summaryrefslogtreecommitdiff
path: root/language/cyrillic
diff options
context:
space:
mode:
authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /language/cyrillic
Initial commit
Diffstat (limited to 'language/cyrillic')
-rw-r--r--language/cyrillic/doc/00readme.tex4
-rw-r--r--language/cyrillic/doc/cyr.note34
-rw-r--r--language/cyrillic/doc/cyracc.def272
-rw-r--r--language/cyrillic/doc/cyrillic.ligs62
-rw-r--r--language/cyrillic/doc/cyrillic.notes419
-rw-r--r--language/cyrillic/doc/cyrmemo.def85
-rw-r--r--language/cyrillic/doc/cyrmemo.tex171
-rw-r--r--language/cyrillic/doc/lettermappings211
-rw-r--r--language/cyrillic/doc/rsam.ter999
-rw-r--r--language/cyrillic/inputs/rmacro.sty106
-rw-r--r--language/cyrillic/programs/gost2ascii.c28
-rw-r--r--language/cyrillic/programs/trr.pas259
12 files changed, 2650 insertions, 0 deletions
diff --git a/language/cyrillic/doc/00readme.tex b/language/cyrillic/doc/00readme.tex
new file mode 100644
index 0000000000..be92a10f20
--- /dev/null
+++ b/language/cyrillic/doc/00readme.tex
@@ -0,0 +1,4 @@
+% langs/cyrillic
+\par\begin{footnotesize}\begin{alltt}
+Contents of README files:\par
+\end{alltt}\end{footnotesize}\par
diff --git a/language/cyrillic/doc/cyr.note b/language/cyrillic/doc/cyr.note
new file mode 100644
index 0000000000..1dced25f9f
--- /dev/null
+++ b/language/cyrillic/doc/cyr.note
@@ -0,0 +1,34 @@
+From uucp Wed Apr 29 10:56:05 1987
+From: cheviot.newcastle.ac.uk!EXETER.AC.UK!BOOTH.CM remote from sot-mao
+Received: from sot-mao by cm.soton.ac.uk; Wed Apr 29 10:56:01 GMT 1987
+Sender: maori.soton.ac.uk!cheviot.newcastle.ac.uk!EXETER.AC.UK!BOOTH.CM
+Received: from cheviot by maori.soton.ac.uk; Mon, 27 Apr 87 16:08:49 BST
+Received: from uk.ac.ex by uk.ac.newcastle.cheviot; Thu, 23 Apr 87 14:38:04 +0100
+Date: Thu, 23 Apr 87 14:37:34 BST
+To: SPQR%UK.AC.SOTON.CM@CHEVIOT.NEWCASTLE.AC.UK
+From: BOOTH.CM@EXETER.AC.UK
+Subject: cyrwotsits
+Message-Id: <BOOTH.CM.OZLX@UK.AC.EXETER>
+
+Status: O
+
+OK, will email them - its just that FTP is safer (ie. less likely to
+corrupt things). There's 8 TFM files, plus 8 corresponding PK files.
+Names are:
+
+MCYB10.TFM MCYB8.TFM MCYB9.TFM MCYR10.TFM
+MCYR6.TFM MCYR7.TFM MCYR8.TFM MCYR9.TFM
+
+MCYB10.300PK MCYB8.300PK MCYB9.300PK MCYR10.300PK
+MCYR6.300PK MCYR7.300PK MCYR8.300PK MCYR9.300PK
+
+will send each as a separate email file, named in the subject slot.
+
+If you can get a reasonable Cyrillic transliteration scheme going without
+the documentation then let me know... if you get hold of the proper docs
+plus CYRACC.DEF before I do then would love that too!
+
+Also have a query re TeX and Unix - who's the distribution agent??
+
+cathy
+
diff --git a/language/cyrillic/doc/cyracc.def b/language/cyrillic/doc/cyracc.def
new file mode 100644
index 0000000000..ddc4aaaf75
--- /dev/null
+++ b/language/cyrillic/doc/cyracc.def
@@ -0,0 +1,272 @@
+%% filename: cyracc.def
+%% version: 2.2b
+%% date: 2001/10/01
+%%
+%% American Mathematical Society
+%% Technical Support
+%% Publications Technical Group
+%% 201 Charles Street
+%% Providence, RI 02904
+%% USA
+%% tel: (401) 455-4080
+%% (800) 321-4267 (USA and Canada only)
+%% fax: (401) 331-3842
+%% email: tech-support@ams.org
+%%
+%% Copyright 1996, 2001, 2009 American Mathematical Society.
+%%
+%% Unlimited copying and redistribution of this file are permitted as
+%% long as this file is not modified. Modifications, and distribution
+%% of modified versions, are permitted, but only if the resulting file
+%% is renamed.
+%%
+%% ====================================================================
+%%
+%% This file is intended for use only with Plain TeX and AMS-TeX.
+%% It is not compatible with LaTeX.
+%%
+%% The \font specification(s) should be made elsewhere, and should include
+%% \newfam\cyrfam
+%% \font\...cyr=wncyr... (e.g. \font\tencyr=wncyr10 )
+%% An appropriate definition for cyrillic, usable in math and text, is
+%% \def\cyr{\fam\cyrfam\...cyr\cyracc}
+%% More extensive instructions for using cyrillic fonts are included
+%% in the AMSFonts 2.2 User's Guide.
+%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chardef\tempcat=\the\catcode`\@
+\catcode`\@=11
+
+% The first set of definitions is what will be in effect outside of cyrillic,
+% i.e., in transliterated text.
+
+% Definition of \cydot is not ideal; real dot should be in an accent font.
+\def\cydot{{\mathsurround=0pt$\cdot$}}
+
+% \ubar is the definition of \b from PLAIN; it may not work in math mode.
+\def\ubar#1{\oalign{#1\crcr\hidewidth
+ \vbox to.2ex{\hbox{\char22}\vss}\hidewidth}}
+
+% Soft and hard signs are represented in transliteration by prime and
+% double prime respectively.
+\def\cprime{\/{\mathsurround=0pt$'$}}
+\def\Cprime{{\mathsurround=0pt$'$}}
+\def\cdprime{\/{\mathsurround=0pt$''$}}
+\def\Cdprime{{\mathsurround=0pt$\ubar{\hbox{$''$}}$}}
+
+\def\dbar{dj} % make real barred d when accent font available
+\def\Dbar{Dj} % ""
+
+% It would be nice to make these control sequences unnecessary; that will
+% probably require d to become active.
+\def\dz{dz}
+\def\Dz{Dz}
+\def\dzh{dzh\cydot }
+\def\Dzh{Dzh\cydot }
+
+
+% Stress marks are sometimes used in cyrillic text, mainly for pedagogic
+% reasons. These definitions support stress marks within {\cyr ...};
+% in transliteration, they are suppressed. Stress is indicated in
+% input by \! preceding a letter on which a stress mark is to appear;
+% an acute accent will appear in the output. Since \! is also a plain
+% command, for negative thin space in math mode, test for math mode and
+% include the plain definition as appropriate.
+
+\def\@gobble#1{}
+\def\@testgrave{\`}
+\def\@stressit{\futurelet\chartest\@stresschar }
+
+\def\@stresschar#1{%
+ \ifx #1y\def\result{\futurelet\chartest\@yligature}%
+ \else \ifx #1Y\def\result{\futurelet\chartest\@Yligature}%
+ \else \ifx\chartest\@testgrave \def\result{\accent"26 }%
+ \else \def\result{\accent"26 #1}%
+ \fi \fi \fi
+ \result }
+
+\def\@yligature{%
+ \ifx a\chartest \def\result{\accent"26 \char"1F \@gobble}%
+ \else \ifx u\chartest \def\result{\accent"26 \char"18 \@gobble}%
+ \else \def\result{\accent"26 y}%
+ \fi \fi
+ \result }
+
+\def\@Yligature{%
+ \ifx a\chartest \def\result{\accent"26 \char"17 \@gobble}%
+ \else \ifx A\chartest \def\result{\accent"26 \char"17 \@gobble}%
+ \else \ifx u\chartest \def\result{\accent"26 \char"10 \@gobble}%
+ \else \ifx U\chartest \def\result{\accent"26 \char"10 \@gobble}%
+ \else \def\result{\accent"26 Y}%
+ \fi \fi \fi \fi
+ \result }
+
+\def\!{\ifmmode \mskip-\thinmuskip \fi}
+
+
+% These are the definitions that will produce cyrillic letters within
+% {\cyr ...} for letters represented in input by control sequences and
+% accented latin letters.
+
+\def\cyracc{%
+ \def\cydot{{\kern0pt}}%
+ \def\cprime{\char"7E }\def\Cprime{\char"5E }%
+ \def\cdprime{\char"7F }\def\Cdprime{\char"5F }%
+ \def\dbar{dj}\def\Dbar{Dj}%
+ \def\dz{\char"1E }\def\Dz{\char"16 }%
+ \def\dzh{\char"0A }\def\Dzh{\char"02 }%
+ \def\'##1{\if c##1\char"0F %
+ \else \if C##1\char"07 %
+ \else \accent"26 ##1\fi \fi }%
+ \def\`##1{\if e##1\char"0B %
+ \else \if E##1\char"03 %
+ \else \errmessage{accent \string\` not defined in cyrillic}%
+ ##1\fi \fi }%
+ \def\=##1{\if e##1\char"0D %
+ \else \if E##1\char"05 %
+ \else \if \i##1\char"0C %
+ \else \if I##1\char"04 %
+ \else \errmessage{accent \string\= not defined in cyrillic}%
+ ##1\fi \fi \fi \fi }%
+ \def\u##1{\if \i##1\accent"24 i%
+ \else \accent"24 ##1\fi }%
+ \def\"##1{\if \i##1\accent"20 \char"3D %
+ \else \if I##1\accent"20 \char"04 %
+ \else \accent"20 ##1\fi \fi }%
+ \def\!{\ifmmode \def\result{\mskip-\thinmuskip}%
+ \else \def\result{\@stressit}\fi \result}}
+
+
+% If cyrillic strings are to be included in \mark's, the accents need
+% to be kept in unexpanded form until the \mark's are interpreted.
+% See note on \mark below for details.
+
+\def\keep@cyracc{\let\cyr=\relax \let\i=\relax
+ \let\ubar=\relax \let\cydot=\relax
+ \let\cprime=\relax \let\Cprime=\relax
+ \let\cdprime=\relax \let\Cdprime=\relax
+ \let\dbar=\relax \let\Dbar=\relax
+ \let\dz=\relax \let\Dz=\relax
+ \let\dzh=\relax \let\Dzh=\relax
+ \let\'=\relax \let\`=\relax \let\==\relax
+ \let\u=\relax \let\"=\relax \let\!=\relax }
+
+
+\catcode`\@=\tempcat
+\endinput
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% ***** CYRACC.DEF *****
+%
+% Access to the cyrillic is through the MR 1980 transliteration scheme,
+% using TeX/Metafont ligature capability. (An alternate set of ligatures
+% exists, for accessing letters beyond the 26 located in the font positions
+% of the 26 roman letters. An authoritative list of the ligature rules is
+% given below, under the heading Ligatures.) Successful use of this file
+% requires appropriate cyrillic and accent fonts, arranged according to
+% the AMS/MR scheme.
+%
+% There are some weaknesses in this ligaturing and accent system.
+% The following are known to be less than satisfactory:
+%
+% the intermediate `ligatures' for shch access numerals;
+% primes (transliteration of hard/soft signs) use math mode;
+% underbar on `cap' double prime is too low (hard sign);
+% thorn d's don't yet exist;
+% \cydot uses math mode;
+% this scheme is not compatible with automatic Russian hyphenation.
+%
+%
+% Notes on the macros:
+%
+% The single space following each hex character code is necessary
+% to prevent the next input character from being gobbled.
+%
+%
+% Note on \mark :
+%
+% Control sequences such as these cyrillic accents should remain
+% unexpanded when generating \mark's; otherwise, the definition of
+% the expanded strings in effect when the \mark is used may be
+% inappropriate. By \let\...=\relax , the \... takes on the important
+% characteristic of a primitive that it will not be expanded further.
+% The following code has been shown to generate correct \mark entries
+% that can be used successfully in running heads:
+%
+% \newtoks\marktoks
+% \def\domark{\keep@cyracc \mark{\the\marktoks}}
+%
+% In running heads, the marks should be accessed using \the to expand
+% the tokens strings properly.
+%
+%
+% Ligatures
+%
+% This is a list of all the letter ligatures in the AMS cyrillic fonts,
+% and in other cyrillic fonts (such as those developed at the University
+% of Washington that use the AMS arrangement).
+%
+% LOWER CASE LIGATURES
+%
+% A. All-letter ligatures
+%
+% ch = `q
+% dj = '016
+% kh = `h
+% lj = '011
+% nj = '010
+% sh = `x; xc = `7 (shc); 7h = `w (shch)
+% ts = `c
+% ya = '037
+% yu = '030
+% zh = '031
+%
+% B. Ligatures with keyed numerals
+%
+% c1 = '017
+% d1 = '016 (dj); d2 = '012 (dzh); d3 = '036 (dz)
+% e0 = '033; e1 = '013; e2 = '015
+% i0 = '032; i1 = '014
+% j1 = '037 (ya); j2 = '030 (yu)
+% l1 = '011 (lj)
+% n1 = '010 (nj)
+% p1 = '176; p2 = '177
+% z1 = '031 (zh)
+%
+% UPPER CASE LIGATURES
+% A. All-letter ligatures
+%
+% CH, Ch = `Q
+% KH, Kh = `H
+% LJ, Lj = '001
+% NJ, Nj = '000
+% SH, Sh = `X; XH, Xh = `6 (SHC, SHc, Shc);
+% 6H, 6h = `W (SHCH, SHCh, SHch, Shch)
+% TS, Ts = `C
+% YA, Ya = '027
+% YU, Yu = '020
+% ZH, Zh = '021
+%
+% B. Ligatures with keyed numerals
+%
+% C1 = '007
+% D1 = '006 (DJ); D2 = '002 (DZH); D3 = '026 (DZ)
+% E0 = '023; E1 = '003; E2 = '005
+% I0 = '022; I1 = '004
+% J1 = '027 (YA); J2 = '020 (YU)
+% L1 = '001 (LJ)
+% N0 = '175 (Number sign); N1 = '000 (NJ)
+% P1 = '136; P2 = '137
+% Z1 = '021 (ZH)
+%
+% DEACTIVATED LIGATURES
+%
+% The dzh and DZH ligatures were originally built in the following manner,
+% but the results were not compatible with desired keyboarding schemes.
+%
+% dz = '036; '036(roman s)h = '012 (dzh)
+% DZ = '026; '026(roman S)H = '002 (DZH)
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
diff --git a/language/cyrillic/doc/cyrillic.ligs b/language/cyrillic/doc/cyrillic.ligs
new file mode 100644
index 0000000000..8055a2426b
--- /dev/null
+++ b/language/cyrillic/doc/cyrillic.ligs
@@ -0,0 +1,62 @@
+<mf82.amf>CYRILLIC.LIGS This is a list of all the letter ligatures in
+the AMS cyrillic fonts. Please keep this file up to date. 29 Jun 84
+
+LOWER CASE LIGATURES
+ A. All-letter ligatures
+
+ch = `q
+dj = '016
+kh = `h
+lj = '011
+nj = '010
+sh = `x; xc = `7 (shc); 7h = `w (shch)
+ts = `c
+ya = '037
+yu = '030
+zh = '031
+
+ B. Ligatures with keyed numerals
+
+c1 = '017
+d1 = '016 (dj); d2 = '012 (dzh); d3 = '036 (dz)
+e1 = '013; e2 = '015
+i1 = '014
+j1 = '037 (ya); j2 = '030 (yu)
+l1 = '011 (lj)
+n1 = '010 (nj)
+p1 = '176; p2 = '177
+z1 = '031 (zh)
+
+UPPER CASE LIGATURES
+ A. All-letter ligatures
+
+CH, Ch = `Q
+KH, Kh = `H
+LJ, Lj = '001
+NJ, Nj = '000
+SH, Sh = `X; XH, Xh = `6 (SHC, SHc, Shc); 6H, 6h = `W (SHCH, SHCh, SHch, Shch)
+TS, Ts = `C
+YA, Ya = '027
+YU, Yu = '020
+ZH, Zh = '021
+
+ B. Ligatures with keyed numerals
+
+C1 = '007
+D1 = '006 (DJ); D2 = '002 (DZH); D3 = '026 (DZ)
+E1 = '003; E2 = '005
+I1 = '004
+J1 = '027 (YA); J2 = '020 (YU)
+L1 = '001 (LJ)
+N0 = '175 (Number sign); N1 = '000 (NJ)
+P1 = '136; P2 = '137
+Z1 = '021 (ZH)
+
+DEACTIVATED LIGATURES
+The following were the original way of building dzh and DZH ligs, but were not
+compatible with desired keyboarding schemes.
+
+dz = '036; '036(roman s)h = '012 (dzh)
+DZ = '026; '026(roman S)H = '002 (DZH)
+-------
+
diff --git a/language/cyrillic/doc/cyrillic.notes b/language/cyrillic/doc/cyrillic.notes
new file mode 100644
index 0000000000..77f3e15161
--- /dev/null
+++ b/language/cyrillic/doc/cyrillic.notes
@@ -0,0 +1,419 @@
+From uucp Tue May 12 06:33:32 1987
+From: cheviot.newcastle.ac.uk!EXETER.AC.UK!BOOTH.CM remote from sot-mao
+Received: from sot-mao by cm.soton.ac.uk; Tue May 12 06:33:29 GMT 1987
+Sender: maori.soton.ac.uk!cheviot.newcastle.ac.uk!EXETER.AC.UK!BOOTH.CM
+Received: from cheviot by maori.soton.ac.uk; Tue, 12 May 87 06:07:50 BST
+Received: from uk.ac.ex by uk.ac.newcastle.cheviot; Mon, 11 May 87 17:16:06 +0100
+Date: Mon, 11 May 87 16:54:49 BST
+To: SPQR%UK.AC.SOTON.CM@CHEVIOT.NEWCASTLE.AC.UK
+From: BOOTH.CM@EXETER.AC.UK
+Subject: cyrillix
+Message-Id: <BOOTH.CM.RIJL@UK.AC.EXETER>
+
+
+Here's the cyrillic files from barbara beeton:
+
+cyracc.def - definitions supporting the cyrillic fonts
+cyrmemo.def and cyrmemo.tex - input instructions
+cyrillic.ligs - details of the ligaturing scheme used to
+ implement the input scheme (for info)
+
+cathy
+
+
+Message 90 -- ************************
+ 8-May-87 22:00:50-EDT,12420;000000000001
+Return-Path: <BEETON@Score.Stanford.EDU>
+Received: from ohio-state.ARPA (OSU-EDDIE.#Internet) by OSU-20 with TCP; Fri 8 May 87 21:56:51-EDT
+Return-Path: <BEETON@Score.Stanford.EDU>
+Received: from Score.Stanford.EDU (score.stanford.edu.ARPA) by ohio-state.ARPA (4.12/6.1.OSU-CIS)
+ id AA08807; Fri, 8 May 87 21:55:51 edt
+Date: Fri 8 May 87 18:50:44-PDT
+From: Barbara Beeton <BEETON@Score.Stanford.EDU>
+Subject: Re: [mcvax!ux63.bath.ac.uk!cc_dc@seismo.CSS.GOV: Documentation and CYRACC.DEF for Cyrillic]
+To: crawford-j@osu-eddie
+In-Reply-To: <8705081740.AA02272@ohio-state.ARPA>
+Message-Id: <12300865214.13.BEETON@Score.Stanford.EDU>
+
+be glad to ftp the files. in fact, ...
+
+% ***** CYRACC.DEF ***** 11 Aug 85, bb
+%
+% This file contains definitions of accents and special characters
+% required for cyrillic. The \font specification(s) should be made
+% elsewhere, and should include
+% \newfam\cyrfam
+% \font\...cyr=mcyr...
+%
+% An appropriate definition for cyrillic, usable in math and text, is
+% \def\cyr{\fam\cyrfam\...cyr\cyracc}
+%
+% See end of file (after \endinput) for notes.
+
+
+\def\ubar#1{\oalign{#1\crcr\hidewidth
+ \vbox to.2ex{\hbox{\char22}\vss}\hidewidth}}
+% this is definition of \b from PLAIN; it may not work in math mode
+\def\cydot{$\cdot$} % temporary -- real dot will be in accent font
+
+\def\cprime{$'$}
+\def\Cprime{$'$}
+\def\cdprime{$''$}
+\def\Cdprime{$\ubar{\hbox{$''$}}$}
+
+\def\dbar{dj} % make real barred d when accent font available
+\def\Dbar{Dj} % ""
+
+\def\dz{dz} % ultimately, d will have to become active, to
+\def\Dz{Dz} % make these control sequences unnecessary
+\def\dzh{dzh\cydot }
+\def\Dzh{Dzh\cydot }
+
+\def\cyracc{\def\cydot{{\kern0pt}}%
+ \def\cprime{\char"7E }\def\Cprime{\char"5E }%
+ \def\cdprime{\char"7F }\def\Cdprime{\char"5F }%
+ \def\dbar{dj}\def\Dbar{Dj}%
+ \def\dz{\char"1E }\def \Dz{\char"16 }%
+ \def\dzh{\char"0A }\def \Dzh{\char"02 }%
+ \def\'##1{\if c##1\char"0F %
+ \else \if C##1\char"07 %
+ \else \accent"26 ##1\fi \fi }%
+ \def\`##1{\if e##1\char"0B %
+ \else \if E##1\char"03 %
+ \else \errmessage{accent \string\` not defined in cyrillic}%
+ ##1\fi \fi }%
+ \def\=##1{\if e##1\char"0D %
+ \else \if E##1\char"05 %
+ \else \if \i##1\char"0C %
+ \else \if I##1\char"04 %
+ \else \errmessage{accent \string\= not defined in cyrillic}%
+ ##1\fi \fi \fi \fi }%
+ \def\u##1{\if \i##1\accent"24 i%
+ \else \accent"24 ##1\fi }%
+ \def\"##1{\if \i##1\accent"20 \char"3D %
+ \else \if I##1\accent"20 \char"04 %
+ \else \accent"20 ##1\fi \fi }}
+
+\endinput
+ % octal 214 removed jmcosu
+
+% ***** CYRMEMO.TEX ***** 18 Aug 84, bb
+%
+% Access to the cyrillic is through the new MR transliteration scheme,
+% using TeX/Metafont ligature capability. (An alternate set of
+% ligatures exists, for accessing letters beyond the 26 located in
+% the font positions of the 26 roman letters. An authoritative list
+% of the ligature rules is in the file cyrillic.ligs.) Successful
+% use of this file requires appropriate cyrillic and accent fonts,
+% arranged according to the AMS/MR scheme.
+%
+% This is an interim version. Not everything works yet.
+% The following are known to be less than satisfactory:
+%
+% the intermediate `ligatures' for shch access numerals;
+% primes (transliteration of hard/soft signs) use math mode;
+% underbar on `cap' double prime is too low (hard sign);
+% thorn d's don't yet exist;
+% \cydot uses math mode.
+%
+%
+% Notes on the macros:
+%
+% The single space following each hex character code is necessary
+% to prevent the next input character from being gobbled.
+
+%%%%%%%%%%
+
+\input cyrmemo.def
+
+\date 12 August 1985<
+\fromname Barbara N. Beeton\\
+ Computer Services Division<
+
+\toname Users of AMS cyrillic in \TeX<
+
+\longsub \TeX82 Cyrillic input instructions<
+\shortsub \TeX82 Cyrillic input<
+
+\topinfo
+
+The AMS cyrillic fonts have been designed so that input using the
+``new'' (post-1982) Math.~Reviews cyrillic transliteration will be
+converted directly to cyrillic text. An alternate input form is
+available for most cyrillic letters which are not transliterated by
+the equivalent single roman letters. Numerals and punctuation follow
+the normal input conventions for roman. Cyrillic is indicated to
+\TeX\ by the command |{\cyr...}|.
