Документ взят из кэша поисковой машины. Адрес оригинального документа : http://herba.msu.ru/shipunov/software/tex/catlatex.pdf
Дата изменения: Sat Jun 22 02:50:08 2002
Дата индексирования: Tue Oct 2 02:43:05 2012
Кодировка: Windows-1251

.. , ..

A L TEX

Draft, 1996 .

A L TEX
, , , ( , \name name). , , . 0 10 20 30 40 50 60 70 80 90 100 110 120 0 ` ffi ( 2 < F P Z d n x 1 ? е - ffl ) 3 = G Q [ e o y 2 ^ 3 ~ ! + 5 ? I S ] g q { 4 Е " , 6 @ J T ^ h r | 5 i # 7 A K U _ i s } 6 њ " $ . 8 B L V ` j t ~ 7 " ff % / 9 C M W a k u 8 fi & 0 : D N X b l v 9 ? fl ' 1 ; E O Y c m w

* 4 > H R \ f p z

\ , , . \ . , TEX . \TeX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TEX \TeX\ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TEX , : $x>0,\ y\le 1,\ z\ge 2$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x > 0, y 1, z 2 2

. $x>0$, $y\le1$, $z\ge2$ ( , , ). . !` !` LR . . \! (-1/6 . \quad). ! , "" : $\int\!\!\!\int_{\cal D} {e^{x+y}\over x+y+1}dxdy$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . " . , "F1 17. . \chari. \"char (Е char o) LR . \"e, \"a, \"o, \"O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Е, Е, Е O e a o, Е i \"\i ( \"i Е i). . #i , (i 1 9 ). \# # . . $form $ form , , . , $x - y > 3$ x - y > 3. A L TEX , , $x - y > 3$ \begin{math}x - y > 3\end{math}, , , . . \$ $ . . $$form $$ , , form . , $$x - y > 3$$ x - y > 3.
A L TEX , , \[x - y > 3\] \begin{displaymath}x - y > 3\end{displaymath}. , ex+y D x+y +1

dxdy

3

\documentstyle fleqn, , displaymath \[ \], , \mathindent , , - . , \documentstyle fleqn, \[ \]. % . TEX , , , ( , , - ). , ( TEX'). \% % . . & . . \& & . . ' , , $x'$ x . \'char (? char LR o) , tabbing. \a'char. . $form $ LR , form ; \begin{math} form \end{math} $form $. $, $ . \) . \(. *{i}{pre } , array tabular . i pre , i , pre . \* : $(x+y)\*(z+t)$. , (x + y )(z + t). , ( + )Ч , (z + t) . .

4

+ + . . \+ tabbing left-margintab ( ) 1. . tabbing. . \, ( ). 3mu. (. \quad), $\int_a^bf(x)dx$, $\int_a^bf(x)\,dx$ . . . . . . . . . . . . . . - -; (-). en- - (-) em- (--) LR . \- tabbing , . , . tabbing left-tab-margin ( ) 1. . tabbing. . \.char (o) char LR . . \/ ( , , ). , : {\it Good} buy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Good buy {\it Good}\/ buy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Good buy {\sl Good} buy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Good buy {\sl Good\/} buy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Good buy : . : ( ). ; \colon. . \boldmath. \: ( ), . 4mu plus 2mu minus 4mu. , plain TEX'e \>. . \; ( ), . 5mu plus 5mu. . 5
b a

f (x)dx,

b a

f (x) dx

< <. \langle. !`, \tt, <.1 \< tabbing \+. . tabbing. . = = ; .

\= tabbing . . \=char (? char o) LR , tabbing. \a=char . \=occam, \=assis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ? occam, ? is ass \bar. , $\bar z$. plain TEXa , z z ? , \overline:

$\overline{z}+\overline{k}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . z + k $\overline{\strut z}+\overline{strut k}$ . . . . . . . . . . . . . . . . . . . . . . . . z + k \strut (): . \overline , "" . $\overline{\mathstrut(u+v)}=\overline {\mathstrut u}+\overline{\mathstrut v}$ . . . . . . . . . . . . . . . (u + v ) = u + v . > >. ; \rangle. ?`, \tt, >.2 \> tabbing . . tabbing. , plain TEX'e . . ?` ?` LR . .
1 L T X' A E <, 2 L T X' A E >,

. .

6

\@ , , , , , ( , ? , ). , . Warner Bros. . Warner Bros.\ . \@. , .

. , .

\ . , , , ; . @{text } @-, array, tabular . . text xx x xx tabular*. text , . ,

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.794 0.725 0.697 0.693 0.707 0.736 0.779 0.837 0.910 1.0

: $$ \arraycolsep=4pt \begin{array}{|l||*{10}{r@{.}l|}} x&0&1&0&2&0&3&0&4 0&6&0&7&0&8&0&9 % x^x & 0 & 794 & 0 & 725 & 0 & 697 0 & 736 & 0 & 779 & 0 & 837 \hline \end{array} $$ 7

\hline &0&5& & 1 & 0 \\ \hline & 0 & 693 & 0 & 707 & & 0 & 910 & 1 & 0 \\

\arraycolsep , , array. , *{i}{pre} i pre, pre . @- @{.} ; @- , , . @article{key, field-list } BibTEX'a, , . @book{key, field-list } BibTEX'a, , . @booklet{key, field-list } BibTEX'a , , , . @conference{key, field-list } BibTEX'a, , - . ( , @inproceedings.) @inbook{key, field-list } BibTEX'a, . . @incollection{key, field-list } BibTEX'a, , . , , . @inproceedings{key, field-list } BibTEX'a, , . ( , @conference.) \@listi , list list. , . \@listii , list list. , . 8

\@listiii , list list. , . \@listiv , list list. , . \@listv , list list. , . \@listvi , list list. , . @manual{key, field-list } BibTEX'a, . @masterthesis{key, field-list } BibTEX'a, . @misc{key, field-list } BibTEX'a, , , , . @phdthesis{key, field-list } BibTEX'a, . @proceedings{key, field-list } BibTEX'a, , . @string{abbrv =text } bib-, abbrv text , . @techreport{key, field-list } BibTEX'a, , , , . @unpublished{key, field-list } BibTEX'a, , , , , . . 9

1 1+ 1+ e-2
5 5 5

1+
5

=

5
5-1 2 5/2

- -1

5+ 2 1 2 e
/ 5

.

e-4 1+

53

/4

e-6

1 + .. . $$ {1 \over\displaystyle 1 + {\strut e^{-2\pi\sqrt{5}} \over\displaystyle 1 + {\strut e^{-4\pi\sqrt{5}} \over\displaystyle 1 + {\strut e^{-6\pi\sqrt{5}} \over\displaystyle 1 + {\rule{0mm}{2mm} \makebox[5mm]{} \atop \ddots}% }}}} = \left( {\sqrt{5} \over 1 + \sqrt[5]{5^{3/4} \left( {\sqrt{5} - 1 \over 2} \right)^{5/2} - 1}} {\sqrt{5} + 1 \over 2} \right) e^{2\pi / \sqrt{5}}. $$ . 1. , . \[form \] , form , , fleqn , \mathindent. \begin{displaymath}form \end{displaymath}. \[, \] . . $$form $$ .1, .10. \\[len ] . len , , . , . \\*[len ] \\[len ], , , , . . \] \[. form1 ^form2 form2 form1 . , $x^i$ xi . form2 , 10

. , $y^{i+1}$ y i+1 . \sp. , form1 \spform2 form1 ^form2 . . .1, .10. . \^char (^) o char LR . . form1 _form2 form2 form1 . , $x_i$ xi . form2 , . , $y_{i+1}$ yi+1 . \sb. , form1 \sbform2 form1 _form2 . . \_ _, . Plus\_Grand\_Commun\_Diviseur . . . . . . . . . Plus_Grand_Commun_Diviseur . ` . , `12 10. . \chari. \`char (` char LR o) , tabbing, \a`char . . { } , . \{ { . , \lbrace. . .5 .21 .6 .22. . | |, \vert; \left \right . . .5 .21 .6 .22. em-, \tt, |. array, tabular tabular* . . , , @{text }. . \| , \Vert; , \left \right . . .5 .21 .6 .22. . 11

} {. \} } . , \rbrace. . .5 .21 .6 .22. . ~ . \~char (~ char o) LR . . 11pt \documentstyle. , 11 , 10 . . .16, .79 .7, .24. 12pt \documentstyle. , 12 , 10 .

a
\a'char tabbing, (? char . . o) \a=char tabbing, (? char . . o) \a`char tabbing, (` char . . o) \aa -- (њ a) LR . . њ \ -- (A) LR . x = 3њ $x=3$\AA. A њ , \AA\ . . A abbrv \bibliographystyle. (, [17]). , , , . {form1 \above len form2 } form1 , form2 len . TEX'a. y +z $x+{y+z\above 1pt v+w}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x + v+w 12

a b c d e

\abovedisplayskip + \baselineskip \belowdisplayskip + \baselineskip \abovedisplayshortskip + \baselineskip \belowdisplayshortskip + \baselineskip 2 em

.................................. T a 1 . . . . . . . . . . . . . . . . .c . . . .. T b . . . .c . . . ..

............................................ . T . . . c .e .' E 2 . . . . . . . . . . . . . . . . . . .c . . . .. T d . . . .c . . . ..

. 2. "" "" .

13

$\displaystyle x+{y+z\above 1pt v+w}$ . . . . . . . . . . . . . . . . . . . . . . x +

y+z v+w

\abovedisplayshortskip , , "" , \documentstyle fleqn ( , \baselineskip). "" , e .2 .13 2 em, m . , . . \abovedisplayskip. ( TEX'a . , .) , \protect. \abovedisplayskip , , "" , \documentstyle fleqn ( , \baselineskip). "" , , 2 m . .2 .13 1 "" . , . \belowdisplayskip \belowdisplayshortskip. plain : \abovedisplayskip=12pt plus 3pt minus 9pt \abovedisplayhortskip=0pt plus 3pt \belowdisplayskip=\abovedisplayskip \belowdisplayshortskip=7pt plus 3pt minus 3pt ( TEX'a . , , .). , \protect. abstract , article report . document \maketitle. . .7, .24. , \noindent. \acute . , $\acute x$ x. . ?

14

\addcontentsline{ext}{sec-unit}{entry} , ext , lof, lot toc. secunit , ; ext lof, sec-unit figure, ext lot, sec-unit table, ext toc, sec-unit part, chapter ( article), section, subsection, paragraph subparagraph. (, sec-unit , , section, \section). entry , , , , . , , , entry \numberline. , : \addcontentsline{lof}{figure} {\protect\numberline{12.3} { .}} entry \numberline , , . address BibTEX'a, . , . \address{text } , letter. . text \\. . letter \addtocontents{ext }{text} text , ext , lof, lot toc. text , . text , , A L TEX'a. \addtocounter{ctr }{i} , ctr i ctr . , 3 , footnote: \addtocounter{footnote}{-1} , footnote 1, 3 . .
3 3

footnote , c 1 .

15

\addtolength{cmd }{len} cmd , , len . .3 .17, . 4 .18. . \addvspace{len } len . : \addvspace{len 1 }\addvspace{len 2 }, leni , leni len1 len2 . , , , , . . \ae , LR (ж) ( oe \oe). ros\ae, \oe d\`eme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . rosж, oed`me e , , , ? . \AE , LR (Ж). \AE SOPE ЖSOPE. , \AE . . \aleph , . . alph \pagenumbering. , . \alph{ctr } ctr , 27 . , \alph{page} p. . Alph \pagenumbering. , . . \pagenumbering. \lph{ctr } ctr , 27 . , \Alph{page} P. . alpha \bibliographystyle. , . , [Lak76]. \alpha , . . 16

\begin{figure}[p] {\parskip=-1.5pt {\large \setlength{\parindent}{1in} - \addtolength{\parindent}{1em}\par \addtolength{\parindent}{4em}\par : `` \addtolength{\parindent}{.5em}\par \addtolength{\parindent}{0.5em}\par -\par} {\normalsize \setlength{\parindent}{1.9in} , \addtolength{\parindent}{-1.5em}\par \addtolength{\parindent}{-.5em}\par \addtolength{\parindent}{-1em}\par , \addtolength{\parindent}{-1em}\par {\it } \addtolength{\parindent}{-.5em}\par -\par} {\small \setlength{\parindent}{1.35in} . \addtolength{\parindent}{1.5em}\par \addtolength{\parindent}{1.5em}\par ... \par} {\footnotesize \setlength{\parindent}{2.45in} \addtolength{\parindent}{3em}\par \addtolength{\parindent}{-2em}\par \addtolength{\parindent}{-1.5em}\par .''\par} {\scriptsize \setlength{\parindent}{2.1in} \addtolength{\parindent}{-1.75em}\par ... .'' \addtolength{\parindent}{.5em}\par --- ,\par}{\tiny \setlength{\parindent}{1.75in} \addtolength{\parindent}{-1.5em}\par , --\addtolength{\parindent}{-1.5em}\par - \addtolength{\parindent}{-1em}\par ... \addtolength{\parindent}{-1.5em}\par \addtolength{\parindent}{1.25em}\par \addtolength{\parindent}{1em}\par .~ \addtolength{\parindent}{.75em}\par~\par}} \caption{ `` ''.} \label{taleout} \end{figure} . 3. " " .

17

- : " , , . , ,
."
: " , , ." ,

, - . , .

. 4. " ".

18

\amalg

. . y

$x\amalg y$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x \coprod: $\amalg$ $\coprod$ $\displaystyle\coprod$ . . . . . . . . . . . . . . . . . . . . .

and author editor BibTEX'a . and others BibTEX'a. `et al.' \and \author. . \angle , . $\angle AMB$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AM B -: $\widehat{ABM}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AB M . annote BibTEX'a. , . \appendix , . book report "" , article "" . . . \approx , . , \simeq ( ) \cong ()? . = arabic \pagenumbering. , . . \pagenumbering. \arabic{ctr} ctr . , \arabic{page} 19. . \arccos (arccos), . , . .

