diff options
author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
---|---|---|
committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /language/cyrillic |
Initial commit
Diffstat (limited to 'language/cyrillic')
-rw-r--r-- | language/cyrillic/doc/00readme.tex | 4 | ||||
-rw-r--r-- | language/cyrillic/doc/cyr.note | 34 | ||||
-rw-r--r-- | language/cyrillic/doc/cyracc.def | 272 | ||||
-rw-r--r-- | language/cyrillic/doc/cyrillic.ligs | 62 | ||||
-rw-r--r-- | language/cyrillic/doc/cyrillic.notes | 419 | ||||
-rw-r--r-- | language/cyrillic/doc/cyrmemo.def | 85 | ||||
-rw-r--r-- | language/cyrillic/doc/cyrmemo.tex | 171 | ||||
-rw-r--r-- | language/cyrillic/doc/lettermappings | 211 | ||||
-rw-r--r-- | language/cyrillic/doc/rsam.ter | 999 | ||||
-rw-r--r-- | language/cyrillic/inputs/rmacro.sty | 106 | ||||
-rw-r--r-- | language/cyrillic/programs/gost2ascii.c | 28 | ||||
-rw-r--r-- | language/cyrillic/programs/trr.pas | 259 |
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. |