\batchmode \input href \catcode`\@=11 % open access to private macros %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Page size and output program %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \hsize=17cm \hoffset=-0.54cm \voffset=-0.54cm \vsize=9.9in \footline={} \def\rhead{} \def\leftheadline{ \hbox to \hsize{\vbox to 10 pt {}% \llap{\tenbf\folio\kern 1pc}\tenit\rhead\hfil } } \def\rightheadline{ \hbox to \hsize{\vbox to 10 pt {}% \tenit\hfil\rhead\rlap{\kern 1pc\tenbf\folio} } } \def\makeheadline{ \vbox to 0pt{\vskip-22.5pt\ifodd\pageno\rightheadline\else\leftheadline\fi\vss} \nointerlineskip } %%%%%%%%%%%%%%%%%%%%%%%%%%% %% Page output parameters %%%%%%%%%%%%%%%%%%%%%%%%%%% \widowpenalty=10000 \clubpenalty=10000 %%%%%%%%%%%%%%%%%%%%%%%%%%% %% Sections %%%%%%%%%%%%%%%%%%%%%%%%%%% \def\heading#1{ { \bf\let\nl=\par % \tolerance=10000 \bigskip \hyphenpenalty=10000 \advance\leftskip by 0pt plus 1fill \advance\rightskip by 0pt plus 1fill \narrower \uppercase{#1} \par \nobreak\bigskip } } \newif\ifchapno \chapnofalse \newcount\chapno \chapno=0 \newcount\subchno \newcount\subsubchno \newcount\subsubsubchno \newcount\footno \newcount\excerno \footno=1 \excerno=0 \def\chapter#1{\penalty-250 \advance\chapno by 1 \subchno=0 \footno=1 \excerno=1 \bigskip\noindent \centerline{\bf\ifchapno\the\chapno.~\fi#1}\nobreak\medskip\nobreak } \def\subchap#1{\medskip \advance\subchno by 1 \subsubchno=0 \centerline{{\bf\ifchapno\the\chapno.\the\subchno.~\fi#1}}\nobreak\smallskip\nobreak } \def\subsubchap#1{\medskip \advance\subsubchno by 1 \ifchapno\centerline{{\bf\the\chapno.\the\subchno.\the\subsubchno.~#1}}\nobreak\smallskip% \else{\bf#1 }\fi% } \def\subsubsubchap#1{\medskip \advance\subsubsubchno by 1 \ifchapno{\bf\the\chapno.\the\subchno.\the\subsubchno.\the\subsubsubchno.~#1. }% \else{\bf#1. }\fi% } \def\section#1.{\smallskip{\bf#1.}} \def\qsection#1?{\smallskip{\bf#1?}} \def\boxit#1{\vbox{\hrule\hbox{\vrule\kern 1pt \vbox{\kern 1pt #1 \kern 1pt}\kern 1pt\vrule}\hrule}} \def\bskip{\hskip 0.5em} \def\frac#1/#2{\leavevmode\kern.1em \raise.5ex\hbox{\the\scriptfont0 #1}\kern-.1em /\kern-.15em\lower.25ex\hbox{\the\scriptfont0 #2}} \def\N{\char252\relax} \def\emph#1{{\it #1\/}} \def\dfn#1{{\it#1\/}} \def\cP{{\cal P}} \def\cJ{{\cal J}} \def\cR{{\cal R}} \def\cS{{\cal S}} \def\cM{{\cal M}} \def\nvec#1{({#1}_1,{#1}_2, \ldots, {#1}_n)} \def\fmod#1{\;({\rm mod}\,\,#1)} %% "mod" sign in ellipse \def\ellmod#1{\;({\rm mod}\,\,#1)} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Mathematical functions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\perm#1#2{{\left(#1\atop#2\right)}} \def\stir#1#2{{\left[#1\atop#2\right]}} \def\Stir#1#2{{\left\{#1\atop#2\right\}}} \def\stirstir#1#2{{\left[\left[#1\atop#2\right]\right]}} \def\eul#1#2{{\left\langle#1\atop#2\right\rangle}} \def\Eul#1#2{{\left\langle\left\langle#1\atop#2\right\rangle\right\rangle}} \def\floor#1{{\left\lfloor#1\right\rfloor}} \def\ceil#1{{\left\lceil#1\right\rceil}} \def\entier#1{{\left[#1\right]}} \def\abs#1{{\left\vert #1\right\vert}} \def\Abs#1{{\left\Vert #1\right\Vert}} \def\dlp{\left(\left(} \def\drp{\right)\right)} \def\Prsup{\overline{\Pr}} \def\Prsub{\underline{\Pr}} \def\fsup{\overline{f}} \def\fsub{\underline{f}} %% \def\simlt{\mathrel{\mathpalette\@versim{<}}} % "<" over \sim \def\@versim#1#2{\lower.5\p@\vbox{\baselineskip\z@skip\lineskip-.5\p@ \ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr\sim\crcr}}} %% \def\{{\ifmmode\lbrace\else{\tt\char"7B\relax}\fi} \def\}{\ifmmode\rbrace\else{\tt\char"7D\relax}\fi} \def\true{{\it true}} \def\GE{$\ge$} \def\LE{$\le$} \def\NE{\ifmmode\not=\else$\not=$\fi} \def\TO{\ifmmode\to\else$\to$\fi} \def\NULL{\ifmmode\Lambda\else$\Lambda$\fi} \def\note#1#2{\footnote{\ifmmode^{\the\footno}\else$^{\the\footno}$\fi}{#2}\global\advance\footno by 1} \def\cite{\bgroup\medskip\narrower} \def\endcite{\par\medskip\egroup} \def\epigraph#1\signed#2\par{{\parindent=0pt\let\nl=\par\hbox to \hsize{\hfill\vbox{{\divide\hsize by 2#1\par}}}% \hbox to \hsize{\hfill\vbox{{\divide\hsize by 2#2\par}}}}\bigskip} \def\bsl{\ifmmode\backslash\else{\tt\char`\\}\fi} \def\DIV{\mathbin{{\rm DIV}}} \def\MOD{\mathbin{{\rm MOD}}} \def\ror{\mathbin{{\hbox{\rm или}}}} \def\rand{\mathbin{{\hbox{\rm и}}}} \def\mean{\mathop{\rm mean}\nolimits} \def\var{\mathop{\rm var}\nolimits} \def\covar{\mathop{\rm covar}\nolimits} \def\ave{\mathop{\rm ave}\nolimits} \def\dev{\mathop{\rm dev}\nolimits} \def\ctg{\mathop{\rm ctg}\nolimits} \def\sign{\mathop{\rm sign}\nolimits} \def\adj{\mathop{\rm adj}\nolimits} \def\round{\mathop{\rm round}\nolimits} \def\trunc{\mathop{\rm trunc}\nolimits} \def\нод{\mathop{\rm нод}\nolimits} \def\нок{\mathop{\rm нок}\nolimits} \def\T{\mathbin{\top}} \def\set#1{\{\, #1\,\}} \def\oct#1{{\it #1}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Ordered and unordered list %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newcount\itemcnt \def\enumerate{% \bgroup\itemcnt=1\medskip\narrower \def\li{\item{\the\itemcnt)~}\advance\itemcnt by 1} } \def\enumend{\medskip\egroup} \def\itemize{% \bgroup\medskip\narrower \def\li{\item{$\bullet$}} } \def\itemend{\medskip\egroup} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Table autoformatting %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\ctable#1{$$\vbox{\halign{#1}}$$} \newbox\tbox \newbox\ttbox \newdimen\tdim \newif\ifhtablepassone \def\embedpar#1{\ifhtablepassone\relax\else{\hsize=\tdim #1\par}\fi} \def\htable#1#2#3{{\let\nl=\par \htablepassonetrue \setbox\tbox\vbox{\halign{#3}}\tdim=\wd\tbox \htablepassonefalse \setbox\tbox\vbox{\halign{#3}}\setbox\ttbox\hbox{#2} \ifdim\wd\tbox>\wd\ttbox\tdim=\wd\tbox\else\tdim=\wd\ttbox\fi $$\vbox{\hbox to\tdim{\hfill#1}\hbox to\tdim{\hfill#2\hfill} \hbox to\tdim{\hfill\box\tbox\hfill}}$$% }} \def\UDC#1{\leftline{УДК #1}} \def\btable#1{{\offinterlineskip$$\boxit{\vbox{\halign{#1}}}$$}} \def\rrq{"} \def\rlq{"} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Excercise formatting macros %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\excercises{\bigskip\centerline{Уп└ажнени╧}\medskip\global\excerno=1} \def\ex[#1]#2\par{\item{\the\excerno.}[#1]#2\par\global\advance\excerno by 1} \def\rex[#1]#2\par{\item{\btr\the\excerno.}[#1]#2\par\global\advance\excerno by 1} \def\exhead(#1){{\sl(#1)\/}} \def\btr{{\tt >}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\rem#1{\qquad\hbox{#1}} \def\MIX{{\tt MIX}} \def\MIXAL{{\tt MIXAL}} \def\MIXTEC{{\tt MIXTEC}} \def\MIXT{{\tt MIXT}} \def\hslogo{$\bigtriangleup\atop\bigtriangledown$} \def\strong#1{{\bf #1}} \def\endmark{\vrule depth 0pt height 10 pt width 0.5em} \def\hiddenpar{\par} %%%%%%%%%%%%%%%%%%%%%%%% %% algorithm definition %%%%%%%%%%%%%%%%%%%%%%%% \newcount\stepno \def\alg #1.