19

\arcsin (arcsin), . , . . \arctan (arctan), . , . \arctg: \def\arctg{\mathop{\rm arctg}\nolimits} . \arg (arg), : $\arg(zz')=\arg z+\arg z'$ . . . . . . . . . . . . . . . . . . . . . . arg(z z ) = arg z + arg z , . . array , , . : $$ \begin{array}{ccc} \bf \Phi & \Psi & B \\ \mit\Gamma & \Gamma & \cal S \\ T & \rm A & Z \end{array} $$

B S TAZ

, , . , : &, \\ \end{array}. \arraycolsep , , , array. . @{text }. , \protect. \arrayrulewidth , , array. , \protect. \arraystretch . ,

20

\left( \tempest \right)

\left\{ \tempest \right\}

\left[ \tempest \right]

\left\lgroup \tempest \right\rgroup

\left\lceil \tempest \right\rceil

\left\lfloor \tempest \right\rfloor

\left\uparrow \tempest \right\Uparrow

\left\updownarrow \tempest \right\Updownarrow

\left\downarrow \tempest \right\Downarrow

\left\lmoustache \tempest \right\rmoustache

\left\arrowvert \tempest \right\Arrowvert

\left\bracevert \tempest \right\bracevert

\left\langle \tempest \right\rangle

\left\vert \tempest \right\Vert

\left\backslash \tempest \right/

\def\tempest% {\begin{array}{ccc} 2 & 7 & 6 \\ 9 & 5 & 1 \\ 4&3&8 \end{array}} . 5. TEX'e ( ). array, tabular tabular*, , . 1, 1.25, , \renewcommand \def, 1.25 . \arrowvert , \left \right , .5 .21 .6 .22, . \rrowvert , \left \right , .5 .21 21

276 9 5 1 438

2 9 4

7 5 3

6 1 8 6 1 8 6 1 8

27 9 5 43 2 9 4

6 1 8

2 7 6 9 5 1 438

2 9 4 2 9 4

7 5 3

7 6 5 1 38

2 7 6 9 5 1 4 3 8 2 7 6 9 5 1 438

7 5 3

2 7 9 5 43

6 1 8

2 7 9 5 4 3 2 9 4

6 1 8

2 9 4 2 9 4

7 5 3

6 1 8

276 951 438

76 51 38

7 5 3

6 1 8

. 6. TEX' () .6 .22, . article , doc-style \documentstyle. "", , () . , , , . plain, , , . \raggedbottom, , . BibTEX, \bibliographystyle document, \bibliography. , , .7, .24.

22

thebibliography, \end{document} ( , ). \maketitle, , , document. \maketitle, \title \author. \date, ; \date , . , . , , , \documentstyle titlepage. ( , .) \title. , , \title \\. \title \thanks. . \author. , \and. , \title, \\ \thanks . \date (, , ). , A L TEX' . , \title, \\, \thanks. , abstract. document; \maketitle. article : \part, \section, \subsection, \subsubsection, \paragraph \subparagraph. .8, .24 , , , , , , , , .4 , , , tocdepth secnumdepth. ( ) , tocdepth,
4 \tableofcontents.

,

,

23

\documentstyle[11pt,own,russian]{article} \title{ \LaTeX } \author{.\and .} \begin{document} \bibliographystyle{plain} \maketitle \begin{abstract} \noindent \LaTeX ... \end{abstract} \noindent . \nocite{*} \bibliography{pom} \end{document} . 7. article \part \section \subsection \subsubsection \paragraph \subparagraph 0 1 2 3 4 5

. 8. article. , secnumdepth. 3. .8, .24 , . , , . , , \section, section. , , . , . equation eqnarray,

24

, 1. , , 1. , , 1. , , , 1. \ast , . . . \asymp . . ,

{form1 \atop form2 } , : form 1 form 2 : $x+{u\atop v+w}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x + $\displaystyle x+{u\atop v+w}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x + $\displaystyle S=\sum_{\scriptstyle 1 1
u v+w
JK

Ai B

\scriptstyle . , . \scriptscriptstyle (5 7), \atop . TEX'a. {form1 \atopwithdelims delim1 delim2 form2 } , , form1 form2 , , delim1 , a delim2 : \def\toto{\atopwithdelims<>} $q+{x+u \toto x+vw}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . q + $\displaystyle q+{x+u \toto x+vw}$ . . . . . . . . . . . . . . . . . . . . . . q +
x+u x+v w

x+u x + vw TEX'a, \brace, \brack \choose. author BibTEX'a, . \author{text} , . text , \and. text \\ , \thanks, . \thanks , , , \ . 25

aux , , .

b
\b char \b{char} (o) ? char LR . \b x, \b o, \b k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x, o, k ??? \underline, . , , : $\underline{PAO}$, \underline{PAO} . . . . . . . . . . . . . . . . . . . . . . . . . P AO, PAO . \backslash \ ( ). : $H\backslash G/K$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H \G/K \setminus ( ), : $H\setminus G$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H \ G $H\backslash G$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H \G `\' \tt, \char`\\. \backslash \left \right, (. .5 .21 .6 .22). . \bar (x). ? . , : , z $\bar z$. \overline: $\bar z+\bar k$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . z + k ?? $\overline{z}+\overline{k}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . z + k $\overline{\mathstrut z}+\overline{\mathstrut k}$ . . . . . . . . . . . . . . z + k \mathstrut ( , ). \overline . .

26

\baselineskip , , \baselinestretch, . ( TEX'a.) , . , \par: {\baselineskip=14pt...\par}, . , , , . , , . , \baselineskip , , \tiny \large. ( . \baselineskip . , \baselinestretch.) \protect. \baselinestretch , 1. \baselineskip, \baselinestretch. \batchmode , TEX'. ( \documentstyle), , TEX , . .log. .bbl , BibTEX'a , . - , . \begin{env} env . \end{env}. . \belowdisplayshortskip , , "" , \documentstyle fleqn. "" , \abovedisplayshortskip, 27

- . . . - . . . - . . . - . . . - . . . - . . . - ... . . . . . . . {\bf {\it {\rm {\sc {\sf {\sl {\tt {\bf {\it {\rm {\sc {\sf {\sl {\tt

- - - - - - - {\em \/} \/ {\em } {\em \/} {\em \/} {\em \/} \/ {\em } {\em \/} ...} ...} ...} ...} ...} ...} ...}

.} .} .} .} .} .} .}

. 9. , . .2, .13. TEX'a, , , \protect. \belowdisplayskip , , "" , \documentstyle fleqn. "" \abovedisplayshortskip .2, .13. TEX'a, , , \protect. \beta , . . \bf , . .9 .28. , .. : {\bf } . . . . . . . . . . . . . . . , \bf .... , - (, \rm, \it \sl). . .bib , BibTEX'a. 28

\bibindent , \documentstyle openbib , thebibliography. , \protect. \bibitem[text]{key } , thebibliography. key , , . \cite A . text , L TEX , , , [31]. ( text ) [text]. , text . . \bibliography{bib-file-list} \cite{key}, BibTEX , bib-file-list, key . , , , bib-. bib-file-list , . \bibliographystyle{bib-style } BibTEX' , . bib-style abbrv, alpha, plain unsrt. , , agsm, dcu kluwer, harvard \documentstyle. \big plain TEX. . . : \big ( , , , ..) , : \bigl, \bigr \bigm. \bigl , \bigr (`l' `r' ): $f\bigl(x+(y+z)\bigr)$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . f x + (y + z ) . , . \bigm : $(x\in A(n)|y\in B(m))$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (x A(n)|y B (m)) $\big(x\in A(n)\big|y\in B(m)\big)$ . . . . . . . . . . . . . . x A(n) y B (m) $\bigl(x\in A(n)\bigm|y\in B(m)\bigr)$ . . . . . . . . . x A(n) y B (m) , : \big , \bigl , \bigr \bigm, .

29

, \Big, \bigg : \Biggl(\biggl(\Bigl(\bigl( () \bigr)\Bigr)\biggr)\Biggr)
i=N

()
i=1 k=1

\Big plain TEX. 50% "" \big. , - : \Bigl, \Bigr, \Bigm, \Big. . . \bigcap . : U
U A

$\displaystyle\overline A= \bigcap_{U\supset A}U$ . . . . . . . . A =

, `A'. A, \overline{\! A}. , . , . . \bigcirc \bigcup . . . . :

$\displaystyle{\buildrel\circ\over A}=\bigcup_{U\subset A}U$ . . . . . . ..................................................................A =
U A

U

A , = "". \mathop{A\kern0pt}^\circ (\kern `A' ). A , (\circ) . - \circ({\buildrel\,\,\circ\over A}) :

A=
U A

U

. \bigodot , . , . , . . 30

\bigoplus :

, E
iI i

$\displaystyle E=\bigoplus_{i\in I}E_i$ . . . . . . . . . . . . . . . . . . . . E =

, . , . . \bigotimes : $\bigvee\limits^n E=\bigl({\textstyle
n

,

\bigotimes}^n E\bigr)/S_n(E)$ . . . . . . . . . . . . . . . . . . . .

E=

n

E /Sn (E )

, . , . . \bigskip , \bigskipamount \vspace{\bigskipamount}. , plain TEX'e. . \bigskipamount , 12pt plus 4pt minus 4pt. \bigsqcup , . , . , . . \bigtriangledown . . \bigtriangleup . . , , -

\biguplus , . , . , . . \bigvee , . , . 31

, . . \bigwedge , . , . , . . .blg , BibTEX'a. , BibTEX'. \bmod ( mod ), . . \boldmath , , , , , ( ), . : , + : ; ! ? ( ) [ ] , ( ), , \left \right. . book , doc-style \documentstyle. book report (. ), . \documentstyle twoside, . . headings, , , . , \pagestyle myheadings , plain empty. \raggedbottom, . , , \flushbottom . \maketitle document . , \author \title \date; \thanks. book abstract. eqnarray, , X.1, X , X.2, .. , X.1, X.2, . . ., X . 32

\part \chapter \section \subsection \subsubsection \paragraph \subparagraph

-1 0 1 2 3 4 5

. 10. book report.

(X.1, X.2, . . ., X ). , , , , , , X.1 eqnarray, \chapter, X 0. . article .5 .33. booktitle BibTEX'a. , . \bordematrix plain TEX'a . . : \bordematrix{form11 & form12 & . . . & form1n \cr form21 & form22 & . . . & form2n \cr . . . formm1 & formm2 & . . . & formmn \cr} \pmatrix, : $$A=\bordermatrix{ &p &q p & I_p & O q&O & J_q \cr \cr \cr

}$$

A=

p q

p Ip O

q O Jq

n Ч n (n + 1) Ч (n + 1), (1, 1) . TEX , . \bot , . $(E+F)^\bot=E^\bot\cap F^\bot$ . . . . . . . . . . . . . . . . . . . (E + F ) = E F

\perp, \vdash \dashv, , , , , . . 33

\bottomfraction 0 1. , . \def \renewcommand. 0.3. twocolumn, ; . bottomnumber , , , , . 1. twocolumn, . . \bowtie . . , -

\Box P, . , plain TEX'e . . bp TEX'a (big point), , : 1 =72 bp. (, 1 bp= 0.0139in= 0.35mm= 1.004pt). {form1 \brace form2 } , form1 form2 , , . plain TEX'a. . \over: $p+{n \brace k}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p + $\displaystyle p+{n \brace k}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p +
n k

n k

\bracevert , \left, \right , .5, .21 .6, .22. {form1 \brack form2 } , form1 form2 , , . plain TEX'a. \over. $k+{n\brack k}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . k + $\displaystyle{n\brack k}+k$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
n k

n +k k

\breve "" ( ). . $\breve a$, $\breve x$, $t\,\breve{}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . a, x, t . 34

\buildrel plain TEX - . : $x \buildrel def \over{=} 1$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x = 1 $x\buildrel\mbox{\scriptsize } \over{\longrightarrow} 0$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x - 0 $T\buildrel\mbox{\scriptsize }\over {\hbox to 2cm{\rightarrowfill}} 1$ . . . . . . . . . . . . . . . . . . . . T - - - - - 1 - - - -
A L TEX \stackrel def

. .

\bullet ћ, . `', $\circ$. ( !).

c
\c char \c{char} (o) е char LR : hame\c con, FRAN\c CON, \c S . . . . . . . . . . . . . . . . . . . hameе , FRANCON, S con е е \cal . : $\cal A$, ${\cal H}-{\cal X}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A, H - X , : $\cal A*b+c*T+x/y-z$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A + T + / - . \cap : $A\cap B)\cap C=A\cap(B\cap C)$ . . . . . . . . . . . . . . A B ) C = A (B C ) . \caption{heading} , figure, figure*, table table*. . , , , heading , - \caption \label. .3 .17, . 4 .18. , : 35

.\ref{talein} .\pageref{talein}, ... .\ref{taleout} .\pageref{taleout}. \listoffigures \listoftables, heading . , heading , \protect. (). \caption[entry]{heading} , \caption{heading}, , \listoftables \listoffigures, entry . entry , heading. . \cases . Plain TEX. : , : $\varphi(x) = \cases{ 0 & $x\leq 0 $,\cr e^{-1/x}& . \cr } (x) = 0 e-1 x 0, .

/x

, $ . , (" $X\leq 0$"). , \noalign{\smallskip} \cr. cc TEX'a , 1 cc=12 dd. (, 1 cc=0.1777 in=4.51 mm=12.84 pt.) \cc{text} , letter. "carbon copies" , A . L TEX `cc:' text . .16 .79, . 17 .80. text \\. \cdot ћ (, ). . , , : $x\cdot y=x_1y_1+\cdots+x_ny_n$ . . . . . . . . . . . . . . . x ћ y = x1 y1 + ћ ћ ћ + xn y
n

, \cdotp, . . \cdotp , , , . Plain TEX, , , \cdots. 36

\cdots (ћ ћ ћ), "" , . \cdot ( `s' ). +, -, Ч, =, >, , <, . . center , ( ). , , , \\. A L TEX . \centering , , ( ), , . , TEX'a . A L TEX'e \@centering. chapter BibTEX'a, , . chapter , . 0, \chapter , . , \setcounter. (, , , 0, \setcounter{chapter}{-1}.) \chapter[entry]{heading} , . article. report book, 0. . ( , secnumdepth.) entry , ( ) heading . ( , tocdepth.) entry , heading , entry. entry , , , heading. . \chapter*{heading} , , . . \chari , i. i , , i , 15 '17 "F . \char`017, \char 15 \char"F , ASCII 15. `ffl' `ffl' . \tt `'.