+
+The table below is in alphabetical order as given in the table published
+in the 1983 MR Author Index. The three paired columns contain:\ \ %
+(1)~cyrillic;
+(2)~transliteration-style input;
+(3)~alternate input, if any.
+
+\bigskip
+
+\parindent=0pt
+\parskip=0pt
+\baselineskip=15pt
+
+\newbox\BoxA
+\newbox\BoxB
+
+\def\TwoUp{\centerline{%
+ \valign{##\vfil\cr
+ \box\BoxA\cr
+ \noalign{\hfil\vrule\hfil}
+ \box\BoxB\cr}}}
+
+\newbox\TestBox
+\setbox\TestBox=\hbox{\quad\cyr Zh}
+\newdimen\cyrwd
+\cyrwd=\wd\TestBox
+\setbox\TestBox=\hbox{\enskip\tt xCdprime}
+\newdimen\ttawd
+\ttawd=\wd\TestBox
+\setbox\TestBox=\hbox{\enskip\tt N0}
+\newdimen\ttbwd
+\ttbwd=\wd\TestBox
+
+
+\settabs \+\hskip\cyrwd &\hskip\cyrwd\quad
+ &\hskip\ttawd &\hskip\ttawd\quad
+ &\hskip\ttbwd &\hskip\ttbwd\cr
+
+% \def\1 #1,#2;#3,#4;#5,#6<{\+{\cyr\ignorespaces#1}%
+% &{\cyr\ignorespaces#2\hfil}%
+% &\ignorespaces#3\hfil &\ignorespaces#4\hfil
+% &{\tt\ignorespaces#5\hfil}&{\tt\ignorespaces#6\hfil}}
+
+\setbox\BoxA=\vbox{\hsize=.45\hsize \tt
+\+{\cyr A}&{\cyr a}& |A| & |a| & & \cr
+\+{\cyr B}&{\cyr b}& |B| & |b| & & \cr
+\+{\cyr V}&{\cyr v}& |V| & |v| & & \cr
+\+{\cyr G}&{\cyr g}& |G| & |g| & & \cr
+\+{\cyr D}&{\cyr d}& |D| & |d| & & \cr
+\+{\cyr Dj}&{\cyr dj}& |Dj| & |dj| & D1 & d1\cr
+\+{\cyr \'G}&{\cyr \'g}& |\'G| & |\'g| & & \cr
+\+{\cyr E}&{\cyr e}& |E| & |e| & & \cr
+\+{\cyr \"E}&{\cyr \"e}& |\"E| & |\"e| & & \cr
+\+{\cyr \=E}&{\cyr \=e}& |\=E| & |\=e| & E2 & e2\cr
+\+{\cyr Zh}&{\cyr zh}& |Zh| & |zh| & Z1 & z1\cr
+\+{\cyr Z}&{\cyr z}& |Z| & |z| & & \cr
+\+{\cyr I}&{\cyr i}& |I| & |i| & & \cr
+\+{\cyr \=I}&{\cyr \=\i}& |\=I| & |\=\i| & I1 & i1\cr
+\+{\cyr \"I}&{\cyr \"\i}& |\"I| & |\"\i| & & \cr
+\+{\cyr J}&{\cyr j}& |J| & |j| & & \cr
+\+{\cyr \u I}&{\cyr \u\i}& |\u I| & |\u\i| & & \cr
+\+{\cyr K}&{\cyr k}& |K| & |k| & & \cr
+\+{\cyr L}&{\cyr l}& |L| & |l| & & \cr
+\+{\cyr Lj}&{\cyr lj}& |Lj| & |lj| & L1 & l1\cr
+\+{\cyr M}&{\cyr m}& |M| & |m| & & \cr
+\+{\cyr N}&{\cyr n}& |N| & |n| & & \cr
+\+{\cyr Nj}&{\cyr nj}& |Nj| & |nj| & N1 & n1\cr
+\+{\cyr O}&{\cyr o}& |O| & |o| & & \cr
+\+{\cyr P}&{\cyr p}& |P| & |p| & & \cr
+} % end \BoxA
+
+\setbox\BoxB=\vbox{\hsize=.45\hsize \tt
+\+{\cyr R}&{\cyr r}& |R| & |r| & & \cr
+\+{\cyr S}&{\cyr s}& |S| & |s| & & \cr
+\+{\cyr T}&{\cyr t}& |T| & |t| & & \cr
+\+{\cyr \'C}&{\cyr \'c}& |\'C| & |\'c| & C1 & c1\cr
+\+{\cyr \'K}&{\cyr \'k}& |\'K| & |\'k| & & \cr
+\+{\cyr U}&{\cyr u}& |U| & |u| & & \cr
+\+{\cyr \u U}&{\cyr \u u}& |\u U| & |\u u| & & \cr
+\+{\cyr F}&{\cyr f}& |F| & |f| & & \cr
+\+{\cyr Kh}&{\cyr kh}& |Kh| & |kh| & H & h\cr
+\+{\cyr Ts}&{\cyr ts}& |Ts| & |ts| & C & c\cr
+\+{\cyr Ch}&{\cyr ch}& |Ch| & |ch| & Q & q\cr
+\+{\cyr \Dzh}&{\cyr \dzh}& |\Dzh| & |\dzh| & D2 & d2\cr
+\+{\cyr Sh}&{\cyr sh}& |Sh| & |sh| & X & x\cr
+\+{\cyr Shch}&{\cyr shch}& |Shch| & |shch| & W & w\cr
+\+{\cyr \Cdprime}&{\cyr \cdprime}& |\Cdprime| & |\cdprime| & P2 & p2\cr
+\+{\cyr Y}&{\cyr y}& |Y| & |y| & & \cr
+\+{\cyr \Cprime}&{\cyr \cprime}& |\Cprime| & |\cprime| & P1 & p1\cr
+\+{\cyr \`E}&{\cyr \`e}& |\`E| & |\`e| & E1 & e1\cr
+\+{\cyr Yu}&{\cyr yu}& |Yu| & |yu| & J2 & j2\cr
+\+{\cyr Ya}&{\cyr ya}& |Ya| & |ya| & J1 & j1\cr
+\+{\cyr \Dz}&{\cyr \dz}& |\Dz| & |\dz| & D3 & d3\cr
+\+{\cyr N0}& & & & N0 & \cr
+\+{\cyr <}& & |<| & & & \cr
+\+{\cyr >}& & |>| & & & \cr
+\+\hbox to \hsize{}\cr
+} % end \BoxB
+
+\TwoUp
+
+\bigskip
+\normalbaselines
+
+\noindent In addition to the input codes shown in the table, the code
+|\cydot| is used between letters that ordinarily become ligatures to
+indicate that they are really separate letters. For example,
+|t\cydot s|${}\mapsto{}${\cyr t\cydot s} (in transliteration, t\cydot s)
+as opposed to |ts|${}\mapsto{}${\cyr ts}.
+
+\medskip
+
+\noindent {\bf Technical notes:}\ \ The names of the AMS cyrillic fonts
+begin with the letters ``|MC|'' (for ``Math Society cyrillic''). Only
+|MCYR| (lightface) is available at present, but several other styles
+are under construction: |MCB| (bold), |MCSS| (sans serif),
+|MCSSB| (bold sans serif), and others may be added from time to time.
+These fonts were prepared using {\smc Metafont79}.
+In addition to the font files, the file |CYRACC.DEF| must also be
+input for the complete cyrillic alphabet to be usable according to these
+instructions.
+
+\vfil\end
+
+%%%%%%%%%%
+
+% ***** CYRMEMO.DEF ***** 11 Aug 85, bb
+%
+% This file contains the instructions necessary to produce the memos
+% which describe the use of the AMS cyrillic font. PLAIN is presumed
+% to be preloaded. The cyrillic 10-point font is required, as is
+% the file CYRACC.DEF.
+
+\newfam\cyrfam
+\font\tencyr=mcyr10
+\font\tensmc=amcsc10 \def\smc{\tensmc}
+
+\input cyracc.def
+
+\def\cyr{\tencyr\cyracc}
+
+
+\newif\iffirstpage
+\firstpagetrue
+\newdimen\pagelgt
+\pagelgt=9in
+\newbox\letterhead
+\setbox\letterhead=\vbox{\vskip 1pc
+ \vbox to 0pt{\halign{\hss{#}\hss\cr
+ \bf American Mathematical Society\cr
+ P.\thinspace O.~Box 6248\cr
+ Providence, RI 02940\cr}\vss}}
+\vsize=\pagelgt
+\advance\vsize by-\ht\letterhead
+
+\headline={\iffirstpage \centerline{\bf INTEROFFICE MEMORANDUM}\else
+ \line{\ssub \hfil \rdate\quad Page \folio}\fi}
+\footline={\iffirstpage \rightline{\box\letterhead}\global\vsize=\pagelgt
+ \global\firstpagefalse \fi}
+
+\def \topitem#1#2{\leavevmode \hangindent 5pc \hbox to 5pc{\bf #1\hss}#2\par }
+
+\def \toname #1<{\gdef\mto{\topitem{To:}{#1}}}
+\def \fromname #1<{\gdef\mfrom{\topitem{From:}{#1}}}
+\def \longsub #1<{\gdef\lsub{\topitem{Subject:}{#1}}}
+\def \shortsub #1<{\gdef\ssub{#1}}
+
+\def \date #1<{\gdef\mdate{\topitem{\bf Date:}{#1}}
+ \gdef\rdate{#1}}
+
+\def \topinfo{{\parindent=0pt
+ \parskip=.5\baselineskip
+ \def \\{\hfil\break }
+ \mdate
+ \mto
+ \mfrom
+ \lsub
+ \vskip\baselineskip }}
+
+ % octal 214 removed jmcosu
+
+% Support verbatim listing of TeX source, as defined in TeXbook, p. 421
+% lifted from MANMAC.TEX, and modified slightly as for TUGboat
+
+\chardef\other=12
+\def\ttverbatim{\begingroup
+ \catcode`\\=\other \catcode`\{=\other
+ \catcode`\}=\other \catcode`\$=\other \catcode`\&=\other
+ \catcode`\#=\other \catcode`\%=\other \catcode`\~=\other
+ \catcode`\_=\other \catcode`\^=\other
+ \obeyspaces \obeylines \tt}
+
+\newdimen\ttrightskip
+\ttrightskip=5pc
+
+\outer\def\begintt{$$\let\par=\endgraf \ttverbatim \parskip=\z@
+ \catcode`\|=0 \rightskip=-\ttrightskip \ttfinish}
+{\catcode`\|=0 |catcode`|\=\other % | is temporary escape character
+ |obeylines % end of line is active
+ |gdef|ttfinish#1^^M#2\endtt{#1|vbox{#2}|endgroup$$}}
+
+\catcode`\|=\active
+{\obeylines \gdef|{\ttverbatim \spaceskip\ttglue \let^^M=\ \let|=\endgroup}}
+
+\newskip\ttglue
+{\tentt \global\ttglue=.5em plus .25em minus .15em}
+% this should be installed in each font
+
+
+%%%%%%%%%%
+
+<mf82.amf>CYRILLIC.LIGS This is a list of all the letter ligatures in
+the AMS cyrillic fonts. Please keep this file up to date. 29 Jun 84
+
+LOWER CASE LIGATURES
+ A. All-letter ligatures
+
+ch = `q
+dj = '016
+kh = `h
+lj = '011
+nj = '010
+sh = `x; xc = `7 (shc); 7h = `w (shch)
+ts = `c
+ya = '037
+yu = '030
+zh = '031
+
+ B. Ligatures with keyed numerals
+
+c1 = '017
+d1 = '016 (dj); d2 = '012 (dzh); d3 = '036 (dz)
+e1 = '013; e2 = '015
+i1 = '014
+j1 = '037 (ya); j2 = '030 (yu)
+l1 = '011 (lj)
+n1 = '010 (nj)
+p1 = '176; p2 = '177
+z1 = '031 (zh)
+
+UPPER CASE LIGATURES
+ A. All-letter ligatures
+
+CH, Ch = `Q
+KH, Kh = `H
+LJ, Lj = '001
+NJ, Nj = '000
+SH, Sh = `X; XH, Xh = `6 (SHC, SHc, Shc); 6H, 6h = `W (SHCH, SHCh, SHch, Shch)
+TS, Ts = `C
+YA, Ya = '027
+YU, Yu = '020
+ZH, Zh = '021
+
+ B. Ligatures with keyed numerals
+
+C1 = '007
+D1 = '006 (DJ); D2 = '002 (DZH); D3 = '026 (DZ)
+E1 = '003; E2 = '005
+I1 = '004
+J1 = '027 (YA); J2 = '020 (YU)
+L1 = '001 (LJ)
+N0 = '175 (Number sign); N1 = '000 (NJ)
+P1 = '136; P2 = '137
+Z1 = '021 (ZH)
+
+DEACTIVATED LIGATURES
+The following were the original way of building dzh and DZH ligs, but were not
+compatible with desired keyboarding schemes.
+
+dz = '036; '036(roman s)h = '012 (dzh)
+DZ = '026; '026(roman S)H = '002 (DZH)
+-------
+
diff --git a/language/cyrillic/doc/cyrmemo.def b/language/cyrillic/doc/cyrmemo.def
new file mode 100644
index 0000000000..37b686a76f
--- /dev/null
+++ b/language/cyrillic/doc/cyrmemo.def
@@ -0,0 +1,85 @@
+%%%%%%%%%%
+
+% ***** CYRMEMO.DEF ***** 11 Aug 85, bb
+%
+% This file contains the instructions necessary to produce the memos
+% which describe the use of the AMS cyrillic font. PLAIN is presumed
+% to be preloaded. The cyrillic 10-point font is required, as is
+% the file CYRACC.DEF.
+
+\newfam\cyrfam
+\font\tencyr=mcyr10
+\font\tensmc=amcsc10 \def\smc{\tensmc}
+
+\input cyracc.def
+
+\def\cyr{\tencyr\cyracc}
+
+
+\newif\iffirstpage
+\firstpagetrue
+\newdimen\pagelgt
+\pagelgt=9in
+\newbox\letterhead
+\setbox\letterhead=\vbox{\vskip 1pc
+ \vbox to 0pt{\halign{\hss{#}\hss\cr
+ \bf American Mathematical Society\cr
+ P.\thinspace O.~Box 6248\cr
+ Providence, RI 02940\cr}\vss}}
+\vsize=\pagelgt
+\advance\vsize by-\ht\letterhead
+
+\headline={\iffirstpage \centerline{\bf INTEROFFICE MEMORANDUM}\else
+ \line{\ssub \hfil \rdate\quad Page \folio}\fi}
+\footline={\iffirstpage \rightline{\box\letterhead}\global\vsize=\pagelgt
+ \global\firstpagefalse \fi}
+
+\def \topitem#1#2{\leavevmode \hangindent 5pc \hbox to 5pc{\bf #1\hss}#2\par }
+
+\def \toname #1<{\gdef\mto{\topitem{To:}{#1}}}
+\def \fromname #1<{\gdef\mfrom{\topitem{From:}{#1}}}
+\def \longsub #1<{\gdef\lsub{\topitem{Subject:}{#1}}}
+\def \shortsub #1<{\gdef\ssub{#1}}
+
+\def \date #1<{\gdef\mdate{\topitem{\bf Date:}{#1}}
+ \gdef\rdate{#1}}
+
+\def \topinfo{{\parindent=0pt
+ \parskip=.5\baselineskip
+ \def \\{\hfil\break }
+ \mdate
+ \mto
+ \mfrom
+ \lsub
+ \vskip\baselineskip }}
+
+ % octal 214 removed jmcosu
+
+% Support verbatim listing of TeX source, as defined in TeXbook, p. 421
+% lifted from MANMAC.TEX, and modified slightly as for TUGboat
+
+\chardef\other=12
+\def\ttverbatim{\begingroup
+ \catcode`\\=\other \catcode`\{=\other
+ \catcode`\}=\other \catcode`\$=\other \catcode`\&=\other
+ \catcode`\#=\other \catcode`\%=\other \catcode`\~=\other
+ \catcode`\_=\other \catcode`\^=\other
+ \obeyspaces \obeylines \tt}
+
+\newdimen\ttrightskip
+\ttrightskip=5pc
+
+\outer\def\begintt{$$\let\par=\endgraf \ttverbatim \parskip=\z@
+ \catcode`\|=0 \rightskip=-\ttrightskip \ttfinish}
+{\catcode`\|=0 |catcode`|\=\other % | is temporary escape character
+ |obeylines % end of line is active
+ |gdef|ttfinish#1^^M#2\endtt{#1|vbox{#2}|endgroup$$}}
+
+\catcode`\|=\active
+{\obeylines \gdef|{\ttverbatim \spaceskip\ttglue \let^^M=\ \let|=\endgroup}}
+
+\newskip\ttglue
+{\tentt \global\ttglue=.5em plus .25em minus .15em}
+% this should be installed in each font
+
+
diff --git a/language/cyrillic/doc/cyrmemo.tex b/language/cyrillic/doc/cyrmemo.tex
new file mode 100644
index 0000000000..0c694b200c
--- /dev/null
+++ b/language/cyrillic/doc/cyrmemo.tex
@@ -0,0 +1,171 @@
+% ***** CYRMEMO.TEX ***** 18 Aug 84, bb
+%
+% Access to the cyrillic is through the new MR transliteration scheme,
+% using TeX/Metafont ligature capability. (An alternate set of
+% ligatures exists, for accessing letters beyond the 26 located in
+% the font positions of the 26 roman letters. An authoritative list
+% of the ligature rules is in the file cyrillic.ligs.) Successful
+% use of this file requires appropriate cyrillic and accent fonts,
+% arranged according to the AMS/MR scheme.
+%
+% This is an interim version. Not everything works yet.
+% The following are known to be less than satisfactory:
+%
+% the intermediate `ligatures' for shch access numerals;
+% primes (transliteration of hard/soft signs) use math mode;
+% underbar on `cap' double prime is too low (hard sign);
+% thorn d's don't yet exist;
+% \cydot uses math mode.
+%
+%
+% Notes on the macros:
+%
+% The single space following each hex character code is necessary
+% to prevent the next input character from being gobbled.
+
+%%%%%%%%%%
+
+\input cyrmemo.def
+
+\date 12 August 1985<
+\fromname Barbara N. Beeton\\
+ Computer Services Division<
+
+\toname Users of AMS cyrillic in \TeX<
+
+\longsub \TeX82 Cyrillic input instructions<
+\shortsub \TeX82 Cyrillic input<
+
+\topinfo
+
+The AMS cyrillic fonts have been designed so that input using the
+``new'' (post-1982) Math.~Reviews cyrillic transliteration will be
+converted directly to cyrillic text. An alternate input form is
+available for most cyrillic letters which are not transliterated by
+the equivalent single roman letters. Numerals and punctuation follow
+the normal input conventions for roman. Cyrillic is indicated to
+\TeX\ by the command |{\cyr...}|.
+
+The table below is in alphabetical order as given in the table published
+in the 1983 MR Author Index. The three paired columns contain:\ \ %
+(1)~cyrillic;
+(2)~transliteration-style input;
+(3)~alternate input, if any.
+
+\bigskip
+
+\parindent=0pt
+\parskip=0pt
+\baselineskip=15pt
+
+\newbox\BoxA
+\newbox\BoxB
+
+\def\TwoUp{\centerline{%
+ \valign{##\vfil\cr
+ \box\BoxA\cr
+ \noalign{\hfil\vrule\hfil}
+ \box\BoxB\cr}}}
+
+\newbox\TestBox
+\setbox\TestBox=\hbox{\quad\cyr Zh}
+\newdimen\cyrwd
+\cyrwd=\wd\TestBox
+\setbox\TestBox=\hbox{\enskip\tt xCdprime}
+\newdimen\ttawd
+\ttawd=\wd\TestBox
+\setbox\TestBox=\hbox{\enskip\tt N0}
+\newdimen\ttbwd
+\ttbwd=\wd\TestBox
+
+
+\settabs \+\hskip\cyrwd &\hskip\cyrwd\quad
+ &\hskip\ttawd &\hskip\ttawd\quad
+ &\hskip\ttbwd &\hskip\ttbwd\cr
+
+% \def\1 #1,#2;#3,#4;#5,#6<{\+{\cyr\ignorespaces#1}%
+% &{\cyr\ignorespaces#2\hfil}%
+% &\ignorespaces#3\hfil &\ignorespaces#4\hfil
+% &{\tt\ignorespaces#5\hfil}&{\tt\ignorespaces#6\hfil}}
+
+\setbox\BoxA=\vbox{\hsize=.45\hsize \tt
+\+{\cyr A}&{\cyr a}& |A| & |a| & & \cr
+\+{\cyr B}&{\cyr b}& |B| & |b| & & \cr
+\+{\cyr V}&{\cyr v}& |V| & |v| & & \cr
+\+{\cyr G}&{\cyr g}& |G| & |g| & & \cr
+\+{\cyr D}&{\cyr d}& |D| & |d| & & \cr
+\+{\cyr Dj}&{\cyr dj}& |Dj| & |dj| & D1 & d1\cr
+\+{\cyr \'G}&{\cyr \'g}& |\'G| & |\'g| & & \cr
+\+{\cyr E}&{\cyr e}& |E| & |e| & & \cr
+\+{\cyr \"E}&{\cyr \"e}& |\"E| & |\"e| & & \cr
+\+{\cyr \=E}&{\cyr \=e}& |\=E| & |\=e| & E2 & e2\cr
+\+{\cyr Zh}&{\cyr zh}& |Zh| & |zh| & Z1 & z1\cr
+\+{\cyr Z}&{\cyr z}& |Z| & |z| & & \cr
+\+{\cyr I}&{\cyr i}& |I| & |i| & & \cr
+\+{\cyr \=I}&{\cyr \=\i}& |\=I| & |\=\i| & I1 & i1\cr
+\+{\cyr \"I}&{\cyr \"\i}& |\"I| & |\"\i| & & \cr
+\+{\cyr J}&{\cyr j}& |J| & |j| & & \cr
+\+{\cyr \u I}&{\cyr \u\i}& |\u I| & |\u\i| & & \cr
+\+{\cyr K}&{\cyr k}& |K| & |k| & & \cr
+\+{\cyr L}&{\cyr l}& |L| & |l| & & \cr
+\+{\cyr Lj}&{\cyr lj}& |Lj| & |lj| & L1 & l1\cr
+\+{\cyr M}&{\cyr m}& |M| & |m| & & \cr
+\+{\cyr N}&{\cyr n}& |N| & |n| & & \cr
+\+{\cyr Nj}&{\cyr nj}& |Nj| & |nj| & N1 & n1\cr
+\+{\cyr O}&{\cyr o}& |O| & |o| & & \cr
+\+{\cyr P}&{\cyr p}& |P| & |p| & & \cr
+} % end \BoxA
+
+\setbox\BoxB=\vbox{\hsize=.45\hsize \tt
+\+{\cyr R}&{\cyr r}& |R| & |r| & & \cr
+\+{\cyr S}&{\cyr s}& |S| & |s| & & \cr
+\+{\cyr T}&{\cyr t}& |T| & |t| & & \cr
+\+{\cyr \'C}&{\cyr \'c}& |\'C| & |\'c| & C1 & c1\cr
+\+{\cyr \'K}&{\cyr \'k}& |\'K| & |\'k| & & \cr
+\+{\cyr U}&{\cyr u}& |U| & |u| & & \cr
+\+{\cyr \u U}&{\cyr \u u}& |\u U| & |\u u| & & \cr
+\+{\cyr F}&{\cyr f}& |F| & |f| & & \cr
+\+{\cyr Kh}&{\cyr kh}& |Kh| & |kh| & H & h\cr
+\+{\cyr Ts}&{\cyr ts}& |Ts| & |ts| & C & c\cr
+\+{\cyr Ch}&{\cyr ch}& |Ch| & |ch| & Q & q\cr
+\+{\cyr \Dzh}&{\cyr \dzh}& |\Dzh| & |\dzh| & D2 & d2\cr
+\+{\cyr Sh}&{\cyr sh}& |Sh| & |sh| & X & x\cr
+\+{\cyr Shch}&{\cyr shch}& |Shch| & |shch| & W & w\cr
+\+{\cyr \Cdprime}&{\cyr \cdprime}& |\Cdprime| & |\cdprime| & P2 & p2\cr
+\+{\cyr Y}&{\cyr y}& |Y| & |y| & & \cr
+\+{\cyr \Cprime}&{\cyr \cprime}& |\Cprime| & |\cprime| & P1 & p1\cr
+\+{\cyr \`E}&{\cyr \`e}& |\`E| & |\`e| & E1 & e1\cr
+\+{\cyr Yu}&{\cyr yu}& |Yu| & |yu| & J2 & j2\cr
+\+{\cyr Ya}&{\cyr ya}& |Ya| & |ya| & J1 & j1\cr
+\+{\cyr \Dz}&{\cyr \dz}& |\Dz| & |\dz| & D3 & d3\cr
+\+{\cyr N0}& & & & N0 & \cr
+\+{\cyr <}& & |<| & & & \cr
+\+{\cyr >}& & |>| & & & \cr
+\+\hbox to \hsize{}\cr
+} % end \BoxB
+
+\TwoUp
+
+\bigskip
+\normalbaselines
+
+\noindent In addition to the input codes shown in the table, the code
+|\cydot| is used between letters that ordinarily become ligatures to
+indicate that they are really separate letters. For example,
+|t\cydot s|${}\mapsto{}${\cyr t\cydot s} (in transliteration, t\cydot s)
+as opposed to |ts|${}\mapsto{}${\cyr ts}.