(#2){\medskip\gdef\alglettr{#1}{\bf Алго└и┬м #1. }{\sl(#2)\/ }% \global\stepno=1} \def\st{\item{\alglettr\the\stepno\global\advance\stepno by 1}} \def\asg{\ifmmode\leftarrow\else$\leftarrow$\fi} \def\rasg{\ifmmode\rightarrow\else$\rightarrow$\fi} \def\xchg{\ifmmode\leftrightarrow\else$\leftrightarrow$\fi} \def\Asg{\ifmmode\Leftarrow\else$\Leftarrow$\fi} \def\Rasg{\ifmmode\Rightarrow\else$\Rightarrow$\fi} \def\To{\ifmmode\Rightarrow\else$\Rightarrow$\fi} \def\stp#1{{\bf\alglettr#1}} \def\algend{\endmark\medskip} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% program definition %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newcount\prgstepno \def\prog #1.(#2){\medskip\gdef\prglettr{#1}{\bf П└ог└амма #1. }{\sl(#2)\/ }% \global\prgstepno=1} \def\pst{\item{\prglettr\the\stepno\global\advance\prgstepno by 1}} \def\progend{\endmark\medskip} %% {\obeyspaces\gdef {\ }} \catcode`\|=\active \def\code{\nobreak\medskip\bgroup\let\par=\cr\obeylines% % --- \def|{{\tt\char`\|}}% \halign\bgroup\tt##\bskip&\tt##\bskip&\tt##\bskip&\hfill$##$\hfill&\bskip##\hfill\cr} \def\endcode{\egroup\egroup\medbreak\noindent} \def\twocols{\noalign\bgroup% \halign\bgroup\tt##\bskip&\tt##\bskip&\tt##\bskip&\tt##\bskip&\tt##\bskip&\tt##\bskip&\hfill$##$\hfill&\bskip##\hfill\cr} \def\endtwocols{\egroup\egroup} \def|{\bgroup\tt\def|{\egroup}} \def\bdispl{\bgroup$$\vbox\bgroup\obeylines} \def\edispl{\egroup$$\egroup} %% MIX code \newcount\pcntr \def\condcr{\ifnum\pcntr>0\cr\else\relax\fi} \def\mixcode{\bgroup\let\par=\condcr\obeylines\pcntr=0% \vtop\bgroup\halign\bgroup% \global\advance\pcntr by 1% \ifnum\pcntr<10{}0\else\relax\fi% \the\pcntr~% \tt##\hfil\bskip&\tt##\hfil\bskip&\bskip##\hfill\cr} \def\endmixcode{\egroup\egroup\egroup} %% %% \def\picture#1{$${\hbox{{Picture:\hskip4ex\vtop{\hsize=13cm\noindent\ignorespaces#1}\par}}}$$} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% tricky macros borrowed from LaTeX %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \long\def\@ifnextchar#1#2#3{% \let\reserved@d=#1% \def\reserved@a{#2}% \def\reserved@b{#3}% \futurelet\@let@token\@ifnch} \def\@ifnch{% \ifx\@let@token\@sptoken \let\reserved@c\@xifnch \else \ifx\@let@token\reserved@d \let\reserved@c\reserved@a \else \let\reserved@c\reserved@b \fi \fi \reserved@c} \def\:{\let\@sptoken= } \: % this makes \@sptoken a space token \def\:{\@xifnch} \expandafter\def\: {\futurelet\@let@token\@ifnch} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Displayed equations wrapper %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\@labEQ[#1]#2{\anchor{#1}$$#2\eqno(#1)$$\ignorespaces} \def\@nonumEQ#1{$$#1$$\ignorespaces}% \def\EQ{\@ifnextchar[{\@labEQ}{\@nonumEQ}}% \def\eqref[#1]{\link[#1]{(#1)}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Proof %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\hproof[#1]{\medskip{\sl Доказа┬ел╠┴┬во #1. }\ignorespaces} \def\hlproof{\medskip{\sl Доказа┬ел╠┴┬во. }\ignorespaces}% \def\proof{\@ifnextchar[{\hproof}{\hlproof}}% \def\proofend{\endmark\medskip} \def\eproofend{\medskip} % \def\solution{\medskip{\sl