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-%%
-%% SIAM Plain TeX macro documentation.
-%% Paul Duggan
-%% 9-15-94
-
-\input siamptex.sty
-
-% The definitions are to provide a verbatim text environment
-
-\def\uncatcodespecials{\def\do##1{\catcode`##1=12 }\dospecials}
-\def\setupverbatim{\tt%
-  \def\par{\leavevmode\endgraf}%
-  \obeylines\uncatcodespecials\obeyspaces}
-{\obeyspaces\global\let =\ }
-\def\doverbatim#1{\def\next##1#1{##1\endgroup}\next}
-\def\verbatim{\begingroup\setupverbatim\doverbatim}
-
-
-\overfullrule=0pt
-
-\topmatter
-\vol{1}
-\no{1, pp.~000--000}
-\SIMAC
-\date{October 1994}
-\copyyear{1994}
-\code{000}
-
-\title Using SIAM's \TeX\ Macros\endtitle
-
-\shorttitle{USING SIAM'S \TeX\ MACROS}
-
-\recdate{*}{August 9, 1994. 
-This work was supported by the Society for Industrial
-and Applied Mathematics}
-
-\author Paul Duggan\fnmark{$^{\dag}$}\endauthor
-
-\address{$^{\dag}$}{Society for Industrial and Applied Mathematics,
-Philadelphia, Pennsylvania ({\tt duggan@siam.org}). Questions, comments,
-or corrections to this document may be directed to that e-mail address} 
-
-\abstract{Documentation is given for use of the SIAM \TeX\ macros.
-Instructions and suggestions for compliance with SIAM style
-standards are also included.}
-\subjclass\endsubjclass
-\keywords\endkeywords
-
-
-\endtopmatter
-
-
-\heading{1}{Introduction}
-This file is documentation for the SIAM \TeX\ macros and provides
-instruction for submission of files formatted in \TeX.
-
-To accommodate authors who electronically typeset their manuscripts,
-SIAM supports the use of \TeX. To ensure quality typesetting according
-to SIAM style standards, SIAM provides a \TeX\ macro style file.
-Using \TeX\ to format a manuscript should simplify the editorial process
-and lessen the author's proofreading burden. However,
-it is still necessary to proofread the galley proofs with care.
-
-Electronic files should not be submitted until the paper has been
-accepted, and then not until requested to do so by someone in the SIAM
-office. Once an article is slated for an issue,
-someone from the SIAM office will contact the author about any or all
-of the following: editorial and stylistic queries, 
-supplying the source files (and any supplementary macros)
-for the properly formatted article, and handling figures.
-
-When submitting electronic files  (electronic submissions) 
-(to {\tt tex@siam.org}) write  the journal, issue, and author's
-name in the subject line of the message. 
-Authors are responsible for ensuring  that the paper generated 
-from the source files exactly matches the paper that
-was accepted for publication by the review editor. If it does not,
-information on how it differs should be indicated in the transmission 
-of the file. When submitting a file, please be sure to include any 
-additional macros (other than those provided by SIAM) that will be 
-needed to run the paper. 
-
-SIAM uses MS-DOS-based computers for \TeX\ processing. Therefore
-all filenames should be restricted to eight characters or less,
-plus a three character extension.
-
-Once the files are corrected here at SIAM, we will mail the revised 
-proofs to be read against the original edited hardcopy 
-manuscript. We are not
-set up to shuttle back and forth varying electronic versions of each
-paper, so we must rely on hard copy of the galleys. The author's proofreading
-is an important but easily overlooked step. Even if SIAM were not
-to introduce a single editorial change into your manuscript, there
-would still be a need to check, because electronic transmission
-can introduce errors.
-
-
-This distribution contains the following items: {\tt siamptex.sty}, the
-main macro package; this documentation file; and a sample file {\tt
-pexample.tex}. The sample file is representative of the standard way 
-to apply the macros. The rest of this paper emphasizes some aspects 
-of applying the macros, points out options and special cases, and 
-describes the SIAM style standards.
-The SIAM macros make use of the small caps font, {\tt cmcsc}, which
-is not installed in some systems. This font along with other 
-AMS-\TeX\ fonts can be retrieved from the American Mathematical
-Society via anonymous FTP to {\tt e-math.ams.com}.
-
-\heading{2}{Headings}
-The top matter of a journal is in a standard format. The macro
-and initial definitions should be included as follows.
-
-\verbatim:
-\input siamptex.sty
-\overfullrule=0pt
-
-:
-
-The \verbatim:\overfullrule: should be set wider than zero points
-while still being edited by the author to assist in locating 
-lines that extend beyond the margins.
-
-
-The ``slugline,'' which contains the journal and copyright information, is
-created by special commands following the \verbatim:\topmatter:.
-
-\verbatim:
-\SIMAX
-\vol{0}
-\no{0, pp.~000--000}
-\date{April 1995}
-\copyyear{1995}
-\code{000}
-
-:
-Because authors will probably not know exact 
-volume, number, date, or code, insert zeros in their place as
-above. SIAM will place the appropriate information in
-the commands in production; however, the commands must be used.
-\verbatim:\SIMAX:, \verbatim:\SIAP:, \verbatim:\SICOMP:,
-\verbatim:\SICON:, \verbatim:\SIDMA:, \verbatim:\SIMA:,
-\verbatim:\SIMAX:, \verbatim:\SINUM:, \verbatim:\SIOPT:,
-\verbatim:\SISC:, and \verbatim:\SIREV: are the commands provided
-to include the journal title in the heading. 
-
-The title and author(s) of the paper are indicated by the
-\verbatim:\title\endtitle: and \verbatim:\author\endauthor: commands.
-Author support and address information is indicated as follows.
-
-\verbatim:
-\author A.~U. Thorone\fnmark{$^{\dag}$}  
-        \and A.~U. Thortwo\fnmark{$^{\ddag}$}\endauthor
-
-\address{$^{\dag}$}{Address of the first author and support}
-\address{$^{\ddag}$}{Address of the second author and support}
-
-:
-
-If more than two authors are included, each should be separated
-by a comma after the \verbatim:\fnmark{}: command. If more than one
-author shares common footnote information, then a common footnote
-and footnote mark should be used.
- 
-The commands \verbatim:\shorttitle{}: and \verbatim:\shortauthor{}:
-are used to designate the running heads for the paper.
-
-The \verbatim:\abstract{}:, \verbatim:\keywords\endkeywords:, and
-\verbatim:\subjclass\endsubjclass:\break commands are used to include the
-abstract, key words, and AMS subject classification numbers, respectively.
-If there is to be only one subject classification number, the
-\verbatim:\subjclass: command should be preceded by
-\verbatim:\oneclass:. (If the AMS numbers are unknown, leave that
-information blank.) Authors are responsible for providing AMS numbers.
-They can be found in the Annual Index of Math Reviews or
-through {\tt e-Math} ({\tt telnet e-math.ams.com}; login
-and password are both {\tt e-math}).
