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authorKarl Berry <karl@freefriends.org>2011-01-03 23:45:17 +0000
committerKarl Berry <karl@freefriends.org>2011-01-03 23:45:17 +0000
commitb90e3db7f33fec4598e155d820951f823a0721a1 (patch)
tree752938cb8f906748b1b7647d4a1d653ac86f4a44
parentd003fbe90a482efcf1e038687b21935f059cb898 (diff)
new latex package aomart 1.1 (2jan11)
git-svn-id: svn://tug.org/texlive/trunk@20919 c570f23f-e606-0410-a88d-b1316a301751
-rw-r--r--Master/texmf-dist/bibtex/bst/aomart/aomalpha.bst1460
-rw-r--r--Master/texmf-dist/bibtex/bst/aomart/aomplain.bst1315
-rw-r--r--Master/texmf-dist/doc/latex/aomart/Makefile65
-rw-r--r--Master/texmf-dist/doc/latex/aomart/README7
-rw-r--r--Master/texmf-dist/doc/latex/aomart/aomart.bib123
-rw-r--r--Master/texmf-dist/doc/latex/aomart/aomart.pdfbin0 -> 279994 bytes
-rw-r--r--Master/texmf-dist/doc/latex/aomart/aomsample.bib241
-rw-r--r--Master/texmf-dist/doc/latex/aomart/aomsample.pdfbin0 -> 383625 bytes
-rw-r--r--Master/texmf-dist/doc/latex/aomart/aomsample.tex1729
-rw-r--r--Master/texmf-dist/doc/latex/aomart/aomsample1.pdfbin0 -> 383639 bytes
-rw-r--r--Master/texmf-dist/doc/latex/aomart/aomsample1.tex1722
-rw-r--r--Master/texmf-dist/doc/latex/aomart/fullref.pl62
-rw-r--r--Master/texmf-dist/source/latex/aomart/aomart.dtx1732
-rw-r--r--Master/texmf-dist/source/latex/aomart/aomart.ins29
-rw-r--r--Master/texmf-dist/tex/latex/aomart/aomart.cls407
-rwxr-xr-xMaster/tlpkg/bin/tlpkg-ctan-check2
-rw-r--r--Master/tlpkg/tlpsrc/aomart.tlpsrc0
-rw-r--r--Master/tlpkg/tlpsrc/collection-publishers.tlpsrc1
18 files changed, 8894 insertions, 1 deletions
diff --git a/Master/texmf-dist/bibtex/bst/aomart/aomalpha.bst b/Master/texmf-dist/bibtex/bst/aomart/aomalpha.bst
new file mode 100644
index 00000000000..03022a2940b
--- /dev/null
+++ b/Master/texmf-dist/bibtex/bst/aomart/aomalpha.bst
@@ -0,0 +1,1460 @@
+%%%
+%%% This is aomplain.bst file, based on amsplain.bst by AMS
+%%% to support Annals of Mathematics specific fields.
+%%%
+% Copyright 2010, The Annals of Mathematics.
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either
+% version 1.3 of this license or (at your option) any
+% later version.
+% The latest version of the license is in
+% http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of
+% LaTeX version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Boris Veytsman,
+% <borisv@lk.net>
+%
+% This work consists of the file aomart.dtx the
+% derived file aomart.cls, and the file aomplain.bst
+%
+% Version 0.10, 2010/12/18
+%
+%%%
+
+% See the file btxbst.doc for extra documentation other than
+% what is included here. And see btxhak.tex for a description
+% of the BibTeX language and how to use it.
+
+% This defines the types of fields that can occur in a database entry
+% for this particular bibliography style. Except for `language',
+% this is the standard list from alpha.bst.
+
+%% Types of entries currently allowed in a BibTeX file:
+%%
+%% ARTICLE -- An article from a journal or magazine.
+%%
+%% BOOK -- A book with an explicit publisher.
+%%
+%% BOOKLET -- A work that is printed and bound,
+%% but without a named publisher or sponsoring institution.
+%%
+%% CONFERENCE -- The same as INPROCEEDINGS,
+%% included for Scribe compatibility.
+%%
+%% INBOOK -- A part of a book,
+%% which may be a chapter (or section or whatever) and/or a range of pages.
+%%
+%% INCOLLECTION -- A part of a book having its own title.
+%%
+%% INPROCEEDINGS -- An article in a conference proceedings.
+%%
+%% MANUAL -- Technical documentation.
+%%
+%% MASTERSTHESIS -- A Master's thesis.
+%%
+%% MISC -- Use this type when nothing else fits.
+%%
+%% PHDTHESIS -- A PhD thesis.
+%%
+%% PROCEEDINGS -- The proceedings of a conference.
+%%
+%% TECHREPORT -- A report published by a school or other institution,
+%% usually numbered within a series.
+%%
+%% UNPUBLISHED -- A document having an author and title, but not formally
+%% published.
+
+ENTRY
+ {
+ address
+ arxiv
+ author
+ booktitle
+ chapter
+ doi
+ edition
+ editor
+ howpublished
+ institution
+ jfmnumber
+ journal
+ key
+ language
+ month
+ mrnumber
+ note
+ number
+ organization
+ pages
+ publisher
+ school
+ series
+ title
+ type
+ venue
+ volume
+ year
+ zblnumber
+ }
+ {}
+ { label extra.label sort.label bysame }
+
+% Removed after.sentence, after.block---not needed.
+
+INTEGERS { output.state before.all mid.sentence }
+
+FUNCTION {init.state.consts}
+{ #0 'before.all :=
+ #1 'mid.sentence :=
+}
+
+% Scratch variables:
+
+STRINGS { s t }
+
+% Utility functions
+
+FUNCTION {shows}
+{ duplicate$ ":::: `" swap$ * "'" * top$
+}
+
+FUNCTION {showstack}
+{"STACK====================================================================="
+top$
+stack$
+"ENDSTACK=================================================================="
+top$
+}
+
+FUNCTION {not}
+{ { #0 }
+ { #1 }
+ if$
+}
+
+FUNCTION {and}
+{ 'skip$
+ { pop$ #0 }
+ if$
+}
+
+FUNCTION {or}
+{ { pop$ #1 }
+ 'skip$
+ if$
+}
+
+FUNCTION {field.or.null}
+{ duplicate$ empty$
+ { pop$ "" }
+ 'skip$
+ if$
+}
+
+FUNCTION {emphasize}
+{ duplicate$ empty$
+ { pop$ "" }
+ { "\emph{" swap$ * "}" * }
+ if$
+}
+
+% n.dashify is used to make sure page ranges get the TeX code
+% (two hyphens) for en-dashes.
+
+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$
+}
+
+% tie.or.space.connect connects two items with a ~ if the
+% second item is less than 3 letters long, otherwise it just puts an
+% ordinary space.
+
+FUNCTION {tie.or.space.connect}
+{ duplicate$ text.length$ #3 <
+ { "~" }
+ { " " }
+ if$
+ swap$ * *
+}
+
+FUNCTION {add.space.if.necessary}
+{ duplicate$ "" =
+ 'skip$
+ { " " * }
+ if$
+}
+
+% either.or.check gives a warning if two mutually exclusive fields
+% were used in the database.
+
+FUNCTION {either.or.check}
+{ empty$
+ 'pop$
+ { "can't use both " swap$ * " fields in " * cite$ * warning$ }
+ if$
+}
+
+% output.nonnull is called by output.
+
+FUNCTION {output.nonnull}
+% remove the top item from the stack because it's in the way.
+{ 's :=
+ output.state mid.sentence =
+% If we're in mid-sentence, add a comma to the new top item and write it
+ { ", " * write$ }
+% Otherwise, if we're at the beginning of a bibitem,
+ { output.state before.all =
+% just write out the top item from the stack;
+ 'write$
+% and the last alternative is that we're at the end of the current
+% bibitem, so we add a period to the top stack item and write it out.
+ { add.period$ " " * write$ }
+ if$
+ mid.sentence 'output.state :=
+ }
+ if$
+% Put the top item back on the stack that we removed earlier.
+ s
+}
+
+% Output checks to see if the stack top is empty; if not, it
+% calls output.nonnull to write it out.
+
+FUNCTION {output}
+{ duplicate$ empty$
+ 'pop$
+ 'output.nonnull
+ if$
+}
+
+% Standard warning message for a missing or empty field. For the user
+% we call any such field `missing' without respect to the distinction
+% made by BibTeX between missing and empty.
+
+FUNCTION {missing.warning}
+{ "missing " swap$ * " in " * cite$ * warning$ }
+
+% Output.check is like output except that it gives a warning on-screen
+% if the given field in the database entry is empty. t is the field
+% name.
+
+FUNCTION {output.check}
+{ 't :=
+ duplicate$ empty$
+ { pop$ t missing.warning }
+ 'output.nonnull
+ if$
+}
+
+FUNCTION {output.bibitem}
+{ newline$
+ "\bibitem[" write$
+ label write$
+ "]{" write$
+ cite$ write$
+ "}" write$
+ newline$
+% This empty string is the first thing that will be written
+% the next time write$ is called. Done this way because each
+% item is saved on the stack until we find out what punctuation
+% should be added after it. Therefore we need an empty first item.
+ ""
+ before.all 'output.state :=
+}
+
+FUNCTION {output.nonempty.mrnumber}
+{ duplicate$ missing$
+ { pop$ "" }
+ 'skip$
+ if$
+ duplicate$ empty$
+ 'pop$
+ { " \mr{" swap$ * "}. " * write$ }
+ if$
+}
+
+FUNCTION {output.nonempty.zblnumber}
+{ duplicate$ missing$
+ { pop$ "" }
+ 'skip$
+ if$
+ duplicate$ empty$
+ 'pop$
+ { " \zbl{" swap$ * "}. " * write$ }
+ if$
+}
+
+
+FUNCTION {output.nonempty.jfmnumber}
+{ duplicate$ missing$
+ { pop$ "" }
+ 'skip$
+ if$
+ duplicate$ empty$
+ 'pop$
+ { " \jfm{" swap$ * "}. " * write$ }
+ if$
+}
+
+
+FUNCTION {output.nonempty.arxiv}
+{ duplicate$ missing$
+ { pop$ "" }
+ 'skip$
+ if$
+ duplicate$ empty$
+ 'pop$
+ { " \arxiv{" swap$ * "}. " * write$ }
+ if$
+}
+
+FUNCTION {output.nonempty.doi}
+{ duplicate$ missing$
+ { pop$ "" }
+ 'skip$
+ if$
+ duplicate$ empty$
+ 'pop$
+ { " \doi{" swap$ * "}. " * write$ }
+ if$
+}
+
+
+FUNCTION {fin.entry}
+{ add.period$
+ write$
+ mrnumber output.nonempty.mrnumber
+ zblnumber output.nonempty.zblnumber
+ jfmnumber output.nonempty.jfmnumber
+ arxiv output.nonempty.arxiv
+ doi output.nonempty.doi
+ newline$
+}
+
+% Removed new.block, new.block.checka, new.block.checkb, new.sentence,
+% new.sentence.checka, and new.sentence.checkb functions here, since they
+% don't seem to be needed in the AMS style. Also moved some real
+% basic functions like `and' and 'or' earlier in the file.
+
+INTEGERS { nameptr namesleft numnames }
+
+% The extra section to write out a language field was added
+% for AMSPLAIN.BST. Not present in plain.bst.
+
+FUNCTION {format.language}
+{ language empty$
+ { "" }
+ { " (" language * ")" * }
+ if$
+}
+
+% This version of format.names puts names in the format
+%
+% F. von Last, Jr.
+%
+% (i.e., first name first, abbreviating initials).
+
+FUNCTION {format.names}
+{ 's :=
+ #1 'nameptr :=
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { s nameptr "\bgroup\scshape{{}}{f.~}{vv~}{ll}{, jj}\egroup{{}}" 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$
+}
+
+FUNCTION {format.authors}
+{ author empty$
+ { "" }
+ { bysame "\bysame" =
+ { bysame }
+ { author format.names }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.editors}
+{ editor empty$
+ { "" }
+ { editor format.names
+ editor num.names$ #1 >
+ { " (eds.)" * }
+ { " (ed.)" * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.nonauthor.editors}
+{ editor empty$
+ { "" }
+ { editor format.names
+ editor num.names$ #1 >
+ { ", eds." * }
+ { ", ed." * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.title}
+{ title empty$
+ { "" }
+ { title "t" change.case$ }
+ if$
+}
+
+FUNCTION {format.booktitle}
+{ title empty$
+ { "" }
+ { title emphasize }
+ if$
+}
+
+
+FUNCTION {format.journal.vol.year}
+{ journal empty$
+ { "journal name" missing.warning ""}
+ { " \emph{" journal * "}" * }
+ if$
+ volume empty$
+ 'skip$
+ { " \textbf{" * volume * "}" * }
+ if$
+ year empty$
+ { "year" missing.warning }
+ { " (" * year * ")" * }
+ if$
+}
+
+% For formatting the issue number for a journal article.
+
+FUNCTION {format.number}
+{ number empty$
+ { "" }
+ { "no.~" number * }
+ if$
+}
+
+% For formatting miscellaneous dates
+
+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$
+}
+
+%% The volume, series and number information is sort of tricky.
+%% This code handles it as follows:
+%% If the series is present, and the volume, but not the number,
+%% then we do "\emph{Book title}, \emph{Series Name} \bf{000}"
+%% If the series is present, and the number, but not the volume,
+%% then we do "\emph{Book title}, \emph{Series Name} no. 000"
+%% If the series is present, and both number and volume,
+%% then we do "\emph{Book title}, \bf{XX} \emph{Series Name} no. 000"
+%% Finally, if the series is absent,
+%% then we do "\emph{Book title}, \bf{XX}"
+%% or "\emph{Book title}, no. 000"
+%% and if both volume and number are present, give a warning message.
+
+FUNCTION {format.bookvolume.series.number}
+{ volume empty$
+ { "" % Push the empty string as a placeholder in case everything else
+ % is empty too.
+ series empty$
+ 'skip$
+ { pop$ "\emph{" series * "}" * } % if series is not empty put in stack
+ if$
+ number empty$
+ 'skip$
+ { duplicate$ empty$ % if no preceding material,
+ 'skip$ % do nothing, otherwise
+ { " " * } % add a space to separate.
+ if$
+ "no." number tie.or.space.connect * % add the number information
+ }
+ if$
+ }
+%% If the volume is NOT EMPTY:
+ { "\textbf{" volume * "}" *
+ number empty$
+ { series empty$
+ 'skip$
+ { "\emph{" series * "}" * " " * swap$ *} % Series Name, vol. XX
+ if$
+ }
+ { series empty$
+ { "can't use both volume and number if series info is missing"
+ warning$
+ "in BibTeX entry type `" type$ * "'" * top$
+ }
+ { " " * series * " no." * number tie.or.space.connect }
+ if$
+ }
+ if$
+ }
+ if$
+
+} % end of format.bookvolume.series.number
+
+
+%% format.inproc.title.where.editors is used by inproceedings entry types
+
+%% No case changing or emphasizing for the title. We want initial
+%% caps, roman.
+%% We add parentheses around the venue (place where conference
+%% was held).
+%% Likewise we add parentheses around the editors' names.
+
+FUNCTION {format.inproc.title.venue.editors}
+{ booktitle empty$
+ { "" }
+ { " in \emph{" booktitle * "}" *
+ venue empty$
+ 'skip$
+ { add.space.if.necessary "(" * venue * ")" * }
+ if$
+ editor empty$
+ 'skip$
+ { add.space.if.necessary "(" * format.nonauthor.editors * ")" * }
+ if$
+ }
+ if$
+}
+
+%% format.incoll.title.editors is similar to format.inproc... but
+%% omits the address. For collections that are not proceedings volumes.
+
+FUNCTION {format.incoll.title.editors}
+{ booktitle empty$
+ { "" }
+ { editor empty$
+ { " in \emph{" booktitle * "}" * }
+ { " in \emph{" booktitle * "}" *
+ add.space.if.necessary "(" * format.nonauthor.editors * ")" *
+ }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.edition}
+{ edition empty$
+ { "" }
+ { output.state mid.sentence =
+ { edition "l" change.case$ " ed." * }
+ { edition "t" change.case$ " ed." * }
+ if$
+ }
+ 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 n.dashify }
+ if$
+}
+
+FUNCTION {format.book.pages}
+{ pages empty$
+ { "" }
+ { pages multi.page.check
+ { "pp.~" pages n.dashify * }
+ { "p.~" pages * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.chapter.pages}
+{ chapter empty$
+ 'format.book.pages
+ { type empty$
+ { "ch.~" }
+ { type "l" change.case$ " " * }
+ if$
+ chapter *
+ pages empty$
+ 'skip$
+ { ", " * format.book.pages * }
+ 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 "t" change.case$
+ }
+ if$
+}
+
+FUNCTION {format.tr.number}
+{ type empty$
+ { "Tech. Report" }
+ 'type
+ if$
+ number empty$
+ { "t" change.case$ }
+ { number tie.or.space.connect }
+ if$
+}
+
+% The format.crossref functions haven't been paid much attention
+% at the present time (June 1990) and could probably use some
+% work. MJD
+
+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 tie.or.space.connect
+ " 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 \emph{" booktitle * "}" * }
+ if$
+ }
+ { "in " key * }
+ if$
+ }
+ { "in " format.crossref.editor * }
+ if$
+ " \cite{" * crossref * "}" *
+}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% The main functions for each entry type.
+
+% journal, vol and year are formatted together because they are
+% not separated by commas.
+
+FUNCTION {article}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ crossref missing$
+ { format.journal.vol.year "journal, volume, and year" output.check
+ format.pages "pages" output.check
+ }
+ { format.article.crossref output.nonnull
+ format.pages "pages" output.check
+ }
+ if$
+ format.language *
+ 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.booktitle "title" output.check
+ format.edition output
+ crossref missing$
+ { format.bookvolume.series.number output
+ publisher "publisher" output.check
+ address output
+ }
+ { format.book.crossref output.nonnull
+ }
+ if$
+ format.date "year" output.check
+ format.language *
+ note output
+ fin.entry
+}
+
+FUNCTION {booklet}
+{ output.bibitem
+ format.authors output
+ format.booktitle "title" output.check
+ howpublished output
+ address output
+ format.date output
+ 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.booktitle "title" output.check
+ format.edition output
+ crossref missing$
+ { format.bookvolume.series.number output
+ format.chapter.pages "chapter and pages" output.check
+ publisher "publisher" output.check
+ address output
+ }
+ { format.chapter.pages "chapter and pages" output.check
+ format.book.crossref output.nonnull
+ }
+ if$
+ format.date "year" output.check
+ format.language *
+ note output
+ fin.entry
+}
+
+FUNCTION {incollection}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ crossref missing$
+ { format.incoll.title.editors "booktitle" output.check
+ format.bookvolume.series.number output
+ publisher "publisher" output.check
+ address output
+ format.edition output
+ format.date "year" output.check
+ }
+ { format.incoll.inproc.crossref output.nonnull
+ }
+ if$
+ note output
+ format.book.pages output
+ format.language *
+ fin.entry
+}
+
+FUNCTION {inproceedings}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ crossref missing$
+ { format.inproc.title.venue.editors "booktitle" output.check
+ format.bookvolume.series.number output
+ organization output
+ publisher output
+ address output
+ format.date "year" output.check
+ }
+ { format.incoll.inproc.crossref output.nonnull
+ }
+ if$
+ note output
+ format.book.pages output
+ format.language *
+ fin.entry
+}
+
+FUNCTION {conference} { inproceedings }
+
+FUNCTION {manual}
+{ output.bibitem
+ author empty$
+ { organization empty$
+ 'skip$
+ { organization output.nonnull
+ address output
+ }
+ if$
+ }
+ { format.authors output.nonnull }
+ if$
+ format.booktitle "title" output.check
+ author empty$
+ { organization empty$
+ { address output }
+ 'skip$
+ if$
+ }
+ { organization output
+ address output
+ }
+ if$
+ format.edition output
+ format.date output
+ note output
+ fin.entry
+}
+
+FUNCTION {mastersthesis}
+{ output.bibitem
+ format.authors "author" output.check
+ format.booktitle "title" output.check
+ "Master's thesis" format.thesis.type output.nonnull
+ school "school" output.check
+ address output
+ format.date "year" output.check
+ note output
+ format.book.pages output
+ fin.entry
+}
+
+FUNCTION {misc}
+{ output.bibitem
+ format.authors output
+ format.title output
+ howpublished output
+ format.date output
+ note output
+ format.book.pages output
+ fin.entry
+ empty.misc.check
+}
+
+FUNCTION {phdthesis}
+{ output.bibitem
+ format.authors "author" output.check
+ format.booktitle "title" output.check
+ "Ph.D. thesis" format.thesis.type output.nonnull
+ school "school" output.check
+ address output
+ format.date "year" output.check
+ note output
+ format.book.pages output
+ fin.entry
+}
+
+FUNCTION {proceedings}
+{ output.bibitem
+ editor empty$
+ { organization output }
+ { format.editors output.nonnull }
+ if$
+ format.booktitle "title" output.check
+ venue empty$
+ 'skip$
+ { add.space.if.necessary "(" * venue * ")" * }
+ if$
+ format.bookvolume.series.number output
+ address empty$
+ { editor empty$
+ 'skip$
+ { organization output }
+ if$
+ publisher output
+ format.date "year" output.check
+ }
+ { address output.nonnull
+ editor empty$
+ 'skip$
+ { organization output }
+ if$
+ publisher output
+ format.date "year" output.check
+ }
+ if$
+ note output
+ fin.entry
+}
+
+FUNCTION {techreport}
+{ output.bibitem
+ format.authors "author" output.check
+ format.booktitle "title" output.check
+ format.tr.number output.nonnull
+ institution "institution" output.check
+ address output
+ format.date "year" output.check
+ note output
+ fin.entry
+}
+
+FUNCTION {unpublished}
+{ output.bibitem
+ format.authors "author" output.check
+ format.booktitle "title" output.check
+ note "note" output.check
+ format.date output
+ fin.entry
+}
+
+FUNCTION {default.type} { misc }
+
+MACRO {jan} {"January"}
+
+MACRO {feb} {"February"}
+
+MACRO {mar} {"March"}
+
+MACRO {apr} {"April"}
+
+MACRO {may} {"May"}
+
+MACRO {jun} {"June"}
+
+MACRO {jul} {"July"}
+
+MACRO {aug} {"August"}
+
+MACRO {sep} {"September"}
+
+MACRO {oct} {"October"}
+
+MACRO {nov} {"November"}
+
+MACRO {dec} {"December"}
+
+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$
+}
+
+INTEGERS { et.al.char.used }
+
+FUNCTION {initialize.et.al.char.used}
+{ #0 'et.al.char.used :=
+}
+
+EXECUTE {initialize.et.al.char.used}
+
+FUNCTION {format.lab.names}
+{ 's :=
+ s num.names$ 'numnames :=
+ numnames #1 >
+ { numnames #4 >
+ { #3 'namesleft := }
+ { numnames 'namesleft := }
+ if$
+ #1 'nameptr :=
+ ""
+ { namesleft #0 > }
+ { nameptr numnames =
+ { s nameptr "{ff }{vv }{ll}{ jj}" format.name$ "others" =
+ { "{\etalchar{+}}" *
+ #1 'et.al.char.used :=
+ }
+ { s nameptr "{v{}}{l{}}" format.name$ * }
+ if$
+ }
+ { s nameptr "{v{}}{l{}}" format.name$ * }
+ if$
+ nameptr #1 + 'nameptr :=
+ namesleft #1 - 'namesleft :=
+ }
+ while$
+ numnames #4 >
+ { "{\etalchar{+}}" *
+ #1 'et.al.char.used :=
+ }
+ 'skip$
+ if$
+ }
+ { s #1 "{v{}}{l{}}" format.name$
+ duplicate$ text.length$ #2 <
+ { pop$ s #1 "{ll}" format.name$ #3 text.prefix$ }
+ 'skip$
+ if$
+ }
+ if$
+}
+
+FUNCTION {author.key.label}
+{ author empty$
+ { key empty$
+ { cite$ #1 #3 substring$ }
+ { key #3 text.prefix$ }
+ if$
+ }
+ { author format.lab.names }
+ if$
+}
+
+FUNCTION {author.editor.key.label}
+{ author empty$
+ { editor empty$
+ { key empty$
+ { cite$ #1 #3 substring$ }
+ { key #3 text.prefix$ }
+ if$
+ }
+ { editor format.lab.names }
+ if$
+ }
+ { author format.lab.names }
+ if$
+}
+
+FUNCTION {author.key.organization.label}
+{ author empty$
+ { key empty$
+ { organization empty$
+ { cite$ #1 #3 substring$ }
+ { "The " #4 organization chop.word #3 text.prefix$ }
+ if$
+ }
+ { key #3 text.prefix$ }
+ if$
+ }
+ { author format.lab.names }
+ if$
+}
+
+FUNCTION {editor.key.organization.label}
+{ editor empty$
+ { key empty$
+ { organization empty$
+ { cite$ #1 #3 substring$ }
+ { "The " #4 organization chop.word #3 text.prefix$ }
+ if$
+ }
+ { key #3 text.prefix$ }
+ if$
+ }
+ { editor format.lab.names }
+ if$
+}
+
+FUNCTION {calc.label}
+{ type$ "book" =
+ type$ "inbook" =
+ or
+ 'author.editor.key.label
+ { type$ "proceedings" =
+ 'editor.key.organization.label
+ { type$ "manual" =
+ 'author.key.organization.label
+ 'author.key.label
+ if$
+ }
+ if$
+ }
+ if$
+ duplicate$
+ year field.or.null purify$ #-1 #2 substring$
+ *
+ 'label :=
+ year field.or.null purify$ #-1 #4 substring$
+ *
+ sortify 'sort.label :=
+}
+
+FUNCTION {sort.format.names}
+{ 's :=
+ #1 'nameptr :=
+ ""
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { nameptr #1 >
+ { " " * }
+ 'skip$
+ if$
+ s nameptr "{vv{ } }{ll{ }}{ ff{ }}{ 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}
+{ calc.label ""
+ 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 last.sort.label next.extra prev.author this.author
+}
+
+INTEGERS { longest.label.width last.extra.num }
+
+FUNCTION {initialize.longest.label}
+{ "" 'longest.label :=
+ #0 int.to.chr$ 'last.sort.label :=
+ "" 'next.extra :=
+ #0 'longest.label.width :=
+ #0 'last.extra.num :=
+ "abcxyz" 'prev.author :=
+ "" 'this.author :=
+}
+
+FUNCTION {forward.pass}
+{ last.sort.label sort.label =
+ { last.extra.num #1 + 'last.extra.num :=
+ last.extra.num int.to.chr$ 'extra.label :=
+ }
+ { "a" chr.to.int$ 'last.extra.num :=
+ "" 'extra.label :=
+ sort.label 'last.sort.label :=
+ }
+ if$
+ author empty$ { editor empty$ { "" } 'editor if$ } 'author if$
+ 'this.author :=
+ this.author prev.author =
+ { "\bysame" 'bysame := }
+ { "" 'bysame :=
+ this.author "" =
+ { "abcxyz" }
+ 'this.author
+ if$
+ 'prev.author :=
+ }
+ if$
+}
+
+FUNCTION {reverse.pass}
+{ next.extra "b" =
+ { "a" 'extra.label := }
+ 'skip$
+ if$
+ label extra.label * 'label :=
+ label width$ longest.label.width >
+ { label 'longest.label :=
+ label width$ 'longest.label.width :=
+ }
+ 'skip$
+ if$
+ extra.label 'next.extra :=
+}
+
+EXECUTE {initialize.longest.label}
+
+ITERATE {forward.pass}
+
+REVERSE {reverse.pass}
+
+FUNCTION {begin.bib}
+{ preamble$ empty$
+ 'skip$
+ { preamble$ write$ newline$ }
+ if$
+ "\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}"
+ write$ newline$
+ "\providecommand{\mr}[1]{\href{http://www.ams.org/mathscinet-getitem?mr=#1}{MR~#1}}"
+ write$ newline$
+ "\providecommand{\zbl}[1]{\href{http://www.zentralblatt-math.org/zmath/en/search/?q=an:#1}{Zbl~#1}}"
+ write$ newline$
+ "\providecommand{\jfm}[1]{\href{http://www.emis.de/cgi-bin/JFM-item?#1}{JFM~#1}}"
+ write$ newline$
+ "\providecommand{\arxiv}[1]{\href{http://www.arxiv.org/abs/#1}{arXiV~#1}}"
+ write$ newline$
+ "\providecommand{\doi}[1]{\href{http://dx.doi.org/#1}{doi: #1}}"
+ write$ newline$
+ "\providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR }"
+ write$ newline$
+ "% \MRhref is called by the amsart/book/proc definition of \MR."
+ write$ newline$
+ "\providecommand{\MRhref}[2]{%"
+ write$ newline$
+ " \href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}"
+ write$ newline$
+ "}"
+ write$ newline$
+ "\providecommand{\href}[2]{#2}"
+ write$ newline$
+ "\begin{thebibliography}{" longest.label * "}" *
+ write$ newline$
+}
+
+EXECUTE {begin.bib}
+
+EXECUTE {init.state.consts}
+
+ITERATE {call.type$}
+
+FUNCTION {end.bib}
+{ newline$
+ "\end{thebibliography}" write$ newline$
+}
+
+EXECUTE {end.bib}
+%% \CharacterTable
+%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%% Digits \0\1\2\3\4\5\6\7\8\9
+%% Exclamation \! Double quote \" Hash (number) \#
+%% Dollar \$ Percent \% Ampersand \&
+%% Acute accent \' Left paren \( Right paren \)
+%% Asterisk \* Plus \+ Comma \,
+%% Minus \- Point \. Solidus \/
+%% Colon \: Semicolon \; Less than \<
+%% Equals \= Greater than \> Question mark \?
+%% Commercial at \@ Left bracket \[ Backslash \\
+%% Right bracket \] Circumflex \^ Underscore \_
+%% Grave accent \` Left brace \{ Vertical bar \|
+%% Right brace \} Tilde \~}
diff --git a/Master/texmf-dist/bibtex/bst/aomart/aomplain.bst b/Master/texmf-dist/bibtex/bst/aomart/aomplain.bst
new file mode 100644
index 00000000000..80ab83f5e49
--- /dev/null
+++ b/Master/texmf-dist/bibtex/bst/aomart/aomplain.bst
@@ -0,0 +1,1315 @@
+%%%
+%%% This is aomplain.bst file, based on amsplain.bst by AMS
+%%% to support Annals of Mathematics specific fields.
+%%%
+% Copyright 2010, The Annals of Mathematics.
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either
+% version 1.3 of this license or (at your option) any
+% later version.
+% The latest version of the license is in
+% http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of
+% LaTeX version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Boris Veytsman,
+% <borisv@lk.net>
+%
+% This work consists of the file aomart.dtx the
+% derived file aomart.cls, and the file aomplain.bst
+%
+% Version 0.9, 2010/12/04
+%
+%%%
+
+
+% This defines the types of fields that can occur in a database entry
+% for this particular bibliography style. Except for `language',
+% this is the standard list from plain.bst.
+
+%% Types of entries currently allowed in a BibTeX file:
+%%
+%% ARTICLE -- An article from a journal or magazine.
+%%
+%% BOOK -- A book with an explicit publisher.
+%%
+%% BOOKLET -- A work that is printed and bound,
+%% but without a named publisher or sponsoring institution.
+%%
+%% CONFERENCE -- The same as INPROCEEDINGS,
+%% included for Scribe compatibility.
+%%
+%% INBOOK -- A part of a book,
+%% which may be a chapter (or section or whatever) and/or a range of pages.
+%%
+%% INCOLLECTION -- A part of a book having its own title.
+%%
+%% INPROCEEDINGS -- An article in a conference proceedings.
+%%
+%% MANUAL -- Technical documentation.
+%%
+%% MASTERSTHESIS -- A Master's thesis.
+%%
+%% MISC -- Use this type when nothing else fits.
+%%
+%% PHDTHESIS -- A PhD thesis.
+%%
+%% PROCEEDINGS -- The proceedings of a conference.
+%%
+%% TECHREPORT -- A report published by a school or other institution,
+%% usually numbered within a series.
+%%
+%% UNPUBLISHED -- A document having an author and title, but not formally
+%% published.
+
+ENTRY
+ {
+ address
+ arxiv
+ author
+ booktitle
+ chapter
+ doi
+ edition
+ editor
+ howpublished
+ institution
+ jfmnumber
+ journal
+ key
+ language
+ month
+ mrnumber
+ note
+ number
+ organization
+ pages
+ publisher
+ school
+ series
+ title
+ type
+ venue
+ volume
+ year
+ zblnumber
+ }
+ {}
+ { label bysame }
+
+% Removed after.sentence, after.block---not needed.
+
+INTEGERS { output.state before.all mid.sentence }
+
+FUNCTION {init.state.consts}
+{ #0 'before.all :=
+ #1 'mid.sentence :=
+}
+
+% Scratch variables:
+
+STRINGS { s t }
+
+% Utility functions
+
+FUNCTION {shows}
+{ duplicate$ ":::: `" swap$ * "'" * top$
+}
+
+FUNCTION {showstack}
+{"STACK====================================================================="
+top$
+stack$
+"ENDSTACK=================================================================="
+top$
+}
+
+FUNCTION {not}
+{ { #0 }
+ { #1 }
+ if$
+}
+
+FUNCTION {and}
+{ 'skip$
+ { pop$ #0 }
+ if$
+}
+
+FUNCTION {or}
+{ { pop$ #1 }
+ 'skip$
+ if$
+}
+
+FUNCTION {field.or.null}
+{ duplicate$ empty$
+ { pop$ "" }
+ 'skip$
+ if$
+}
+
+FUNCTION {emphasize}
+{ duplicate$ empty$
+ { pop$ "" }
+ { "\emph{" swap$ * "}" * }
+ if$
+}
+
+% n.dashify is used to make sure page ranges get the TeX code
+% (two hyphens) for en-dashes.
+
+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$
+}
+
+% tie.or.space.connect connects two items with a ~ if the
+% second item is less than 3 letters long, otherwise it just puts an
+% ordinary space.
+
+FUNCTION {tie.or.space.connect}
+{ duplicate$ text.length$ #3 <
+ { "~" }
+ { " " }
+ if$
+ swap$ * *
+}
+
+FUNCTION {add.space.if.necessary}
+{ duplicate$ "" =
+ 'skip$
+ { " " * }
+ if$
+}
+
+% either.or.check gives a warning if two mutually exclusive fields
+% were used in the database.
+
+FUNCTION {either.or.check}
+{ empty$
+ 'pop$
+ { "can't use both " swap$ * " fields in " * cite$ * warning$ }
+ if$
+}
+
+% output.nonnull is called by output.
+
+FUNCTION {output.nonnull}
+% remove the top item from the stack because it's in the way.
+{ 's :=
+ output.state mid.sentence =
+% If we're in mid-sentence, add a comma to the new top item and write it
+ { ", " * write$ }
+% Otherwise, if we're at the beginning of a bibitem,
+ { output.state before.all =
+% just write out the top item from the stack;
+ 'write$
+% and the last alternative is that we're at the end of the current
+% bibitem, so we add a period to the top stack item and write it out.
+ { add.period$ " " * write$ }
+ if$
+ mid.sentence 'output.state :=
+ }
+ if$
+% Put the top item back on the stack that we removed earlier.
+ s
+}
+
+% Output checks to see if the stack top is empty; if not, it
+% calls output.nonnull to write it out.
+
+FUNCTION {output}
+{ duplicate$ empty$
+ 'pop$
+ 'output.nonnull
+ if$
+}
+
+% Standard warning message for a missing or empty field. For the user
+% we call any such field `missing' without respect to the distinction
+% made by BibTeX between missing and empty.
+
+FUNCTION {missing.warning}
+{ "missing " swap$ * " in " * cite$ * warning$ }
+
+% Output.check is like output except that it gives a warning on-screen
+% if the given field in the database entry is empty. t is the field
+% name.
+
+FUNCTION {output.check}
+{ 't :=
+ duplicate$ empty$
+ { pop$ t missing.warning }
+ 'output.nonnull
+ if$
+}
+
+FUNCTION {output.bibitem}
+{ newline$
+ "\bibitem{" write$
+ cite$ write$
+ "}" write$
+ newline$
+% This empty string is the first thing that will be written
+% the next time write$ is called. Done this way because each
+% item is saved on the stack until we find out what punctuation
+% should be added after it. Therefore we need an empty first item.
+ ""
+ before.all 'output.state :=
+}
+
+FUNCTION {output.nonempty.mrnumber}
+{ duplicate$ missing$
+ { pop$ "" }
+ 'skip$
+ if$
+ duplicate$ empty$
+ 'pop$
+ { " \mr{" swap$ * "}. " * write$ }
+ if$
+}
+
+
+FUNCTION {output.nonempty.zblnumber}
+{ duplicate$ missing$
+ { pop$ "" }
+ 'skip$
+ if$
+ duplicate$ empty$
+ 'pop$
+ { " \zbl{" swap$ * "}. " * write$ }
+ if$
+}
+
+FUNCTION {output.nonempty.jfmnumber}
+{ duplicate$ missing$
+ { pop$ "" }
+ 'skip$
+ if$
+ duplicate$ empty$
+ 'pop$
+ { " \jfm{" swap$ * "}. " * write$ }
+ if$
+}
+
+
+FUNCTION {output.nonempty.arxiv}
+{ duplicate$ missing$
+ { pop$ "" }
+ 'skip$
+ if$
+ duplicate$ empty$
+ 'pop$
+ { " \arxiv{" swap$ * "}. " * write$ }
+ if$
+}
+
+FUNCTION {output.nonempty.doi}
+{ duplicate$ missing$
+ { pop$ "" }
+ 'skip$
+ if$
+ duplicate$ empty$
+ 'pop$
+ { " \doi{" swap$ * "}. " * write$ }
+ if$
+}
+
+
+FUNCTION {fin.entry}
+{ add.period$
+ write$
+ mrnumber output.nonempty.mrnumber
+ zblnumber output.nonempty.zblnumber
+ jfmnumber output.nonempty.jfmnumber
+ arxiv output.nonempty.arxiv
+ doi output.nonempty.doi
+ newline$
+}
+
+% Removed new.block, new.block.checka, new.block.checkb, new.sentence,
+% new.sentence.checka, and new.sentence.checkb functions here, since they
+% don't seem to be needed in the AMS style. Also moved some real
+% basic functions like `and' and 'or' earlier in the file.
+
+INTEGERS { nameptr namesleft numnames }
+
+% The extra section to write out a language field was added
+% for AMSPLAIN.BST. Not present in plain.bst.
+
+FUNCTION {format.language}
+{ language empty$
+ { "" }
+ { " (" language * ")" * }
+ if$
+}
+
+% This version of format.names puts names in the format
+%
+% F. von Last, Jr.
+%
+% (i.e., first name first, abbreviating initials).
+
+FUNCTION {format.names}
+{ 's :=
+ #1 'nameptr :=
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { s nameptr "\bgroup\scshape{{}}{f.~}{vv~}{ll}{, jj}\egroup{{}}" 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$
+}
+
+FUNCTION {format.authors}
+{ author empty$
+ { "" }
+ { bysame "\bysame" =
+ {"\bysame"}
+ { author format.names }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.editors}
+{ editor empty$
+ { "" }
+ { editor format.names
+ editor num.names$ #1 >
+ { " (eds.)" * }
+ { " (ed.)" * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.nonauthor.editors}
+{ editor empty$
+ { "" }
+ { editor format.names
+ editor num.names$ #1 >
+ { ", eds." * }
+ { ", ed." * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.title}
+{ title empty$
+ { "" }
+ { title "t" change.case$ }
+ if$
+}
+
+FUNCTION {format.booktitle}
+{ title empty$
+ { "" }
+ { title emphasize }
+ if$
+}
+
+
+FUNCTION {format.journal.vol.year}
+{ journal empty$
+ { "journal name" missing.warning ""}
+ { " \emph{" journal * "}" * }
+ if$
+ volume empty$
+ 'skip$
+ { " \textbf{" * volume * "}" * }
+ if$
+ year empty$
+ { "year" missing.warning }
+ { " (" * year * ")" * }
+ if$
+}
+
+% For formatting the issue number for a journal article.
