%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\pagestyle{myheadings}      % стиль оформления страницы -- колонтитулы
                            % в вместе с номерами страниц

\evensidemargin=-0.11 cm    % то же для страниц с четными номерами
                            % (при одно сторонней печати игнорируются)
\oddsidemargin=0 cm         % 1 дюйм = 2.54 cм
%\oddsidemargin=0 cm        % 1 дюйм = 2.54 cм


%\voffset=-1cm              % сдвиг всей страницы вверх на ___  как единого целого

%%\topmargin=0.6 cm         % расстояние от верхнего края до нижнего
                            % колонтитула минус 1 дюйм

\textwidth=16 cm            % ширина текста
\textheight=21.5 cm         % высота текста

\footskip=1 cm


\def\baselinestretch{1.1}   % печать с большим интервалом
\parindent= 7mm             % абзацный отступ

%\flushbottom               % все страницы одинаковой высоты
%\raggedbottom
\tolerance=1000             % терпимость к "жидким" строкам
\relpenalty=10000           % запрет разрывов строк после бинарных
                            % операций во внутритекстовых формулах
\binoppenalty=10000         % запрет разрывов строк после бинарных
                            % отношений во внутритекстовых формулах
%\emergencystretch = 5pt

%\thispagestyle{empty}      % удаляет с headers&footers с текущей страницы


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% Убедительно просим не создавать новых макроопределений, кроме жизненно
%% необходимых (внимательно изучите введеные ниже макроопределения,
%% при составлении вашей статьи необходимо пользоваться только ими).
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\DeclareMathOperator{\im}{Im}
\DeclareMathOperator{\re}{Re}
\DeclareMathOperator{\Div}{div}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\dist}{dist}
\DeclareMathOperator{\col}{col}
\DeclareMathOperator{\var}{var}
\DeclareMathOperator{\sgn}{sgn}
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\DeclareMathOperator{\diag}{diag}
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\DeclareMathOperator{\loc}{loc}
\DeclareMathOperator{\per}{per}
\DeclareMathOperator{\cov}{cov}
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\DeclareMathOperator{\cf}{cf}
\DeclareMathOperator{\add}{add}
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\DeclareMathOperator{\meas}{meas}
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%%%%%

\DeclareMathOperator{\Sadj}{Sadj}%
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\def\const{\textrm{const}}
\def\Box{\square}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\sectionmark#1{}
\def\subsectionmark#1{}
\def\ps@copyright{\let\@mkboth\@gobbletwo
  \def\@oddhead{}%
  \let\@evenhead\@oddhead
  \def\@oddfoot{\small\sl
    \def\@tempa{0}
    \ifx\@volume\@tempa
      Preprint submitted to \@journal\hfil\@date\/%
    \else
      Article published in \@jou@vol@pag\hfil\hbox{}\fi}%
  \let\@evenfoot\@oddfoot
}
%ay
\def\printed#1{\tiny\textbf{\emph{Статья поступила в редакцию #1}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Обозначения для числовых множеств

\def\R{\mathbb R}
\def\C{\mathbb C}
\def\N{\mathbb N}
\def\Z{\mathbb Z}

\theoremstyle{plain}                             %% This is the default

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Определение окружений типа "теорема" (без нумерации; текст утверждения
% печатается курсивом)

\newtheorem*{theorem*}{Theorem}
\newtheorem*{corollary*}{Corollary}
\newtheorem*{lemma*}{Lemma}
\newtheorem*{property*}{Property}
\newtheorem*{statement*}{Statement}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Определение окружений типа "теорема" (без нумерации; текст утверждения
% печатается курсивом) {РУССКИЙ ЯЗЫК}

\newtheorem*{theoremr*}{Теорема}
\newtheorem*{corollaryr*}{Следствие}
\newtheorem*{lemmar*}{Лемма}
\newtheorem*{propertyr*}{Свойство}
\newtheorem*{statementr*}{Утверждение}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Определение окружений типа "теорема" (без нумерации; текст утверждения
% печатается курсивом) {УКРАИНСКИЙ ЯЗЫК}

\newtheorem*{theoremukr*}{Теорема}
\newtheorem*{corollaryukr*}{Наслідок}
\newtheorem*{lemmaukr*}{Лема}
\newtheorem*{propertyukr*}{Свойство}
\newtheorem*{statementukr*}{Твердження}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Определение окружений типа "теорема" (с одинарной нумерацией; текст --
% курсивом)

\newtheorem{theorem}{Theorem}%[section] -- добавить к определениям всех
\newtheorem{corollary}{Corollary}%%подобных окружений для двойной нумерации
\newtheorem{lemma}{Lemma}
\newtheorem{property}{Property}
\newtheorem{statement}{Statement}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Определение окружений типа "теорема" (с одинарной нумерацией; текст --
% курсивом) {РУССКИЙ ЯЗЫК}