37

TEX , , : \char`\A , ASCII- , A ( `\ , ). , \tt, \char`\{ `{', \char`\\ `\' ( !). , , ( `ffl' ). TEX', . \check "", . , . $\check x*\check C+D\check{}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x C + D "" . , "" `D'. , : \def\tcheche#1{#1\mkern2.5mu\check{}} \mkern . mu ( ). ? , : \displaystyle, \textstyle, \scriptstyle \scriptscriptstyle. mu . ( $\tcheche A+\tcheche B$): A+ B+ C+ D+ M+ X+ Y + Z A+ B+ C+ D+ M+ X+ Y + Z
A B C D M X Y Z +++++++
A B C D M X Y Z ++++ +++

. \chi . . {form1 \choose form2 } , form1 form2 , , . plain TEX'. \over, " " \atopwithdelims: $p+{n\choose n+k}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p + $\displaystyle p+{n\choose n+k}$ . . . . . . . . . . . . . . . . . . . . . . . . . . p +
n n+k

n n+k

38

'$ # "! &% `a b c d e f g h i j k l m n pq r s t u v w x y z { | } ~

\unitlength=1pt \begin{picture}(122,200)(-25,-120) \put(30,40){\circle{16}} \put(30,40){\circle{20}} \put(30,40){\circle{24}} ... \put(0,0){\circle{1}} \put(0,-1.5){\circle{2}} \put(0,-4.0){\circle{3}} ... \put(60,0){\circle*{1}} \put(60,-1.5){\circle*{2}} \put(60,-4.0){\circle*{3}} ...

. 11. , picture. \circ , . $(f\circ g)'=f'\circ g\times g'$ . . . . . . . . . . . . . . . . . . . (f g ) = f g Ч g , , : $u{\circ}v$, $u\mathord\circ v$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . uv , uv , , : 1 ), 1$^\circ$). . \circle{d} , \put \multiput picture. , \put(i, j ){\circle{d}} d , (i, j ). , A L TEX . , , 40 pt ( ). . A , , L TEX , . . .11 .39. . \circle*{d} , \circle{d}, , A . , L TEX 39

. , , , 15 ( ). . A , , L TEX , . . .11 .39. . \cite[text ]{key-list } , BibTEX'o . key-list , , bib, thebibliography. , thebibliography: \begin{thebibliography} \bibitem{...} ... \bibitem{Lamp} Leslie Lamport, ``{\it \LaTeX\ A Document Preparation System}'', Addison-Wesley, 1986. \bibitem{...} ... \end{thebibliography} [2] \cite{Lamp}. text , . . \cleardoublepage . , , \flushbottom. "". , , . twocolumn, \cleardoublepage , . . \clearpage . . , , \flushbottom. , "", . twocolumn, \clearpage , . . \cline{i-j } array, tabular tabular*. \hline

40

, i- j -, . i, j , . , , \\ \cline. tabular array: $13.65 .01 92.50 33.33 8.99 \begin{tabular}{||l|lr||} & &\$13.65 \\ \cline{2-3} & & .01 \\ & & 92.50 \\ \cline{1-1} \cline{3-3} & & 33.33 \hline & & 8.99 \hline \end{tabular} \hline

\hline

\\ \\

1 0 C= 0 0

0 1 0 0

0 0

0 0 1 0

0

. 0

$$ \def\temp{\multicolumn{1}{c|}{0}} C = \left[ \begin{array}{cccccc} 1 & 0 & \ast & 0 & \ast & \ast \\ \cline{1-1} \temp & 1 & \ast & 0 & \ast & \ast \\ \cline{2-3} 0 & 0 & \temp & 1 & \ast & \ast \\ \cline{4-6} 0 &0&0 &0&0 &0 \end{array} \right]. $$ , text . .16 .79,

\closing{text } , letter. . , . 17 .80.

\clubsuit , . .

41

cm TEX'a , , : 1 =2.54 cm. (, 1 cm=0.3937 in=28.45 pt.) \colon plain TEXa (:) : : . . , \colon. : f: X Y f :XY

$f \colon X \to Y$ $f : X \to Y$

\columsep , , \documentstyle twocolumn. , \protect. \columseprule , , , \documentstyle twocolumn. 0 , , . , \protect. \cong , = . \simeq, .. \coprod , ( ) . . \amalg: $\amalg$, $\coprod$, $\displaystyle\coprod$ . . . . . . . . . . . . . . . . , , .

, . , . . \copyright c . . \cos (cos), . $\cos^2x+\sin^2x=1$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cos2 x + sin2 x = 1 . .

42

\cosh (cosh), . $\cosh^2t-\sinh^2t=1$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cosh2 t - sinh2 t = 1 \cosh , : \def\ch{\mathop{\rm ch\nolimits}} . . \cot (cot), . cotg, , \ch. $\cot(x)=\cos(x)/\sin(x)$ . . . . . . . . . . . . . . . . . . . . . . . . . cot(x) = cos(x)/ sin(x) . . \coth (coth), . $\coth x=\cosh x/\sinh x$ . . . . . . . . . . . . . . . . . . . . . . . . . coth x = cosh x/ sinh x , . ? . . \cr TEX'a, \bordermatrix, \cases, \displaylines, \matrix, \pmatrix . . . \csc (csc), . . . \cup , . $(A\cup B)\cap C=(A\cap C) \cup(B\cap C)$ . . . . . . . . . . . . . . . . . . . . . . . . . . . (A B ) C = (A C ) (B C ) \bigcup: $\cup$, $\bigcup$, $\displaystyle\bigcup$ . . . . . . . . . . . . . . . . . . . . , ,

, , \bigcap. .

d
43

\d char \d{char } (o) . char LR . kr\d sna, KR\d SNA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . krsna, KRSNA . . . \dag "" . . \dagger , . . \dashbox{h}(i, j )[pos]{ } picture. , . , \makebox (. ), h, , . .12, .45. . \dashv , . ( ), \vdash. . \date{text} (1) , text , . , A L TEX' . , , text \\, \thanks, , . \thanks , , \ . (2) letter, . text \\, \thanks. \dblfloatpagefraction , twocolumn. 0 1, , , . , 0.6, 60% . \def \renewcommand. 0.5. \dblfloatsep \documentstyle twocolumn,

44

d d d d d d d d d

\begin{center} % \unitlength=1mm \begin{picture}(110,50)(0,5) % \put(55,45){\makebox(0,0){ }} \put(20,5){\makebox(0,0)% {\framebox(50,9){ }}} \put(90,5){\makebox(0,0){\dashbox{1.5}(58,9)% { }}} % \put(50,40){\line(-1,-1){30}} \put(60,40){\line(1,-1){30}} % \end{picture} % \end{center} . 12. \makebox, \dashbox \framebox picture.

45

. , , , . , \protect. \dbltextfloatsep , , twocolumn. , . , \protect. \dbltopfraction , twocolumn. 0 1, , . 0.7 \def \renewcommand. dbltopnumber , , twocolumn. , . 2. dd TEX'a (didot point ), , 1157 dd=1238 pt. (, 1 dd=0.0148 in=0.376 mm=1.07 pt.) \ddag . . \ddager , . . \ddot . , : $\ddot x(t)=f(x,t)$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x(t) = f (x, t) Е . . \ddots . . , , . . \defcmd #1#2...#i{def } cmd , def . 9 . , cmd{arg1 }{arg2 }. . . {argi }, def , #j ( 1 j i) argi . , , #j . \def. 20 (1993). TEX'a. 46

\deg , "deg" . : $\deg(FG)=\deg F+\deg G$ . . . . . . . . . . . . . . . . . . . . . . . deg(F G) = deg F + deg G , : \def\degres{$^\circ$} 138\degres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 . . \delta , . \partial. . \Delta , . . description . \item[text ] text . , \begin{description} \item[] ``'' , . \item[] , . \item[] , . \end{description} - : "" , . , . , . , \item, , , A L TEX', . \item , , , , : \begin{description} \item[\tt chapter] , \item[${[x]}X$]

\LaTeX' .

47

. \item[\it ] . \end{description} :
A chapter , L TEX' .

[x]X . . \item[${[x]}X$] . , A L TEX , , , . \det det ( ). : $\det A\ne 0$, $A^{-1}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . det A = 0, A-1 . \left|\matrix{...}\right|. , . . \diamond , . $x\diamond y=xy/(x+y)$ . . . . . . . . . . . . . . . . . . . x y = xy /(x + y ) . \Diamond Q, . , plain TEX'e . . \diamondsuit , . . \dim (dim) ( ). : $\dim(U+V)=\dim U+\dim V-\dim U\cap V$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . dim(U + V ) = dim U + dim V - dim U V . . \displaylimits cmd\displaylimits_form1 ^form2 ( ) form1 , cmd , form2 . ( , , ...), \limits \nolimits. TEX'a. \displaylines{form1 \cr form2 \cr ...formn \cr} formi . : $$\displaylines{ x_1+\cdots+x_n=y_1+\cdots+y_m,\cr A=B+C. \cr }$$ : x1 + ћ ћ ћ + xn = y1 + ћ ћ ћ + ym , A = B + C. , . , \cr. , \cr. TEX , . \cr, , , , (\crcr), TEX . , , , . , , , , .. : $$\displaylines{ ... ...\cr$$ \cr, . TEX' . . . ! TEX'a. \displaymath . : \[form\] $$form$$, 49

fleqn A \documentstyle. L TEX . \displaystyle , . TEX' , .. , : , (\textstyle). . C. \displaystyle ( \textstyle, \displaystyle, ): $\displaystyle\sum_{n=0}
n=

^{n=\infty}{x_n\over 1+x_n^2}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
n=0

xn 1 + x2 n

\textstyle: $\sum_{n=0}^{n=\infty }{x_n\over1+x_n^2}$ . . . . . . . . . . . . . . . . , \displaystyle: ${a\over b}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $\displaystyle{a\over b}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
a b n= xn n=0 1+x2 n

a b ${\displaystyle a\over b}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a b ${a\over\displaystyle b}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TEX'. . \div ч, : $15\div 4=3$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 ч 4 = 3 . \divide . TEX. \divide\dimen117 by 12 \dimen117 12, .. \dimen117:=\dimen117 div 12. .doc , , sty-, . document . A L TEX' :
a

b

50

\documentstyle[opt-list]{doc-style} dec-seq \begin{document} text \end{document}
A L TEX', \documentstyle document, . dec-seq , .

\documentstyle[opt-list]{doc-style} , A L TEX'a. . article, report, book letter, . doc-style , \documentstyle doc-style.sty. 11pt, 12pt, draft, fleqn, leqno, openbib, titlepage, twocolumn twoside.5 , . A opt , opt-list , L TEX \ds@opt ( ), opt.sty. \documentstyle ; , \batchmode, \errorstopmode, \nonstopmode \scrollmode. .16 .79, .17 .80. \dot , . . : $\dot x(t)=f\bigl(x(t),t\bigr)$ . . . . . . . . . . . . . . . . . . . . . . . . x(t) = f x(t), t plain TEX \bigl \bigr, ( , ). - a \ddot. . . \doteq =, . . \dotfill , , , .13, .52. . .
5 L T X, A E russian.

51

\makebox[2in]{\hrulefill} \makebox[2in]{\downbracefill} \makebox[2in]{\upbracefill} ................................ - - - - - - - - - - - - - - - - - - - - - - - -- -- - - - - - - - - - - - - - - - - - - - - - - - \makebox[2in]{\dotfill} \makebox[2in]{\leftarrowfill} \makebox[2in]{\rightarrowfill}

. 13. fill-.

\doublerulesep , , , || array, tabular tabular*, , \hline. , \protect. \downarrow , . \left \right . 12 , , : \left\downarrow\vbox to 6mm{}\right. . .5 .21 .6 .22. . \Downarrow , . \left \right . .. \downbracefill , , . .13, .52. draft \documentstyle. , , , . \ds@opt opt \documentstyle, \dsopt opt.sty. .dvi (device independent) , A L TEX' ( tex). 52

e
edition ( BibTEX'.) , . , 7 " ". , , . editor ( BibTEX'a.) ( , ) , ( , ). \ell , . , : $l-l*x_1^2+y_l^\alpha$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l - l x2 + y 1 $\ell-\ell*x_\ell^2+y_\ell^\alpha$ . . . . . . . . . . . . . . . . . . . . . . - x2 + y : \imath ( $\vec\jmath$ i em \quad,
l

(i) \jmath (). - ): $\vec\imath$ . . . \qquad.

. - , . \enskip \enspace

\em . \it , \rm , \em , . , \rm, \em \it, \it, \em \rm . .9 .28. . empty \pagestyle \thispagestyle. . A , L TEX . , \thispagestyle{empty}. \emptyset , . \O (Ш), . . \encl{text } letter. A . L TEX `encl:', text . text \\.

\end{env } env . . \enskip , \hskip .5em\relax) . \relax \hskip , " plus", " Plus", " minus" " Minus". TEX' , \hskip .5em plus..., plus. plain TEX'a, . \enspace , em. \enskip, , , . plain TEX'a. enumerate . A L TEX' : 1) : ) Q R (P Q) (P R). ) ((P Q) P ) P . 2) : ) (x)(P x Qx) (x)P x (x)Qx. ) (x)(y )P xy (y )(x)P xy . : \begin{enumerate} \item % \begin{enumerate} \item $Q \Rightarrow R \vdash (P \item \label{PEIRCE} $\vdash ((P \Rightarrow Q) \end{enumerate} % \item % \begin{enumerate} \item 54

:

\lor Q) \Rightarrow (P \lor R)$.

\Rightarrow P) \Rightarrow P$.