-Complete the topmatter section by including \verbatim:\endtopmatter:.
-
- 
-
-\heading{3}{Equations and mathematics}
-Equations and mathematics
-are handled by standard \TeX\ commands. SIAM style is
-for numbered equations to appear flush with the left margin. The
-\verbatim:\leqno: and \verbatim:\leqalignno{}: commands are used for
-this purpose. If any letters indicating subequations are to be used
-with the numbers, they should be set in roman type.
-
-Clear equation formatting using \TeX\ can be challenging. Aside from
-the regular \TeX\ documentation, authors will find Nicholas 
-J. Higham's book {\it Handbook of Writing for the Mathematical
-Sciences\/} [1] useful for guidelines and tips on formatting with
-\TeX. The book covers many other topics related to article
-writing as well.                
-
-Authors commonly make mistakes by using
- \verbatim:<:, \verbatim:>:, \verbatim:\mid:, and 
-\verbatim:\parallel: as delimiters, instead of 
-\verbatim:\langle:, \verbatim:\rangle:, \verbatim:|:,
-and \verbatim:\|:. The incorrect symbols have particular 
-meanings distinct from the correct ones and should not be confused.
-
-\bigskip
-\eightpoint
-\halign{#\hfil\quad&&#\hfil\quad\cr
-&{\bf Wrong} &&&& {\bf Right}&\cr
-&\verbatim:<x, y>: & $<x, y>$   &&&
-   \verbatim:\langle x, y\rangle: & $\langle x, y\rangle$ \cr
-&\verbatim:5 < \mid A \mid: &  $5 < \mid A \mid$ &&&
-   \verbatim:5 < |A|: &  $5 < |A|$ \cr
-&  \verbatim:6x = \parallel x: \cr
-&\verbatim:    - 1\parallel_{i}: & $6x = \parallel x - 1\parallel_{i}$ &&&
-   \verbatim:6x = \|x - 1\|_{i}: & $6x = \| x - 1\|_{i}$\cr}
-   \tenpoint\rm 
-\bigskip
-
-Another common author error is to put large (and even medium sized)
-matrices in-line with the text, rather than displaying them. This
-creates unattractive line spacing problems, and should be assiduously
-avoided. Text-sized matrices (like $({a \atop b} {b \atop c})$) might
-be used but anything much more complex than the example cited will
-not be easy to read and should be displayed.
-
-More information on the formatting of equations and aligned
-equations is found in Knuth [2]. Authors bear primary responsibility
-for formatting their equations within margins and in an aesthetically
-pleasing and informative manner.
-
-The SIAM macros include additional roman math words, or ``log-like"
-functions, to those provided in standard \TeX.  The following
-commands are added: \verbatim:\const:, \verbatim:\diag:, \verbatim:\grad:,
-\verbatim:\Range:, \verbatim:\rank:, and \verbatim:\supp:.
-These commands produce the same word as the command name
-in math mode, in roman type.
-
-                     
-Groups of equations that are not directly related to each other
-should normally be centered independently. This may be done through
-the \TeX\ math command \verbatim:\displaylines{}:. Numbering 
-independently centered equations can be difficult, so Seroul and 
-Levy's [3] macro \verbatim:\ldisplaylinesno{}: has been included 
-in {\tt siamptex.sty}. \verbatim:\ldisplaylinesno{}: works just 
-like \verbatim:\leqalignno:, except no ampersand is used to align 
-the equations, since they are to be centered.
-
-\heading{4}{Text formatting}
-Section and subsection headings are both included using the
-\verbatim:\heading{}{}: command, which requires two arguments. The 
-first argument is for the number, and the second 
-is the title of the section or
-subsection. 
-
-No extra spacing should be placed between paragraphs. The
-\verbatim:\heading: command inserts the required spacing between 
-sections.
-
-SIAM style does not normally make use of plain \TeX's 
-\verbatim:\item: command. The \verbatim:\meti: command is preferred for
-lists of items beginning with, for instance, bullets ($\bullet$) or
-roman numerals (iv). The \verbatim:\meti: command retains normal
-paragraph shape but places all labels aligned flush right. For
-example:
-
-\verbatim:
-\meti{(i)} This is the first item.
-\meti{(ii)} This is the second item of the series.
-
-:
-
-produces
-
-\meti{(i)} This is the first item.
-\meti{(ii)} This is the second item of the series. 
-\medskip
-
-The \verbatim:\meti: macro was adapted from Seroul and Levy [3].
-
-\heading{4.1}{Punctuation}
-All standard punctuation and all numerals should be set in roman type
-(upright) even within italic text. 
-The only exceptions are periods and commas. They may
-be set to match the surrounding text.
-
-References to sections should use the symbol \S, generated by
-\verbatim:\S:. (If the reference begins a sentence, the term ``Section''
-should be spelled out in full.) Authors should not redefine
-\verbatim:\S:, say, to be a calligraphic S, because \verbatim:\S:
-must be reserved for use as the section symbol.  
-
-Authors sometimes confuse the use of various types of dashes.
-Hyphens (\verbatim:-:, -) are used for some compound words (many
-such words should have no hyphen but must be run together, 
-like ``nonzero,'' or split apart, like ``well defined.'' 
-Minus signs (\verbatim:$-$:, $-$)
-should be used in math to represent subtraction or negative numbers.
-En dashes (\verbatim:--:, --) are used for ranges (like 3--5, 
-June--August), or for joined names (like Runge--Kutta). Em dashes
-(\verbatim:---:, ---) are used to set off a clause---such as this 
-one---from the rest of the sentence. 
-
-\heading{4.2}{Theorems, lemmas, and proofs}
-Theorems, lemmas, propositions, and so forth, have macros included
-for correct formatting. Below is an example.
-
-\verbatim:
-\thm{Theorem 4.1}
-Sample theorem included for illustration.  
-Numbers and parentheses, like equation $(3.2)$, should be set 
-in roman type.  Note that words in displayed equations, such as
-$$ x^2 = Y^2 \sin z^2 \hbox{ for all } x $$
-will appear in italic type in a theorem, though normally
-they should appear in roman.\endthm
-
-:
-
-This sample produces Theorem 4.1 below.
-
-\thm{Theorem 4.1}
-Sample theorem included for illustration.  
-Numbers and parentheses, like equation $(3.2)$, should be set 
-in roman type.  Note that words in displayed equations, such as
-$$ x^2 = Y^2 \sin z^2 \hbox{ for all } x $$
-will appear in italic type in a theorem, though normally
-they should appear in roman.\endthm
-
-
-The \verbatim:\cor:, \verbatim:\dfn:, \verbatim:\lem:, and 
-\verbatim:\prop:  commands
-all work similarly. Named theorems should be designated with the
-title in roman type, enclosed in parentheses.