+
+FUNCTION {format.number}
+{ number empty$
+ { "" }
+ { "no.~" number * }
+ if$
+}
+
+% For formatting miscellaneous dates
+
+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$
+}
+
+%% The volume, series and number information is sort of tricky.
+%% This code handles it as follows:
+%% If the series is present, and the volume, but not the number,
+%% then we do "\emph{Book title}, \emph{Series Name} \bf{000}"
+%% If the series is present, and the number, but not the volume,
+%% then we do "\emph{Book title}, \emph{Series Name} no. 000"
+%% If the series is present, and both number and volume,
+%% then we do "\emph{Book title}, \bf{XX} \emph{Series Name} no. 000"
+%% Finally, if the series is absent,
+%% then we do "\emph{Book title}, \bf{XX}"
+%% or "\emph{Book title}, no. 000"
+%% and if both volume and number are present, give a warning message.
+
+FUNCTION {format.bookvolume.series.number}
+{ volume empty$
+ { "" % Push the empty string as a placeholder in case everything else
+ % is empty too.
+ series empty$
+ 'skip$
+ { pop$ "\emph{" series * "}" * } % if series is not empty put in stack
+ if$
+ number empty$
+ 'skip$
+ { duplicate$ empty$ % if no preceding material,
+ 'skip$ % do nothing, otherwise
+ { " " * } % add a space to separate.
+ if$
+ "no." number tie.or.space.connect * % add the number information
+ }
+ if$
+ }
+%% If the volume is NOT EMPTY:
+ { "\textbf{" volume * "}" *
+ number empty$
+ { series empty$
+ 'skip$
+ { "\emph{" series * "}" * " " * swap$ *} % Series Name, vol. XX
+ if$
+ }
+ { series empty$
+ { "can't use both volume and number if series info is missing"
+ warning$
+ "in BibTeX entry type `" type$ * "'" * top$
+ }
+ { " " * series * " no." * number tie.or.space.connect }
+ if$
+ }
+ if$
+ }
+ if$
+
+} % end of format.bookvolume.series.number
+
+%% format.inproc.title.where.editors is used by inproceedings entry types
+
+%% No case changing or emphasizing for the title. We want initial
+%% caps, roman.
+%% We add parentheses around the venue (place where conference
+%% was held).
+%% Likewise we add parentheses around the editors' names.
+
+FUNCTION {format.inproc.title.venue.editors}
+{ booktitle empty$
+ { "" }
+ { " in \emph{" booktitle * "}" *
+ venue empty$
+ 'skip$
+ { add.space.if.necessary "(" * venue * ")" * }
+ if$
+ editor empty$
+ 'skip$
+ { add.space.if.necessary "(" * format.nonauthor.editors * ")" * }
+ if$
+ }
+ if$
+}
+
+%% format.incoll.title.editors is similar to format.inproc... but
+%% omits the address. For collections that are not proceedings volumes.
+
+FUNCTION {format.incoll.title.editors}
+{ booktitle empty$
+ { "" }
+ { editor empty$
+ { " in \emph{" booktitle * "}" * }
+ { " in \emph{" booktitle * "}" *
+ add.space.if.necessary "(" * format.nonauthor.editors * ")" *
+ }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.edition}
+{ edition empty$
+ { "" }
+ { output.state mid.sentence =
+ { edition "l" change.case$ " ed." * }
+ { edition "t" change.case$ " ed." * }
+ if$
+ }
+ 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 n.dashify }
+ if$
+}
+
+FUNCTION {format.book.pages}
+{ pages empty$
+ { "" }
+ { pages multi.page.check
+ { "pp.~" pages n.dashify * }
+ { "p.~" pages * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.chapter.pages}
+{ chapter empty$
+ 'format.book.pages
+ { type empty$
+ { "ch.~" }
+ { type "l" change.case$ " " * }
+ if$
+ chapter *
+ pages empty$
+ 'skip$
+ { ", " * format.book.pages * }
+ 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 "t" change.case$
+ }
+ if$
+}
+
+FUNCTION {format.tr.number}
+{ type empty$
+ { "Tech. Report" }
+ 'type
+ if$
+ number empty$
+ { "t" change.case$ }
+ { number tie.or.space.connect }
+ if$
+}
+
+% The format.crossref functions haven't been paid much attention
+% at the present time (June 1990) and could probably use some
+% work. MJD
+
+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 tie.or.space.connect
+ " 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 \emph{" booktitle * "}" * }
+ if$
+ }
+ { "in " key * }
+ if$
+ }
+ { "in " format.crossref.editor * }
+ if$
+ " \cite{" * crossref * "}" *
+}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% The main functions for each entry type.
+
+% journal, vol and year are formatted together because they are
+% not separated by commas.
+
+FUNCTION {article}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ crossref missing$
+ { format.journal.vol.year output
+ format.pages "pages" output.check
+ }
+ { format.article.crossref output.nonnull
+ format.pages "pages" output.check
+ }
+ if$
+ format.language *
+ 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.booktitle "title" output.check
+ format.edition output
+ crossref missing$
+ { format.bookvolume.series.number output
+ publisher "publisher" output.check
+ address output
+ }
+ { format.book.crossref output.nonnull
+ }
+ if$
+ format.date "year" output.check
+ format.language *
+ note output
+ fin.entry
+}
+
+FUNCTION {booklet}
+{ output.bibitem
+ format.authors output
+ format.title "title" output.check
+ howpublished output
+ address output
+ format.date output
+ 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.booktitle "title" output.check
+ format.edition output
+ crossref missing$
+ { format.bookvolume.series.number output
+ format.chapter.pages "chapter and pages" output.check
+ publisher "publisher" output.check
+ address output
+ }
+ { format.chapter.pages "chapter and pages" output.check
+ format.book.crossref output.nonnull
+ }
+ if$
+ format.date "year" output.check
+ format.language *
+ note output
+ fin.entry
+}
+
+FUNCTION {incollection}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ crossref missing$
+ { format.incoll.title.editors "booktitle" output.check
+ format.bookvolume.series.number output
+ publisher "publisher" output.check
+ address output
+ format.edition output
+ format.date "year" output.check
+ }
+ { format.incoll.inproc.crossref output.nonnull
+ }
+ if$
+ note output
+ format.book.pages output
+ format.language *
+ fin.entry
+}
+
+FUNCTION {inproceedings}
+{ output.bibitem
+ format.authors "author" output.check
+ format.title "title" output.check
+ crossref missing$
+ { format.inproc.title.venue.editors "booktitle" output.check
+ format.bookvolume.series.number output
+ organization output
+ publisher output
+ address output
+ format.date "year" output.check
+ }
+ { format.incoll.inproc.crossref output.nonnull
+ }
+ if$
+ note output
+ format.book.pages output
+ format.language *
+ fin.entry
+}
+
+FUNCTION {conference} { inproceedings }
+
+FUNCTION {manual}
+{ output.bibitem
+ author empty$
+ { organization empty$
+ 'skip$
+ { organization output.nonnull
+ address output
+ }
+ if$
+ }
+ { format.authors output.nonnull }
+ if$
+ format.booktitle "title" output.check
+ author empty$
+ { organization empty$
+ { address output }
+ 'skip$
+ if$
+ }
+ { organization output
+ address output
+ }
+ if$
+ format.edition output
+ format.date output
+ note output
+ fin.entry
+}
+
+FUNCTION {mastersthesis}
+{ output.bibitem
+ format.authors "author" output.check
+ format.booktitle "title" output.check
+ "Master's thesis" format.thesis.type output.nonnull
+ school "school" output.check
+ address output
+ format.date "year" output.check
+ note output
+ format.book.pages output
+ fin.entry
+}
+
+FUNCTION {misc}
+{ output.bibitem
+ format.authors output
+ format.title output
+ howpublished output
+ format.date output
+ note output
+ format.book.pages output
+ fin.entry
+ empty.misc.check
+}
+
+FUNCTION {phdthesis}
+{ output.bibitem
+ format.authors "author" output.check
+ format.booktitle "title" output.check
+ "Ph.D. thesis" format.thesis.type output.nonnull
+ school "school" output.check
+ address output
+ format.date "year" output.check
+ note output
+ format.book.pages output
+ fin.entry
+}
+
+FUNCTION {proceedings}
+{ output.bibitem
+ editor empty$
+ { organization output }
+ { format.editors output.nonnull }
+ if$
+ format.booktitle "title" output.check
+ venue empty$
+ 'skip$
+ { add.space.if.necessary "(" * venue * ")" * }
+ if$
+ format.bookvolume.series.number output
+ address empty$
+ { editor empty$
+ 'skip$
+ { organization output }
+ if$
+ publisher output
+ format.date "year" output.check
+ }
+ { address output.nonnull
+ editor empty$
+ 'skip$
+ { organization output }
+ if$
+ publisher output
+ format.date "year" output.check
+ }
+ if$
+ note output
+ fin.entry
+}
+
+FUNCTION {techreport}
+{ output.bibitem
+ format.authors "author" output.check
+ format.booktitle "title" output.check
+ format.tr.number output.nonnull
+ institution "institution" output.check
+ address output
+ format.date "year" output.check
+ note output
+ fin.entry
+}
+
+FUNCTION {unpublished}
+{ output.bibitem
+ format.authors "author" output.check
+ format.booktitle "title" output.check
+ note "note" output.check
+ format.date output
+ fin.entry
+}
+
+FUNCTION {default.type} { misc }
+
+MACRO {jan} {"January"}
+
+MACRO {feb} {"February"}
+
+MACRO {mar} {"March"}
+
+MACRO {apr} {"April"}
+
+MACRO {may} {"May"}
+
+MACRO {jun} {"June"}
+
+MACRO {jul} {"July"}
+
+MACRO {aug} {"August"}
+
+MACRO {sep} {"September"}
+
+MACRO {oct} {"October"}
+
+MACRO {nov} {"November"}
+
+MACRO {dec} {"December"}
+
+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{ }}{ ff{ }}{ 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 prev.author this.author }
+
+INTEGERS { number.label longest.label.width }
+
+FUNCTION {initialize.longest.label}
+{ "" 'longest.label :=
+ #1 'number.label :=
+ #0 'longest.label.width :=
+ "abcxyz" 'prev.author :=
+ "" 'this.author :=
+}
+
+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$
+ author empty$
+ { editor empty$
+ { "" }
+ 'editor
+ if$
+ }
+ 'author
+ if$
+ 'this.author :=
+ this.author prev.author =
+ { "\bysame" 'bysame := }
+ { "" 'bysame :=
+ this.author "" =
+ { "abcxyz" }
+ 'this.author
+ if$
+ 'prev.author :=
+ }
+ if$
+}
+
+EXECUTE {initialize.longest.label}
+
+ITERATE {longest.label.pass}
+
+FUNCTION {write.lines}
+{ { duplicate$ "." = NOT }
+ { write$ newline$ }
+ while$
+ pop$
+}
+
+FUNCTION {begin.bib}
+{ preamble$ empty$
+ 'skip$
+ { preamble$ write$ newline$ }
+ if$
+ "\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}"
+ write$ newline$
+ "\providecommand{\mr}[1]{\href{http://www.ams.org/mathscinet-getitem?mr=#1}{MR~#1}}"
+ write$ newline$
+ "\providecommand{\zbl}[1]{\href{http://www.zentralblatt-math.org/zmath/en/search/?q=an:#1}{Zbl~#1}}"
+ write$ newline$
+ "\providecommand{\jfm}[1]{\href{http://www.emis.de/cgi-bin/JFM-item?#1}{JFM~#1}}"
+ write$ newline$
+ "\providecommand{\arxiv}[1]{\href{http://www.arxiv.org/abs/#1}{arXiV~#1}}"
+ write$ newline$
+ "\providecommand{\doi}[1]{\href{http://dx.doi.org/#1}{doi: #1}}"
+ write$ newline$
+ "\providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR }"
+ write$ newline$
+ "% \MRhref is called by the amsart/book/proc definition of \MR."
+ write$ newline$
+ "\providecommand{\MRhref}[2]{%"
+ write$ newline$
+ " \href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}"
+ write$ newline$
+ "}"
+ write$ newline$
+ "\providecommand{\href}[2]{#2}"
+ write$ newline$
+ "\begin{thebibliography}{" longest.label * "}" *
+ write$ newline$
+}
+
+EXECUTE {begin.bib}
+
+EXECUTE {init.state.consts}
+
+ITERATE {call.type$}
+
+FUNCTION {end.bib}
+{ newline$
+ "\end{thebibliography}" write$ newline$
+}
+
+EXECUTE {end.bib}
+%% \CharacterTable
+%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%% Digits \0\1\2\3\4\5\6\7\8\9
+%% Exclamation \! Double quote \" Hash (number) \#
+%% Dollar \$ Percent \% Ampersand \&
+%% Acute accent \' Left paren \( Right paren \)
+%% Asterisk \* Plus \+ Comma \,
+%% Minus \- Point \. Solidus \/
+%% Colon \: Semicolon \; Less than \<
+%% Equals \= Greater than \> Question mark \?
+%% Commercial at \@ Left bracket \[ Backslash \\
+%% Right bracket \] Circumflex \^ Underscore \_
+%% Grave accent \` Left brace \{ Vertical bar \|
+%% Right brace \} Tilde \~}
diff --git a/Master/texmf-dist/doc/latex/aomart/Makefile b/Master/texmf-dist/doc/latex/aomart/Makefile
new file mode 100644
index 00000000000..f98c622f0b0
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/aomart/Makefile
@@ -0,0 +1,65 @@
+#
+# Makefile for aomart package
+#
+# This file is in public domain
+#
+# $Id: Makefile,v 1.3 2010-10-25 01:46:35 boris Exp $
+#
+
+PACKAGE=aomart
+
+SAMPLES = \
+ aomsample.tex\
+ aomsample1.tex
+
+PDF = $(PACKAGE).pdf ${SAMPLES:%.tex=%.pdf}
+
+all: ${PDF}
+
+
+%.pdf: %.dtx $(PACKAGE).cls
+ pdflatex $<
+ - bibtex $*
+ pdflatex $<
+ - makeindex -s gind.ist -o $*.ind $*.idx
+ - makeindex -s gglo.ist -o $*.gls $*.glo
+ pdflatex $<
+ while ( grep -q '^LaTeX Warning: Label(s) may have changed' $*.log) \
+ do pdflatex $<; done
+
+
+%.cls: %.ins %.dtx
+ pdflatex $<
+
+%.pdf: %.tex $(PACKAGE).cls
+ pdflatex $<
+ - bibtex $*
+ pdflatex $<
+ while ( grep -q '^LaTeX Warning: Label(s) may have changed' $*.log) \
+ do pdflatex $<; done
+
+aomsample1.tex: fullref.pl aomsample.tex
+ perl fullref.pl aomsample.tex > aomsample1.tex
+
+
+.PRECIOUS: $(PACKAGE).cfg $(PACKAGE).cls
+
+
+clean:
+ $(RM) $(PACKAGE).cls *.log *.aux \
+ *.cfg *.glo *.idx *.toc \
+ *.ilg *.ind *.out *.lof \
+ *.lot *.bbl *.blg *.gls \
+ *.dvi *.ps *.thm *.tgz *.zip
+
+distclean: clean
+ $(RM) $(PDF) aomsample1.tex
+
+#
+# Archive for the distribution. Includes typeset documentation
+#
+archive: all clean
+ tar -czvf $(PACKAGE).tgz --exclude '*~' --exclude '*.tgz' --exclude '*.zip' --exclude CVS .
+
+zip: all clean
+ zip -r $(PACKAGE).zip * -x '*~' -x '*.tgz' -x '*.zip' -x CVS -x 'CVS/*' \ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/aomart/README b/Master/texmf-dist/doc/latex/aomart/README
new file mode 100644
index 00000000000..4ad6fc0c555
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/aomart/README
@@ -0,0 +1,7 @@
+ LaTeX Class for The Annals of Mathematics
+ Boris Veytsman
+ Version 1.1
+
+This package provides the class for typesetting articles for The Annals
+of Mathematics, http://annals.princeton.edu/.
+
diff --git a/Master/texmf-dist/doc/latex/aomart/aomart.bib b/Master/texmf-dist/doc/latex/aomart/aomart.bib
new file mode 100644
index 00000000000..2746077e4a6
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/aomart/aomart.bib
@@ -0,0 +1,123 @@
+Generated on Sun Jan 2 17:18:36 2011 (1294006716).
+
+
+,-------------------.
+| BIBTEX ENTRIES |
+`-------------------'
+
+@book{Graetzer00:MathIntoLaTeX,
+ address = {Boston},
+ author = {George Gr\"aetzer},
+ edition = {Third},
+ publisher = {Birkh\"auser},
+ title = {Math into \LaTeX},
+ year = {2000},
+}
+
+@misc{TeXFAQ,
+ author = {{UK \TeX{} Users Group}},
+ howpublished = {\url{http://www.tex.ac.uk/cgi-bin/texfaq2html}},
+ title = {{UK} List of {\TeX} Frequently Asked Questions},
+ year = {2008},
+}
+
+@manual{Downes04:amsart,
+ author = {Michael Downes and Barbara Beeton},
+ month = {August},
+ note =
+ {\url{http://mirrors.ctan.org/macros/latex/required/amslatex/classes}},
+ organization = {American Mathematical Society},
+ title = {The \textsf{amsart}, \textsf{amsproc}, and
+ \textsf{amsbook} document~classes},
+ year = {2004},
+}
+
+@manual{Rahtz06:Hyperref,
+ author = {Sebastian Rahtz and Heiko Oberdiek},
+ month = {September},
+ note =
+ {\url{http://mirrors.ctan.org/macros/latex/contrib/hyperref}},
+ title = {Hypertext Marks in \LaTeX: a Manual for Hyperref},
+ year = {2006},
+}
+
+@manual{Oberdiek06:Ifpdf,
+ author = {Heiko Oberdiek},
+ month = {February},
+ note =
+ {\url{http://mirrors.ctan.org/macros/latex/contrib/oberdiek}},
+ title = {The \textsf{ifpdf} Package},
+ year = {2006},
+}
+
+@manual{Oostrum04:Fancyhdr,
+ author = {van Oostrum, Piet},
+ month = {March},
+ note =
+ {\url{http://mirrors.ctan.org/macros/latex/contrib/fancyhdr}},
+ title = {Page Layout in \LaTeX},
+ year = {2004},
+}
+
+@manual{Znamenskii03:Cmtiup,
+ author = {Sergei V. Znamenskii},
+ month = {January},
+ note = {\url{http://mirrors.ctan.org/fonts/cm/cmtiup}},
+ title = {Unslanted Punctuation in {Computer Modern} Italic},
+ year = {2003},
+}
+
+@manual{Haralambous96:Yhmath,
+ author = {Yannis Haralambous},
+ month = {January},
+ note =
+ {\url{http://mirrors.ctan.org/macros/latex/contrib/yhmath/}},
+ title = {My Humble Additions to {(La)\TeX} Mathematics},
+ year = {1996},
+}
+
+@manual{amsldoc,
+ month = {February},
+ note =
+ {\url{http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pd%
+f}},
+ organization = {American Mathematical Society},
+ title = {User's Guide for the \textsf{amsmath} Package
+ (Version~2.0)},
+ year = {2002},
+}
+
+@manual{instr-l,
+ month = {August},
+ note =
+ {\url{http://mirrors.ctan.org/macros/latex/required/amslatex/classes/instr-l%
+.pdf}},
+ organization = {American Mathematical Society},
+ title = {Instructions for Preparation of Papers and
+ Monographs, {AMS\LaTeX}},
+ year = {2004},
+}
+
+@manual{amsthdoc,
+ month = {August},
+ note =
+ {\url{http://mirrors.ctan.org/macros/latex/required/amslatex/classes/amsthdo%
+c.pdf}},
+ organization = {American Mathematical Society},
+ title = {Using the \texttt{amsthm} Package},
+ year = {2004},
+}
+
+@book{Goossens97:LateXGraphicsCompanion,
+ address = {Reading, Ma.},
+ author = {Michel Goossens and Sebastian Rahtz and
+ Frank Mittelbach},
+ chapter = {},
+ publisher = {Addison-Wesley},
+ series = {Addison-Wesley Series on Tools and Techniques for
+ Computer Typesetting},
+ title = {The \LaTeX{} Graphics Companion: Illustrating
+ Documents With \TeX{} and {PostScript}},
+ year = {1997},
+}
+
diff --git a/Master/texmf-dist/doc/latex/aomart/aomart.pdf b/Master/texmf-dist/doc/latex/aomart/aomart.pdf
new file mode 100644
index 00000000000..431c2e133ac
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/aomart/aomart.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/aomart/aomsample.bib b/Master/texmf-dist/doc/latex/aomart/aomsample.bib
new file mode 100644
index 00000000000..8eb847605bd
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/aomart/aomsample.bib
@@ -0,0 +1,241 @@
+
+@Article{dihe:newdir,
+ author = {W. Diffie and E. Hellman},
+ title = {New directions in Cryptography},
+ journal = {IEEE Transactions on Information Theory},
+ year = 1976,
+ volume = 22,
+ number = 5,
+ pages = {644--654}
+}
+
+
+
+
+
+@Misc{fre:cichon,
+ author = {D. H. Fremlin},
+ title = {Cichon's Diagram},
+ howpublished = {presented at the
+S{\'e}minaire Initiation {\`a} l'Analyse, G. Choquet, M. Rogalski, J.
+Saint Raymond, at the Universit{\'e} Pierre et Marie Curie, Paris, 23e
+ann{\'e}e.},
+ year = {1983/194}
+}
+
+
+
+
+
+@Book{fre:riesz,
+ author = {D. H. Fremlin},
+ title = {Topological {R}iesz Spaces and Measure Theory},
+ publisher = {Cambridge University Press},
+ year = 2008
+}
+
+
+@Article{gouja:lagrmeth,
+ author = {I. P. Goulden and D. M. Jackson},
+ title = {The Enumeration of Directed
+Closed {E}uler Trails and Directed {H}amiltonian Circuits by
+{L}angrangian Methods},
+ journal = {European Journal of Combinatorics},
+ year = 1981,
+ volume = 2,
+ pages = {131--212}
+}
+
+
+
+@Book{hapa:graphenum,
+ author = {F. Harary and E. M. Palmer},
+ title = {Graphical Enumeration},
+ publisher = {Academic Press},
+ year = 1973
+}
+
+
+
+
+@InProceedings{imlelu:oneway,
+ author = {R. Impagliazzo and L. Levin and M. Luby},
+ title = {Pseudo-random Generation from One-Way Functions},
+ booktitle = {Proc. 21st STOC},
+ pages = {12--24},
+ year = 1989,
+ venue = {Seattle, WA, USA},
+ address = {New York},
+ publisher = {ACM}
+}
+
+
+
+
+@TechReport{komiyo:unipfunc,
+ author = {M. Kojima and S. Mizuno and A. Yoshise},
+ title = {A New Continuation Method
+for Complementarity Problems With Uniform $p$-Functions},
+ institution = {Tokyo Inst. of Technology, Dept. of Information Sciences},
+ year = 1987,
+ number = {B-194},
+ address = {Tokyo}
+}
+
+
+
+
+@TechReport{komiyo:lincomp,
+ author = {M. Kojima and S. Mizuno and A. Yoshise},
+ title = {A Polynomial-Time Algorithm For a Class of Linear
+Complementarity Problems},
+ institution = {Tokyo Inst. of Technology, Dept. of Information Sciences},
+ year = 1987,
+ number = {B-193},
+ address = {Tokyo}
+}
+
+
+
+
+@Article{liuchow:formalsum,
+ author = {C. J. Liu and Yutze Chow},
+ title = {On Operator and Formal Sum Methods for
+Graph Enumeration Problems},
+ journal = {SIAM Journal of Algorithms and Discrete Methods},
+ year = 1984,
+ volume = 5,
+ pages = {384--438}
+}
+
+
+
+
+@Article{mami:matrixth,
+ author = {M. Marcus and H. Minc},
+ title = {A Survey of Matrix Theory and Matrix
+Inequalities},
+ journal = {Complementary Series in Mathematics},
+ year = 1964,
+ volume = 14,
+ pages = {21--48}
+}
+
+
+
+
+@TechReport{miyoki:lincomp,
+ author = {S. Mizuno and A. Yoshise and T. Kikuchi},
+ title = {Practical Polynomial Time
+Algorithms for Linear Complementarity Problems},
+ institution = {Tokyo Inst. of Technology, Dept. of Industrial Engineering
+and Management},
+ year = 1988,
+ number = 13,
+ address = {Tokyo},
+ month = {April}
+}
+
+
+
+
+@TechReport{moad:quadpro,
+ author = {R. D. Monteiro and I. Adler},
+ title = {Interior Path Following Primal-Dual
+Algorithms, Part {II}: Quadratic Programming},
+ institution = {Dept. of Industrial Engineering and Operations Research},
+ year = 1987,
+ type = {Working Paper},
+ month = {August}
+}
+
+
+
+
+@Book{ste:sint,
+ author = {E. M. Stein},
+ title = {Singular Integrals and Differentiability Properties
+of Functions},
+ publisher = {Princeton Univ. Press},
+ year = 1970,
+ address = {Princeton, NJ}
+}
+
+
+
+
+
+@PhdThesis{ye:intalg,
+ author = {Y. Ye},
+ title = {Interior Algorithms for Linear, Quadratic and Linearly
+Constrained Convex Programming},
+ school = {Stanford Univ., Dept. of Engineering--Economic Systems},
+ year = 1987,
+ address = {Palo Alto, CA},
+ month = {July}
+}
+
+@article{Lenstra74,
+author= {Lenstra, Jr., Hendrik W. and Oort, Frans},
+title= {Simple abelian varieties having a prescribed formal isogeny type.},
+journal="J. Pure Appl. Algebra ",
+volume= 4 ,
+pages= {47--53},
+year= 1974,
+doi = "10.1016/0022-4049(74)90029-2",
+zblnumber = {50:7163},
+mrnumber = {0279.14009}
+}
+
+
+
+@Unpublished{Minasyan08,
+ author = {A. Minasyan and D. Osin},
+ title = {Normal Automorphisms of Relatively Hyperbolic Groups},
+ arxiv = {0809.2408},
+ year = 2008
+}
+
+@Article{Zarhin92,
+ author = {Zarhin, Yuri G.},
+ title = {Abelian Varieties Having a Reduction of {K3} Type},
+ journal = {Duke Math J.},
+ year = 1992,
+ volume = 65,
+ number = 3,
+ pages = {511--527},
+ mrnumber= {1154181},
+ zblnumber = {0774.14039}
+}
+
+@Book{Arnold89:MathMethodsMechanics,
+ author = {Arnold, V. I.},
+ title = {Mathematical Methods of Classical Mechanics},
+ publisher = {Springer},
+ year = 1989,
+ volume = 60,
+ series = {Graduate Texts in Mathematics},
+ address = {New York},
+ edition = {Second}
+}
+
+@Book{Michal48,
+ author = {A. D. Michal},
+ title = {Matrix and Tensor Calculus},
+ publisher = {John Wiley \& Sons, Inc.; Chapman \& Hall, Ltd.},
+ year = 1948,
+ series = {GALCIT Aeronautical Series},
+ address = {New York; London}
+}
+
+
+@Article{Michal38,
+ author = {A. D. Michal},
+ title = {Differential Calculus in Linear Topological Spaces},
+ journal = {Proc. nat. Acad. Sci. USA},
+ year = 1938,
+ volume = 24,
+ jfmnumber = {64.0366.02},
+ pages = {340--342}
+}
+
diff --git a/Master/texmf-dist/doc/latex/aomart/aomsample.pdf b/Master/texmf-dist/doc/latex/aomart/aomsample.pdf
new file mode 100644
index 00000000000..2050fcf922c
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/aomart/aomsample.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/aomart/aomsample.tex b/Master/texmf-dist/doc/latex/aomart/aomsample.tex
new file mode 100644
index 00000000000..ed82b05ac26
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/aomart/aomsample.tex
@@ -0,0 +1,1729 @@
+%%% ====================================================================
+%%% @LaTeX-file{
+%%% filename = "aomsample.tex",
+%%% copyright = "Copyright 1995, 1999 American Mathematical Society,
+%%% 2005 Hebrew University Magnes Press,
+%%% all rights reserved. Copying of this file is
+%%% authorized only if either:
+%%% (1) you make absolutely no changes to your copy,
+%%% including name; OR
+%%% (2) if you do make changes, you first rename it
+%%% to some other name.",
+%%% }
+%%% ====================================================================
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1994/12/01]% LaTeX date must December 1994 or later
+\documentclass[manuscript]{aomart}
+%\documentclass[screen]{aomart}
+%\documentclass{aomart}
+% Some definitions useful in producing this sort of documentation:
+\chardef\bslash=`\\ % p. 424, TeXbook
+% Normalized (nonbold, nonitalic) tt font, to avoid font
+% substitution warning messages if tt is used inside section
+% headings and other places where odd font combinations might
+% result.
+\newcommand{\ntt}{\normalfont\ttfamily}
+% command name
+\newcommand{\cn}[1]{{\protect\ntt\bslash#1}}
+% LaTeX package name
+\newcommand{\pkg}[1]{{\protect\ntt#1}}
+% File name
+\newcommand{\fn}[1]{{\protect\ntt#1}}
+% environment name
+\newcommand{\env}[1]{{\protect\ntt#1}}
+\hfuzz1pc % Don't bother to report overfull boxes if overage is < 1pc
+
+% Theorem environments
+
+%% \theoremstyle{plain} %% This is the default
+\newtheorem[{}\it]{thm}{Theorem}[section]
+\newtheorem{cor}[thm]{Corollary}
+\newtheorem{lem}[thm]{Lemma}
+\newtheorem{prop}[thm]{Proposition}
+\newtheorem{ax}{Axiom}
+
+\theoremstyle{definition}
+\newtheorem{defn}{Definition}[section]
+\newtheorem{rem}{Remark}[section]
+\newtheorem*[{}\it]{notation}{Notation}
+\newtheorem{step}{Step}
+
+%\numberwithin{equation}{section}
+
+\newcommand{\thmref}[1]{Theorem~\ref{#1}}
+\newcommand{\secref}[1]{\S\ref{#1}}
+\newcommand{\lemref}[1]{Lemma~\ref{#1}}
+
+
+% Math definitions
+
+\newcommand{\A}{\mathcal{A}}
+\newcommand{\B}{\mathcal{B}}
+\newcommand{\st}{\sigma}
+\newcommand{\XcY}{{(X,Y)}}
+\newcommand{\SX}{{S_X}}
+\newcommand{\SY}{{S_Y}}
+\newcommand{\SXY}{{S_{X,Y}}}
+\newcommand{\SXgYy}{{S_{X|Y}(y)}}
+\newcommand{\Cw}[1]{{\hat C_#1(X|Y)}}
+\newcommand{\G}{{G(X|Y)}}
+\newcommand{\PY}{{P_{\mathcal{Y}}}}
+\newcommand{\X}{\mathcal{X}}
+\newcommand{\wt}{\widetilde}
+\newcommand{\wh}{\widehat}
+
+\DeclareMathOperator{\per}{per}
+\DeclareMathOperator{\cov}{cov}
+\DeclareMathOperator{\non}{non}
+\DeclareMathOperator{\cf}{cf}
+\DeclareMathOperator{\add}{add}
+\DeclareMathOperator{\Cham}{Cham}
+\DeclareMathOperator{\IM}{Im}
+\DeclareMathOperator{\esssup}{ess\,sup}
+\DeclareMathOperator{\meas}{meas}
+\DeclareMathOperator{\seg}{seg}
+
+% \interval is used to provide better spacing after a [ that
+% is used as a closing delimiter.
+\newcommand{\interval}[1]{\mathinner{#1}}
+
+% Notation for an expression evaluated at a particular condition. The
+% optional argument can be used to override automatic sizing of the
+% right vert bar, e.g. \eval[\biggr]{...}_{...}
+\newcommand{\eval}[2][\right]{\relax
+ \ifx#1\right\relax \left.\fi#2#1\rvert}
+
+% Enclose the argument in vert-bar delimiters:
+\newcommand{\envert}[1]{\left\lvert#1\right\rvert}
+\let\abs=\envert
+
+% Enclose the argument in double-vert-bar delimiters:
+\newcommand{\enVert}[1]{\left\lVert#1\right\rVert}
+\let\norm=\enVert
+
+%\setcounter{tocdepth}{5}
+
+\title[Sample Paper]{Sample Paper for the \pkg{aomart}
+ Class}
+\author[AMS]{American Mathematical Society}
+\address{AMS\\
+Providence, Rhode Island}
+\email{tech-support@ams.org}
+\author{Boris Veytsman}
+\address{George Mason University\\
+Fairfax, Virginia}
+\email{borisv@lk.net}
+\urladdr{http://borisv.lk.net}
+\givenname{Boris}
+\surname{Veytsman}
+\thanks{The class was commissioned by Annals of Mathematics}
+
+\keyword{Hamiltonian paths}
+\keyword{Typesetting}
+\subject{primary}{matsc2000}{123456789}
+\subject{secondary}{matsc2000}{FFFF}
+
+\received{\formatdate{2004-12-24}}
+\revised{\formatdate{2006-04-12}}
+\accepted{\formatdate{2007-10-02}}
+\published{\formatdate{2008-04-02}}
+\publishedonline{\formatdate{2007-11-12}}
+
+\volumenumber{160}
+\issuenumber{1}
+\publicationyear{2008}
+\papernumber{12}
+\startpage{17}
+\endpage{}
+
+\proposed{E. D. Itor}
+\seconded{A. S. Sociate}
+\corresponding{A. U. Thor}
+\version{2.1}
+
+%\doinumber{10.1215/S0012-7094-92-06520-3}
+\mrnumber{MR1154181}
+\zblnumber{0774.14039}
+
+
+
+\begin{document}
+
+
+\begin{abstract}
+ This is a test file for \textsf{aomart} class based on the
+ \texttt{testmath.tex} file from the \textsf{amsmath} distribution.
+
+ It was changed to test the features of the Annals of Mathematics
+ class.
+\end{abstract}
+
+\maketitle
+\tableofcontents
+
+\section{Introduction}
+
+
+This paper demonstrates the use of \texttt{aomart} class. It is based
+on \texttt{testmath.tex} from \AmS-\LaTeX{} distribution. The text
+is (slightly) reformatted according to the requirements of the
+\texttt{aomart} style. See also
+\cite{Lenstra74,Zarhin92,Minasyan08,Arnold89:MathMethodsMechanics,%
+Michal48,Michal38}.
+\EditorialComment{Are these
+ quotations necessary?}
+
+
+\section{Enumeration of Hamiltonian paths in a graph}
+
+Let $\mathbf{A}=(a_{ij})$ be the adjacency matrix of graph $G$. The
+corresponding Kirchhoff matrix $\mathbf{K}=(k_{ij})$ is obtained from
+$\mathbf{A}$ by replacing in $-\mathbf{A}$ each diagonal entry by the
+degree of its corresponding vertex; i.e., the $i$th diagonal entry is
+identified with the degree of the $i$th vertex. It is well known that
+\begin{equation}
+\det\mathbf{K}(i|i)=\text{ the number of spanning trees of $G$},
+\quad i=1,\dots,n
+\end{equation}
+where $\mathbf{K}(i|i)$ is the $i$th principal submatrix of
+$\mathbf{K}$.
+\begin{verbatim}
+\det\mathbf{K}(i|i)=\text{ the number of spanning trees of $G$},
+\end{verbatim}
+
+Let $C_{i(j)}$ be the set of graphs obtained from $G$ by attaching edge
+$(v_iv_j)$ to each spanning tree of $G$. Denote by $C_i=\bigcup_j
+C_{i(j)}$. It is obvious that the collection of Hamiltonian cycles is a
+subset of $C_i$. Note that the cardinality of $C_i$ is $k_{ii}\det
+\mathbf{K}(i|i)$. Let $\wh X=\{\hat x_1,\dots,\hat x_n\}$.
+\begin{verbatim}
+$\wh X=\{\hat x_1,\dots,\hat x_n\}$
+\end{verbatim}
+Define multiplication for the elements of $\wh X$ by
+\begin{equation}\label{multdef}
+\hat x_i\hat x_j=\hat x_j\hat x_i,\quad \hat x^2_i=0,\quad
+i,j=1,\dots,n.
+\end{equation}
+Let $\hat k_{ij}=k_{ij}\hat x_j$ and $\hat k_{ij}=-\sum_{j\not=i} \hat
+k_{ij}$. Then the number of Hamiltonian cycles $H_c$ is given by the
+relation \cite{liuchow:formalsum}
+\begin{equation}\label{H-cycles}
+\biggl(\prod^n_{\,j=1}\hat x_j\biggr)H_c=\frac{1}{2}\hat k_{ij}\det
+\wh{\mathbf{K}}(i|i),\qquad i=1,\dots,n.
+\end{equation}
+The task here is to express \eqref{H-cycles}
+in a form free of any $\hat x_i$,
+$i=1,\dots,n$. The result also leads to the resolution of enumeration of
+Hamiltonian paths in a graph.
+
+It is well known that the enumeration of Hamiltonian cycles and paths in
+a complete graph $K_n$ and in a complete bipartite graph $K_{n_1n_2}$
+can only be found from \textit{first combinatorial principles}
+\cite{hapa:graphenum}. One wonders if there exists a formula which can
+be used very efficiently to produce $K_n$ and $K_{n_1n_2}$. Recently,
+using Lagrangian methods, Goulden and Jackson have shown that $H_c$ can
+be expressed in terms of the determinant and permanent of the adjacency
+matrix \cite{gouja:lagrmeth}. However, the formula of Goulden and
+Jackson determines neither $K_n$ nor $K_{n_1n_2}$ effectively. In this
+paper, using an algebraic method, we parametrize the adjacency matrix.
+The resulting formula also involves the determinant and permanent, but
+it can easily be applied to $K_n$ and $K_{n_1n_2}$. In addition, we
+eliminate the permanent from $H_c$ and show that $H_c$ can be
+represented by a determinantal function of multivariables, each variable
+with domain $\{0,1\}$. Furthermore, we show that $H_c$ can be written by
+number of spanning trees of subgraphs. Finally, we apply the formulas to
+a complete multigraph $K_{n_1\dots n_p}$.
+
+The conditions $a_{ij}=a_{ji}$, $i,j=1,\dots,n$, are not required in
+this paper. All formulas can be extended to a digraph simply by
+multiplying $H_c$ by 2. Some other discussion can be found
+in~\cite{fre:riesz,fre:cichon}.
+
+\section{Main theorem}
+\label{s:mt}
+
+\begin{notation} For $p,q\in P$ and $n\in\omega$ we write
+$(q,n)\le(p,n)$ if $q\le p$ and $A_{q,n}=A_{p,n}$.
+\begin{verbatim}
+\begin{notation} For $p,q\in P$ and $n\in\omega$
+...
+\end{notation}
+\end{verbatim}
+\end{notation}
+
+Let $\mathbf{B}=(b_{ij})$ be an $n\times n$ matrix. Let $\mathbf{n}=\{1,
+\dots,n\}$. Using the properties of \eqref{multdef}, it is readily seen
+that
+
+\begin{lem}\label{lem-per}
+\begin{equation}
+\prod_{i\in\mathbf{n}}
+\biggl(\sum_{\,j\in\mathbf{n}}b_{ij}\hat x_i\biggr)
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)\per \mathbf{B}
+\end{equation}
+where $\per \mathbf{B}$ is the permanent of $\mathbf{B}$.
+\end{lem}
+
+Let $\wh Y=\{\hat y_1,\dots,\hat y_n\}$. Define multiplication
+for the elements of $\wh Y$ by
+\begin{equation}
+\hat y_i\hat y_j+\hat y_j\hat y_i=0,\quad i,j=1,\dots,n.
+\end{equation}
+Then, it follows that
+\begin{lem}\label{lem-det}
+\begin{equation}\label{detprod}
+\prod_{i\in\mathbf{n}}
+\biggl(\sum_{\,j\in\mathbf{n}}b_{ij}\hat y_j\biggr)
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat y_i\biggr)\det\mathbf{B}.