+
+\medskip
+
+\noindent {\bf Technical notes:}\ \ The names of the AMS cyrillic fonts
+begin with the letters ``|MC|'' (for ``Math Society cyrillic''). Only
+|MCYR| (lightface) is available at present, but several other styles
+are under construction: |MCB| (bold), |MCSS| (sans serif),
+|MCSSB| (bold sans serif), and others may be added from time to time.
+These fonts were prepared using {\smc Metafont79}.
+In addition to the font files, the file |CYRACC.DEF| must also be
+input for the complete cyrillic alphabet to be usable according to these
+instructions.
+
+\vfil\end
+
diff --git a/language/cyrillic/doc/lettermappings b/language/cyrillic/doc/lettermappings
new file mode 100644
index 0000000000..ecfd178c8f
--- /dev/null
+++ b/language/cyrillic/doc/lettermappings
@@ -0,0 +1,211 @@
+Part 1: control characters (0--20, 7F--A0)
+
+1 ASCII / GOSTCII
+2 EBCDIC CP 500 (Note 1)
+3 Column 1 to DKOI (Russian EBCDIC) per GOST 19768-87
+
+1 2 3 Meaning (Note 2)
+00 00 00 PUS Pusto Null CC NUL
+01 01 01 NZ Nachalo zagolovka Start of heading CC SOH (Ctrl-A)
+02 02 02 NT Nachalo teksta Start of text CC STX (Ctrl-B)
+03 03 03 KT Konets teksta End of text CC ETX (Ctrl-C)
+04 37 37 KP Konets peredachi End of transmission CC EOT (Ctrl-D)
+05 2D 2D KTM Kto tam? Enquiry CC ENQ (Ctrl-E)
+06 2E 2E DA Podtverzhdenie Acknowledge CC ACK (Ctrl-F)
+07 2F 2F ZV Zvonok Bell CC BEL (Ctrl-G)
+08 16 16 VSh Vozvrat na shag Backspace CC BS (Ctrl-H)
+09 05 05 GT Gorizontal'naya tabulyatsiya Horizontal tabulation CC HT (Ctrl-I)
+0A 25 25 PS Perevod stroki Line feed CC LF (Ctrl-J)
+0B 0B 0B VT Vertikal'naya tabulyatsiya Vertical tabulation CC VT (Ctrl-K)
+0C 0C 0C PF Perevod formata Form feed CC FF (Ctrl-L)
+0D 0D 0D VK Vozvrat karetki Carriage return CC CR (Ctrl-M)
+0E 0E 0E VYKh Vykhod Shift out return CC SO (Ctrl-N)
+0F 0F 0F VKh Vkhod Shift in return CC SI (Ctrl-O)
+10 10 10 AR1 Avtoregistr 1 Data link escape CC DLE (Ctrl-P)
+11 11 11 SU1 Simvol upravleniya 1 Device control 1 CC DC1 (X-Off, Ctrl-Q)
+12 12 12 SU2 Simvol upravleniya 2 Device control 2 CC DC2 (Ctrl-R)
+13 13 13 SU3 Simvol upravleniya 3 Device control 3 DC3 / Tape mark CC TM
+(E) (X-On, Ctrl-S)
+14 3C 3C STP Stop Device control 4 CC DC4 (Ctrl-T)
+15 3D 3D NET Otritsanie Negative acknowledge CC NAK (Ctrl-U)
+16 32 32 SIN Sinkhronizatsiya Synchronous idle CC SYN (Ctrl-V)
+17 26 26 KB Konets blokov End of transmission block CC ETB (Ctrl-
+W)
+18 18 18 AN Annulirovanie Cancel CC CAN (Ctrl-X)
+19 19 19 KN Konets nositelya End of medium CC EM (Ctrl-Y)
+1A 3F 3F ZM Zamena Substitute CC SUB (Ctrl-Z)
+1B 27 27 AR2 Avtoregistr 2 Escape CC ESC : Prefix PRE (Escape, Ctr
+l+Left Bracket)
+1C 1C 1C RF Razdelitel' fajlov FS : Interchange file separator CC IFS
+(Ctrl+Backslash)
+1D 1D 1D RG Razdelitel' grupp GS : Interchange group separator CC IGS
+ (Ctrl+Right Bracket)
+1E 1E 1E RZ Razdelitel' zapisej ES : Interchange record separator CC IR
+S (Ctrl+6)
+1F 1F 1F RE Razdelitel' `elementov US : Interchange unit (trans blk) sep C
+C IUS (ITB) (Ctrl+Minus)
+20 40 40 Probel Space
+ ...
+7F 07 07 Delete CC DEL
+80 20 20 VTsF Vybor tsifry Digit selector CC DS
+81 21 21 NZN Nachalo znachimosti Start of significance CC SOS
+82 22 22 RP Razdelitel' polej Field separator CC FS
+83 23 23 Word Underscore CC WUS
+84 24 24 BK Blokirovka Bypass CC BYP / Inhibit presentation IN
+P
+85 15 15 NS Novaya stroka New line CC NL
+86 06 06 NP Nizhnee polozhenie Lower case CC LC / Required new line RN
+L
+87 17 17 OZhD Ozhidanie Idle CC IL
+88 28 28 Set attribute CC SA
+89 29 29 Start field extended CC SFE
+8A 2A 2A UR Ustanovlenie rezhima Set mode CC SM / Switch SW
+8B 2B 2B SP2 Simvol pol'zovatelya 2 Customer use 2 CC CU2 / Control Seq Pre
+fix CSP
+8C 2C 2C Modify field attribute CC MFA
+8D 09 09 Superscript CC SPS
+8E 0A 0A NRB Nachalo ruchnogo vvoda Start of manual message CC SMM / Repeat
+ RPT
+8F 1B 1B SP1 Simvol pol'zovatelya 1 Customer use 1 CC CU1
+90 30 30
+91 31 31
+92 1A 1A UUK Upravlenie ukazatelem Cursor CC CC / Unit backspace UBS
+93 33 33 Index return CC IR
+94 34 34 VKP Vklyuchenie perforatora Punch on CC PN
+95 35 35 OSU Ostanovka schityvayushchego Reader stop CC RS / Transparent TRN
+96 36 36 VP Verkhnee polozhenie Upper case CC UC / Num backspace NBS
+97 08 08 Graphic escape CC GE
+98 38 38 Subscript CC SBS
+99 39 39 Indent tab CC IT
+9A 3A 3A Required form feed CC RFF
+9B 3B 3B SP3 Simvol pol'zovatelya 3 Customer use 3 CC CU3
+9C 04 04 VYP Vyklyuchenie perforatora Punch off CC PF / Select SEL (E)
+9D 14 14 VST Vosstanovlenie Restore CC RES / Enable presentation EN
+P
+9E 3E 3E
+9F FF E1 Eight ones EO (Note 3)
+A0 41 41 No-break space CC NBSP : Required space
+ RSP (E)
+
+Part 2: Mappings from characters above A0, including historical ones.
+
+1 ASCII / GOSTCII
+2 EBCDIC CP 500
+3 Column 1 to DKOI (Russian EBCDIC) per GOST 19768-87
+4 Column 1 to EBCDIC per GOST 19768-74
+5 KOI-8 per GOST 19768-74 (Russian A = Latin a+80, etc), when defined
+
+1 2 3 4 5 Meaning (Note 4)
+A1 AA 42 42 Cyrillic capital letter Io (E+umlaut)
+A2 4A 43 43 Serbocroatian Cyrillic capital letter Dje (Note 5)
+A3 B1 44 44 Macedonian Cyrillic capital letter Gje (Note 5)
+A4 9F 45 45 Ukrainian Cyrillic capital letter rounded Ie (Note 5)
+A5 B2 46 46 Macedonian Cyrillic capital letter Dze (Note 5)
+A6 6A 47 47 Cyrillic capital letter I decimal (Note 5)
+A7 B5 48 48 Ukrainian Cyrillic capital letter Yi (Note 5)
+A8 BD 49 49 Cyrillic capital letter Je (Note 5)
+A9 B4 51 51 Cyrillic capital letter Lje (Note 5)
+AA 9A 52 52 Cyrillic capital letter Nje (Note 5)
+AB 8A 53 53 Serbocroatian Cyrillic capital letter Chje (Note 5)
+AC 5F 54 54 Macedonian Cyrillic capital letter Kje (Note 5)
+AD CA 55 55 Soft hyphen CC SHY (Note 5)
+AE AF 56 56 Byelorussian Cyrillic capital letter short U (Note 5)
+AF BC 57 57 Cyrillic capital letter Dze (Note 5)
+B0 90 B9 58 E1 Cyrillic capital letter A
+B1 8F BA 59 E2 Cyrillic capital letter Be
+B2 EA ED 62 F7 Cyrillic capital letter Ve
+B3 FA BF 63 E7 Cyrillic capital letter Ghe
+B4 BE BC 64 E4 Cyrillic capital letter De
+B5 A0 BD 65 E5 Cyrillic capital letter Ie
+B6 B6 EC 66 F6 Cyrillic capital letter Zhe
+B7 B3 FA 67 FA Cyrillic capital letter Ze
+B8 9D CB 68 E9 Cyrillic capital letter I
+B9 DA CC 69 EA Cyrillic capital letter short I
+BA 9B CD 70 EB Cyrillic capital letter Ka
+BB 8B CE 71 EC Cyrillic capital letter El
+BC B7 CF 72 ED Cyrillic capital letter Em
+BD B8 DA 73 EE Cyrillic capital letter En
+BE B9 DB 74 EF Cyrillic capital letter O
+BF AB DC 75 F0 Cyrillic capital letter Pe
+C0 64 DE 76 F2 Cyrillic capital letter Er
+C1 65 DF 77 F3 Cyrillic capital letter Es
+C2 62 EA 78 F4 Cyrillic capital letter Te
+C3 66 EB 80 F5 Cyrillic capital letter U
+C4 63 BE 8A E6 Cyrillic capital letter Ef
+C5 67 CA 8B E8 Cyrillic capital letter Kha
+C6 9E BB 8C E3 Cyrillic capital letter Tse
+C7 68 FE 8D FE Cyrillic capital letter Che
+C8 74 FB 8E FB Cyrillic capital letter Sha
+C9 71 FD 8F FD Cyrillic capital letter Shcha
+CA 72 75 90 FF Cyrillic capital hard sign (Ier)
+CB 73 EF 9A F9 Cyrillic capital letter Y (Iery)
+CC 78 EE 9B F8 Cyrillic capital soft sign (Ierik)
+CD 75 FC 9C FC Cyrillic capital letter reverse rounded E
+CE 76 B8 9D E0 Cyrillic capital letter Yu
+CF 77 DD 9E F1 Cyrillic capital letter Ya
+D0 AC 77 9F C1 Cyrillic small letter a
+D1 69 78 A0 C2 Cyrillic small letter be
+D2 ED AF AA D7 Cyrillic small letter ve
+D3 EE 8D AB C7 Cyrillic small letter ghe
+D4 EB 8A AC C4 Cyrillic small letter de
+D5 EF 8B AD C5 Cyrillic small letter ie
+D6 EC AE AE D6 Cyrillic small letter zhe
+D7 BF B2 AF DA Cyrillic small letter z
+D8 80 8F B0 C9 Cyrillic small letter i
+D9 FD 90 B1 CA Cyrillic small letter short i
+DA FE 9A B2 CB Cyrillic small letter ka
+DB FB 9B B3 CC Cyrillic small letter el
+DC FC 9C B4 CD Cyrillic small letter em
+DD AD 9D B5 CE Cyrillic small letter en
+DE AE 9E B6 CF Cyrillic small letter o
+DF 59 9F B7 D0 Cyrillic small letter pe
+E0 44 AA B8 D2 Cyrillic small letter er
+E1 45 AB B9 D3 Cyrillic small letter es
+E2 42 AC BA D4 Cyrillic small letter te
+E3 46 AD BB D5 Cyrillic small letter u
+E4 43 8C BC C6 Cyrillic small letter ef
+E5 47 8E BD C8 Cyrillic small letter kha
+E6 9C 80 BE C3 Cyrillic small letter tse
+E7 48 B6 BF DE Cyrillic small letter che
+E8 54 B3 CA DB Cyrillic small letter sha
+E9 51 B5 CB DD Cyrillic small letter shcha
+EA 52 B7 CC DF Cyrillic small hard sign (ier)
+EB 53 B1 CD D9 Cyrillic small letter y (iery)
+EC 58 B0 CE D8 Cyrillic small soft sign (ierik)
+ED 55 B4 CF DC Cyrillic small letter reverse rounded e
+EE 56 76 DA C0 Cyrillic small letter yu
+EF 57 A0 DB D1 Cyrillic small letter ya
+F0 8C 58 DC Number acronym (ligature) (Note 5)
+F1 49 59 DD Cyrillic small letter io (e+umlaut)
+F2 CD 62 DE Serbocroatian Cyrillic small letter Dje (Note 5)
+F3 CE 63 DF Macedonian Cyrillic small letter Gje (Note 5)
+F4 CB 64 EA Ukrainian Cyrillic small letter rounded Ie (Note 5)
+F5 CF 65 EB Macedonian Cyrillic small letter Dze (Note 5)
+F6 CC 66 EC Cyrillic small letter i decimal (Note 5)
+F7 E1 67 ED Ukrainian Cyrillic small letter Yi (Note 5)
+F8 70 68 EE Cyrillic small letter Je (Note 5)
+F9 DD 69 EF Cyrillic small letter Lje (Note 5)
+FA DE 70 FA Cyrillic small letter Nje (Note 5)
+FB DB 71 FB Serbocroatian Cyrillic small letter Chje (Note 5)
+FC DC 72 FC Macedonian Cyrillic small letter Kje (Note 5)
+FD 8D 73 FD Paragraph sign (U.S. Section) (Note 5)
+FE 8E 74 FE Byelorussian Cyrillic small letter short u (Note 5)
+FF DF FF FF Cyrillic small letter Dze (Note 5)
+
+Note 1: The following characters: exclamation mark / bang, opening square
+bracket, closing square bracket, circumflex accent, logical OR / solid vertical
+bar are mapped according to CP 500 (as opposed to CP 037, et al).
+
+Note 2: Russian meanings are transliterated.
+
+Note 3: Note that 'most people' map ASCII 9F to EBCDIC FF (Eight Ones) while
+GOST 19768-87 maps 9F to E1 and maps ASCII FF to DKOI FF. This is the only
+difference between columns 2 and 3 in part 1.
+
+Note 4: Letter names are per ECMA 113, more or less; some are known to be
+erroneous. See the previous discussion on RUSTEX-L for more correct names.
+
+Note 5: Positions defined in ECMA 113/ISO 8859-5, but not in GOST 19768-87.
+
+Acknowledgement: I [Dimitri Vulis] received much of the information
+above from Johan W. van Wingen, for which I am very grateful.
diff --git a/language/cyrillic/doc/rsam.ter b/language/cyrillic/doc/rsam.ter
new file mode 100644
index 0000000000..51746fbcf5
--- /dev/null
+++ b/language/cyrillic/doc/rsam.ter
@@ -0,0 +1,999 @@
+\input rmacro.sty
+%\hsize16383.99999pt %uncomment to display all hyphens in the log file
+%\parfillskip 0pt plus0pt minus0pt
+%\showboxdepth-1
+%\tolerance-1
+%\hbadness0
+%\hyphenpenalty=-1000 %just have lots of hyphenation in the dvi file
+%\pretolerance-1
+\tolerance=1000
+%\doublehyphendemerits=-100000
+%\finalhyphendemerits=-100000
+\uchyph=1
+\defaulthyphenchar=`\-
+\hyphenchar\tenrm=-1
+
+%Load the fonts
+\font\cyr=xncyr10\relax %upright
+\font\bcyr=xncyrb10\relax %bold
+\font\icyr=xncyri10\relax %italic
+\font\ccyr=xncyrc10\relax %small caps
+\font\hcyr=xncyrh10\relax %sans serif
+\font\sf=cmss10\relax %Latin sans serif
+% AMSTeX ripoff
+\font\teneuf=eufm10
+\font\tenmsy=msym10
+\newfam\euffam
+\newfam\msyfam
+\textfont\euffam=\teneuf
+\textfont\msyfam=\tenmsy
+\def\frak#1{{\fam\euffam#1}}
+\def\Bbb#1{{\fam\msyfam#1}}
+%\let\Bbb=\relax %If you don't have these
+%\let\frak=\relax %If you don't have these
+
+\def\acircle{\mathaccent"7017 } %circle over math accent
+\def\qed{\ifhmode\unskip\nobreak\fi\ifmmode\ifinner\else\hskip5pt\fi\fi
+ \hbox{\ \vrule width4pt height6pt depth1.5pt\hskip0pt}}
+
+\cdefTranslitX
+
+\noindent{\rm Russian alphabet, transliterated one way:}
+
+\hbox{0123456789:;<=>?@ABCDEFGHIJKLMNO}
+
+\hbox{PQRSTUVWXYZ[\]^_`abcdefghijklmno}
+
+\cdefTranslitY
+
+\noindent{\rm Russian alphabet, transliterated another way:}
+
+\hbox{0123456789:;<=>?@ABCDEFGHIJKLMNO}
+
+\hbox{PQRSTUVWXYZ[\]^_`abcdefghijklmno}
+
+\cdefRussian
+
+\cyr
+\noindent{\rm Russian alphabet, native:}
+
+\hbox{0123456789:;<=>?@ABCDEFGHIJKLMNO}
+
+\hbox{PQRSTUVWXYZ[\]^_`abcdefghijklmno}
+
+{\icyr
+\noindent{\rm Russian alphabet,} Zc`aXR:
+
+\hbox{0123456789:;<=>?@ABCDEFGHIJKLMNO}
+
+\hbox{PQRSTUVWXYZ[\]^_`abcdefghijklmno}
+
+}
+
+\bigskip\noindent{\sf From} {\hcyr 4.0. Ac_`c]U]Z^, <3`c__k \Pb`Xf>}
+
+<PZaX\P[l]kU ]U_`XR^TX\kU [^ZP[l]^ S`c__k $GL(n,{\Bbb R})$ ]PT _^[U\
+RUiUabRU]]ke gXaU[ $\Bbb R$ ^_XaP]]k Ac_`c]U]Z^ R abPblU (9), STU cabP]^R[U]k
+a[UTcniXU bU^`U\k:
+
+1. 5a[X ]UgUb]^U gXa[^ $n>1$, b^ R $GL(n,{\Bbb R})$ ]Ub ]U_`XR^TX\ke [^ZP[l]^
+]X[l_^bU]b]ke _^TS`c__.
+
+2. 5a[X $n$---gUb]^U gXa[^, ]U oR[oniUUao abU_U]ln TR^YZX, b^ R $GL(n,{\Bbb
+R})$ a b^g]^abln T^ a^_`oVU]]^abX X\UUbao b^[lZ^ ^T]P \PZaX\P[l]Po ]U_`XR^TX\Po
+[^ZP[l]^ ]X[l_^bU]b]Po _^TS`c__P.
+
+3. 5a[X $n=2^\alpha\quad(\alpha\ge1)$, b^ \]^VUabR^ RaUe \PZaX\P[l]ke
+]U_`XR^TX\ke [^ZP[l]^ ]X[l_^bU]b]ke _^TS`c__ S`c__ $GL(n,{\Bbb R})$ `PWQXRPUbao
+]P TRP Z[PaaP a^_`oVU]]ke _^TS`c__.
+
+4. ;nQPo ]U_`XR^TX\Po [^ZP[l]^ ]X[l_^bU]b]Po _^TS`c__P R $GL(n,{\Bbb R})$ _`X
+$n>2$ X\_`X\XbXR]P.
+
+\bigskip\noindent{\sf From} {\hcyr =.2. 3^S^[l, <BP`Pa 1c[lQP>}
+
+:^[UQ]c[Pal Rao b^[_P. A]PgP[P ]P \XS _`^]Ua[^al _^ RaU\c QU`USc \^[gP]XU,
+Z^b^`^U cabP]PR[XRPUbao _U`UT aRX`U_^n Qc`UY, X _^b^\ RT`cS _^T]o[Xal `UgX, X
+RUal WPS^R^`X[ QU`US.
+
+---:PZ, gb^Qk VXTk TU`VP[X ]P P`U]TU e`XabXP]aZXU fU`ZRX! Gb^Qk ZaU]TWk
+WP_`oSP[X R ^S[^Q[X _`PR^a[PR]ke e`XabXP]! :PZ, gb^Qk _^_cabXbl bPZXU \cgU]Xo
+]P `caaZ^Y WU\[U ^b _`^Z[obke ]UT^RU`Z^R! Gb^Qk R^b bPZ _^abc_P[X a
+_^[Z^R]XZP\X X SUbl\P]^\! 4P ]U QcTUb VU aUS^, ]U QcTUb!
+
+BPZXU a[^RP _U`U[UbP[X _^ RaU\ Z^]fP\. 7Phc\U[X WP_^`^Vfk X _^gco[X aR^n aX[k.
+Bcb cVU ]U Qk[^ R^[]U]XY [USZ^\ka[U]]^S^ ]P`^TP; R^[]^RP[Xal RaU eP`PZbU`k
+boVU[kU X Z`U_ZXU, Z^b^`kU ]U aZ^`^ ]PZP[o[Xal, ]^, ]PZP[XRhXal, c_^`]^ X T^[S^
+e`P]X[X R aUQU R]cb`U]]XY VP`.
+
+---?U`URUhPbl Ran VXT^Rc!---`PWTP[^al XW b^[_k.---?cabl VU ]U hlnb XW _^_^RaZXe
+`XW nQ^Z aR^X\ VXT^RZP\! ?cabl VU ]U abPRob W]PgZ^R ]P aRobke _PaePe!
+?U`Ub^_Xbl Xe RaUe, _^SP]fUR, R 4]U_`U.---A[^RP mbX, _`^XW]UaU]]kU ZU\-b^ XW
+b^[_k, _`^[UbU[X \^[]XUY _^ RaU\ S^[^RP\, X b^[_P `X]c[Pal ]P _`UT\UablU, a
+VU[P]XU\ _U`U`UWPbl RaUe VXT^R.