-
-\verbatim:
-\thm{Theorem 3.2 {\rm (sample theorem with title)}}
-
-:
-
-Proofs are illustrated in the following example:
-
-\verbatim:
-\prf{Proof}
-The body of the proof.
-\qquad\endproof
-
-:
-
-If the proof ends with a displayed equation, the \verbatim:\endproof:
-box \endproof\  should appear two ems (\verbatim:\qquad:)
-from the end of the equation on line with it horizontally. 
-
-\heading{5}{Figures and tables}
-Figures and tables are best handled in \TeX\ by putting them within a
-\verbatim:\topinsert \endinsert: or \verbatim:\midinsert \endinsert: 
-environment. The appropriate amount
-of space should be left for the figure, and the caption should be
-formatted to be centered or as a paragraph if more than one line. Text
-should be italic, eight-point type, with the words ``Fig.~\#'' in small
-caps. A sample follows.
-
-\verbatim:
-\midinsert
-\vskip 22pc
-\centerline{\eightpoint{\smc Fig.~5.1}. \it Italic caption text.}
-\endinsert
-
-:
-
-SIAM tables should be formatted in eight-point type, with enough
-space left between entries and surrounding lines so that they do not
-touch. Take particular care with super- and subscript characters.
-See Knuth [2] or Seroul and Levy [3] for more information on
-the formatting of tables in \TeX. Table captions are similar to
-figure captions, but the word ``Table'' and the number appear on 
-a separate line from the caption text.
-
-SIAM supports the use of {\tt psfig} for including {\smc PostScript}
-figures. All {\smc Post\-Script} figures should be sent in separate
-files. See the {\tt psfig} documentation (from wherever you acquired 
-{\tt psfig}) for more details on the use
-of this style option. It is a good idea to submit high-quality
-hardcopy of all {\smc Post\-Script} figures just in case there 
-is difficulty in the reproduction of the figure. Figures produced 
-by other non-\TeX\ methods should be included as high-quality 
-hardcopy when  the manuscript is submitted.
-
-\heading{6}{Bibliographies}
-References are handled using the \verbatim:\Refs: command. 
-All names are to be keyed initial upper case cap and small 
-caps. Only the first and middle initials, followed by the 
-last name, are to be used. Last names should never be listed first. 
-Some representative sample entries are illustrated below:
-
-\verbatim|
-\Refs
-
-\ref 1\\ {\smc A.~U Thorone}, {\it Title of paper with lower case
-letters}, SIAM J. Abbrev. Correctly, 2 (1992), pp.~000--000.\endref
-
-\ref 2\\ \sameauthor, % generates a 3-em rule
-{\it Title of paper appearing in book}, in Book Title: 
-With All Initial Caps, Publisher, Location, 1992.\endref
-
-\ref 3\\ {\smc W. Riter},
-{\it Title of another paper appearing in a book}, in The Book 
-Title, E.~D. One, E.~D. Two, and A.~N. Othereditor, eds., 
-Publisher, Location, 1992, pp.~000--000.\endref
-
-\ref 4\\ {\smc A.~U. Thorone, A.~U. Thortwo, and A.~U. Thorthree},
-{\it Title of Book{\rm III:} Note Initial Caps}, 
-Publisher, Location, pp.~000--000, 1994.\endref
-
-\ref 5\\ {\smc A. Notherauth}, {\it Title of paper that's not yet
-published}, SIAM J. Abbrev. Correctly, to appear.\endref
-|
-
-Other types of references fall into the same general pattern. See the
-sample file or any SIAM journal for other examples. Authors must
-correctly format their bibliography to be considered as having used
-the macros correctly. An incorrectly formatted bibliography is not 
-only time-consuming for SIAM to process 
-but it is possible that errors may be introduced by 
-keyboarders/copy editors.
-
-As an alternative to the above style of reference, an alphanumeric
-code may be used in place of the number (e.g., [AUTh90]). The same
-\verbatim:\Refs: and \verbatim:\ref: commands are used, but the
-command \verbatim:\resetrefindent{}: must be used before the 
-\verbatim:\Refs: command, with the widest expected alphanumeric code
-as an argument.
-
-Another alternative is no number, simply the authors' names and
-the year of publication following in parentheses. The rest of the
-format is identical. To get an entry with no number in brackets 
-before it, use the \verbatim:\xref: command. This method is acceptable
-but not encouraged.
-
-\heading{7}{Conclusion} Many other style suggestions and tips
-could be given to help authors but are beyond the scope of this
-document. Simple mistakes can be avoided by increasing your familiarity
-with how \TeX\ functions. The books referred to throughout this document
-are also useful to the author who wants clear, beautiful typography
-with minimal mistakes. 
-
-\Refs
-
-\ref 1\\ {\smc N.~J. Higham}, {\it Handbook of Writing for
-the Mathematical Sciences}, Society for Industrial and Applied
-Mathematics, Philadelphia, PA, 1993.\endref
-
-\ref 2\\ {\smc D.~E. Knuth}, {\it The \TeX book}, Addison Wesley,
-Reading, MA, 1986.\endref
-
-\ref 3\\ {\smc R. Seroul and S. Levy}, {\it A Beginner's Book of
-{\rm \TeX}}, Springer-Verlag, Berlin, New York, 1991.\endref
-
-
-\bye 
diff --git a/Master/texmf-dist/tex/plain/siam/pexample.tex b/Master/texmf-dist/tex/plain/siam/pexample.tex
deleted file mode 100644
index eb2c2f50101..00000000000
--- a/Master/texmf-dist/tex/plain/siam/pexample.tex
+++ /dev/null
@@ -1,523 +0,0 @@
-% Sample file for SIAM's plain TeX macro package.
-% 9-14-94 Paul Duggan
-\input siamptex.sty
-
-% author defined macros included for illustrative purposes only.
-% symbols for real numbers, complex, ... (\Bbb font from AMS-TeX
-% fonts v2.x also usable)
-
-\def\fR{{\bf R}}
-\def\fC{{\bf C}}
-\def\fK{{\bf K}}
-
-% misc. operators
-\def\Span {\mathop{\hbox{\rm span}}\nolimits}
-\def\Range{\mathop{\hbox{\rm Range}}\nolimits}
-\def\Det  {\mathop{\hbox{\rm det}}}
-\def\Re   {\mathop{\hbox{\rm Re}}}
-\def\Im   {\mathop{\hbox{\rm Im}}}
-\def\Deg  {\mathop{\hbox{\rm deg}}}
-
-% misc.
-
-\def\Kr{\hbox{\bf  K}}
-\def\K {     {      K}}
-\def\sT{\hbox{$\cal T$}}
-\def\sB{\hbox{$\cal B$}}
-
-\def\bmatrix#1{\left[ \matrix{#1} \right]}
-
-% Each of the following commands have to be filled in with
-% something. If the data is unknown, the arguments can be
-% left blank.