+\end{equation}
+\end{lem}
+
+Note that all basic properties of determinants are direct consequences
+of Lemma~\ref{lem-det}. Write
+\begin{equation}\label{sum-bij}
+\sum_{j\in\mathbf{n}}b_{ij}\hat y_j=\sum_{j\in\mathbf{n}}b^{(\lambda)}
+_{ij}\hat y_j+(b_{ii}-\lambda_i)\hat y_i\hat y
+\end{equation}
+where
+\begin{equation}
+b^{(\lambda)}_{ii}=\lambda_i,\quad b^{(\lambda)}_{ij}=b_{ij},
+\quad i\not=j.
+\end{equation}
+Let $\mathbf{B}^{(\lambda)}=(b^{(\lambda)}_{ij})$. By \eqref{detprod}
+and \eqref{sum-bij}, it is
+straightforward to show the following
+result:
+\begin{thm}\label{thm-main}
+\begin{equation}\label{detB}
+\det\mathbf{B}=
+\sum^n_{l =0}\sum_{I_l \subseteq n}
+\prod_{i\in I_l}(b_{ii}-\lambda_i)
+\det\mathbf{B}^{(\lambda)}(I_l |I_l ),
+\end{equation}
+where $I_l =\{i_1,\dots,i_l \}$ and $\mathbf{B}^{(\lambda)}(I_l |I_l )$
+is the principal submatrix (obtained from $\mathbf{B}^{(\lambda)}$
+by deleting its $i_1,\dots,i_l $ rows and columns).
+\end{thm}
+
+\begin{rem}[convention]
+Let $\mathbf{M}$ be an $n\times n$ matrix. The convention
+$\mathbf{M}(\mathbf{n}|\mathbf{n})=1$ has been used in \eqref{detB} and
+hereafter.
+\end{rem}
+
+Before proceeding with our discussion, we pause to note that
+\thmref{thm-main} yields immediately a fundamental formula which can be
+used to compute the coefficients of a characteristic polynomial
+\cite{mami:matrixth}:
+\begin{cor}\label{BI}
+Write $\det(\mathbf{B}-x\mathbf{I})=\sum^n_{l =0}(-1)
+^l b_l x^l $. Then
+\begin{equation}\label{bl-sum}
+b_l =\sum_{I_l \subseteq\mathbf{n}}\det\mathbf{B}(I_l |I_l ).
+\end{equation}
+\end{cor}
+Let
+\begin{equation}
+\mathbf{K}(t,t_1,\dots,t_n)
+=\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\
+-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\
+\hdotsfor[2]{4}\\
+-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix},
+\end{equation}
+\begin{verbatim}
+\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\
+-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\
+\hdotsfor[2]{4}\\
+-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix}
+\end{verbatim}
+where
+\begin{equation}
+D_i=\sum_{j\in\mathbf{n}}a_{ij}t_j,\quad i=1,\dots,n.
+\end{equation}
+
+Set
+\begin{equation*}
+D(t_1,\dots,t_n)=\frac{\delta}{\delta t}\eval{\det\mathbf{K}(t,t_1,\dots,t_n)
+}_{t=1}.
+\end{equation*}
+Then
+\begin{equation}\label{sum-Di}
+D(t_1,\dots,t_n)
+=\sum_{i\in\mathbf{n}}D_i\det\mathbf{K}(t=1,t_1,\dots,t_n; i|i),
+\end{equation}
+where $\mathbf{K}(t=1,t_1,\dots,t_n; i|i)$ is the $i$th principal
+submatrix of $\mathbf{K}(t=1,t_1,\dots,t_n)$.
+
+Theorem ~\ref{thm-main} leads to
+\begin{equation}\label{detK1}
+\det\mathbf{K}(t_1,t_1,\dots,t_n)
+=\sum_{I\in\mathbf{n}}(-1)^{\envert{I}}t^{n-\envert{I}}
+\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A}
+^{(\lambda t)}(\overline{I}|\overline I).
+\end{equation}
+Note that
+\begin{equation}\label{detK2}
+\det\mathbf{K}(t=1,t_1,\dots,t_n)=\sum_{I\in\mathbf{n}}(-1)^{\envert{I}}
+\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A}
+^{(\lambda)}(\overline{I}|\overline{I})=0.
+\end{equation}
+
+Let $t_i=\hat x_i,i=1,\dots,n$. Lemma ~\ref{lem-per} yields
+\begin{multline}
+\biggl(\sum_{\,i\in\mathbf{n}}a_{l _i}x_i\biggr)
+\det\mathbf{K}(t=1,x_1,\dots,x_n;l |l )\\
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)
+\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\envert{I}}\per\mathbf{A}^{(\lambda)}(I|I)
+\det\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \}).
+\label{sum-ali}
+\end{multline}
+\begin{verbatim}
+\begin{multline}
+\biggl(\sum_{\,i\in\mathbf{n}}a_{l _i}x_i\biggr)
+\det\mathbf{K}(t=1,x_1,\dots,x_n;l |l )\\
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)
+\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\envert{I}}\per\mathbf{A}^{(\lambda)}(I|I)
+\det\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \}).
+\label{sum-ali}
+\end{multline}
+\end{verbatim}
+
+By \eqref{H-cycles}, \eqref{detprod}, and \eqref{sum-bij}, we have
+\begin{prop}\label{prop:eg}
+\begin{equation}
+H_c=\frac1{2n}\sum^n_{l =0}(-1)^{l}
+D_{l},
+\end{equation}
+where
+\begin{equation}\label{delta-l}
+D_{l}=\eval[2]{\sum_{I_{l}\subseteq \mathbf{n}}
+D(t_1,\dots,t_n)}_{t_i=\left\{\begin{smallmatrix}
+0,& \text{if }i\in I_{l}\quad\\% \quad added for centering
+1,& \text{otherwise}\end{smallmatrix}\right.\;,\;\; i=1,\dots,n}.
+\end{equation}
+\end{prop}
+
+\section{Application}
+\label{lincomp}
+
+We consider here the applications of Theorems~\ref{th-info-ow-ow} and
+~\ref{th-weak-ske-owf} to a complete
+multipartite graph $K_{n_1\dots n_p}$. It can be shown that the
+number of spanning trees of $K_{n_1\dots n_p}$
+may be written
+\begin{equation}\label{e:st}
+T=n^{p-2}\prod^p_{i=1}
+(n-n_i)^{n_i-1}
+\end{equation}
+where
+\begin{equation}
+n=n_1+\dots+n_p.
+\end{equation}
+
+It follows from Theorems~\ref{th-info-ow-ow} and
+~\ref{th-weak-ske-owf} that
+\begin{equation}\label{e:barwq}
+\begin{split}
+H_c&=\frac1{2n}
+\sum^n_{{l}=0}(-1)^{l}(n-{l})^{p-2}
+\sum_{l _1+\dots+l _p=l}\prod^p_{i=1}
+\binom{n_i}{l _i}\\
+&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
+\biggl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\biggr].\end{split}
+\end{equation}
+\begin{verbatim}
+... \binom{n_i}{l _i}\\
+\end{verbatim}
+and
+\begin{equation}\label{joe}
+\begin{split}
+H_c&=\frac12\sum^{n-1}_{l =0}
+(-1)^{l}(n-l )^{p-2}
+\sum_{l _1+\dots+l _p=l}
+\prod^p_{i=1}\binom{n_i}{l _i}\\
+&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}
+\left(1-\frac{l _p}{n_p}\right)
+[(n-l )-(n_p-l _p)].
+\end{split}
+\end{equation}
+
+The enumeration of $H_c$ in a $K_{n_1\dotsm n_p}$ graph can also be
+carried out by Theorem ~\ref{thm-H-param} or ~\ref{thm-asym}
+together with the algebraic method of \eqref{multdef}.
+Some elegant representations may be obtained. For example, $H_c$ in
+a $K_{n_1n_2n_3}$ graph may be written
+\begin{equation}\label{j:mark}
+\begin{split}
+H_c=&
+\frac{n_1!\,n_2!\,n_3!}
+{n_1+n_2+n_3}\sum_i\left[\binom{n_1}{i}
+\binom{n_2}{n_3-n_1+i}\binom{n_3}{n_3-n_2+i}\right.\\
+&+\left.\binom{n_1-1}{i}
+\binom{n_2-1}{n_3-n_1+i}
+\binom{n_3-1}{n_3-n_2+i}\right].\end{split}
+\end{equation}
+
+\section{Secret key exchanges}
+\label{SKE}
+
+Modern cryptography is fundamentally concerned with the problem of
+secure private communication. A Secret Key Exchange is a protocol
+where Alice and Bob, having no secret information in common to start,
+are able to agree on a common secret key, conversing over a public
+channel. The notion of a Secret Key Exchange protocol was first
+introduced in the seminal paper of Diffie and Hellman
+\cite{dihe:newdir}. \cite{dihe:newdir} presented a concrete
+implementation of a Secret Key Exchange protocol, dependent on a
+specific assumption (a variant on the discrete log), specially
+tailored to yield Secret Key Exchange. Secret Key Exchange is of
+course trivial if trapdoor permutations exist. However, there is no
+known implementation based on a weaker general assumption.
+
+The concept of an informationally one-way function was introduced
+in \cite{imlelu:oneway}. We give only an informal definition here:
+
+\begin{defn}[one way] A polynomial time
+computable function $f = \{f_k\}$ is informationally
+one-way if there is no probabilistic polynomial time algorithm which
+(with probability of the form $1 - k^{-e}$ for some $e > 0$)
+returns on input $y \in \{0,1\}^{k}$ a random element of $f^{-1}(y)$.
+\end{defn}
+In the non-uniform setting \cite{imlelu:oneway} show that these are not
+weaker than one-way functions:
+\begin{thm}[\cite{imlelu:oneway} (non-uniform)]
+\label{th-info-ow-ow}
+The existence of informationally one-way functions
+implies the existence of one-way functions.
+\end{thm}
+We will stick to the convention introduced above of saying
+``non-uniform'' before the theorem statement when the theorem
+makes use of non-uniformity. It should be understood that
+if nothing is said then the result holds for both the uniform and
+the non-uniform models.
+
+It now follows from \thmref{th-info-ow-ow} that
+
+\begin{thm}[non-uniform]\label{th-weak-ske-owf} Weak SKE
+implies the existence of a one-way function.
+\end{thm}
+
+More recently, the polynomial-time, interior point algorithms for linear
+programming have been extended to the case of convex quadratic programs
+\cite{moad:quadpro,ye:intalg}, certain linear complementarity problems
+\cite{komiyo:lincomp,miyoki:lincomp}, and the nonlinear complementarity
+problem \cite{komiyo:unipfunc}. The connection between these algorithms
+and the classical Newton method for nonlinear equations is well
+explained in \cite{komiyo:lincomp}.
+
+\section{Review}
+\label{computation}
+
+We begin our discussion with the following definition:
+
+\begin{defn}
+
+A function $H\colon \Re^n \to \Re^n$ is said to be
+\emph{B-differentiable} at the point $z$ if (i)~$H$ is Lipschitz
+continuous in a neighborhood of $z$, and (ii)~ there exists a positive
+homogeneous function $BH(z)\colon \Re^n \to \Re^n$, called the
+\emph{B-derivative} of $H$ at $z$, such that
+\[ \lim_{v \to 0} \frac{H(z+v) - H(z) - BH(z)v}{\enVert{v}} = 0. \]
+The function $H$ is \textit{B-differentiable in set $S$} if it is
+B-differentiable at every point in $S$. The B-derivative $BH(z)$ is said
+to be \textit{strong} if
+\[ \lim_{(v,v') \to (0,0)} \frac{H(z+v) - H(z+v') - BH(z)(v
+ -v')}{\enVert{v - v'}} = 0. \]
+\end{defn}
+
+
+\begin{lem}\label{limbog} There exists a smooth function $\psi_0(z)$
+defined for $\abs{z}>1-2a$ satisfying the following properties\textup{:}
+\begin{enumerate}
+\renewcommand{\labelenumi}{(\roman{enumi})}
+\item $\psi_0(z)$ is bounded above and below by positive constants
+$c_1\leq \psi_0(z)\leq c_2$.
+\item If $\abs{z}>1$, then $\psi_0(z)=1$.
+\item For all $z$ in the domain of $\psi_0$, $\Delta_0\ln \psi_0\geq 0$.
+\item If $1-2a<\abs{z}<1-a$, then $\Delta_0\ln \psi_0\geq
+c_3>0$.
+\end{enumerate}
+\end{lem}
+
+\begin{proof}
+We choose $\psi_0(z)$ to be a radial function depending only on $r=\abs{z}$.
+Let $h(r)\geq 0$ be a suitable smooth function satisfying $h(r)\geq c_3$
+for $1-2a<\abs{z}<1-a$, and $h(r)=0$ for $\abs{z}>1-\tfrac a2$. The radial
+Laplacian
+\[\Delta_0\ln\psi_0(r)=\left(\frac {d^2}{dr^2}+\frac
+1r\frac d{dr}\right)\ln\psi_0(r)\]
+has smooth coefficients for $r>1-2a$. Therefore, we may
+apply the existence and uniqueness theory for ordinary differential
+equations. Simply let $\ln \psi_0(r)$ be the solution of the differential
+equation
+\[\left(\frac{d^2}{dr^2}+\frac 1r\frac d{dr}\right)\ln \psi_0(r)=h(r)\]
+with initial conditions given by $\ln \psi_0(1)=0$ and
+$\ln\psi_0'(1)=0$.
+
+Next, let $D_\nu$ be a finite collection of pairwise disjoint disks,
+all of which are contained in the unit disk centered at the origin in
+$C$. We assume that $D_\nu=\{z\mid \abs{z-z_\nu}<\delta\}$. Suppose that
+$D_\nu(a)$ denotes the smaller concentric disk $D_\nu(a)=\{z\mid
+\abs{z-z_\nu}\leq (1-2a)\delta\}$. We define a smooth weight function
+$\Phi_0(z)$ for $z\in C-\bigcup_\nu D_\nu(a)$ by setting $\Phi_
+0(z)=1$ when $z\notin \bigcup_\nu D_\nu$ and $\Phi_
+0(z)=\psi_0((z-z_\nu)/\delta)$ when $z$ is an element of $D_\nu$. It
+follows from \lemref{limbog} that $\Phi_ 0$ satisfies the properties:
+\begin{enumerate}
+\renewcommand{\labelenumi}{(\roman{enumi})}
+\item \label{boundab}$\Phi_ 0(z)$ is bounded above and below by
+positive constants $c_1\leq \Phi_ 0(z)\leq c_2$.
+\item \label{d:over}$\Delta_0\ln\Phi_ 0\geq 0$ for all
+$z\in C-\bigcup_\nu D_\nu(a)$,
+the domain where the function $\Phi_ 0$ is defined.
+\item \label{d:ad}$\Delta_0\ln\Phi_ 0\geq c_3\delta^{-2}$
+when $(1-2a)\delta<\abs{z-z_\nu}<(1-a)\delta$.
+\end{enumerate}
+Let $A_\nu$ denote the annulus $A_\nu=\{(1-2a)\delta<\abs{z-z_\nu}<(1-a)
+\delta \}$, and set $A=\bigcup_\nu A_\nu$. The
+properties (\ref{d:over}) and (\ref{d:ad}) of $\Phi_ 0$
+may be summarized as $\Delta_0\ln \Phi_ 0\geq c_3\delta^{-2}\chi_A$,
+where $\chi _A$ is the characteristic function of $A$.
+\end{proof}
+
+Suppose that $\alpha$ is a nonnegative real constant. We apply
+Proposition~\ref{prop:eg} with $\Phi(z)=\Phi_ 0(z) e^{\alpha\abs{z}^2}$. If
+$u\in C^\infty_0(R^2-\bigcup_\nu D_\nu(a))$, assume that $\mathcal{D}$
+is a bounded domain containing the support of $u$ and $A\subset
+\mathcal{D}\subset R^2-\bigcup_\nu D_\nu(a)$. A calculation gives
+\[\int_{\mathcal{D}}\abs{\overline\partial u}^2\Phi_ 0(z) e^{\alpha\abs{z}^2}
+\geq c_4\alpha\int_{\mathcal{D}}\abs{u}^2\Phi_ 0e^{\alpha\abs{z}^2}
++c_5\delta^{-2}\int_ A\abs{u}^2\Phi_ 0e^{\alpha\abs{z}^2}.\]
+
+The boundedness, property (\ref{boundab}) of $\Phi_ 0$, then yields
+\[\int_{\mathcal{D}}\abs{\overline\partial u}^2e^{\alpha\abs{z}^2}\geq c_6\alpha
+\int_{\mathcal{D}}\abs{u}^2e^{\alpha\abs{z}^2}
++c_7\delta^{-2}\int_ A\abs{u}^2e^{\alpha\abs{z}^2}.\]
+
+Let $B(X)$ be the set of blocks of $\Lambda_{X}$
+and let $b(X) = \abs{B(X)}$. If $\phi \in Q_{X}$ then
+$\phi$ is constant on the blocks of $\Lambda_{X}$.
+\begin{equation}\label{far-d}
+ P_{X} = \{ \phi \in M \mid \Lambda_{\phi} = \Lambda_{X} \},
+\qquad
+Q_{X} = \{\phi \in M \mid \Lambda_{\phi} \geq \Lambda_{X} \}.
+\end{equation}
+If $\Lambda_{\phi} \geq \Lambda_{X}$ then
+$\Lambda_{\phi} = \Lambda_{Y}$ for some $Y \geq X$ so that
+\[ Q_{X} = \bigcup_{Y \geq X} P_{Y}. \]
+Thus by M\"obius inversion
+\[ \abs{P_{Y}}= \sum_{X\geq Y} \mu (Y,X)\abs{Q_{X}}.\]
+Thus there is a bijection from $Q_{X}$ to $W^{B(X)}$.
+In particular $\abs{Q_{X}} = w^{b(X)}$.
+
+Next note that $b(X)=\dim X$. We see this by choosing a
+basis for $X$ consisting of vectors $v^{k}$ defined by
+\[v^{k}_{i}=
+\begin{cases} 1 & \text{if $i \in \Lambda_{k}$},\\
+0 &\text{otherwise.} \end{cases}
+\]
+\begin{verbatim}
+\[v^{k}_{i}=
+\begin{cases} 1 & \text{if $i \in \Lambda_{k}$},\\
+0 &\text{otherwise.} \end{cases}
+\]
+\end{verbatim}
+
+\begin{lem}\label{p0201}
+Let $\A$ be an arrangement. Then
+\[ \chi (\A,t) = \sum_{\B \subseteq \A}
+(-1)^{\abs{\B}} t^{\dim T(\B)}. \]
+\end{lem}
+
+In order to compute $R''$ recall the definition
+of $S(X,Y)$ from \lemref{lem-per}. Since $H \in \B$,
+$\A_{H} \subseteq \B$. Thus if $T(\B) = Y$ then
+$\B \in S(H,Y)$. Let $L'' = L(\A'')$. Then
+\begin{equation}\label{E_SXgYy}
+\begin{split}
+R''&= \sum_{H\in \B \subseteq \A} (-1)^{\abs{\B}}
+t^{\dim T(\B)}\\
+&= \sum_{Y \in L''} \sum_{\B \in S(H,Y)}
+(-1)^{\abs{\B}}t^{\dim Y} \\
+&= -\sum_{Y \in L''} \sum_{\B \in S(H,Y)} (-1)^
+{\abs{\B - \A_{H}}} t^{\dim Y} \\
+&= -\sum_{Y \in L''} \mu (H,Y)t^{\dim Y} \\
+&= -\chi (\A '',t).
+\end{split}
+\end{equation}
+
+\begin{cor}\label{tripleA}
+Let $(\A,\A',\A'')$ be a triple of arrangements. Then
+\[ \pi (\A,t) = \pi (\A',t) + t \pi (\A'',t). \]
+\end{cor}
+
+\begin{defn}
+Let $(\A,\A',\A'')$ be a triple with respect to
+the hyperplane $H \in \A$. Call $H$ a \textit{separator}
+if $T(\A) \not\in L(\A')$.
+\end{defn}
+
+\begin{cor}\label{nsep}
+Let $(\A,\A',\A'')$ be a triple with respect to $H \in \A$.
+\begin{enumerate}
+\renewcommand{\labelenumi}{(\roman{enumi})}
+\item
+If $H$ is a separator then
+\[ \mu (\A) = - \mu (\A'') \]
+and hence
+\[ \abs{\mu (\A)} = \abs{ \mu (\A'')}. \]
+
+\item If $H$ is not a separator then
+\[\mu (\A) = \mu (\A') - \mu (\A'') \]
+and
+\[ \abs{\mu (\A)} = \abs{\mu (\A')} + \abs{\mu (\A'')}. \]
+\end{enumerate}
+\end{cor}
+
+\begin{proof}
+It follows from \thmref{th-info-ow-ow} that $\pi(\A,t)$
+has leading term
+\[(-1)^{r(\A)}\mu (\A)t^{r(\A)}.\]
+The conclusion
+follows by comparing coefficients of the leading
+terms on both sides of the equation in
+Corollary~\ref{tripleA}. If $H$ is a separator then
+$r(\A') < r(\A)$ and there is no contribution
+from $\pi (\A',t)$.
+\end{proof}
+
+The Poincar\'e polynomial of an arrangement
+will appear repeatedly
+in these notes. It will be shown to equal the
+Poincar\'e polynomial
+of the graded algebras which we are going to
+associate with $\A$. It is also the Poincar\'e
+polynomial of the complement $M(\A)$ for a
+complex arrangement. Here we prove
+that the Poincar\'e polynomial is the chamber
+counting function for a real arrangement. The
+complement $M(\A)$ is a disjoint union of chambers
+\[M(\A) = \bigcup_{C \in \Cham(\A)} C.\]
+The number
+of chambers is determined by the Poincar\'e
+polynomial as follows.
+
+\begin{thm}\label{th-realarr}
+Let $\A_{\mathbf{R}}$ be a real arrangement. Then
+\[ \abs{\Cham(\A_{\mathbf{R}})} = \pi (\A_{\mathbf{R}},1). \]
+\end{thm}
+
+\begin{proof}
+We check the properties required in Corollary~\ref{nsep}:
+(i) follows from $\pi (\Phi_{ l},t) = 1$, and (ii) is a
+consequence of Corollary~\ref{BI}.
+\end{proof}
+
+\begin{figure}
+\vspace{5cm}
+\caption[]{$Q(\A_{1}) = xyz(x-z)(x+z)(y-z)(y+z)$}
+\end{figure}
+
+\begin{figure}
+\vspace{5cm}
+\caption[]{$Q(\A_{2})= xyz(x+y+z)(x+y-z)(x-y+z)(x-y-z)$}
+\end{figure}
+
+
+\begin{thm}
+\label{T_first_the_int}
+Let $\phi$ be a protocol for a random pair $\XcY$.
+If one of $\st_\phi(x',y)$ and $\st_\phi(x,y')$ is a prefix of the other
+and $(x,y)\in\SXY$, then
+\[
+\langle \st_j(x',y)\rangle_{j=1}^\infty
+=\langle \st_j(x,y)\rangle_{j=1}^\infty
+=\langle \st_j(x,y')\rangle_{j=1}^\infty .
+\]
+\end{thm}
+\begin{proof}
+We show by induction on $i$ that
+\[
+\langle \st_j(x',y)\rangle_{j=1}^i
+=\langle \st_j(x,y)\rangle_{j=1}^i
+=\langle \st_j(x,y')\rangle_{j=1}^i.
+\]
+The induction hypothesis holds vacuously for $i=0$. Assume it holds for
+$i-1$, in particular
+$[\st_j(x',y)]_{j=1}^{i-1}=[\st_j(x,y')]_{j=1}^{i-1}$. Then one of
+$[\st_j(x',y)]_{j=i}^{\infty}$ and $[\st_j(x,y')]_{j=i}^{\infty}$ is a
+prefix of the other which implies that one of $\st_i(x',y)$ and
+$\st_i(x,y')$ is a prefix of the other. If the $i$th message is
+transmitted by $P_\X$ then, by the separate-transmissions property and
+the induction hypothesis, $\st_i(x,y)=\st_i(x,y')$, hence one of
+$\st_i(x,y)$ and $\st_i(x',y)$ is a prefix of the other. By the
+implicit-termination property, neither $\st_i(x,y)$ nor $\st_i(x',y)$
+can be a proper prefix of the other, hence they must be the same and
+$\st_i(x',y)=\st_i(x,y)=\st_i(x,y')$. If the $i$th message is
+transmitted by $\PY$ then, symmetrically, $\st_i(x,y)=\st_i(x',y)$ by
+the induction hypothesis and the separate-transmissions property, and,
+then, $\st_i(x,y)=\st_i(x,y')$ by the implicit-termination property,
+proving the induction step.
+\end{proof}
+
+If $\phi$ is a protocol for $(X,Y)$, and $(x,y)$, $(x',y)$ are distinct
+inputs in $\SXY$, then, by the correct-decision property,
+$\langle\st_j(x,y)\rangle_{j=1}^\infty\ne\langle
+\st_j(x',y)\rangle_{j=1}^\infty$.
+
+Equation~(\ref{E_SXgYy}) defined $\PY$'s ambiguity set $\SXgYy$
+to be the set of possible $X$ values when $Y=y$.
+The last corollary implies that for all $y\in\SY$,
+the multiset%
+\footnote{A multiset allows multiplicity of elements.
+Hence, $\{0,01,01\}$ is prefix free as a set, but not as a multiset.}
+of codewords $\{\st_\phi(x,y):x\in\SXgYy\}$ is prefix free.
+
+\section{One-way complexity}
+\label{S_Cp1}
+
+$\Cw1$, the one-way complexity of a random pair $\XcY$,
+is the number of bits $P_\X$ must transmit in the worst case
+when $\PY$ is not permitted to transmit any feedback messages.
+Starting with $\SXY$, the support set of $\XcY$, we define $\G$,
+the \textit{characteristic hypergraph} of $\XcY$, and show that
+\[
+\Cw1=\lceil\,\log\chi(\G)\rceil\ .
+\]
+
+Let $\XcY$ be a random pair. For each $y$ in $\SY$, the support set of
+$Y$, equation~(\ref{E_SXgYy}) defined $\SXgYy$ to be the set of possible
+$x$ values when $Y=y$. The \textit{characteristic hypergraph} $\G$ of
+$\XcY$ has $\SX$ as its vertex set and the hyperedge $\SXgYy$ for each
+$y\in\SY$.
+
+
+We can now prove a continuity theorem.
+\begin{thm}\label{t:conl}
+Let $\Omega \subset\mathbf{R}^n$ be an open set, let
+$u\in BV(\Omega ;\mathbf{R}^m)$, and let
+\begin{equation}\label{quts}
+T^u_x=\left\{y\in\mathbf{R}^m:
+ y=\tilde u(x)+\left\langle \frac{Du}{\abs{Du}}(x),z
+\right\rangle \text{ for some }z\in\mathbf{R}^n\right\}
+\end{equation}
+for every $x\in\Omega \backslash S_u$. Let $f\colon \mathbf{R}^m\to
+\mathbf{R}^k$ be a Lipschitz continuous function such that $f(0)=0$, and
+let $v=f(u)\colon \Omega \to \mathbf{R}^k$. Then $v\in BV(\Omega
+;\mathbf{R}^k)$ and
+\begin{equation}
+Jv=\eval{(f(u^+)-f(u^-))\otimes \nu_u\cdot\,
+\mathcal{H}_{n-1}}_{S_u}.
+\end{equation}
+In addition, for $\abs{\wt{D}u}$-almost every $x\in\Omega $ the
+restriction of the function $f$ to $T^u_x$ is differentiable at $\tilde
+u(x)$ and
+\begin{equation}
+\wt{D}v=\nabla (\eval{f}_{T^u_x})(\tilde u)
+\frac{\wt{D}u}{\abs{\wt{D}u}}\cdot\abs{\wt{D}u}.\end{equation}
+\end{thm}
+
+Before proving the theorem, we state without proof three elementary
+remarks which will be useful in the sequel.
+\begin{rem}\label{r:omb}
+Let $\omega\colon \left]0,+\infty\right[\to \left]0,+\infty\right[$
+be a continuous function such that $\omega (t)\to 0$ as $t\to
+0$. Then
+\[\lim_{h\to 0^+}g(\omega(h))=L\Leftrightarrow\lim_{h\to
+0^+}g(h)=L\]
+for any function $g\colon \left]0,+\infty\right[\to \mathbf{R}$.
+\end{rem}
+\begin{rem}\label{r:dif}
+Let $g \colon \mathbf{R}^n\to \mathbf{R}$ be a Lipschitz
+continuous function and assume that
+\[L(z)=\lim_{h\to 0^+}\frac{g(hz)-g(0)}h\]
+exists for every $z\in\mathbf{Q}^n$ and that $L$ is a linear function of
+$z$. Then $g$ is differentiable at 0.
+\end{rem}
+\begin{rem}\label{r:dif0}
+Let $A \colon \mathbf{R}^n\to \mathbf{R}^m$ be a linear function, and
+let $f \colon \mathbf{R}^m\to \mathbf{R}$ be a function. Then the
+restriction of $f$ to the range of $A$ is differentiable at 0 if and
+only if $f(A)\colon \mathbf{R}^n\to \mathbf{R}$ is differentiable at 0
+and
+\[\nabla(\eval{f}_{\IM(A)})(0)A=\nabla (f(A))(0).\]
+\end{rem}
+
+\begin{proof}
+ We begin by showing that $v\in BV(\Omega;\mathbf{R}^k)$ and
+\begin{equation}\label{e:bomb}
+\abs{Dv}(B)\le K\abs{Du}(B)\qquad\forall B\in\mathbf{B}(\Omega ),
+\end{equation}
+where $K>0$ is the Lipschitz constant of $f$. By \eqref{sum-Di} and by
+the approximation result quoted in \secref{s:mt}, it is possible to find
+a sequence $(u_h)\subset C^1(\Omega ;\mathbf{R}^m)$ converging to $u$ in
+$L^1(\Omega ;\mathbf{R}^m)$ and such that
+\[\lim_{h\to +\infty}\int_\Omega \abs{\nabla u_h}\,dx=\abs{Du}(\Omega ).\]
+The functions $v_h=f(u_h)$ are locally Lipschitz continuous in $\Omega
+$, and the definition of differential implies that $\abs{\nabla v_h}\le
+K\abs{\nabla u_h}$ almost everywhere in $\Omega $. The lower semicontinuity
+of the total variation and \eqref{sum-Di} yield
+\begin{equation}
+\begin{split}
+\abs{Dv}(\Omega )\le\liminf_{h\to +\infty}\abs{Dv_h}(\Omega) &
+=\liminf_{h\to +\infty}\int_\Omega \abs{\nabla v_h}\,dx\\
+&\le K\liminf_{h\to +\infty}\int_\Omega
+\abs{\nabla u_h}\,dx=K\abs{Du}(\Omega).
+\end{split}\end{equation}
+Since $f(0)=0$, we have also
+\[\int_\Omega \abs{v}\,dx\le K\int_\Omega \abs{u}\,dx;\]
+therefore $u\in BV(\Omega ;\mathbf{R}^k)$. Repeating the same argument
+for every open set $A\subset\Omega $, we get \eqref{e:bomb} for every
+$B\in\mathbf{B}(\Omega)$, because $\abs{Dv}$, $\abs{Du}$ are Radon measures. To
+prove \lemref{limbog}, first we observe that
+\begin{equation}\label{e:SS}
+S_v\subset S_u,\qquad\tilde v(x)=f(\tilde u(x))\qquad \forall x\in\Omega
+\backslash S_u.\end{equation}
+In fact, for every $\varepsilon >0$ we have
+\[\{y\in B_\rho(x): \abs{v(y)-f(\tilde u(x))}>\varepsilon \}\subset \{y\in
+B_\rho(x): \abs{u(y)-\tilde u(x)}>\varepsilon /K\},\]
+hence
+\[\lim_{\rho\to 0^+}\frac{\abs{\{y\in B_\rho(x): \abs{v(y)-f(\tilde u(x))}>
+\varepsilon \}}}{\rho^n}=0\]
+whenever $x\in\Omega \backslash S_u$. By a similar argument, if $x\in
+S_u$ is a point such that there exists a triplet $(u^+,u^-,\nu_u)$
+satisfying \eqref{detK1}, \eqref{detK2}, then
+\[
+(v^+(x)-v^-(x))\otimes \nu_v=(f(u^+(x))-f(u^-(x)))\otimes\nu_u\quad
+\text{if }x\in S_v
+\]
+and $f(u^-(x))=f(u^+(x))$ if $x\in S_u\backslash S_v$. Hence, by (1.8)
+we get
+\begin{equation*}\begin{split}
+Jv(B)=\int_{B\cap S_v}(v^+-v^-)\otimes \nu_v\,d\mathcal{H}_{n-1}&=
+\int_{B\cap S_v}(f(u^+)-f(u^-))\otimes \nu_u\,d\mathcal{H}_{n-1}\\
+&=\int_{B\cap S_u}(f(u^+)-f(u^-))\otimes \nu_u\,d\mathcal{H}_{n-1}
+\end{split}\end{equation*}
+and \lemref{limbog} is proved.
+\end{proof}
+
+To prove \eqref{e:SS}, it is not restrictive to assume that $k=1$.
+Moreover, to simplify our notation, from now on we shall assume that
+$\Omega = \mathbf{R}^n$. The proof of \eqref{e:SS} is divided into two
+steps. In the first step we prove the statement in the one-dimensional
+case $(n=1)$, using \thmref{th-weak-ske-owf}. In the second step we
+achieve the general result using \thmref{t:conl}.
+
+\begin{step}
+Assume that $n=1$. Since $S_u$ is at most countable, \eqref{sum-bij}
+yields that $\abs{\wt{D}v}(S_u\backslash S_v)=0$, so that
+\eqref{e:st} and \eqref{e:barwq} imply that $Dv=\wt{D}v+Jv$ is
+the Radon-Nikod\'ym decomposition of $Dv$ in absolutely continuous and
+singular part with respect to $\abs{\wt{D} u}$. By
+\thmref{th-weak-ske-owf}, we have
+\begin{equation*}
+\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{s\to t^+}
+\frac{Dv(\interval{\left[t,s\right[})}
+{\abs{\wt{D}u}(\interval{\left[t,s\right[})},\qquad
+\frac{\wt{D}u}{\abs{\wt{D}u}}(t)=\lim_{s\to t^+}
+\frac{Du(\interval{\left[t,s\right[})}
+{\abs{\wt{D}u}(\interval{\left[t,s\right[})}
+\end{equation*}
+$\abs{\wt{D}u}$-almost everywhere in $\mathbf{R}$. It is well known
+(see, for instance, \cite[2.5.16]{ste:sint}) that every one-dimensional
+function of bounded variation $w$ has a unique left continuous
+representative, i.e., a function $\hat w$ such that $\hat w=w$ almost
+everywhere and $\lim_{s\to t^-}\hat w(s)=\hat w(t)$ for every $t\in
+\mathbf{R}$. These conditions imply
+\begin{equation}
+\hat u(t)=Du(\interval{\left]-\infty,t\right[}),
+\qquad \hat v(t)=Dv(\interval{\left]-\infty,t\right[})\qquad
+\forall t\in\mathbf{R}
+\end{equation}
+and
+\begin{equation}\label{alimo}
+\hat v(t)=f(\hat u(t))\qquad\forall t\in\mathbf{R}.\end{equation}
+Let $t\in\mathbf{R}$ be such that
+$\abs{\wt{D}u}(\interval{\left[t,s\right[})>0$ for every $s>t$ and
+assume that the limits in \eqref{joe} exist. By \eqref{j:mark} and
+\eqref{far-d} we get
+\begin{equation*}\begin{split}
+\frac{\hat v(s)-\hat
+v(t)}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}&=\frac {f(\hat
+u(s))-f(\hat u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\\
+&=\frac{f(\hat u(s))-f(\hat
+u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)\abs{\wt{D}u
+}(\interval{\left[t,s\right[}))}%
+{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\\
+&+\frac
+{f(\hat u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)\abs{\wt{D}
+u}(\interval{\left[t,s\right[}))-f(\hat
+u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}
+\end{split}\end{equation*}
+for every $s>t$. Using the Lipschitz condition on $f$ we find
+{\setlength{\multlinegap}{0pt}
+\begin{multline*}
+\left\lvert\frac{\hat v(s)-\hat
+v(t)}{\abs{\wt{D}u}(\interval{\left[t,s\right[})} -\frac{f(\hat
+u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)
+\abs{\wt{D}u}(\interval{\left[t,s\right[}))-f(\hat
+u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\right\rvert\\
+\le K\left\lvert
+\frac{\hat u(s)-\hat u(t)}
+ {\abs{\wt{D}u}(\interval{\left[t,s\right[})}
+-\frac{\wt{D}u}{\abs{
+\wt{D}u}}(t)\right\rvert.\end{multline*}
+}% end of group with \multlinegap=0pt
+By \eqref{e:bomb}, the function $s\to
+\abs{\wt{D}u}(\interval{\left[t,s\right[})$ is continuous and
+converges to 0 as $s\downarrow t$. Therefore Remark~\ref{r:omb} and the
+previous inequality imply
+\[\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{h\to 0^+}
+\frac{f(\hat u(t)+h\dfrac{\wt{D}u}{\abs{\wt{D}u}}
+(t))-f(\hat u(t))}h\quad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}.\]
+By \eqref{joe}, $\hat u(x)=\tilde u(x)$ for every
+$x\in\mathbf{R}\backslash S_u$; moreover, applying the same argument to
+the functions $u'(t)=u(-t)$, $v'(t)=f(u'(t))=v(-t)$, we get
+\[\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{h\to 0}
+\frac{f(\tilde u(t)
++h\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t))-f(\tilde u(t))}{h}
+\qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}\]
+and our statement is proved.
+\end{step}
+
+\begin{step}
+Let us consider now the general case $n>1$. Let $\nu\in \mathbf{R}^n$ be
+such that $\abs{\nu}=1$, and let $\pi_\nu=\{y\in\mathbf{R}^n: \langle
+y,\nu\rangle =0\}$. In the following, we shall identify $\mathbf{R}^n$
+with $\pi_\nu\times\mathbf{R}$, and we shall denote by $y$ the variable
+ranging in $\pi_\nu$ and by $t$ the variable ranging in $\mathbf{R}$. By
+the just proven one-dimensional result, and by \thmref{thm-main}, we get
+\[\lim_{h\to 0}\frac{f(\tilde u(y+t\nu)+h\dfrac{\wt{D}u_y}{\abs{
+\wt{D}u_y}}(t))-f(\tilde u(y+t\nu))}h=\frac{\wt{D}v_y}{\abs{
+\wt{D}u_y}}(t)\qquad\abs{\wt{D}u_y}\text{-a.e. in }\mathbf{R}\]
+for $\mathcal{H}_{n-1}$-almost every $y\in \pi_\nu$. We claim that
+\begin{equation}
+\frac{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle
+}}(y+t\nu)=\frac{\wt{D}u_y}
+{\abs{\wt{D}u_y}}(t)\qquad\abs{\wt{D}u_y}\text{-a.e. in }\mathbf{R}
+\end{equation}
+for $\mathcal{H}_{n-1}$-almost every $y\in\pi_\nu$. In fact, by
+\eqref{sum-ali} and \eqref{delta-l} we get
+\begin{multline*}
+\int_{\pi_\nu}\frac{\wt{D}u_y}{\abs{\wt{D}u_y}}\cdot\abs{\wt{D}u_y
+}\,d\mathcal{H}_{n-1}(y)=\int_{\pi_\nu}\wt{D}u_y\,d\mathcal{H}_{n-1}(y)\\
+=\langle \wt{D}u,\nu\rangle =\frac
+{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}}\cdot
+\abs{\langle \wt{D}u,\nu\rangle }=\int_{\pi_\nu}\frac{
+\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}
+(y+\cdot \nu)\cdot\abs{\wt{D}u_y}\,d\mathcal{H}_{n-1}(y)
+\end{multline*}
+and \eqref{far-d} follows from \eqref{sum-Di}. By the same argument it
+is possible to prove that
+\begin{equation}
+\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle
+}}(y+t\nu)=\frac{\wt{D}v_y}{\abs{\wt{D}u_y}}(t)\qquad\abs{
+\wt{D}u_y}\text{-a.e. in }\mathbf{R}\end{equation}
+for $\mathcal{H}_{n-1}$-almost every $y\in \pi_\nu$. By \eqref{far-d}
+and \eqref{E_SXgYy} we get
+\[
+\lim_{h\to 0}\frac{f(\tilde u(y+t\nu)+h\dfrac{\langle \wt{D}
+u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(y+t\nu))-f(\tilde
+u(y+t\nu))}{h}
+=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle
+\wt{D}u,\nu\rangle }}(y+t\nu)\]
+for $\mathcal{H}_{n-1}$-almost every $y\in\pi_\nu$, and using again
+\eqref{detK1}, \eqref{detK2} we get
+\[
+\lim_{h\to 0}\frac{f(\tilde u(x)+h\dfrac{\langle
+\wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(x))-f(\tilde
+u(x))}{h}=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu
+\rangle }}(x)
+\]
+$\abs{\langle \wt{D}u,\nu\rangle}$-a.e. in $\mathbf{R}^n$.