+
+1UT]kU ak]k 8W`PX[o, `PabU`oRhX RaU _`XacbabRXU aR^US^ X QUW b^S^ \U[Z^S^ TceP,
+_`obP[Xal R _cabke S^`U[^g]ke Q^gZPe, R _UgZPe X TPVU WP_^[WkRP[X _^T nQZX
+aR^Xe VXT^R^Z; ]^ Z^WPZX RUWTU Xe ]Pe^TX[X.
+
+---Oa]^RU[l\^V]kU _P]k!---Z`XgP[ ^TX], Rka^ZXY X T[X]]kY, ZPZ _P[ZP, VXT,
+Rkac]cRhX XW ZcgX aR^Xe b^RP`XiUY VP[Zcn aR^n `^Vc, XaZ^RU`ZP]]cn
+ab`Pe^\.---Oa]^RU[l\^V]kU _P]k! A[^R^ b^[lZ^ TPYbU ]P\ aZPWPbl, ^T]^ a[^R^! <k
+bPZ^U ^QloRX\ RP\, gUS^ UiU ]XZ^STP ]U a[khP[X, bPZ^U RPV]^U, gb^ ]U \^V]^
+aZPWPbl ZPZ^U RPV]^U!
+
+---=c, _cabl aZPVcb,---aZPWP[ 1c[lQP, Z^b^`kY RaUSTP [nQX[ Rka[chPbl
+^QRX]oU\^S^.
+
+---Oa]kU _P]k!---_`^XW]Ua VXT.---BPZXe _P]^R UiU ]XZ^STP ]U RXTkRP]^. 5Y Q^Sc,
+]XZ^STP! BPZXe T^Q`ke, e^`^hXe X e`PQ`ke ]U Qk[^ UiU ]P aRUbU!..---3^[^a US^
+c\X`P[ X T`^VP[ ^b ab`PeP.---:PZ \^V]^, gb^Qk \k Tc\P[X _`^ WP_^`^VfUR
+gb^-]XQcTl ]Ue^`^hUU! BU a^RaU\ ]U ]PhX, bU, gb^ P`U]TPbc`abRcnb ]P CZ`PY]U! 5Y
+Q^Sc, ]U ]PhX! B^ a^RaU\ ]U VXTk; b^ gU`b W]PUb gb^. B^ bPZ^U, gb^ b^[lZ^
+_^_[URPbl ]P ]US^, TP X Q`^aXbl! 2^b X ^]X aZPVcb b^ VU. =U _`PRTP [X, H[U\P,
+X[X bk, H\c[l?
+
+---5Y Q^Sc, _`PRTP!---^bRUgP[X XW b^[_k H[U\P X H\c[l R XW^T`P]]ke o[^\ZPe, ^QP
+QU[kU, ZPZ S[X]P.
+
+---<k ]XZ^STP UiU,---_`^T^[VP[ T[X]]ke VXT,---]U a^S[PhP[Xal a ]U_`XobU[o\X. 0
+ZPb^[XZ^R \k X W]Pbl ]U e^bX\; _cabl X\ gU`b _`Xa]Xbao! <k a WP_^`^VfP\X ZPZ
+Q`Pblo `^T]kU...
+
+---:PZ? Gb^Qk WP_^`^Vfk Qk[X a RP\X Q`Pblo?---_`^XW]Ua ^TX] XW b^[_k.---=U
+T^VTUbUal, _`^Z[obkU VXTk! 2 4]U_` Xe, _P]^RU! 2aUe _^b^_Xbl, _^SP]fUR!
+
+MbX a[^RP Qk[X aXS]P[^\. 6XT^R `PaeRPbP[X _^ `cZP\ X ]PgP[X hRk`obl R R^[]k.
+6P[ZXY Z`XZ `PWTP[ao a^ RaUe ab^`^], ]^ ac`^RkU WP_^`^Vfk b^[lZ^ a\Uo[Xal,
+RXTo, ZPZ VXT^RaZXU ]^SX R QPh\PZPe X gc[ZPe Q^[bP[Xal ]P R^WTceU. 1UT]kY
+^`Pb^`, ]PZ[XZPRhXY aP\ ]P aR^n hUn QUTc, RkaZ^gX[ XW ZPdbP]P, WP Z^b^`kY Qk[^
+US^ ceRPbX[X, R ^T]^\ _US^\ X cWZ^\ ZP\W^[U, aeRPbX[ WP ]^SX 1c[lQc X VP[ZX\
+S^[^a^\ \^[X[:
+
+---2U[XZXY S^a_^TX], oa]^RU[l\^V]kY _P]! O W]P[ X Q`PbP RPhUS^, _^Z^Y]^S^
+4^`^hP! 1k[ R^X] ]P cZ`PhU]XU RaU\c `kfP`abRc. O U\c R^aU\la^b fUZX]^R TP[,
+Z^STP ]cV]^ Qk[^ RkZc_Xblao XW _[U]P c bc`Z^R.
+
+---Bk W]P[ Q`PbP?---a_`^aX[ BP`Pa.
+
+---5Y Q^Sc, W]P[! 2U[XZ^Tch]kY Qk[ _P].
+
+---0 ZPZ bUQo W^Rcb?
+
+---O]ZU[l.
+
+---E^`^h^,---aZPWP[ BP`Pa X _^b^\, _^Tc\PR, ^Q`PbX[ao Z Z^WPZP\ X _`^S^R^`X[
+bPZ:---6XTP QcTUb RaUSTP R`U\o _^RUaXbl, Z^STP QcTUb ]cV]^, P ]P aUS^T]o
+^bTPYbU US^ \]U.---AZPWPRhX mb^, BP`Pa _^RU[ US^ Z aR^U\c ^Q^Wc, R^W[U Z^b^`^S^
+ab^o[X Z^WPZX US^.---=c, _^[UWPY _^T bU[USc, [UVX bP\ X ]U _^hURU[Xal; P Rk,
+Q`Pbfk, ]U Rk_caZPYbU VXTP.
+
+\bigskip\noindent{\sf From} {\hcyr D.8. :P`_U[URXg, ;.5. APT^RaZXY, <M[U\U]bk
+[X]UY]^Y P[SUQ`k X [X]UY]^S^ _`^S`P\\X`^RP]Xo>}
+
+\centerline{\bcyr \S1.9 @P]S \Pb`Xfk}
+
+1. ?`UT_^[^VX\, gb^ ]P\ TP]P \Pb`XfP $U$ XW $m$ ab`^Z X $n$ ab^[Qf^R:
+$$U = \left(\matrix{
+a_{11} & a_{12} & \ldots & a_{1n} \cr
+a_{21} & a_{22} & \ldots & a_{2n} \cr
+\ldots & \ldots & \ldots & \ldots \cr
+a_{m1} & a_{m2} & \ldots & a_{mn} \cr
+}\right).$$
+2kTU[X\ R ]UY _`^XWR^[l]^ $k$ ab`^Z X $k$ ab^[Qf^R. M[U\U]bk, ab^oiXU ]P
+_U`UaUgU]XX RkTU[U]]ke ab`^Z X ab^[Qf^R, ^Q`PWcnb ZRPT`Pb]cn \Pb`Xfc $k$-S^
+_^`oTZP. >_`UTU[XbU[l mb^Y \Pb`Xfk ]PWkRPUbao {\icyr \X]^`^\} $k$-S^ _^`oTZP
+\Pb`Xfk $U$. 2kQX`Po RaUR^W\^V]k\X a_^a^QP\X _^ $k$ ab`^Z X $k$ ab^[Qf^R,
+_^[cgPU\ RaUR^W\^V]kU \X]^`k $k$-S^ _^`oTZP \Pb`Xfk $U$. >gURXT]^, gb^ ^QiUU
+gXa[^ bPZXe \X]^`^R a^abPR[oUb $C_m^k C_n^k$.
+
+<Pb`XfP $U$ ^Q[PTPUb, bPZX\ ^Q`PW^\, \X]^`P\X `PW[Xg]ke _^`oTZ^R. <X]^`P\X
+_U`R^S^ _^`oTZP oR[onbao aP\X m[U\U]bk \Pb`Xfk $U$. <PZaX\P[l]^ R^W\^V]kY
+_^`oT^Z \X]^`^R `PRU], ^gURXT]^, ]PX\U]lhU\c XW gXaU[ $m$ X $n$.
+
+2. @Paa\^b`X\ R \Pb`XfU $U$ RaU UU \X]^`k RaUe R^W\^V]ke _^`oTZ^R. 2kTU[X\ bU
+XW ]Xe, Z^b^`kU ^b[Xg]k ^b ]c[o. 2RUTU\ a[UTcniUU ^_`UTU[U]XU.
+
+{\ccyr >_`UTU[U]XU 4.} =PXQ^[lhXY XW _^`oTZ^R \X]^`^R, ^b[Xg]ke ^b ]c[o,
+]PWkRPUbao {\icyr `P]S^\ \Pb`Xfk.}
+
+{\ccyr @PWjoa]U]XU.} 5a[X `P]S \Pb`Xfk $U$ `PRU] $r$, b^ mb^ ^W]PgPUb, gb^ R
+\Pb`XfU $U$ X\UUbao ^b[Xg]kY ^b ]c[o \X]^` _^`oTZP $r$, ]^ RaoZXY \X]^` _^`oTZP
+Q^[lhUS^, gU\ $r$, `PRU] ]c[n.
+
+5a[X a`UTX m[U\U]b^R \Pb`Xfk X\UUbao e^bo Qk ^TX] ^b[Xg]kY ^b ]c[o, b^ `P]S
+\Pb`Xfk WPRUT^\^ ]U \U]lhU UTX]Xfk $(r\ge1)$, bPZ ZPZ \X]^`P\X _U`R^S^ _^`oTZP
+oR[onbao aP\X m[U\U]bk \Pb`Xfk. 5a[X VU RaU m[U\U]bk \Pb`Xfk `PR]k ]c[n, b^ X
+`P]S UU _`X]X\Pnb `PR]k\ ]c[n.
+
+@P]S \Pb`Xfk $U$ ^Q^W]PgPUbao gU`UW $r(U)$. 2 TP[l]UYhU\ _^[UW]^ X\Ubl R RXTc
+a[UTcnicn [U\\c.
+
+{\ccyr ;U\\P 1.} {\icyr 5a[X RaU \X]^`k $l$-S^ _^`oTZP \Pb`Xfk $U$ `PR]k ]c[n,
+b^ RaU UU \X]^`k _^`oTZ^R Q^[lhXe, gU\ $l$, bPZVU `PR]k ]c[n.}
+
+{\ccyr 4^ZPWPbU[labR^.} ?cabl, a^S[Pa]^ ca[^RXn [U\\k, RaU \X]^`k $l$-S^
+_^`oTZP WPTP]]^Y \Pb`Xfk `PR]k ]c[n. 4^ZPVU\ a]PgP[P, gb^ `PR]k ]c[n RaU UU
+\X]^`k $l+1$-S^ _^`oTZP. 2 aP\^\ TU[U, `Paa\^b`X\ [nQ^Y \X]^` $l+1$-S^ _^`oTZP.
+Mb^b \X]^`, ZPZ ^_`UTU[XbU[l $l+1$-S^ _^`oTZP, `PRU] ac\\U _`^XWRUTU]XY
+m[U\U]b^R ZPZ^S^-[XQ^ US^ ab^[QfP ]P Xe P[SUQ`PXgUaZXU T^_^[]U]Xo.
+0[SUQ`PXgUaZ^U T^_^[]U]XU [nQ^S^ m[U\U]bP \X]^`P $M$ oR[oUbao, ^gURXT]^,
+]UZ^b^`k\ \X]^`^\ $l$-S^ _^`oTZP \Pb`Xfk $U$, RWobk\ a a^^bRUbabRcniX\ W]PZ^\.
+?^mb^\c P[SUQ`PXgUaZ^U T^_^[]U]XU [nQ^S^ m[U\U]bP \X]^`P $M$ `PR]^ ]c[n, P
+W]PgXb, `PRU] ]c[n X aP\ \X]^` $M$.
+
+0]P[^SXg]k\X `PaacVTU]Xo\X, Xa_^[lWco cVU T^ZPWP]]kY ]P\X dPZb `PRU]abRP ]c[n
+RaUe \X]^`^R $l+1$-S^ _^`oTZP, T^ZPWkRPU\ `PRU]abR^ ]c[n RaUe \X]^`^R $l+2$-S^
+_^`oTZP X b.T. ;U\\P T^ZPWP]P. \qed
+
+\bigskip\noindent{\sf From} {\hcyr DUT^` <XePY[^RXg 4^ab^URaZXY, <?`Uabc_[U]XU
+X ]PZPWP]XU>}
+
+2 ]PgP[U Xn[o, R g`UWRkgPY]^ VP`Z^U R`U\o, _^T RUgU`, ^TX] \^[^T^Y gU[^RUZ
+RkhU[ XW aR^UY ZP\^`ZX, Z^b^`cn ]P]X\P[ ^b VX[lf^R R Ab^[o`]^\ _U`Uc[ZU, ]P
+c[Xfc, X \UT[U]]^, ZPZ Qk R ]U`UhX\^abX, ^b_`PRX[ao Z :^ZchZX]c \^abc.
+
+>] Q[PS^_^[cg]^ XWQUS]c[ Rab`UgX a^ aR^UY e^WoYZ^Y ]P [Uab]XfU. :P\^`ZP US^
+_`Xe^TX[Pal _^T aP\^n Z`^R[UY Rka^Z^S^ _obXmbPV]^S^ T^\P X _^e^TX[P Q^[UU ]P
+hZPd, gU\ ]P ZRP`bX`c. :RP`bX`]Po VU e^WoYZP US^, c Z^b^`^Y ^] ]P]X\P[ mbc
+ZP\^`Zc a ^QUT^\ X _`Xa[cS^Y, _^\UiP[Pal ^T]^Y [Uab]XfUY ]XVU, R ^bTU[l]^Y
+ZRP`bX`U, X ZPVTkY `PW, _`X Rke^TU ]P c[Xfc, U\c ]U_`U\U]]^ ]PT^ Qk[^ _`^e^TXbl
+\X\^ e^WoYZX]^Y Zce]X, _^gbX RaUSTP ]PabUVl ^bR^`U]]^Y ]P [Uab]Xfc. 8 ZPVTkY
+`PW \^[^T^Y gU[^RUZ, _`^e^To \X\^, gcRabR^RP[ ZPZ^U-b^ Q^[UW]U]]^U X b`ca[XR^U
+^iciU]XU, Z^b^`^S^ abkTX[ao X ^b Z^b^`^S^ \^`iX[ao. >] Qk[ T^[VU] Z`cS^\
+e^WoYZU X Q^o[ao a ]UY Rab`UbXblao.
+
+=U b^ gb^Q ^] Qk[ bPZ b`ca[XR X WPQXb, a^RaU\ TPVU ]P_`^bXR; ]^ a ]UZ^b^`^S^
+R`U\U]X ^] Qk[ R `PWT`PVXbU[l]^\ X ]P_`oVU]]^\ a^ab^o]XX, _^e^VU\ ]P
+X_^e^]T`Xn. >] T^ b^S^ cS[cQX[ao R aUQo X cUTX]X[ao ^b RaUe, gb^ Q^o[ao TPVU
+RaoZ^Y Rab`UgX, ]U b^[lZ^ Rab`UgX a e^WoYZ^Y. >] Qk[ WPTPR[U] QUT]^abln; ]^
+TPVU abUa]U]]^U _^[^VU]XU _U`UabP[^ R _^a[UT]UU R`U\o boS^bXbl US^. =Paci]k\X
+TU[P\X aR^X\X ^] a^RaU\ _U`UabP[ X ]U e^bU[ WP]X\Pblao. =XZPZ^Y e^WoYZX R
+aci]^abX ^] ]U Q^o[ao, gb^ Qk bP ]X WP\kh[o[P _`^bXR ]US^. =^ ^abP]PR[XRPblao
+]P [Uab]XfU, a[chPbl RaoZXY RWT^` _`^ Ran mbc ^QkTU]]cn T`UQUTU]l, T^ Z^b^`^Y
+U\c ]Ub ]XZPZ^S^ TU[P, RaU mbX _`XabPRP]Xo ^ _[PbUVU, cS`^Wk, VP[^Qk, X _`X
+mb^\ aP\^\c XWR^`PgXRPblao, XWRX]oblao, [SPbl---]Ub, cV [cghU _`^aZ^[lW]cbl
+ZPZ-]XQcTl Z^hZ^Y _^ [Uab]XfU X c[XW]cbl, gb^Qk ]XZb^ ]U RXTP[.
+
+2_`^gU\, ]P mb^b `PW ab`Pe Rab`UgX a^ aR^UY Z`UTXb^`hUY TPVU US^ aP\^S^ _^`PWX[
+_^ Rke^TU ]P c[Xfc.
+
+\bigskip\noindent{\sf From} {\hcyr 5.A. 2U]fU[l ({\sf aka} 8. 3`UZ^RP),
+<BU^`Xo RU`^ob]^abUY>}
+
+\centerline{\bcyr 11.4. Cb^g]U]XU `UWc[lbPb^R, _^[cgU]]ke \Ub^T^\ [X]UP`XWPfXX}
+
+2 ]UZ^b^`ke WPTPgPe _`PZbXZX R^W]XZPUb a^\]U]XU R _`X\U]X\^abX \Ub^TP
+[X]UP`XWPfXX R aRoWX a bU\, gb^ TXP_PW^] a[cgPY]ke P`Sc\U]b^R ]U ]Pab^[lZ^ \P[,
+gb^Qk R US^ _`UTU[Pe dc]ZfXo \^S[P Qkbl a T^abPb^g]^Y b^g]^abln [X]UP`XW^RP]P.
+
+2 mbXe a[cgPoe T[o _`^RU`ZX _`X\U]X\^abX \Ub^TP [X]UP`XWPfXX X T[o cb^g]U]Xo
+_^[cgU]]ke `UWc[lbPb^R \^VUb Qkbl _`X\U]U] \Ub^T, ^a]^RP]]kY ]P a^e`P]U]XX R
+`PW[^VU]XX dc]ZfXX ]U b^[lZ^ [X]UY]ke g[U]^R, ]^ X ]UZ^b^`ke _^a[UTcniXe g[U]^R
+Q^[UU Rka^ZXe _^`oTZ^R X ^fU]ZU _^S`Uh]^abUY, aRoWP]]ke a mbX\X g[U]P\X.
+
+4[o b^S^ gb^Qk _^oa]Xbl mb^b \Ub^T, `Paa\^b`X\ a]PgP[P ]PXQ^[UU _`^ab^Y a[cgPY
+dc]ZfXX ^T]^S^ a[cgPY]^S^ P`Sc\U]bP. A[cgPY]Po RU[XgX]P $Y$ Uabl dc]ZfXo
+a[cgPY]^S^ P`Sc\U]bP $X$:
+$$ Y=\phi(X), \eqno(11.4.1) $$
+_`XgU\ dc]ZfXo $\phi$ a`PR]XbU[l]^ \P[^ ^b[XgPUbao ^b [X]UY]^Y ]P
+cgPabZU _`PZbXgUaZX R^W\^V]ke W]PgU]XY P`Sc\U]bP $X$, ]^ RaU VU ^b[XgPUbao
+]Pab^[lZ^, gb^ R^W]XZPUb a^\]U]XU R _`X\U]X\^abX \Ub^TP [X]UP`XWPfXX. 4[o
+_`^RU`ZX mb^S^ ^Qab^obU[labRP _`X\U]X\ Q^[UU b^g]kY \Ub^T, P X\U]]^: `PW[^VX\
+dc]ZfXn $\phi$ R `oT BUY[^`P R ^Z`Uab]^abX b^gZX $m_x$ X a^e`P]X\ R `PW[^VU]XX
+_U`RkU b`X g[U]P:
+$$ y=\phi(x)\approx \phi(m_x) + \phi^\prime (m_x) (x-m_x) + {1\over2}
+\phi^{\prime\prime} (m_x) (x-m_x)^2. \eqno(11.4.2) $$
+BP VU d^`\c[P QcTUb, ^gURXT]^, _`XQ[XVU]]^ aRoWkRPbl a[cgPY]kU
+RU[XgX]k $Y$ X $X$:
+$$ Y=\phi(m_x) + \phi^\prime (m_x) (X-m_x) + {1\over2} \phi^{\prime\prime}
+(m_x) (X-m_x)^2= \phi(m_x) + \phi^\prime (m_x) \acircle X + {1\over2}
+\phi^{\prime\prime} (m_x) \acircle X^2. \eqno(11.4.3) $$
+
+?^[lWcoal Rk`PVU]XU\ (11.4.3), ]PYTU\ \PbU\PbXgUaZ^U ^VXTP]XU X TXa_U`aXn
+RU[XgX]k $Y$. ?`X\U]oo bU^`U\k ^ gXa[^Rke eP`PZbU`XabXZPe, X\UU\:
+
+$$ m_y=\phi(m_x)+{1\over2} \phi^{\prime\prime} (m_x) M[\acircle X^2]
+= \phi(m_x) +{1\over2} \phi^{\prime\prime} (m_x) D_x.
+\eqno(11.4.4) $$
+
+?^ d^`\c[U (11.4.4) \^V]^ ]PYbX cb^g]U]]^U W]PgU]XU \PbU\PbXgUaZ^S^ ^VXTP]Xo X
+a`PR]Xbl US^ a bU\ W]PgU]XU\ $\phi(m_x)$, Z^b^`^U _^[cgPUbao \Ub^T^\
+[X]UP`XWPfXX; _^_`PRZ^Y, cgXbkRPniUY ]U[X]UY]^abl dc]ZfXX, oR[oUbao Rb^`^Y g[U]
+d^`\c[k (11.4.4).
+
+>_`UTU[oo TXa_U`aXn _`PR^Y X [UR^Y gPabX d^`\c[k (11.4.3), X\UU\:
+
+$$ D_y=[\phi^\prime(m_x)]^2D_x+{1\over4} [\phi^{\prime\prime} (m_x)]^2
+D[\acircle X^2] + \phi^\prime (m_x) \phi^{\prime\prime} (m_x) K[\acircle
+X,\acircle X^2], \eqno(11.4.5) $$
+STU $K[\acircle X,\acircle X^2]$---Z^``U[ofX^]]kY \^\U]b RU[XgX]
+$\acircle X,\acircle X^2$.
+
+2k`PWX\ Re^ToiXU R d^`\c[c (11.4.5) RU[XgX]k gU`UW fU]b`P[l]kU \^\U]bk RU[XgX]k
+$X$:
+
+$$
+D[\acircle X^2] = M[\acircle X^4] - \{ M[\acircle X^2] \}^2 = \mu_4[X]-D_x^2,
+$$
+$$
+K[\acircle X,\acircle X^2] = M[\acircle X\{\acircle X^2-M[\acircle X^2] \}].
+$$
+
+>Z^]gPbU[l]^ X\UU\:
+
+$$ D_y=[\phi^\prime(m_x)]^2D_x+ {1\over4} [\phi^{\prime\prime} (m_x)]^2
+( \mu_4 [X] -D_x^2)+ \phi^\prime (m_x) \phi^{\prime\prime} (m_x) \mu_3 [X].