-
-\topmatter
-\journal{SIAM J. E{\smc XAMPLE} F{\smc ILES}}
-\vol{1}
-\no{1, pp.~000--000}
-\date{October 1994}
-\copyyear{1994}
-\code{000}
-
-
-\title SAMPLE FILE FOR SIAM PLAIN \TeX\ MACRO
-PACKAGE\endtitle 
-
-\shorttitle{SIAM MACRO EXAMPLE}
-
-\recdate{*}{October 1, 1994; accepted by the editors Month, x,
-xxxx. This work was supported by the Society for Industrial
-and Applied Mathematics, Philadelphia, Pennsylvania}
-
-\author Paul Duggan\fnmark{$^{\dag}$} \and Various A.~U.
-Thors\fnmark{$^{\ddag}$}\endauthor
-
-\address{$^{\dag}$}{Composition Department, Society for
-Industrial and Applied Mathematics, 3600 University City
-Science Center, Philadelphia, Pennsylvania, 19104-2688
-({\tt duggan@siam.org})}
-
-\address{$^{\ddag}$}{Various affiliations, supported by
-various foundation grants}
-
-\abstract{An example of SIAM \TeX\ macros is presented.
-Various aspects of composing manuscripts for SIAM's journals
-are illustrated with actual examples from accepted
-manuscripts. SIAM's stylistic standards are adhered to
-throughout, and illustrated.}
-
-\keywords polynomials, SI model\endkeywords
-
-\subjclass 33H40, 35C01\endsubjclass
-
-% if there is only one AMS subject number, the
-% command \oneclass should precede the \subjclass command.
-
-\endtopmatter
-
-\heading{1}{Introduction and examples}
-This paper presents a sample file for the use of SIAM's
-\TeX\ macro package. It illustrates the features of the
-macro package, using actual examples culled from various
-papers published in SIAM's journals. This sample will provide 
-examples of how to use the
-macros to generate standard elements of journal papers,
-e.g., equations, theorems, or figures. This paper also
-serves as an exmple of SIAM's stylistic preferences for the
-formatting of such elements as bibliographic references,
-displayed equations, and aligned equations, among others.
-Some special circumstances are not dealt with this the
-sample file; for that information, please see the
-associated documentation file.
-
-{\it Note}. This paper is not to be read in any form for
-content. The conglomeration of equations, lemmas, and other
-text elements were put together solely for typographic
-illustrative purposes.
-
-For theoretical reasons, it is desirable to find characterizations of the
-conditions of breakdown of the algorithms that are based on the key {\it
-spaces} $\Kr_n(r^{(0)},A)$ and $\Kr_n(\tilde r^{(0)},A^*)$ rather than
-the {\it formulas} for the algorithms.  In particular, we will
-characterize breakdown of the three Lanczos algorithms in terms of the
-{\it moment matrices} $\K_n(\tilde r^{(0)},A^*)^*\K_n(r^{(0)},A)$ and
-$\K_n(\tilde r^{(0)},A^*)^*A\K_n(r^{(0)},A)$.  Here we define the matrix
-$\K_n(v,A)=\bmatrix{v&Av&\cdots&A^{n-1}v\cr}$, a matrix whose columns span
-the Krylov space $\Kr_n(v,A)$.
-
-The following three theorems give exact conditions for breakdown of the
-above algorithms.  Detailed proofs may be found in [3].  A
-result similar to Theorem 2 is found in [1]; see also [5].
-
-
-\thm{Theorem 1 {\rm (Lanczos--Orthodir breakdown)}}
-Suppose Lanczos/Orthodir has successfully generated
-$u^{(n-1)}\not=u$.  Then the following are equivalent:
-
-\meti{$\bullet$} The algorithm does not break down at step $n$.
-
-\meti{$\bullet$} The matrix $\K_n(\tilde r^{(0)},A^*)^*A\K_n(r^{(0)},A)$
-is nonsingular.
-
-\meti{$\bullet$} There exists a unique iterate $u^{(n)}$ satisfying $(2)$.
-\endthm
-
-
-\thm{Theorem 2 {\rm (Lanczos--Orthomin breakdown)}}
-Suppose Lanczos/Orthomin has successfully generated $u^{(n-1)}\not=u$.
-Then the following are equivalent:
-
-\meti{$\bullet$} The algorithm breaks down at step $n$.
-
-\meti{$\bullet$} Either
-$\K_{n-1}(\tilde r^{(0)},A^*)^*\K_{n-1}(r^{(0)},A)$ or
-$\K_n(\tilde r^{(0)},A^*)^*A\K_n(r^{(0)},A)$ is singular.
-\endthm
-
-
-\prop{Proposition 3 {\rm (zero sets of polynomials)}}
-Let $\fK=\fR$ or $\fC$.  If $P$ is a complex nonzero polynomial in the
-variables $x_1,x_2,\ldots ,x_N\in\fK$, then $P(x)\not=0$ for almost every
-$x=(x_1,x_2,\ldots,x_N)\in \fK^N$.
-\endprop
-
-\prf{Proof}
-If $\fK=\fR$ and $P$ is nonzero, then either $\Re P(z)$ or $\Im P(z)$
-is a nonzero (real) polynomial; if $\fK=\fC$, we may decompose each $x_i$
-into real and imaginary parts, giving $2N$ variables, and consider the
-real polynomial $P(x)^*P(x)$.  In any case, we may assume without loss of
-generality that $P$ is a nonzero real polynomial of real variables.
-
-We know that for any point $x$, the polynomial $P$ is the zero polynomial
-if and only if the polynomial and all its derivatives are zero at $x$.
-Let $V_0$ denote the set of zeros of $P$ in $\fR^N$.  Suppose the set
-$V_0$ has nonzero measure.  We know from integration theory (see, for
-example, [6, pp.\ 128f]) that almost every point of $V_0$ is
-a point of density in each of the $N$ coordinate directions.  We recall
-that $x\in\fR$ is a point of density of a measurable subset
-$S\subseteq\fR$ if for any sequence of intervals $I_n$ such that
-$x\in I_n$ with measure $m(I_n)\rightarrow 0$ we have
-$m(S\cap I_n)/m(I_n)\rightarrow 1$.
-
-It is easily seen that at such points in $V_0$, the first
-partial derivatives of $P$ must necessarily be zero.  Let $V_1$ be the
-points of $V_0$ where all first derivatives are also zero.  We have just
-shown that $V_0$ and $V_1$ both have the same nonzero measure.  The
-argument
-may be repeated for $V_1$ to show all second partial derivatives of $f$
-are zero at almost every point of $V_0$, and so forth, resulting in the
-fact that $P$ and all its derivatives are zero on a set which has nonzero
-measure.  The proof is completed by selecting any one of these points.
-\qquad\endproof
-
-\thm{Theorem 4 {\rm (Lanczos breakdown, iterate $n$)}}
-Let $\fK=\fR$ or $\fC$, $A, \tilde Z\in\fK^{N\times N}$, and $n\leq d(A)$.