+
+Since the function $\abs{\langle \wt{D}u,\nu\rangle }/\abs{\wt{D}u}$
+is strictly positive $\abs{\langle \wt{D}u,\nu\rangle }$-almost everywhere,
+we obtain also
+\begin{multline*}
+\lim_{h\to 0}\frac{f(\tilde u(x)+h\dfrac{\abs{\langle
+\wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}(x)\dfrac{\langle \wt{D}
+u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(x))-f(\tilde u(x))}{h}\\
+=\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}(x)\frac
+{\langle \wt{D}v,\nu\rangle }{\abs{\langle
+\wt{D}u,\nu\rangle }}(x)
+\end{multline*}
+$\abs{\langle \wt{D}u,\nu\rangle }$-almost everywhere in $\mathbf{R}^n$.
+
+Finally, since
+\begin{align*}
+&\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}
+\frac{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}}
+=\frac{\langle \wt{D}u,\nu\rangle }{\abs{\wt{D}u}}
+=\left\langle \frac{\wt{D}u}{\abs{\wt{D}u}},\nu\right\rangle
+ \qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}^n\\
+&\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}
+\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}}
+=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\wt{D}u}}
+=\left\langle \frac{\wt{D}v}{\abs{\wt{D}u}},\nu\right\rangle
+ \qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}^n
+\end{align*}
+and since both sides of \eqref{alimo}
+are zero $\abs{\wt{D}u}$-almost everywhere
+on $\abs{\langle \wt{D}u,\nu\rangle }$-negligible sets, we conclude that
+\[
+\lim_{h\to 0}\frac{f\left(
+\tilde u(x)+h\left\langle \dfrac{\wt{D}
+u}{\abs{\wt{D}u}}(x),\nu\right\rangle \right)-f(\tilde u(x))}h
+=\left\langle \frac{\wt{D}v}{\abs{\wt{D}u}}(x),\nu\right\rangle,
+\]
+$\abs{\wt{D}u}$-a.e. in $\mathbf{R}^n$.
+Since $\nu$ is arbitrary, by Remarks \ref{r:dif} and~\ref{r:dif0}
+the restriction of $f$ to
+the affine space $T^u_x$ is differentiable at $\tilde u(x)$ for $\abs{\wt{D}
+u}$-almost every $x\in \mathbf{R}^n$ and \eqref{quts} holds.\qed
+\end{step}
+
+It follows from \eqref{sum-Di}, \eqref{detK1}, and \eqref{detK2} that
+\begin{equation}\label{Dt}
+D(t_1,\dots,t_n)=\sum_{I\in\mathbf{n}}(-1)^{\abs{I}-1}\abs{I}
+\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A}^{(\lambda)}
+(\overline I|\overline I).
+\end{equation}
+Let $t_i=\hat x_i$, $i=1,\dots,n$. Lemma 1 leads to
+\begin{equation}\label{Dx}
+D(\hat x_1,\dots,\hat x_n)=\prod_{i\in\mathbf{n}}\hat x_i
+\sum_{I\in\mathbf{n}}(-1)^{\abs{I}-1}\abs{I}\per \mathbf{A}
+^{(\lambda)}(I|I)\det\mathbf{A}^{(\lambda)}(\overline I|\overline I).
+\end{equation}
+By \eqref{H-cycles}, \eqref{sum-Di}, and \eqref{Dx},
+we have the following result:
+\begin{thm}\label{thm-H-param}
+\begin{equation}\label{H-param}
+H_c=\frac{1}{2n}\sum^n_{l =1}l (-1)^{l -1}A_{l}
+^{(\lambda)},
+\end{equation}
+where
+\begin{equation}\label{A-l-lambda}
+A^{(\lambda)}_l =\sum_{I_l \subseteq\mathbf{n}}\per \mathbf{A}
+^{(\lambda)}(I_l |I_l )\det\mathbf{A}^{(\lambda)}
+(\overline I_{l}|\overline I_l ),\abs{I_{l}}=l .
+\end{equation}
+\end{thm}
+
+It is worth noting that $A_l ^{(\lambda)}$ of \eqref{A-l-lambda} is
+similar to the coefficients $b_l $ of the characteristic polynomial of
+\eqref{bl-sum}. It is well known in graph theory that the coefficients
+$b_l $ can be expressed as a sum over certain subgraphs. It is
+interesting to see whether $A_l $, $\lambda=0$, structural properties
+of a graph.
+
+We may call \eqref{H-param} a parametric representation of $H_c$. In
+computation, the parameter $\lambda_i$ plays very important roles. The
+choice of the parameter usually depends on the properties of the given
+graph. For a complete graph $K_n$, let $\lambda_i=1$, $i=1,\dots,n$.
+It follows from \eqref{A-l-lambda} that
+\begin{equation}\label{compl-gr}
+A^{(1)}_l =\begin{cases} n!,&\text{if }l =1\\
+0,&\text{otherwise}.\end{cases}
+\end{equation}
+By \eqref{H-param}
+\begin{equation}
+H_c=\frac 12(n-1)!.
+\end{equation}
+For a complete bipartite graph $K_{n_1n_2}$, let $\lambda_i=0$, $i=1,\dots,n$.
+By \eqref{A-l-lambda},
+\begin{equation}
+A_l =
+\begin{cases} -n_1!n_2!\delta_{n_1n_2},&\text{if }l =2\\
+0,&\text{otherwise }.\end{cases}
+\label{compl-bip-gr}
+\end{equation}
+Theorem ~\ref{thm-H-param}
+leads to
+\begin{equation}
+H_c=\frac1{n_1+n_2}n_1!n_2!\delta_{n_1n_2}.
+\end{equation}
+
+Now, we consider an asymmetrical approach. Theorem \ref{thm-main} leads to
+\begin{multline}
+\det\mathbf{K}(t=1,t_1,\dots,t_n;l |l )\\
+=\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\abs{I}}\prod_{i\in I}t_i\prod_{j\in I}
+(D_j+\lambda_jt_j)\det\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \}).
+\end{multline}
+
+By \eqref{H-cycles} and \eqref{sum-ali} we have the following asymmetrical
+result:
+\begin{thm}\label{thm-asym}
+\begin{equation}
+H_c=\frac12\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\abs{I}}\per\mathbf{A}^{(\lambda)}(I|I)\det
+\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \})
+\end{equation}
+which reduces to Goulden--Jackson's formula when $\lambda_i=0,i=1,\dots,n$
+\cite{mami:matrixth}.
+\end{thm}
+
+
+\section{Various font features of the \pkg{amsmath} package}
+\label{s:font}
+\subsection{Bold versions of special symbols}
+
+In the \pkg{amsmath} package \cn{boldsymbol} is used for getting
+individual bold math symbols and bold Greek letters---everything in
+math except for letters of the Latin alphabet,
+where you'd use \cn{mathbf}. For example,
+\begin{verbatim}
+A_\infty + \pi A_0 \sim
+\mathbf{A}_{\boldsymbol{\infty}} \boldsymbol{+}
+\boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}
+\end{verbatim}
+looks like this:
+\[A_\infty + \pi A_0 \sim \mathbf{A}_{\boldsymbol{\infty}}
+\boldsymbol{+} \boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}\]
+
+\subsection{``Poor man's bold''}
+If a bold version of a particular symbol doesn't exist in the
+available fonts,
+then \cn{boldsymbol} can't be used to make that symbol bold.
+At the present time, this means that
+\cn{boldsymbol} can't be used with symbols from
+the \fn{msam} and \fn{msbm} fonts, among others.
+In some cases, poor man's bold (\cn{pmb}) can be used instead
+of \cn{boldsymbol}:
+% Can't show example from msam or msbm because this document is
+% supposed to be TeXable even if the user doesn't have
+% AMSFonts. MJD 5-JUL-1990
+\[\frac{\partial x}{\partial y}
+\pmb{\bigg\vert}
+\frac{\partial y}{\partial z}\]
+\begin{verbatim}
+\[\frac{\partial x}{\partial y}
+\pmb{\bigg\vert}
+\frac{\partial y}{\partial z}\]
+\end{verbatim}
+So-called ``large operator'' symbols such as $\sum$ and $\prod$
+require an additional command, \cn{mathop},
+to produce proper spacing and limits when \cn{pmb} is used.
+For further details see \textit{The \TeX book}.
+\[\sum_{\substack{i<B\\\text{$i$ odd}}}
+\prod_\kappa \kappa F(r_i)\qquad
+\mathop{\pmb{\sum}}_{\substack{i<B\\\text{$i$ odd}}}
+\mathop{\pmb{\prod}}_\kappa \kappa(r_i)
+\]
+\begin{verbatim}
+\[\sum_{\substack{i<B\\\text{$i$ odd}}}
+\prod_\kappa \kappa F(r_i)\qquad
+\mathop{\pmb{\sum}}_{\substack{i<B\\\text{$i$ odd}}}
+\mathop{\pmb{\prod}}_\kappa \kappa(r_i)
+\]
+\end{verbatim}
+
+\section{Compound symbols and other features}
+\label{s:comp}
+\subsection{Multiple integral signs}
+\cn{iint}, \cn{iiint}, and \cn{iiiint} give multiple integral signs
+with the spacing between them nicely adjusted, in both text and
+display style. \cn{idotsint} gives two integral signs with dots
+between them.
+\begin{gather}
+\iint\limits_A f(x,y)\,dx\,dy\qquad\iiint\limits_A
+f(x,y,z)\,dx\,dy\,dz\\
+\iiiint\limits_A
+f(w,x,y,z)\,dw\,dx\,dy\,dz\qquad\idotsint\limits_A f(x_1,\dots,x_k)
+\end{gather}
+
+\subsection{Over and under arrows}
+Some extra over and under arrow operations are provided in
+the \pkg{amsmath} package. (Basic \LaTeX\ provides
+\cn{overrightarrow} and \cn{overleftarrow}).
+\begin{align*}
+\overrightarrow{\psi_\delta(t) E_t h}&
+=\underrightarrow{\psi_\delta(t) E_t h}\\
+\overleftarrow{\psi_\delta(t) E_t h}&
+=\underleftarrow{\psi_\delta(t) E_t h}\\
+\overleftrightarrow{\psi_\delta(t) E_t h}&
+=\underleftrightarrow{\psi_\delta(t) E_t h}
+\end{align*}
+\begin{verbatim}
+\begin{align*}
+\overrightarrow{\psi_\delta(t) E_t h}&
+=\underrightarrow{\psi_\delta(t) E_t h}\\
+\overleftarrow{\psi_\delta(t) E_t h}&
+=\underleftarrow{\psi_\delta(t) E_t h}\\
+\overleftrightarrow{\psi_\delta(t) E_t h}&
+=\underleftrightarrow{\psi_\delta(t) E_t h}
+\end{align*}
+\end{verbatim}
+These all scale properly in subscript sizes:
+\[\int_{\overrightarrow{AB}} ax\,dx\]
+\begin{verbatim}
+\[\int_{\overrightarrow{AB}} ax\,dx\]
+\end{verbatim}
+
+\subsection{Dots}
+
+Normally you need only type \cn{dots} for ellipsis dots in a
+math formula. The main exception is when the dots
+fall at the end of the formula; then you need to
+specify one of \cn{dotsc} (series dots, after a comma),
+\cn{dotsb} (binary dots, for binary relations or operators),
+\cn{dotsm} (multiplication dots), or \cn{dotsi} (dots after
+an integral). For example, the input
+\begin{verbatim}
+Then we have the series $A_1,A_2,\dotsc$,
+the regional sum $A_1+A_2+\dotsb$,
+the orthogonal product $A_1A_2\dotsm$,
+and the infinite integral
+\[\int_{A_1}\int_{A_2}\dotsi\].
+\end{verbatim}
+produces
+\begin{quotation}
+Then we have the series $A_1,A_2,\dotsc$,
+the regional sum $A_1+A_2+\dotsb$,
+the orthogonal product $A_1A_2\dotsm$,
+and the infinite integral
+\[\int_{A_1}\int_{A_2}\dotsi\]
+\end{quotation}
+
+\subsection{Accents in math}
+
+Double accents:
+\[\Hat{\Hat{H}}\quad\Check{\Check{C}}\quad
+\Tilde{\Tilde{T}}\quad\Acute{\Acute{A}}\quad
+\Grave{\Grave{G}}\quad\Dot{\Dot{D}}\quad
+\Ddot{\Ddot{D}}\quad\Breve{\Breve{B}}\quad
+\Bar{\Bar{B}}\quad\Vec{\Vec{V}}\]
+\begin{verbatim}
+\[\Hat{\Hat{H}}\quad\Check{\Check{C}}\quad
+\Tilde{\Tilde{T}}\quad\Acute{\Acute{A}}\quad
+\Grave{\Grave{G}}\quad\Dot{\Dot{D}}\quad
+\Ddot{\Ddot{D}}\quad\Breve{\Breve{B}}\quad
+\Bar{\Bar{B}}\quad\Vec{\Vec{V}}\]
+\end{verbatim}
+This double accent operation is complicated
+and tends to slow down the processing of a \LaTeX\ file.
+
+
+\subsection{Dot accents}
+\cn{dddot} and \cn{ddddot} are available to
+produce triple and quadruple dot accents
+in addition to the \cn{dot} and \cn{ddot} accents already available
+in \LaTeX:
+\[\dddot{Q}\qquad\ddddot{R}\]
+\begin{verbatim}
+\[\dddot{Q}\qquad\ddddot{R}\]
+\end{verbatim}
+
+\subsection{Roots}
+
+In the \pkg{amsmath} package \cn{leftroot} and \cn{uproot} allow you to adjust
+the position of the root index of a radical:
+\begin{verbatim}
+\sqrt[\leftroot{-2}\uproot{2}\beta]{k}
+\end{verbatim}
+gives good positioning of the $\beta$:
+\[\sqrt[\leftroot{-2}\uproot{2}\beta]{k}\]
+
+\subsection{Boxed formulas} The command \cn{boxed} puts a box around its
+argument, like \cn{fbox} except that the contents are in math mode:
+\begin{verbatim}
+\boxed{W_t-F\subseteq V(P_i)\subseteq W_t}
+\end{verbatim}
+\[\boxed{W_t-F\subseteq V(P_i)\subseteq W_t}.\]
+
+\subsection{Extensible arrows}
+\cn{xleftarrow} and \cn{xrightarrow} produce
+arrows that extend automatically to accommodate unusually wide
+subscripts or superscripts. The text of the subscript or superscript
+are given as an optional resp.\@ mandatory argument:
+Example:
+\[0 \xleftarrow[\zeta]{\alpha} F\times\triangle[n-1]
+ \xrightarrow{\partial_0\alpha(b)} E^{\partial_0b}\]
+\begin{verbatim}
+\[0 \xleftarrow[\zeta]{\alpha} F\times\triangle[n-1]
+ \xrightarrow{\partial_0\alpha(b)} E^{\partial_0b}\]
+\end{verbatim}
+
+\subsection{\cn{overset}, \cn{underset}, and \cn{sideset}}
+Examples:
+\[\overset{*}{X}\qquad\underset{*}{X}\qquad
+\overset{a}{\underset{b}{X}}\]
+\begin{verbatim}
+\[\overset{*}{X}\qquad\underset{*}{X}\qquad
+\overset{a}{\underset{b}{X}}\]
+\end{verbatim}
+
+The command \cn{sideset} is for a rather special
+purpose: putting symbols at the subscript and superscript
+corners of a large operator symbol such as $\sum$ or $\prod$,
+without affecting the placement of limits.
+Examples:
+\[\sideset{_*^*}{_*^*}\prod_k\qquad
+\sideset{}{'}\sum_{0\le i\le m} E_i\beta x
+\]
+\begin{verbatim}
+\[\sideset{_*^*}{_*^*}\prod_k\qquad
+\sideset{}{'}\sum_{0\le i\le m} E_i\beta x
+\]
+\end{verbatim}
+
+\subsection{The \cn{text} command}
+The main use of the command \cn{text} is for words or phrases in a
+display:
+\[\mathbf{y}=\mathbf{y}'\quad\text{if and only if}\quad
+y'_k=\delta_k y_{\tau(k)}\]
+\begin{verbatim}
+\[\mathbf{y}=\mathbf{y}'\quad\text{if and only if}\quad
+y'_k=\delta_k y_{\tau(k)}\]
+\end{verbatim}
+
+\subsection{Operator names}
+The more common math functions such as $\log$, $\sin$, and $\lim$
+have predefined control sequences: \verb=\log=, \verb=\sin=,
+\verb=\lim=.
+The \pkg{amsmath} package provides \cn{DeclareMathOperator} and
+\cn{DeclareMathOperator*}
+for producing new function names that will have the
+same typographical treatment.
+Examples:
+\[\norm{f}_\infty=
+\esssup_{x\in R^n}\abs{f(x)}\]
+\begin{verbatim}
+\[\norm{f}_\infty=
+\esssup_{x\in R^n}\abs{f(x)}\]
+\end{verbatim}
+\[\meas_1\{u\in R_+^1\colon f^*(u)>\alpha\}
+=\meas_n\{x\in R^n\colon \abs{f(x)}\geq\alpha\}
+\quad \forall\alpha>0.\]
+\begin{verbatim}
+\[\meas_1\{u\in R_+^1\colon f^*(u)>\alpha\}
+=\meas_n\{x\in R^n\colon \abs{f(x)}\geq\alpha\}
+\quad \forall\alpha>0.\]
+\end{verbatim}
+\cn{esssup} and \cn{meas} would be defined in the document preamble as
+\begin{verbatim}
+\DeclareMathOperator*{\esssup}{ess\,sup}
+\DeclareMathOperator{\meas}{meas}
+\end{verbatim}
+
+The following special operator names are predefined in the \pkg{amsmath}
+package: \cn{varlimsup}, \cn{varliminf}, \cn{varinjlim}, and
+\cn{varprojlim}. Here's what they look like in use:
+\begin{align}
+&\varlimsup_{n\rightarrow\infty}
+ \mathcal{Q}(u_n,u_n-u^{\#})\le0\\
+&\varliminf_{n\rightarrow\infty}
+ \left\lvert a_{n+1}\right\rvert/\left\lvert a_n\right\rvert=0\\
+&\varinjlim (m_i^\lambda\cdot)^*\le0\\
+&\varprojlim_{p\in S(A)}A_p\le0
+\end{align}
+\begin{verbatim}
+\begin{align}
+&\varlimsup_{n\rightarrow\infty}
+ \mathcal{Q}(u_n,u_n-u^{\#})\le0\\
+&\varliminf_{n\rightarrow\infty}
+ \left\lvert a_{n+1}\right\rvert/\left\lvert a_n\right\rvert=0\\
+&\varinjlim (m_i^\lambda\cdot)^*\le0\\
+&\varprojlim_{p\in S(A)}A_p\le0
+\end{align}
+\end{verbatim}
+
+\subsection{\cn{mod} and its relatives}
+The commands \cn{mod} and \cn{pod} are variants of
+\cn{pmod} preferred by some authors; \cn{mod} omits the parentheses,
+whereas \cn{pod} omits the `mod' and retains the parentheses.
+Examples:
+\begin{align}
+x&\equiv y+1\pmod{m^2}\\
+x&\equiv y+1\mod{m^2}\\
+x&\equiv y+1\pod{m^2}
+\end{align}
+\begin{verbatim}
+\begin{align}
+x&\equiv y+1\pmod{m^2}\\
+x&\equiv y+1\mod{m^2}\\
+x&\equiv y+1\pod{m^2}
+\end{align}
+\end{verbatim}
+
+\subsection{Fractions and related constructions}
+\label{fracs}
+
+The usual notation for binomials is similar to the fraction concept,
+so it has a similar command \cn{binom} with two arguments. Example:
+\begin{equation}
+\begin{split}
+\sum_{\gamma\in\Gamma_C} I_\gamma&
+=2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}\\
+&\quad+\dots+(-1)^l\binom{k}{l}2^{k-l}
++\dots+(-1)^k\\
+&=(2-1)^k=1
+\end{split}
+\end{equation}
+\begin{verbatim}
+\begin{equation}
+\begin{split}
+[\sum_{\gamma\in\Gamma_C} I_\gamma&
+=2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}\\
+&\quad+\dots+(-1)^l\binom{k}{l}2^{k-l}
++\dots+(-1)^k\\
+&=(2-1)^k=1
+\end{split}
+\end{equation}
+\end{verbatim}
+There are also abbreviations
+\begin{verbatim}
+\dfrac \dbinom
+\tfrac \tbinom
+\end{verbatim}
+for the commonly needed constructions
+\begin{verbatim}
+{\displaystyle\frac ... } {\displaystyle\binom ... }
+{\textstyle\frac ... } {\textstyle\binom ... }
+\end{verbatim}
+
+The generalized fraction command \cn{genfrac} provides full access to
+the six \TeX{} fraction primitives:
+\begin{align}
+\text{\cn{over}: }&\genfrac{}{}{}{}{n+1}{2}&
+\text{\cn{overwithdelims}: }&
+ \genfrac{\langle}{\rangle}{}{}{n+1}{2}\\
+\text{\cn{atop}: }&\genfrac{}{}{0pt}{}{n+1}{2}&
+\text{\cn{atopwithdelims}: }&
+ \genfrac{(}{)}{0pt}{}{n+1}{2}\\
+\text{\cn{above}: }&\genfrac{}{}{1pt}{}{n+1}{2}&
+\text{\cn{abovewithdelims}: }&
+ \genfrac{[}{]}{1pt}{}{n+1}{2}
+\end{align}
+\begin{verbatim}
+\text{\cn{over}: }&\genfrac{}{}{}{}{n+1}{2}&
+\text{\cn{overwithdelims}: }&
+ \genfrac{\langle}{\rangle}{}{}{n+1}{2}\\
+\text{\cn{atop}: }&\genfrac{}{}{0pt}{}{n+1}{2}&
+\text{\cn{atopwithdelims}: }&
+ \genfrac{(}{)}{0pt}{}{n+1}{2}\\
+\text{\cn{above}: }&\genfrac{}{}{1pt}{}{n+1}{2}&
+\text{\cn{abovewithdelims}: }&
+ \genfrac{[}{]}{1pt}{}{n+1}{2}
+\end{verbatim}
+
+\subsection{Continued fractions}
+The continued fraction
+\begin{equation}
+\cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+\dotsb
+}}}}}
+\end{equation}
+can be obtained by typing
+\begin{verbatim}
+\cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+\dotsb
+}}}}}
+\end{verbatim}
+Left or right placement of any of the numerators is accomplished by using
+\cn{cfrac[l]} or \cn{cfrac[r]} instead of \cn{cfrac}.
+
+\subsection{Smash}
+
+In \pkg{amsmath} there are optional arguments \verb"t" and \verb"b" for
+the plain \TeX\ command \cn{smash}, because sometimes it is advantageous
+to be able to `smash' only the top or only the bottom of something while
+retaining the natural depth or height. In the formula
+$X_j=(1/\sqrt{\smash[b]{\lambda_j}})X_j'$ \cn{smash}\verb=[b]= has been
+used to limit the size of the radical symbol.
+\begin{verbatim}
+$X_j=(1/\sqrt{\smash[b]{\lambda_j}})X_j'$
+\end{verbatim}
+Without the use of \cn{smash}\verb=[b]= the formula would have appeared
+thus: $X_j=(1/\sqrt{\lambda_j})X_j'$, with the radical extending to
+encompass the depth of the subscript $j$.
+
+\subsection{The `cases' environment}
+`Cases' constructions like the following can be produced using
+the \env{cases} environment.
+\begin{equation}
+P_{r-j}=
+ \begin{cases}
+ 0& \text{if $r-j$ is odd},\\
+ r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}.
+ \end{cases}
+\end{equation}
+\begin{verbatim}
+\begin{equation} P_{r-j}=
+ \begin{cases}
+ 0& \text{if $r-j$ is odd},\\
+ r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}.
+ \end{cases}
+\end{equation}
+\end{verbatim}
+Notice the use of \cn{text} and the embedded math.
+
+\subsection{Matrix}
+
+Here are samples of the matrix environments,
+\cn{matrix}, \cn{pmatrix}, \cn{bmatrix}, \cn{Bmatrix}, \cn{vmatrix}
+and \cn{Vmatrix}:
+\begin{equation}
+\begin{matrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{matrix}\quad
+\begin{pmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{pmatrix}\quad
+\begin{bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{bmatrix}\quad
+\begin{Bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Bmatrix}\quad
+\begin{vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{vmatrix}\quad
+\begin{Vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Vmatrix}
+\end{equation}
+%
+\begin{verbatim}
+\begin{matrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{matrix}\quad
+\begin{pmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{pmatrix}\quad
+\begin{bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{bmatrix}\quad
+\begin{Bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Bmatrix}\quad
+\begin{vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{vmatrix}\quad
+\begin{Vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Vmatrix}
+\end{verbatim}
+
+To produce a small matrix suitable for use in text, use the
+\env{smallmatrix} environment.
+\begin{verbatim}
+\begin{math}
+ \bigl( \begin{smallmatrix}
+ a&b\\ c&d
+ \end{smallmatrix} \bigr)
+\end{math}
+\end{verbatim}
+To show
+the effect of the matrix on the surrounding lines of
+a paragraph, we put it here: \begin{math}
+ \bigl( \begin{smallmatrix}
+ a&b\\ c&d
+ \end{smallmatrix} \bigr)
+\end{math}
+and follow it with enough text to ensure that there will
+be at least one full line below the matrix.
+
+\cn{hdotsfor}\verb"{"\textit{number}\verb"}" produces a row of dots in a matrix
+spanning the given number of columns:
+\[W(\Phi)= \begin{Vmatrix}
+\dfrac\varphi{(\varphi_1,\varepsilon_1)}&0&\dots&0\\
+\dfrac{\varphi k_{n2}}{(\varphi_2,\varepsilon_1)}&
+\dfrac\varphi{(\varphi_2,\varepsilon_2)}&\dots&0\\
+\hdotsfor{5}\\
+\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}&
+\dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}&\dots&
+\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})}&
+\dfrac{\varphi}{(\varphi_n,\varepsilon_n)}
+\end{Vmatrix}\]
+\begin{verbatim}
+\[W(\Phi)= \begin{Vmatrix}
+\dfrac\varphi{(\varphi_1,\varepsilon_1)}&0&\dots&0\\
+\dfrac{\varphi k_{n2}}{(\varphi_2,\varepsilon_1)}&
+\dfrac\varphi{(\varphi_2,\varepsilon_2)}&\dots&0\\
+\hdotsfor{5}\\
+\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}&
+\dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}&\dots&
+\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})}&
+\dfrac{\varphi}{(\varphi_n,\varepsilon_n)}
+\end{Vmatrix}\]
+\end{verbatim}
+The spacing of the dots can be varied through use of a square-bracket
+option, for example, \verb"\hdotsfor[1.5]{3}". The number in square brackets
+will be used as a multiplier; the normal value is 1.
+
+\subsection{The \cn{substack} command}
+
+The \cn{substack} command can be used to produce a multiline
+subscript or superscript:
+for example
+\begin{verbatim}
+\sum_{\substack{0\le i\le m\\ 0<j<n}} P(i,j)
+\end{verbatim}
+produces a two-line subscript underneath the sum:
+\begin{equation}
+\sum_{\substack{0\le i\le m\\ 0<j<n}} P(i,j)
+\end{equation}
+A slightly more generalized form is the \env{subarray} environment which
+allows you to specify that each line should be left-aligned instead of
+centered, as here:\EditorialComment{Maybe ``\dots{} as below''?}
+\begin{equation}
+\sum_{\begin{subarray}{l}
+ 0\le i\le m\\ 0<j<n
+ \end{subarray}}
+ P(i,j)
+\end{equation}
+\begin{verbatim}
+\sum_{\begin{subarray}{l}
+ 0\le i\le m\\ 0<j<n
+ \end{subarray}}
+ P(i,j)
+\end{verbatim}
+
+
+\subsection{Big-g-g delimiters}
+
+Here are some big delimiters, first in \cn{normalsize}:
+\[\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ \biggr)
+\]
+\begin{verbatim}
+\[\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ \biggr)
+\]
+\end{verbatim}
+and now in \cn{Large} size:
+{\Large
+\[\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ \biggr)
+\]}
+\begin{verbatim}
+{\Large
+\[\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ \biggr)
+\]}
+\end{verbatim}
+
+
+\bibliography{aomsample}
+\bibliographystyle{aomplain}
+
+\end{document}
+\endinput
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+%%% ====================================================================
+%%% @LaTeX-file{
+%%% filename = "aomsample.tex",
+%%% copyright = "Copyright 1995, 1999 American Mathematical Society,
+%%% 2005 Hebrew University Magnes Press,
+%%% all rights reserved. Copying of this file is
+%%% authorized only if either:
+%%% (1) you make absolutely no changes to your copy,
+%%% including name; OR
+%%% (2) if you do make changes, you first rename it
+%%% to some other name.",
+%%% }
+%%% ====================================================================
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1994/12/01]% LaTeX date must December 1994 or later
+\documentclass[manuscript]{aomart}
+%\documentclass[screen]{aomart}
+%\documentclass{aomart}
+% Some definitions useful in producing this sort of documentation:
+\chardef\bslash=`\\ % p. 424, TeXbook
+% Normalized (nonbold, nonitalic) tt font, to avoid font
+% substitution warning messages if tt is used inside section
+% headings and other places where odd font combinations might
+% result.
+\newcommand{\ntt}{\normalfont\ttfamily}
+% command name
+\newcommand{\cn}[1]{{\protect\ntt\bslash#1}}
+% LaTeX package name
+\newcommand{\pkg}[1]{{\protect\ntt#1}}
+% File name
+\newcommand{\fn}[1]{{\protect\ntt#1}}
+% environment name
+\newcommand{\env}[1]{{\protect\ntt#1}}
+\hfuzz1pc % Don't bother to report overfull boxes if overage is < 1pc
+
+% Theorem environments
+
+%% \theoremstyle{plain} %% This is the default
+\newtheorem[{}\it]{thm}{Theorem}[section]
+\newtheorem{cor}[thm]{Corollary}
+\newtheorem{lem}[thm]{Lemma}
+\newtheorem{prop}[thm]{Proposition}
+\newtheorem{ax}{Axiom}
+
+\theoremstyle{definition}
+\newtheorem{defn}{Definition}[section]
+\newtheorem{rem}{Remark}[section]
+\newtheorem*[{}\it]{notation}{Notation}
+\newtheorem{step}{Step}
+
+%\numberwithin{equation}{section}
+
+\newcommand{\thmref}[1]{Theorem~\ref{#1}}
+\newcommand{\secref}[1]{\S\ref{#1}}
+\newcommand{\lemref}[1]{Lemma~\ref{#1}}
+
+
+% Math definitions
+
+\newcommand{\A}{\mathcal{A}}
+\newcommand{\B}{\mathcal{B}}
+\newcommand{\st}{\sigma}
+\newcommand{\XcY}{{(X,Y)}}
+\newcommand{\SX}{{S_X}}
+\newcommand{\SY}{{S_Y}}
+\newcommand{\SXY}{{S_{X,Y}}}
+\newcommand{\SXgYy}{{S_{X|Y}(y)}}
+\newcommand{\Cw}[1]{{\hat C_#1(X|Y)}}
+\newcommand{\G}{{G(X|Y)}}
+\newcommand{\PY}{{P_{\mathcal{Y}}}}
+\newcommand{\X}{\mathcal{X}}
+\newcommand{\wt}{\widetilde}
+\newcommand{\wh}{\widehat}
+
+\DeclareMathOperator{\per}{per}
+\DeclareMathOperator{\cov}{cov}
+\DeclareMathOperator{\non}{non}
+\DeclareMathOperator{\cf}{cf}
+\DeclareMathOperator{\add}{add}
+\DeclareMathOperator{\Cham}{Cham}
+\DeclareMathOperator{\IM}{Im}
+\DeclareMathOperator{\esssup}{ess\,sup}
+\DeclareMathOperator{\meas}{meas}
+\DeclareMathOperator{\seg}{seg}
+
+% \interval is used to provide better spacing after a [ that
+% is used as a closing delimiter.
+\newcommand{\interval}[1]{\mathinner{#1}}
+
+% Notation for an expression evaluated at a particular condition. The
+% optional argument can be used to override automatic sizing of the
+% right vert bar, e.g. \eval[\biggr]{...}_{...}
+\newcommand{\eval}[2][\right]{\relax
+ \ifx#1\right\relax \left.\fi#2#1\rvert}
+
+% Enclose the argument in vert-bar delimiters:
+\newcommand{\envert}[1]{\left\lvert#1\right\rvert}
+\let\abs=\envert
+
+% Enclose the argument in double-vert-bar delimiters:
+\newcommand{\enVert}[1]{\left\lVert#1\right\rVert}
+\let\norm=\enVert
+
+%\setcounter{tocdepth}{5}
+
+\title[Sample Paper]{Sample Paper for the \pkg{aomart}
+ Class}
+\author[AMS]{American Mathematical Society}
+\address{AMS\\
+Providence, Rhode Island}
+\email{tech-support@ams.org}
+\author{Boris Veytsman}
+\address{George Mason University\\
+Fairfax, Virginia}
+\email{borisv@lk.net}
+\urladdr{http://borisv.lk.net}
+\givenname{Boris}
+\surname{Veytsman}
+\thanks{The class was commissioned by Annals of Mathematics}
+
+\keyword{Hamiltonian paths}
+\keyword{Typesetting}
+\subject{primary}{matsc2000}{123456789}
+\subject{secondary}{matsc2000}{FFFF}
+
+\received{\formatdate{2004-12-24}}
+\revised{\formatdate{2006-04-12}}
+\accepted{\formatdate{2007-10-02}}
+\published{\formatdate{2008-04-02}}
+\publishedonline{\formatdate{2007-11-12}}
+
+\volumenumber{160}
+\issuenumber{1}
+\publicationyear{2008}
+\papernumber{12}
+\startpage{17}
+\endpage{}
+
+\proposed{E. D. Itor}
+\seconded{A. S. Sociate}
+\corresponding{A. U. Thor}
+\version{2.1}
+
+%\doinumber{10.1215/S0012-7094-92-06520-3}
+\mrnumber{MR1154181}
+\zblnumber{0774.14039}
+
+
+
+\begin{document}
+
+
+\begin{abstract}
+ This is a test file for \textsf{aomart} class based on the
+ \texttt{testmath.tex} file from the \textsf{amsmath} distribution.
+
+ It was changed to test the features of the Annals of Mathematics
+ class.
+\end{abstract}
+
+\maketitle
+\tableofcontents
+
+\section{Introduction}
+
+
+This paper demonstrates the use of \texttt{aomart} class. It is based
+on \texttt{testmath.tex} from \AmS-\LaTeX{} distribution. The text
+is (slightly) reformatted according to the requirements of the
+\texttt{aomart} style. See also
+\cite{Lenstra74,Zarhin92,Minasyan08,Arnold89:MathMethodsMechanics,%
+Michal48,Michal38}.
+\EditorialComment{Are these
+ quotations necessary?}
+
+
+\section{Enumeration of Hamiltonian paths in a graph}
+
+Let $\mathbf{A}=(a_{ij})$ be the adjacency matrix of graph $G$. The
+corresponding Kirchhoff matrix $\mathbf{K}=(k_{ij})$ is obtained from
+$\mathbf{A}$ by replacing in $-\mathbf{A}$ each diagonal entry by the
+degree of its corresponding vertex; i.e., the $i$th diagonal entry is
+identified with the degree of the $i$th vertex. It is well known that
+\begin{equation}
+\det\mathbf{K}(i|i)=\text{ the number of spanning trees of $G$},
+\quad i=1,\dots,n
+\end{equation}
+where $\mathbf{K}(i|i)$ is the $i$th principal submatrix of
+$\mathbf{K}$.
+\begin{verbatim}
+\det\mathbf{K}(i|i)=\text{ the number of spanning trees of $G$},
+\end{verbatim}
+
+Let $C_{i(j)}$ be the set of graphs obtained from $G$ by attaching edge
+$(v_iv_j)$ to each spanning tree of $G$. Denote by $C_i=\bigcup_j
+C_{i(j)}$. It is obvious that the collection of Hamiltonian cycles is a
+subset of $C_i$. Note that the cardinality of $C_i$ is $k_{ii}\det
+\mathbf{K}(i|i)$. Let $\wh X=\{\hat x_1,\dots,\hat x_n\}$.
+\begin{verbatim}
+$\wh X=\{\hat x_1,\dots,\hat x_n\}$
+\end{verbatim}
+Define multiplication for the elements of $\wh X$ by
+\begin{equation}\label{multdef}
+\hat x_i\hat x_j=\hat x_j\hat x_i,\quad \hat x^2_i=0,\quad
+i,j=1,\dots,n.
+\end{equation}
+Let $\hat k_{ij}=k_{ij}\hat x_j$ and $\hat k_{ij}=-\sum_{j\not=i} \hat
+k_{ij}$. Then the number of Hamiltonian cycles $H_c$ is given by the
+relation \cite{liuchow:formalsum}
+\begin{equation}\label{H-cycles}
+\biggl(\prod^n_{\,j=1}\hat x_j\biggr)H_c=\frac{1}{2}\hat k_{ij}\det
+\wh{\mathbf{K}}(i|i),\qquad i=1,\dots,n.
+\end{equation}
+The task here is to express \eqref{H-cycles}
+in a form free of any $\hat x_i$,
+$i=1,\dots,n$. The result also leads to the resolution of enumeration of
+Hamiltonian paths in a graph.
+
+It is well known that the enumeration of Hamiltonian cycles and paths in
+a complete graph $K_n$ and in a complete bipartite graph $K_{n_1n_2}$
+can only be found from \textit{first combinatorial principles}
+\cite{hapa:graphenum}. One wonders if there exists a formula which can
+be used very efficiently to produce $K_n$ and $K_{n_1n_2}$. Recently,
+using Lagrangian methods, Goulden and Jackson have shown that $H_c$ can
+be expressed in terms of the determinant and permanent of the adjacency
+matrix \cite{gouja:lagrmeth}. However, the formula of Goulden and
+Jackson determines neither $K_n$ nor $K_{n_1n_2}$ effectively. In this
+paper, using an algebraic method, we parametrize the adjacency matrix.
+The resulting formula also involves the determinant and permanent, but
+it can easily be applied to $K_n$ and $K_{n_1n_2}$. In addition, we
+eliminate the permanent from $H_c$ and show that $H_c$ can be
+represented by a determinantal function of multivariables, each variable
+with domain $\{0,1\}$. Furthermore, we show that $H_c$ can be written by
+number of spanning trees of subgraphs. Finally, we apply the formulas to
+a complete multigraph $K_{n_1\dots n_p}$.
