-  format.title "title" output.check
-  howpublished new.block.checka
-  howpublished output
-  address output
-  format.date output
-  new.block
-  note output
-  fin.entry
-}
-
-FUNCTION {inbook}
-{ output.bibitem
-  author empty$
-    { format.editors "author and editor" output.check }
-    { format.authors output.nonnull
-      crossref missing$
-	{ "author and editor" editor either.or.check }
-	'skip$
-      if$
-    }
-  if$
-  format.btitle "title" output.check
-  crossref missing$
-    { format.bvolume output
-      format.number.series output
-      publisher "publisher" output.check
-      address output
-    }
-    { format.book.crossref output.nonnull }
-  if$
-  format.edition output
-  format.date "year" output.check
-  format.chapter.pages "chapter and pages" output.check
-  new.block
-  note output
-  fin.entry
-}
-
-FUNCTION {incollection}
-{ output.bibitem
-  format.authors "author" output.check
-  format.title "title" output.check
-  crossref missing$
-    { format.in.ed.booktitle "booktitle" output.check
-      format.bvolume output
-      format.number.series output
-      publisher "publisher" output.check
-      address output
-      format.edition output
-      format.date "year" output.check
-    }
-    { format.incoll.inproc.crossref output.nonnull }
-  if$
-  format.chapter.pages output
-  new.block
-  note output
-  fin.entry
-}
-
-FUNCTION {inproceedings}
-{ output.bibitem
-  format.authors "author" output.check
-  format.title "title" output.check
-  crossref missing$
-    { format.in.ed.booktitle "booktitle" output.check
-      format.bvolume output
-      format.number.series output
-      address empty$
-	{ organization output
-	  publisher output
-	  format.date "year" output.check
-	}
-	{ address output.nonnull
-	  format.date "year" output.check
-	  organization output
-	  publisher output
-	}
-      if$
-    }
-    { format.incoll.inproc.crossref output.nonnull }
-  if$
-  format.pages output
-  new.block
-  note output
-  fin.entry
-}
-
-FUNCTION {conference} { inproceedings }
-
-FUNCTION {manual}
-{ output.bibitem
-  author empty$
-    { format.organization output }
-    { format.authors output.nonnull }
-  if$
-  format.btitle "title" output.check
-  author empty$
-    'skip$
-    { organization output }
-  if$
-  address output
-  format.edition output
-  format.date output
-  new.block
-  note output
-  fin.entry
-}
-
-FUNCTION {mastersthesis}
-{ output.bibitem
-  format.authors "author" output.check
-  format.title "title" output.check
-  "Master's thesis" format.thesis.type output.nonnull
-  school "school" output.check
-  address output
-  format.date "year" output.check
-  new.block
-  note output
-  fin.entry
-}
-
-FUNCTION {misc}
-{ output.bibitem
-  format.authors output
-  format.title output
-  howpublished new.block.checka
-  howpublished output
-  format.date output
-  new.block
-  note output
-  fin.entry
-  empty.misc.check
-}
-
-FUNCTION {phdthesis}
-{ output.bibitem
-  format.authors "author" output.check
-  format.btitle "title" output.check
-  "PhD thesis" format.thesis.type output.nonnull
-  school "school" output.check
-  address output
-  format.date "year" output.check
-  new.block
-  note output
-  fin.entry
-}
-
-FUNCTION {proceedings}
-{ output.bibitem
-  editor empty$
-    { format.organization output }
-    { format.editors output.nonnull }
-  if$
-  format.btitle "title" output.check
-  format.bvolume output
-  format.number.series output
-  address empty$
-    { editor empty$
-	'skip$
-	{ organization output }
-      if$
-      publisher output
-      format.date "year" output.check
-    }
-    { address output.nonnull
-      format.date "year" output.check
-      editor empty$
-	'skip$
-	{ organization output }
-      if$
-      publisher output
-    }
-  if$
-  new.block
-  note output
-  fin.entry
-}
-
-FUNCTION {techreport}
-{ output.bibitem
-  format.authors "author" output.check
-  format.title "title" output.check
-  format.tr.number output.nonnull
-  institution "institution" output.check
-  address output
-  format.date "year" output.check
-  new.block
-  note output
-  fin.entry
-}
-
-FUNCTION {unpublished}
-{ output.bibitem
-  format.authors "author" output.check
-  format.title "title" output.check
-  new.block
-  note "note" output.check
-  format.date output
-  fin.entry
-}
-
-FUNCTION {default.type} { misc }
-
-MACRO {jan} {"Jan."}
-
-MACRO {feb} {"Feb."}
-
-MACRO {mar} {"Mar."}