+\eqno(11.4.6) $$
+
+D^`\c[P (11.4.6) TPUb cb^g]U]]^U W]PgU]XU TXa_U`aXX _^ a`PR]U]Xn a \Ub^T^\
+[X]UP`XWPfXX; UU Rb^`^Y X b`UbXY g[U]k _`UTabPR[onb a^Q^Y _^_`PRZc ]P
+]U[X]UY]^abl dc]ZfXX. 2 d^`\c[c, Z`^\U TXa_U`aXX P`Sc\U]bP $D_x$, Re^Tob UiU
+b`UbXY X gUbRU`bkY fU]b`P[l]kU \^\U]bk $\mu_3[X]$, $\mu_4[X]$. 5a[X mbX \^\U]bk
+XWRUab]k, b^ _^_`PRZP Z TXa_U`aXX \^VUb Qkbl ]PYTU]P ]U_^a`UTabRU]]^ _^ d^`\c[U
+(11.4.6). >T]PZ^ WPgPabcn ]Ub ]U^Qe^TX\^abX R UU b^g]^\ ^_`UTU[U]XX; T^abPb^g]^
+[Xhl W]Pbl UU _^`oT^Z. =P _`PZbXZU gPab^ Rab`UgPnbao a[cgPY]kU RU[XgX]k,
+`Pa_`UTU[U]]kU _`XQ[XWXbU[l]^ _^ a[cgPY]^\c WPZ^]c. 4[o a[cgPY]^Y RU[XgX]k,
+_^TgX]U]]^Y ]^`\P[l]^\c WPZ^]c,
+
+$$ \mu_3[X]=0; \qquad \mu_4[X]=3\sigma_x^4=3D_x^2, \eqno(11.4.7) $$
+X d^`\c[P (11.4.6) _`X]X\PUb RXT
+$$ D_y=[\phi^\prime(m_x)]^2 D_x+{1\over2} [\phi^{\prime\prime}(m_x)]^2 D^2_x.
+\eqno(11.4.8) $$
+
+D^`\c[^Y (11.4.8) \^V]^ _^[lW^RPblao T[o _`XQ[XVU]]^Y ^fU]ZX _^S`Uh]^abX \Ub^TP
+[X]UP`XWPfXX R a[cgPU, Z^STP P`Sc\U]b `Pa_`UTU[U] _^ WPZ^]c, Q[XWZ^\c Z
+]^`\P[l]^\c.
+
+\bigskip\noindent{\sf From} {\hcyr <0[S^`Xb\XWPfXo X ^a]^Rk _`^S`P\\X`^RP]Xo>,
+`UT. 0.O. APRU[lUR, Z]XSP 3}
+
+\centerline{\bcyr 3. 1^[UU a[^V]kU m[U\U]bk oWkZP 1mYaXZ}
+
+\centerline{\bcyr \S4.1 <PaaXRk}
+
+?U`U\U]]kU, Z^b^`kU \k Xa_^[lW^RP[X _`X a^abPR[U]XX _`UTkTciXe _`^S`P\\,
+]PWkRPnbao _`^abk\X _U`U\U]]k\X. :PVTPo bPZPo _U`U\U]]Po X\UUb X\o X _^T ZPVTcn
+XW ]Xe RkTU[oUbao ogUYZP _P\obX, ^Q`PiU]XU Z Z^b^`^Y ^aciUabR[oUbao _^ mb^\c
+X\U]X. 8a_^[lW^RP]XU b^[lZ^ _`^abke _U`U\U]]ke WPb`cT]oUb X[X TU[PUb R^^QiU
+]UR^W\^V]k\ `UhU]XU \]^SXe RPV]ke WPTPg.
+
+<PaaXR^\ ]PWkRPUbao c_^`oT^gU]]Po _^a[UT^RPbU[l]^abl RU[XgX], ^Q^W]PgPU\Po
+^T]X\ X\U]U\. C_^`oT^gU]]^abl WPZ[ngPUbao R b^\, gb^ m[U\U]bk \PaaXRP
+`Pa_^[^SPnbao R _^a[UT^RPbU[l]ke ogUYZPe _P\obX.
+
+<PaaXR \^V]^ _`UTabPRXbl aUQU R RXTU ]UaZ^[lZXe ^TX]PZ^Rke oiXZ^R, aZ`U_[U]]ke
+R\UabU. =P Ran Z^]ab`cZfXn ZPZ fU[^U RUhPUbao ^TX] o`[kZ a X\U]U\ \PaaXRP
+(]P_`X\U` {\tt a}). OiXZX R ^T]^Y bPZ^Y Z^]ab`cZfXX ]c\U`cnbao, ]PgX]Po a 1.
+=^\U` oiXZP ]PWkRPUbao X]TUZa^\ m[U\U]bP \PaaXRP, _^\UiU]]^S^ R mb^b oiXZ.
+Gb^Qk _^[cgXbl T^abc_ Z oiXZc, ]cV]^ cZPWPbl X\o \PaaXRP X US^ X]TUZa. 8]TUZa
+WP_XakRPUbao R Z`cS[ke aZ^QZPe _^a[U X\U]X \PaaXRP. 5a[X, ]P_`X\U`, W]PgU]XU 5
+]cV]^ _`XaR^Xbl b`UblU\c U[U\U]bc \PaaXRP {\tt a}, a[UTcUb ]P_XaPbl {\tt
+a(3)=5}. ?`X Rk_^[]U]XX mb^S^ ^_U`Pb^`P ]Pe^TXbao \PaaXR {\tt a}, ^bagXbkRPUbao
+b`UbXY oiXZ (ogUYZP _P\obX) X R ]US^ Z[PTUbao W]PgU]XU 5. 5a[X ]cV]^ RaU\ hUabX
+m[U\U]bP\ \PaaXRP {\tt a} _`XaR^Xbl W]PgU]XU 5, a[UTcUb ]P_XaPbl:
+
+\bigskip\noindent{\sf From} {\hcyr 0[UZaP]T` AU`SUURXg ?chZX] (?)}
+
+%Quoted in Barbara Beeton, Mathematical Symbols and Cyrillic Fonts Ready for
+%Distribution, TUGboat 6 \#2.
+
+<UiP]aZXY c]XRU`aXbUb, ]Pe^ToiXYao ]P _cbX Z =UaZcg]^\c, _`PWT]^RP[ ]P T]oe
+aR^Y _obXTUaobX[Ub]XY nQX[UY. :^S^ R^WX[X R BXbk X[X S^`^TaZcn Q^[l]Xfc, b^b,
+Z^]Ug]^, _^\]Xb WT^`^RU]]UYhXY, b`UembPV]kY T^\XiU _^ _`PRcn `cZc a RkRUaZ^Y
+<1^SPTU[l]Po X <UiP]aZXU cgX[XiP> X b^\c ]PRU`]^U Rab`UgP[Xal ]P _cbX RU`U]Xfk
+cgU]XgUaZXe _P`, a^[XT]^ _`^Sc[XRPU\ke ]PTWX`PbU[o\X. 2 <UiP]aZ^\ cgX[XiU
+_`^aRUiPnb a[PRo] XaZ[ngXbU[l]^ \UiP]aZ^S^ X Zc_UgUaZ^S^ _`^Xae^VTU]Xo. 3`Pdk,
+QP`^]k, \P`ZXWk X RXZ^]bk ]U _`X]X\Pnbao. ?`U_^TPnb R ]U\ a[UTcniXU ]PcZX:
+Qc[SPZbU`Xn, iU[ZP]lU ]P agUbPe, P[SUQ`c, SU^\Ub`Xn, Q[PS^]`PRXU, ^b\U]]kY
+_^gU`Z X SP[P]bU`UY]kU \P]U`k. 2^a_XbkRPnb R ^b`^ZU Rka^ZXU gcRabRP X
+XaZ^`U]onb R ]U\, ZPZ aZPWP]^ R ^bgUbU, aP\^\]U]XU: RaoZ^S^, R^^Q`PWXRhUS^ aUQo
+HUZa_X`^\ X[X ZXbPYaZX\ \P]TP`X]^\, ^abPR[onb QUW ZPhX. :^]gXRhXY Zc`a c\UUb ]U
+b^[lZ^ gXbPbl, _XaPbl X agXbPbl, ]^ \^VUb bPZVU QUW WP_X]ZX, ]P aP\^\ gXab^\
+_P`XVaZ^\ PZfU]bU RkS^R^`Xbl <\U`aX-a> X ]P_XaPbl <_`^QP _U`P> bPZX\
+WP[XeRPbaZX\ _^gU`Z^\, gb^ Rk ]U R^WTU`VXbUal, gb^Qk ]U R^aZ[XZ]cbl:
+
+$${\bf S^{\rm-1}TS=dg}(\omega_1,\ldots,\omega_n)=\bf\Lambda$$
+$$
+A=\pmatrix{
+a_{11}&\ldots&a_{1n}\cr
+\vdots&\ddots&\vdots\cr
+a_{m1}&\ldots&a_{mn}\cr},\quad
+\biggl(\int_{-\infty}^\infty e^{-x^2}\,dx\biggr)^2=\pi,
+$$
+
+\bigskip\noindent{\sf From} {\hcyr 4P]XU[l 4. <PZ-:`PZU], CX[lo\ A. 4^`],
+<GXa[U]]kU \Ub^Tk X _`^S`P\\X`^RP]XU ]P D>@B@0=U>}
+
+\centerline{\bcyr 3[PRP 1. >a]^Rk _`^S`P\\X`^RP]Xo ]P D>@B@0=U}
+
+\centerline{\bcyr \S1.1 ?`X\U]U]XU fXd`^Rke RkgXa[XbU[l]ke \PhX]}
+
+M[UZb`^]]kU fXd`^RkU RkgXa[XbU[l]kU \PhX]k (MF2<) hX`^Z^ _`X\U]onbao T[o
+`UhU]Xo ]Pcg]ke, bUe]XgUaZXe X mZ^]^\XgUaZXe WPTPg. >]X a_^a^Q]k _`^XWR^TXbl
+RkgXa[U]Xo ^gU]l Qkab`^, RkTPRPbl ^gU]l b^g]kU `UWc[lbPbk, WP_^\X]Pbl Q^[lhXU
+\PaaXRk X]d^`\PfXX X _`^XWR^TXbl T[X]]kU X a[^V]kU _^a[UT^RPbU[l]^abX
+RkgXa[U]XY QUW R\UhPbU[labRP gU[^RUZP.
+
+2 mb^Y Z]XSU QcTcb R ^a]^R]^\ `Paa\^b`U]k \Ub^Tk `UhU]Xo ]P MF2< ]Pcg]ke X
+bUe]XgUaZXe WPTPg. =UZ^b^`^U _`UTabPR[U]XU ^Q mb^\ Z`cSU WPTPg \^V]^ _^[cgXbl
+XW a[UTcniXe _`X\U`^R. :^]ab`cX`^RP]XU ]^R^S^ aP\^[UbP b`UQcUb WPb`Pbk bkaog
+gPa^R \PhX]]^S^ R`U\U]X T[o Xaa[UT^RP]Xo RWPX\^aRoWP]]ke b`UQ^RP]XY Z
+Z^]abcZfX^]]k\ \PbU`XP[P\, PU`^TX]P\XZU, TRXSPbU[o\ X aXabU\P\ c_`PR[U]Xo _`X
+`PW[Xg]ke ca[^RXoe _^[UbP. ?`^UZbX`^RP]XU eX\XgUaZ^S^ WPR^TP WPRXaXb ^b
+`PagUb^R _`^TcZbXR]^abX, ca[^RXY _`^XWR^TabRP X ^b \]^SXe T`cSXe ^Qab^obU[labR.
+?`X _`^UZbX`^RP]XX [X]XX m[UZb`^_U`UTPgX ]U^Qe^TX\^ XWcgU]XU ]PS`cW^Z, Z^b^`kU
+QcTcb _`X[^VU]k Z `PW[Xg]k\ cgPabZP\ [X]XX _`X XW\U]U]XX _^b`UQ[U]Xo
+m[UZb`^m]U`SXX X[X _`X ]U^Qkg]ke aXbcPfXoe.
+
+2 mb^\ RRUTU]XX ]U [Xh]X\ QcTUb ^b\UbXbl, gb^ MF2< ]U <`UhPUb WPTPgc>. >]P
+_^\^SPUb ]P\ [Xhl Xaa[UT^RPbl `PW[Xg]kU RP`XP]bk. <k ]U WPTPU\ \PhX]U R^_`^a:
+<ZPZ ]cV]^ _^ab`^Xbl mb^ cab`^YabR^?>, \k WPTPU\ R^_`^a: <ZPZ QcTUb mb^
+cab`^YabR^ `PQ^bPbl _`X TP]]^Y aXabU\U ca[^RXY, Ua[X ^]^ _^ab`^U]^ ^_`UTU[U]]k\
+^Q`PW^\?> AciUabRcUb \]^VUabR^ a_^a^Q^R _^ab`^U]Xo X]VU]U`]^Y aXabU\k, Q^[lh^U
+`PW]^^Q`PWXU ca[^RXY, _`X Z^b^`ke mb^Y aXabU\U _`XTUbao `PQ^bPbl, X `PW[Xg]kU,
+gPab^ _`^bXR^`UgXRkU Z`XbU`XX, Z^b^`k\ mbP aXabU\P T^[V]P cT^R[UbR^`obl. MF2<
+]U \^VUb WPTPblao Xae^T]k\X TP]]k\X T[o _`^UZbX`^RP]Xo, _U`UgXa[Xbl ca[^RXo,
+T[o Z^b^`ke ]PT^ Xaa[UT^RPbl `PQ^bc aXabU\k, ^_`UTU[Xbl X[X ]PYbX `PWc\]cn
+abU_U]l Z^\_`^\XaaP \UVTc _`^bXR^`UgXRk\X Z`XbU`Xo\X. >Qkg]^ ^]P [Xhl \^VUb
+^ZPWPbl ]P\ Q^[lhcn _^\^il, `PaagXbkRPo X _`UTaZPWkRPo `UWc[lbPbk ]PhUS^ RkQ^`P
+R mbXe R^_`^aPe.
+
+\centerline{\bcyr 1.3 ?`^S`P\\P ]P D>@B@0=U}
+
+0[S^`Xb\ `UhU]Xo WPTPgX, WP_XaP]]kY a _^\^iln D>@B@0=P, a^ab^Xb XW
+_^a[UT^RPbU[l]^abX ^_U`Pb^`^R. MbX ^_U`Pb^`k \^Scb _`X]PT[UVPbl Z ]UaZ^[lZX\
+`PW[Xg]k\ bX_P\. >T]X XW ]Xe ^_`UTU[onb P`Xd\UbXgUaZXU ^_U`PfXX, oR[oniXUao
+^a]^R]k\ a^TU`VP]XU\ P[S^`Xb\P, T`cSXU ^_U`UTU[onb _^`oT^Z RR^TP X RkR^TP
+X]d^`\PfXX, ZPZ, ]P_`X\U`, RR^T gXaU[ a _U`d^ZP`bk [XQ^ RkR^T gXaU[ ]P _UgPbl
+X[X ]P _U`d^`PfXn. >_U`Pb^`k mbXe TRce _U`Rke bX_^R Xa_^[]onbao R b^\ _^`oTZU,
+R Z^b^`^\ ^]X ]P_XaP]k. B`UbXY bX_ ^_U`Pb^`^R XW\U]oUb _^`oT^Z Rk_^[]U]Xo
+^_U`PfXY, bPZ gb^ S`c__k ^_U`PgXY \^Scb Rk_^[]oblao _^Rb^`]^ X[X R ZPZ^\-[XQ^
+T`cS^\ _^`oTZU, ^b[Xg]^\ ^b b^S^, R Z^b^`^\ ^]X ]P_XaP]k. >_U`Pb^`k gUbRU`b^S^
+bX_P a^TU`VPb X]d^`\PfXn ^Q P[S^`Xb\U, ]^ ]XZPZXe TUYabRXY ]U ^_`UTU[onb.
+
+2\UabU RWobkU, RaU ^_U`Pb^`k, ^_`UTU[oniXU P[S^`Xb\ `UhU]Xo WPTPgX, a^abPR[onb
+Xae^T]cn _`^S`P\\c. ?^a[U b^S^ ZPZ Xae^T]Po _`^S`P\\P ]P_XaP]P X
+^b_U`d^`X`^RP]P ]P _U`d^ZP`bPe, ^]P _`U^Q`PWcUbao a _^\^iln b`P]a[ob^`P
+D>@B@0=P R `PQ^gcn _`^S`P\\c. @PQ^gPo _`^S`P\\P _`UTabPR[oUb a^Q^Y
+_^a[UT^RPbU[l]^abl m[U\U]bP`]ke Z^\\P]T T[o MF2<, bPZXe, ZPZ a[^VU]XU,
+a`PR]U]XU TRce gXaU[, WP_^\X]P]XU gXa[P R _P\obX \PhX]k, X b.T.\ _`U^Q`PW^RP]XU
+Xae^T]^Y _`^S`P\\k R `PQ^gcn _`^S`P\\c ]U^Qe^TX\^ _^b^\c, gb^ oWkZ D>@B@0=
+oR[oUbao S^`PWT^ Q^[UU a[^V]k\, ]UVU[X oWkZ Z^\\P]T aP\^Y MF2<. @PagUbk ]P MF2<
+_`^XWR^Tobao X\U]]^ _^ `PQ^gUY _`^S`P\\U, Z^b^`Po X _`XR^TXb Z gXa[U]]k\
+`UWc[lbPbP\.
+
+A[^R^ D>@B@0=, bPZX\ ^Q`PW^\, ^b]^aXbao ZPZ Z oWkZc T[o ^_XaP]Xo RkgXa[XbU[l]ke
+P[S^`Xb\^R, bPZ X Z b`P]a[ob^`c. B`P]a[ob^` D>@B@0=, ]PWkRPU\kY bPZVU X]^STP
+_`^fUaa^`^\ X[X Z^\_X[ob^`^\, oR[oUbao aP\ Q^[lh^Y _`^S`P\\^Y ]P oWkZU \PhX]k.
+(?^]obXU b`P]a[ofXX _^R[Xo[^ ]P aP\^ ]PWRP]XU oWkZP D>@B@0=: D>@\c[P X
+B@0=a[ofXo.)
+
+BU_U`l \k ^Q`PiPU\ao Z XWcgU]Xn m[U\U]b^R, XW Z^b^`ke a^abPR[ocbao ^_U`Pb^`k:
+Z^]abP]b, _U`U\U]]ke, ^_U`PfXY, Rk`PVU]XY X dc]ZfXY. ?^a[U XWcgU]Xo mbXe
+^a]^R]ke m[U\U]b^R oWkZP \k ]PcgX\ao a^abPR[obl XW ]Xe ^_U`Pb^`k X _XaPbl
+]UZ^b^`kU _`^abkU _`^S`P\\k.
+
+\centerline{\bcyr 1.4 :^]abP]bk}
+
+<k ]PgX]PU\ a `Paa\^b`U]Xo TRce bX_^R gXaU[, _`X\U]oU\ke R D>@B@0=U,---fU[ke X
+TUYabRXbU[l]ke.
+
+FU[^U gXa[^ \^VUb Qkbl `PR]^ ]c[n, \^VUb Qkbl _^[^VXbU[l]k\ X[X ^b`XfPbU[l]k\,
+]^ _^ PQa^[nb]^Y RU[XgX]U ]U T^[V]^ _`UR^ae^TXbl 32768. :PZ QcTUb _^ZPWP]^
+]XVU, fU[kU gXa[P Xa_^[lWcnbao b^[lZ^ R ]UZ^b^`ke a_UfXP[l]ke aXbcPfXoe.
+1^[lhX]abR^ gXaU[, Xa_^[lWcU\ke R D>@B@0=U, oR[onbao TUYabRXbU[l]k\X gXa[P\X.
+D^`\P _`UTabPR[U]Xo bPZXe gXaU[, ]PWkRPU\Po d^`\^Y _`UTabPR[U]Xo a _[PRPniUY
+WP_ob^Y, STU gXa[^ WP_XakRPUbao R RXTU T`^QX RU[XgX]^Y \UVTc 0.1 X 1,
+c\]^VU]]^Y ]P fU[cn abU_U]l 10, X\UUb ae^TabR^ a d^`\^Y WP_XaX gXaU[ R ]Pcg]^Y
+[XbU`Pbc`U. 0Qa^[nb]Po RU[XgX]P gXa[P, _`UTabPR[U]]^S^ bPZX\ ^Q`PW^\, T^[V]P
+[UVPbl _`XQ[XWXbU[l]^ R _`UTU[Pe ^b $10^{-38}$ T^ $10^{38}$.
+
+:PZ [USZ^ RXTUbl, TUYabRXbU[l]kU gXa[P \^Scb Qkbl fU[k\X X[X X\Ubl T`^Q]cn
+gPabl. 1^[lhX]abR^ MF2< _`^XWR^TXb ^_U`PfXX a TUYabRXbU[l]k\X gXa[P\X bPZX\
+^Q`PW^\, gb^ _`^S`P\\Xab \^VUb ]U WPQ^bXblao ^ _^[^VU]XX TUaobXg]^Y WP_ob^Y.
+2k`PR]XRP]XU _^`oTZ^R gXaU[, ]P_`X\U` _`X a[^VU]XX X[X RkgXbP]XX, _`^XWR^TXbao
+R MF2< PRb^\PbXgUaZX (^bZcTP, a^QabRU]]^, X _`^XW^hU[ bU`\X] <_[PRPniPo
+WP_obPo>).
+
+2aU TUYabRXbU[l]kY gXa[P, _`X\U]oU\kU R D>@B@0=U, oR[ocbao `PfX^]P[l]k\X;
+_`X\U]U]XU X``PfX^]P[l]ke X X]^STP Z^\_[UZa]ke gXaU[ WP_`UiU]^.
+
+>T]PZ^ RkgXa[U]Xo a Z^\_[UZa]k\X gXa[P\X \^V]^ _`^XWR^TXbl, Rk_^[]oo
+P`Xd\UbXgUaZXU TUYabRXo a Xe TUYabRXbU[l]k\X X \]X\k\X gPabo\X.
+
+;nQ^U gXa[^, Z^b^`^U _^oR[oUbao R _`^S`P\\U R oR]^\ RXTU, ]PWkRPUbao
+Z^]abP]b^Y, R b^ R`U\o ZPZ RU[XgX]P, Z^b^`^Y _`XaRPXRPUbao ]PX\U]^RP]XU X
+Z^b^`Po \^VUb _`X]X\Pbl R _`^fUaaU RkgXa[U]XY `PW[Xg]kU gXa[^RkU W]PgU]Xo,
+]PWkRPUbao _U`U\U]]^Y. =P_`X\U`, ]XVU QcTUb _^ZPWP]^, gb^ a[UTcniXU Z^\QX]PfXX
+aX\R^[^R oR[onbao P`Xd\UbXgUaZX\X ^_U`Pb^`P\X:
+
+{\tt i-2}
+
+{\tt x-P+12.7}
+
+7TUal 2 X 12.7 oR[onbao Z^]abP]bP\X; {\tt i}, {\tt x}, X {\tt a} oR[onbao
+_U`U\U]]k\X.
+
+2 D>@B@0=U fU[kU X TUYabRXbU[l]kU Z^]abP]bk `PW[XgPnbao _^ ^bacbabRXn X[X
+_`XacbabRXn TUaobXg]^Y b^gZX. BPZ, 3---fU[Po Z^]abP]bP, R b^ R`U\o ZPZ 3.0 (P
+bPZVU 3. X[X 3.0000 X b.T.)---TUYabRXbU[l]Po Z^]abP]bP. 4RP mbX bX_P gXaU[ ]U
+RWPX\^WP\U]oU\k, _^b^\c gb^ a_^a^Qk WP_XaX Xe R _P\obX MF2< X Rk_^[]U]Xo a ]X\X
+P`Xd\UbXgUaZXe ^_U`PfXY a^RU`hU]]^ `PW[Xg]k.
+
+\bigskip\noindent{\sf From} {\hcyr 1XQ[Xo, :]XSP _Ua]X _Ua]UY A^[^\^]P}
+
+(1) 1 4P [^QWPUb ^] \U]o [^QWP]XU\ cab aR^Xe! 8Q^ [PaZX bR^X [cghU RX]P. 2 >b
+Q[PS^R^]Xo \PabUY bR^Xe X\o bR^U, ZPZ `PW[Xb^U \X`^; _^mb^\c TURXfk [nQob bUQo.