+
+The conditions $a_{ij}=a_{ji}$, $i,j=1,\dots,n$, are not required in
+this paper. All formulas can be extended to a digraph simply by
+multiplying $H_c$ by 2. Some other discussion can be found
+in~\cite{fre:riesz,fre:cichon}.
+
+\section{Main theorem}
+\label{s:mt}
+
+\begin{notation} For $p,q\in P$ and $n\in\omega$ we write
+$(q,n)\le(p,n)$ if $q\le p$ and $A_{q,n}=A_{p,n}$.
+\begin{verbatim}
+\begin{notation} For $p,q\in P$ and $n\in\omega$
+...
+\end{notation}
+\end{verbatim}
+\end{notation}
+
+Let $\mathbf{B}=(b_{ij})$ be an $n\times n$ matrix. Let $\mathbf{n}=\{1,
+\dots,n\}$. Using the properties of \eqref{multdef}, it is readily seen
+that
+
+\begin{lem}\label{lem-per}
+\begin{equation}
+\prod_{i\in\mathbf{n}}
+\biggl(\sum_{\,j\in\mathbf{n}}b_{ij}\hat x_i\biggr)
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)\per \mathbf{B}
+\end{equation}
+where $\per \mathbf{B}$ is the permanent of $\mathbf{B}$.
+\end{lem}
+
+Let $\wh Y=\{\hat y_1,\dots,\hat y_n\}$. Define multiplication
+for the elements of $\wh Y$ by
+\begin{equation}
+\hat y_i\hat y_j+\hat y_j\hat y_i=0,\quad i,j=1,\dots,n.
+\end{equation}
+Then, it follows that
+\begin{lem}\label{lem-det}
+\begin{equation}\label{detprod}
+\prod_{i\in\mathbf{n}}
+\biggl(\sum_{\,j\in\mathbf{n}}b_{ij}\hat y_j\biggr)
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat y_i\biggr)\det\mathbf{B}.
+\end{equation}
+\end{lem}
+
+Note that all basic properties of determinants are direct consequences
+of \fullref{Lemma}{lem-det}. Write
+\begin{equation}\label{sum-bij}
+\sum_{j\in\mathbf{n}}b_{ij}\hat y_j=\sum_{j\in\mathbf{n}}b^{(\lambda)}
+_{ij}\hat y_j+(b_{ii}-\lambda_i)\hat y_i\hat y
+\end{equation}
+where
+\begin{equation}
+b^{(\lambda)}_{ii}=\lambda_i,\quad b^{(\lambda)}_{ij}=b_{ij},
+\quad i\not=j.
+\end{equation}
+Let $\mathbf{B}^{(\lambda)}=(b^{(\lambda)}_{ij})$. By \eqref{detprod}
+and \eqref{sum-bij}, it is
+straightforward to show the following
+result:
+\begin{thm}\label{thm-main}
+\begin{equation}\label{detB}
+\det\mathbf{B}=
+\sum^n_{l =0}\sum_{I_l \subseteq n}
+\prod_{i\in I_l}(b_{ii}-\lambda_i)
+\det\mathbf{B}^{(\lambda)}(I_l |I_l ),
+\end{equation}
+where $I_l =\{i_1,\dots,i_l \}$ and $\mathbf{B}^{(\lambda)}(I_l |I_l )$
+is the principal submatrix (obtained from $\mathbf{B}^{(\lambda)}$
+by deleting its $i_1,\dots,i_l $ rows and columns).
+\end{thm}
+
+\begin{rem}[convention]
+Let $\mathbf{M}$ be an $n\times n$ matrix. The convention
+$\mathbf{M}(\mathbf{n}|\mathbf{n})=1$ has been used in \eqref{detB} and
+hereafter.
+\end{rem}
+
+Before proceeding with our discussion, we pause to note that
+\thmref{thm-main} yields immediately a fundamental formula which can be
+used to compute the coefficients of a characteristic polynomial
+\cite{mami:matrixth}:
+\begin{cor}\label{BI}
+Write $\det(\mathbf{B}-x\mathbf{I})=\sum^n_{l =0}(-1)
+^l b_l x^l $. Then
+\begin{equation}\label{bl-sum}
+b_l =\sum_{I_l \subseteq\mathbf{n}}\det\mathbf{B}(I_l |I_l ).
+\end{equation}
+\end{cor}
+Let
+\begin{equation}
+\mathbf{K}(t,t_1,\dots,t_n)
+=\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\
+-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\
+\hdotsfor[2]{4}\\
+-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix},
+\end{equation}
+\begin{verbatim}
+\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\
+-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\
+\hdotsfor[2]{4}\\
+-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix}
+\end{verbatim}
+where
+\begin{equation}
+D_i=\sum_{j\in\mathbf{n}}a_{ij}t_j,\quad i=1,\dots,n.
+\end{equation}
+
+Set
+\begin{equation*}
+D(t_1,\dots,t_n)=\frac{\delta}{\delta t}\eval{\det\mathbf{K}(t,t_1,\dots,t_n)
+}_{t=1}.
+\end{equation*}
+Then
+\begin{equation}\label{sum-Di}
+D(t_1,\dots,t_n)
+=\sum_{i\in\mathbf{n}}D_i\det\mathbf{K}(t=1,t_1,\dots,t_n; i|i),
+\end{equation}
+where $\mathbf{K}(t=1,t_1,\dots,t_n; i|i)$ is the $i$th principal
+submatrix of $\mathbf{K}(t=1,t_1,\dots,t_n)$.
+
+\fullref{Theorem}{thm-main} leads to
+\begin{equation}\label{detK1}
+\det\mathbf{K}(t_1,t_1,\dots,t_n)
+=\sum_{I\in\mathbf{n}}(-1)^{\envert{I}}t^{n-\envert{I}}
+\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A}
+^{(\lambda t)}(\overline{I}|\overline I).
+\end{equation}
+Note that
+\begin{equation}\label{detK2}
+\det\mathbf{K}(t=1,t_1,\dots,t_n)=\sum_{I\in\mathbf{n}}(-1)^{\envert{I}}
+\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A}
+^{(\lambda)}(\overline{I}|\overline{I})=0.
+\end{equation}
+
+Let $t_i=\hat x_i,i=1,\dots,n$. \fullref{Lemma}{lem-per} yields
+\begin{multline}
+\biggl(\sum_{\,i\in\mathbf{n}}a_{l _i}x_i\biggr)
+\det\mathbf{K}(t=1,x_1,\dots,x_n;l |l )\\
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)
+\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\envert{I}}\per\mathbf{A}^{(\lambda)}(I|I)
+\det\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \}).
+\label{sum-ali}
+\end{multline}
+\begin{verbatim}
+\begin{multline}
+\biggl(\sum_{\,i\in\mathbf{n}}a_{l _i}x_i\biggr)
+\det\mathbf{K}(t=1,x_1,\dots,x_n;l |l )\\
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)
+\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\envert{I}}\per\mathbf{A}^{(\lambda)}(I|I)
+\det\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \}).
+\label{sum-ali}
+\end{multline}
+\end{verbatim}
+
+By \eqref{H-cycles}, \eqref{detprod}, and \eqref{sum-bij}, we have
+\begin{prop}\label{prop:eg}
+\begin{equation}
+H_c=\frac1{2n}\sum^n_{l =0}(-1)^{l}
+D_{l},
+\end{equation}
+where
+\begin{equation}\label{delta-l}
+D_{l}=\eval[2]{\sum_{I_{l}\subseteq \mathbf{n}}
+D(t_1,\dots,t_n)}_{t_i=\left\{\begin{smallmatrix}
+0,& \text{if }i\in I_{l}\quad\\% \quad added for centering
+1,& \text{otherwise}\end{smallmatrix}\right.\;,\;\; i=1,\dots,n}.
+\end{equation}
+\end{prop}
+
+\section{Application}
+\label{lincomp}
+
+We consider here the applications of \fullref{Theorems}{th-info-ow-ow} \fullref{and}{th-weak-ske-owf} to a complete
+multipartite graph $K_{n_1\dots n_p}$. It can be shown that the
+number of spanning trees of $K_{n_1\dots n_p}$
+may be written
+\begin{equation}\label{e:st}
+T=n^{p-2}\prod^p_{i=1}
+(n-n_i)^{n_i-1}
+\end{equation}
+where
+\begin{equation}
+n=n_1+\dots+n_p.
+\end{equation}
+
+It follows from \fullref{Theorems}{th-info-ow-ow} \fullref{and}{th-weak-ske-owf} that
+\begin{equation}\label{e:barwq}
+\begin{split}
+H_c&=\frac1{2n}
+\sum^n_{{l}=0}(-1)^{l}(n-{l})^{p-2}
+\sum_{l _1+\dots+l _p=l}\prod^p_{i=1}
+\binom{n_i}{l _i}\\
+&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
+\biggl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\biggr].\end{split}
+\end{equation}
+\begin{verbatim}
+... \binom{n_i}{l _i}\\
+\end{verbatim}
+and
+\begin{equation}\label{joe}
+\begin{split}
+H_c&=\frac12\sum^{n-1}_{l =0}
+(-1)^{l}(n-l )^{p-2}
+\sum_{l _1+\dots+l _p=l}
+\prod^p_{i=1}\binom{n_i}{l _i}\\
+&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}
+\left(1-\frac{l _p}{n_p}\right)
+[(n-l )-(n_p-l _p)].
+\end{split}
+\end{equation}
+
+The enumeration of $H_c$ in a $K_{n_1\dotsm n_p}$ graph can also be
+carried out by \fullref{Theorem}{thm-H-param} \fullref{or}{thm-asym}
+together with the algebraic method of \eqref{multdef}.
+Some elegant representations may be obtained. For example, $H_c$ in
+a $K_{n_1n_2n_3}$ graph may be written
+\begin{equation}\label{j:mark}
+\begin{split}
+H_c=&
+\frac{n_1!\,n_2!\,n_3!}
+{n_1+n_2+n_3}\sum_i\left[\binom{n_1}{i}
+\binom{n_2}{n_3-n_1+i}\binom{n_3}{n_3-n_2+i}\right.\\
+&+\left.\binom{n_1-1}{i}
+\binom{n_2-1}{n_3-n_1+i}
+\binom{n_3-1}{n_3-n_2+i}\right].\end{split}
+\end{equation}
+
+\section{Secret key exchanges}
+\label{SKE}
+
+Modern cryptography is fundamentally concerned with the problem of
+secure private communication. A Secret Key Exchange is a protocol
+where Alice and Bob, having no secret information in common to start,
+are able to agree on a common secret key, conversing over a public
+channel. The notion of a Secret Key Exchange protocol was first
+introduced in the seminal paper of Diffie and Hellman
+\cite{dihe:newdir}. \cite{dihe:newdir} presented a concrete
+implementation of a Secret Key Exchange protocol, dependent on a
+specific assumption (a variant on the discrete log), specially
+tailored to yield Secret Key Exchange. Secret Key Exchange is of
+course trivial if trapdoor permutations exist. However, there is no
+known implementation based on a weaker general assumption.
+
+The concept of an informationally one-way function was introduced
+in \cite{imlelu:oneway}. We give only an informal definition here:
+
+\begin{defn}[one way] A polynomial time
+computable function $f = \{f_k\}$ is informationally
+one-way if there is no probabilistic polynomial time algorithm which
+(with probability of the form $1 - k^{-e}$ for some $e > 0$)
+returns on input $y \in \{0,1\}^{k}$ a random element of $f^{-1}(y)$.
+\end{defn}
+In the non-uniform setting \cite{imlelu:oneway} show that these are not
+weaker than one-way functions:
+\begin{thm}[\cite{imlelu:oneway} (non-uniform)]
+\label{th-info-ow-ow}
+The existence of informationally one-way functions
+implies the existence of one-way functions.
+\end{thm}
+We will stick to the convention introduced above of saying
+``non-uniform'' before the theorem statement when the theorem
+makes use of non-uniformity. It should be understood that
+if nothing is said then the result holds for both the uniform and
+the non-uniform models.
+
+It now follows from \thmref{th-info-ow-ow} that
+
+\begin{thm}[non-uniform]\label{th-weak-ske-owf} Weak SKE
+implies the existence of a one-way function.
+\end{thm}
+
+More recently, the polynomial-time, interior point algorithms for linear
+programming have been extended to the case of convex quadratic programs
+\cite{moad:quadpro,ye:intalg}, certain linear complementarity problems
+\cite{komiyo:lincomp,miyoki:lincomp}, and the nonlinear complementarity
+problem \cite{komiyo:unipfunc}. The connection between these algorithms
+and the classical Newton method for nonlinear equations is well
+explained in \cite{komiyo:lincomp}.
+
+\section{Review}
+\label{computation}
+
+We begin our discussion with the following definition:
+
+\begin{defn}
+
+A function $H\colon \Re^n \to \Re^n$ is said to be
+\emph{B-differentiable} at the point $z$ if (i)~$H$ is Lipschitz
+continuous in a neighborhood of $z$, and (ii)~ there exists a positive
+homogeneous function $BH(z)\colon \Re^n \to \Re^n$, called the
+\emph{B-derivative} of $H$ at $z$, such that
+\[ \lim_{v \to 0} \frac{H(z+v) - H(z) - BH(z)v}{\enVert{v}} = 0. \]
+The function $H$ is \textit{B-differentiable in set $S$} if it is
+B-differentiable at every point in $S$. The B-derivative $BH(z)$ is said
+to be \textit{strong} if
+\[ \lim_{(v,v') \to (0,0)} \frac{H(z+v) - H(z+v') - BH(z)(v
+ -v')}{\enVert{v - v'}} = 0. \]
+\end{defn}
+
+
+\begin{lem}\label{limbog} There exists a smooth function $\psi_0(z)$
+defined for $\abs{z}>1-2a$ satisfying the following properties\textup{:}
+\begin{enumerate}
+\renewcommand{\labelenumi}{(\roman{enumi})}
+\item $\psi_0(z)$ is bounded above and below by positive constants
+$c_1\leq \psi_0(z)\leq c_2$.
+\item If $\abs{z}>1$, then $\psi_0(z)=1$.
+\item For all $z$ in the domain of $\psi_0$, $\Delta_0\ln \psi_0\geq 0$.
+\item If $1-2a<\abs{z}<1-a$, then $\Delta_0\ln \psi_0\geq
+c_3>0$.
+\end{enumerate}
+\end{lem}
+
+\begin{proof}
+We choose $\psi_0(z)$ to be a radial function depending only on $r=\abs{z}$.
+Let $h(r)\geq 0$ be a suitable smooth function satisfying $h(r)\geq c_3$
+for $1-2a<\abs{z}<1-a$, and $h(r)=0$ for $\abs{z}>1-\tfrac a2$. The radial
+Laplacian
+\[\Delta_0\ln\psi_0(r)=\left(\frac {d^2}{dr^2}+\frac
+1r\frac d{dr}\right)\ln\psi_0(r)\]
+has smooth coefficients for $r>1-2a$. Therefore, we may
+apply the existence and uniqueness theory for ordinary differential
+equations. Simply let $\ln \psi_0(r)$ be the solution of the differential
+equation
+\[\left(\frac{d^2}{dr^2}+\frac 1r\frac d{dr}\right)\ln \psi_0(r)=h(r)\]
+with initial conditions given by $\ln \psi_0(1)=0$ and
+$\ln\psi_0'(1)=0$.
+
+Next, let $D_\nu$ be a finite collection of pairwise disjoint disks,
+all of which are contained in the unit disk centered at the origin in
+$C$. We assume that $D_\nu=\{z\mid \abs{z-z_\nu}<\delta\}$. Suppose that
+$D_\nu(a)$ denotes the smaller concentric disk $D_\nu(a)=\{z\mid
+\abs{z-z_\nu}\leq (1-2a)\delta\}$. We define a smooth weight function
+$\Phi_0(z)$ for $z\in C-\bigcup_\nu D_\nu(a)$ by setting $\Phi_
+0(z)=1$ when $z\notin \bigcup_\nu D_\nu$ and $\Phi_
+0(z)=\psi_0((z-z_\nu)/\delta)$ when $z$ is an element of $D_\nu$. It
+follows from \lemref{limbog} that $\Phi_ 0$ satisfies the properties:
+\begin{enumerate}
+\renewcommand{\labelenumi}{(\roman{enumi})}
+\item \label{boundab}$\Phi_ 0(z)$ is bounded above and below by
+positive constants $c_1\leq \Phi_ 0(z)\leq c_2$.
+\item \label{d:over}$\Delta_0\ln\Phi_ 0\geq 0$ for all
+$z\in C-\bigcup_\nu D_\nu(a)$,
+the domain where the function $\Phi_ 0$ is defined.
+\item \label{d:ad}$\Delta_0\ln\Phi_ 0\geq c_3\delta^{-2}$
+when $(1-2a)\delta<\abs{z-z_\nu}<(1-a)\delta$.
+\end{enumerate}
+Let $A_\nu$ denote the annulus $A_\nu=\{(1-2a)\delta<\abs{z-z_\nu}<(1-a)
+\delta \}$, and set $A=\bigcup_\nu A_\nu$. The
+\pfullref{properties}{d:over} and (\ref{d:ad}) of $\Phi_ 0$
+may be summarized as $\Delta_0\ln \Phi_ 0\geq c_3\delta^{-2}\chi_A$,
+where $\chi _A$ is the characteristic function of $A$.
+\end{proof}
+
+Suppose that $\alpha$ is a nonnegative real constant. We apply
+\fullref{Proposition}{prop:eg} with $\Phi(z)=\Phi_ 0(z) e^{\alpha\abs{z}^2}$. If
+$u\in C^\infty_0(R^2-\bigcup_\nu D_\nu(a))$, assume that $\mathcal{D}$
+is a bounded domain containing the support of $u$ and $A\subset
+\mathcal{D}\subset R^2-\bigcup_\nu D_\nu(a)$. A calculation gives
+\[\int_{\mathcal{D}}\abs{\overline\partial u}^2\Phi_ 0(z) e^{\alpha\abs{z}^2}
+\geq c_4\alpha\int_{\mathcal{D}}\abs{u}^2\Phi_ 0e^{\alpha\abs{z}^2}
++c_5\delta^{-2}\int_ A\abs{u}^2\Phi_ 0e^{\alpha\abs{z}^2}.\]
+
+The boundedness, \pfullref{property}{boundab} of $\Phi_ 0$, then yields
+\[\int_{\mathcal{D}}\abs{\overline\partial u}^2e^{\alpha\abs{z}^2}\geq c_6\alpha
+\int_{\mathcal{D}}\abs{u}^2e^{\alpha\abs{z}^2}
++c_7\delta^{-2}\int_ A\abs{u}^2e^{\alpha\abs{z}^2}.\]
+
+Let $B(X)$ be the set of blocks of $\Lambda_{X}$
+and let $b(X) = \abs{B(X)}$. If $\phi \in Q_{X}$ then
+$\phi$ is constant on the blocks of $\Lambda_{X}$.
+\begin{equation}\label{far-d}
+ P_{X} = \{ \phi \in M \mid \Lambda_{\phi} = \Lambda_{X} \},
+\qquad
+Q_{X} = \{\phi \in M \mid \Lambda_{\phi} \geq \Lambda_{X} \}.
+\end{equation}
+If $\Lambda_{\phi} \geq \Lambda_{X}$ then
+$\Lambda_{\phi} = \Lambda_{Y}$ for some $Y \geq X$ so that
+\[ Q_{X} = \bigcup_{Y \geq X} P_{Y}. \]
+Thus by M\"obius inversion
+\[ \abs{P_{Y}}= \sum_{X\geq Y} \mu (Y,X)\abs{Q_{X}}.\]
+Thus there is a bijection from $Q_{X}$ to $W^{B(X)}$.
+In particular $\abs{Q_{X}} = w^{b(X)}$.
+
+Next note that $b(X)=\dim X$. We see this by choosing a
+basis for $X$ consisting of vectors $v^{k}$ defined by
+\[v^{k}_{i}=
+\begin{cases} 1 & \text{if $i \in \Lambda_{k}$},\\
+0 &\text{otherwise.} \end{cases}
+\]
+\begin{verbatim}
+\[v^{k}_{i}=
+\begin{cases} 1 & \text{if $i \in \Lambda_{k}$},\\
+0 &\text{otherwise.} \end{cases}
+\]
+\end{verbatim}
+
+\begin{lem}\label{p0201}
+Let $\A$ be an arrangement. Then
+\[ \chi (\A,t) = \sum_{\B \subseteq \A}
+(-1)^{\abs{\B}} t^{\dim T(\B)}. \]
+\end{lem}
+
+In order to compute $R''$ recall the definition
+of $S(X,Y)$ from \lemref{lem-per}. Since $H \in \B$,
+$\A_{H} \subseteq \B$. Thus if $T(\B) = Y$ then
+$\B \in S(H,Y)$. Let $L'' = L(\A'')$. Then
+\begin{equation}\label{E_SXgYy}
+\begin{split}
+R''&= \sum_{H\in \B \subseteq \A} (-1)^{\abs{\B}}
+t^{\dim T(\B)}\\
+&= \sum_{Y \in L''} \sum_{\B \in S(H,Y)}
+(-1)^{\abs{\B}}t^{\dim Y} \\
+&= -\sum_{Y \in L''} \sum_{\B \in S(H,Y)} (-1)^
+{\abs{\B - \A_{H}}} t^{\dim Y} \\
+&= -\sum_{Y \in L''} \mu (H,Y)t^{\dim Y} \\
+&= -\chi (\A '',t).
+\end{split}
+\end{equation}
+
+\begin{cor}\label{tripleA}
+Let $(\A,\A',\A'')$ be a triple of arrangements. Then
+\[ \pi (\A,t) = \pi (\A',t) + t \pi (\A'',t). \]
+\end{cor}
+
+\begin{defn}
+Let $(\A,\A',\A'')$ be a triple with respect to
+the hyperplane $H \in \A$. Call $H$ a \textit{separator}
+if $T(\A) \not\in L(\A')$.
+\end{defn}
+
+\begin{cor}\label{nsep}
+Let $(\A,\A',\A'')$ be a triple with respect to $H \in \A$.
+\begin{enumerate}
+\renewcommand{\labelenumi}{(\roman{enumi})}
+\item
+If $H$ is a separator then
+\[ \mu (\A) = - \mu (\A'') \]
+and hence
+\[ \abs{\mu (\A)} = \abs{ \mu (\A'')}. \]
+
+\item If $H$ is not a separator then
+\[\mu (\A) = \mu (\A') - \mu (\A'') \]
+and
+\[ \abs{\mu (\A)} = \abs{\mu (\A')} + \abs{\mu (\A'')}. \]
+\end{enumerate}
+\end{cor}
+
+\begin{proof}
+It follows from \thmref{th-info-ow-ow} that $\pi(\A,t)$
+has leading term
+\[(-1)^{r(\A)}\mu (\A)t^{r(\A)}.\]
+The conclusion
+follows by comparing coefficients of the leading
+terms on both sides of the equation in
+\fullref{Corollary}{tripleA}. If $H$ is a separator then
+$r(\A') < r(\A)$ and there is no contribution
+from $\pi (\A',t)$.
+\end{proof}
+
+The Poincar\'e polynomial of an arrangement
+will appear repeatedly
+in these notes. It will be shown to equal the
+Poincar\'e polynomial
+of the graded algebras which we are going to
+associate with $\A$. It is also the Poincar\'e
+polynomial of the complement $M(\A)$ for a
+complex arrangement. Here we prove
+that the Poincar\'e polynomial is the chamber
+counting function for a real arrangement. The
+complement $M(\A)$ is a disjoint union of chambers
+\[M(\A) = \bigcup_{C \in \Cham(\A)} C.\]
+The number
+of chambers is determined by the Poincar\'e
+polynomial as follows.
+
+\begin{thm}\label{th-realarr}
+Let $\A_{\mathbf{R}}$ be a real arrangement. Then
+\[ \abs{\Cham(\A_{\mathbf{R}})} = \pi (\A_{\mathbf{R}},1). \]
+\end{thm}
+
+\begin{proof}
+We check the properties required in \fullref{Corollary}{nsep}:
+(i) follows from $\pi (\Phi_{ l},t) = 1$, and (ii) is a
+consequence of \fullref{Corollary}{BI}.
+\end{proof}
+
+\begin{figure}
+\vspace{5cm}
+\caption[]{$Q(\A_{1}) = xyz(x-z)(x+z)(y-z)(y+z)$}
+\end{figure}
+
+\begin{figure}
+\vspace{5cm}
+\caption[]{$Q(\A_{2})= xyz(x+y+z)(x+y-z)(x-y+z)(x-y-z)$}
+\end{figure}
+
+
+\begin{thm}
+\label{T_first_the_int}
+Let $\phi$ be a protocol for a random pair $\XcY$.
+If one of $\st_\phi(x',y)$ and $\st_\phi(x,y')$ is a prefix of the other
+and $(x,y)\in\SXY$, then
+\[
+\langle \st_j(x',y)\rangle_{j=1}^\infty
+=\langle \st_j(x,y)\rangle_{j=1}^\infty
+=\langle \st_j(x,y')\rangle_{j=1}^\infty .
+\]
+\end{thm}
+\begin{proof}
+We show by induction on $i$ that
+\[
+\langle \st_j(x',y)\rangle_{j=1}^i
+=\langle \st_j(x,y)\rangle_{j=1}^i
+=\langle \st_j(x,y')\rangle_{j=1}^i.
+\]
+The induction hypothesis holds vacuously for $i=0$. Assume it holds for
+$i-1$, in particular
+$[\st_j(x',y)]_{j=1}^{i-1}=[\st_j(x,y')]_{j=1}^{i-1}$. Then one of
+$[\st_j(x',y)]_{j=i}^{\infty}$ and $[\st_j(x,y')]_{j=i}^{\infty}$ is a
+prefix of the other which implies that one of $\st_i(x',y)$ and
+$\st_i(x,y')$ is a prefix of the other. If the $i$th message is
+transmitted by $P_\X$ then, by the separate-transmissions property and
+the induction hypothesis, $\st_i(x,y)=\st_i(x,y')$, hence one of
+$\st_i(x,y)$ and $\st_i(x',y)$ is a prefix of the other. By the
+implicit-termination property, neither $\st_i(x,y)$ nor $\st_i(x',y)$
+can be a proper prefix of the other, hence they must be the same and
+$\st_i(x',y)=\st_i(x,y)=\st_i(x,y')$. If the $i$th message is
+transmitted by $\PY$ then, symmetrically, $\st_i(x,y)=\st_i(x',y)$ by
+the induction hypothesis and the separate-transmissions property, and,
+then, $\st_i(x,y)=\st_i(x,y')$ by the implicit-termination property,
+proving the induction step.
+\end{proof}
+
+If $\phi$ is a protocol for $(X,Y)$, and $(x,y)$, $(x',y)$ are distinct
+inputs in $\SXY$, then, by the correct-decision property,
+$\langle\st_j(x,y)\rangle_{j=1}^\infty\ne\langle
+\st_j(x',y)\rangle_{j=1}^\infty$.
+
+\pfullref{Equation~}{E_SXgYy} defined $\PY$'s ambiguity set $\SXgYy$
+to be the set of possible $X$ values when $Y=y$.
+The last corollary implies that for all $y\in\SY$,
+the multiset%
+\footnote{A multiset allows multiplicity of elements.
+Hence, $\{0,01,01\}$ is prefix free as a set, but not as a multiset.}
+of codewords $\{\st_\phi(x,y):x\in\SXgYy\}$ is prefix free.
+
+\section{One-way complexity}
+\label{S_Cp1}
+
+$\Cw1$, the one-way complexity of a random pair $\XcY$,
+is the number of bits $P_\X$ must transmit in the worst case
+when $\PY$ is not permitted to transmit any feedback messages.
+Starting with $\SXY$, the support set of $\XcY$, we define $\G$,
+the \textit{characteristic hypergraph} of $\XcY$, and show that
+\[
+\Cw1=\lceil\,\log\chi(\G)\rceil\ .
+\]
+
+Let $\XcY$ be a random pair. For each $y$ in $\SY$, the support set of
+$Y$, \pfullref{equation~}{E_SXgYy} defined $\SXgYy$ to be the set of possible
+$x$ values when $Y=y$. The \textit{characteristic hypergraph} $\G$ of
+$\XcY$ has $\SX$ as its vertex set and the hyperedge $\SXgYy$ for each
+$y\in\SY$.
+
+
+We can now prove a continuity theorem.
+\begin{thm}\label{t:conl}
+Let $\Omega \subset\mathbf{R}^n$ be an open set, let
+$u\in BV(\Omega ;\mathbf{R}^m)$, and let
+\begin{equation}\label{quts}
+T^u_x=\left\{y\in\mathbf{R}^m:
+ y=\tilde u(x)+\left\langle \frac{Du}{\abs{Du}}(x),z
+\right\rangle \text{ for some }z\in\mathbf{R}^n\right\}
+\end{equation}
+for every $x\in\Omega \backslash S_u$. Let $f\colon \mathbf{R}^m\to
+\mathbf{R}^k$ be a Lipschitz continuous function such that $f(0)=0$, and
+let $v=f(u)\colon \Omega \to \mathbf{R}^k$. Then $v\in BV(\Omega
+;\mathbf{R}^k)$ and
+\begin{equation}
+Jv=\eval{(f(u^+)-f(u^-))\otimes \nu_u\cdot\,
+\mathcal{H}_{n-1}}_{S_u}.
+\end{equation}
+In addition, for $\abs{\wt{D}u}$-almost every $x\in\Omega $ the
+restriction of the function $f$ to $T^u_x$ is differentiable at $\tilde
+u(x)$ and
+\begin{equation}
+\wt{D}v=\nabla (\eval{f}_{T^u_x})(\tilde u)
+\frac{\wt{D}u}{\abs{\wt{D}u}}\cdot\abs{\wt{D}u}.\end{equation}
+\end{thm}
+
+Before proving the theorem, we state without proof three elementary
+remarks which will be useful in the sequel.
+\begin{rem}\label{r:omb}
+Let $\omega\colon \left]0,+\infty\right[\to \left]0,+\infty\right[$
+be a continuous function such that $\omega (t)\to 0$ as $t\to
+0$. Then
+\[\lim_{h\to 0^+}g(\omega(h))=L\Leftrightarrow\lim_{h\to
+0^+}g(h)=L\]
+for any function $g\colon \left]0,+\infty\right[\to \mathbf{R}$.
+\end{rem}
+\begin{rem}\label{r:dif}
+Let $g \colon \mathbf{R}^n\to \mathbf{R}$ be a Lipschitz
+continuous function and assume that
+\[L(z)=\lim_{h\to 0^+}\frac{g(hz)-g(0)}h\]
+exists for every $z\in\mathbf{Q}^n$ and that $L$ is a linear function of
+$z$. Then $g$ is differentiable at 0.
+\end{rem}
+\begin{rem}\label{r:dif0}
+Let $A \colon \mathbf{R}^n\to \mathbf{R}^m$ be a linear function, and
+let $f \colon \mathbf{R}^m\to \mathbf{R}$ be a function. Then the
+restriction of $f$ to the range of $A$ is differentiable at 0 if and
+only if $f(A)\colon \mathbf{R}^n\to \mathbf{R}$ is differentiable at 0
+and
+\[\nabla(\eval{f}_{\IM(A)})(0)A=\nabla (f(A))(0).\]
+\end{rem}
+
+\begin{proof}
+ We begin by showing that $v\in BV(\Omega;\mathbf{R}^k)$ and
+\begin{equation}\label{e:bomb}
+\abs{Dv}(B)\le K\abs{Du}(B)\qquad\forall B\in\mathbf{B}(\Omega ),
+\end{equation}
+where $K>0$ is the Lipschitz constant of $f$. By \eqref{sum-Di} and by
+the approximation result quoted in \secref{s:mt}, it is possible to find
+a sequence $(u_h)\subset C^1(\Omega ;\mathbf{R}^m)$ converging to $u$ in
+$L^1(\Omega ;\mathbf{R}^m)$ and such that
+\[\lim_{h\to +\infty}\int_\Omega \abs{\nabla u_h}\,dx=\abs{Du}(\Omega ).\]
+The functions $v_h=f(u_h)$ are locally Lipschitz continuous in $\Omega
+$, and the definition of differential implies that $\abs{\nabla v_h}\le
+K\abs{\nabla u_h}$ almost everywhere in $\Omega $. The lower semicontinuity
+of the total variation and \eqref{sum-Di} yield
+\begin{equation}
+\begin{split}
+\abs{Dv}(\Omega )\le\liminf_{h\to +\infty}\abs{Dv_h}(\Omega) &
+=\liminf_{h\to +\infty}\int_\Omega \abs{\nabla v_h}\,dx\\
+&\le K\liminf_{h\to +\infty}\int_\Omega
+\abs{\nabla u_h}\,dx=K\abs{Du}(\Omega).
+\end{split}\end{equation}
+Since $f(0)=0$, we have also
+\[\int_\Omega \abs{v}\,dx\le K\int_\Omega \abs{u}\,dx;\]
+therefore $u\in BV(\Omega ;\mathbf{R}^k)$. Repeating the same argument
+for every open set $A\subset\Omega $, we get \eqref{e:bomb} for every
+$B\in\mathbf{B}(\Omega)$, because $\abs{Dv}$, $\abs{Du}$ are Radon measures. To
+prove \lemref{limbog}, first we observe that
+\begin{equation}\label{e:SS}
+S_v\subset S_u,\qquad\tilde v(x)=f(\tilde u(x))\qquad \forall x\in\Omega
+\backslash S_u.\end{equation}
+In fact, for every $\varepsilon >0$ we have
+\[\{y\in B_\rho(x): \abs{v(y)-f(\tilde u(x))}>\varepsilon \}\subset \{y\in
+B_\rho(x): \abs{u(y)-\tilde u(x)}>\varepsilon /K\},\]
+hence
+\[\lim_{\rho\to 0^+}\frac{\abs{\{y\in B_\rho(x): \abs{v(y)-f(\tilde u(x))}>
+\varepsilon \}}}{\rho^n}=0\]
+whenever $x\in\Omega \backslash S_u$. By a similar argument, if $x\in
+S_u$ is a point such that there exists a triplet $(u^+,u^-,\nu_u)$
+satisfying \eqref{detK1}, \eqref{detK2}, then
+\[
+(v^+(x)-v^-(x))\otimes \nu_v=(f(u^+(x))-f(u^-(x)))\otimes\nu_u\quad
+\text{if }x\in S_v
+\]
+and $f(u^-(x))=f(u^+(x))$ if $x\in S_u\backslash S_v$. Hence, by (1.8)
+we get
+\begin{equation*}\begin{split}
+Jv(B)=\int_{B\cap S_v}(v^+-v^-)\otimes \nu_v\,d\mathcal{H}_{n-1}&=
+\int_{B\cap S_v}(f(u^+)-f(u^-))\otimes \nu_u\,d\mathcal{H}_{n-1}\\
+&=\int_{B\cap S_u}(f(u^+)-f(u^-))\otimes \nu_u\,d\mathcal{H}_{n-1}
+\end{split}\end{equation*}
+and \lemref{limbog} is proved.
+\end{proof}
+
+To prove \eqref{e:SS}, it is not restrictive to assume that $k=1$.
+Moreover, to simplify our notation, from now on we shall assume that
+$\Omega = \mathbf{R}^n$. The proof of \eqref{e:SS} is divided into two
+steps. In the first step we prove the statement in the one-dimensional
+case $(n=1)$, using \thmref{th-weak-ske-owf}. In the second step we
+achieve the general result using \thmref{t:conl}.
+
+\begin{step}
+Assume that $n=1$. Since $S_u$ is at most countable, \eqref{sum-bij}
+yields that $\abs{\wt{D}v}(S_u\backslash S_v)=0$, so that \eqref{e:st} and \eqref{e:barwq} imply that $Dv=\wt{D}v+Jv$ is
+the Radon-Nikod\'ym decomposition of $Dv$ in absolutely continuous and
+singular part with respect to $\abs{\wt{D} u}$. By
+\thmref{th-weak-ske-owf}, we have
+\begin{equation*}
+\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{s\to t^+}
+\frac{Dv(\interval{\left[t,s\right[})}
+{\abs{\wt{D}u}(\interval{\left[t,s\right[})},\qquad
+\frac{\wt{D}u}{\abs{\wt{D}u}}(t)=\lim_{s\to t^+}
+\frac{Du(\interval{\left[t,s\right[})}
+{\abs{\wt{D}u}(\interval{\left[t,s\right[})}
+\end{equation*}
+$\abs{\wt{D}u}$-almost everywhere in $\mathbf{R}$. It is well known
+(see, for instance, \cite[2.5.16]{ste:sint}) that every one-dimensional
+function of bounded variation $w$ has a unique left continuous
+representative, i.e., a function $\hat w$ such that $\hat w=w$ almost
+everywhere and $\lim_{s\to t^-}\hat w(s)=\hat w(t)$ for every $t\in
+\mathbf{R}$. These conditions imply
+\begin{equation}
+\hat u(t)=Du(\interval{\left]-\infty,t\right[}),
+\qquad \hat v(t)=Dv(\interval{\left]-\infty,t\right[})\qquad
+\forall t\in\mathbf{R}
+\end{equation}
+and
+\begin{equation}\label{alimo}
+\hat v(t)=f(\hat u(t))\qquad\forall t\in\mathbf{R}.\end{equation}
+Let $t\in\mathbf{R}$ be such that
+$\abs{\wt{D}u}(\interval{\left[t,s\right[})>0$ for every $s>t$ and
+assume that the limits in \eqref{joe} exist. By \eqref{j:mark} and \eqref{far-d} we get
+\begin{equation*}\begin{split}
+\frac{\hat v(s)-\hat
+v(t)}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}&=\frac {f(\hat
+u(s))-f(\hat u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\\
+&=\frac{f(\hat u(s))-f(\hat
+u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)\abs{\wt{D}u
+}(\interval{\left[t,s\right[}))}%
+{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\\
+&+\frac
+{f(\hat u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)\abs{\wt{D}
+u}(\interval{\left[t,s\right[}))-f(\hat
+u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}
+\end{split}\end{equation*}
+for every $s>t$. Using the Lipschitz condition on $f$ we find
+{\setlength{\multlinegap}{0pt}
+\begin{multline*}
+\left\lvert\frac{\hat v(s)-\hat
+v(t)}{\abs{\wt{D}u}(\interval{\left[t,s\right[})} -\frac{f(\hat
+u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)
+\abs{\wt{D}u}(\interval{\left[t,s\right[}))-f(\hat
+u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\right\rvert\\
+\le K\left\lvert
+\frac{\hat u(s)-\hat u(t)}
+ {\abs{\wt{D}u}(\interval{\left[t,s\right[})}
+-\frac{\wt{D}u}{\abs{
+\wt{D}u}}(t)\right\rvert.\end{multline*}
+}% end of group with \multlinegap=0pt
+By \eqref{e:bomb}, the function $s\to
+\abs{\wt{D}u}(\interval{\left[t,s\right[})$ is continuous and
+converges to 0 as $s\downarrow t$. Therefore \fullref{Remark}{r:omb} and the
+previous inequality imply
+\[\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{h\to 0^+}
+\frac{f(\hat u(t)+h\dfrac{\wt{D}u}{\abs{\wt{D}u}}
+(t))-f(\hat u(t))}h\quad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}.\]
+By \eqref{joe}, $\hat u(x)=\tilde u(x)$ for every
+$x\in\mathbf{R}\backslash S_u$; moreover, applying the same argument to
+the functions $u'(t)=u(-t)$, $v'(t)=f(u'(t))=v(-t)$, we get
+\[\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{h\to 0}
+\frac{f(\tilde u(t)
++h\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t))-f(\tilde u(t))}{h}
+\qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}\]
+and our statement is proved.