:

$(\forall x) (Px \Rightarrow Qx) \vdash (\forall x) Px \Rightarrow (\forall x) Qx$. \item $(\exists x)(\forall y) Pxy \vdash (\forall y)(\exists x) Pxy$. \end{enumerate} % \end{enumerate} . 1., 2. .., (a), (b) .., i., ii. .., A., B. .. , : enumi, enumii, enumiii enumiv. \item enumerate . , , \begin{enumerate} \item[(1)] $Q \Rightarrow R \vdash (P \lor Q) \Rightarrow (P \lor R)$. \item[(2)] $\vdash ((P \Rightarrow Q) \Rightarrow P) \Rightarrow P$. \end{enumerate} : (1) Q R (2) (P Q) (P R).

((P Q) P ) P .

\item , . enumi enumerate, enumerate. enumii enumerate, enumerate. enumiii enumerate, enumerate. enumiv enumerate, enumerate. \epsilon , . , \varepsilon, \in.

55

eqnarray ( .) , . ( , eqnarray*.) A L TEX . , \begin{eqnarray} (x + y + z)^2 & = & (x + y + z) (x + y + z), \label{BB} \\ & = & x^2 + 2xy + y^2 \nonumber \\ & & \qquad \mbox{} + 2yz + z^2 + 2zx. \label{CC} \end{eqnarray} : (x + y + z )2 = (x + y + z )(x + y + z ), = x2 + 2xy + y 2 + 2y z + z 2 + 2z x. (1) (2)

\nonumber , . eqnarray* . array rcl , , . eqnarray \multicolumn. \\, &. . - , . , \begin{eqnarray*} {[x]} E &=& {[x]} x &=& {[x]} E x & = & {[x]} E X & = & {[x]} X E & = & {[x]} X Y & = & \end{eqnarray*}

{\bf {\bf E, \\ {\bf {\bf {\bf

K} E, \\ I}, \\ B} E ([x] X), \\ C} ([x] X) E, \\ S} ([x] X) ([x] Y).

: [x]E = KE , [x]x = I, [x]E x = E , 56

[x]E X [x]X E [x]X Y

= BE ([x]X ), = C([x]X )E , = S([x]X )([x]Y ).

. , , , , - . \eqno TEX'a, , . $$e^{i\pi}=-1\eqno{\rm ()}$$ ei = -1 , \leqno: $$e^{i\pi}=-1\leqno{\rm ()}$$ ei = -1 ()

()

\rm, - , ? : , . : \eqno \displaylines. , \eqno . equation , equation eqnarray, , . equation , , . article , (1), . report book , (X.1), X , . , (x + y )(x - y ) = x2 - y 2 . : \begin{equation} (x + y)(x - y) = x^2 - y^2. \label{AA} \end{equation} 57 (3)

\label . \equiv , . $\not\equiv$. . \errorstopmode TEX', TEX, , . . , \documentstyle. \eta , . . \evensidemargin , . \evensidemargin . (. .23 .137.) , \protect. ex , `x', . . \exists , . , " ": , f x, R+ R h < , |h| < |f (x + h) - f (x)| < : {\sl $f$ $x$, $\forall\varepsilon \in {\bf R}_\ast^+\>\> \exists\nu\in{\bf R}_\ast^+$ , $\forall h\in{\bf R} $ $h<\nu$, $\vert h\vert < \nu$ $\vert f(x + h) - f(x)\vert<\varepsilon$} . \exp (exp), . . $\exp(x+y)=\exp x\exp y$ . . . . . . . . . . . . . . . . . . . . . . . . exp(x + y ) = exp x exp y
+

, h R

58

\extracolsep{len } , @- array, tabular tabular*. len , @-.

f
\fbox{text } \framebox. text , picture, text LR . \fboxrule, , text , \fboxsep. , text , \fboxrule \fboxsep. . \fboxrule , "" , \fbox \framebox, picture. picture . \fboxsep , , , text \fbox \framebox, , "", picture. picture . figure , figure figure*. , \caption. figure , . .3 .17 . 4 .18. twocolumn, pos b h. , figure* (. ). figure* , . \caption, `Figure'6 . twocolumn, . : \begin{figure*}[pos ] text \end{figure*}
6

`.'

59

text \textwidth. pos , b, h, p t. : b ; h , ; p , ; t . pos tbp. \fill , "" . \flat , . . fleqn : , \[ \], displaymath, equation, eqnarray eqnarray*, , , , \mathindent. , . , fleqn. \floatpagefraction 0 1. , , . , 0.6, 60% . 0.5, \def \renewcommand. twocolumn, ; . \dblfloatpagefraction. \floatsep , , . twocolumn, ; . \dblfloatsep. , \protect. \flushbottom , , , , . flushleft , , . 60

flushright , , . \fnsymbol{ctr } ctr , 1 9, . , , ctr , : , , , , , |, , . , : \newcounter{stone}\setcounter{stone}{4}$\fnsymbol{stone}$ . . \footheight , . , . . .23 .137. , \protect. footnote . book report , article . \footnote \footnotetext . \footnote[i]{text } , minipage . , i , footnote . , \footnote, , text . i , footnote , i 1995 . minipage , , (. minipage. , i ( ), . , \footnote plain TEX'a. . \footnotemark[i] , , . i , footnote . i, , , footnote , i. \footnotetext. .
1995 , , \footnote[1995]{, , ...}.

61

- . . .

\tiny\temp \scriptsize\temp \footnotesize\temp \small\temp \normalsize\temp \large\temp \Large\temp \LARGE\temp \huge\temp \Huge\temp

- . . .

- . . .

- . . .

- . . .

- . . .

- . . .

- . . .

- . . .

- . . .
. 14. .

\footnoterule . A \footnoterule. L TEX : \def\footnoterule{\kern -3pt \hrule width .4\columnwidth \kern 2.6pt} plain TEX. (width) . \footnotesep , , , , , \footnoterule. , \protect. \footnotesize , . . , , \scriptsize , \small. . .14 .62. . \footnotetext[i]{text } . , \footnote, , , , . \footnotemark. . \footskip , .

62

text len \framebox[len][l]{text} text len \framebox[len]{text} text len \framebox[len][r]{text} . 15. pos \framebox. . . .23 .137. , \protect. \forall , . . \exists. . \frac{top }{bot } , top bot : \frac{n!}{i!(n-1)!} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \frame{ } picture. , , . , picture \put(0,0){\frame{\shortstack{L\\A\\T\\E\\X}}} : L A T E X . .
n! i!(n-1)!

63

\framebox[len ][pos ]{text } picture text LR , "" , .15, . 63. . \framebox(i, j )[pos ]{ } picture. , \makebox. \makebox , "" . .12, .45.7 . \frenchspacing . , , - , . , . , , , . , (\frenchspacing \nonfrenchspacing?) , . \nonfrenchspacing ( plain ), . . \frown . . ,

\fussy . , . , .

g
\gamma , . . \Gamma , . . \gcd " " (gcd), . .
7 , picture \fboxsep , .

64

\ge (greater or equal) . . \geq. \le (lower or equal ) \leq. `<' `>' . . \geq , . . \ge. . \gets , . , \leftarrow. . \gg , . $\ll$. \langle \rangle ( ""): $\ll\kern 1cm\gg$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $\langle\!\langle\kern 1cm\rangle\!\rangle$ . . . . . . . . . . . . . . . . . 1 TEX \kern. . .glo , , \makeglossary ( \nofiles). \glossaryentry{text }{p} \glossary{text }, ( ). \global \def , , , , . TEX'a. \glossary{text } , glo ( ) \glossaryentry{text }{p}. text ( , \{ \}, ) , \glossary text , . \glossaryentry{text}{p} glo-, A L TEX' , \glossary{text } ( \makeglossary \nofiles). p , \glossary{text }. \grave , . $\grave a$, $\grave +$, $\grave X$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a, +, X `` ` .

65

66

h
\H char \H{char} ( o) char LR . . \hat . "" ( ). "" , \^. $\hat x$, $\hat +$, $\hat q$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x, +, q ^^^ . \hbar ? , . h . \hbox{text} ; text . -, TEX'a . ( \vbox), ( \vcenter) ( \vtop). \hbox . TEX'a. \headheight , . , . . .23 .137. , \protect. headings \pagestyle \thispagestyle. , , ( ), . book ( ). . book report. \headsep , . . . .23 .137. , \protect. \heartsuit , . . \hfill \hspace{\fill}. .

\hline array, tabular tabular*. , , \\. \cline \multicolumn, tabular. \hom (hom), . ( ) . . \hookleftarrow , . . \hookrightarrow , . . howpublished ( BibTEX'a.) , . . \hrulefill , . , .13, .52. . \hspace{len} len , , . . \hspace*{len} len , , . . \huge ,

.

. , \LARGE , \Huge. . .14 .62. . \Huge ,

. .

, , \huge. . .14 .62. . \hyphenation{ } , . - , TEX . : \hyphenation{----- ---}

67

, . , . .

i
\i i LR . (\^\i, \"\i). . .idx , , \makeindex ( \nofiles). C \indexentry{text}{p} \index{text} ( ). \iff (If and only if .) . , \;\Longleftrightarrow\;, , . . \Im . . , ( ?). , `m': $\Im z$, $\Im m\, z$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . z , mz - \,. , . : \def\IM{\mathop{\Im m}\nolimits} $\IM z$, $\IM(z+z')$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m z , m(z + z ) $\Re$, . e : , \RE. () , \Im \Re plain. . \imath i, . . in TEX'a (inch), : 1 in=72.27 pt=25.4 mm.

68

\in , . . \include{file} \includeonly{filelist} , . , file , , file.tex \clearpage. . \includeonly{file-list} . file-list . , ( file file.tex). file-list file , \include{file} A . , L TEX', , file-list. . \indent , , A L TEX', , \parindent. . \index{text} , idx ( ) \indexentry{text}{p}. text ( , \{ \}, ), , \index . text , . .
A \indexentry{text}{p} idx-. L TEX , \index{text}. ( , \makeindex \nofiles.) p , \index{text}.

\indexspace , theindex , . \inf (inf ), : $m=\inf_{t\in T}t$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m = inf
tT tT

t

$\displaystyle m=\inf_{t\in T}t$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m = inf t . \textstyle \displaystyle, \inf\limits_{t\in T} \inf\nolimits_{t\in T}. . 69

\infty , . . \input{file} , file . file , file.tex. . institution ( BibTEX'.) , "Programming Research Group" . \int ,

. , . , . _ () ^ ( ) . $\displaystyle\Gamma(z)=\int_0^\infty e^{-t}t^{z-1}dt$ . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (z ) =
0

e-t t

z -1

dt

, \int\limits, "" : $\displaystyle\Gamma(z)=\int\limits

_0^\infty e^{-t}t^{z-1}dt$ . . . . . . . . . . . . . . . . . . . . . . . . . . . (z ) =
0

e-t t

z -1

dt

. \intextsep , , , ( h). , \protect. \iota , . , i , , \imath. . \it . .9 .28. .

\item[text] enumerate, description, list, itemize, theindex trivlist (. ). , . plain TEX'a . .

70

\itemindent , list, .18, .81. , \protect. \itemize , , \item . , ћ ћ .

.

ћ . : \begin{itemize} \item --- . \item --- . \item . \end{itemize} . , , ћ ($\bullet$), - ({\bf --}), ($\ast$) ћ ($\cdot$). "" : \labelitemi, \labelitemii, \labelitemiii \labelitemiv, . , , ћ , \labelitemi : \def\labelitemi{$\spadesuit$} \renewcommand{\labelitemi}{$spadesuit$} .

.

. . \itemize \item . , :

71

.

.

. : \begin{itemize} \item[$\heartsuit$] --- . \item[$\diamondsuit$] --- . \item[$\clubsuit$] . \end{itemize} \itemsep , list, .18, .81. , \protect.

j
\j LR . . \jmath , . . \jobname . \Join I, . plain TEX'e . . \jot , , eqnarray eqnarray*. journal ( BibTEX'a.) , . .

k
72

\kappa , . . \ker (ker), : $x\in\ker u$ $u(x)=0$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x ker u u(x) = 0 , . \kern TEX, , .. , , . \gg. \mkern. key ( BibTEX'a.) key , \cite! , . \kill tabbing, , , , , . : \begin{tabbing} 123\=456\=789\=\kill \> \\ \> \\ \>\> \\ \>\> \\ \>\>\> \\ \>\>\> \\ \>\> \\ \>\> \\ \> \\ \> \end{tabbing}

tabbing , A \kill L TEX' , . \= . , tabbing \= . tabbing, \a=. , Computer modern, , , em.

73

\> . \kill next-tab-stop left-margin-tab .

l
\l LR l (l). . \L LR L (L). .

\label{key} . key , \ref \pageref. , .\ref{taleout} .\pageref{taleout ".4 .18", , .3 .17, \label{taleout}. , , \caption, \protect. \labelitemi itemize. article, report, book letter ћ ($\bullet$). "" \def \renewcommand. . itemize. \labelitemii itemize, itemize. article, report, book letter - ({\bf -}). "" \def \renewcommand. . itemize. \labelitemiii itemize, itemize. article, report, book letter ($\ast$). "" \def \renewcommand. . itemize. \labelitemiv itemize, itemize. article, report, book letter ћ ($\cdot$). "" \def \renewcommand. . itemize.

74

\labelsep , list, .18, .81. , \protect. \lambda , . . \Lambda , . . \land (logical and "") , . : \def\\#1{\overrightarrow{#1}} $(\\u\land\\v)\land\\w= (\\v\cdot\\w)\,\\u-(\\u\cdot\\w)\,\\v$ (- - ) - = (- ћ - ) - - (- ћ - ) - u v w vwu uwv . \langle , . \rangle. , \langle\!\langle \rangle\!\rangle: | A, B |2 | A, A
+

| Ч | B+, B |

"" `<'. . \large . . , \normalsize , \Large. . .14 .62. . \Large . . , \large, , \LARGE. . .14 .62. . \LARGE

.

. , \Large, , \huge. . .14 .62. .
A \LaTeX L TEX. "" , : {\LaTeX}, \LaTeX{} \LaTeX\ .