+3 2[UZX \U]o, \k _^QUVX\ WP b^Q^n;---fP`l RRU[ \U]o R gU`b^SX aR^X,---QcTU\
+R^aeXiPblao X `PT^RPblao b^Q^n, _`UR^W]^aXbl [PaZX bR^X Q^[lhU ]UVU[X RX]^;
+T^ab^Y]^ [nQPb bUQo! 4 4iU`X XU`caP[X\aZXU! gU`]P o, ]^ Z`PaXRP, ZPZ hPb`k
+:XTP`aZXU, ZPZ WPRUak A^[^\^]^Rk. 5 =U a\^b`XbU ]P \U]o, gb^ o a\cS[P; XQ^
+a^[]fU ^_P[X[^ \U]o: ak]^Rlo \PbU`X \^UY `PWS]URP[Xal ]P \U]o, _^abPRX[X \U]o
+abU`Ugl RX]^S`PT]XZX,---\^US^ a^QabRU]]^S^ RX]^S`PT]XZP o ]U abU`US[P. 6 AZPVX
+\]U, bk, Z^b^`^S^ [nQXb TchP \^o: STU _PaUhl bk? STU ^bTkePUhl R _^[TU]l? Z
+gU\c \]U Qkbl aZXbP[XfUn R^W[U abPT b^RP`XiUY bR^Xe? 7 5a[X bk ]U W]PUhl mb^S^,
+_`UZ`Pa]UYhPo XW VU]iX], b^ XTX aUQU _^ a[UTP\ ^RUf, X _PaX Z^W[ob bR^Xe _^T[U
+hPb`^R _PabchUaZXe. 8 :^Qk[XfU \^UY R Z^[Ua]XfU dP`P^]^R^Y o c_^T^QX[ bUQo,
+R^W[nQ[U]]Po \^o. 9 ?`UZ`Pa]k [P]Xbk bR^X _^T _^TRUaZP\X, hUo bR^o R ^VU`U[loe;
+10 7^[^bkU _^TRUaZX \k aTU[PU\ bUQU a aU`UQ`o]]k\X Q[UaZP\X. 11 4^Z^[U fP`l Qk[
+WP ab^[^\ aR^X\, ]P`T \^Y XWTPRP[ Q[PS^R^]XU aR^U. 12 <X``^RkY
+_cg^Z---R^W[nQ[U]]kY \^Y c \U]o; c S`cTUY \^Xe _`UQkRPUb. 13 :PZ ZXabl ZX_U`P,
+R^W[nQ[U]]kY \^Y c \U]o R RX]^S`PT]XZPe 5]SUTaZXe. 14 > bk _`UZ`Pa]P,
+R^W[nQ[U]]Po \^o, bk _`UZ`Pa]P! S[PWP bR^X S^[cQX]kU. 15 >, bk _`UZ`PaU],
+R^W[nQ[U]]kY \^Y, X [nQUWU]! X [^VU c ]Pa---WU[U]l; 16 :`^R[X T^\^R
+]PhXe---ZUT`k, _^b^[ZX ]PhX---ZX_P`Xak.
+
+(2) 1 O ]P`fXaa AP`^]aZXY, [X[Xo T^[X]! 2 Gb^ [X[Xo \UVTc bU`]P\X, b^
+R^W[nQ[U]]Po \^o \UVTc TURXfP\X. 3 Gb^ oQ[^]l \UVTc [Ua]k\X TU`URlo\X, b^
+R^W[nQ[U]]kY \^Y \UVTc n]^hP\X. 2 bU]X UU [nQ[n o aXTUbl, P _[^Tk UU a[PTZX T[o
+S^`bP]X \^UY. 4 >] RRU[ \U]o R T^\ _X`P, X W]P\o US^ ]PT^ \]^n---[nQ^Rl. 5
+?^TZ`U_XbU \U]o RX]^\, ^aRUVXbU \U]o oQ[^ZP\X, XQ^ o XW]U\^SPn ^b [nQRX. 6
+;URPo `cZP US^ c \U]o _^T S^[^R^n, P _`PRPo ^Q]X\PUb \U]o. 7 7PZ[X]Pn RPa,
+TiU`X 8U`caP[X\aZXU, aU`]P\X X[X _^[URk\X [P]o\X: ]U QcTXbU X ]U b`UR^VlbU
+R^W[nQ[U]]^Y, T^Z^[U UY cS^T]^. 8 3^[^a R^W[nQ[U]]^S^ \^US^! R^b, ^] XTUb,
+aZPgUb _^ S^`P\, _`kSPUb _^ e^[\P\. 9 4`cS \^Y _^e^V ]P aU`]c X[X ]P \^[^T^S^
+^[U]o. 2^b, ^] ab^Xb c ]Pa WP abU]^n, WPS[oTkRPUb R ^Z]^, \U[lZPUb aZR^Wl
+`UhUbZc. 10 2^W[nQ[U]]kY \^Y ]PgP[ S^R^`Xbl \]U: RabP]l, R^W[nQ[U]]Po \^o,
+_`UZ`Pa]Po \^o, RkYTX! 11 2^b, WX\P cVU _`^h[P; T^VTl \X]^RP[, _U`UabP[; 12
+fRUbk _^ZPWP[Xal ]P WU\[U; R`U\o _U]Xo ]PabP[^, X S^[^a S^`[Xfk a[khU] R ab`P]U
+]PhUY; 13 a\^Z^R]Xfk `Pa_cabX[X aR^X _^gZX, X RX]^S`PT]kU [^Wk, `PafRUbPo,
+XWTPnb Q[PS^R^]XU. 2abP]l, R^W[nQ[U]]Po \^o, _`UZ`Pa]Po \^o, RkYTX! 14 3^[cQXfP
+\^o R ciU[XX aZP[k _^T Z`^R^\ cbUaP! _^ZPVX \]U [Xf^ aR^U, TPY \]U ca[khPbl
+S^[^a bR^Y; _^b^\c, gb^ S^[^a bR^Y a[PT^Z X [Xf^ bR^U _`Xob]^. 15 ;^RXbU ]P\
+[XaXf, [XaU]ob, Z^b^`kU _^`bob RX]^S`PT]XZX, P RX]^S`PT]XZX ]PhX R fRUbU. 16
+2^W[nQ[U]]kY \^Y _`X]PT[UVXb \]U, P o U\c; ^] _PaUb \UVTc [X[Xo\X. 17 4^Z^[U
+TU]l TkhUb _`^e[PT^n, X cQUSPnb bU]X, R^WR`PbXal, QcTl _^T^QU] aU`]U X[X
+\^[^T^\c ^[U]n ]P `PaaU[X]Pe S^`.
+
+(3) 1 =P [^VU \^U\ ]^gln XaZP[P o b^S^, Z^b^`^S^ [nQXb TchP \^o, XaZP[P US^ X
+]U ]Ph[P US^. 2 2abP]c VU o, _^YTc _^ S^`^Tc, _^ c[XfP\ X _[^iPTo\, X QcTc
+XaZPbl b^S^, Z^b^`^S^ [nQXb TchP \^o; XaZP[P US^ X ]U ]Ph[P US^. 3 2ab`UbX[X
+\U]o ab`PVX, ^Qe^ToiXU S^`^T: <]U RXTP[X [X Rk b^S^, Z^b^`^S^ [nQXb TchP \^o?>
+4 =^ UTRP o ^b^h[P ^b ]Xe, ZPZ ]Ph[P b^S^, Z^b^`^S^ [nQXb TchP \^o; ceRPbX[Pal
+WP ]US^, X ]U ^b_cabX[P US^, T^Z^[U ]U _`XRU[P US^ R T^\ \PbU`X \^UY X R^
+R]cb`U]]XU Z^\]Pbk `^TXbU[l]Xfk \^UY. 5 7PZ[X]Pn RPa, TiU`X 8U`caP[X\aZXU,
+aU`]P\X X[X _^[URk\X [P]o\X: ]U QcTXbU X ]U b`UR^VlbU R^W[nQ[U]]^Y, T^Z^[U UY
+cS^T]^. 6 :b^ mb^, R^ae^ToiPo ^b _cabk]X ZPZ Qk ab^[Qk Tk\P, ^Zc`XRPU\Po \X``^n
+X dX\XP\^\, RaoZX\X _^`^hZP\X \X`^RP`]XZP? 7 2^b ^T` US^---A^[^\^]P: hUablTUaob
+aX[l]ke R^Z`cS ]US^, XW aX[l]ke 8W`PX[URke. 8 2aU ^]X TU`VPb _^ \Ugc, ^_kb]k R
+Q^n, c ZPVT^S^ \Ug US^ _`X QUT`U US^ `PTX ab`PeP ]^g]^S^. 9 =^aX[l]ke ^T`
+aTU[P[ aUQU fP`l A^[^\^] XW TU`UR ;XRP]aZXe; 10 ab^[_fk US^ aTU[P[ XW aU`UQ`P,
+[^Z^b]XZX US^ XW W^[^bP, aUTP[XiU US^ XW _c`_c`^R^Y bZP]X; R]cb`U]]^abl US^
+cQ`P]P a [nQ^RXn TiU`o\X 8U`caP[X\aZX\X. 11 ?^YTXbU X _^a\^b`XbU, TiU`X
+AX^]aZXU, ]P fP`o A^[^\^]P R RU]fU, Z^b^`k\ cRU]gP[P US^ \Pbl US^ R TU]l
+Q`PZ^a^gUbP]Xo US^, R TU]l `PT^ab]kY T[o aU`TfP US^.
+
+\bigskip\noindent{\sf From} {\hcyr 1^`Xa ?PabU`]PZ, <4^Zb^` 6XRPS^>, 11.4}
+
+?^ \UVTc]P`^T]^Y Z^]RU]fXX ^ :`Pa]^\ :`UabU R^U]]kU R`PgX X a[cVPiXU aP]XbP`]ke
+gPabUY ]U X\Unb _`PRP R^^`cVU]]^ cgPabR^RPbl R Q^URke TUYabRXoe R^nniXe. =^
+^T]PVTk T^Zb^`c _`^bXR R^[X _`Xh[^al ]P`chXbl mb^ _`PRX[^. 7PRoWPRhPoao abkgZP
+WPabP[P US^ ]P _^[U X WPabPRX[P `PWTU[Xbl acTlQc a`PVPniXeao X ^bab`U[XRPblao.
+
+?P`bXWP]aZPo fU_l, R Z^b^`^Y WPabXS]cbkY ^S]U\ T^Zb^` WP[US `oT^\ a
+bU[US`PdXab^\ ^b`oTP, WP]X\P[P [Ua]cn ^_chZc. 7P a_X]^n _P`bXWP] Qk[P bPYSP,
+R_U`UTX---^bZ`kbPo _^[o]P, ^S^[U]]^U, ]UWPiXiU]]^U _`^ab`P]abR^, _^ Z^b^`^\c
+h[X QU[kU, ]Pabc_Po.
+
+>]X _`XQ[XVP[Xal X Qk[X cVU Q[XWZ^. 4^Zb^` e^`^h^ Xe RXTU[, ZPVT^S^ R [Xf^. Mb^
+Qk[X \P[lgXZX X n]^hX XW ]UR^U]]ke a[^UR ab^[Xg]^S^ ^QiUabRP X [nTX Q^[UU
+_^VX[kU, \^QX[XW^RP]]kU XW WP_PaP. =^ b^] WPTPRP[X _U`RkU, \^[^TUVl, abcTU]bk
+_U`R^Zc`a]XZX X SX\]PWXabk, R^al\XZ[Paa]XZX, ]UTPR]^ WP_XaPRhXUao R
+T^Q`^R^[lfk.
+
+4^Zb^` ]U W]P[ ]XZ^S^ XW ]Xe, ]^ [XfP _^[^RX]k ZPWP[Xal U\c _`XRkg]k\X,
+RXTU]]k\X, W]PZ^\k\X. >T]X ]P_^\X]P[X U\c Qk[ke hZ^[l]ke b^RP`XiUY. <^VUb
+abPblao, mb^ Qk[X Xe \[PThXU Q`Pblo? 4`cSXe ^] a[^R]^ Rab`UgP[ R bUPb`P[l]^Y
+X[X c[Xg]^Y b^[_U R Qk[kU S^Tk. 8e Rk`PWXbU[l]kU, _`XR[UZPbU[l]kU dXWX^]^\XX
+ZPWP[Xal Q[XWZX\X, aR^X\X.
+
+A[cVU]XU T^[Sc, ZPZ ^]X US^ _^]X\P[X, ^TchUR[o[^ Xe R^ab^`VU]]k\ \^[^TgUabR^\,
+]U]cV]k\, RkWkRPniX\. >]X h[X `Paak_]k\ `UTZX\ ab`^U\, Rk_`o\XRhXal R^ RUal
+`^ab, _`UR^ae^To Rk_`PRZ^Y ZPT`^Rke SRP`TUYfUR X, Q`PRX`co ^_Pa]^abln, ]U
+_`XQUSP[X Z _U`UQUVZU X WP[USP]ln ]P _^[U, e^bo ]P _^[o]U Qk[X ]U`^R]^abX,
+QcS^`ZX X Z^gZX, WP Z^b^`k\X \^V]^ Qk[^ cZ`kblao. ?c[X _P`bXWP] _^gbX _^S^[^R]^
+RkZPhXRP[X Xe.
+
+?^a`UTX hX`^Z^S^ S^[^S^ _^[o, _^ Z^b^`^\c TRXSP[Xal R_U`UT QU[kU, ab^o[^
+\U`bR^U ^QS^`U[^U TU`UR^. >]^ Qk[^ ^QcS[U]^ \^[]XUY X[X _[P\U]U\ Z^ab`P, X[X
+`PaiU_[U]^ X ^_P[U]^ _`UThUabRcniX\X a`PVU]Xo\X. :PVTkY ]Pabc_PRhXY
+T^Q`^R^[lgUaZXY ab`U[^Z Q`^aP[ ]P ]US^ RWS[oTk, Q^`oal a XaZchU]XU\ WPYbX WP
+US^ abR^[ T[o Q^[UU QUW^_Pa]^S^ X RkRU`U]]^S^ _`XfU[P, ]^ _`U]UQ`USP[ a^Q[PW]^\
+X hU[ TP[lhU.
+
+C _P`bXWP] Qk[^ ^S`P]XgU]]^U gXa[^ _Pb`^]^R. 8e a[UT^RP[^ QU`Ugl. 8\U[ao
+_`XZPW, _^TTU`VP]]kY Z`cS^Rk\ cS^R^`^\, ab`U[obl a Z^`^bZXe TXabP]fXY, X
+RX]b^R^Z, `PR]ke gXa[c RXTX\ke \XhU]UY.
+
+4^Zb^` [UVP[ QUW ^`cVXo R b`PRU X ]PQ[nTP[ WP e^T^\ Q^o. 2aU US^ a^gcRabRXU
+Qk[^ ]P ab^`^]U SU`^XgUaZX SXQ]cRhXe TUbUY. >] ^b TchX VU[P[ X\ cTPgX. Mb^ Qk[X
+^b_`kaZX aU\UYabR, RU`^ob]^, Q[XWZXe U\c _^ Tcec, US^ R^a_XbP]Xo, US^
+]`PRabRU]]^S^ aZ[PTP, US^ _^]obXY.
+
+HURU[l]c[Pal c ]US^ \ka[l RkQUVPbl Z ]X\ ]P _^[o]c X aTPblao, X bPZX\ ^Q`PW^\
+^Q`UabX XWQPR[U]XU. =^ hPS Qk[ `XaZ^RP]]kY, a^_`oVU]]kY a ^_Pa]^abln.
+
+?^ZP ^] T^QUVP[ Qk T^ aU`UTX]k _^[o]k, _^T]oR RRU`e `cZX, US^ \^S[X Qk c[^VXbl
+a ^QUXe ab^`^], _^`PVU]]k\ R S`cTl X a_X]c, aR^X---R ]PZPWP]XU WP a^RU`hU]]cn
+XW\U]c, gcVXU---]U `PW^Q`PR US^ ]P\U`U]XY. >] RUTl ]U `PW QkRP[ R _^T^Q]ke
+_^[^VU]Xoe, _`^Tc\P[ RaU R^W\^V]^abX X TPR]^ _`XW]P[ mbX _[P]k a_PaU]Xo
+]U_`XS^T]k\X. 8, \X`oal a TR^YabRU]]^abln gcRabR, T^Zb^` _`^T^[VP[ [UVPbl ]P
+VXR^bU, [Xf^\ Z _^[o]U X QUW ^`cVXo a[UTXbl XW b`PRk WP e^T^\ Q^o.
+
+>T]PZ^, a^WU`fPbl X _`UQkRPbl R QUWTUYabRXX a`UTX ZX_URhUY Z`cS^\ Q^`lQk ]U ]P
+VXR^b, P ]P a\U`bl, Qk[^ ]U\ka[X\^ X RkhU gU[^RUgUaZXe aX[. 8 TU[^ Qk[^ ]U R
+US^ a^QabRU]]^Y aP\^WPiXbU, P R a[UT^RP]XX _^`oTZc a^RU`hPRhUS^ao, R _^TgX]U]XX
+WPZ^]P\ b^S^, gb^ `PWkS`kRP[^al _U`UT ]X\ X R^Z`cS ]US^. 1k[^ _`^bXR _`PRX[
+^abPRPblao Z mb^\c R QUWcgPabXX. =PT^ Qk[^ TU[Pbl b^ VU, gb^ TU[P[X T`cSXU. HU[
+Q^Y. 2 ]US^ X b^RP`XiUY ab`U[o[X. =PT^ Qk[^ ^bab`U[XRPblao.
+
+8 Z^STP bU[Ud^]Xab `oT^\ a ]X\ R fU_X WPQX[ao R acT^`^SPe X _^b^\ WP\U` X
+Rkbo]c[ao, WPabkR R ]U_^TRXV]^abX, N`XY 0]T`UURXg _^[WZ^\ _^Tbo]c[ao Z ]U\c,
+a]o[ a ]US^ ac\Zc, RWo[ US^ RX]b^RZc X RU`]cRhXal ]P _`UV]UU \Uab^, abP[
+`PW`oVPbl UU Rkab`U[ WP Rkab`U[^\.
+
+=^ VP[^abl ]U _^WR^[o[P U\c fU[Xblao R \^[^Tke [nTUY, Z^b^`k\X ^] [nQ^RP[ao X
+Z^b^`k\ a^gcRabR^RP[. 0 ab`U[obl aTc`c R R^WTce Qk[^ a[XhZ^\ S[c_k\ X _`PWT]k\
+WP]obXU\, _`^bXRX`UgPiX\ US^ ]P\U`U]Xo\. 8 RkQX`Po \X]cbk, Z^STP \UVTc ]X\ X
+US^ \XhU]ln ]U abP]^RX[ao ]XZb^ XW ]P_PTPniXe, ^] abP[ ab`U[obl R fU[l _^
+^QS^`U[^\c TU`URc. C ]US^ Qk[X bcb aR^X _`XU\k.
+
+FU[oal X _^ \U`U RaU cb^g]oniUYao ]PR^TZX ]UWP\Ub]^ X ]U T^ Z^]fP caX[XRPo
+]PVX\ a^QPgZX, ZPZ Qk QUW `PagUbP Z^STP-]XQcTl Rkab`U[Xbl, _^ZP a_caZ Zc`ZP X
+Rkab`U[ ]U a[UT^RP[X aP\X a^Q^Y ZPZ Qk aRU`e ^VXTP]Xo, T^Zb^` abP[ a _`XRkg]^Y
+\UbZ^abln `PWQ`PakRPbl R^Z`cS _^\U`bRU[^S^ TU`URP aQXbkU a ]US^ ]XV]XU ^ba^ehXU
+acglo.
+
+=^, ^ cVPa! :PZ ]X ^abU`USP[ao T^Zb^`, ZPZ Qk ]U _^_Pabl R Z^S^-]XQcTl, b^
+^TX], b^ T`cS^Y ]Pabc_PniXY RTRXSP[Xal R `UhPniXY \XS \UVTc ]X\ X TU`UR^\, X
+_U`UaUZP[X _`XfU[l]cn [X]Xn R \^\U]b `cVUY]^S^ `PW`oTP. 4Rce ^] WPTU[ X `P]X[,
+P b`UblU\c ]UagPab[XRfc, aRP[XRhU\cao ]UTP[UZ^ ^b TU`URP, mb^ ab^X[^ VXW]X.
+
+\bigskip\noindent{\sf From} {\hcyr 1XQ[Xo, A^Q^`]^U _^a[P]XU aRob^S^ P_^ab^[P
+8cTk}
+
+1 8cTP, `PQ 8XacaP E`XabP, Q`Pb 8PZ^RP, _`XWRP]]k\, Z^b^`kU ^aRoiU]k 1^S^\
+>bf^\ X a^e`P]U]k 8Xaca^\ E`Xab^\: 2 \X[^abl RP\ X \X` X [nQ^Rl TP c\]^VPbao. 3
+2^W[nQ[U]]kU! X\Uo RaU caU`TXU _XaPbl RP\ ^Q ^QiU\ a_PaU]XX, o _^gU[ WP ]cV]^U
+]P_XaPbl RP\ cRUiURP]XU---_^TRXWPblao WP RU`c, ^T]PVTk _`UTP]]cn aRobk\. 4 8Q^
+RZ`P[Xal ]UZ^b^`kU [nTX, XWT`UR[U _`UT]PW]PgU]]kU Z aU\c ^acVTU]Xn, ]UgUabXRkU,
+^Q`PiPniXU Q[PS^TPbl 1^SP ]PhUS^ R _^R^T Z `Pa_cbabRc X ^bRU`SPniXUao UTX]^S^
+2[PTkZX 1^SP X 3^a_^TP ]PhUS^ 8XacaP E`XabP. 5 O e^gc ]P_^\]Xbl RP\, cVU
+W]PniX\ mb^, gb^ 3^a_^Tl, XWQPRXR ]P`^T XW WU\[X 5SX_UbaZ^Y, _^b^\ ]URU`^RPRhXe
+_^ScQX[, 6 X P]SU[^R, ]U a^e`P]XRhXe aR^US^ T^ab^X]abRP, ]^ ^abPRXRhXe aR^U
+VX[XiU, a^Q[nTPUb R RUg]ke cWPe, _^T \`PZ^\, ]P acT RU[XZ^S^ T]o. 7 :PZ A^T^\ X
+3^\^``P X ^Z`Uab]kU S^`^TP, _^T^Q]^ X\ Q[cT^TUYabR^RPhXU X e^TXRhXU WP X]^n
+_[^bXn, _^TRU`ShXal ZPW]X ^S]o RUg]^S^, _^abPR[U]k R _`X\U`,---8 bPZ b^g]^
+QcTUb X a aX\X \UgbPbU[o\X, Z^b^`kU ^aZRU`]onb _[^bl, ^bRU`SPnb ]PgP[labRP X
+W[^a[^Rob Rka^ZXU R[PabX. 9 <XePX[ 0`eP]SU[, Z^STP S^R^`X[ a TXPR^[^\, a_^`o ^
+<^XaUUR^\ bU[U, ]U a\U[ _`^XW]Uabl cZ^`XW]U]]^S^ acTP, ]^ aZPWP[: <TP WP_`UbXb
+bUQU 3^a_^Tl>. 10 0 aXX W[^a[^Rob b^, gUS^ ]U W]Pnb; gb^ VU _^ _`X`^TU, ZPZ
+QUaa[^RUa]kU VXR^b]kU W]Pnb, bU\ `Pab[URPnb aUQo. 11 3^`U X\, _^b^\c gb^ XTcb
+_cbU\ :PX]^Rk\, _`UTPnbao ^Q^[liU]Xn \WTk, ZPZ 2P[PP\, X R c_^`abRU _^SXQPnb,
+ZPZ :^`UY. 12 BPZ^RkU QkRPnb a^Q[PW]^\ ]P RPhXe RUgU`oe [nQRX: _X`hUabRco a
+RP\X, QUW ab`PeP cbcg]onb aUQo; mb^---QUWR^T]kU ^Q[PZP, ]^aX\kU RUb`^\; ^aU]]XU
+TU`URlo, QUa_[^T]kU, TRPVTk c\U`hXU, Xab^`S]cbkU; 13 aRX`U_kU \^`aZXU R^[]k,
+_U]oiXUao a`P\^bP\X aR^X\X; WRUWTk Q[cVTPniXU, Z^b^`k\ Q[nTUbao \`PZ bl\k ]P
+RUZX. 14 > ]Xe _`^`^gUabR^RP[ X 5]^e, aUTl\kY ^b 0TP\P, S^R^`o: <aU, XTUb
+3^a_^Tl a^ bl\P\X aRobke (0]SU[^R) aR^Xe---15 a^bR^`Xbl acT ]PT RaU\X X
+^Q[XgXbl RaUe \UVTc ]X\X ]UgUabXRke R^ RaUe TU[Pe, Z^b^`kU _`^XWRU[^ Xe
+]UgUabXU, X R^ RaUe VUab^ZXe (a[^RPe), Z^b^`kU _`^XW]^aX[X ]P =US^ ]UgUabXRkU
+S`Uh]XZX>. 16 Mb^ `^_^b]XZX, ]XgU\ ]UT^R^[l]kU, _^abc_PniXU _^ aR^X\ _^e^bo\
+(]UgUabXR^ X QUWWPZ^]]^); cabP Xe _`^XW]^aob ]PTcbkU a[^RP; ^]X ^ZPWkRPnb
+[XfU_`XobXU T[o Z^`kabX. 17 =^ Rk, R^W[nQ[U]]kU, _^\]XbU _`UTaZPWP]]^U
+0_^ab^[P\X 3^a_^TP ]PhUS^ 8XacaP E`XabP; 18 ^]X S^R^`X[X RP\, gb^ R _^a[UT]UU
+R`U\o _^oRobao `cSPbU[X, _^abc_PniXU _^ aR^X\ ]UgUabXRk\ _^e^bo\. 19
+Mb^---[nTX, ^bTU[oniXU aUQo (^b UTX]abRP RU`k), TchUR]kU, ]U X\UniXU TceP. 20 0
+Rk, R^W[nQ[U]]kU, ]PWXTPo aUQo ]P aRobUYhUY RU`U RPhUY, \^[oal 4ce^\ ARobk\, 21
+a^e`P]oYbU aUQo R [nQRX 1^VXUY, ^VXTPo \X[^abX ^b 3^a_^TP ]PhUS^ 8XacaP E`XabP,
+T[o RUg]^Y VXW]X. 22 8 Z ^T]X\ QcTlbU \X[^abXRk, a `Paa\^b`U]XU\; 23 P T`cSXe
+ab`Pe^\ a_PaPYbU, Xab^`SPo XW ^S]o, ^Q[XgPYbU VU a^ ab`Pe^\, S]chPoal TPVU
+^TUVT^n, Z^b^`Po ^aZRU`]U]P _[^bln. 24 <^SciU\c VU a^Q[nabX RPa ^b _PTU]Xo X
+_^abPRXbl _`UT a[PR^n AR^Un ]U_^`^g]k\ R `PT^abX, 25 UTX]^\c _`U\cT`^\c 1^Sc,
+a_PaXbU[n ]PhU\c g`UW 8XacaP E`XabP 3^a_^TP ]PhUS^, a[PRP X RU[XgXU, aX[P X
+R[Pabl _`UVTU RaUe RUZ^R, ]k]U X R^ RaU RUZX. 0\X]l.