+\end{step}
+
+\begin{step}
+Let us consider now the general case $n>1$. Let $\nu\in \mathbf{R}^n$ be
+such that $\abs{\nu}=1$, and let $\pi_\nu=\{y\in\mathbf{R}^n: \langle
+y,\nu\rangle =0\}$. In the following, we shall identify $\mathbf{R}^n$
+with $\pi_\nu\times\mathbf{R}$, and we shall denote by $y$ the variable
+ranging in $\pi_\nu$ and by $t$ the variable ranging in $\mathbf{R}$. By
+the just proven one-dimensional result, and by \thmref{thm-main}, we get
+\[\lim_{h\to 0}\frac{f(\tilde u(y+t\nu)+h\dfrac{\wt{D}u_y}{\abs{
+\wt{D}u_y}}(t))-f(\tilde u(y+t\nu))}h=\frac{\wt{D}v_y}{\abs{
+\wt{D}u_y}}(t)\qquad\abs{\wt{D}u_y}\text{-a.e. in }\mathbf{R}\]
+for $\mathcal{H}_{n-1}$-almost every $y\in \pi_\nu$. We claim that
+\begin{equation}
+\frac{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle
+}}(y+t\nu)=\frac{\wt{D}u_y}
+{\abs{\wt{D}u_y}}(t)\qquad\abs{\wt{D}u_y}\text{-a.e. in }\mathbf{R}
+\end{equation}
+for $\mathcal{H}_{n-1}$-almost every $y\in\pi_\nu$. In fact, by \eqref{sum-ali} and \eqref{delta-l} we get
+\begin{multline*}
+\int_{\pi_\nu}\frac{\wt{D}u_y}{\abs{\wt{D}u_y}}\cdot\abs{\wt{D}u_y
+}\,d\mathcal{H}_{n-1}(y)=\int_{\pi_\nu}\wt{D}u_y\,d\mathcal{H}_{n-1}(y)\\
+=\langle \wt{D}u,\nu\rangle =\frac
+{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}}\cdot
+\abs{\langle \wt{D}u,\nu\rangle }=\int_{\pi_\nu}\frac{
+\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}
+(y+\cdot \nu)\cdot\abs{\wt{D}u_y}\,d\mathcal{H}_{n-1}(y)
+\end{multline*}
+and \eqref{far-d} follows from \eqref{sum-Di}. By the same argument it
+is possible to prove that
+\begin{equation}
+\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle
+}}(y+t\nu)=\frac{\wt{D}v_y}{\abs{\wt{D}u_y}}(t)\qquad\abs{
+\wt{D}u_y}\text{-a.e. in }\mathbf{R}\end{equation}
+for $\mathcal{H}_{n-1}$-almost every $y\in \pi_\nu$. By \eqref{far-d}
+and \eqref{E_SXgYy} we get
+\[
+\lim_{h\to 0}\frac{f(\tilde u(y+t\nu)+h\dfrac{\langle \wt{D}
+u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(y+t\nu))-f(\tilde
+u(y+t\nu))}{h}
+=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle
+\wt{D}u,\nu\rangle }}(y+t\nu)\]
+for $\mathcal{H}_{n-1}$-almost every $y\in\pi_\nu$, and using again \eqref{detK1}, \eqref{detK2} we get
+\[
+\lim_{h\to 0}\frac{f(\tilde u(x)+h\dfrac{\langle
+\wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(x))-f(\tilde
+u(x))}{h}=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu
+\rangle }}(x)
+\]
+$\abs{\langle \wt{D}u,\nu\rangle}$-a.e. in $\mathbf{R}^n$.
+
+Since the function $\abs{\langle \wt{D}u,\nu\rangle }/\abs{\wt{D}u}$
+is strictly positive $\abs{\langle \wt{D}u,\nu\rangle }$-almost everywhere,
+we obtain also
+\begin{multline*}
+\lim_{h\to 0}\frac{f(\tilde u(x)+h\dfrac{\abs{\langle
+\wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}(x)\dfrac{\langle \wt{D}
+u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(x))-f(\tilde u(x))}{h}\\
+=\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}(x)\frac
+{\langle \wt{D}v,\nu\rangle }{\abs{\langle
+\wt{D}u,\nu\rangle }}(x)
+\end{multline*}
+$\abs{\langle \wt{D}u,\nu\rangle }$-almost everywhere in $\mathbf{R}^n$.
+
+Finally, since
+\begin{align*}
+&\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}
+\frac{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}}
+=\frac{\langle \wt{D}u,\nu\rangle }{\abs{\wt{D}u}}
+=\left\langle \frac{\wt{D}u}{\abs{\wt{D}u}},\nu\right\rangle
+ \qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}^n\\
+&\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}
+\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}}
+=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\wt{D}u}}
+=\left\langle \frac{\wt{D}v}{\abs{\wt{D}u}},\nu\right\rangle
+ \qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}^n
+\end{align*}
+and since both sides of \eqref{alimo}
+are zero $\abs{\wt{D}u}$-almost everywhere
+on $\abs{\langle \wt{D}u,\nu\rangle }$-negligible sets, we conclude that
+\[
+\lim_{h\to 0}\frac{f\left(
+\tilde u(x)+h\left\langle \dfrac{\wt{D}
+u}{\abs{\wt{D}u}}(x),\nu\right\rangle \right)-f(\tilde u(x))}h
+=\left\langle \frac{\wt{D}v}{\abs{\wt{D}u}}(x),\nu\right\rangle,
+\]
+$\abs{\wt{D}u}$-a.e. in $\mathbf{R}^n$.
+Since $\nu$ is arbitrary, by \fullref{Remarks}{r:dif} \fullref{and}{r:dif0}
+the restriction of $f$ to
+the affine space $T^u_x$ is differentiable at $\tilde u(x)$ for $\abs{\wt{D}
+u}$-almost every $x\in \mathbf{R}^n$ and \eqref{quts} holds.\qed
+\end{step}
+
+It follows from \eqref{sum-Di}, \eqref{detK1}, and \eqref{detK2} that
+\begin{equation}\label{Dt}
+D(t_1,\dots,t_n)=\sum_{I\in\mathbf{n}}(-1)^{\abs{I}-1}\abs{I}
+\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A}^{(\lambda)}
+(\overline I|\overline I).
+\end{equation}
+Let $t_i=\hat x_i$, $i=1,\dots,n$. Lemma 1 leads to
+\begin{equation}\label{Dx}
+D(\hat x_1,\dots,\hat x_n)=\prod_{i\in\mathbf{n}}\hat x_i
+\sum_{I\in\mathbf{n}}(-1)^{\abs{I}-1}\abs{I}\per \mathbf{A}
+^{(\lambda)}(I|I)\det\mathbf{A}^{(\lambda)}(\overline I|\overline I).
+\end{equation}
+By \eqref{H-cycles}, \eqref{sum-Di}, and \eqref{Dx},
+we have the following result:
+\begin{thm}\label{thm-H-param}
+\begin{equation}\label{H-param}
+H_c=\frac{1}{2n}\sum^n_{l =1}l (-1)^{l -1}A_{l}
+^{(\lambda)},
+\end{equation}
+where
+\begin{equation}\label{A-l-lambda}
+A^{(\lambda)}_l =\sum_{I_l \subseteq\mathbf{n}}\per \mathbf{A}
+^{(\lambda)}(I_l |I_l )\det\mathbf{A}^{(\lambda)}
+(\overline I_{l}|\overline I_l ),\abs{I_{l}}=l .
+\end{equation}
+\end{thm}
+
+It is worth noting that $A_l ^{(\lambda)}$ of \eqref{A-l-lambda} is
+similar to the coefficients $b_l $ of the characteristic polynomial of \eqref{bl-sum}. It is well known in graph theory that the coefficients
+$b_l $ can be expressed as a sum over certain subgraphs. It is
+interesting to see whether $A_l $, $\lambda=0$, structural properties
+of a graph.
+
+We may call \eqref{H-param} a parametric representation of $H_c$. In
+computation, the parameter $\lambda_i$ plays very important roles. The
+choice of the parameter usually depends on the properties of the given
+graph. For a complete graph $K_n$, let $\lambda_i=1$, $i=1,\dots,n$.
+It follows from \eqref{A-l-lambda} that
+\begin{equation}\label{compl-gr}
+A^{(1)}_l =\begin{cases} n!,&\text{if }l =1\\
+0,&\text{otherwise}.\end{cases}
+\end{equation}
+By \eqref{H-param}
+\begin{equation}
+H_c=\frac 12(n-1)!.
+\end{equation}
+For a complete bipartite graph $K_{n_1n_2}$, let $\lambda_i=0$, $i=1,\dots,n$.
+By \eqref{A-l-lambda},
+\begin{equation}
+A_l =
+\begin{cases} -n_1!n_2!\delta_{n_1n_2},&\text{if }l =2\\
+0,&\text{otherwise }.\end{cases}
+\label{compl-bip-gr}
+\end{equation}
+\fullref{Theorem}{thm-H-param}
+leads to
+\begin{equation}
+H_c=\frac1{n_1+n_2}n_1!n_2!\delta_{n_1n_2}.
+\end{equation}
+
+Now, we consider an asymmetrical approach. \fullref{Theorem}{thm-main} leads to
+\begin{multline}
+\det\mathbf{K}(t=1,t_1,\dots,t_n;l |l )\\
+=\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\abs{I}}\prod_{i\in I}t_i\prod_{j\in I}
+(D_j+\lambda_jt_j)\det\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \}).
+\end{multline}
+
+By \eqref{H-cycles} and \eqref{sum-ali} we have the following asymmetrical
+result:
+\begin{thm}\label{thm-asym}
+\begin{equation}
+H_c=\frac12\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\abs{I}}\per\mathbf{A}^{(\lambda)}(I|I)\det
+\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \})
+\end{equation}
+which reduces to Goulden--Jackson's formula when $\lambda_i=0,i=1,\dots,n$
+\cite{mami:matrixth}.
+\end{thm}
+
+
+\section{Various font features of the \pkg{amsmath} package}
+\label{s:font}
+\subsection{Bold versions of special symbols}
+
+In the \pkg{amsmath} package \cn{boldsymbol} is used for getting
+individual bold math symbols and bold Greek letters---everything in
+math except for letters of the Latin alphabet,
+where you'd use \cn{mathbf}. For example,
+\begin{verbatim}
+A_\infty + \pi A_0 \sim
+\mathbf{A}_{\boldsymbol{\infty}} \boldsymbol{+}
+\boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}
+\end{verbatim}
+looks like this:
+\[A_\infty + \pi A_0 \sim \mathbf{A}_{\boldsymbol{\infty}}
+\boldsymbol{+} \boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}\]
+
+\subsection{``Poor man's bold''}
+If a bold version of a particular symbol doesn't exist in the
+available fonts,
+then \cn{boldsymbol} can't be used to make that symbol bold.
+At the present time, this means that
+\cn{boldsymbol} can't be used with symbols from
+the \fn{msam} and \fn{msbm} fonts, among others.
+In some cases, poor man's bold (\cn{pmb}) can be used instead
+of \cn{boldsymbol}:
+% Can't show example from msam or msbm because this document is
+% supposed to be TeXable even if the user doesn't have
+% AMSFonts. MJD 5-JUL-1990
+\[\frac{\partial x}{\partial y}
+\pmb{\bigg\vert}
+\frac{\partial y}{\partial z}\]
+\begin{verbatim}
+\[\frac{\partial x}{\partial y}
+\pmb{\bigg\vert}
+\frac{\partial y}{\partial z}\]
+\end{verbatim}
+So-called ``large operator'' symbols such as $\sum$ and $\prod$
+require an additional command, \cn{mathop},
+to produce proper spacing and limits when \cn{pmb} is used.
+For further details see \textit{The \TeX book}.
+\[\sum_{\substack{i<B\\\text{$i$ odd}}}
+\prod_\kappa \kappa F(r_i)\qquad
+\mathop{\pmb{\sum}}_{\substack{i<B\\\text{$i$ odd}}}
+\mathop{\pmb{\prod}}_\kappa \kappa(r_i)
+\]
+\begin{verbatim}
+\[\sum_{\substack{i<B\\\text{$i$ odd}}}
+\prod_\kappa \kappa F(r_i)\qquad
+\mathop{\pmb{\sum}}_{\substack{i<B\\\text{$i$ odd}}}
+\mathop{\pmb{\prod}}_\kappa \kappa(r_i)
+\]
+\end{verbatim}
+
+\section{Compound symbols and other features}
+\label{s:comp}
+\subsection{Multiple integral signs}
+\cn{iint}, \cn{iiint}, and \cn{iiiint} give multiple integral signs
+with the spacing between them nicely adjusted, in both text and
+display style. \cn{idotsint} gives two integral signs with dots
+between them.
+\begin{gather}
+\iint\limits_A f(x,y)\,dx\,dy\qquad\iiint\limits_A
+f(x,y,z)\,dx\,dy\,dz\\
+\iiiint\limits_A
+f(w,x,y,z)\,dw\,dx\,dy\,dz\qquad\idotsint\limits_A f(x_1,\dots,x_k)
+\end{gather}
+
+\subsection{Over and under arrows}
+Some extra over and under arrow operations are provided in
+the \pkg{amsmath} package. (Basic \LaTeX\ provides
+\cn{overrightarrow} and \cn{overleftarrow}).
+\begin{align*}
+\overrightarrow{\psi_\delta(t) E_t h}&
+=\underrightarrow{\psi_\delta(t) E_t h}\\
+\overleftarrow{\psi_\delta(t) E_t h}&
+=\underleftarrow{\psi_\delta(t) E_t h}\\
+\overleftrightarrow{\psi_\delta(t) E_t h}&
+=\underleftrightarrow{\psi_\delta(t) E_t h}
+\end{align*}
+\begin{verbatim}
+\begin{align*}
+\overrightarrow{\psi_\delta(t) E_t h}&
+=\underrightarrow{\psi_\delta(t) E_t h}\\
+\overleftarrow{\psi_\delta(t) E_t h}&
+=\underleftarrow{\psi_\delta(t) E_t h}\\
+\overleftrightarrow{\psi_\delta(t) E_t h}&
+=\underleftrightarrow{\psi_\delta(t) E_t h}
+\end{align*}
+\end{verbatim}
+These all scale properly in subscript sizes:
+\[\int_{\overrightarrow{AB}} ax\,dx\]
+\begin{verbatim}
+\[\int_{\overrightarrow{AB}} ax\,dx\]
+\end{verbatim}
+
+\subsection{Dots}
+
+Normally you need only type \cn{dots} for ellipsis dots in a
+math formula. The main exception is when the dots
+fall at the end of the formula; then you need to
+specify one of \cn{dotsc} (series dots, after a comma),
+\cn{dotsb} (binary dots, for binary relations or operators),
+\cn{dotsm} (multiplication dots), or \cn{dotsi} (dots after
+an integral). For example, the input
+\begin{verbatim}
+Then we have the series $A_1,A_2,\dotsc$,
+the regional sum $A_1+A_2+\dotsb$,
+the orthogonal product $A_1A_2\dotsm$,
+and the infinite integral
+\[\int_{A_1}\int_{A_2}\dotsi\].
+\end{verbatim}
+produces
+\begin{quotation}
+Then we have the series $A_1,A_2,\dotsc$,
+the regional sum $A_1+A_2+\dotsb$,
+the orthogonal product $A_1A_2\dotsm$,
+and the infinite integral
+\[\int_{A_1}\int_{A_2}\dotsi\]
+\end{quotation}
+
+\subsection{Accents in math}
+
+Double accents:
+\[\Hat{\Hat{H}}\quad\Check{\Check{C}}\quad
+\Tilde{\Tilde{T}}\quad\Acute{\Acute{A}}\quad
+\Grave{\Grave{G}}\quad\Dot{\Dot{D}}\quad
+\Ddot{\Ddot{D}}\quad\Breve{\Breve{B}}\quad
+\Bar{\Bar{B}}\quad\Vec{\Vec{V}}\]
+\begin{verbatim}
+\[\Hat{\Hat{H}}\quad\Check{\Check{C}}\quad
+\Tilde{\Tilde{T}}\quad\Acute{\Acute{A}}\quad
+\Grave{\Grave{G}}\quad\Dot{\Dot{D}}\quad
+\Ddot{\Ddot{D}}\quad\Breve{\Breve{B}}\quad
+\Bar{\Bar{B}}\quad\Vec{\Vec{V}}\]
+\end{verbatim}
+This double accent operation is complicated
+and tends to slow down the processing of a \LaTeX\ file.
+
+
+\subsection{Dot accents}
+\cn{dddot} and \cn{ddddot} are available to
+produce triple and quadruple dot accents
+in addition to the \cn{dot} and \cn{ddot} accents already available
+in \LaTeX:
+\[\dddot{Q}\qquad\ddddot{R}\]
+\begin{verbatim}
+\[\dddot{Q}\qquad\ddddot{R}\]
+\end{verbatim}
+
+\subsection{Roots}
+
+In the \pkg{amsmath} package \cn{leftroot} and \cn{uproot} allow you to adjust
+the position of the root index of a radical:
+\begin{verbatim}
+\sqrt[\leftroot{-2}\uproot{2}\beta]{k}
+\end{verbatim}
+gives good positioning of the $\beta$:
+\[\sqrt[\leftroot{-2}\uproot{2}\beta]{k}\]
+
+\subsection{Boxed formulas} The command \cn{boxed} puts a box around its
+argument, like \cn{fbox} except that the contents are in math mode:
+\begin{verbatim}
+\boxed{W_t-F\subseteq V(P_i)\subseteq W_t}
+\end{verbatim}
+\[\boxed{W_t-F\subseteq V(P_i)\subseteq W_t}.\]
+
+\subsection{Extensible arrows}
+\cn{xleftarrow} and \cn{xrightarrow} produce
+arrows that extend automatically to accommodate unusually wide
+subscripts or superscripts. The text of the subscript or superscript
+are given as an optional resp.\@ mandatory argument:
+Example:
+\[0 \xleftarrow[\zeta]{\alpha} F\times\triangle[n-1]
+ \xrightarrow{\partial_0\alpha(b)} E^{\partial_0b}\]
+\begin{verbatim}
+\[0 \xleftarrow[\zeta]{\alpha} F\times\triangle[n-1]
+ \xrightarrow{\partial_0\alpha(b)} E^{\partial_0b}\]
+\end{verbatim}
+
+\subsection{\cn{overset}, \cn{underset}, and \cn{sideset}}
+Examples:
+\[\overset{*}{X}\qquad\underset{*}{X}\qquad
+\overset{a}{\underset{b}{X}}\]
+\begin{verbatim}
+\[\overset{*}{X}\qquad\underset{*}{X}\qquad
+\overset{a}{\underset{b}{X}}\]
+\end{verbatim}
+
+The command \cn{sideset} is for a rather special
+purpose: putting symbols at the subscript and superscript
+corners of a large operator symbol such as $\sum$ or $\prod$,
+without affecting the placement of limits.
+Examples:
+\[\sideset{_*^*}{_*^*}\prod_k\qquad
+\sideset{}{'}\sum_{0\le i\le m} E_i\beta x
+\]
+\begin{verbatim}
+\[\sideset{_*^*}{_*^*}\prod_k\qquad
+\sideset{}{'}\sum_{0\le i\le m} E_i\beta x
+\]
+\end{verbatim}
+
+\subsection{The \cn{text} command}
+The main use of the command \cn{text} is for words or phrases in a
+display:
+\[\mathbf{y}=\mathbf{y}'\quad\text{if and only if}\quad
+y'_k=\delta_k y_{\tau(k)}\]
+\begin{verbatim}
+\[\mathbf{y}=\mathbf{y}'\quad\text{if and only if}\quad
+y'_k=\delta_k y_{\tau(k)}\]
+\end{verbatim}
+
+\subsection{Operator names}
+The more common math functions such as $\log$, $\sin$, and $\lim$
+have predefined control sequences: \verb=\log=, \verb=\sin=,
+\verb=\lim=.
+The \pkg{amsmath} package provides \cn{DeclareMathOperator} and
+\cn{DeclareMathOperator*}
+for producing new function names that will have the
+same typographical treatment.
+Examples:
+\[\norm{f}_\infty=
+\esssup_{x\in R^n}\abs{f(x)}\]
+\begin{verbatim}
+\[\norm{f}_\infty=
+\esssup_{x\in R^n}\abs{f(x)}\]
+\end{verbatim}
+\[\meas_1\{u\in R_+^1\colon f^*(u)>\alpha\}
+=\meas_n\{x\in R^n\colon \abs{f(x)}\geq\alpha\}
+\quad \forall\alpha>0.\]
+\begin{verbatim}
+\[\meas_1\{u\in R_+^1\colon f^*(u)>\alpha\}
+=\meas_n\{x\in R^n\colon \abs{f(x)}\geq\alpha\}
+\quad \forall\alpha>0.\]
+\end{verbatim}
+\cn{esssup} and \cn{meas} would be defined in the document preamble as
+\begin{verbatim}
+\DeclareMathOperator*{\esssup}{ess\,sup}
+\DeclareMathOperator{\meas}{meas}
+\end{verbatim}
+
+The following special operator names are predefined in the \pkg{amsmath}
+package: \cn{varlimsup}, \cn{varliminf}, \cn{varinjlim}, and
+\cn{varprojlim}. Here's what they look like in use:
+\begin{align}
+&\varlimsup_{n\rightarrow\infty}
+ \mathcal{Q}(u_n,u_n-u^{\#})\le0\\
+&\varliminf_{n\rightarrow\infty}
+ \left\lvert a_{n+1}\right\rvert/\left\lvert a_n\right\rvert=0\\
+&\varinjlim (m_i^\lambda\cdot)^*\le0\\
+&\varprojlim_{p\in S(A)}A_p\le0
+\end{align}
+\begin{verbatim}
+\begin{align}
+&\varlimsup_{n\rightarrow\infty}
+ \mathcal{Q}(u_n,u_n-u^{\#})\le0\\
+&\varliminf_{n\rightarrow\infty}
+ \left\lvert a_{n+1}\right\rvert/\left\lvert a_n\right\rvert=0\\
+&\varinjlim (m_i^\lambda\cdot)^*\le0\\
+&\varprojlim_{p\in S(A)}A_p\le0
+\end{align}
+\end{verbatim}
+
+\subsection{\cn{mod} and its relatives}
+The commands \cn{mod} and \cn{pod} are variants of
+\cn{pmod} preferred by some authors; \cn{mod} omits the parentheses,
+whereas \cn{pod} omits the `mod' and retains the parentheses.
+Examples:
+\begin{align}
+x&\equiv y+1\pmod{m^2}\\
+x&\equiv y+1\mod{m^2}\\
+x&\equiv y+1\pod{m^2}
+\end{align}
+\begin{verbatim}
+\begin{align}
+x&\equiv y+1\pmod{m^2}\\
+x&\equiv y+1\mod{m^2}\\
+x&\equiv y+1\pod{m^2}
+\end{align}
+\end{verbatim}
+
+\subsection{Fractions and related constructions}
+\label{fracs}
+
+The usual notation for binomials is similar to the fraction concept,
+so it has a similar command \cn{binom} with two arguments. Example:
+\begin{equation}
+\begin{split}
+\sum_{\gamma\in\Gamma_C} I_\gamma&
+=2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}\\
+&\quad+\dots+(-1)^l\binom{k}{l}2^{k-l}
++\dots+(-1)^k\\
+&=(2-1)^k=1
+\end{split}
+\end{equation}
+\begin{verbatim}
+\begin{equation}
+\begin{split}
+[\sum_{\gamma\in\Gamma_C} I_\gamma&
+=2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}\\
+&\quad+\dots+(-1)^l\binom{k}{l}2^{k-l}
++\dots+(-1)^k\\
+&=(2-1)^k=1
+\end{split}
+\end{equation}
+\end{verbatim}
+There are also abbreviations
+\begin{verbatim}
+\dfrac \dbinom
+\tfrac \tbinom
+\end{verbatim}
+for the commonly needed constructions
+\begin{verbatim}
+{\displaystyle\frac ... } {\displaystyle\binom ... }
+{\textstyle\frac ... } {\textstyle\binom ... }
+\end{verbatim}
+
+The generalized fraction command \cn{genfrac} provides full access to
+the six \TeX{} fraction primitives:
+\begin{align}
+\text{\cn{over}: }&\genfrac{}{}{}{}{n+1}{2}&
+\text{\cn{overwithdelims}: }&
+ \genfrac{\langle}{\rangle}{}{}{n+1}{2}\\
+\text{\cn{atop}: }&\genfrac{}{}{0pt}{}{n+1}{2}&
+\text{\cn{atopwithdelims}: }&
+ \genfrac{(}{)}{0pt}{}{n+1}{2}\\
+\text{\cn{above}: }&\genfrac{}{}{1pt}{}{n+1}{2}&
+\text{\cn{abovewithdelims}: }&
+ \genfrac{[}{]}{1pt}{}{n+1}{2}
+\end{align}
+\begin{verbatim}
+\text{\cn{over}: }&\genfrac{}{}{}{}{n+1}{2}&
+\text{\cn{overwithdelims}: }&
+ \genfrac{\langle}{\rangle}{}{}{n+1}{2}\\
+\text{\cn{atop}: }&\genfrac{}{}{0pt}{}{n+1}{2}&
+\text{\cn{atopwithdelims}: }&
+ \genfrac{(}{)}{0pt}{}{n+1}{2}\\
+\text{\cn{above}: }&\genfrac{}{}{1pt}{}{n+1}{2}&
+\text{\cn{abovewithdelims}: }&
+ \genfrac{[}{]}{1pt}{}{n+1}{2}
+\end{verbatim}
+
+\subsection{Continued fractions}
+The continued fraction
+\begin{equation}
+\cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+\dotsb
+}}}}}
+\end{equation}
+can be obtained by typing
+\begin{verbatim}
+\cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+\dotsb
+}}}}}
+\end{verbatim}
+Left or right placement of any of the numerators is accomplished by using
+\cn{cfrac[l]} or \cn{cfrac[r]} instead of \cn{cfrac}.
+
+\subsection{Smash}
+
+In \pkg{amsmath} there are optional arguments \verb"t" and \verb"b" for
+the plain \TeX\ command \cn{smash}, because sometimes it is advantageous
+to be able to `smash' only the top or only the bottom of something while
+retaining the natural depth or height. In the formula
+$X_j=(1/\sqrt{\smash[b]{\lambda_j}})X_j'$ \cn{smash}\verb=[b]= has been
+used to limit the size of the radical symbol.
+\begin{verbatim}
+$X_j=(1/\sqrt{\smash[b]{\lambda_j}})X_j'$
+\end{verbatim}
+Without the use of \cn{smash}\verb=[b]= the formula would have appeared
+thus: $X_j=(1/\sqrt{\lambda_j})X_j'$, with the radical extending to
+encompass the depth of the subscript $j$.
+
+\subsection{The `cases' environment}
+`Cases' constructions like the following can be produced using
+the \env{cases} environment.
+\begin{equation}
+P_{r-j}=
+ \begin{cases}
+ 0& \text{if $r-j$ is odd},\\
+ r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}.
+ \end{cases}
+\end{equation}
+\begin{verbatim}
+\begin{equation} P_{r-j}=
+ \begin{cases}
+ 0& \text{if $r-j$ is odd},\\
+ r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}.
+ \end{cases}
+\end{equation}
+\end{verbatim}
+Notice the use of \cn{text} and the embedded math.
+
+\subsection{Matrix}
+
+Here are samples of the matrix environments,
+\cn{matrix}, \cn{pmatrix}, \cn{bmatrix}, \cn{Bmatrix}, \cn{vmatrix}
+and \cn{Vmatrix}:
+\begin{equation}
+\begin{matrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{matrix}\quad
+\begin{pmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{pmatrix}\quad
+\begin{bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{bmatrix}\quad
+\begin{Bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Bmatrix}\quad
+\begin{vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{vmatrix}\quad
+\begin{Vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Vmatrix}
+\end{equation}
+%
+\begin{verbatim}
+\begin{matrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{matrix}\quad
+\begin{pmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{pmatrix}\quad
+\begin{bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{bmatrix}\quad
+\begin{Bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Bmatrix}\quad
+\begin{vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{vmatrix}\quad
+\begin{Vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Vmatrix}
+\end{verbatim}
+
+To produce a small matrix suitable for use in text, use the
+\env{smallmatrix} environment.
+\begin{verbatim}
+\begin{math}
+ \bigl( \begin{smallmatrix}
+ a&b\\ c&d
+ \end{smallmatrix} \bigr)
+\end{math}
+\end{verbatim}
+To show
+the effect of the matrix on the surrounding lines of
+a paragraph, we put it here: \begin{math}
+ \bigl( \begin{smallmatrix}
+ a&b\\ c&d
+ \end{smallmatrix} \bigr)
+\end{math}
+and follow it with enough text to ensure that there will
+be at least one full line below the matrix.
+
+\cn{hdotsfor}\verb"{"\textit{number}\verb"}" produces a row of dots in a matrix
+spanning the given number of columns:
+\[W(\Phi)= \begin{Vmatrix}
+\dfrac\varphi{(\varphi_1,\varepsilon_1)}&0&\dots&0\\
+\dfrac{\varphi k_{n2}}{(\varphi_2,\varepsilon_1)}&
+\dfrac\varphi{(\varphi_2,\varepsilon_2)}&\dots&0\\
+\hdotsfor{5}\\
+\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}&
+\dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}&\dots&
+\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})}&
+\dfrac{\varphi}{(\varphi_n,\varepsilon_n)}
+\end{Vmatrix}\]
+\begin{verbatim}
+\[W(\Phi)= \begin{Vmatrix}
+\dfrac\varphi{(\varphi_1,\varepsilon_1)}&0&\dots&0\\
+\dfrac{\varphi k_{n2}}{(\varphi_2,\varepsilon_1)}&
+\dfrac\varphi{(\varphi_2,\varepsilon_2)}&\dots&0\\
+\hdotsfor{5}\\
+\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}&
+\dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}&\dots&
+\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})}&
+\dfrac{\varphi}{(\varphi_n,\varepsilon_n)}
+\end{Vmatrix}\]
+\end{verbatim}
+The spacing of the dots can be varied through use of a square-bracket
+option, for example, \verb"\hdotsfor[1.5]{3}". The number in square brackets
+will be used as a multiplier; the normal value is 1.
+
+\subsection{The \cn{substack} command}
+
+The \cn{substack} command can be used to produce a multiline
+subscript or superscript:
+for example
+\begin{verbatim}
+\sum_{\substack{0\le i\le m\\ 0<j<n}} P(i,j)
+\end{verbatim}
+produces a two-line subscript underneath the sum:
+\begin{equation}
+\sum_{\substack{0\le i\le m\\ 0<j<n}} P(i,j)
+\end{equation}
+A slightly more generalized form is the \env{subarray} environment which
+allows you to specify that each line should be left-aligned instead of
+centered, as here:\EditorialComment{Maybe ``\dots{} as below''?}
+\begin{equation}
+\sum_{\begin{subarray}{l}
+ 0\le i\le m\\ 0<j<n
+ \end{subarray}}
+ P(i,j)
+\end{equation}
+\begin{verbatim}
+\sum_{\begin{subarray}{l}
+ 0\le i\le m\\ 0<j<n
+ \end{subarray}}
+ P(i,j)
+\end{verbatim}
+
+
+\subsection{Big-g-g delimiters}
+
+Here are some big delimiters, first in \cn{normalsize}:
+\[\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ \biggr)
+\]
+\begin{verbatim}
+\[\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ \biggr)
+\]
+\end{verbatim}
+and now in \cn{Large} size:
+{\Large
+\[\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ \biggr)
+\]}
+\begin{verbatim}
+{\Large
+\[\biggl(\mathbf{E}_{y}
+ \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+ \biggr)
+\]}
+\end{verbatim}
+
+
+\bibliography{aomsample}
+\bibliographystyle{aomplain}
+
+\end{document}
+\endinput
diff --git a/Master/texmf-dist/doc/latex/aomart/fullref.pl b/Master/texmf-dist/doc/latex/aomart/fullref.pl
new file mode 100644
index 00000000000..0414089ea00
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/aomart/fullref.pl
@@ -0,0 +1,62 @@
+#!/usr/bin/perl
+#
+# Convert the refences to \fullref. Usage:
+# perl fullref.pl original.tex > converted.tex
+#
+#
+# Copyright (C) 2010 Annals of Mathematics. Public domain.
+#
+# Author: Boris Veytsman
+#
+# Version: 0.9, 2010/12/04
+
+use strict;
+
+# List of patterns for 'equation' words
+my @eqsynonyms = ('\S*equa\S*', 'relat\S*', 'item\S*',
+ 'condition\S*',
+ '\S*propert\S*');
+
+# First we skip preamble
+while(<>) {
+ print;
+ last if (/\\begin\{document\}/);
+}
+
+# This is a trick to catch \ref being the first word on the line
+my $prevline = "";
+
+# Processing document
+while (<>) {
+ if ((/^[\s~]*\(?\\ref/) || (/^[\s~]*\\eqref/)) {
+ chomp $prevline;
+ $_ = "$prevline $_";
+ } else {
+ print $prevline;
+ }
+
+ # Now the meat of the substitutions
+ # We add initial space, so all words have space before them.
+ $_ = " $_";
+ foreach my $synonym (@eqsynonyms) {
+ s/(\s)($synonym)[\s~]*\(\\ref\{([^\}]+)\}\)/$1\\pfullref{$2}{$3}/gi;
+ s/(\s)($synonym)[\s~]*\\eqref\{([^\}]+)\}/$1\\eqfullref{$2}{$3}/gi;
+ }
+ s/(\s)([^\s\\]\S*[^~\s\(\)\[\]])[\s~]*\[\\ref\{([^\}]+)\}\]/$1\\bfullref{$2}{$3}/g;
+ s/(\s)([^\s\\]\S*[^~\s\(\)\[\]])[\s~]*\\ref\{([^\}]+)\}/$1\\fullref{$2}{$3}/g;
+
+ # Now delete the extra space
+ s/^ //;
+ $prevline=$_;
+ if (/\\end\{document\}/) {
+ print;
+ last;
+ }
+}
+
+# And processing whatever is left
+while (<>) {
+ print;
+}
+
+exit 0;
diff --git a/Master/texmf-dist/source/latex/aomart/aomart.dtx b/Master/texmf-dist/source/latex/aomart/aomart.dtx
new file mode 100644
index 00000000000..b2c94d1bc46
--- /dev/null
+++ b/Master/texmf-dist/source/latex/aomart/aomart.dtx
@@ -0,0 +1,1732 @@
+% \iffalse
+% $Id: aomart.dtx,v 1.41 2011-01-02 22:20:16 boris Exp $
+%
+% Copyright 2010, The Annals of Mathematics.
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either
+% version 1.3 of this license or (at your option) any
+% later version.
+% The latest version of the license is in
+% http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of
+% LaTeX version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Boris Veytsman,
+% <borisv@lk.net>
+%
+% This work consists of the file aomart.dtx and the
+% derived file aomart.cls, and files aomplain.bst and aomalpha.bst
+%
+% The file fullref.pl, included with this package, is in
+% public domain.
+%
+% \fi
+% \CheckSum{988}
+%
+%
+%% \CharacterTable
+%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%% Digits \0\1\2\3\4\5\6\7\8\9
+%% Exclamation \! Double quote \" Hash (number) \#
+%% Dollar \$ Percent \% Ampersand \&
+%% Acute accent \' Left paren \( Right paren \)
+%% Asterisk \* Plus \+ Comma \,
+%% Minus \- Point \. Solidus \/
+%% Colon \: Semicolon \; Less than \<
+%% Equals \= Greater than \> Question mark \?
+%% Commercial at \@ Left bracket \[ Backslash \\
+%% Right bracket \] Circumflex \^ Underscore \_
+%% Grave accent \` Left brace \{ Vertical bar \|
+%% Right brace \} Tilde \~}
+%
+%\iffalse
+% Taken from xkeyval.dtx
+%\fi
+%\makeatletter
+%\def\DescribeOption#1{\leavevmode\@bsphack
+% \marginpar{\raggedleft\PrintDescribeOption{#1}}%
+% \SpecialOptionIndex{#1}\@esphack\ignorespaces}
+%\def\PrintDescribeOption#1{\strut\emph{option}\\\MacroFont #1\ }
+%\def\SpecialOptionIndex#1{\@bsphack
+% \index{#1\actualchar{\protect\ttfamily#1}
+% (option)\encapchar usage}%
+% \index{options:\levelchar#1\actualchar{\protect\ttfamily#1}\encapchar
+% usage}\@esphack}
+%\def\DescribeOptions#1{\leavevmode\@bsphack
+% \marginpar{\raggedleft\strut\emph{options}%
+% \@for\@tempa:=#1\do{%
+% \\\strut\MacroFont\@tempa\SpecialOptionIndex\@tempa
+% }}\@esphack\ignorespaces}
+%\makeatother
+%
+% \MakeShortVerb{|}
+% \GetFileInfo{aomart.dtx}
+% \newcommand{\progname}[1]{\textsf{#1}}
+% \title{\LaTeX{} Class for The \emph{Annals of
+% Mathematics}\thanks{\copyright 2010, Annals of Mathematics}}
+% \author{Boris Veytsman\thanks{%
+% \href{mailto:borisv@lk.net}{\texttt{borisv@lk.net}},
+% \href{mailto:boris@varphi.com}{\texttt{boris@varphi.com}}}}
+% \date{\filedate, \fileversion}
+% \maketitle
+% \begin{abstract}
+% This package provides a class for typesetting articles for
+% The \emph{Annals of Mathematics}
+% \end{abstract}
+% \tableofcontents
+%
+% \changes{v0.2}{2010/08/24}{First fully functional version}
+% \changes{v0.3}{2010/09/27}{Documentation update}
+% \changes{v0.4}{2010/09/29}{Documentation update}
+% \changes{v0.6}{2010/10/03}{Changes to bst files}
+% \changes{v0.6}{2010/10/03}{Fullref.pl is much less agressive now}
+% \changes{v0.7}{2010/10/09}{Bibliography styles changed}
+% \changes{v0.8}{2010/11/16}{Documentation update}
+% \changes{v0.8}{2010/11/21}{Bibliography styles update}
+% \changes{v0.9}{2010/12/04}{Bibliography styles update}
+% \changes{v0.9}{2010/12/04}{Documentation update}
+% \changes{v0.10}{2010/12/20}{Bibliography styles update}
+% \changes{v0.10}{2010/12/20}{Documentation update}
+% \changes{v1.0}{2010/12/21}{Top matter macros are now only in preamble}
+%
+% \clearpage
+%
+%\section{Introduction}
+%\label{sec:intro}
+%
+% The \emph{Annals of Mathematics} is published bimonthly with the
+% cooperation of Princeton University and the Institute for Advanced
+% Study. Founded in 1884 by Ormond Stone of the University of
+% Virginia, the journal was transferred in 1899 to Harvard University,
+% and in 1911 to Princeton University. Since 1933, the Annals has been
+% edited jointly by Princeton University and the Institute for
+% Advanced Study (see
+% \url{http://annals.princeton.edu/annals/about/journal/about.html}).
+%
+% This class presents a complete redesign of the journal style---with
+% new fonts and new interface.
+%
+%
+% An author well acquainted with AMS\LaTeX{} should find this package
+% easy to use and configurable. The User Manual below illustrates the
+% basic use of the class and discusses the differences with \progname{amsart}.
+% For an in-depth tutorial of AMS\LaTeX{} I could recommend the
+% excellent book~\cite{Graetzer00:MathIntoLaTeX}.
+%
+%
+%\section{User's Guide}
+%\label{sec:manual}
+%
+%
+%\subsection{Installation}
+%\label{sec:installation}
+%
+% The installation of the class follows the usual
+% practice~\cite{TeXFAQ} for \LaTeX{} packages:
+% \begin{enumerate}
+% \item Run \progname{latex} on |aomart.ins|. This will produce the file
+% |aomart.cls|.
+% \item Put the file |aomart.cls| to
+% the place where \LaTeX{} can find them (see
+% \cite{TeXFAQ} or the documentation for your \TeX{}
+% system).\label{item:install}
+% \item Update the database of file names. Again, see \cite{TeXFAQ}
+% or the documentation for your \TeX{} system for the system-specific
+% details.\label{item:update}
+% \item The file |aomart.pdf| provides the documentation for the
+% package (this is the file you are probably reading now).
+% \end{enumerate}
+% As an alternative to items~\ref{item:install} and~\ref{item:update}
+% you can just put the files in the working directory where your
+% |.tex| file is.