-Then exactly one of the following three conditions holds for the Lanczos
-method with $\tilde r^{(0)}=\tilde Z^* r^{(0)}$.
-
-\meti{\rm (i)} Hard breakdown at step $n$ occurs for every vector
-$r^{(0)}\in\sT_n(A)\cap\fK^N$ $($and thus at least for almost every
-$r^{(0)}\in\fK^N)$.
-
-\meti{\rm (ii)} Hard breakdown at step $n$ occurs for a nonempty measure-zero
-set of vectors $r^{(0)}\in\sT_n(A)\cap\fK^N$
-$($and thus a nonempty measure-zero set of vectors in $\fK^N)$.
-
-\meti{\rm (iii)} Hard breakdown at step $n$ occurs for no vectors
-$r^{(0)}\in\sT_n(A)\cap\fK^N$ $($and thus for at most a measure-zero set of
-vectors in $\fK^N)$.
-
-Furthermore, the same result holds if ``hard breakdown'' is replaced by
-``soft breakdown'' in the statement of this theorem.
-\endthm
-
-
-\prf{Proof}
-For vectors $r^{(0)}\in\sT_n(A)\cap\fK^N$, breakdown is equivalent to
-singularity of an appropriate moment matrix.  The set $\sT_n(A)\cap\fK^N$
-amounts to almost
-every vector in $\fK^N$.  Now, by Corollary 5, the set $S_n$ of vectors in
-$\fK^N$ for which the moment matrix of dimension $n$ is singular is either
-the set of all vectors or a subset of measure zero.  If the moment matrix
-is singular for every vector (i.e., $S_n=\fK^N$), then it is singular for
-every vector in $\sT_n(A)\cap\fK^N$, giving case (i) above.  Otherwise the
-set $S_n$ is measure zero in $\fK^N$.  Thus
-$\sB_n\equiv S_n\cap(\sT_n(A)\cap\fK^N)$ is of measure zero
-and is either empty or nonempty.
-\qquad\endproof
-
-\heading{2}{Tables and figures}
-In Tables 1 and 2 we consider the unpreconditioned problem and also the (left) 
-ILU- and MILU-preconditioned problem (see [2] and [4]).  Runs for which 
-convergence was not possible in ITMAX iterations are labeled by (--).
-
-
-\topinsert
-\hbox{\vbox{ \eightpoint
-{\parindent 0pt
-\centerline{\smc Table 1}
-\centerline{\it Model problem, $h^{-1}=128$, {\rm ITMAX=3000}.
-            Number of iterations.}\vskip 6pt
-\hfil\vbox{\offinterlineskip
-\hrule
-\halign{&\vrule#&\strut\ \hfil#\ \cr
-height2pt&\omit&&\omit&&\omit&&\omit&&\omit
- &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr
-&{\rm method $\backslash$ Dh: } &
-                   &0&&2${}^{-3}$&&2${}^{-2}$&&2${}^{-1}$&&2${}^{0}$&
-           &2${}^{1}$&&2${}^{ 2}$&&2${}^{ 3}$&&2${}^{ 4}$&&2${}^{5}$&\cr
-height2pt&\omit&&\omit&&\omit&&\omit&&\omit
- &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr
-\noalign{\hrule}
-height2pt&\omit&&\omit&&\omit&&\omit&&\omit
- &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr
-&{GMRES}($\infty$) \hfill &
-& 290&& 269&& 245&& 220&& 200&& 189&& 186&& 189&& 207&& 249&\cr
-&{BCG} \hfill &
-& 308&& 341&& 299&&1518&& -- && -- && -- && -- && 533&& -- &\cr
-&{BCG}{\rm, random $u^{(0)}$} \hfill &
-& 309&& 354&& 300&& 310&& 313&& 301&& 299&& 302&& 290&& 293&\cr
-&{BCGNB} \hfill &
-& 308&& 353&& 284&& 338&& 253&& 240&& 243&& 240&& 302&& 962&\cr
-&{CGS} \hfill &
-& 272&& 254&& 222&& -- && -- && -- && -- && -- && -- && -- &\cr
-&{CGS}{\rm, random $u^{(0)}$} \hfill &
-& 193&& 189&& 200&& 192&& 193&& 175&& 225&& 212&& 216&& 197&\cr
-&{CGSNB} \hfill &
-& 272&& 284&& 212&& 196&& 151&& 162&& 158&& 173&& 156&& 256&\cr
-height1pt&\omit&&\omit&&\omit&&\omit&&\omit
- &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr
-} \hrule}\hfil}}}
-\endinsert
-
-
-\topinsert
-
-\hbox{\vbox{ \eightpoint
-{\parindent 0pt
-\centerline{\smc Table 2}
-
-\centerline{\it Model Problem, $h^{-1}=128$,} 
-\centerline{\it {\rm MILU}-preconditioning, {\rm ITMAX=500.} 
-Number of iterations.}
-
-\medskip
-
-\hfil\vbox{\offinterlineskip
-\hrule
-\halign{&\vrule#&\strut\ \hfil#\ \cr
-height2pt&\omit&&\omit&&\omit&&\omit&&\omit
- &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr
-&{\rm Method $\backslash$ Dh: } &
-                   &0&&2${}^{-3}$&&2${}^{-2}$&&2${}^{-1}$&&2${}^{0}$&
-           &2${}^{1}$&&2${}^{ 2}$&&2${}^{ 3}$&&2${}^{ 4}$&&2${}^{5}$&\cr
-height2pt&\omit&&\omit&&\omit&&\omit&&\omit
- &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr
-\noalign{\hrule}
-height2pt&\omit&&\omit&&\omit&&\omit&&\omit
- &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr
-&{\rm {GMRES}($\infty$)} \hfill &
-&  27&&  25&&  24&&  26&&  28&&  28&&  25&&  19&&  14&&  10&\cr
-&{\rm {GMRES}($\infty$), random $u^{(0)}$} \hfill &
-&  33&&  29&&  28&&  29&&  31&&  31&&  29&&  24&&  19&&  14&\cr
-&{\rm {BCG}} \hfill &
-&  31&&  27&&  29&&  33&&  30&&  37&&  30&&  23&&  15&&  10&\cr
-% &{BCG}, random $u^{(0)}$, $\gamma=.1$ \hfill &
-% &  35&&  30&&  31&&  35&&  40&&  37&&  34&&  27&&  20&&  15&\cr
-&{\rm {BCG}, random $u^{(0)}$} \hfill &
-&  38&&  34&&  33&&  37&&  44&&  40&&  38&&  29&&  23&&  18&\cr
-&{\rm {BCGNB}} \hfill &
-&  28&&  27&&  29&&  30&&  34&&  35&&  30&&  23&&  15&&  10&\cr
-&{\rm {CGS}} \hfill &
-&  21&&  18&&  17&&  20&&  22&&  22&&  19&&  15&&   9&&   6&\cr
-&{\rm {CGS}, random $u^{(0)}$} \hfill &
-&  24&&  18&&  20&&  22&&  22&&  23&&  21&&  16&&  12&&   9&\cr
-&{\rm {CGSNB}} \hfill &
-&  21&&  18&&  17&&  20&&  22&&  27&&  20&&  15&&   9&&   6&\cr
-height1pt&\omit&&\omit&&\omit&&\omit&&\omit
- &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr
-} \hrule}\hfil}}}
-\endinsert
-
-We make the following observations about these runs.