75

\lbrace , `{' `}' TEX' . , $\lbrace$, , $\{$. : $\rbrace$ $\}$. . plain TEX \big \left...\right. , $$E=\bigl\{x\mid P(x)\bigr\}$$ : E = x | P (x) . .5 .21 .6 .22. . \lceil , . , \lbrace: $\lceil x\rceil$ --- $n\geq x$ . . . . . . . . . . . . . . . . ......................................... x . \ldots (. . . ), "" . $x=(x_1,\ldots,x_n)$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x = (x1 , . . . , xn ) $x=(x_1,...,x_n)$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x = (x1 , ..., xn ) , ? (.., `=' `+', , , Sn = x1 + ћ ћ ћ + xn ), \cdots. . \le , . , \leq. . \leadsto Y, . plain TEX'e . . \leftdelim1 form \rightdelim2 . form , . \left \right , - , delim1 delim2 . .5, .21 .6, .22, \downarrow. \left, \right . \leftarrow , . \gets. \longleftarrow. \rightarrow \longrightarrow. \uparrow \downarrow. . 76 n x

\Leftarrow , . \Longleftarrow. . . . , ! . \leftarrowfill , . .13, .52. \lefteqn{form} eqnarray eqnarray*. form , TEX , . , . \leftharpoondown , . \rightharpoondown, . . \leftharpoonup , . \rightharpoonup, . . \leftmargin , list, .18, .81. list list, \leftmargin \leftmargini; list list, \leftmargin \leftmarginii; . . . ; list list, \leftmargin \leftmarginvi; . , \protect. \leftmargini , , list. . \leftmargin. , \protect. \leftmarginii , , list. . \leftmargin. , \protect. \leftmarginiii , , list. . \leftmargin. , \protect. \leftmarginiv , , list. . \leftmargin. , \protect. 77

\leftmarginv , , list. . \leftmargin. , \protect. \leftmarginvi , , list. . \leftmargin. , \protect. \leftrightarrow , . \longleftrightarrow: . . \Leftrightarrow , . \Longleftrightarrow: . . \leq (lower or equal ) . . \le. . leqno \documentstyle. A , L TEX , . , . \leqno plain TEX'a, , . . \eqno. , : ( ) (x.M )N M [x := N ]. (x.M )N M [x := N ]. $$(\lambda x.M)N \rightarrow M[x:=N].\leqno(\beta)$$, $$(\lambda x.M)N \rightarrow M[x:=N].\eqno(\beta)$$. letter \documentstyle. . . .16 .79 .17 .80. letter , letter (c. .16 .79 .17 .80). . letter. : \begin{letter}{text1 } text2 \end{letter} ( )

78

\documentstyle[11pt]{letter} \address{27 Hudson Street,\\ Athens,\\ Wessex,\\ A26 7YY.} \signature{ } \begin{document} % \begin{letter} \begin{letter}{Dr Albert Grovenor,\\ ``Appleblossom'',\\ Whittington Green,\\ Hampshire.} \opening{ !} 16 1991 . , , , . \closing{ ,} \ps{PS: 22-.} \cc{ \\ .~} \end{letter} % \end{document} . 16. letter. , text1 , , , \protect. . text1 \\, . , text1 . . letter . \lfloor , . : $\lfloor x\rfloor =E(x)$( ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x = E (x)( ) . \lg (lg), . . . 79

27 Hudson Street, Athens, Wessex, A26 7YY. 10 1992 .

Dr Albert Grovenor, "Appleblossom", Whittington Green, Hemlock.

! 30 1992 . . , , , .

,

PS: 22-. cc: .

A . 17. , L TEX'.

80

a b c d e

\topsep + \parskip or \topsep + \parskip + \partopsep \itemsep + \parsep f \leftmargin \parsep g \listparindent \labelwidth h \rightmargin \labelsep i \parindent

T a c 1

d ' E e 2 ' E

T b c

g ' f ' E E

Tc c h ' E

T a i ' E c

. 18. list .

81

\lgroup , , ; \left \right (c. .5 .21 .6 .22). \lhd ?, . , plain TEX' . . \lim (lim), . . $\lim_{x\rightarrow 0}{\sin x\over x}=1$ . . . . . . . . . . . . . . limx0 $\displaystyle \lim_{x\rightarrow 0} sin x =1 x0 x , \limits \nolimits. . {\sin x\over x}=1$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lim \liminf (lim inf ), . , . $\liminf_{x\rightarrow 0}f(x)$ . . . . . . . . . . . . . . . . . . . . . . . . . . lim inf lim : \def\liminf{\mathop{\underline{\rm lim}}} $\liminf_{\,x\rightarrow 0}f(x)$ . . . . . . . . . . . . . . . . . . . . . . . . . . . lim
x0 x0 x0 sin x x

=1

f (x)

f (x)

$\displaystyle\liminf_{x\rightarrow 0}f(x)$ . . . . . . . . . . . . . . . . . lim f (x) \limsup . \underline \overline \liminf: \def\limsup{\mathop{\overline{\hbox{\rm lim}}}} $\limsup_{x\rightarrow 0}f(x)$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lim
x0 x0

f (x)

$\displaystyle\limsup_{x\rightarrow 0}f(x)$ . . . . . . . . . . . . . . . . . lim f (x) . \limits cmd \limits_form1 ^form2 , form1 , cmd , form2 . (, \mathop). . : \def\Som{\mathop{\bf S}} \Som_{i=0}^{i=n}a_i - , ( , 82

\textstyle), ( , \displaystyle): $\Som_{i=0}^{i=n}a_i$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Si i
=n =0

ai

$$\Som_{i=0}^{i=n}a_i$$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S ai
i=0

i=n

, , . \textstyle S, \displaystyle S. \limits , , \displaystyle: \def\Tom{\mathop{\bf T}\limits} $\Tom_{i=0}^{i=n}a_i$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T ai
i=0 i=n

$\displaystyle\Tom_{i=0}^{i=n}a_i$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T ai
i=0

i=n

\limits, \limits, \nolimits: $\Tom\nolimits_{i=0}^{i=n}a_i$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ti i $\displaystyle\Tom\nolimits_{i=0}^{i=n}a_i$ . . . . . . . . . . . . . . . . . .
=n =0 i=n Ti=0

ai ai

\nolimits (, \int), \nolimits, \limits. ( . \int). TEX' . \limsup (lim sup), . . . \liminf. . \line \put \multiput picture. : \put(i, j ){\line(p, q ){l }} , (i, j ) x l . ( , l .) (p, q ), , p x q y -. p, q -6 +6 , . p q , A A L TEXe, .19, .84. , L TEX' \line plain TEX' . .

83

?? ? ? ? ? ? ? ? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ? ?? ? ?? ? ?? ? ?? ? ?? ? ?? ? ?? ? ?? ? ? ?? ? ? ?? ? ? ?? ? ? ?? ? ? ?? ? ? ?? ? ? ?? ? ? ?? ? ? ?? ? ? ? ?? ? ? ? ?? ? ? ? ?? ? ? ? ?? ? ? ? ?? ? ? ? ?? ? ? ? ( 7 ?? ? ? ? 7 ( ? ? ? ? ? 7 ( ? ? ? ? ? 7 ( D 5 7 ? ? ? ? ? D (5 & 7 ?? ? ? ? D ( 5& &4 D4 7 ??? ?? 54 Е (& 3 7 54 ????? ЕЕ & (DDЕ 3 & 7 54 3 2 ???? Е$ ? ( Е33$ 4 $ D 5 & @ 7 3$$ ?????( 2@2@@ Е$2@22 3 D4 5 & 4 Е 3 $$ 22 @@@ 7 ?? @ 2 $ Е 3 4 5 ( ? & D ??

\unitlength=1pt \begin{picture}(165,900)(0,-10) \put(0,0){\line(0,1){150}} \put(0,0){\line(1,0){150}} \put(0,0){\line(6,1){150}} \put(0,0){\line(5,1){150}} \put(0,0){\line(4,1){150}} \put(0,0){\line(3,1){150}} \put(0,0){\line(2,1){150}} \put(0,0){\line(1,1){150}} \put(0,0){\line(5,2){150}} \put(0,0){\line(3,2){150}} \put(0,0){\line(1,2){150}} \put(0,0){\line(5,3){150}} \put(0,0){\line(4,3){150}} \put(0,0){\line(1,3){150}} \put(0,0){\line(5,4){150}} \put(0,0){\line(3,4){150}} \put(0,0){\line(1,4){150}} \put(0,0){\line(6,5){150}} \put(0,0){\line(4,5){150}} \put(0,0){\line(3,5){150}} \put(0,0){\line(2,5){150}} \put(0,0){\line(1,5){150}} \put(0,0){\line(1,6){150}} \put(0,0){\line(5,6){150}} \end{picture}

. 19. , picture . \line. 84

\linebreak[i] i 0, 1, 2, 3 4. 4, \linebreak . - \linebreak , . ( .) i 0, TEX , , , . i 1, 2 3, TEX' , i, . . \linethickness{len } picture len . \linewidth . , ( quotation). , \protect. list . . ; . .18 .81. ( \parindent , .) list: \begin{list}{text1 }{dec-list } text2 \end{list} text1 , \item, , dec-list , .18, .81. - , \@listi, . . . , \@listv \@listvi ( ), dec-list . , text2 , ; \item. , , dec-list \usecounter. \listoffigures . A L TEX lof ( , , . \nofiles).

85

\listoftables , . , A L TEX . lot ( \nofiles). \listparindent , list ( .18, .81). , \protect. \ll , . ( ) , , \gg. . \llap plain TEX'a, . , , . - OOO\llap{$|||||$} MMM, TEX "OOO MMM", " |||||" "OOO", "OOO MMM". . ||||| , , , \rlap. , , . : \def\toto{\mathrel{\vbox{\hsize=9pt\hrule\kern1pt \centerline{$\circ$}\kern.6pt\hrule}}} $P\toto Q$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P Q . , \toto $\toto$\llap{/\kern2pt}, . :

\def\nototo{\setbox1=\hbox{$\toto$\llap{\raise1pt\hbox{\big/} \kern 2pt}} \mathrel{\box1}} $P\nototo Q$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P Q , , : \llap{$\diamond$\quad} ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \llap \displaylines, . \lmoustache , , .5, .21 .6, .22. , \left \right. \rmoustache: $\left\lmoustache \right\rmoustache$ . . . . . . . . . . . . . 86

\ln (ln), . , . \lnot (logical not "".) ѓ, . , \neg. . \load{size}{style} , size , style ; size \tiny, \scriptsize, \footnotesize, \small, \normalsize, \large, \Large, \LARGE, \huge \Huge; style \bf, \it, \sc, \sf, \sl \tt. .lof , , \listoffigures ( \nofiles). Ta lof- , . \caption, figure figure*. \listoffigures, lof-.
A .log , L TEX'a , , .

\log (log), . , . . \longleftarrow -, . . \Longleftarrow =, . . \longleftrightarrow , . . \Longleftrightarrow , . . \longmapsto -, . . \longrightarrow -, . . \Longrightarrow =, . .

87

\lor (logical or "".) , . , \vee. : $a\lor(b\land c)=(a\lor b)\land(a\lor c)$ a (b c) = (a b) (a c) . .lot , , \listoftables ( \nofiles). lot- , . \caption, table table*. \listoftables, lot-.

m
\makebox[len ][pos ]{text } picture \framebox (. ), "". . \makebox(i,j )[pos ]{ } A picture L TEX', , , . (i, j ) , .. i j . , \unitlength. pos , \makebox. pos , . , pos - . , , : l,r,t b. , : l ; r ; t ; b . 88

pos : tl ; tr ; br ; bl . \makebox , , \framebox \dashbox. \framebox , \makebox. , \framebox . . .12, .45. \makeglossary . glo, \glossaryentry, \glossary, . \nofiles ( ) glo. \makeindex . idx, \indexentry, \index . \nofiles ( ) idx. \makelabel{text } , list \item, text . \@list..., . \renewcommand. \makelabels letter. , , , . . \maketitle article, report book. , article . . \maketitle document. , \title \author \date. . .7 .24. \mapsto , . . 89

\marginpar[text1 ]{text2 } . , \marginpar{!}. text1 , text2 . text1 , text2 , a text1 . . \marginparpush ; . , . , \protect. \marginparsep ; . . ( , . , . , . \reversemarginpar.) , \protect. \marginparwidth , . , . , \protect. \markboth{text1 }{text2 } myheadings \pagestyle \thispagestyle. text1 , a text2 . . \markright{text} myheadings \pagestyle \thispagestyle. text , . . math , , , , . $form $ A $form $. math L TEX . \mathindent , , fleqn. , \protect. 90

!

\mathop TEX : , \textstyle "-" \displaystyle. : \def\min{\mathop{\rm min}} \limits \nolimits. , , : \def\airy{\mathop{\rm Airy}\nolimits} . \limits. \mathord TEX . , \circ . $u\circ v$, u v . , . , : $u\mathord\circ v$ uv . : $u{\circ}v$. \mathstrut plain TEX'a, , , , . \math..., . \mathstrut , \strut, . (\mathstrut ): (\ \hbox{\mathstrut\vrule}\ ) \hbox{\strut\vrule} . . . . . . . . . . . . . . ( ) \matrix plain TEX'a : \matrix{form11 & form12 & . . . & form1n \cr form21 & form22 & . . . & form2n \cr . . . formm1 & formm2 & . . . & formmn \cr} , - . : $$A=\matrix{ a &b_1+\cdots+b_n \cr \cr }$$ A= \alpha &\beta a b1 + ћ ћ ћ + b
n

\pmatrix (`p' parantheses). , \left ... \right . : $$\left|\matrix{...}\right|$$

91

, \det " det" . : $$\left\{\matrix{...}\right.\legno(\Sigma)$$ (\right.) " " \legno(\Sigma), ( ). \max (max), . $M=\max_{i\in I}x_i$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M = maxi
I

xi

$\displaystyle M=\max_{i\in I}x_i$ . . . . . . . . . . . . . . . . . . . . . . . . M = max xi
iI

. \limits. . \mbox{text } . text LR . , , A \mbox, text , L TEX LR . , , A , L TEX . , {\it $17>\mbox{}$} 17 > . . \medskip , \medskipamount. \vspace{\medskipamount}. , plain TEX'e. . \medskipamount , 6pt plus 2pt minus 2pt. \mho H, . , plain TEX'e . . \mid |, . $I=\{t | 0

len , pos b t. b , t . , \begin{center} \begin{minipage}{4in} , -, , , {\it `` ''} {\it ``''}.\footnote{ `` '' `` ''.} , , , ( ), \ldots \end{minipage} \end{center} : , , , , " " "" .a , , , ( ), . . .
a " " " ".