+
+\bigskip\noindent{\sf From} {\hcyr 0.?.\ GUe^R, <B^[abkY X b^]ZXY>}
+
+=P R^ZWP[U =XZ^[PURaZ^Y VU[UW]^Y T^`^SX Rab`UbX[Xal TRP _`XobU[o: ^TX] b^[abkY,
+T`cS^Y b^]ZXY. B^[abkY b^[lZ^ gb^ _^^QUTP[ ]P R^ZWP[U, X ScQk US^, _^TU`]cbkU
+\Pa[^\, [^a]X[Xal ZPZ a_U[kU RXh]X. ?Pe[^ ^b ]US^ eU`Ua^\ X d[U`T^`P]VU\.
+B^]ZXY VU b^[lZ^ gb^ RkhU[ XW RPS^]P X Qk[ ]PRlngU] gU\^TP]P\X, cW[P\X X
+ZP`b^]ZP\X. ?Pe[^ ^b ]US^ RUbgX]^Y X Z^dUY]^Y SciUY. 8W-WP US^ a_X]k
+RkS[oTkRP[P ecTU]lZPo VU]iX]P a T[X]]k\ _^TQ^`^TZ^\---US^ VU]P, X Rka^ZXY
+SX\]PWXab a _`Xic`U]]k\ S[PW^\---US^ ak].
+
+---?^`dX`XY!---R^aZ[XZ]c[ b^[abkY, cRXTUR b^]Z^S^. ---Bk [X mb^? 3^[cQgXZ \^Y!
+AZ^[lZ^ WX\, aZ^[lZ^ [Ub!
+
+---1PbnhZX!---XWc\X[ao b^]ZXY.---<XhP! 4`cS TUbabRP! >bZcTP bk RWo[ao?
+
+?`XobU[X b`^UZ`Pb]^ ^Q[^QkWP[Xal X cab`U\X[X T`cS ]P T`cSP S[PWP, _^[]kU a[UW.
+>QP Qk[X _`Xob]^ ^hU[^\[U]k.
+
+---<X[kY \^Y!---]PgP[ b^]ZXY _^a[U [^QkWP]Xo.---2^b ]U ^VXTP[! 2^b an`_`XW! =c,
+TP _^S[oTX VU ]P \U]o e^`^hU]lZ^! BPZ^Y VU Z`PaPRUf, ZPZ X Qk[! BPZ^Y VU
+Tch^]^Z X iUS^[l! 0e bk, S^a_^TX! =c, gb^ VU bk? 1^SPb? 6U]Pb? O cVU VU]Pb, ZPZ
+RXTXhl... Mb^ R^b \^o VU]P, ;cXWP, c`^VTU]]Po 2P]fU]QPe... [nbU`P]ZP... P mb^
+ak] \^Y, =PdP]PX[, cgU]XZ b`UblUS^ Z[PaaP. Mb^, =PdP]o, T`cS \^US^ TUbabRP! 2
+SX\]PWXX R\UabU cgX[Xal!
+
+=PdP]PX[ ]U\]^S^ _^Tc\P[ X a]o[ hP_Zc.
+
+---2 SX\]PWXX R\UabU cgX[Xal!---_`^T^[VP[ b^]ZXY. ---?^\]Xhl, ZPZ bUQo
+T`PW]X[X? BUQo T`PW]X[X 3U`^ab`Pb^\ WP b^, gb^ bk ZPWU]]cn Z]XVZc _P_X`^aZ^Y
+_`^VUS, P \U]o MdXP[lb^\ WP b^, gb^ o oQUT]XgPbl [nQX[. E^-e^... 4Ubl\X Qk[X!
+=U Q^Yao, =PdP]o! ?^T^YTX Z ]U\c _^Q[XVU... 0 mb^ R^b \^o VU]P, c`^VTU]]Po
+2P]fU]QPe... [nbU`P]ZP...
+
+=PdP]PX[ ]U\]^S^ _^Tc\P[ X a_`obP[ao WP a_X]c ^bfP.
+
+---=c, ZPZ VXRUhl, T`cS?---a_`^aX[ b^[abkY, R^ab^`VU]]^ S[oTo ]P
+T`cSP.---A[cVXhl STU? 4^a[cVX[ao?
+
+---A[cVc, \X[kY \^Y! :^[[UVaZX\ PaUaa^`^\ cVU Rb^`^Y S^T X AbP]Xa[PRP X\Un.
+6P[^RP]XU _[^e^U... =c, TP Q^S a ]X\! 6U]P c`^ZX TPUb, o _^`baXSP`k _`XRPb]^ XW
+TU`URP TU[Pn. >b[Xg]kU _^`baXSP`k! ?^ `cQ[n WP hbcZc _`^TPn. 5a[X Zb^ QU`Ub
+TUaobl hbcZ X Q^[UU, b^\c, _^]X\PUhl, cabc_ZP. ?`^QPR[oU\ao Z^U-ZPZ. A[cVX[,
+W]PUhl, R TU_P`bP\U]bU, P bU_U`l anTP _U`URUTU] ab^[^]PgP[l]XZ^\ _^ b^\c VU
+RUT^\abRc... 7TUal QcTc a[cVXbl. =c, P bk ZPZ? =UQ^al cVU abPbaZXY? 0?
+
+---=Ub, \X[kY \^Y, _^Tk\PY _^RkhU,---aZPWP[ b^[abkY.---O cVU T^ bPY]^S^
+T^a[cVX[ao... 4RU WRUWTk X\Un.
+
+B^]ZXY RT`cS _^Q[UT]U[, ^ZP\U]U[, ]^ aZ^`^ [Xf^ US^ XaZ`XRX[^al R^ RaU ab^`^]k
+hX`^gPYhUY c[kQZ^Y; ZPWP[^al, gb^ ^b [XfP X S[PW US^ _^ak_P[Xal XaZ`k. AP\ ^]
+ajUVX[ao, aS^`QX[ao, acWX[ao... 5S^ gU\^TP]k, cW[k X ZP`b^]ZX ajUVX[Xal,
+_^\^`iX[Xal... 4[X]]kY _^TQ^`^T^Z VU]k abP[ UiU T[X]]UU; =PdP]PX[ Rkbo]c[ao R^
+d`c]b X WPabUS]c[ RaU _cS^RZX aR^US^ \c]TX`P...
+
+---O, RPhU _`UR^ae^TXbU[labR^... >gU]l _`Xob]^! 4`cS, \^V]^ aZPWPbl, TUbabRP X
+RT`cS Rkh[X R bPZXU RU[l\^VX! EX-eX-a.
+
+---=c, _^[]^!---_^\^`iX[ao b^[abkY.---4[o gUS^ mb^b b^]? <k a b^Q^Y T`cWlo
+TUbabRP---X Z gU\c bcb mb^ gX]^_^gXbP]XU!
+
+---?^\X[cYbU... Gb^ Rk-a...---WPeXeXZP[ b^]ZXY, UiU Q^[UU
+ajUVXRPoal.---<X[^abXR^U R]X\P]XU RPhUS^ _`UR^ae^TXbU[labRP... 2`^TU ZPZ Qk
+VXRXbU[l]^Y R[PSX... Mb^ R^b, RPhU _`UR^ae^TXbU[labR^, ak] \^Y =PdP]PX[... 6U]P
+;cXWP, [nbU`P]ZP, ]UZ^b^`k\ ^Q`PW^\...
+
+B^[abkY e^bU[ Qk[^ R^W`PWXbl gb^-b^, ]^ ]P [XfU c b^]Z^S^ Qk[^ ]P_XaP]^ ab^[lZ^
+Q[PS^S^RU]Xo, a[PT^abX X _^gbXbU[l]^Y ZXa[^bk, gb^ bPY]^S^ a^RUb]XZP ab^h]X[^.
+>] ^bRU`]c[ao ^b b^]Z^S^ X _^TP[ U\c ]P _`^iP]lU `cZc.
+
+B^]ZXY _^VP[ b`X _P[lfP, _^Z[^]X[ao RaU\ bc[^RXiU\ X WPeXeXZP[, ZPZ ZXbPUf:
+<eX-eX-eX>. 6U]P c[kQ]c[Pal. =PdP]PX[ hP`Z]c[ ]^S^Y X c`^]X[ dc`PVZc. 2aU b`^U
+Qk[X _`Xob]^ ^hU[^\[U]k.
+
+\bigskip\noindent{\sf From} {\hcyr 2.>. :[ngURaZXY, <:c`a `caaZ^Y Xab^`XX>}
+
+2k _`^a[chP[X cVU ]UaZ^[lZ^ Zc`a^R _^ RaU^QiUY Xab^`XX, _^W]PZ^\X[Xal a
+WPTPgP\X X _`XU\P\X c]XRU`aXbUbaZ^S^ XWcgU]XP mb^Y ]PcZX. =PgX]Po Zc`a `caaZ^Y
+Xab^`XX, o _`UT_^h[n U\c ]UaZ^[lZ^ aP\ke ^QiXe U[U\U]bP`]ke a^^Q`PVU]XY, fU[l
+Z^b^`ke---aRoWPbl aTU[P]]kU RP\X ]PQ[nTU]Xo X Rk]UaU]]kU R_UgPb[U]Xo _^
+RaU^QiUY Xab^`XX a WPTPgUY X _`XU\P\X ^bTU[l]^S^ XWcgU]Xo Xab^`XX @^aaXX.
+
+{\bcyr =Pcg]Po WPTPgP XWcgU]Xo \Uab]^Y Xab^`XX}\quad ?^]obU] _`PZbXgUaZXY
+X]bU`Ua, _^QcVTPniXY ]Pa XWcgPbl Xab^`Xn @^aaXX ^a^Q^, RkTU[oo UU XW a^abPRP
+RaU^QiUY Xab^`XX: RUTl mb^ Xab^`Xo ]PhUS^ ^bUgUabRP. =^ mb^b R^a_XbPbU[l]kY,
+b.U.\ _`PZbXgUaZXY, X]bU`Ua ]U XaZ[ngPUb ]Pcg]^S^, ]P_`^bXR, T^[VU] b^[lZ^
+_`XTPRPbl U\c Q^[UU TXTPZbXgUaZ^Y aX[k. 8bPZ, ]PgX]Po ^a^QkY Zc`a `caaZ^Y
+Xab^`XX, \^V]^ _^abPRXbl bPZ^Y ^QiXY R^_`^a: ZPZcn ]Pcg]cn fU[l \^VUb X\Ubl
+a_UfXP[l]^U XWcgU]XU Xab^`XX ^T]^Y ZPZ^Y-[XQ^ ab`P]k, ZPZ^S^-[XQ^ ^bTU[l]^S^
+]P`^TP? MbP fU[l T^[V]P Qkbl RkRUTU]P XW ^QiXe WPTPg Xab^`XgUaZ^S^ XWcgU]Xo,
+b.U.\ XW WPTPg XWcgU]Xo ^QiUY Xab^`XX gU[^RUgUabRP.
+
+{\bcyr 8ab^`XgUaZXY _`^fUaa}\quad =P ]Pcg]^\ oWkZU a[^R^ <Xab^`Xo>
+c_^b`UQ[oUbao R TR^oZ^\ a\ka[U: 1) ZPZ TRXVU]XU R^ R`U\U]X, _`^fUaa, X 2) ZPZ
+_^W]P]XU _`^fUaaP. ?^mb^\c RaU, gb^ a^RU`hPUbao R^ R`U\U]X X\UUb aR^n Xab^`Xn.
+A^TU`VP]XU\ Xab^`XX, ZPZ ^bTU[l]^Y ]PcZX, a_UfXP[l]^Y ^b`Pa[X ]Pcg]^S^ W]P]Xo,
+a[cVXb Xab^`XgUaZXY _`^fUaa, b.U.\ e^T, ca[^RXo X ca_UeX gU[^RUgUaZ^S^
+^QiUVXbXo X[X VXW]l gU[^RUgUabRP R UU `PWRXbXX X `UWc[lbPbPe. GU[^RUgUaZ^U
+^QiUVXbXU---bPZ^Y VU dPZb \X`^R^S^ QkbXo, ZPZ X VXW]l ^Z`cVPniUY ]Pa _`X`^Tk, X
+]Pcg]^U _^W]P]XU mb^S^ dPZbP---bPZPo VU ]Ucab`P]X\Po _^b`UQ]^abl gU[^RUgUaZ^S^
+c\P, ZPZ X XWcgU]XU VXW]X mb^Y _`X`^Tk. GU[^RUgUaZ^U ^QiUVXbXU Rk`PVPUbao R
+`PW]^^Q`PW]ke [nTaZXe a^nWPe, Z^b^`kU \^Scb Qkbl ]PWRP]k Xab^`XgUaZX\X bU[P\X X
+Z^b^`kU R^W]XZPnb, `Pabcb X `PW\]^VPnbao _^T^Q]^ ^`SP]XgUaZX\ bU[P\ _`X`^Tk.
+2^W]XZ]^RU]XU, `^ab X a\U]P mbXe a^nW^R a^ RaU\X ca[^RXo\X X _^a[UTabRXo\X Xe
+VXW]X X Uabl b^, gb^ \k ]PWkRPU\ Xab^`XgUaZX\ _`^fUaa^\.
+
+\bigskip\noindent{\sf From} {\hcyr ;X_\P] 1U`a, <<PbU\PbXgUaZXU R^_`^ak
+T^WRcZ^R^Y X ^Z^[^WRcZ^R^Y SPW^R^Y TX]P\XZX>}
+
+\centerline{\bcyr ?`UTXa[^RXU PRb^`P Z `caaZ^\c XWTP]Xn}
+
+O ^gU]l `PT, gb^ \^o \^]^S`PdXo ^ ]UZ^b^`ke \PbU\PbXgUaZXe WPTPgPe SPW^R^Y
+TX]P\XZX _^oR[oUbao R `caaZ^\ _U`UR^TU. O Q[PS^TP`U] _U`UR^TgXZc X `UTPZb^`c, P
+bPZVU X bU\ Z^[[USP\, Z^b^`kU cZPWP[X ^hXQZX X ^_UgPbZX, T^_ciU]]kU R
+P]S[XYaZ^\ XWTP]XX.
+
+:^STP `cZ^_Xal Qk[P WPZ^]gU]P, o X\U[ a\U[^abl ]PTUoblao, gb^ ^]P _`UTabPR[oUb
+a^Q^Y T^abPb^g]^ _^[]kY ^QW^` a^ab^o]Xo bU^`XX R bUe cWZXe _`UTU[Pe, Z^b^`kU
+Qk[X ]P\UgU]k. AUS^T]o mb^b ^QW^` _^ ]U^Qe^TX\^abX ]UaZ^[lZ^ cabP`U[. O c_^\o]c
+b^[lZ^ ^ b`Ue R^_`^aPe, Z^b^`kU ]U_`U\U]]^ a[UT^RP[^ Qk RZ[ngXbl R a[cgPU
+_U`Ua\^b`P bUZabP. Mb^ _`UVTU RaUS^ `UWc[lbPbk 4U-4V^`TVX (1) X =PhP (1),
+Z^b^`k\ cTP[^al aciUabRU]]^ _`^]XZ]cbl R bU^`Xn ZRPWX[X]UY]ke c`PR]U]XY \]^SXe
+_U`U\U]]ke, P bPZVU ]UTPR]UU c_`^iU]XU T^ZPWUbU[labRP, _`UT[^VU]]^U <^WU`^\
+(1). 7PbU\ ]U^Qe^TX\^ Qk[^ Qk ^b`PWXbl Q^[lhcn `PQ^bc, _`^TU[P]]cn _^ gXa[U]]k\
+`PagUbP\ bUgU]Xo WP aX[l]k\ ^ba^UTX]U]]k\ aZPgZ^\ (R gPab]^abX, \Ub^Tk
+4^`^T]Xfk]P (1,2), 3P`PQUTo]P (1), @Xeb\PYU`P (1) X 2P] 4PYZP (1,2)), X,
+]PZ^]Uf, TP]]^U 6U`\U]^\ ^_XaP]XU bUgU]Xo RQ[XWX _U`UaUgU]Xo aZPgZP a WRcZ^R^Y
+(`UhPniUU WPTPgc, _^abPR[U]]cn ]P ab`.~134--136).
+
+A T`cS^Y ab^`^]k, \^V]^ ^b\UbXbl, gb^ Q^[lhPo gPabl WPTPg, ad^`\c[X`^RP]]ke R
+mb^Y Z]XSU, RaU UiU ^abPUbao ]U`UhU]]^Y.
+
+;X_\P] 1U`a, 30 \Po 1960 S.
+
+\centerline{\bcyr 3[PRP 1. 4XddU`U]fXP[l]kU c`PR]U]Xo _^bU]fXP[l]^S^ bUgU]Xo
+SPWP}
+
+\centerline{\bcyr \S2. 4XddU`U]fXP[l]kU c`PR]U]Xo X Z`PURkU ca[^RXo}
+
+<k Z`PbZ^ _^Rb^`X\ RkR^T c`PR]U]XY T[o _^bU]fXP[P bUgU]Xo aVX\PU\^Y VXTZ^abX.
+1^[UU TUbP[l]^U ^_XaP]XU \^V]^ ]PYbX R^ \]^SXe Z]XSPe (a\., ]P_`X\U` :c`P]b X
+D`XT`Xea (1)).
+
+>a]^R]kU c`PR]U]Xo. BUgU]XU a^RU`hU]]^Y VXTZ^abX ^_XakRPUbao R bPZ ]PWkRPU\^\
+mY[U`^R^\ _`UTabPR[U]XX WPTP]XU\ _[^b]^abX $\rho$ X Z^\_^]U]b^R aZ^`^abX $u_1$,
+$u_2$, $u_3$ ZPZ dc]ZfXY TUZP`b^Rke Z^^`TX]Pb $x_1$, $x_2$, $x_3$ X R`U\U]X
+$t$. ?^[]^U ^_XaP]XU b`UQcUb bPZVU W]P]Xo TRce T`cSXe bU`\^TX]P\XgUaZXe
+RU[XgX], aZPVU\ TPR[U]Xo $p$ X bU\_U`Pbc`k X[X TPR[U]Xo X m]b`^_XX. >T]PZ^ \k
+X\UU\ TU[^ a PTXPQPbXgUaZX\ X XW^m]b`^_XgUaZX\ bUgU]XU\. 2 mb^\ a[cgPU TPR[U]XU
+Uabl XWRUab]Po dc]ZfXo _[^b]^abX. 4[o XTUP[l]^S^ SPWP
+$$
+p=c \rho^\tau,
+\eqno(2.1)
+$$
+STU $\tau>1$---_^ab^o]]Po (^b]^hU]XU cTU[l]ke bU_[^U\Z^abUY). AbP]TP`b]^U
+W]PgU]XU $\tau$ T[o R^WTceP `PR]^ $1{,}4$. =P\ QcTUb cT^Q]^ ]U ^S`P]XgXRPblao
+mbX\ a^^b]^hU]XU\ \UVTc TPR[U]XU\ X _[^b]^abln, P `Paa\Pb`XRPbl bPZVU ^QiXY
+a[cgPY QP`^b`^_]^Y VXTZ^abX, b.U.\ VXTZ^abX R Z^b^`^Y
+$$
+p=p(\rho),
+\eqno(2.2)
+$$
+STU $p(\rho)$---]UZ^b^`Po T^abPb^g]^ S[PTZPo R^W`PabPniPo dc]ZfXo.
+
+:^\_^]U]bk aZ^`^abX X _[^b]^abl aRoWP]k c`PR]U]XU\ ]U`PW`kR]^abX, Rk`PVPniX\
+WPZ^] a^e`P]U]Xo \Paak,
+$$
+{\partial\rho\over\partial t} +
+\sum_{i=1}^3 {\partial(\rho u_i)\over\partial x_i}=0.
+\eqno(2.3)
+$$
+
+A T`cS^Y ab^`^]k, Z^\_^]U]bk aZ^`^abX T^[V]k cT^R[UbR^`obl mY[U`^Rk\ c`PR]U]Xo\
+TRXVU]Xo, oR[oniX\ao Rk`PVU]XU\ Rb^`^S^ WPZ^]P =lnb^]P. 5a[X _`U]UQ`Ugl
+\Paa^Rk\X aX[P\X, R gPab]^abX boVUabln, b^ mbX c`PR]U]Xo X\Unb RXT
+$$
+{\partial u_i\over\partial t}
+\sum_{j=1}^3 u_i
+{\partial u_i\over\partial x_j} + {1\over\rho}
+{\partial p\over\partial x_i}=0
+\quad (i=1,2,3).