-
-\meti{$\bullet$} For the unpreconditioned problem, the standard
-{BCG} and {CGS} algorithms break down in a number of cases, but the use 
-of random $u^{(0)}$ or the use of {BCGNB} or {CGSNB}
-resulted in convergence.  Furthermore, the iteration counts for the
-algorithms {BCG} and {BCGNB} are in
-general comparatively close to those of the ``best'' method,
-{GMRES}($\infty$), while these algorithms have short economical
-recurrences, unlike {GMRES}($\infty$).  This underscores the 
-importance of the Lanczos algorithms as economical solution techniques.
-
-\meti{$\bullet$} For the ILU-preconditioned problems, in most cases
-all methods worked well.  For the case of $Dh=1$, {BCG} gave
-an excessive number of iterations, but this was remedied significantly
-by {BCGNB} and much more so
-by the use of random $u^{(0)}$.  Similarly, {CGS} could
-not converge, but {CGSNB} and {CGS} with random
-$u^{(0)}$ both converged.
-
-\meti{$\bullet$} For all of the MILU-preconditioned problems, all of
-the Lanczos-type algorithms performed quite well.  In particular, the
-{BCG} algorithm gave approximately the same number of
-iterations as {GMRES}($\infty$).
-
-Figures 1 and 2 give representative plots of the convergence behavior of the
-algorithms for the case of $h^{-1}=128$, $Dh=4$, and no preconditioning.
-These results show that the new algorithms keep the residual size 
-better behaved than the standard {BCG} and {CGS}
-algorithms over the course of the run.
-
-\topinsert
-\vskip 3.2in
-\centerline{\eightpoint\smc Fig.~1. \it Residual 
-behavior: $h^{-1}=128$, $Dh=4$.}
-\endinsert
-
-
-\topinsert
- \vskip 3.2in
-\centerline{\eightpoint\smc Fig.~2. \it  Residual 
-behavior: $h^{-1}=128$, $Dh=4$.}
-\endinsert
-
-We now consider a more difficult class of finite difference problems,
-namely, central finite differencing applied to the Dirichlet problem
-$$ -u_{xx}(x,y) - u_{yy}(x,y) +
-   D[(y-\textstyle{1\over 2}\displaystyle) u_x(x,y) +
-     (x-\textstyle{1\over 3}\displaystyle)
-     (x-\textstyle{2\over 3}\displaystyle) u_y(x,y)], $$ 
-$$ - 43\pi^2u(x,y) = G(x,y) \quad {\rm on}\ \Omega=[0,1]^2,$$
-$$u(x,y) = 1 + xy \quad \hbox{\rm on}\ \partial\Omega,$$
-with $G(x,y)$ chosen as before so that the true solution is $u(x,y)=1+xy$.
-Again, we let $h$ denote the mesh size in each direction.  For $D=0$
-and $h$ small, the matrix generated by this problem is a symmetric
-indefinite matrix with 16 distinct negative eigenvalues and the rest
-of the spectrum positive.
-
-The standard conjugate residual algorithm applied to this problem with
-$h^{-1}=128$ and $D=0$ requires 766 iterations to converge to
-$||r^{(n)}||/||b||<\zeta=10^{-6}$.  In any case, this is a difficult
-problem to solve.
-
-  \def\qed{\vrule height8pt width4pt depth0pt\par\medskip} 
-  \def\Zero{{\bf 0}} 
-  \def\dis{\displaystyle} 
-  \def\b{\beta} 
-  \def\r{\rho} 
-  \def\X{{\bf X}} 
-  \def\Y{{\bf Y}} 
-  \def\bb{{\bar \beta}} 
-   \def\tbcr{\theta\bb c_h \rho_h} 
-  \def\ep{\varepsilon} 
-
-
- 
-Figures 3(a) and 3(b) show the compartmental diagrams for SI models without 
-and with deaths due to the disease, for  the situation in which the infectious
-period has only one stage. Figures 4(a) and 4(b) give the corresponding models 
-with $m$ stages of infection. Venereal 
-warts, caused by the human papilloma virus, and ordinary herpes are examples 
-of sexually transmitted diseases without deaths 
-due to the disease, although both are not quite SI diseases because of 
-partial immunity. AIDS is the example of an SI disease with death due to 
-the disease. Although our main focus is on the latter, we present results 
-on SI models without deaths due to the 
-disease because the simplification in the dynamics of such models 
- throws light on the case with disease-related deaths. 
- 
-\topinsert
-\vskip 2in
-\centerline{\eightpoint {\smc Fig.} 3(a). SI {\it model for subgroup $i$, without death
-due to the disease.}}
-\vskip 2in
-\centerline{\eightpoint {\smc Fig.} 3(b). SI {\it model with death due to the disease.}} 
-\endinsert
-
-\topinsert
-\vskip 2in
-\centerline{\eightpoint {\smc Fig.} 4(a). SI {\it model without deaths due to the
-disease with $m$ stages of infection.}}
-\vskip 2in
-\centerline{\eightpoint {\smc Fig.} 4(b). SI {\it model with deaths due to the disease,
-with $m$ stages of infection.}} 
-\endinsert
-
-\heading{3}{Equations and alignments} 
-The equations for the system follow directly from the definitions and the 
-compartmental diagrams. For one infected stage with no disease-related 
-deaths, the equations are
-$$ \dot X_i=-X_ig_i-\mu X_i+U_i, \leqno(1)$$ 
-$$ \dot Y_i=X_ig_i-\mu Y_i. \leqno(2)$$ 
-If there are multiple stages to the infection, (2) is replaced by 
-(3)--(5) as follows:
-$$\leqalignno{\dot Y_{i1}&=X_ig_i-(k+\mu)Y_{i1}, &(3)\cr 
-\dot Y_{ir}&=kY_{i,r-1}-(k+\mu)Y_{ir},\qquad  r=2,\ldots,m-1 &(4)\cr 
-\dot Y_{im}&=kY_{i,m-1}-\mu Y_{im}. &(5)\cr }$$ 
- 
- 
-
-\heading{3.1}{The SI model with structured mixing}
-In this subsection we write the equations for the SI model with 
-structured mixing, with one infected stage and with deaths due to the 
-disease. The equations for multiple infected stages follow easily, as do 
-those for SI models without death due to the disease. Recall that $f_{is}$ 
-gives  the fraction of population subgroup $i$'s 
-contacts that are made in activity group $s$. The total contact rate of 
-susceptibles from population subgroup $i$ in activity group $s$ must be 
-$c_iX_if_{is}$. Let $\rho_{ij}(s)$ be the fraction of the contacts of group 
-$i$ that are with members of group $j$, within activity group $s$. 