+%
+%
+% The class uses some other \LaTeX{} classes or packages. Most
+% probably, they are already installed on your system. If not (or if
+% their versions are very old), you need to download and
+% install them. Here is the list:
+% \begin{enumerate}
+% \item \progname{amsart} class and related
+% packages~\cite{Downes04:amsart},
+% \item Package \progname{hyperref}~\cite{Rahtz06:Hyperref},
+% \item \progname{ifpdf} package~\cite{Oberdiek06:Ifpdf},
+% \item \progname{fancyhdr} package~\cite{Oostrum04:Fancyhdr},
+% \item \progname{cmtiup} package~\cite{Znamenskii03:Cmtiup} for
+% ``special italics'' with uprgiht digits and punctuation. Note that
+% since many distributions do not include this package, you may need
+% to install it yourself. Just download the file
+% \url{http://mirrors.ctan.org/fonts/cm/cmtiup.zip}, unzip it in your
+% \path{TEXMF} directory and rebuild the file names database with the
+% command like |mktexlsr|,
+% \item \progname{yhmath} package~\cite{Haralambous96:Yhmath}.
+% \end{enumerate}
+%
+%
+%\subsection{Invocation}
+%\label{sec:invocation}
+%
+% To use the class, put in the preamble of your document
+% \begin{flushleft}
+% |\documentclass[|\meta{options}|]{aomart}|
+% \end{flushleft}
+% The class internally loads \progname{amsart}, so all facilities of
+% \progname{amsart}~\cite{Graetzer00:MathIntoLaTeX, amsldoc} can be used in the
+% source.
+%
+%
+%
+% \DescribeOptions{draft,final}
+% The options |draft| and |final| work in the same way as for
+% \progname{amsart} and standard \LaTeX. If the option |draft| is
+% chosen, the overfull lines are marked by black boxes on the margins
+% \emph{and} the |\includegraphics| prints blank placeholders for the
+% images. The option |final| (default) switches off the marking of
+% overfull lines and restores the behavior of |\includegraphics|. To
+% switch on just the overfull marks, without changing the behavior of
+% |\includegraphics|, one can either explicitly pass the option final
+% to \progname{graphics} package:
+% \begin{verbatim}
+% \documentclass[draft]{aomart}
+% \usepackage[final]{graphics}
+% \end{verbatim}
+% or add in the beginning of the document
+% \begin{verbatim}
+% \overfullrule=5pt
+% \end{verbatim}
+%
+% \DescribeOption{manuscript}
+% The option |manuscript| is intended to faciliate the communications
+% between the editor and the author. It enables two things:
+% \begin{enumerate}
+% \item Numbering of lines in the manuscript is switched off in the
+% normal mode, but is on in the manuscript mode.
+% \item Command |\EditorialComment| is no-op in normal mode, but
+% produces mariginal commentaries in the manuscript
+% \item Hyperlinks are black in normal mode, but blue in manuscript
+% mode.
+% \end{enumerate}
+%
+% \DescribeOption{screen}
+% The option |screen| is intended for the onscreen version of the
+% acticle. If this option is selected, the links are blue colored,
+% and the margins are reduced.
+%
+% \DescribeOptions{8pt,9pt,10pt,11pt,12pt}
+% The size-changing options of \progname{amsart} class (|8pt|, |9pt|,
+% \dots, |12pt|) have no effect other than producing a warning in the
+% log since the journal is designed for
+% only one type size (roughly corresponding to |11pt| of
+% \progname{amsart}).
+%
+%
+%
+%
+%\subsection{Top Matter}
+%\label{sec:top_matter}
+%
+%
+% There are two kinds of top matter commands: the ones used primarily
+% for authors and the ones used primarily for editors. We describe
+% them separately.
+%
+% The macros descibed below must be issued in the preamble of the
+% document, i.e. before |\begin{document}|. They produce fatal error
+% otherwise. This behavior is required by the way non-\TeX{} scripts
+% process the files to produce metadata.
+%
+% The only exception is abstract, which should be placed between
+% after |\begin{document}|.
+%
+%
+%\subsubsection{Commands for Authors}
+%\label{sec:authors_commands}
+%
+%
+% \DescribeMacro{\title}
+% The command |\title|, as in \progname{amsart} class, has two arguments: one
+% optional, and one mandatory:
+% \begin{flushleft}
+% |\title[|\meta{ShortTitle}|]{|\meta{FullTitle}|}|
+% \end{flushleft}
+% The mandatory argument is the full title of the article. The
+% optional argument, if present, defines the shorter version of the
+% title for running heads. If the optional argument is absent, the
+% full title is used instead.
+%
+% The optional argument should be used in two cases: when the full
+% title is too long to fit in the running head, \emph{and} when the
+% author wants to add a footnote or linebreaks to the title.
+%
+%
+% \DescribeMacro{\author}
+% \DescribeMacro{\email}
+% \DescribeMacro{\address} \DescribeMacro{\curraddr}
+% \DescribeMacro{\urladdr}
+% The interface for specifying the authors
+% and their affiliations is close the the one of
+% \progname{amsart}~\cite{instr-l} (and different from the standard \LaTeX).
+% For each author a separate command |\author| should be used,
+% followed by |\address| and (optionally) |\curraddr|, |\email| and
+% |\urladdr|. Note that the house style of the \emph{Annals of
+% Mathematics} requires writing |\address| in the form
+% \emph{Institution, City, State} (or \emph{Institution, City,
+% Country} for non-US locations).
+% Like the newer versions of \progname{amsart}, \progname{aomart} does
+% \emph{not}
+% require the doubling of the |@| symbols in the e-mail addresses.
+% The macro |\author| has two arguments, similarly to |\title|:
+% \begin{flushleft}
+% |\author[|\meta{AbbrevName}|]{|\meta{FullName}|}|
+% \end{flushleft}
+% The optional argument defines the shorter form of the author's name
+% to be included in the running head.
+%
+% \DescribeMacro{\givenname} \DescribeMacro{\surname}
+% The papers published in the \emph{Annals of Mathematics} are
+% included in various databases. For the indexing purposes it is
+% important to correctly separate the authors' names into ``First
+% Name/Surname'' parts. This operation is not easy for the
+% computers. Therefore we decided that the authors should know best
+% how to deal with their names. The macros |\givenname| and
+% |\surname| are used to indicate how to split the name into the
+% parts.
+%
+% \DescribeMacro{\shortauthors}
+% In some cases the authors list may be too long for the running head,
+% even if the abbreviated forms are used for each author. In this
+% case it is possible to change the running head by a
+% \emph{redefinition} of the command |\shortauthors|. This
+% redefinition must be done after all |\author| commands, but before
+% |\maketitle|:
+% \begin{verbatim}
+% \renewcommand{\shortauthors}{A.~Smith et al}
+% \end{verbatim}
+%
+%
+% \DescribeMacro{\thanks}
+% Like \progname{amsart} (and unlike standard \LaTeX{}),
+% \progname{aomart} allows |\thanks| only \emph{outside} of commands
+% |\title| and |\author|.
+%
+%
+% \DescribeEnv{abstract}
+% The abstract of the paper must be put between |\begin{abstract}| and
+% |\end{abstract}|. Unlike the situation in \progname{amsart}
+% class, abstract may be put \emph{after} |\maketitle|.
+%
+% \DescribeMacro{\maketitle}
+% The macro |\maketitle| typesets the top matter. All top matter
+% information should be specified before this command.
+%
+%
+%\subsubsection{Commands for Editors}
+%\label{sec:editors_commands}
+%
+% The commands described in this section should be used by the editors
+% to insert the information about the published paper. They must be
+% put before the |\maketitle| command.
+%
+% \DescribeMacro{\keyword}
+% The command |\keyword| adds a keyword to the list of keywords. This
+% command may be repeated, for example
+% \begin{verbatim}
+% \keyword{Embedding theorem}
+% \keyword{Relatively hyperbolic group}
+% \end{verbatim}
+%
+% \DescribeMacro{\subject}
+% The command |\subject| has three parameters: whether the subject is
+% primary or secondary, the classification scheme and the subject
+% itself, for example
+% \begin{verbatim}
+% \subject{primary}{msc2000}{20E45}
+% \subject{secondary}{msc2000}{20F65}
+% \end{verbatim}
+%
+%
+% \DescribeMacro{\formatdate}
+% The macro |\formatdate| is used to format the dates in the
+% commands. Its argument is the date in the format |YYYY-MM-DD|, for
+% example
+% \begin{verbatim}
+% \formatdate{2010-08-13}
+% \end{verbatim}
+%
+% \DescribeMacro{\received}
+% \DescribeMacro{\revised}
+% \DescribeMacro{\accepted}
+% \DescribeMacro{\published}
+% \DescribeMacro{\publishedonline}
+% The commands |\received|, |\revised|, |\accepted|, |\published|,
+% |\publishedonline| accept as a parameter a date in the form
+% |\formatdate|\marg{YYYY-MM-DD}, for example
+% \begin{verbatim}
+% \received{\formatdate{2004-12-24}}
+% \revised{\formatdate{2006-04-12}}
+% \accepted{\formatdate{2007-10-02}}
+% \end{verbatim}
+%
+% \DescribeMacro{\proposed}
+% \DescribeMacro{\seconded}
+% \DescribeMacro{\corresponding}
+% \DescribeMacro{\editor}
+% \DescribeMacro{\version}
+% The macros |\proposed|, |\seconded|, |\corresponding|, |\editor|,
+% |\version| are used to set the corresponding metadata for the
+% editorial process, for example
+% \begin{verbatim}
+% \proposed{E. D. Itor}
+% \seconded{A. S. Sociate}
+% \corresponding{A. U. Thor}
+% \version{2.1}
+% \end{verbatim}
+%
+%
+%
+% \DescribeMacro{\volumenumber}
+% \DescribeMacro{\issuenumber}
+% \DescribeMacro{\publicationyear}
+% \DescribeMacro{\papernumber}
+% \DescribeMacro{\startpage}
+% \DescribeMacro{\endpage}
+% The macros |\volumenumber|, |\issuenumber|, |\publicationyear|,
+% |\papernumber|, |\startpage|, |\endpage| set up the corresponding
+% data for the paper, for example:
+% \begin{verbatim}
+% \volumenumber{172}
+% \issuenumber{1}
+% \publicationyear{2010}
+% \papernumber{1}
+% \startpage{1}
+% \endpage{39}
+% \end{verbatim}
+% Note that if the argument of |\endpage| is empty, \LaTeX{} tries to
+% calculate the last page number as best as it can.
+%
+%
+% \DescribeMacro{\doinumber}
+% \DescribeMacro{\mrnumber}
+% \DescribeMacro{\zblnumber}
+% The macros |\doinumber|, |\mrnumber| and |\zblnumber| set the
+% information about paper in four major reference databases: DOI
+% (\url{http://www.doi.org/}), MathSciNet
+% (\url{http://www.ams.org/mathscinet/}, Zentralblatt MATH
+% (\url{http://www.zentralblatt-math.org/zmath/}). The use of these
+% macros should be obvious:
+% \begin{verbatim}
+% \doinumber{10.1215/S0012-7094-92-06520-3}
+% \mrnumber{1154181}
+% \zblnumber{0774.14039}
+% \end{verbatim}
+% Note the difference between these commands and the bibliography
+% commands discussed in Section~\ref{sec:biblio}. Commands in this
+% Section set up the data for the \emph{current article.} Commands in
+% Section~\ref{sec:biblio} set up the data for the articles in the
+% bibliography list.
+%
+% Normally you should \emph{not} use |\doinumber| command, since the
+% class will construct the standard DOI for the paper from the volume,
+% issue and paper information. Use it \emph{only} if the result is by
+% any reason wrong.
+%
+%
+%\subsection{Additional Macros}
+%\label{sec:add_guide}
+%
+% \DescribeEnv{eqnarray}
+% \DescribeEnv{eqnarray*}
+% Thee class \progname{aomart} loads the class \progname{amsart}.
+% Therefore all familiar \progname{amsmath} commands~\cite{amsldoc}
+% are available. In particular, there are many commands for writing
+% multiline equations (|split|, |align|, |gather|, |multline|,
+% \dots). The environments |eqnarray| and |eqnarray*|, while still
+% avilable, are \emph{not} recommended and should be avoided if
+% possible.
+%
+% \DescribeMacro{\widetilde}
+% \DescribeMacro{\widehat}
+% \DescribeMacro{\widetriangle}
+% \DescribeMacro{\wideparen}
+% \DescribeMacro{\widering}
+% \DescribeMacro{\widebar}
+% A number of ``wide'' mathematical accents is available due to the
+% (internally loaded) package
+% \progname{yhmath}~\cite{Haralambous96:Yhmath}: |\widetilde|,
+% |\widehat|, |\widetriangle|, |\wideparen|, |\widering|, |\widebar|. See
+% Table~\ref{tab:accents} for the example of the usage.
+%
+% \begin{table}
+% \centering
+% \begin{tabular}{ll}
+% \toprule
+% Code & Example \\
+% \midrule
+% |\widetilde{AB}| & $\widetilde{AB}$\\
+% |\widehat{AB}| & $\widehat{AB}$\\
+% |\widetriangle{AB}| & $\widetriangle{AB}$\\
+% |\wideparen{AB}| & $\wideparen{AB}$\\
+% |\widering{AB}| & $\widering{AB}$\\
+% |\widebar{AB}| & $\widebar{AB}$\\
+% \bottomrule
+% \end{tabular}
+% \caption{Wide Mathematical Accents}
+% \label{tab:accents}
+% \end{table}
+%
+%
+% \DescribeMacro{\EditorialComment}
+% The macro |\EditorialComment|\oarg{comments} typesets the comments
+% on the margins in the |manuscript| mode, for example,
+% \begin{verbatim}
+% Erd\"os proved the following theorem.\EditorialComment{A citation is
+% needed}
+% \end{verbatim}
+%
+%
+% \DescribeMacro{\fullref}
+% \DescribeMacro{\pfullref}
+% \DescribeMacro{\bfullref}
+% \DescribeMacro{\eqfullref}
+% A set of macros is used to make more convenient clickable references
+% in the online versions of papers. The
+% package~\progname{hyperref}~\cite{Rahtz06:Hyperref}
+% makes clickable reference numbers in the phrases like
+% \begin{verbatim}
+% ...in theorem~\ref{thm:Noeter}...
+% ...see equation~\eqref{eq:alpha}...
+% \end{verbatim}
+% However, it is more convenient for the readers if both
+% the number \emph{and} the word ``theorem'' or ``equation'' were
+% clickable. The macros |\*fullref| solve this problem. Each macro
+% has two arguments: the word and the reference, for example
+% \begin{verbatim}
+% ...in \fullref{theorem}{thm:Noeter}...
+% \end{verbatim}
+% The command |\pfullref| typesets
+% the reference in parentheses. The command |\bfullref| typesets it
+% in brackets, and the command |\eqfullref| uses the |\eqref|
+% command, for example,
+% \begin{verbatim}
+% ...see \eqfullref{equation}{eq:alpha}...
+% \end{verbatim}
+%
+% The \progname{Perl} script \path{fullref.pl} can be used to convert
+% change all references to the |\fullref| commands. It works in the
+% following way:
+% \begin{verbatim}
+% perl fullref.pl original.pl > result.pl
+% \end{verbatim}
+% The script converts all instances of combinations ``|word \ref{reference}|''
+% and ``|word~\ref{reference}|''
+% to ``|\fullref{word}{reference}|, and similarly for
+% parenthesized references or |\eqref| commands. To prevent the
+% converting, just put |\ref{reference}| or |\eqref{reference}| inside
+% braces. The ``word'' here must not start with a backslash
+% (i.e. must not be a macro itself). This prevents disastrous results
+% for phrases like ``|see~\ref{a}, \ref{b}|''.
+%
+%
+% The distribution includes two sample files, \path{aomsample.tex} and
+% \path{aomsample1.tex}, the latter being obtained from the former by
+% the script \path{fullref.pl}.
+%
+%
+% Note that |\autoref| command of \progname{hyperref} provides for
+% another mechanism that achieves the same goal. Unlike |\fullref|
+% command, the command |\autoref| tries to figure out the name of the
+% reference from the context. See the manual~\cite{Rahtz06:Hyperref}
+% for more information.
+%
+%\subsection{Theorems}
+%\label{sec:theorems}
+%
+% \DescribeMacro{\newtheorem}
+% You can use the commands of \progname{amsthm}
+% package~\cite{amsthdoc} like
+% |\newtheorem{lem}{Lemma}| for numbered theorems, or
+% |\newtheorem*{KL}{Klein's Lemma}| for unnumbered theorems, or
+% tune the numbering using the optional arguments of these commands.
+%
+% To provide backward compatibility with some other classes used
+% internally by the \emph{Annals of Mathematics,} the class provides
+% yet another optional argument for the command |\newtheorem|,
+% allowing constructions like |\newtheorem[\it]{lem}{Lemma}|. This
+% optional parameter is not used in our typesetting.
+%
+%
+% The class provides two theorem styles:
+% \begin{description}
+% \item[plain:] This is the default theorem style. It is used for
+% Theorem, Lemma, Proposition, Conjecture, Corollary and Claim.
+% \item[definition:] This style is used for Definition, Remark,
+% Notation, Condition, Example etc.
+% \end{description}
+% Note that AMS classes define the third theorem style,
+% \textbf{remark.} In our class remarks are typeset in the
+% \textbf{definition} style. To make the authors' lives easier we
+% define the theorem style \textbf{remark,} which is identical to the
+% theorem style \textbf{definition.}
+%
+%\subsection{Illustrations}
+%\label{sec:illustrations}
+%
+% The authors can use the \progname{graphics}, \progname{graphicx},
+% \progname{PSTricks}, \progname{pgf/tikz}, \progname{Metapost} or
+% other tools to include illustrations
+% (see~\cite{Goossens97:LateXGraphicsCompanion} for a comprehensive
+% discussion of \LaTeX{} graphics possibilities).
+%
+%
+%\subsection{Bibliography}
+%\label{sec:biblio}
+%
+% The authors are encouraged to use Bib\TeX{} for uniform style of
+% bibliography. The distribution includes the BST files
+% \path{aomplain.bst} and \path{aomalpha.bst}. These files have
+% several additional non-standard fields:
+% \begin{description}
+% \item[mrnumber:] MathSciNet number for the article.
+% \item[zblnumber:] Zentralblatt number for the article.
+% \item[doi:] DOI number for the article.
+% \item[jfmnumber:] JFM number for the article.
+% \item[arxiv:] ArXiv reference for the ArXiv manuscript.
+% \item[venue:] (for \texttt{conference} entries) the place where the
+% conference took place.
+% \end{description}
+%
+%
+% \DescribeMacro{\repeatedauthors}
+% If you do not use Bib\TeX{} and produce your bibliography manually,
+% you may want to have repeated authors to
+% be suppressed in the bibliography list, like it is done in the
+% example. The command |\repeatedauthors| should be used in this
+% case, for example:
+% \begin{verbatim}
+% \bibitem{fre:cichon}
+% D.~H. Fremlin, \emph{Cichon's diagram}, presented at the
+% S{\'e}minaire Initiation {\`a} l'Analyse, G. Choquet, M. Rogalski,
+% J. Saint Raymond, at the Universit{\'e} Pierre et Marie Curie,
+% Paris, 23e ann{\'e}e., 1983/194.
+%
+% \bibitem{fre:riesz}
+% \repeatedauthors{D.~H. Fremlin}, \emph{Topological {R}iesz spaces
+% and measure theory}, Cambridge University Press, 2008.
+% \end{verbatim}
+%
+%
+% \DescribeMacro{\doi}
+% \DescribeMacro{\mr}
+% \DescribeMacro{\zbl}
+% \DescribeMacro{\jfm}
+% \DescribeMacro{\arxiv}
+% There are several databases routinely used in the science and
+% mathematics communities. Among them are DOI, MathSciNet,
+% Zentralblatt, Jahrbuch Database, ArXiv. Many bibliographies include
+% references to
+% these databases. The commands |\doi|, |\mr|, |\zbl|, |\jfm|, |\arxiv| are
+% used to typeset these references. If you use Bib\TeX{}, these
+% commands are automatically used for the corresponding fields in your
+% database entries.
+%
+%
+% \StopEventually{%
+% \clearpage
+%
+% \bibliography{aomart}
+% \bibliographystyle{unsrt}}
+%
+% \clearpage
+%
+%
+%\section{Implementation}
+%\label{sec:impl}
+%
+%\subsection{Identification}
+%\label{sec:ident}
+%
+% We start with the declaration who we are. Most |.dtx| files put
+% driver code in a separate driver file |.drv|. We roll this code into the
+% main file, and use the pseudo-guard |<gobble>| for it.
+% \begin{macrocode}
+%<class>\NeedsTeXFormat{LaTeX2e}
+%<*gobble>
+\ProvidesFile{aomart.dtx}
+%</gobble>
+%<class>\ProvidesClass{aomart}
+[2010/12/31 v1.1 Typesetting articles for the Annals of Mathematics]
+% \end{macrocode}
+%
+%
+%
+% And the driver code:
+% \begin{macrocode}
+%<*gobble>
+\documentclass{ltxdoc}
+\usepackage{array,booktabs,amsmath,graphics}
+\let\widebar\overline
+\usepackage{url}
+\usepackage{amsfonts,yhmath}
+\usepackage[breaklinks,colorlinks,linkcolor=black,citecolor=black,
+ pagecolor=black,urlcolor=black,hyperindex=false]{hyperref}
+\PageIndex
+\CodelineIndex
+\RecordChanges
+\EnableCrossrefs
+\begin{document}
+ \DocInput{aomart.dtx}
+\end{document}
+%</gobble>
+%<*class>
+% \end{macrocode}
+%
+%
+%\subsection{Options}
+%\label{sec:options}
+%
+%
+% The size-changing options produce a warning:
+% \begin{macrocode}
+\long\def\aom@size@warning#1{%
+ \ClassWarning{aomart}{Size-changing option #1 will not be
+ honored}}%
+\DeclareOption{8pt}{\aom@size@warning{\CurrentOption}}%
+\DeclareOption{9pt}{\aom@size@warning{\CurrentOption}}%
+\DeclareOption{10pt}{\aom@size@warning{\CurrentOption}}%
+\DeclareOption{11pt}{\aom@size@warning{\CurrentOption}}%
+\DeclareOption{12pt}{\aom@size@warning{\CurrentOption}}%
+% \end{macrocode}
+%
+% \begin{macro}{\if@aom@manuscript@mode}
+% \changes{v0.3}{2010/09/28}{Added manuscript mode}
+% Check whether we are in the manuscript mode
+% \begin{macrocode}
+\newif\if@aom@manuscript@mode
+\@aom@manuscript@modefalse
+\DeclareOption{manuscript}{\@aom@manuscript@modetrue}
+% \end{macrocode}
+%
+% \end{macro}
+%
+%
+% \begin{macro}{\if@aom@screen@mode}
+% \changes{v0.10}{2010/12/20}{Added screen mode}
+% Check whether we are in the screen mode
+% \begin{macrocode}
+\newif\if@aom@screen@mode
+\@aom@screen@modefalse
+\DeclareOption{screen}{\@aom@screen@modetrue}
+% \end{macrocode}
+%
+% \end{macro}
+%
+% All other options are passed to \progname{amsart}:
+% \begin{macrocode}
+\DeclareOption*{\PassOptionsToClass{\CurrentOption}{amsart}}
+% \end{macrocode}
+%
+% Now we read the configuration file
+% \begin{macrocode}
+\InputIfFileExists{aomart.cfg}{%
+ \ClassInfo{aomart}{%
+ Loading configuration file aomart.cfg}}{%
+ \ClassInfo{aomart}{%
+ Configuration file aomart.cfg is not found}}
+% \end{macrocode}
+% And process the options:
+% \begin{macrocode}
+\ProcessOptions\relax
+% \end{macrocode}
+%
+%
+%\subsection{Loading Class and Packages}
+%\label{sec:loading}
+%
+% We start with the base class
+% \begin{macrocode}
+\LoadClass[11pt,noamsfonts]{amsart}
+% \end{macrocode}
+%
+% A bunch of packages:
+% \changes{v0.5}{2010/10/24}{Made Roman font the default URL font}
+% \changes{v0.10}{2010/12/20}{Screen mode triggers special URL
+% settings}
+% \changes{v1.1}{2010/12/31}{In manuscript mode the links are always blue}
+% \begin{macrocode}
+\RequirePackage{fancyhdr, lastpage, ifpdf}
+\RequirePackage[breaklinks,colorlinks]{hyperref}
+\if@aom@screen@mode
+\hypersetup{linkcolor=blue,citecolor=blue,
+ urlcolor=blue, pdfpagescrop={110 705 500 80}}%
+\else\if@aom@manuscript@mode
+\hypersetup{linkcolor=blue,citecolor=blue,
+ urlcolor=blue}%
+\else
+\hypersetup{linkcolor=black,citecolor=black,
+ urlcolor=black}%
+\fi\fi
+\urlstyle{rm}
+% \end{macrocode}
+%
+% \changes{v0.4}{2010/09/29}{Deleted lineno package dependence}
+%
+%\subsection{Fonts}
+%\label{sec:fonts}
+%
+% \changes{v0.8}{2010/1/16}{Added yhmath}
+% We use \progname{yhmath} for wide symbols:
+% \begin{macrocode}
+\RequirePackage{yhmath}
+% \end{macrocode}
+%
+%
+% \changes{v0.3}{2010/09/26}{Added package mdputu}
+% \changes{v0.4}{2010/09/28}{Switched to upright digits in italics
+% everywhere}
+% \changes{v0.8}{2010/1/16}{Switched to cmtiup}
+% We need \progname{cmtiup} package, but we may find out it is not
+% installed.
+% \begin{macrocode}
+\IfFileExists{cmtiup.sty}{%
+ \RequirePackage{cmtiup}}{%
+ \ClassWarning{aomart}{The package mdputu is not found.\MessageBreak
+ You need this package to get italics with upright digits!}}
+% \end{macrocode}
+%
+% \begin{macro}{\specialdigits}
+% \changes{v0.8}{2010/1/16}{Redefined to noop}
+% A legacy macro. We do not need it anymore.
+% \begin{macrocode}
+\def\specialdigits{}%
+\let\sishape=\itshape
+\let\textsi=\textit
+% \end{macrocode}
+%
+% \end{macro}
+%
+% The \progname{amsart} class defines several options for different
+% font sizes (10pt, 11pt, etc). We have just one design size for the
+% articles.
+%
+% \begin{macro}{\@typesizes}
+% \changes{v0.5}{2010/10/24}{Increased LARGE from 16 pt to 17 pt}
+% \changes{v0.5}{2010/10/24}{Corrected typo in the definition of Small}
+% The font information in \progname{amsart} is stored in
+% |\@typesizes| macro. It has 11 typesizes: 5 below and 5 above
+% |\normalsize| .
+% \begin{macrocode}
+\def\@typesizes{%
+ \or{\@vipt}{9}\or{\@viipt}{9}\or{\@viiipt}{9}\or{\@ixpt}{12}%
+ \or{\@xpt}{13}%
+ \or{\@xipt}{14}% normalsize
+ \or{\@xiipt}{15}\or{13}{17}\or{\@xviipt}{20}%
+ \or{19}{23.2}\or{22}{27.8}}%
+\normalsize \linespacing=\baselineskip
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\widebar}
+% The functionality of |\widebar| coincides with that of
+% \progname{amsmath} |\overline|:
+% \begin{macrocode}
+\let\widebar\overline
+% \end{macrocode}
+% \end{macro}
+%
+%\subsection{Page Dimensions and Paragraphing}
+%\label{sec:page}
+%
+% \begin{macro}{\textwidth}
+% \begin{macro}{\textheight}
+% These are from the old \progname{aomamlt2e}:
+% \begin{macrocode}
+\setlength{\textwidth}{31pc}
+\setlength{\textheight}{48pc}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\evensidemargin}
+% \begin{macro}{\oddsidemargin}
+% The margins:
+% \begin{macrocode}
+\oddsidemargin=.65in
+\evensidemargin=.65in
+% \end{macrocode}
+%
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\footins}
+% \begin{macro}{\topskip}
+% \begin{macro}{\abovedisplayskip}
+% \begin{macro}{\belowdisplayskip}
+% \changes{v0.6}{2010/10/03}{Changed belowdisplayskip}
+% Some skips from \progname{aomamlt2e}:
+% \begin{macrocode}
+\setlength{\topskip}{12pt}
+\setlength{\abovedisplayskip}{6.95pt plus3.5pt minus 3pt}
+\setlength{\belowdisplayskip}{6.95pt plus4.5pt minus 3pt}
+\setlength{\skip\footins}{20pt}
+\setlength{\dimen\footins}{3in}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\footskip}
+% Some space for footnotes:
+% \begin{macrocode}
+\setlength\footskip{30pt}
+% \end{macrocode}
+%
+% \end{macro}
+%
+% \begin{macro}{\parskip}
+% \begin{macro}{\parindent}
+% Paragraph shape:
+% \begin{macrocode}
+\setlength{\parindent}{22pt}
+\setlength{\parskip}{\z@}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\widowpenalty}
+% \begin{macro}{\clubpenalty}
+% We suppress widows and clubs:
+% \begin{macrocode}
+\widowpenalty=10000
+\clubpenalty=10000
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+%\subsection{Headers}
+%\label{sec:headers}
+%
+% \begin{macro}{\headsep}
+% Separation between the header and the body
+% \begin{macrocode}
+\setlength{\headsep}{14pt}
+% \end{macrocode}
+%
+% \end{macro}
+% \begin{macro}{\headrulewidth}
+% \begin{macro}{\footrulewidth}
+% We do not want decorative rules in the journal:
+% \begin{macrocode}
+\renewcommand{\headrulewidth}{0pt}
+\renewcommand{\footrulewidth}{0pt}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\@aom@linecount}
+% \changes{v0.4}{2010/09/29}{Added macro}
+% This is the box displayed in the manuscript mode
+% \begin{macrocode}
+\if@aom@manuscript@mode
+ \newsavebox{\@aom@linecount}
+ \savebox{\@aom@linecount}[4em][t]{\parbox[t]{4em}{%
+ \@tempcnta\@ne\relax
+ \loop{\underline{\scriptsize\the\@tempcnta}}\\
+ \advance\@tempcnta by \@ne\ifnum\@tempcnta<43\repeat}}
+\fi
+% \end{macrocode}
+%
+% \end{macro}
+%
+% \changes{v0.4}{2010/09/29}{Used line numbers for headings}
+% \changes{v0.5}{2010/10/24}{Added extra footer in manuscript mode}
+% \changes{v0.5}{2010/10/24}{Corrected the byg with math in headers}
+% \changes{v0.8}{2010/11/16}{Changed authors in header}
+% It is easy to set up headers with \progname{fancyhdr}:
+% \begin{macrocode}
+\pagestyle{fancy}
+\fancyhead{}
+\fancyfoot{}
+\fancyhead[CO]{\scriptsize\shorttitle}
+\fancyhead[RO,LE]{\footnotesize\thepage}
+\if@aom@manuscript@mode
+ \fancyhead[LE]{\footnotesize\thepage\begin{picture}(0,0)%
+ \put(-26,-25){\usebox{\@aom@linecount}}%
+ \end{picture}}
+ \fancyhead[LO]{\begin{picture}(0,0)%
+ \put(-21,-25){\usebox{\@aom@linecount}}%
+ \end{picture}}
+ \fancyfoot[C]{\scriptsize Proof: page numbers may be temporary}
+\fi
+\fancyhead[CE]{\scriptsize\MakeUppercase\shortauthors}
+% \end{macrocode}
+%
+% \changes{v0.3}{2010/09/26}{Addec DOI number in headers}
+% \changes{v0.9}{2010/12/04}{Changed font for the folio on the first page}
+% The first page has the special headers. The style |firstpage| is
+% invoked by \progname{amsart}; here we just redefine it.
+% \begin{macrocode}
+\fancypagestyle{firstpage}{%
+ \fancyhf{}%
+ \if@aom@manuscript@mode
+ \lhead{\begin{picture}(0,0)%
+ \put(-21,-25){\usebox{\@aom@linecount}}%
+ \end{picture}}
+ \fi
+ \chead{\scriptsize%
+ \href{\@annalsurl}{Annals of Mathematics} \textbf{\currentvolume}
+ (\currentyear),
+ \start@page--\end@page\\
+ \ifx\@doinumber\@empty\else
+ \doi{\@doinumber}\fi}%
+ \cfoot{\footnotesize\thepage}}%
+% \end{macrocode}
+%
+% \begin{macro}{\annalsurl}
+% The command to set up the URL of the journal
+% \begin{macrocode}
+\def\annalsurl#1{\gdef\@annalsurl{#1}}
+\annalsurl{http://annals.math.princeton.edu/annals/about/cover/cover.html}
+% \end{macrocode}
+%
+% \end{macro}
+%
+%
+%\subsection{Top Matter Macros}
+%\label{sec:top_matter_code}
+%
+% We make these macros allowed only in the preamble:
+% \begin{macrocode}
+\@onlypreamble{\title}
+\@onlypreamble{\author}
+\@onlypreamble{\email}
+\@onlypreamble{\address}
+\@onlypreamble{\curraddr}
+\@onlypreamble{\urladdr}
+\@onlypreamble{\givenname}
+\@onlypreamble{\surname}
+\@onlypreamble{\thanks}
+\@onlypreamble{\keyword}
+\@onlypreamble{\subject}
+\@onlypreamble{\received}
+\@onlypreamble{\revised}
+\@onlypreamble{\accepted}
+\@onlypreamble{\published}
+\@onlypreamble{\publishedonline}
+\@onlypreamble{\proposed}
+\@onlypreamble{\seconded}
+\@onlypreamble{\corresponding}
+\@onlypreamble{\editor}
+\@onlypreamble{\version}
+\@onlypreamble{\volumenumber}
+\@onlypreamble{\issuenumber}
+\@onlypreamble{\publicationyear}
+\@onlypreamble{\papernumber}
+\@onlypreamble{\startpage}
+\@onlypreamble{\endpage}
+\@onlypreamble{\doinumber}
+\@onlypreamble{\mrnumber}
+\@onlypreamble{\zblnumber}
+% \end{macrocode}
+%
+%
+% Most top matter macros are defined in \progname{amsart}. Here we
+% just add some new macros and redefine some.
+%
+% \begin{macro}{\givenname}
+% \begin{macro}{\surname}
+% These commands at present do nothing: they are for machine
+% indexing only.
+% \begin{macrocode}
+\let\givenname=\@gobble
+\let\surname=\@gobble
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\keyword}
+% Actually \progname{amsart} has |\kewords| macro. It redefines
+% |\@keywords|. Our macro adds to the stack instead.
+% \begin{macrocode}
+\def\keyword#1{\ifx\@keywords\@empty\gdef\@keywords{#1}\else
+ \g@addto@macro\@keywords{, #1}\fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\subject}
+% We do not typeset subject, but use it for PDF info.
+% \begin{macrocode}
+\let\@subjects\@empty
+\def\subject#1#2#3{\ifx\@subjects\@empty\gdef\@subjects{#1:#2:#3}\else
+ \g@addto@macro\@subjects{, #1:#2:#3}\fi}
+% \end{macrocode}
+%
+% \end{macro}
+%
+%
+% \begin{macro}{\formatdate}
+% This just sends the date to the special macro |\@formatdate|
+% \begin{macrocode}
+\def\formatdate#1{\@formatdate#1\@endformatdate}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@formatdate}
+% This macro takes date in the form YYYY-MM-DD and properly formats
+% it. Note how we delete the leading zero in dates like April 02.
+% \begin{macrocode}
+\def\@formatdate#1-#2-#3\@endformatdate{%
+ \@tempcnta=#3\relax
+ \ifcase#2\or
+ January\or February\or March\or April\or May\or June\or
+ July\or August\or September\or October\or November\or December\fi
+ \space\the\@tempcnta,\space#1}
+% \end{macrocode}
+%
+% \end{macro}
+%
+% \begin{macro}{\received}
+% \begin{macro}{\revised}
+% \begin{macro}{\accepted}
+% \begin{macro}{\published}
+% \begin{macro}{\publishedonline}
+% The following macros add stuff to the footnotes material:
+% \begin{macrocode}
+\def\received#1{\def\@received{#1}}
+\let\@received\@empty
+\def\revised#1{\def\@revised{#1}}
+\let\@revised\@empty
+\def\accepted#1{\def\@accepted{#1}}
+\let\@accepted\@empty
+\def\published#1{\def\@published{#1}}
+\let\@published\@empty
+\def\publishedonline#1{\def\@publishedonline{#1}}
+\let\@publishedonline\@empty
+% \end{macrocode}
+%
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% The next macros mimic the functionality of \progname{amsart}
+% |\issueinfo| command. Note that |\issueinfo| still works.
+% \begin{macro}{\volumenumber}
+% This sets the volume of the paper
+% \begin{macrocode}
+\def\volumenumber#1{\def\currentvolume{#1}}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\issuenumber}
+% This sets the issue of the paper:
+% \begin{macrocode}
+\def\issuenumber#1{\def\currentissue{#1}}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\publicationyear}
+% This sets the year of the paper
+% \begin{macrocode}
+\def\publicationyear#1{\def\currentyear{#1}}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\papernumber}
+% \changes{v1.0}{2010/12/21}{Added macro}
+% This is absent from the |\issueinfo|.
+% \begin{macrocode}
+\def\papernumber#1{\def\currentpaper{#1}}
+\papernumber{0000}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\startpage}
+% This defines the starting page of the paper. We have some nice
+% features to set up roman page numbers for editorial
+% stuff---probably not needed for this journal at this time\dots
+% \begin{macrocode}
+\def\startpage#1{\pagenumbering{arabic}\setcounter{page}{#1}%
+ \def\start@page{#1}%
+ \ifnum\c@page<\z@ \pagenumbering{roman}\setcounter{page}{-#1}%
+ \def\start@page{\romannumeral#1}%
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\endpage}
+% This macro again has a twist in it: if the argument is not set, it
+% calculates the last page number itself.
+% \begin{macrocode}
+\def\endpage#1{\def\@tempa{#1}%
+ \ifx\@tempa\@empty\def\end@page{\pageref{LastPage}}%
+ \else\def\end@page{#1}\fi}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\pagespan}
+% This macro is different from the one provided by \progname{amsart}
+% because we want to have the option of automatic calculation of the
+% last page number.