-
-MACRO {apr} {"Apr."}
-
-MACRO {may} {"May"}
-
-MACRO {jun} {"June"}
-
-MACRO {jul} {"July"}
-
-MACRO {aug} {"Aug."}
-
-MACRO {sep} {"Sept."}
-
-MACRO {oct} {"Oct."}
-
-MACRO {nov} {"Nov."}
-
-MACRO {dec} {"Dec."}
-
-MACRO {acmcs} {"ACM Comput. Surveys"}
-
-MACRO {acta} {"Acta Inf."}
-
-MACRO {cacm} {"Comm. ACM"}
-
-MACRO {ibmjrd} {"IBM J. Res. Dev."}
-
-MACRO {ibmsj} {"IBM Syst.~J."}
-
-MACRO {ieeese} {"IEEE Trans. Softw. Eng."}
-
-MACRO {ieeetc} {"IEEE Trans. Comput."}
-
-MACRO {ieeetcad}
- {"IEEE Trans. Comput.-Aided Design Integrated Circuits"}
-
-MACRO {ipl} {"Inf. Process. Lett."}
-
-MACRO {jacm} {"J.~Assoc. Comput. Mach."}
-
-MACRO {jcss} {"J.~Comput. System Sci."}
-
-MACRO {scp} {"Sci. Comput. Programming"}
-
-MACRO {sicomp} {"SIAM J. Comput."}
-
-MACRO {tocs} {"ACM Trans. Comput. Syst."}
-
-MACRO {tods} {"ACM Trans. Database Syst."}
-
-MACRO {tog} {"ACM Trans. Gr."}
-
-MACRO {toms} {"ACM Trans. Math. Softw."}
-
-MACRO {toois} {"ACM Trans. Office Inf. Syst."}
-
-MACRO {toplas} {"ACM Trans. Prog. Lang. Syst."}
-
-MACRO {tcs} {"Theoretical Comput. Sci."}
-
-READ
-
-FUNCTION {sortify}
-{ purify$
-  "l" change.case$
-}
-
-INTEGERS { len }
-
-FUNCTION {chop.word}
-{ 's :=
-  'len :=
-  s #1 len substring$ =
-    { s len #1 + global.max$ substring$ }
-    's
-  if$
-}
-
-FUNCTION {sort.format.names}
-{ 's :=
-  #1 'nameptr :=
-  ""
-  s num.names$ 'numnames :=
-  numnames 'namesleft :=
-    { namesleft #0 > }
-    { nameptr #1 >
-	{ "   " * }
-	'skip$
-      if$
-      s nameptr "{vv{ } }{ll{ }}{  f{ }}{  jj{ }}" format.name$ 't :=
-      nameptr numnames = t "others" = and
-	{ "et al" * }
-	{ t sortify * }
-      if$
-      nameptr #1 + 'nameptr :=
-      namesleft #1 - 'namesleft :=
-    }
-  while$
-}
-
-FUNCTION {sort.format.title}
-{ 't :=
-  "A " #2
-    "An " #3
-      "The " #4 t chop.word
-    chop.word
-  chop.word
-  sortify
-  #1 global.max$ substring$
-}
-
-FUNCTION {author.sort}
-{ author empty$
-    { key empty$
-	{ "to sort, need author or key in " cite$ * warning$
-	  ""
-	}
-	{ key sortify }
-      if$
-    }
-    { author sort.format.names }
-  if$
-}
-
-FUNCTION {author.editor.sort}
-{ author empty$
-    { editor empty$
-	{ key empty$
-	    { "to sort, need author, editor, or key in " cite$ * warning$
-	      ""
-	    }
-	    { key sortify }
-	  if$
-	}
-	{ editor sort.format.names }
-      if$
-    }
-    { author sort.format.names }
-  if$
-}
-
-FUNCTION {author.organization.sort}
-{ author empty$
-    { organization empty$
-	{ key empty$
-	    { "to sort, need author, organization, or key in " cite$ * warning$
-	      ""
-	    }
-	    { key sortify }
-	  if$
-	}
-	{ "The " #4 organization chop.word sortify }
-      if$
-    }
-    { author sort.format.names }
-  if$
-}
-
-FUNCTION {editor.organization.sort}
-{ editor empty$
-    { organization empty$
-	{ key empty$
-	    { "to sort, need editor, organization, or key in " cite$ * warning$
-	      ""
-	    }
-	    { key sortify }
-	  if$
-	}
-	{ "The " #4 organization chop.word sortify }
-      if$
-    }
-    { editor sort.format.names }
-  if$
-}
-
-FUNCTION {presort}
-{ type$ "book" =
-  type$ "inbook" =
-  or
-    'author.editor.sort
-    { type$ "proceedings" =
-	'editor.organization.sort
-	{ type$ "manual" =
-	    'author.organization.sort
-	    'author.sort
-	  if$
-	}
-      if$
-    }
-  if$
-  "    "
-  *
-  year field.or.null sortify
-  *
-  "    "
-  *
-  title field.or.null
-  sort.format.title
-  *
-  #1 entry.max$ substring$
-  'sort.key$ :=
-}
-
-ITERATE {presort}
-
-SORT
-
-STRINGS { longest.label }
-
-INTEGERS { number.label longest.label.width }
-
-FUNCTION {initialize.longest.label}
-{ "" 'longest.label :=
-  #1 'number.label :=
-  #0 'longest.label.width :=
-}
-
-FUNCTION {longest.label.pass}
-{ number.label int.to.str$ 'label :=
-  number.label #1 + 'number.label :=
-  label width$ longest.label.width >
-    { label 'longest.label :=
-      label width$ 'longest.label.width :=
-    }
-    'skip$
-  if$
-}
-
-EXECUTE {initialize.longest.label}
-
-ITERATE {longest.label.pass}
-
-FUNCTION {begin.bib}
-{ preamble$ empty$
-    'skip$
-    { preamble$ write$ newline$ }
-  if$
-  "\begin{thebibliography}{"  longest.label  * "}" * write$ newline$
-}
-
-EXECUTE {begin.bib}
-
-EXECUTE {init.state.consts}
-
-EXECUTE {init.last.authors}
-
-ITERATE {call.type$}
-
-FUNCTION {end.bib}
-{ newline$
-  "\end{thebibliography}" write$ newline$
-}
-
-EXECUTE {end.bib}
-