-Assuming random allocation of the susceptibles and infecteds from each 
-population subgroup to the activity groups, the fraction infected in group 
-$j$ in activity group $s$ must be $Y_j/N_j$, giving 
-$$ c_iX_if_{is}\rho_{ij}(s)\beta_j{Y_j \over N_j}\leqno(6)  $$ 
-for the rate at which susceptibles in $i$ are infected by contacts 
-with infecteds from $j$ in activity group $s$. Thus, in this case, $g_i$ is 
-given by 
-$$ 
- g_i=c_i\sum_sf_{is}\sum_j\rho_{ij}(s)\beta_j{Y_j \over N_j}, 
-\leqno(7) 
- $$ 
-and (1a) and (1b) become
-$$  \dot X_i=-c_iX_i\sum_sf_{is}\sum_j\rho_{ij}(s)\beta_j{Y_j \over 
-N_j}-\mu X_i+U_i, \leqno(8)  $$ 
-$$  \dot Y_i=c_iX_i\sum_sf_{is}\sum_j\rho_{ij}(s)\beta_j{Y_j \over 
-N_j}-(\mu+k)Y_i. \leqno(9)  $$ 
- 
-\heading{3.2}{Structured mixing within  activity groups} 
-If the mixing within activity groups is proportional mixing, then 
-$\rho_{ij}(s)$ is given by (10): 
-$$\rho_{ij}(s)={f_{js}c_jN_j\over \sum_pf_{ps}c_pN_p}, \leqno(10)$$ 
-and (8) and (9) become (11) and (12): 
-$$\dot X_i=-c_iX_i\sum_sf_{is}{\sum_jf_{js}c_j\beta_jY_j \over 
-\sum_jf_{js}c_jN_j}-\mu X_i+U_i \leqno(11)$$ 
-$$\dot Y_i=c_iX_i\sum_sf_{is}{\sum_jf_{js}c_j\beta_jY_j \over 
-\sum_jf_{js}c_jN_j}-(k+\mu)Y_i. \leqno(12)$$ 
- 
-Expressions (11) and (12) show an important consequence of death due 
-to the disease. If there are no deaths due to the disease, $N_j$ is 
-constant on the asymptotically stable invariant subspace $U_j=\mu 
-N_j$ for all $j$, and the first term, the nonlinear term, in 
-(11) and (12) is a sum of {\it quadratic} terms. If there are deaths 
-due to the disease, $N_j$ is no longer constant and the first term is 
-a sum of rational expressions, each homogeneous of degree one. This 
-observation extends to SIS, SIR, and SIRS models. 
- 
- 
-
-\Refs
-
-
-\ref 1\\
-{\smc R. Fletcher}, {\it Conjugate gradient methods for indefinite
-systems}, in Numerical Analysis Dundee 1975, G.~A. Watson, ed.,
-Springer-Verlag, New York, Lecture Notes in Math. 506, 
-1976, pp. 73--89.
-\endref
-
-
-\ref 2\\
-{\smc I. Gustafsson}, {\it Stability and rate of convergence of
-modified incomplete Cholesky factorization methods}, Ph.D. thesis,
-Chalmers University of Technology and the University of Goteborg,
-Goteborg, Sweden, 1979.
-\endref
-
-
-\ref 3\\
-{\smc W.~D. Joubert}, {\it Generalized conjugate gradient and
-Lanczos methods for the solution of nonsymmetric systems of linear
-equations},  Ph.D. thesis and Report
-CNA-238, Center for Numerical Analysis, University of Texas, 
-Austin, TX, January 1990.
-\endref
-
-
-\ref 4\\
-{\smc J.~A. Meijerink and H.~A. van der Vorst}, {\it An iterative
-solution method for linear systems of which the coefficient matrix is
-a symmetric $M$-matrix}, Math. Comp., 31 (1977), pp.~148--162.
-\endref
-
-
-
-\ref 5\\
-{\smc Y.~Saad}, {\it The Lanczos biorthogonalization algorithm and
-other oblique projection methods for solving large unsymmetric systems},
-SIAM J. Numer. Anal., 19 (1982), pp. 485--506.
-\endref
-
-
-\ref 6\\
-{\smc S. Saks}, {\it The Theory of the Integral}, G.~E. Stechert, 
-New York, 1937.
-\endref
-
-\ref 7\\ 
-{\smc M. Tinkham}, {\it Introduction to
-Superconductivity}, McGraw-Hill, New York, 1975.
-\endref
-
-\bye
diff --git a/Master/texmf-dist/tex/plain/siam/siamptex.sty b/Master/texmf-dist/tex/plain/siam/siamptex.sty
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-        \global\headline={\hss\vtop to \z@ {%
-                \sixpoint\rm\noindent\thejournal \hfill%
-                \rm\copyright{\sevensy}\rm%
-                \ \thecopyyear\ Society for Industrial and Applied Mathematics\par
-                \noindent Vol. \thevol , No. \theno , \thedate\hfill\thecode\par
-        \vss}\hss}%                                   
-        \leavevmode\vskip8pt
-        \vbox{\noindent\raggedcenter\let\\=\break\titlefont\thetitle
-            \ifrecdate@*\fi}
-        \vskip6pt
-        \vbox{\noindent\raggedcenter\let\\=\break\authorfont\theauthor}
-        \ifdedicate@
-                \vskip6pt
-                \vbox{\noindent\raggedcenter\let\\=\break\dedicatefont
-                \thededicate}
-        \fi
-        \vskip14pt
-        {\eightpoint{\bf Abstract.\ }\theabstract\par
-        \ifkeywords@
-                \vskip10pt
-                {\bf Key words.} \thekeywords\par
-        \fi
-        \ifsubjclass@
-                \vskip10pt
-                {\bf AMS subject classification\ifoneclass@\else s\fi. }%
-                \thesubjclass\par
-        \fi}
-        \vskip8pt
-        \tenpoint}
-
-
-%%% THEOREM AND OTHER MACROS
-%%%
-\def\heading#1#2{%
-        \vskip6pt{\bf #1.\enspace\ignorespaces#2.\enspace}\ignorespaces}
-
-\def\thm#1{{\smc #1.}\begingroup\it\enspace\ignorespaces}
-\let\lem=\thm
-\let\cor=\thm
-\let\prop=\thm
-\let\dfn=\thm
-
-\def\endthm{\endgroup}
-\let\endlem=\endthm
-\let\endcor=\endthm
-\let\endprop=\endthm
-\let\enddfn=\endthm
-
-\def\prf#1{{\it #1}.\rm\enspace\ignorespaces}
-\let\rem=\prf