, minipage , , . minipage , .

93

minus len TEX'a ; len , . \mit . . \mkernlen TEX'a, . len , len (mu). ( ) , . \mkern mu (math unit ). (\space \ ) 6mu, , -, 3mu. : \def\,{\mkern 3mu} \mkern , . . \circ. mm TEX'a , , 10 mm = 1 cm. (, 1 mm = 0.03937 in = 2.854 pt.) \models |=, . . month ( BibTEX'a.) jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov dec. \mp . . ,

mpfootnote minipage, . \footnote \footnotetext . , . mu TEX'a , , , 18 mu = 1 em, em 2 . (. \mkern.) \mu ч, . mu, . .

94

\multicolumn{i}{pre }{text } , tabular, tabular* array , . i , , ; pre tabular array, , , text , . \multicolumn , . , - - - - ѓ- ѓѓ- #- - - : \begin{center} \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ } \hline\hline & \hline\hline $\land$- & $\land$- & $\lor$- & $\lor$- $\implies$- & $\implies$- $\neg$- & $\neg$- $\neg\neg$- & $\#$- & $\forall$- & $\forall$- $\exists$- & $\exists$- \hline \end{tabular} \end{center}

- - ѓ-

- -

\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\

\multiply . TEX. : \multiply\count123 by 2, \multiply\dimen7 by 6.

95

ћ ћћ ћћ ћћ ћ ћ ћ ћ ћ ћ ћ ћ ћ ћћ ћ ћ ћ ћ ћ ћ ћ ћ ћ ћ ћ ћ ћ ћ ћ ћ ћ ћ ћ ћћ ћћ ћћ ћћ ћ ћ ћћ ћћ ћ ћ ћ ћ ћ ћ ћћ ћ ћ ћ ћ ћћ ћћ ћ ћћ ћћ ћ ћ ћ

96 \unitlength=1mm \newcommand{\mpt}{\tiny $\bullet$} \begin{picture}(35,35)(-17.5,-35) \multiput(0,0)(0.59,-1.8){16}{\mpt} \multiput(8.8,-27.1)(-1.53,1.12){16}{\mpt} \multiput(-14.3,-10.3)(1.9,0){16}{\mpt} \multiput(14.3,-10.3)(-1.53,-1.12){16}{\mpt} \multiput(-8.8,-27.1)(0.59,1.8){16}{\mpt} \end{picture}

. 20. \multiput picture ( ) \advance, \divide. \multiput(i,j )(m,n){t}{ } picture, t : \put(i, j ){ } \put(i + m, j + n){ } \put(i + 2m, j + 2n){ } . . . \put(i + (t - 1)m, j + (t - 1)n){ }
A L TEX , 100 . .20, .96.

myheadings \pagestyle \thispagestyle, . ( .) , \markboth \markright. . , \thispagestyle{myheadings} \markboth{ }{ }

n
\nabla . .

\natural . .

\ne =, . \neq. \not=. . \nearrow (north east arrow). . . ,

\neg ѓ, . \lnot ( ). . \neq =, . \ne. \not=. . \newcommand{cmd }[i]{def } , cmd ; cmd , \end. i 1 9; , . def . def #j , cmd j - . .20, .96. . \newcounter{ctr1 }[ctr2 ] ; ctr1 , . \thectr1 \arabic{ctr1 }. , \include. ctr2 ( ), ctr2 \stepcounter \refstepcounter, ctr1 . \fnsymbol. . \thectr. \newenvironment{env }[i]{def1 }{def2 } env , env , . , \env . i 1 9 , . def1 , A , L TEX \begin{env }, def2 A , , L TEX \end{env }. def1 def2 def1 def2 . i, : \begin{env }{arg1 }...{arg2 }

97

, def1 , #j argi ( 1 j i). , #j def2 . . \newfont{cmd }{font } cmd LR font : \newfont{\bgbf}{cmbx12 scaled\magstep1} {\bf } . . . . . . . . . . . . . . . . . . . . {\bgbf } . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................... . \newlength{cmd } cmd . . \newline . . \newpage . twocolumn, . . \newsavebox{cmd } cmd , , . \savebox \sbox. . \savebox. \newteorem{env1 }[env2 ]{text }[ctr ] ; env1 . env2 . env2 ctr . text , env1 . env2 , ctr , env1 env1 ( 1) . ctr ( ), env1 i.j , i ctr , a j . env2 ( , \newtheorem), env1 , env2 , . .

98

\ni , . \owns. , ( ) : R
n

x - x + (x)y R

f

m

: $${\bf R}^n\ni x\buildrel f\over{\longmapsto} x+ \phi(x)y\in{\bf R}^m$$ . \noalign{text } TEX'a, text , TEX'. , , A L TEX'a array. , , , \cases. : \noalign{\smallskip}. \nocite{key-list } , BibTEX', , . key-list , , bib. . , bib, document \nocite{*}. .
A \nofiles L TEX , ( ) , , aux, glo, idx, lof, lot toc. (, file .tex, file .aux.) \nofiles , . , - , .

\noindent , . ( \parindent.) \noindent, , , abstract quotation. . \nolinebreak[i] i 0, 1, 2, 3 4. 4, \nolinebreak , . i 0, TEX , . i 1, 2 3, TEX' 99

, i, . . \nolimits cmd \nolimits_form1 ^form2 form1 , cmd , form2 . , : $$\sum\nolimits_{i = 1}^{i = n} i^3$$ . . . . . . . . . . . . . . . . . . . . . . . . $$\sum_{i = 1}^{i = n} i^3$$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
i=1 i=n i=1 i=n

i3 i3

, . TEX'a. \nonumber eqnarray. , . . eqnarray. \nonfrenchspacing TEX , , . \nonfrenchspacing , \frenchspacing. \frenchspacing. . \nonstopmode TEX'a ( ) , . , \documentstyle. \nopagebreak[i] i 0, 1, 2, 3 4. 4, , \nopagebreak, . i 0, TEX , , . i 1, 2 3, TEX' , i, . twocolumn, , . . \normalmarginpar , , . (. \marginpar.) \normalsize . \small \large. . .14 .62. .

100

\not , , . $x\not=y$, $U\not\subset V$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x = y , U V . \llap, "". note ( BibTEX'a.) , . , note="Edited by John Worrall and Elie Zahar". , . \nu . . number ( BibTEX'a.) , . \numberline{sec-unit }{text } \addcontensline (. ). . \nwarrow (north west arrow) . . ,

o
\o LR ш. . \ LR Ш. \emptyset (), . . \oddsidemargin , . \oddsidemargin . .23 .137. , \protect. \odot , . , \bigodot: . . \oe LR (oe): \oe uf, b\oe uf, v\oe ux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . oeuf, boeuf, voeux. `a-e' \ae: n\ae vus nжvus. . 101

\OE LR (OE): L'\OE IL DE CUIVRE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L'OEIL DE CUIVRE . \oint , -

. , , . , . . \omega , . . \Omega , . . \ominus . . ,

\onecolumn , , TEX'a . , \clearpage, . openbib \documentstyle. , thebibliography, ( " "). , , . \bibindent. \opening{text } letter. , . , , "" , text . . .16 .79 .17 .80. \oplus , . $\dim(U\oplus V)=\dim U+\dim V$ . . . . . . . . . . dim(U V ) = dim U + dim V \bigoplus. E
iI i

$\displaystyle E=\bigoplus_{i\in I}E_i$ . . . . . . . . . . . . . . . . . . . . E = .

102

q &

\uni $ tlength=0.5pt \begin{picture}(300,200)(-150,-100) \put(0,0){\oval(140,90)[b]} \put(0,0){\oval(140,90)[rt]} % (0,0){\circle*{3}} \put

. 21. \oval 3/4 organization ( BibTEX'a.) , . \oslash . . ,

\otimes , . $(E\otimes F)\otimes G= \otimes(F\otimes G)$ . . . . . . . . . . . . . . . . . . . . . . . . . (E F ) G = E (F G) \bigotimes: E
iI i

$\displaystyle E=\bigotimes_{i\in I}E_i$ . . . . . . . . . . . . . . . . . . E = .

\oval(p,q )[part ] \put \multiput A picture. L TEX' \put(i,j){\oval(p,q)[part ] , , p , q , (i, j ). part - , , ( , ). . : l . t . r . b . 103

. : tl . tr . br . bl . .21, .103. {form1 \over form2 } , form1 form2 . TEX'a. TEX . ( \textstyle, \displaystyle). 1+ 2 (, 1+a2x b2 ) . + ! : (1 + x2 )/(1 + a2 + b2 ). , "" 1 x 3 y 2 4 . , \over, . , \over \sur: \def\sur{\above.2pt}. .1, .10. \overbrace{form } form, . : $e=\bigl[2,\overbrace{1,2,1}^{k=1},\overbrace{1,4,1}^{k=2}, \overbrace{1,6,1}^{k=3},\ldots, \overbrace{1,2k,1},\ldots\bigr]$
k=1 k=2 k=3

e = 2, 1, 2, 1, 1, 4, 1, 1, 6, 1, . . . , 1, 2k , 1, . . . "" \overbrace, : \overbrace{\strut...}. :
k=1 k=2 k=3

e = 2, 1, 2, 1, 1, 4, 1, 1, 6, 1, . . . , 1, 2k , 1, . . . , , \underbrace. . \downbracefill ( \overbrace) \upbracefill ( \underbrace) (. .13 .52). .

104

- - \overleftarrow{form } form, : -- -- - $\overleftarrow A=\overleftarrow{f(x,y)}$ . . . . . . . . . . . . . . . . A = f (x, y ) \overline{form } form, . \underline. . \bar . \overline , : . , \overline "" \! : A+B+C +M +X +Y +Z A +B +C +M +X +Y +Z : \overline{...}, \overline{\!...}. . - - \overrightarrow{form } form, . : $$\def\vect#1{\overrightarrow{\kern-2pt#1\kern 2pt}} AB^2=AC^2-2\,\vect{AB}\cdot\vect{AB}$$ - -- - AB 2 = AC 2 - 2AB ћAB (\kern-2pt#1\kern 2pt) : - - \overrightarrow{AB} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AB - - \overrightarrow{\kern-2pt AB\kern 2pt} . . . . . . . . . . . . . . . . . . . . . . . . . . . . AB \vec: \vec{AB} AB . \vec : (i, , k ).

\owns , . \ni. .

p
p{len } array tabular. len , , text \parbox[t]{len }{text }. ,

105

. , ; ; , . , ; ; , .

, ; ; , . , ; ; , .

.

: \begin{center} \begin{tabular}{cp{2in}p{2in}} & \multicolumn{1}{c}{\it }& \multicolumn{1}{c}{\it } \\ & & \\ \it . & , ; ; {\it }, . & , ; ; {\it }, . \\ & & \\ \it . & , ; ; {\it }, . & , ; ; {\it }, . \end{tabular} \end{center} \end{table} \\ array tabular, text , , , array, minipage tabular, text \parbox \centering, \raggedright \raggedleft. \P "" . .

106

page , . , . 1, . \pagebreak[i] i 0, 1, 2, 3 4. 4, \pagebreak . , , , , . ( .) i , TEX , \pagebreak , . i 1, 2 3, \pagebreak TEX' , i, . twocolumn , . . \pagenumbering{num-style } ; , . num-style arabic ( ), Roman ( ), alph ( ) Alph ( ). arabic. , 1. , , , . \pagenumbering, : \begin{document} \pagenumbering{roman} % % \maketitle % \thispagestyle{empty} % ... \tableofcontents % \cleardoublepage % 1 . \pagenumbering{arabic} % \unclude{chapter1} \unclude{chapter2} ... \end{document} \pagenumbering \thepage \num-style {page}. . 107

\pageref{key } . , \label{key }. . \label{key }. . pages ( BibTEX'a.) . , "679-703", "33-45,60-63" "3,40-43,70". \pagestyle{page-style } , TEX'a . . , , plain, empty, headings myheadings, , page-style . (. ). . \par , . . paragraph . \paragraph . \setcounter. \chapter, \section, \subsection \subsubsection. \paragraph[entry ]{heading } , . article, report book 4. . ( , secnumdepth.) heading , , , tocdepth. , heading , entry , . entry , , , heading . . \paragraph*{heading } , , . . \parallel , . \| \Vert , , . . \parbox[pos ]{len }{text } text , o len . \parbox minipage : \begin{minipage}[pos ]{len} text \end{minipage} \parbox}[pos ]{len}{text } 108

pos b, t. b , t . : , . . \parbox[b]{1in}{ , .} \ \ \parbox[t]{1in}{ .}

text , center, description, enumerate, flushleft, flushright, itemize, quote, quotation, thebibliography verse, , \newtheorem, tabular, , . . \parfillskip , . : , \parfillskip=0mm. TEX , , , : . . . . , , . , , , .8 {\parfillskip=0mm\sl...\par} ! , TEX , . \par, \parfillskip=0mm, . TEX'a. \parindent , . , \parbox, 0 . , , \setlength. , \protect.
8

., .