+\eqno(2.4)
+$$
+
+7P\UbX\, gb^ a _^\^iln a^^b]^hU]Xo (2.2) TPR[U]XU \^VUb Qkbl XaZ[ngU]^ XW
+c`PR]U]XY MY[U`P. C`PR]U]Xo TRXVU]Xo X c`PR]U]XU ]U`PW`kR]^abX cT^R[UbR^`onb
+_`X]fX_c ^b]^aXbU[l]^abX Z[PaaXgUaZ^Y \UeP]XZX, b.U.\ ^]X a_`PRUT[XRk R [nQ^Y
+X]U`fXP[l]^Y aXabU\U Z^^`TX]Pb, Ua[X ^]X a_`PRUT[XRk R ^T]^Y XW bPZXe aXabU\.
+
+\bigskip\noindent {\sf And naturally$\ldots$}
+
+\bigskip\noindent{\sf From} {\hcyr AU`SUY 8RP]^RXg 0To], <> d`PS\U]bPe a[^RP
+$\Delta$ R S`c__U Z^a>}
+
+3`c__P Z^a ${\frak B}_{n+1}$ WPTPUbao ^Q`PWcniX\X
+$$
+a_1, a_2, \ldots, a_n \eqno(1)
+$$
+X ^_`UTU[oniX\X a^^b]^hU]Xo\X
+$$
+a_i a_j = a_j a_i,\quad \left|i-j\right|>1 \eqno(2)
+$$
+$$
+a_i a_{i+1} a_i = a_{i+1} a_i a_{i+1} \quad (1\le i\le n). \eqno(3)
+$$
+
+1. 2 `PQ^bU [1] 3P`aPYT _^[cgX[ `UhU]XU _^abPR[U]]^Y 0`bX]^\ R `PQ^bU [2]
+_`^Q[U\k a^_`oVU]]^abX T[o S`c__ ${\frak B}_{n+1}$. 2 ^a]^RU T^ZPWPbU[labRP
+[UVPb cabP]^R[U]]kU R [1] aR^YabP bPZ ]PWkRPU\^S^ dc]TP\U]bP[l]^S^ a[^RP
+$$
+\Delta \rightleftharpoons a_1 a_2 \cdots a_n a_1 a_2 \cdots a_{n-1} \cdots
+a_2 a_2 a_3 a_1 a_2 a_1.
+$$
+2 gPab]^abX, $\Delta^2$ _^`^VTPUb fU]b` S`c__k ${\frak B}_{n+1}$.
+
+?cabl $\Pi_{n+1}$ Uabl _^[cS`c__P, WPTP]]Po ^Q`PWcniX\X (1) X ^_`UTU[oniX\X
+^b]^hU]Xo\X (2) X (3). 2 [1] T^ZPWP]^, gb^ $\Pi_{n+1}$ RZ[PTkRPUbao R S`c__c
+${\frak B}_{n+1}$. GU`UW $\doteq$ ^Q^W]PgPUbao `PRU]abR^ a[^R R $\Pi_{n+1}$.
+
+5a[X $X\doteq PQ$, b^ S^R^`ob, gb^ a[^R^ $X$ TU[Xbao R _^[cS`c__U $\Pi_{n+1}$
+a[URP ]P $P$ (a_`PRP ]P $Q$). 8W `UWc[lbPb^R `PQ^bk [1] [USZ^ a[UTcUb, gb^
+dc]TP\U]bP[l]^U a[^R^ $\Delta$ a b^g]^abln T^ `PRU]abRP R $\Pi_{n+1}$ \^V]^
+^_`TU[Xbl ZPZ Z`PbgPYhUU a[^R^ R P[dPRXbU (1), Z^b^`^U TU[Xbao R $\Pi_{n+1}$
+a[URP (a_`PRP) ]P RaU QcZRk (1).
+
+\bigskip\noindent{\sf From}
+{\hcyr 0[UZaUY 8RP]^RXg :^ab`XZX], <2^Z`cS 1U`]aPYTP>}
+
+\centerline{\bcyr \S2.2 A_caZ Z b^]ZX\ am]TRXgP\ (a[cgPY $p \gg n$)}
+
+5a[X ^a]^R]^U _^[U $F$ X\UUb ]c[URcn X[X T^abPb^g]^ Q^[lhcn eP`PZbU`XabXZc (_^
+a`PR]U]Xn a $n$), b^ T^ZPWPbU[labR^ aciUabR^RP]Xo am]TRXgP R P[SUQ`U ;X $L$ a
+ca[^RXU\ $E_n$ aX[l]^ c_`^iPUbao. ?`UVTU gU\ \PbU`XP[XW^RPbl mb^ cbRU`VTU]XU,
+_^a\^b`X\ ]P XTUP[ $E_{n-1}(L)$ R $L$, _^`^VTU]]kY RaU\X m[U\U]bP\X
+$[uv^{n-1}]$ a $u,v\in L$. 8W aZPWP]]^S^ R S[.\ 1 T^R^[l]^ ^gURXT]^, gb^
+$$
+E_{n-1}(L)= \left\langle [ uv^{n-1}] \mid u,v \in L \right\rangle_F
+$$
+---[X]UY]^U _`^ab`P]abR^ ]PT $F$, ]Pbo]cb^U ]P m[U\U]bk $[ uv^{n-1}]$. =PS[oT]^
+mb^ X[[nab`X`cUbao d^`\c[^Y
+$$
+[uv^{n-1}w]=[uwv^{n-1}] + \sum_i \alpha_i [uz_i^{n-1}],
+$$
+[USZ^ RkbUZPniUY XW d^`\c[k (1.2):
+$$
+v^{n-1}w-wv^{n-1}=\sum_{i=0}^{n-2} v^i [vw] v^{n-2-i} =
+\left\{ \matrix{ [vw] & v \cr 1 & n-2 \cr} \right\} =
+\sum_i \alpha_i z_i^{n-1},\quad z \in L.
+$$
+>ZPWkRPUbao, gb^ _`X $p \gg n$ XTUP[ $E_{n-1}(L)$ am]TRXgUR. B^g]UU,
+a_`PRUT[XRP
+
+{\ccyr BU^`U\P 3.1.} {\icyr 4[o [nQ^Y _P`k m[U\U]b^R $u,v$ XW $n-$m]SU[UR^Y
+P[SUQ`k ;X $L$ ]PT _^[U\ $F$ eP`PZbU`XabXZX $p>n+[n/2]$ X\UUb \Uab^ b^VTUabR^}
+$$
+[uv^{n-1}]^2=0.
+$$
+
+\bigskip\noindent{\sf From} {\hcyr =.=. @U_X], <?^[X[X]UY]kU b^VTUabRP R
+Z^[lfPe ;X, Paa^fXX`^RP]]ke a _U`X^TXgUaZX\X S`c__P\X>}
+
+?cabl $B(\infty,p)$---aR^Q^T]Po _U`X^TXgUaZPo S`c__P agUb]^S^ `P]SP _`^ab^S^
+_U`X^TP $p$, P $L(B(\infty,p))$---P[SUQ`P ;X, Paa^fXX`^RP]]Po a mb^Y S`c__^Y. 2
+`PQ^bU [1] 2^m]-;X cZPWP[ aU\UYabR^ _^[X[X]UY]ke b^VTUabR, Rk_^[]U]]ke R
+P[SUQ`U $L(B(\infty,p))$, bPZ^U, gb^ RaoZ^U _^[X[X]UY]^U b^VUTabR^ P[SUQ`k
+$L(B(\infty,p))$ oR[oUbao a[UTabRXU\ b^VTUabR mb^S^ aU\UYabRP.
+
+2 ]Pab^oiUY `PQ^bU _^[cgU] P]P[^SXg]kY `UWc[lbPb T[o S`c__ $B(\infty,q)$
+_`^XWR^[l]^S^ _U`X^TP $q\in {\Bbb N}$.
+
+\centerline{\S1. ?^[X[X]UY]kU b^VTUabRP $K_n (x_1, \ldots, x_n) \equiv 0$}
+
+?cabl ${\frak L}$---aR^Q^T]^U Z^[lf^ ;X ]P ^Q`PWcniXe $x_1,x_2,x_3,\ldots$ a
+fU[k\X Z^UddXfXU]bP\X. ?cabl $S$---Z^]Ug]^U \]^VUabR^ ]Pbc`P[l]ke gXaU[,
+$S=\{i,j,\ldots,k\}$, $i<j<\ldots,k$. :PZ X R `PQ^bU [1], T[o m[U\U]bP
+$u\in{\frak L}$ gU`UW $[u,x_s]$ \k ^Q^W]PgPU\ Z^\\cbPb^` $[u,x_i,
+x_j,\ldots,x_k]$, P gU`UW $[u,\bar x_s]$ m[U\U]b $(-1)^{\mathop{\rm Card} (S)}
+[u,x_k,\ldots, x_j,x_i]$. BPZ^U VU ^Q^W]PgU]XU $[u,x_s]$ \k Xa_^[lWcU\ T[o
+S`c__^R^S^ Z^\\cbPb^`P $[u,x_i, x_j,\ldots,x_k]$ R aR^Q^T]^Y S`c__U $\langle
+x_1, x_2, x_3, \ldots ; \emptyset \rangle$. =U[X]UY]kY _^ ZPZ^Y-[XQ^ ^Q`PWcniUY
+$x_i$ Z^\\cbPb^` ]P _^`^VTPniXe $x_1, x_2, x_3, \ldots $ QcTU\ ]PWkRPbl {\icyr
+$x_i^2$-Z^\\cbPb^`^\.}
+
+\bye
diff --git a/language/cyrillic/inputs/rmacro.sty b/language/cyrillic/inputs/rmacro.sty
new file mode 100644
index 0000000000..0af0f23a40
--- /dev/null
+++ b/language/cyrillic/inputs/rmacro.sty
@@ -0,0 +1,106 @@
+%This code was written by Dimitri Vulis and placed into public domain.
+%There is no copyright associated with this code. Use it as you wish.
+\def\cdefRussian{
+\chardef\Zh='021
+\chardef\zh='031
+\chardef\Ui='022 %uwash
+\chardef\ui='032 %uwash
+%\def\Ui{{\accent"24I}} %Old AMS
+%\def\ui{{\accent"24i}} %Old AMS
+\chardef\Kh='110
+\chardef\kh='150
+\chardef\Ts='103
+\chardef\ts='143
+\chardef\Ch='121
+\chardef\ch='161
+\chardef\Sh='130
+\chardef\sh='170
+\chardef\Shch='127
+\chardef\shch='167
+\chardef\cDprime='137
+\chardef\cdprime='177
+\chardef\cPrime='136
+\chardef\cprime='176
+\chardef\Ee='003
+\chardef\ee='013
+\chardef\Yu='020
+\chardef\yu='030
+\chardef\Ya='027
+\chardef\ya='037
+\chardef\Yo='023 %start uwash only
+\chardef\yo='033
+\chardef\Izhitsa='024
+\chardef\izhitsa='034
+\chardef\Fita='025
+\chardef\fita='035
+\chardef\Yat='043
+\chardef\yat='053 %end uwash only
+}
+\def\cdefTranslitX{
+\def\Zh{\t{Z}{h}}
+\def\zh{\t{z}{h}}
+\def\Ui{\u{I}}
+\def\ui{\u{\i}}
+\def\Kh{\t{K}{h}}
+\def\kh{\t{k}{h}}
+\def\Ts{\t{T}{s}}
+\def\ts{\t{t}{s}}
+\def\Ch{\t{C}{h}}
+\def\ch{\t{c}{h}}
+\def\Sh{\t{S}{h}}
+\def\sh{\t{s}{h}}
+\def\Shch{\t{S}{h}\t{c}{h}}
+\def\shch{\t{s}{h}\t{c}{h}}
+\def\cprime{$^\prime$}
+\def\cPrime{$\underline{^\prime}$}
+\def\cdprime{$^{\prime\prime}$}
+\def\cDprime{$\underline{^{\prime\prime}}$}
+\def\Ee{\`{E}}
+\def\ee{\`{e}}
+\def\Yu{\t{Y}{u}}
+\def\yu{\t{y}{u}}
+\def\Ya{\t{Y}{a}}
+\def\ya{\t{y}{a}}
+\def\Yo{\t{Y}{o}}
+\def\yo{\t{y}{o}}
+\def\Izhitsa{\'{Y}}
+\def\izhitsa{\'{y}}
+\def\Fita{\t{T}{h}}
+\def\fita{\t{t}{h}}
+\def\Yat{\'{E}}
+\def\yat{\'{e}}
+}
+\def\cdefTranslitY{
+\def\Zh{\v{Z}}
+\def\zh{\v{z}}
+\def\Ui{J}
+\def\ui{j}
+\def\Kh{Ch}
+\def\kh{ch}
+\def\Ts{C}
+\def\ts{c}
+\def\Ch{\v{C}}
+\def\ch{\v{c}}
+\def\Sh{\v{S}}
+\def\sh{\v{s}}
+\def\Shch{\v{S}\v{c}}
+\def\shch{\v{s}\v{c}}
+\def\cprime{\kern0pt'\kern0pt\relax}
+\def\cPrime{\kern0pt'\kern0pt\relax}
+\def\cdprime{\kern0pt'\kern0pt'\kern0pt\relax}
+\def\cDprime{\kern0pt'\kern0pt'\kern0pt\relax}
+\def\Ee{\`{E}}
+\def\ee{\`{e}}
+\def\Yu{\t{J}{u}}
+\def\yu{\t{\j}{u}}
+\def\Ya{\t{J}{a}}
+\def\ya{\t{\j}{a}}
+\def\Yo{\t{J}{o}}
+\def\yo{\t{j}{o}}
+\def\Izhitsa{\'{Y}}
+\def\izhitsa{\'{y}}
+\def\Fita{\t{T}{h}}
+\def\fita{\t{t}{h}}
+\def\Yat{\'{E}}
+\def\yat{\'{e}}
+}
diff --git a/language/cyrillic/programs/gost2ascii.c b/language/cyrillic/programs/gost2ascii.c
new file mode 100644
index 0000000000..9622c6b91b
--- /dev/null
+++ b/language/cyrillic/programs/gost2ascii.c
@@ -0,0 +1,28 @@
+#include <stdio.h>
+
+#define CYR_A (0260)
+#define CYR_ya (0357)
+
+static char* map[] = {
+ "A", "B", "V", "G", "D", "E", "{\\Zh}", "Z", "I", "{\\Ui}", "K", "L", "M",
+ "N", "O", "P", "R", "S", "T", "U", "F", "{\\Kh}", "{\\Ts}", "{\\Ch}",
+ "{\\Sh}", "{\\Shch}", "{\\cDprime}", "Y", "{\\cPrime}", "{\\Ee}", "{\\Yu}",
+ "{\\Ya}",
+
+ "a", "b", "v", "g", "d", "e", "{\\zh}", "z", "i", "{\\ui}", "k", "l", "m",
+ "n", "o", "p", "r", "s", "t", "u", "f", "{\\kh}", "{\\ts}", "{\\ch}",
+ "{\\sh}", "{\\shch}", "{\\cdprime}", "y", "{\\cprime}", "{\\ee}", "{\\yu}",
+ "{\\ya}"
+};
+
+main()
+{
+ int c;
+ while ((c = getchar()) != EOF) {
+ if (c >= CYR_A && c <= CYR_ya) {
+ fputs(map[c-CYR_A], stdout);
+ } else {
+ putchar(c);
+ }
+ }
+}
diff --git a/language/cyrillic/programs/trr.pas b/language/cyrillic/programs/trr.pas
new file mode 100644
index 0000000000..8027de2072
--- /dev/null
+++ b/language/cyrillic/programs/trr.pas
@@ -0,0 +1,259 @@
+(*
+This code was written by Dimitri Vulis and placed into public domain.
+There is no copyright associated with this code. Use it as you wish.
+*)
+{$C-} {$K-} {$B-} {Options}
+const
+ CYR_A=176; {0}
+ CYR_ya=239; {o}
+ uppertot=182;
+ BUFFERSIZE=16767;
+type
+ bufferptr=0..BUFFERSIZE;
+var
+ upper:array[0..222] of byte; { values }
+ uppers:array[0..64] of byte; { start }
+ upperm:array[0..63] of boolean; {multi-letter}
+ upperu:byte; { used pointer }
+ infile,outfile:file;
+ inbuf,outbuf:array[0..BUFFERSIZE] of byte;
+ inbufptr,outbufptr,inbuflen:integer;
+ c,i,xbyte:byte;
+
+{We buffer I/O because otherwise it's agonizingly slow}
+function getbyte:boolean; {true if read xbyte, false if end of file}
+begin
+getbyte:=true;
+if inbufptr>=inbuflen then begin
+ blockread(infile, inbuf, BUFFERSIZE+1, inbuflen);
+ if inbuflen=0 then
+ getbyte:=false;
+ inbufptr:=0;
+ end;
+xbyte:=inbuf[inbufptr];
+inbufptr:=inbufptr+1;
+end;
+
+procedure putbyte;
+begin
+outbuf[outbufptr]:=xbyte;
+if outbufptr=BUFFERSIZE then begin
+ blockwrite(outfile, outbuf, BUFFERSIZE+1);
+ outbufptr:=0;
+ end
+else
+ outbufptr:=outbufptr+1;
+end;
+
+procedure closefiles;
+begin
+close(infile);
+if outbufptr>0 then
+ blockwrite(outfile, outbuf, outbufptr);
+close(outfile);
+end;
+
+{Standard PASCAL does not allow statically initialized arrays}
+procedure add1(u1:char);
+begin
+upperm[c]:=false;
+uppers[c]:=upperu;
+upper[upperu]:=ord(u1);
+upperu:=upperu+1;
+c:=c+1;
+end;
+
+procedure add5(u1,u2,u3,u4,u5:char);
+begin
+upperm[c]:=true;
+uppers[c]:=upperu;
+upper[upperu]:=ord(u1);
+upper[upperu+1]:=ord(u2);
+upper[upperu+2]:=ord(u3);
+upper[upperu+3]:=ord(u4);
+upper[upperu+4]:=ord(u5);
+upperu:=upperu+5;
+c:=c+1;
+end;
+
+procedure add7(u1,u2,u3,u4,u5,u6,u7:char);
+begin
+upperm[c]:=true;
+uppers[c]:=upperu;
+upper[upperu]:=ord(u1);
+upper[upperu+1]:=ord(u2);
+upper[upperu+2]:=ord(u3);
+upper[upperu+3]:=ord(u4);
+upper[upperu+4]:=ord(u5);
+upper[upperu+5]:=ord(u6);
+upper[upperu+6]:=ord(u7);
+upperu:=upperu+7;
+c:=c+1;
+end;
+
+procedure add9(u1,u2,u3,u4,u5,u6,u7,u8,u9:char);
+begin
+upperm[c]:=true;
+uppers[c]:=upperu;
+upper[upperu]:=ord(u1);
+upper[upperu+1]:=ord(u2);
+upper[upperu+2]:=ord(u3);
+upper[upperu+3]:=ord(u4);
+upper[upperu+4]:=ord(u5);
+upper[upperu+5]:=ord(u6);
+upper[upperu+6]:=ord(u7);
+upper[upperu+7]:=ord(u8);
+upper[upperu+8]:=ord(u9);
+upperu:=upperu+9;
+c:=c+1;
+end;
+
+procedure add10(u1,u2,u3,u4,u5,u6,u7,u8,u9,u10:char);
+begin
+upperm[c]:=true;
+uppers[c]:=upperu;
+upper[upperu]:=ord(u1);
+upper[upperu+1]:=ord(u2);
+upper[upperu+2]:=ord(u3);
+upper[upperu+3]:=ord(u4);
+upper[upperu+4]:=ord(u5);
+upper[upperu+5]:=ord(u6);
+upper[upperu+6]:=ord(u7);
+upper[upperu+7]:=ord(u8);
+upper[upperu+8]:=ord(u9);
+upper[upperu+9]:=ord(u10);
+upperu:=upperu+10;
+c:=c+1;
+end;
+
+procedure initialize;
+begin
+{We add the being/end group characters to suppress all ligatures. }
+{We could get rid of most of these if we delete the ligtable }
+upperu:=0;
+c:=0;
+add1('A'); {0}
+add1('B'); {1}
+add1('V'); {2}
+add1('G'); {3}
+add1('D'); {4}
+add1('E'); {5}
+add5('{','\','Z','h','}'); {6}
+add1('Z'); {7}
+add1('I'); {8}
+add5('{','\','U','i','}'); {9}
+add1('K'); {:}
+add1('L'); {;}
+add1('M'); {<}
+add1('N'); {=}
+add1('O'); {>}
+add1('P'); {?}
+add1('R'); {@}
+add1('S'); {A}
+add1('T'); {B}
+add1('U'); {C}
+add1('F'); {D}
+add5('{','\','K','h','}'); {E}
+add5('{','\','T','s','}'); {F}
+add5('{','\','C','h','}'); {G}
+add5('{','\','S','h','}'); {H}
+add7('{','\','S','h','c','h','}'); {I}
+add10('{','\','c','D','p','r','i','m','e','}'); {J}
+add1('Y'); {K}
+add9('{','\','c','P','r','i','m','e','}'); {L}
+add5('{','\','E','e','}'); {M}
+add5('{','\','Y','u','}'); {N}
+add5('{','\','Y','a','}'); {O}
+add1('a'); {P}
+add1('b'); {Q}
+add1('v'); {R}
+add1('g'); {S}
+add1('d'); {T}
+add1('e'); {U}
+add5('{','\','z','h','}'); {V}
+add1('z'); {W}
+add1('i'); {X}
+add5('{','\','u','i','}'); {Y}
+add1('k'); {Z}
+add1('l'); {[}
+add1('m'); {\}
+add1('n'); {]}
+add1('o'); {^}
+add1('p'); {_}
+add1('r'); {`}
+add1('s'); {a}
+add1('t'); {b}
+add1('u'); {c}
+add1('f'); {d}
+add5('{','\','k','h','}'); {e}
+add5('{','\','t','s','}'); {f}
+add5('{','\','c','h','}'); {g}
+add5('{','\','s','h','}'); {h}
+add7('{','\','s','h','c','h','}'); {i}
+add10('{','\','c','d','p','r','i','m','e','}'); {j}
+add1('y'); {k}
+add9('{','\','c','p','r','i','m','e','}'); {l}
+add5('{','\','e','e','}'); {m}
+add5('{','\','y','u','}'); {n}
+add5('{','\','y','a','}'); {o}
+uppers[c]:=upperu;
+
+if upperu<>uppertot then
+ writeln('Warning: upperu=',upperu:1,' uppertot=',uppertot:1);
+end {initialize};
+
+procedure openfiles;
+var
+ filename: packed array[0..60] of char;
+begin
+repeat
+ write('Input file: ');
+ readln(filename);
+ assign(infile,filename);
+ {$I-} reset(infile,1); {$I+}
+until ioresult=0;
+repeat
+ write('Output file: ');
+ readln(filename);
+ assign(outfile,filename);
+ {$I-} rewrite(outfile,1); {$I+}
+until ioresult=0;
+
+inbufptr:=1;
+inbuflen:=0;
+outbufptr:=0;
+end {openfiles};
+
+begin {main}
+
+initialize;
+{
+for c:=0 to 63 do begin
+ if upperm[c] then
+ for i:=uppers[c] to uppers[c+1]-1 do write(chr(upper[i]))
+ else write(upper[uppers[c]]);
+ writeln;
+end;
+}
+openfiles;
+
+while getbyte do begin
+if (xbyte>=CYR_A) and (xbyte<=CYR_ya) then begin
+ c:=xbyte-CYR_A;
+ if upperm[c] then begin
+ for i:=uppers[c] to uppers[c+1]-1 do
+ begin
+ xbyte:=upper[i];
+ putbyte;
+ end
+ end
+ else begin
+ xbyte:=upper[uppers[c]];
+ putbyte;
+ end
+ end
+else
+ putbyte;
+end;
+closefiles;
+end.