-\let\case=\prf
-
-\def\endproof{\vbox{\hrule height0.8pt\hbox{%
-   \vrule height1.3ex width0.8pt\hskip0.8ex
-   \vrule width0.8pt}\hrule height0.8pt
-  }}
-
-
-%%% FORMATTING AND MATH
-%%% 
-%%% NEW ROMAN MATH OPERATORS
-%%%
-\def\const{\mathop{\rm const}\nolimits}
-\def\diag{\mathop{\rm diag}\nolimits}
-\def\grad{\mathop{\rm grad}\nolimits}
-\def\Range{\mathop{\rm Range}\nolimits}
-\def\rank{\mathop{\rm rank}\nolimits}
-\def\supp{\mathop{\rm supp}\nolimits}
-
-%%% Centered displays, with numbering
-%%%
-
-\def\ldisplaylinesno#1{\displ@y\halign{
-  \hbox to\displaywidth{$\@lign\hfil\displaystyle##\hfil$}&
-    \kern-\displaywidth\rlap{$##$}\kern\displaywidth\crcr
-  #1\crcr}}
-
-%%% \meti to be used instead of \item
-%%%
-\def\meti#1{\parindent=2\parindent 
-\par\indent\llap{#1\enspace}\ignorespaces\parindent=.5\parindent}
-\def\metimeti#1{\parindent=2\parindent 
-\par\indent\llap{#1\enspace}\ignorespaces\parindent=.5\parindent}
-
-
-%%% Miscellaneous
-
-%%% REFERENCES
-
-\newdimen\refindent@
-\newdimen\refhangindent@
-\newbox\refbox@
-\setbox\refbox@=\hbox{\eightpoint\rm [00]}%   Default 2 digits
-\refindent@=\wd\refbox@
-
-\def\resetrefindent#1{%
-        \setbox\refbox@=\hbox{\eightpoint\rm [#1]}%
-        \refindent@=\wd\refbox@}
-
-\def\Refs{%
-        \unskip\vskip2pc
-        \centerline{\eightpoint\rm REFERENCES}%
-        \penalty10000
-        \vskip4pt
-        \penalty10000
-        \refhangindent@=\refindent@
-        \global\advance\refhangindent@ by 2em
-        \global\everypar{\hangindent\refhangindent@}%
-        \parindent=0pt\eightpoint\rm}
-
-\def\XRefs{%
-        \unskip\vskip2pc
-        \centerline{\eightpoint\rm REFERENCES}%
-        \penalty10000
-        \vskip4pt
-        \penalty10000
-        \refhangindent@=\refindent@
-        \global\everypar{\hangindent\refhangindent@}%
-        \parindent=0pt\eightpoint\rm}
-                                      
-\def\sameauthor{\leavevmode\vbox to 1ex{\vskip 0pt plus 100pt
-    \hbox to 3em{\leaders\hrule\hfil}\vskip 0pt plus 300pt}}
-    
-\def\ref#1\\#2\endref{\leavevmode\hbox to \refindent@{\hfil[#1]}\enspace #2\par}
-
-\def\xref\\#1\endref{\leavevmode #1\par}
-
-%%% OUTPUT
-
-\global\footline={\hss\eightpoint\rm\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={\hss\rightrh\hss{\tenpoint\rm\folio}}%
-  \else
-        \global\headline={\hskip-8pt{\tenpoint\rm\folio}\hss\leftrh\hss}%
-  \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-8\p@\line{\the\footline}}
-\def\dosupereject{\ifnum\insertpenalties>\z@ % something is being held over
-  \line{}\kern-\topskip\nobreak\vfill\supereject\fi}
-
-\def\relaxnext@{\let\next\relax}
-\def\footmarkform@#1{\ifmmode {}^{#1}\else$^{#1}$\fi }
-\let\thefootnotemark\footmarkform@
-\def\makefootnote@#1#2{\insert\footins
-        {\interlinepenalty\interfootnotelinepenalty
-        \eightpoint \splittopskip=\ht\strutbox
-      \splitmaxdepth=\dp\strutbox
-        \floatingpenalty=\@MM 
-   \leftskip=\z@ \rightskip=\z@
-        \spaceskip=\z@ \xspaceskip=\z@
-        \leavevmode{#1}\footstrut\ignorespaces#2\unskip
-        \lower\dp\strutbox\vbox to\dp\strutbox{}}}
-\newcount\footmarkcount@
- \footmarkcount@=\z@                    % Initialization
-\def\footnotemark{\let\@sf=\empty \relaxnext@
-        \ifhmode \edef\@sf{\spacefactor=\the\spacefactor}\/\fi
-        \def\next@{\ifx[\next \let\next=\nextii@ \else
-                \ifx"\next \let\next=\nextiii@ \else
-                        \let\next=\nextiv@ \fi\fi\next}%
-        \def\nextii@[##1]{\footmarkform@{##1}\@sf}%
-        \def\nextiii@"##1"{{##1}\@sf}%
-        \def\nextiv@{\global\advance\footmarkcount@\@ne
-                \footmarkform@{\number\footmarkcount@}\@sf}%
-        \futurelet\next\next@}
-\def\footnotetext{\relaxnext@
-        \def\next@{\ifx[\next \let\next=\nextii@ \else
-                \ifx"\next \let\next=\nextiii@ \else
-                        \let\next=\nextiv@ \fi\fi\next}%
-        \def\nextii@[##1]##2{\makefootnote@{\footmarkform@{##1}}{##2}}%
-        \def\nextiii@"##1"##2{\makefootnote@{##1}{##2}}% 
-        \def\nextiv@##1{\makefootnote@{\footmarkform@{%
-                        \number\footmarkcount@}}{##1}}%
-        \futurelet\next\next@}
-\def\footnote{\let\@sf=\empty \relaxnext@
-        \ifhmode \edef\@sf{\spacefactor\the\spacefactor}\/\fi
-        \def\next@{\ifx[\next \let\next=\nextii@ \else
-                \ifx"\next \let\next=\nextiii@ \else
-                        \let\next=\nextiv@ \fi\fi\next}%
-        \def\nextii@[##1]##2{\footnotemark[##1]\footnotetext[##1]{##2}}%
-        \def\nextiii@"##1"##2{\footnotemark"##1"\footnotetext"##1"{##2}}%
-        \def\nextiv@##1{\footnotemark\footnotetext{##1}}%
-        \futurelet\next\next@}
-\def\adjustfootnotemark#1{\advance\footmarkcount@#1\relax}
-
-\skip\footins=18\p@ plus6\p@ minus6\p@
-
-\def\footnoterule{\kern -4\p@\hrule width 3pc \kern 3.6\p@ } % rule = .4 pt high
-
-
-
-%       Turn off @ as being a letter.
-%
-\catcode`\@=12