+% \begin{macrocode}
+\def\pagespan#1#2{\startpage{#1}\endpage{#2}}
+\pagespan{1}{}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{abstract}
+% \changes{v0.9}{2010/12/04}{Added parindent for the first par}
+% We slightly redefine abstract comparing to \progname{amsart}
+% conventions:
+% \begin{macrocode}
+\renewenvironment{abstract}{%
+ \ifx\maketitle\relax
+ \ClassWarning{aomart}{Abstract should precede
+ \protect\maketitle\space in AMS derived classes}%
+ \fi
+ \global\setbox\abstractbox=\vtop\bgroup%
+ \vglue1pc%
+ {\centering\normalfont\normalsize\bfseries\abstractname\par\vglue1pc}%
+ \list{}{\labelwidth\z@%
+ \leftmargin3pc \rightmargin\leftmargin%
+ \listparindent\normalparindent \itemindent\normalparindent%
+ \parsep\z@ \@plus\p@%
+ \let\fullwidthdisplay\relax%
+ }%
+ \item[]\normalfont\Small%
+}{%
+ \endlist\egroup%
+ \ifx\@setabstract\relax\@setabstracta\fi%
+}
+
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\proposed}
+% \changes{v0.3}{2010/09/26}{Added macro}
+% We do not typeset the name of the proposer
+% \begin{macrocode}
+\let\proposed\@gobble
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\seconded}
+% \changes{v0.3}{2010/09/26}{Added macro}
+% Or the seconder
+% \begin{macrocode}
+\let\seconded\@gobble
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\corresponding}
+% \changes{v0.3}{2010/09/26}{Added macro}
+% This is the corresponding author---again not typeset
+% \begin{macrocode}
+\let\corresponding\@gobble
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\version}
+% \changes{v0.3}{2010/09/26}{Added macro}
+% We do not typeset the current version of the manuscript either\dots
+% \begin{macrocode}
+\let\version\@gobble
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\doinumber}
+% \changes{v0.3}{2010/09/26}{Added macro}
+% \changes{v1.0}{2010/12/21}{Added default}
+% \begin{macro}{\mrnumber}
+% \changes{v0.3}{2010/09/26}{Added macro}
+% \begin{macro}{\zblnumber}
+% \changes{v0.3}{2010/09/26}{Added macro}
+% Now databases' numbers of the article:
+% \begin{macrocode}
+\def\doinumber#1{\gdef\@doinumber{#1}}
+\doinumber{10.4007/annals.\currentyear.\currentvolume.\currentissue.\currentpaper}
+\def\mrnumber#1{\gdef\@mrnumber{#1}}
+\mrnumber{}
+\def\zblnumber#1{\gdef\@zblnumber{#1}}
+\zblnumber{}
+% \end{macrocode}
+%
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%\subsection{Typesetting Top Matter}
+%\label{sec:maketitle}
+%
+%
+% \begin{macro}{\@settitle}
+% We do not uppercase title. Also, we use this occasion to set PDF
+% information:
+% \begin{macrocode}
+\def\@settitle{\begin{center}%
+ \baselineskip20\p@\relax
+ \bfseries\LARGE
+ \@title
+ \ifpdf
+ \hypersetup{pdftitle=\@title}%
+ \fi
+ \end{center}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@setauthors}
+% \changes{v0.6}{2010/11/04}{'By' and 'and' are in Roman font now}
+% Now we typeset authors according to our specs. Again, we use this
+% occasion to set some PDF information:
+% \begin{macrocode}
+\def\@setauthors{%
+ \ifx\authors\@empty\relax\else
+ \begingroup
+ \def\thanks{\protect\thanks@warning}%
+ \trivlist
+ \centering\footnotesize \@topsep30\p@\relax
+ \advance\@topsep by -\baselineskip
+ \item\relax
+ \def\@@and{{\upshape and}}
+ \author@andify\authors
+ \ifpdf
+ \hypersetup{pdfauthor=\authors}%
+ \fi
+ \def\\{\protect\linebreak}%
+ \small By \scshape\authors%
+ \ifx\@empty\contribs
+ \else
+ ,\penalty-3 \space \@setcontribs
+ \@closetoccontribs
+ \fi
+ \endtrivlist
+ \endgroup
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@setcontribs}
+% Contributors are set up in the same way as authors:
+% \begin{macrocode}
+\def\@setcontribs{%
+ \@xcontribs
+ {\scshape \xcontribs}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@adminfootnotes}
+% We do not typeset keywords, so we change the definition:
+% \begin{macrocode}
+\def\@adminfootnotes{%
+ \let\@makefnmark\relax \let\@thefnmark\relax
+ \ifx\@empty\@date\else \@footnotetext{\@setdate}\fi
+ \ifx\@empty\@subjclass\else \@footnotetext{\@setsubjclass}\fi
+ \ifx\@empty\@keywords\else\@setkeywords\fi
+ \ifx\@empty\@subjects\else\@setsubjects\fi
+ \ifx\@empty\thankses\else \@footnotetext{%
+ \def\par{\let\par\@par}\@setthanks}%
+ \fi
+}
+% \end{macrocode}
+%
+% \end{macro}
+%
+%
+% \begin{macro}{\@setkeywords}
+% We do not typeset keywords, but use them for the PDF information
+% \begin{macrocode}
+\def\@setkeywords{%
+ \ifpdf
+ \hypersetup{pdfkeywords=\@keywords}%
+ \fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@setsubjects}
+% We do not typeset subjects, but use them for the PDF information
+% \begin{macrocode}
+\def\@setsubjects{%
+ \ifpdf
+ \hypersetup{pdfsubject=\@subjects}%
+ \fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\@@and}
+% \changes{v0.9}{2010/12/04}{Redefined macro}
+% We want ``and'' in the footers to be lowercase. Since there is
+% some uppercase involved, we protect it:
+% \begin{macrocode}
+\def\@@and{\MakeLowercase{and}}
+% \end{macrocode}
+%
+% \end{macro}
+%
+%\subsection{Typesetting End Matter}
+%\label{sec:endmatter}
+%
+% End matter is typeset at the end of the paper.
+%
+% \begin{macro}{\enddoc@text}
+% \changes{v0.4}{2010/09/28}{Deleted many dates.}
+% This is the main macro for typesetting endmatter.
+% \begin{macrocode}
+\def\enddoc@text{%
+ \ifx\@empty\@translators \else\@settranslators\fi
+ \ifx\@empty\@received \else\@setreceived\fi
+ \ifx\@empty\@revised \else\@setrevised\fi
+ \ifx\@empty\addresses \else\@setaddresses\fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@setreceived}
+% \begin{macro}{\@setrevised}
+% \begin{macro}{\@setaccepted}
+% \begin{macro}{\@setpublished}
+% \begin{macro}{\@setpublishedonline}
+% \changes{v0.5}{2010/10/24}{Decreased font}
+% \changes{v0.9}{2010/12/04}{Increased font}
+% A bunch of macros for setting centered dates
+% \begin{macrocode}
+\def\@setreceived{{\centering(Received: \@received)\par}}
+\def\@setrevised{{\centering(Revised: \@revised)\par}}
+\def\@setaccepted{{\centering(Accepted: \@accepted)\par}}
+\def\@setpublished{{\centering(Published: \@published)\par}}
+\def\@setpublishedonline{{\centering(Published online: \@publishedonline)\par}}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\emailaddrname}
+% \changes{v0.5}{2010/10/24}{Changed macro}
+% We do not want the word ``address'' here:
+% \begin{macrocode}
+\def\emailaddrname{{\itshape E-mail}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@setaddresses}
+% \changes{v0.5}{2010/10/24}{Deleted the word URL}
+% \changes{v0.5}{2010/10/24}{E-mail is now in Roman font}
+% \changes{v0.9}{2010/12/04}{Deleted spurious space in urladdress}
+% The difference between our definition and the one in
+% \progname{amsart} is that we want the e-mail and URL to be clickable
+% \begin{macrocode}
+\def\@setaddresses{\par
+ \nobreak \begingroup
+\footnotesize
+ \def\author##1{\nobreak\addvspace\bigskipamount}%
+ \def\\{\unskip, \ignorespaces}%
+ \interlinepenalty\@M
+ \def\address##1##2{\begingroup
+ \par\addvspace\bigskipamount\indent
+ \@ifnotempty{##1}{(\ignorespaces##1\unskip) }%
+ {\scshape\ignorespaces##2}\par\endgroup}%
+ \def\curraddr##1##2{\begingroup
+ \@ifnotempty{##2}{\nobreak\indent\curraddrname
+ \@ifnotempty{##1}{, \ignorespaces##1\unskip}\hskip0.2em:\space
+ ##2\par}\endgroup}%
+ \def\email##1##2{\begingroup
+ \@ifnotempty{##2}{\nobreak\indent\emailaddrname
+ \@ifnotempty{##1}{, \ignorespaces##1\unskip}\hskip0.2em:\space
+ \href{mailto:##2}{\rmfamily##2}\par}\endgroup}%
+ \def\urladdr##1##2{\begingroup
+ \@ifnotempty{##2}{\nobreak\indent
+ \@ifnotempty{##1}{, \ignorespaces##1\unskip}%
+ \url{##2}\par}\endgroup}%
+ \addresses
+ \endgroup
+}
+% \end{macrocode}
+%
+% \end{macro}
+%
+%
+%\subsection{Sectioning}
+%\label{sec:sectioning}
+%
+% \begin{macro}{\contentsnamefont}
+% This is the font for the word ``Contents'':
+% \begin{macrocode}
+\renewcommand\contentsnamefont{\bfseries}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\section}
+% We want our sections to be centered and bold:
+% \begin{macrocode}
+\def\section{\@startsection{section}{1}%
+ \z@{.7\linespacing\@plus\linespacing}{.5\linespacing}%
+ {\normalfont\bfseries\centering}}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\subsection}
+% \changes{v0.5}{2010/10/24}{Redefined macro}
+% We want our sections to be indented and italic:
+% \begin{macrocode}
+\def\subsection{\@startsection{subsection}{2}%
+ {\parindent}{.5\linespacing\@plus.7\linespacing}{-.5em}%
+ {\normalfont\itshape}}
+% \end{macrocode}
+% \end{macro}
+%
+%
+%
+%\subsection{Figures and Tables}
+%\label{sec:figs}
+%
+% \begin{macro}{\@captionheadfont}
+% This is the font for the words ``Figure'' or ``Table'' in
+% captions. Unlike \progname{amsmath} with is small caps, we want
+% just plain Roman font:
+% \begin{macrocode}
+\def\@captionheadfont{\normalfont}
+% \end{macrocode}
+% \end{macro}
+%
+%
+%
+%
+%\subsection{Theorems}
+%\label{sec:theorems}
+%
+% Here we redefine three main style of \progname{amsart}. Here are
+% the arguments of |\newtheoremstyle| from~\cite{Downes04:amsart}:
+%\begin{verbatim}
+% #1
+% \newtheoremstyle{NAME}%
+% #2 #3 #4
+% {ABOVESPACE}{BELOWSPACE}{BODYFONT}%
+% #5 #6 #7 #8
+% {INDENT}{HEADFONT}{HEADPUNCT}{HEADSPACE}%
+% #9
+% {CUSTOM-HEAD-SPEC}
+%\end{verbatim}
+%
+%
+% \changes{v0.4}{2010/09/28}{Changed plain theorem style}
+% In the |plain| style the name (``theorem'') is in small caps, the
+% number is in normal font, the optional note is also
+% in normal font, and the text is italics.
+% \begin{macrocode}
+\newtheoremstyle{plain}{0.5\linespacing}{0.5\linespacing}{\sishape}%
+ {\parindent}{\scshape}{.}{0.5em}%
+ {\thmname{#1}\thmnumber{ #2}\thmnote{\normalfont{} (#3)}}
+% \end{macrocode}
+%
+% \changes{v0.4}{2010/09/28}{Changed definition theorem style}
+% In the |definition| style the name is italics, and the body font is
+% upright:
+% \begin{macrocode}
+\newtheoremstyle{definition}{0.5\linespacing}{0.5\linespacing}%
+ {\upshape}{\parindent}%
+ {\sishape}{.}{0.5em}%
+ {\thmname{#1}\thmnumber{ #2}\thmnote{\normalfont{} (#3)}}
+% \end{macrocode}
+%
+% \changes{v0.4}{2010/09/28}{Deleted remark theorem style}
+% \changes{v0.5}{2010/10/24}{Made remark theorem style identical to
+% definition theorem style}
+% In our class there is no difference between |remark| and
+% |definition| theorem styles:
+% \begin{macrocode}
+\newtheoremstyle{remark}{0.5\linespacing}{0.5\linespacing}%
+ {\upshape}{\parindent}%
+ {\sishape}{.}{0.5em}%
+ {\thmname{#1}\thmnumber{ #2}\thmnote{\normalfont{} (#3)}}
+% \end{macrocode}
+%
+% \begin{macro}{\newtheorem}
+% \changes{v0.3}{2010/09/26}{Redefined macro}
+% For compatibility reasons we need to accept |\newtheorem| with
+% optional first argument---and silently drop it. The problem is,
+% there is |\newtheorem*|, so we need to check which one we deal
+% with\dots{} The command |\@xnthm| here is from \progname{amsthm};
+% it does the real work with the real parameters.
+% \begin{macrocode}
+\renewcommand{\newtheorem}{\@ifstar{\@aom@newthm@star}{\@aom@newthm}}
+\def\@aom@newthm@star{\@ifnextchar[{\@aom@newthm@star@}{\@aom@newthm@star@[]}}
+\def\@aom@newthm{\@ifnextchar[{\@aom@newthm@}{\@aom@newthm@[]}}
+\def\@aom@newthm@star@[#1]{\@xnthm *}
+\def\@aom@newthm@[#1]{\@xnthm \relax}
+% \end{macrocode}
+%
+% \end{macro}
+%
+% \begin{macro}{proof}
+% \changes{v0.5}{2010/10/24}{Redefined macro}
+% We want our proofs to be indented:
+% \begin{macrocode}
+\renewenvironment{proof}[1][\proofname]{\par
+ \pushQED{\qed}%
+ \normalfont \topsep6\p@\@plus6\p@\relax
+ \trivlist
+ \item[\hskip\labelsep\hskip\parindent
+ \itshape
+ #1\@addpunct{.}]\ignorespaces
+}{%
+ \popQED\endtrivlist\@endpefalse
+}
+% \end{macrocode}
+% \end{macro}
+%
+%
+%\subsection{Bibliography Macros}
+%\label{sec:bibl}
+%
+% \begin{macro}{\repeatedauthors}
+% When the authors are repeated, we change them to |\bysame|:
+% \begin{macrocode}
+\def\repeatedauthors#1{\bysame}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\doi}
+% Typesetting doi\dots
+% \begin{macrocode}
+\def\doi#1{\href{http://dx.doi.org/#1}{doi: #1}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\mr}
+% \changes{v0.3}{2010/09/27}{Added macro}
+% \begin{macro}{\zbl}
+% \changes{v0.3}{2010/09/27}{Added macro}
+% \changes{v0.6}{2010/10/03}{Changed capitalization}
+% \begin{macro}{\arxiv}
+% \changes{v0.3}{2010/09/27}{Added macro}
+% \begin{macro}{\jfm}
+% \changes{v0.10}{2010/12/18}{Added macro}
+% These commands are from the style by Silvio Levy
+% \begin{macrocode}
+\def\mr#1{\href{http://www.ams.org/mathscinet-getitem?mr=#1}{MR~#1}}
+\def\zbl#1{\href{http://www.zentralblatt-math.org/zmath/en/search/?q=an:#1}{Zbl~#1}}
+\def\arxiv#1{\href{http://www.arxiv.org/abs/#1}{arXiV~#1}}
+\def\jfm#1{\href{http://www.emis.de/cgi-bin/JFM-item?#1}{JFM~#1}}
+% \end{macrocode}
+%
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\bibliofont}
+% \changes{v0.6}{2010/10/03}{Changed default}
+% We make this |\small| rather than |\Small| in \progname{amsart}
+% \begin{macrocode}
+\renewcommand{\bibliofont}{\small}
+% \end{macrocode}
+%
+% \end{macro}
+%
+%\subsection{Additional Macros}
+%\label{sec:additional}
+%
+% \begin{macro}{\EditorialComment}
+% \changes{v0.3}{2010/09/28}{Added macro}
+% This macro is noop in normal mode, but is a tiny marginpar in the
+% manusript mode
+% \begin{macrocode}
+\def\EditorialComment#1{\if@aom@manuscript@mode\bgroup
+ \marginparwidth=75pt\marginpar{\scriptsize\raggedright#1}\egroup\fi}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\@fullref}
+% \changes{v0.5}{2010/10/24}{Added macro}
+% This macro creates a wide link for the reference. It has four
+% parameters: the word (theorem, equation,\dots), the ``pre''
+% punctuation, the reference and the ``post'' punctuation.
+% \begin{macrocode}
+\def\@fullref#1#2#3#4{\hyperref[#3]{#1~#2\ref*{#3}#4}}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\fullref}
+% \changes{v0.5}{2010/10/24}{Added macro}
+% A reference without parentheses:
+% \begin{macrocode}
+\newcommand{\fullref}[2]{\@fullref{#1}{}{#2}{}}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\pfullref}
+% \changes{v0.5}{2010/10/24}{Added macro}
+% A reference with parentheses:
+% \begin{macrocode}
+\newcommand{\pfullref}[2]{\@fullref{#1}{(}{#2}{)}}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\bfullref}
+% \changes{v0.5}{2010/10/24}{Added macro}
+% A reference with brackets:
+% \begin{macrocode}
+\newcommand{\bfullref}[2]{\@fullref{#1}{[}{#2}{]}}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\eqfullref}
+% \changes{v0.5}{2010/10/24}{Added macro}
+% Here we do not use the standard common |\@fullref| because we want
+% |\eqref| to work\dots
+% \begin{macrocode}
+\newcommand{\eqfullref}[2]{\hyperref[#2]{#1~\textup{\tagform@{\ref*{#2}}}}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\eqnarray}
+% \changes{v0.9}{2010/12/04}{Redefined standard macro}
+% While we do \emph{not} recommend the use of |eqnarray|, we still
+% would like to correct the ugly spacing around it\dots
+% \begin{macrocode}
+\def\eqnarray{%
+ \stepcounter{equation}%
+ \def\@currentlabel{\p@equation\theequation}%
+ \global\@eqnswtrue
+ \m@th
+ \global\@eqcnt\z@
+ \tabskip\@centering
+ \let\\\@eqncr
+ $$\arraycolsep1\p@
+ \everycr{}\halign to\displaywidth\bgroup
+ \hskip\@centering$\displaystyle\tabskip\z@skip{##}$\@eqnsel
+ &\global\@eqcnt\@ne\hskip \tw@\arraycolsep \hfil${##}$\hfil
+ &\global\@eqcnt\tw@ \hskip \tw@\arraycolsep
+ $\displaystyle{##}$\hfil\tabskip\@centering
+ &\global\@eqcnt\thr@@ \hb@xt@\z@\bgroup\hss##\egroup
+ \tabskip\z@skip
+ \cr
+}
+% \end{macrocode}
+%
+% \end{macro}
+%
+%
+%\subsection{End of Class}
+%\label{end}
+%
+%
+% \begin{macrocode}
+%</class>
+% \end{macrocode}
+%
+%\Finale
+%\clearpage
+%
+%\PrintChanges
+%\clearpage
+%\PrintIndex
+%
+\endinput
diff --git a/Master/texmf-dist/source/latex/aomart/aomart.ins b/Master/texmf-dist/source/latex/aomart/aomart.ins
new file mode 100644
index 00000000000..af374bc57e2
--- /dev/null
+++ b/Master/texmf-dist/source/latex/aomart/aomart.ins
@@ -0,0 +1,29 @@
+%
+% Doctrip file for aomart
+% This file is in public domain
+% $Id: aomart.ins,v 1.1 2010-08-09 02:35:05 boris Exp $
+%
+\def\batchfile{aomart.ins}
+\input docstrip
+\keepsilent
+\showprogress
+
+
+\askforoverwritefalse
+
+\generate{%
+ \file{aomart.cls}{\from{aomart.dtx}{class}}}
+
+\obeyspaces
+\Msg{*****************************************************}%
+\Msg{* Congratulations! You successfully generated the *}%
+\Msg{* aomart package. *}%
+\Msg{* *}%
+\Msg{* Please move the file aomart.cls to where LaTeX *}%
+\Msg{* files are stored in your system. The manual is *}%
+\Msg{* aomart.pdf. *}%
+\Msg{* *}%
+\Msg{* The package is released under LPPL *}%
+\Msg{* *}%
+\Msg{* Happy TeXing! *}%
+\Msg{*****************************************************}% \ No newline at end of file
diff --git a/Master/texmf-dist/tex/latex/aomart/aomart.cls b/Master/texmf-dist/tex/latex/aomart/aomart.cls
new file mode 100644
index 00000000000..69c3343175d
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/aomart/aomart.cls
@@ -0,0 +1,407 @@
+%%
+%% This is file `aomart.cls',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% aomart.dtx (with options: `class')
+%%
+%% IMPORTANT NOTICE:
+%%
+%% For the copyright see the source file.
+%%
+%% Any modified versions of this file must be renamed
+%% with new filenames distinct from aomart.cls.
+%%
+%% For distribution of the original source see the terms
+%% for copying and modification in the file aomart.dtx.
+%%
+%% This generated file may be distributed as long as the
+%% original source files, as listed above, are part of the
+%% same distribution. (The sources need not necessarily be
+%% in the same archive or directory.)
+%% \CharacterTable
+%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%% Digits \0\1\2\3\4\5\6\7\8\9
+%% Exclamation \! Double quote \" Hash (number) \#
+%% Dollar \$ Percent \% Ampersand \&
+%% Acute accent \' Left paren \( Right paren \)
+%% Asterisk \* Plus \+ Comma \,
+%% Minus \- Point \. Solidus \/
+%% Colon \: Semicolon \; Less than \<
+%% Equals \= Greater than \> Question mark \?
+%% Commercial at \@ Left bracket \[ Backslash \\
+%% Right bracket \] Circumflex \^ Underscore \_
+%% Grave accent \` Left brace \{ Vertical bar \|
+%% Right brace \} Tilde \~}
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesClass{aomart}
+[2010/12/31 v1.1 Typesetting articles for the Annals of Mathematics]
+\long\def\aom@size@warning#1{%
+ \ClassWarning{aomart}{Size-changing option #1 will not be
+ honored}}%
+\DeclareOption{8pt}{\aom@size@warning{\CurrentOption}}%
+\DeclareOption{9pt}{\aom@size@warning{\CurrentOption}}%
+\DeclareOption{10pt}{\aom@size@warning{\CurrentOption}}%
+\DeclareOption{11pt}{\aom@size@warning{\CurrentOption}}%
+\DeclareOption{12pt}{\aom@size@warning{\CurrentOption}}%
+\newif\if@aom@manuscript@mode
+\@aom@manuscript@modefalse
+\DeclareOption{manuscript}{\@aom@manuscript@modetrue}
+\newif\if@aom@screen@mode
+\@aom@screen@modefalse
+\DeclareOption{screen}{\@aom@screen@modetrue}
+\DeclareOption*{\PassOptionsToClass{\CurrentOption}{amsart}}
+\InputIfFileExists{aomart.cfg}{%
+ \ClassInfo{aomart}{%
+ Loading configuration file aomart.cfg}}{%
+ \ClassInfo{aomart}{%
+ Configuration file aomart.cfg is not found}}
+\ProcessOptions\relax
+\LoadClass[11pt,noamsfonts]{amsart}
+\RequirePackage{fancyhdr, lastpage, ifpdf}
+\RequirePackage[breaklinks,colorlinks]{hyperref}
+\if@aom@screen@mode
+\hypersetup{linkcolor=blue,citecolor=blue,
+ urlcolor=blue, pdfpagescrop={110 705 500 80}}%
+\else\if@aom@manuscript@mode
+\hypersetup{linkcolor=blue,citecolor=blue,
+ urlcolor=blue}%
+\else
+\hypersetup{linkcolor=black,citecolor=black,
+ urlcolor=black}%
+\fi\fi
+\urlstyle{rm}
+\RequirePackage{yhmath}
+\IfFileExists{cmtiup.sty}{%
+ \RequirePackage{cmtiup}}{%
+ \ClassWarning{aomart}{The package mdputu is not found.\MessageBreak
+ You need this package to get italics with upright digits!}}
+\def\specialdigits{}%
+\let\sishape=\itshape
+\let\textsi=\textit
+\def\@typesizes{%
+ \or{\@vipt}{9}\or{\@viipt}{9}\or{\@viiipt}{9}\or{\@ixpt}{12}%
+ \or{\@xpt}{13}%
+ \or{\@xipt}{14}% normalsize
+ \or{\@xiipt}{15}\or{13}{17}\or{\@xviipt}{20}%
+ \or{19}{23.2}\or{22}{27.8}}%
+\normalsize \linespacing=\baselineskip
+\let\widebar\overline
+\setlength{\textwidth}{31pc}
+\setlength{\textheight}{48pc}
+\oddsidemargin=.65in
+\evensidemargin=.65in
+\setlength{\topskip}{12pt}
+\setlength{\abovedisplayskip}{6.95pt plus3.5pt minus 3pt}
+\setlength{\belowdisplayskip}{6.95pt plus4.5pt minus 3pt}
+\setlength{\skip\footins}{20pt}
+\setlength{\dimen\footins}{3in}
+\setlength\footskip{30pt}
+\setlength{\parindent}{22pt}
+\setlength{\parskip}{\z@}
+\widowpenalty=10000
+\clubpenalty=10000
+\setlength{\headsep}{14pt}
+\renewcommand{\headrulewidth}{0pt}
+\renewcommand{\footrulewidth}{0pt}
+\if@aom@manuscript@mode
+ \newsavebox{\@aom@linecount}
+ \savebox{\@aom@linecount}[4em][t]{\parbox[t]{4em}{%
+ \@tempcnta\@ne\relax
+ \loop{\underline{\scriptsize\the\@tempcnta}}\\
+ \advance\@tempcnta by \@ne\ifnum\@tempcnta<43\repeat}}
+\fi
+\pagestyle{fancy}
+\fancyhead{}
+\fancyfoot{}
+\fancyhead[CO]{\scriptsize\shorttitle}
+\fancyhead[RO,LE]{\footnotesize\thepage}
+\if@aom@manuscript@mode
+ \fancyhead[LE]{\footnotesize\thepage\begin{picture}(0,0)%
+ \put(-26,-25){\usebox{\@aom@linecount}}%
+ \end{picture}}
+ \fancyhead[LO]{\begin{picture}(0,0)%
+ \put(-21,-25){\usebox{\@aom@linecount}}%
+ \end{picture}}
+ \fancyfoot[C]{\scriptsize Proof: page numbers may be temporary}
+\fi
+\fancyhead[CE]{\scriptsize\MakeUppercase\shortauthors}
+\fancypagestyle{firstpage}{%
+ \fancyhf{}%
+ \if@aom@manuscript@mode
+ \lhead{\begin{picture}(0,0)%
+ \put(-21,-25){\usebox{\@aom@linecount}}%
+ \end{picture}}
+ \fi
+ \chead{\scriptsize%
+ \href{\@annalsurl}{Annals of Mathematics} \textbf{\currentvolume}
+ (\currentyear),
+ \start@page--\end@page\\
+ \ifx\@doinumber\@empty\else
+ \doi{\@doinumber}\fi}%
+ \cfoot{\footnotesize\thepage}}%
+\def\annalsurl#1{\gdef\@annalsurl{#1}}
+\annalsurl{http://annals.math.princeton.edu/annals/about/cover/cover.html}
+\@onlypreamble{\title}
+\@onlypreamble{\author}
+\@onlypreamble{\email}
+\@onlypreamble{\address}
+\@onlypreamble{\curraddr}
+\@onlypreamble{\urladdr}
+\@onlypreamble{\givenname}
+\@onlypreamble{\surname}
+\@onlypreamble{\thanks}
+\@onlypreamble{\keyword}
+\@onlypreamble{\subject}
+\@onlypreamble{\received}
+\@onlypreamble{\revised}
+\@onlypreamble{\accepted}
+\@onlypreamble{\published}
+\@onlypreamble{\publishedonline}
+\@onlypreamble{\proposed}
+\@onlypreamble{\seconded}
+\@onlypreamble{\corresponding}
+\@onlypreamble{\editor}
+\@onlypreamble{\version}
+\@onlypreamble{\volumenumber}
+\@onlypreamble{\issuenumber}
+\@onlypreamble{\publicationyear}
+\@onlypreamble{\papernumber}
+\@onlypreamble{\startpage}
+\@onlypreamble{\endpage}
+\@onlypreamble{\doinumber}
+\@onlypreamble{\mrnumber}
+\@onlypreamble{\zblnumber}
+\let\givenname=\@gobble
+\let\surname=\@gobble
+\def\keyword#1{\ifx\@keywords\@empty\gdef\@keywords{#1}\else
+ \g@addto@macro\@keywords{, #1}\fi}
+\let\@subjects\@empty
+\def\subject#1#2#3{\ifx\@subjects\@empty\gdef\@subjects{#1:#2:#3}\else
+ \g@addto@macro\@subjects{, #1:#2:#3}\fi}
+\def\formatdate#1{\@formatdate#1\@endformatdate}
+\def\@formatdate#1-#2-#3\@endformatdate{%
+ \@tempcnta=#3\relax
+ \ifcase#2\or
+ January\or February\or March\or April\or May\or June\or
+ July\or August\or September\or October\or November\or December\fi
+ \space\the\@tempcnta,\space#1}
+\def\received#1{\def\@received{#1}}
+\let\@received\@empty
+\def\revised#1{\def\@revised{#1}}
+\let\@revised\@empty
+\def\accepted#1{\def\@accepted{#1}}
+\let\@accepted\@empty
+\def\published#1{\def\@published{#1}}
+\let\@published\@empty
+\def\publishedonline#1{\def\@publishedonline{#1}}
+\let\@publishedonline\@empty
+\def\volumenumber#1{\def\currentvolume{#1}}
+\def\issuenumber#1{\def\currentissue{#1}}
+\def\publicationyear#1{\def\currentyear{#1}}
+\def\papernumber#1{\def\currentpaper{#1}}
+\papernumber{0000}
+\def\startpage#1{\pagenumbering{arabic}\setcounter{page}{#1}%
+ \def\start@page{#1}%
+ \ifnum\c@page<\z@ \pagenumbering{roman}\setcounter{page}{-#1}%
+ \def\start@page{\romannumeral#1}%
+ \fi}
+\def\endpage#1{\def\@tempa{#1}%
+ \ifx\@tempa\@empty\def\end@page{\pageref{LastPage}}%
+ \else\def\end@page{#1}\fi}
+\def\pagespan#1#2{\startpage{#1}\endpage{#2}}
+\pagespan{1}{}
+\renewenvironment{abstract}{%
+ \ifx\maketitle\relax
+ \ClassWarning{aomart}{Abstract should precede
+ \protect\maketitle\space in AMS derived classes}%
+ \fi
+ \global\setbox\abstractbox=\vtop\bgroup%
+ \vglue1pc%
+ {\centering\normalfont\normalsize\bfseries\abstractname\par\vglue1pc}%
+ \list{}{\labelwidth\z@%
+ \leftmargin3pc \rightmargin\leftmargin%
+ \listparindent\normalparindent \itemindent\normalparindent%
+ \parsep\z@ \@plus\p@%
+ \let\fullwidthdisplay\relax%
+ }%
+ \item[]\normalfont\Small%
+}{%
+ \endlist\egroup%
+ \ifx\@setabstract\relax\@setabstracta\fi%
+}
+
+\let\proposed\@gobble
+\let\seconded\@gobble
+\let\corresponding\@gobble
+\let\version\@gobble
+\def\doinumber#1{\gdef\@doinumber{#1}}
+\doinumber{10.4007/annals.\currentyear.\currentvolume.\currentissue.\currentpaper}
+\def\mrnumber#1{\gdef\@mrnumber{#1}}
+\mrnumber{}
+\def\zblnumber#1{\gdef\@zblnumber{#1}}
+\zblnumber{}
+\def\@settitle{\begin{center}%
+ \baselineskip20\p@\relax
+ \bfseries\LARGE
+ \@title
+ \ifpdf
+ \hypersetup{pdftitle=\@title}%
+ \fi
+ \end{center}%
+}
+\def\@setauthors{%
+ \ifx\authors\@empty\relax\else
+ \begingroup
+ \def\thanks{\protect\thanks@warning}%
+ \trivlist
+ \centering\footnotesize \@topsep30\p@\relax
+ \advance\@topsep by -\baselineskip
+ \item\relax
+ \def\@@and{{\upshape and}}
+ \author@andify\authors
+ \ifpdf
+ \hypersetup{pdfauthor=\authors}%
+ \fi
+ \def\\{\protect\linebreak}%
+ \small By \scshape\authors%
+ \ifx\@empty\contribs
+ \else
+ ,\penalty-3 \space \@setcontribs
+ \@closetoccontribs
+ \fi
+ \endtrivlist
+ \endgroup
+ \fi}
+\def\@setcontribs{%
+ \@xcontribs
+ {\scshape \xcontribs}%
+}
+\def\@adminfootnotes{%
+ \let\@makefnmark\relax \let\@thefnmark\relax
+ \ifx\@empty\@date\else \@footnotetext{\@setdate}\fi
+ \ifx\@empty\@subjclass\else \@footnotetext{\@setsubjclass}\fi
+ \ifx\@empty\@keywords\else\@setkeywords\fi
+ \ifx\@empty\@subjects\else\@setsubjects\fi
+ \ifx\@empty\thankses\else \@footnotetext{%
+ \def\par{\let\par\@par}\@setthanks}%
+ \fi
+}
+\def\@setkeywords{%
+ \ifpdf
+ \hypersetup{pdfkeywords=\@keywords}%
+ \fi
+}
+\def\@setsubjects{%
+ \ifpdf
+ \hypersetup{pdfsubject=\@subjects}%
+ \fi
+}
+\def\@@and{\MakeLowercase{and}}
+\def\enddoc@text{%
+ \ifx\@empty\@translators \else\@settranslators\fi
+ \ifx\@empty\@received \else\@setreceived\fi
+ \ifx\@empty\@revised \else\@setrevised\fi
+ \ifx\@empty\addresses \else\@setaddresses\fi}
+\def\@setreceived{{\centering(Received: \@received)\par}}
+\def\@setrevised{{\centering(Revised: \@revised)\par}}
+\def\@setaccepted{{\centering(Accepted: \@accepted)\par}}
+\def\@setpublished{{\centering(Published: \@published)\par}}
+\def\@setpublishedonline{{\centering(Published online: \@publishedonline)\par}}
+\def\emailaddrname{{\itshape E-mail}}
+\def\@setaddresses{\par
+ \nobreak \begingroup
+\footnotesize
+ \def\author##1{\nobreak\addvspace\bigskipamount}%
+ \def\\{\unskip, \ignorespaces}%
+ \interlinepenalty\@M
+ \def\address##1##2{\begingroup
+ \par\addvspace\bigskipamount\indent
+ \@ifnotempty{##1}{(\ignorespaces##1\unskip) }%
+ {\scshape\ignorespaces##2}\par\endgroup}%
+ \def\curraddr##1##2{\begingroup
+ \@ifnotempty{##2}{\nobreak\indent\curraddrname
+ \@ifnotempty{##1}{, \ignorespaces##1\unskip}\hskip0.2em:\space
+ ##2\par}\endgroup}%
+ \def\email##1##2{\begingroup
+ \@ifnotempty{##2}{\nobreak\indent\emailaddrname
+ \@ifnotempty{##1}{, \ignorespaces##1\unskip}\hskip0.2em:\space
+ \href{mailto:##2}{\rmfamily##2}\par}\endgroup}%
+ \def\urladdr##1##2{\begingroup
+ \@ifnotempty{##2}{\nobreak\indent
+ \@ifnotempty{##1}{, \ignorespaces##1\unskip}%
+ \url{##2}\par}\endgroup}%
+ \addresses
+ \endgroup
+}
+\renewcommand\contentsnamefont{\bfseries}
+\def\section{\@startsection{section}{1}%
+ \z@{.7\linespacing\@plus\linespacing}{.5\linespacing}%
+ {\normalfont\bfseries\centering}}
+\def\subsection{\@startsection{subsection}{2}%
+ {\parindent}{.5\linespacing\@plus.7\linespacing}{-.5em}%
+ {\normalfont\itshape}}
+\def\@captionheadfont{\normalfont}
+\newtheoremstyle{plain}{0.5\linespacing}{0.5\linespacing}{\sishape}%
+ {\parindent}{\scshape}{.}{0.5em}%
+ {\thmname{#1}\thmnumber{ #2}\thmnote{\normalfont{} (#3)}}
+\newtheoremstyle{definition}{0.5\linespacing}{0.5\linespacing}%
+ {\upshape}{\parindent}%
+ {\sishape}{.}{0.5em}%
+ {\thmname{#1}\thmnumber{ #2}\thmnote{\normalfont{} (#3)}}
+\newtheoremstyle{remark}{0.5\linespacing}{0.5\linespacing}%
+ {\upshape}{\parindent}%
+ {\sishape}{.}{0.5em}%
+ {\thmname{#1}\thmnumber{ #2}\thmnote{\normalfont{} (#3)}}
+\renewcommand{\newtheorem}{\@ifstar{\@aom@newthm@star}{\@aom@newthm}}
+\def\@aom@newthm@star{\@ifnextchar[{\@aom@newthm@star@}{\@aom@newthm@star@[]}}
+\def\@aom@newthm{\@ifnextchar[{\@aom@newthm@}{\@aom@newthm@[]}}
+\def\@aom@newthm@star@[#1]{\@xnthm *}
+\def\@aom@newthm@[#1]{\@xnthm \relax}
+\renewenvironment{proof}[1][\proofname]{\par
+ \pushQED{\qed}%
+ \normalfont \topsep6\p@\@plus6\p@\relax
+ \trivlist
+ \item[\hskip\labelsep\hskip\parindent
+ \itshape
+ #1\@addpunct{.}]\ignorespaces
+}{%
+ \popQED\endtrivlist\@endpefalse
+}
+\def\repeatedauthors#1{\bysame}
+\def\doi#1{\href{http://dx.doi.org/#1}{doi: #1}}
+\def\mr#1{\href{http://www.ams.org/mathscinet-getitem?mr=#1}{MR~#1}}
+\def\zbl#1{\href{http://www.zentralblatt-math.org/zmath/en/search/?q=an:#1}{Zbl~#1}}
+\def\arxiv#1{\href{http://www.arxiv.org/abs/#1}{arXiV~#1}}
+\def\jfm#1{\href{http://www.emis.de/cgi-bin/JFM-item?#1}{JFM~#1}}
+\renewcommand{\bibliofont}{\small}
+\def\EditorialComment#1{\if@aom@manuscript@mode\bgroup
+ \marginparwidth=75pt\marginpar{\scriptsize\raggedright#1}\egroup\fi}
+\def\@fullref#1#2#3#4{\hyperref[#3]{#1~#2\ref*{#3}#4}}
+\newcommand{\fullref}[2]{\@fullref{#1}{}{#2}{}}
+\newcommand{\pfullref}[2]{\@fullref{#1}{(}{#2}{)}}
+\newcommand{\bfullref}[2]{\@fullref{#1}{[}{#2}{]}}
+\newcommand{\eqfullref}[2]{\hyperref[#2]{#1~\textup{\tagform@{\ref*{#2}}}}}
+\def\eqnarray{%
+ \stepcounter{equation}%
+ \def\@currentlabel{\p@equation\theequation}%
+ \global\@eqnswtrue
+ \m@th
+ \global\@eqcnt\z@
+ \tabskip\@centering
+ \let\\\@eqncr
+ $$\arraycolsep1\p@
+ \everycr{}\halign to\displaywidth\bgroup
+ \hskip\@centering$\displaystyle\tabskip\z@skip{##}$\@eqnsel
+ &\global\@eqcnt\@ne\hskip \tw@\arraycolsep \hfil${##}$\hfil
+ &\global\@eqcnt\tw@ \hskip \tw@\arraycolsep
+ $\displaystyle{##}$\hfil\tabskip\@centering
+ &\global\@eqcnt\thr@@ \hb@xt@\z@\bgroup\hss##\egroup
+ \tabskip\z@skip
+ \cr
+}
+\endinput
+%%
+%% End of file `aomart.cls'.
diff --git a/Master/tlpkg/bin/tlpkg-ctan-check b/Master/tlpkg/bin/tlpkg-ctan-check
index 7edc9319e1d..e98b65a87cb 100755
--- a/Master/tlpkg/bin/tlpkg-ctan-check
+++ b/Master/tlpkg/bin/tlpkg-ctan-check
@@ -34,7 +34,7 @@ my @TLP_working = qw(
altfont ametsoc amsaddr amscls amsfonts amslatex-primer amsldoc-it
amsmath amsrefs amstex amsthdoc-it
animate anonchap antt answers ANUfinalexam anyfontsize anysize
- apa apacite apalike2 appendix apprends-latex
+ aomart apa apacite apalike2 appendix apprends-latex
arabi arabtex arabxetex archaic arcs arev
around-the-bend arphic arrayjobx arsclassica
arydshln
diff --git a/Master/tlpkg/tlpsrc/aomart.tlpsrc b/Master/tlpkg/tlpsrc/aomart.tlpsrc
new file mode 100644
index 00000000000..e69de29bb2d
--- /dev/null
+++ b/Master/tlpkg/tlpsrc/aomart.tlpsrc
diff --git a/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc b/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc
index 0465eb31a98..7992de478d5 100644
--- a/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc
+++ b/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc
@@ -11,6 +11,7 @@ depend afthesis
depend aguplus
depend aiaa
depend ametsoc
+depend aomart
depend apa
depend arsclassica
depend asaetr