109

\parsep , , list; .18, .81. , \protect. \parskip , , ( \baselineskip ). , \parskip , . , \setlength . , \protect. part . \part , . \setcounter. \part[entry ]{heading } , . article, report book. article 0, report book -1. . ( , secnumdepth.) entry , , , heading . ( , tocdepth.) entry , , heading . entry , , a , heading . . \part*{heading } , , . \partial . : ${\partial^2f\over\partial x\partial }= {\partial^2f\over\partial x\partial }$ . . . . . . . . . . . . . . . . . . \delta. . \partopsep , , list, . . .18 .81. , \protect. pc TEX'a (pica ), , : 1 pc=12 pt. (, 1 pc = 0.166 in = 4.22 mm.)
2f x

=

2f x

110

\perp , ; \bot , . . \phi , . \varphi. . \Phi , . . \pi , . \varpi. . \Pi , . \prod: $\Pi, \prod, \displaystyle\prod$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . picture . .11 .39, .19, .84 . plain \pagestyle \thispagestyle. , . article report. plain \bibliographystyle. , , : [17]. plus len TEX'a, minus ; len , . \pm +, . . \pmatrix plain TEX'. : \pmatrix{form11 & form12 & . . . & form1n \cr form21 & form22 & . . . & form2n \cr . . . formm1 & formm2 & . . . & formmn \cr} \matrix, . : 111 ,

J =

0 0

1

0 ч0 0ч

: $$J=\pmatrix{ \pmatrix{\lambda&1\cr0&\lambda\cr} & 0\cr 0 & \pmatrix{\mu&0\cr 0&\mu\cr}\cr }$$ . \matrix. \pmod , "" . , $m_1 \equiv m_2 \pmod{n}$ m1 m2 (mod n). . \poptabs tabbing, , \pushtabs. \pounds ?. . \Pr (Pr), . . . \prec . . ,

\preceq , . ( ) \succeq. . \prime , . , : $y_1^\prime$ y1 . , $S'$ $S^\prime$. . \prod ( ). . , , . . $${\cal C}(n;a)=e^{-a}\prod_{i=1}^m (-a)^{n_i}\sum_{k\ge 0}\,

112

\prod_{i-1}^m C_{n_i}^{(a)}(k){a^k\over k!}$$
m m

C (n; a) = e

-a i=1

(-a)

n

i

( Cna) (k ) i k0 i-1

ak k!

\propto , . \alpha, : $\propto, \alpha$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . \protect , . ( , .) \ps{text } letter. . .16 .79 .17 A .80. , L TEX `PS', \pps . \psi , . . \Psi , . . pt TEX'a point (), , 1 in = 72.27 pt. (, 1 pt = 0.0138 in=0.35 mm.) publisher ( BibTEX'a.) . , "Oxford University Press" "Springer". \pushtabs , tabbing, ( \poptabs). \put(i,j ){ } picture, (i.j ). (i,j ) . ( , , .) .11 .39, .19, .84 .

q

113

\qquad plain TEX'a; em. \quad plain TEX'a; em. quotation ; A . L TEX . , , \noindent. . . , \begin{quotation} \noindent : , , . (Heath) : % \begin{quotation} \noindent --- , , -- --- $S'$, $S$ \ldots \end{quotation} --- `` .'' \end{quotation}

, : : , , . (Heath) : , , S , S . . . " ."

114

quote , A . L TEX . , . . , : \begin{quote} (Jordan) , 4 , $a$, $M_3^\prime$, $\epsilon_2$ $\Pi_{1,2}^{\prime\prime}$. \end{quote} 9 : (Jordan) , 4 , a, M3 , 2 1,2 .

r
\raggedbottom , . \raggedleft , , . \raggedright , . \raisebox{len1 }[len2 ][len3 ]{text } text LR len1 . len2 , len2 , len3 , len3 . .

\rai \raise .

. : TEX \raise \raise 2mm\vbox{...}
9

Littlewood, J. E. Littlewood's Miscel lany

115

\raise -3mm\hbox{...}. . : \raise , .., , \hbox . \raise : \raise 3pt{...} . : , . \left[\right], , , , ( ):
p-1

sin z = z lim

p

1 -
k=1

k 4p tan 2p
2 2

z

2

, : \def\sur{\above .2pt} \def\crochet#1{\raise -5pt \hbox{$\left#1\vbox to 22pt{}\right.$}} $$\sin z=z\lim_{p\rightarrow\infty}\prod_{k=1}^{p-1} \crochet{[}\1-{z^2\sur\displaystyle 4p^2\tan^2{k\pi\over 2p}} \crochet{]}$$ , :
p-1

1 -

sin z = z lim

z

2

k 2p

p

k=1

4p2 tan2

TEX \lower, . \rangle , . >, . , , \langle. . \rbrace }, . \}. . \lbrace. . \rbrack ]. . \lbrack. . \rceil , . . \lceil. .

116

\Re " ": \Im. . .

. . -

\ref{key } . \ref, key \label{key }. \label. . \refstepcounter{ctr } ctr 1, . , \ref , \thectr. \renewcommand{cmd }[i]{def } \newcommand (. ), , cmd . . \renewenvironment{env }[i]{def1 }{def2 } \newenvironment (. ), , env . . report doc-style \documentstyle. report () article (. ) , , . report \chapter. , twoside \documentstyle. empty, , , . headings, twoside: , . myheadings . \flushbottom, \raggedbottom. . ( twoside, \flushbottom). \maketitle document . , , \maketitle \title \author \date. 6.1.3, \thanks. , \maketitle abstract. .

117

equation eqnarray, , X.1, X , X.2, .. , X.1, X.2, . . ., X . (X.1, X.2, . . ., X ). , , , , , X.1. , equation eqnarray, \chapter, X 0. . article .5 .33. \reversemarginpar , , . . \marginpar. \rfloor , . . \lfloor. . \rgroup , , ; \left, \right. . \lgroup. . \rhd ?, . , plain TEX'e . . \rho , . \varrho. . \right \left. . \left. \rightarrow , . \to. . \Rightarrow , . . \rightarrowfill , , . , \hbox, .. : \hbox to 5cm{ \rightarrowfill\ } . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - - - - - ----- .13, .52. \rightharpoondown . . \rightharpoonup . . ,

, -

118

\rightleftharpoons . .

,

\rightmargin , list, .18, .81 , \protect. \rlap plain TEX'a; , . \displaylines, . \rlap{...}. : \rlap , $, : \rlap{$(\Sigma)$}. . \llap. \rm . .9 .28. \rm... {\rm...}. . . \rmoustache , , .5, .21 .6, .22. , \left \right. roman \pagenumbering. . \roman{ctr } ctr . . Roman \pagenumbering. . \Roman{ctr } ctr . . \root plain TEX : $\root 5\of{1+x^2}$ 5 1 + x2 5 A \textstyle 1 + x2 \displaystyle (). L TEX \sqrt . . $$\root\scriptstyle 3\of{-{q\over 2}+\sqrt{{q^2\over 4} +{p^3\over 27}}}+\root\scriptstyle 3\of{-{q\over 2} -\sqrt{{q^2\over 4}+{p^3\over 27}}}$$
3

q -+ 2

q2 p3 + + 4 27

3

q -- 2

q2 p3 + 4 27

\scriptstyle `3' . 3 \scriptscriptstyle ( ).

119

\rule[len1 ]{len2 }{len3 } len2 len3 , len1 ( , len1 ). len1 0 . \rule[5pt]{10pt}{20pt} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "" . . -

s
\samepage , . \pagebreak. . \S . . \savebox{cmd }[len ][pos ]{text } picture text LR , , cmd , \newsavebox. len , (, 2.3in). , text , pos . pos l, text , pos r, . . \savebox{cmd }(i,j )[pos ]{ } picture. (i,j ), pos , \makebox. cmd , \newsavebox. . : '$'$ '$ '$'$ '$ &%&% &% &%&% &%

120

: \newsavebox{\balls} \savebox{\balls}(120,69.28){% \begin{picture}(120,69.28) \multiput(20,34.64)(40,0){3}{\circle{40}} \multiput(0,69.28)(40,0){3}{\circle{40}} \end{picture}} \begin{picture}(340,173.2) \multiput(0,0)(0,69.28){2} {\multiput(0,0)(120,0){3}{\usebox{\balls}}} \end{picture} \newsavebox \balls. , . , . A , L TEX . : \begin{center} \begin{picture}(100,103.92) \multiput(20,34.64)(40,0){3}{\circle{40}} \multiput(0,69.28)(40,0){3}{\circle{40}} \end{picture} \end{center} . \sb . $x_{83}$, $x\sb{83}$ x83 . \sbox{cmd }{text } \savebox. picture text LR , , cmd , \newsavebox. . \sc , (small capitals) . .9 .28. . school ( BibTEX'a.) , .

121

\scriptsciptstyle TEX , \displaystyle, \textstyle, \scriptstyle \scriptscriptstyle. ( ). 10 , \displaystyle \textstyle 10 , \scriptstyle 7 , \scriptscriptstyle 5 . . : $\displaystyle N=2^{2^{2^{2^2}}}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . N = 2
2
2 22

\scriptstyle, \scriptscriptstyle. 10, 7 5 , \textfont, \scriptfont \scriptscriptfont. TEX'a. . \scriptsize , . . \tiny \footnotesize. . .14 .62. . \scriptstyle , . TEX , , , . , . . \scriptscriptstyle. $${1\over\Gamma(z)}=ze^{Cz}\prod_1^\infty\Bigl(1+{z\over n} \Bigr)e^{\scriptstyle z\over\scriptstyle n}$$ 1 = z eC (z )
z 1

1+

z e n

z n

${z\over n}$ , , \scriptstyle. \scriptstyle , `z' `n' \scriptscriptstyle, . ., 5 , 7 . : $e^{z\over n}$\quad $e^{\scriptstyle z\over\scriptstyle n}$ . . . . . . . . . . . . . . . . . . . . . . . e
z n

e

z n

TEX'a. plain TEXa, . . \scrollmode TEX'a; , , , \input 122

. , \documentstyle. . \batchmode, \errorstopmode \nonstopmode. \searrow (south east arrow). . . ,

\sec (sec), . , . . secnumdepth , , . , . . .8 .24 .5 .33. section . \section . \setcounter. report book \chapter. , X X.1. \section[entry ]{heading } , . article, report book 1. . ( , secnumdepth.) entry , , , heading . ( , tocdepth.) entry , , heading . entry , ; entry , heading . . \section*{heading } , . . . series ( BibTEX'a.) . . \setcounter{ctr }{i} , ctr i. \thectr. . \setlength{cmd }{len } cmd len . , \setlength{\topmargin}{2in} \topmargin . . \setminus \, . \backslash , . . 123

Ч 34 22 0

23 Ч 0 10

19 0 Ч 11

0 4 18 Ч

. 22. 1990-1991 . \settowidth{cmd }{text } cmd text LR . , \newlength{\ee} \settowidth{\ee}{[1996 ]} \ee "1996 ". . \sf , .28. . . .9

\sharp , . . \shortstack[pos ]{col } , . col \\, a pos l ( ), r ( ) , , c ( ). , .22, .124 : \begin{figure}[t] \begin{center} \def\temp#1{\multicolumn{1}{|r|}{#1}} \begin{tabular}{r|c|c|c|c|} \cline{2-5} & \shortstack{\\\\\\\\} & \shortstack{\\\\\\\\\\} & \shortstack{\rule{0mm}{1mm}\\\\\\\\\\\\\\} & \shortstack{\\\\\\} \\ \hline

124

\temp{ } & $\times$ & 23 & 19 & 0 \\ \temp{ } & 34 & $\times$ & 0 & 4 \\ \temp{ } & 22 & 0 & $\times$ & 18 \\ \temp{ } & 0 & 10 & 11 & $\times$ \\ \end{tabular} \end{center} \caption{ 1990--1991~.} \label{stack} \end{figure}

\hline \hline \hline \hline

picture, . . \sigma , . \varsigma. . \Sigma , . ( ). $\Sigma$, $\sum$, $\displaystyle\sum$ . . . . . . . . . . . . . . . . . . . . . . . , . \signature{text } , letter. , text . , text , \\. .16 .79, . 17 .80. \sim , . . \simeq , . \cong \approx, . = . \sin (sin), . {1\over\sin^2z}=\sum_{-\infty}^{+\infty}{1\over(z-n\pi)^2} 1 = sin2 z
+ -

,

1 (z - n )2

. .

125

\sinh (sinh), . . \cosh. "sh", "sinh", \def\sh{\mathop{\rm sh}\nolimits} . . \sl , , . . \sloppy : , . , . sloppypar , , , \sloppy. \small , . , \footnotesize , \normalsize. . .14 .62. . \smallskip , \smallskipamount. \vspace{\smallskipamount}. , plain TEX'e. . \smallskipamount , 3pt plus 1pt minus 1pt. \smash{text } plain TEX'a. text , TEX , , . : - - $\overrightarrow{AB}$, , AB , ( ). . - - $\smash{\overrightarrow{AB}}$, AB . . \smile . . ,

sp TEX'a (scaled point), , TEX . 1 pt = 216 sp(= 65,536 sp). \sp . $x^{75}$, $x\sp{75}$ x75 . . \sb. \space \typeout, .

126

\spadesuit , . . \sqcap , . . \sqcup , . . \sqrt[n]{form } n form, n , form, n , . plain TEX \root . . . \sqsubset `, . , plain TEX'e . . \sqsubseteq . . , -

\sqsupset a, . , plain TEX'e . . \sqsupseteq . . , -

\ss LR `-' (Я). . \stackrel{top }{bot } , , top bot . , top , . , $\stackrel{\wedge}{=}$, =. plain TEX \buildrel . . . \star , . . \stepcounter{ctr } ctr 1, . \stop - , I\stop ( ), . \stretch{fpn } , . , fpn , \fill, fpn , , .

