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committerKarl Berry <karl@freefriends.org>2006-01-12 23:46:46 +0000
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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
new file mode 100644
index 00000000000..eb2c2f50101
--- /dev/null
+++ b/Master/texmf-dist/tex/plain/siam/pexample.tex
@@ -0,0 +1,523 @@
+% 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
new file mode 100644
index 00000000000..3ffce26af64
--- /dev/null
+++ b/Master/texmf-dist/tex/plain/siam/siamptex.sty
@@ -0,0 +1,373 @@
+% SIAMPTEX.STY; 12-11-92; Paul Duggan, Society for Industrial
+% and Applied Mathematics. From
+% Ralph Youngen's siamtex.sty
+% 9-14-94 ; Paul Duggan Revised.
+% This file may be freely distributed but may not be altered in
+% any way.
+%
+% This is a file of macros and definitions for creating an article
+% for publication in a SIAM journal.
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+%
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+
+\def\recdate#1#2{\global\recdate@true
+ \gdef\recdate@{#1Received by the editors \ignorespaces#2\unskip.}%
+ \makefootnote@{}{\recdate@}}
+
+\let\topmatter=\relax
+\def\endtopmatter{%
+ \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