\newtheorem{theoremr}{Теорема}%[section] -- добавить к определениям всех
\newtheorem{corollaryr}{Следствие}%%подобных окружений для двойной нумерации
\newtheorem{lemmar}{Лемма}
\newtheorem{statementr}{Утверждение}

\theoremstyle{definition}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Определение окружений типа "теорема" (с одинарной нумерацией; текст --
% курсивом) {УКРАИНСКИЙ ЯЗЫК}

\newtheorem{theoremukr}{Теорема}%[section] -- добавить к определениям всех
\newtheorem{corollaryukr}{Наслідок}%%подобных окружений для двойной нумерации
\newtheorem{lemmaukr}{Лема}
\newtheorem{statementukr}{Твердження}

\theoremstyle{definition}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Определение окружений типа "теорема" (без нумерации; текст утверждения
% печатается прямым шрифтом)

\newtheorem*{definition*}{Definition}
\newtheorem*{remark*}{Remark}
\newtheorem{proposition*}{Proposition}
\newtheorem*{example*}{Example}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Определение окружений типа "теорема" (без нумерации; текст утверждения
% печатается прямым шрифтом) {РУССКИЙ ЯЗЫК}

\newtheorem*{definitionr*}{Определение}
\newtheorem*{remarkr*}{Замечание}
\newtheorem{propositionr*}{Предложение}
\newtheorem*{exampler*}{Пример}
\newtheorem*{proofr}{Доказательство}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Определение окружений типа "теорема" (без нумерации; текст утверждения
% печатается прямым шрифтом) {УКРАИНСКИЙ ЯЗЫК}

\newtheorem*{definitionukr*}{Означення}
\newtheorem*{remarkukr*}{Зауваження}
\newtheorem*{exampleukr*}{Приклад}
\newtheorem*{proofukr*}{Доведення}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Определение окружений типа "теорема" (с одинарной нумерацией; текст
% утверждения печатается прямым шрифтом)

\newtheorem{definition}{Definition}
\newtheorem{remark}{Remark}
\newtheorem{example}{Example}
\newtheorem{proposition}{Proposition}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Определение окружений типа "теорема" (с одинарной нумерацией; текст
% утверждения печатается прямым шрифтом) {РУССКИЙ ЯЗЫК}

\newtheorem{definitionr}{Определение}
\newtheorem{remarkr}{Замечание}
\newtheorem{exampler}{Пример}
\newtheorem{propositionr}{Предложение}
\newtheorem{propertyr}{Свойство}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Определение окружений типа "теорема" (с одинарной нумерацией; текст
% утверждения печатается прямым шрифтом) {УКРАИНСКИЙ ЯЗЫК}

\newtheorem{definitionukr}{Означення}
\newtheorem{remarkukr}{Зауваження}
\newtheorem{exampleukr}{Приклад}
\newtheorem{propertyukr}{Властивість}
\newtheorem*{proofukr}{Доведення}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\allowdisplaybreaks     % Разрешение переносить на другую страницу часть
                        % многострочной формулы
\sloppy                 %

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                                       %%
%%                    НЕ МЕНЯТЬ!!!                       %%
%%                                                       %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\renewcommand{\refname}{Список литературы}%
\renewcommand{\labelenumi}{\theenumi.}%
\renewcommand{\labelenumii}{\theenumii)}%

%   --------------------    Список литературы  ----------------------
%       Нумерация литературы -- без скобок []
\makeatletter
\renewcommand{\@biblabel}[1]{#1.\hfill}         %    Без []
\makeatother
%

\renewcommand{\keywords}[1]{{\noindent\leftskip=0.5in\rightskip=0.5in
\footnotesize Keywords: #1
\medskip}}

\renewcommand{\author}[1]
{\begin{center} {\bfseries{\copyright~~~#1}}
\end{center}}

\renewcommand{\address}[1]
{\begin{center}
\tiny
{\scshape{#1}}
\end{center}\medskip}

\renewcommand{\email}[1]{\medskip
{\sl e-mail:} \texttt{#1}\medskip}

\renewenvironment{abstract}{
\medskip
\footnotesize}
{\par\medskip}

\renewcommand{\title}[1]{
\begin{center}
{\bfseries #1}
\end{center}}

\setcounter{tocdepth}{0}

\makeatletter
\newcommand{\l@art}[2]%
%{\hbox to\textwidth{#1\dotfill #2}}
{\pagebreak[0]\vspace{1 em plus 1pt}%
\@tempdima=3em%
{\rightskip=\@pnumwidth%
\leftskip=\@tempdima%
\noindent\hspace{-1.5em}%
#1\nolinebreak\dotfill\nolinebreak\rlap%
{\makebox[\@pnumwidth][r]{#2}}\par\nopagebreak[3]}}
\makeatother

%%\numberwithin{equation}{section}%% Двойная нумерация формул