127

\strut plain TEX'a; , \baselineskip, . \strut \mathstrut ( , ). \mathstrut , \strut . (. \bar) . . .1 .10. .sty ( report.sty rep11.sty), . \subitem theindex . \subsubitem , theindex , , , \subitem. subparagraph . \subparagraph . \setcounter. subparagraph \chapter, \section, \subsection, \subsubsection \paragraph. \subparagraph[entry ]{heading } , . article, report book 5. . ( , secnumdepth.) heading , , , tocdepth. , entry , , , heading . entry , , , heading . . \subparagraph*{heading } , , . . subsection . \subsection . \setcounter. \chapter \section. \subsection[entry ]{heading } , . article, report book 2. . ( ,

128

secnumdepth.) heading , , , tocdepth. , heading , entry , entry , . entry , . , heading . . \subsection*{heading } , , . . \subset , . . \subsetq , . . subsubsection . \subsubsection . \setcounter. subsubsection \chapter, \section \subsection. \subsubsection[entry ]{heading } , . article, report book 3. article report book. ( , secnumdepth.) heading , , article, report book. ( , tocdepth. , heading , entry . entry , . entry , heading . . \subsubsection*{heading } , , . . \succ . . , , . ,

\succeq . . \sum . :

$\Sigma$, $\sum$, $\displaystyle\sum$ . . . . . . . . . . . . . . . . . . . . . . . , 129

, . , . . \sup (sup), . , . . \inf. . \supset , . . \supseteq , . . \surd , . $\surd a+\surd\,(b+1)$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a + (b + 1) . \sqrt. . \swarrow (south west arrow). . . ,

\symbol{i} i. , {\tt \symbol{92}char} \char. i ', , " . .

t
\t char1 char2 \t{char1 char2 } (oo) char1 char2 LR . , T\t uut Tuut. . tabbing . :

130

\begin{tabbing} 123\=456\=789\=\kill \> \\ \> \\ \>\> \\ \>\> \\ \>\>\> \\ \>\>\> \\ \>\> \\ \>\> \\ \> \\ \> \end{tabbing}

tabbing , A \kill L TEX' , . \= . , tabbing \= . tabbing, \a=. , Computer modern, , , em. \> .10
A tabbing L TEX , , next-tab-stop ( -) left-margin-tab (-), . , . , . 0, 1 2. leftmargin-tab , next-tab-stop 1. \> i next-tab-stop i next-tab-stop 1. (, \\ , next-tab-stop 1 + left-margin-tab ; left-margin-tab .)

\tabbingsep tabbing \', , , ( 10 plain T X' \> E A . L TEX' \:, .

131

). , \protect. \tabcolsep , , , tabular tabular*. , \protect. table , tabular tabular*. , \caption. table , . \caption, `Table'11 ; figure (. ). table* table, , twocolumn, . \tableofcontents , . , A L TEX . , ( ) toc, , , \nofiles. tabular tabular : \begin{tabular}[pos ]{preamble }row-list \end{tabular} pos . , t , b . preamble , . row-list row , \\. i - 1 , i . (, \multicolumn, .) \\ \hline. \hline , , , \doubleseprule. , , \hline \\. , \hline. ,
11 A L TEX'

`'.

132

Nml UnOps BinOps Ide Exp Cmd

N I E C

: \begin{center} \begin{tabular}{|c|c|c|} \hline & & \hline \hline $\hbox{\it Nml}$ & & $\hbox{\it UnOps}$ & & $\hbox{\it BinOps}$& & $\hbox{\it Ide}$ & & $\hbox{\it Exp}$ & & $\hbox{\it Cmd}$ & & \end{tabular} \end{center}

\\ $N$ $\alpha$ $\omega$ $I$ $E$ $C$ \\ \\ \\ \\ \\ \\ \hline \hline \hline \hline \hline \hline

center , . .12 tabular \shortstack tabular* tabular*: \begin{tabular*}{len }[pos ]{preamble }row-list \end{tabular*} pos , preamble row-list , tabular, len . , , , ; \hfill. \tan (tan), . . , tg, :
12 , | @-, . , \tabcolsep. , | @-. , , @{}.

133

\def\tg{\mathop{\rm tg}\nolimits}} . \tanh (tanh), . th, . . . . \tau , . . \TeX TEX. "" , : {\TeX}, \TeX{} \TeX\ . \textfloatsep , , . twocolumn, ; . \dbltextfloatsep. , \protect. \textfraction , 0 1, , , , , , . , \textfraction 0.6, 60% . \def \renewcommand. 0.2. \textheight , . . .9. , \protect. \textstyle , . TEX , . , , , . , \displaystyle. \textstyle TEX , .., . , , , , \displaystyle, , .. . . \displaystyle, \scriptstyle, \limits \nolimits. TEX'. .

134

\textwidth , . . .23, .137. , \protect. \thanks{text } \author, \date \title. , text . , \thanks , \ , . \thanks : "Counter too large". , text . \thectr \newcounter{ctr } ctr , ctr , , , \arabic A \Roman. , L TEX \thectr , ; \thectr \arabic{ctr }. , \newcounter{instinct} \setcounter{instinct}{7} \theinstinct 7, \setcounter{instinct}{11} \def\theinstinct{\Alph{instinct}} \theinstinct
A K. L TEX'a \thectr .

thebibliography , . , , ( \end{document}): \begin{thebibliography} \bibitem{Knuth} , {\it \TeX}, ., , 1993. \bibitem{Lamp} Leslie Lamport, {\it \LaTeX\ A Document Preparation System}, Addison Wesley, 1985 ... \bibitem{Lis} .., 135

{\it Plain \TeX\ }, 95--58. \end{thebibliography} theindex , ; . \theta , . \vartheta. . \heta , . . \thicklines ( ) picture. A L TEX , , , . \thinlines \thicklines. \thinlines. . . \thinlines ( ) picture, . . \thicklines. . \thispagestyle{page-style } , \pagestyle, , . page-style plain, empty, headings myheadings. . , . , \thispagestyle{empty} (, , ). \tiny . . , , \scriptsize. . .14 .62. . \tilde . $\tilde x+\tilde y$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x + y ~~ \widetilde : $\widetilde {xyz}=\widetilde{xy}*\tilde z$ . . . . . . . . . . . . . . . xy z = xy z ~ . \times Ч, . .

a b c d e

\topmargin +1 in \headheight \headsep \textheight \footskip - \footheight

f g g h

\footheight \oddsidemargin +1 in \evensidemargin +1 in \textwidth

................ T a ..........c... ... T b ..........c... ... T c c... ............. T

... ... ... ...

d

..........c...... ... T e ..........c...... ... T f ..........c...... ... . . . . . . . . . E. . . . . . . . . .

. . . . . . . . . . . . . . . . . . .' E.' . . . . . .g. . . . . . . . . . . .

h

. 23. ,

137

title ( BibTEX'a.) , -. \title{text } article, report book . ( document \maketitle . .7 .24.) , text \\. \thanks, , . \thanks , , \ . titlepage , , article. , , , , . \to , . \rightarrow. . .toc , , \tableofcontents ( \nofiles); toc- . , tocdepth. \tableofcontents, toc-. tocdepth , , , . , . . .8 .24 .5 .33. \today , , dvi, dvi-. , , Jule 4, 1992. LR . . \top , . \perp, \dashv \vdash, , . . \topfraction , 0 1. , . \def \renewcommand. 0.7. twocolumn, ; . \dbltopfraction.

138

\topmargin , . \topmargin . . .23 .137. , \protect. topnumber , , , , . 2. twocolumn, ; . dbltopnumber. \topsep , list . .23, .137. , \protect. \topskip , . \baselineskip, , . , \protect. totalnumber , , . 3. \triangle , . \Delta: $\Delta$, $\triangle$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , \bigtriangleup, \triangle, . . \triangleleft , . . \triangleright , . . trivlist , list . .18, .81. , , , \leftmargin, \labelwidth \itemindent 0 , \parsep \parskip. \tt typewriter (" ") . .9 .28. , . .

139

twocolumn , . \twocolumn{text } , , . , \clearpage, . text , , . . twoside \documentstyle. , -. , , ( ). a book. type ( BibTEX'a.) . , . \typein[cmd ]{text } text , log. text . text \protect, . text , \newcommand \renewcommand, . , \typein[\wife]{Enter wife's name.} I love \wife\ very much. : Enter wife's name. \wife= , , Marina return, \wife Marina, "I love Marina very much.". . \typeout{text } text , log-. : \typeout{Don't foget to revise this!} text . .

u
140

\u char \u{char } ( o) char LR : \u a, \u e, \u\i . a, e i. \unboldmath \boldmath. . \underbrace{form } form , . : $\displaystyle\underbrace{a-2b}_{>0} +\underbrace{y-z+t}_{>0}>0$ . . . . . . . . . . . . . . . . . . . . . . . a - 2b + y - z + t > 0
>0 >0

\downbracefill . .13 .52. \overbrace \upbracefill . . . \underline{form } form . $\underline{b+q}=\underline b+\underline q$ . . . . . . . . . . . . . b + q = b + q , \strut : \def\strit{\vrule depth 1.5pt width 0pt} $\underline{\strit b+q}= \underline{\strit b}+\underline{\strit q}$ . . . . . . . . . . . . . . b + q = b + q . \unitlength , , picture . , picture \unitlength=1mm, . 1 . \circle, \line , picture. , \protect. \unlhd ?, . , plain TEX'e . . \unrhd ?, . , plain TEX'e . . unsrt \bibliographystyle. : [31].

141

\uparrow , . \left \right , , . . \Uparrow , . \left \right , , . . \upbracefill , , . .13, .52. \updownarrow , . \left \right , , . . \Updownarrow , . \left \right , , . . \uplus , . $\uplus$, $\biguplus$, $\displaystyle\biguplus$ . . . . . . . . . . . . , . \usebox{cmd } cmd . . \savebox. . \usecounter{ctr } , dec-list ( ) list. . \upsilon , . `v', : $v$ $\upsilon$ v . . \Upsilon , . . ,

v

142

\v char \v{char } ( o) char LR : \v Ceby\v sev Ceby sev. \check. . \vlue{ctr } . , \setcounter{war}{\value{equation}} war equation. ( war \newcounter{war}.) , \protect. \varepsilon , . \epsilon, \in. . \varphi , . \phi. . \varpi , . \pi. . \varrho , . \rho. . \varsigma , . \sigma. . \vartheta , . \theta. . \vbox{text } . , text, . \vbox . , \vbox, , \hsize. TEX'a. \downarrow. \vdash , . \dashv : . . \vdots . . . .. \vec : $(\vec\imath,\vec\jmath,\vec k)$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (i, , k ) \overrightarrow, :

143

# ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? \unitlength=0.2mm \begin{picture}(165,450)(0,-10) \put(0,0){\vector(0,1){150}} \put(0,0){\vector(1,0){150}} \put(0,0){\vector(4,1){150}} \put(0,0){\vector(3,1){150}} \put(0,0){\vector(2,1){150}} \put(0,0){\vector(1,1){150}} \put(0,0){\vector(3,2){150}} \put(0,0){\vector(1,2){150}} \put(0,0){\vector(4,3){150}} \put(0,0){\vector(1,3){150}} \put(0,0){\vector(3,4){150}} \put(0,0){\vector(1,4){150}} \end{picture}

?? ?? ?? ! ?? ? ? ?? ?? ? ? ?? ? ?? ?? ? U ?? ? ?? ? T ?? ? ?? ? ?? ? & b & Q ?? ? & ? ? ? &Е B Е & ?? ? ЕЕ I & ??? Е$ X $ & ЕЕ ???Е$$$$$ & ? $ Е ? & ? $ E

. 24. , picture \vector.

.

144

- - $\overrightarrow{AB}, \vec{AB}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AB , AB . \vector \put \multiput picture. \put(i,j ){\vector(p,q ){l}} , (i,j ), x l . ( , l .) (p,q ), , p x- q y -. p q , -4 +4 . A p q , L TEX, .24, .144. , . , , . , . : \put(0,0){\line(6,1){150}} \put(150,25){\vector(4,1){0}} . \vee , . \lor. . \verbchar text char text , . char , * text . char text text char . , \verb"{\it text \/}" {\it text \/}. text . \verb*char text char \verb, , text . , \verb*"{\it text \/}" {\it text \/}. verbatim , . A L TEX'a , . \end{verbatim}. (,

145

\end {verbatim} .) , . verbatim* , verbatim, , ` '. verse . . \\, . \vert |, ; , |. \left \right , , . .5 .21, .6 .22, : |||u|||=\sup_{x\hot=0}\left\{ {\|u(x)\|\over\|x\|}\right\} . . . . . . . . . . . . . . . . . . . . . |||u||| = sup
x=0

u(x) x

. \Vert , . \|. \left \right , , . .5 .21, .6 .22, : $$u\cdot v=\left\|{u+v\over2}\right\|^2 +\left\|{u-v\over2}\right\|^2$$ uћv = . \vfill \par\vspace{\fill}. . \vline array tabular, , , . . volume ( BibTEX'a.) , , . \vspace{len } len , " " . \vspace , . . 146 u+v 2
2

+

u-v 2

2

\vspace*{len } , \vspace, , " " . .

w
\wedge , . \land ( ). . \widehat . $\widehat{xyz}$, xy z . : $\hat x,\widehat X,\widehat{AM\!B}$ . . . . . . . . . . . . . . . . . . . . . . . . x, X , AMB ^ . \widetilde . $\widetilde{xyz}$, xy z . . \tilde: $\tilde x$, $\widetilde X$, $\widetilde{XY}$, $\widetilde{XYZ}$ . . . . . . . . . . . . . . . . . . . x, X ,X Y , X Y Z ~ . \wp . : $$\wp(z)={\1\over z^2}+\sum_{\omega\in \Omega^*} \biggl[{1\over(z-\omega)^2}-{1\over\omega^2}\biggr]$$ (z ) = 1 + z2 1 1 -2 (z - )2

plain TEX \biggl \biggr. . \wr . . " " , : $$\matrix{ A&\buildrel u\over{\hbox to 12mm{\rightarrowfill}}&B\cr \wr\bigg\downarrow^&\bigg\downarrow\wr\cr

147

A'&\buildrel u'\over{\hbox to 12mm{\rightarrowfill}}&B'\cr}$$ A A -- - - -
u

B

-- - - - B

u

: , . , . .

x
\xi . . \Xi . .

y
year ( BibTEX'a.) , , . - : 1976, BibTEX'a " 1600", .

z
\zeta , . ,

(s) =
n=1

1 ns

(s) = 1

,

i=1

1 1- s pi

(pi )i1 . : 148

$$\zeta(s)={1\over\displaystyle\prod_{i=1}^\infty \Bigl(1-{1\over p_i^s}\Bigr)}\raise 2pt\hbox{,}$$ plain \displaystyle TEX \raise2pt\hbox{,}, - . .

[1] , TEX, ., , 1993.
A [2] Leslie Lamport, L TEX A Document Preparation System, Addison Wesley, 1985. A [3] Antony Diller, L TEX Line by Line, John Wiley & Sons, 1993.

[4] .., ..,TEX , , -, 1995. [5] .., Plain TEX , 95-58.

149