Ре╚ение. }\ignorespaces} % \def\leaf#1{\hbox{\vbox{\hrule\hbox{\vrule\kern1pt\vbox{\kern1pt\hbox{#1}\kern1pt}\kern1pt\vrule}\hrule}}} \def\node#1{\hbox{$(#1)$}} \def\elnode#1{\hbox{$<#1>$}} \def\]{\leavevmode\hbox{\tt\char`\ }} \def\roundit#1{(#1)} \def\<#1>{\left\langle#1\right\rangle} \def\upup{\mathop{\rm upup}\nolimits} \def\dndn{\mathop{\rm dndn}\nolimits} \def\lflf{\mathop{\rm lflf}\nolimits} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Special alignment for equations %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\eqalignrem#1{\null\,\vcenter{\openup1\jot \halign{\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$\hfil&$\displaystyle{{}\rem{##}}$\hfil \crcr#1\crcr}}\,} \def\displaynarrow#1{\null\,\vcenter{\openup1\jot \halign{$\hfil\displaystyle##\hfil$\crcr #1\crcr}}} \def\eqalignter#1{\null\,\vcenter{\openup1\jot \halign{\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$\hfil&$\displaystyle{{}##}$\hfil \crcr#1\crcr}}\,} \def\twocoleqalign#1{\null\,\vcenter{\openup1\jot \halign{\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}\qquad$\hfil&\hfil$\displaystyle{##}$&$\displaystyle{{}##}$\hfil \crcr#1\crcr}}\,} \def\displaylinesno#1{\displ@y \tabskip\centering \halign to\displaywidth{\hfil$\@lign\displaystyle{{}##}$\hfil\tabskip\centering &\llap{$\@lign##$}\tabskip\z@skip\crcr #1\crcr}} %%% \def\descrtable#1{ \setbox\tbox\vbox{\halign{##\bskip&\hbox to 0pt{\hss ## \hss}\cr#1}} $$\vbox{\halign{##\bskip\hfil&\vtop{\advance\hsize by -\wd\tbox\noindent ##}\cr #1}}$$ } \def\descralign#1{ \setbox\tbox\vbox{\halign{$\displaystyle{##{}}$&\hbox to 0pt{\hss ## \hss}\cr#1}} \vbox{\halign{\strut\hfil$\displaystyle{##{}}$&\vtop{\advance\hsize by -\wd\tbox\noindent ##}\cr #1}} } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Tableau %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newbox\cellbox \newdimen\cellwd \def\cell#1{\strut\bskip#1\hfil\bskip} \def\measurecell#1{\setbox\cellbox=\hbox{\cell{#1}}\ifnum\wd\cellbox>\cellwd\global\cellwd=\wd\cellbox\else\relax\fi} \def\tblout#1{\vcenter{\halign{\vrule\vbox{\hbox to\cellwd{\cell{##}}\hrule}\vrule&&\vbox{\hbox to\cellwd{\cell{##}}\hrule}\vrule\cr \noalign{\hrule} #1% }}} \def\tableau#1{ \offinterlineskip\cellwd=0pt \setbox\tbox=\vbox{\halign{\vrule\measurecell{##}\vrule&&\measurecell{##}\vrule\cr#1}} \ifmmode\tblout{#1}\else$\displaystyle\tblout{#1}$\fi } % \def\revtblout#1{\vcenter{\halign{\vrule\vbox{\hrule\hbox to\cellwd{\cell{##}}}\vrule&&\vbox{\hrule\hbox to\cellwd{\cell{##}}}\vrule\cr #1% \noalign{\hrule} }}} \def\revtableau#1{ \offinterlineskip\cellwd=0pt \setbox\tbox=\vbox{\halign{\vrule\measurecell{##}\vrule&&\measurecell{##}\vrule\cr#1}} \ifmmode\revtblout{#1}\else$\displaystyle\revtblout{#1}$\fi } %%% \def\fpaligncell#1#2#3{ \vbox{\halign{ \strut $##{}$&\hfil$##$&&\hfil$##$\hfil\cr U=\cr V=\cr \noalign{\hrule} W=\cr }} } \def\fpalignex(#1)#2#3#4{{ \boxit{ \vbox{ \halign{ \hskip 0.5em ## \hskip 0.5em\cr \fpaligncell{#2}{#3}{#4}\cr \hfill\hbox{(#1)}\hfill\cr } } } }} %%%%%%%%%%%%%%%%%%%%%% %% TV scripts %%%%%%%%%%%%%%%%%%%%%% \def\tvscript#1.#2\body#3\endtvscript{{\bf #1.}#2\descrtable{#3}\par} %\def\endtvscript{\egroup} %% hide private macros \catcode`\@=12