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\begin{document}

 \head{F.F. Author, L.L.  Author, S.S. Author} %% ����������

\newpage

\vestuken{UDC number(s)}{PP}{doi}%

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\copAutor{0}{F.\,F.\,Author, L.\,L.\,Author, S.\,S.\,Author}%%%% ������� �������� %%%%
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\title{Title of the paper}

\author{F.F. Author$^1$, L.L.  Author$^2$, S.S. Author$^{1,2}$}
{ \begin{tabular}{c}%
$^1$Unknown State University, Another Town, 4 Street, Zipcode,
Country\\
$^{2}$Wellknown State University, Another City, 101 Street, Zipcode, Country\\
name1@email.com, name2@email.com, name3@email.com
\end{tabular}}

\abstract{ Abstract in language \# {\bf 1} (in Ukrainian {\bf or} in
Russian {\bf or} in English) Short abstract in language \# 1
 Short abstract in language \# 1 Short abstract in language \# 1  Short abstract in language \# 1  Short abstract in language \# 1
    Short abstract in language \# 1 Short abstract in language \# 1  Short abstract in language \# 1 Short abstract in language \# 1  Short abstract in language \#
    1. \\
{\it Keywords:} eng  {\bf or} {\it ������ �����:} ukr  {\bf or}
{\it �������� �����:} rus;  text; text }

\abstract{{Author F.F.,  Author L.L.,  Author S.S.} {\bf Title of
the paper in language \# 2.} Short abstract in language \# 2 (in
Ukrainian {\bf or} in Russian {\bf or} in English) Short abstract in
language \# 2
 Short abstract in language \# 2  Short abstract in language \# 2  Short abstract in language \# 2  Short abstract in language \#
  2    Short abstract in language \# 2. \\
 {\it Keywords:} eng  {\bf or} {\it ������ �����:} ukr  {\bf or}
{\it �������� �����:} rus;  text; text }

\abstract{{Author F.F.,  Author L.L.,  Author S.S.} {\bf Title of
the paper in language \# 3.} Short abstract in language \# 3 (in
Ukrainian {\bf or} in Russian {\bf or} in English) Short abstract in
language \# 3
 Short abstract in language \# 3  Short abstract in language \# 3  Short abstract in language \# 3  Short abstract in language \#
  3    abstract in language \# 3. \\
  {\it Keywords:} eng  {\bf or} {\it ������ �����:} ukr  {\bf or}
{\it �������� �����:} rus;  text; text\\
   \smallskip
 {\it 2010 Mathematics Subject Classification} xxSzz, aaRbb. }

\medskip
\centerline{\bf 1. Introduction}

\medskip

Manuscript should be prepared in \LaTeXe using the following files:\par
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 The file \href{http://vestnik-math.univer.kharkov.ua/Visnyk-2018-11.tex}{\usebox{\VueTEX}} contains all the definitions
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The
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We recommend to use the last volume of the journal:

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as an example in manuscript preparation. �����������
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(\href{http://vestnik-math.univer.kharkov.ua/currentv.htm}{http://vestnik-math.univer.kharkov.ua/currentv.htm})
� ����� \href{http://vestnik-math.univer.kharkov.ua/currentv.htm}{\bf ������ ����������}.



If you experience difficulties with the manuscript submission,
please contact the Managing Editor of the Journal (Alexander
Rezounenko (�.�.���������)) vestnik-khnu@ukr.net.


 This is an example of using
references inside of a paper. See for example \cite{Pontryagin-1964}
(for definitions and main properties see \cite{Chueshov-2015} and
\cite[Part 3]{Lyapunov-1892}).

\begin{definition}\cite{Lyapunov-1892}.  Consider an autonomous nonlinear system
${\dot {x}}=f(x(t)),$ %%%$\; x(0)=x_{0},$
where
$x(t)\in {\mathcal {D}}\subseteq \mathbb{R}^{n}$
denotes the system state vector, ${\mathcal {D}}$ an open set, %%containing the origin,
and $ f:{\mathcal {D}} \rightarrow \mathbb{R}^{n}$ continuous on $ {\mathcal {D}}.$ Suppose ${\displaystyle f}$ has an equilibrium at $x_{e}$ so that $f(x_{e})=0$. Then this equilibrium is said to be {\bf Lyapunov stable}, if, for every $ {\displaystyle \epsilon >0},$ there exists a ${\displaystyle \delta >0}$ such that, if $ \|x(0)-x_{e}\|<\delta,$ then for every $t\geq 0$ we have $ \|x(t)-x_{e}\|<\epsilon$.

The equilibrium of the above system is said to be {\bf asymptotically stable} if it is Lyapunov stable and there exists $\delta >0$ such that if $\|x(0)-x_{e}\|<\delta$, then $\lim_{t\rightarrow \infty }\|x(t)-x_{e}\|=0.$
\end{definition}

\begin{remark}
The meanings of the above terms are the following:

    Lyapunov stability of an equilibrium means that solutions starting "close enough" \, to the equilibrium (within a distance $ \delta$ from it) remain "close enough" \, forever (within a distance $\epsilon$ from it). Note that this must be true for any $\epsilon$ that one may want to choose.
    Asymptotic stability means that solutions that start close enough not only remain close enough but also eventually converge to the equilibrium.
\end{remark}

Text text text text text text text text text text text text text
text text text text text \cite{Visnyk-2015-ukr,Visnyk-2015-en} text
text text text text text text text text text text text text text
text text text text text text text text text text text a formula



$$ \begin{array}{l}
A_l^\pm=\left(\alpha_{k-j}^\pm\right)_{k,j=0}^l>0 \quad
\mbox{as } \ l=1,\ldots,v^\pm(N)-1,\\
 A_l^\pm=\left(\alpha_{k-j}^\pm\right)_{k,j=0}^l\geq0,\ \ \det A_l^\pm=0
\quad \mbox{as }\ l\geq v^\pm(N).
\end{array}\eqno(1)$$


Thus we have the following main result.

\begin{theorem}[On the solution of the
unknown problem].

If A then B.
\end{theorem}

{\it Proof}. Text \cite{Visnyk-2015-ukr,Visnyk-2015-en} text text
text text text text text text text text text text text text text
text text text text text text text text text text text


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%\includegraphics[width=10.7cm]{AuthoR1-name-2016-1.jpg}
%������� ���������
%\centerline{�i�. 1. Name of the picture}     %For English text
%\end{figure}
%\bigskip


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%%\centering
%%\includegraphics[width=6.7cm]{author1-name-2010-1.bmp}
%%\centerline{�i�. 1. Name of the picture}     %For English text
%%\end{figure}
%%\bigskip


Use PDF-LaTeX to generate picture in PDF file.  Text
\cite{Visnyk-2015-ukr,Visnyk-2015-en} text text text text text text
text text text text text text text text text text text text text
text text text text text text text text text text text text text
text text text text text


This is an example of using references inside of a paper. See for
example \cite{Pontryagin-1964} (for definitions and main properties
see \cite[Part 3]{Lyapunov-1892}).
 Text text text text text text text text text text text text
text text text text text text text text text text text text text

\medskip
\centerline{\bf 2. Properties }

\medskip


This is an example of using references inside of a paper. See for
example \cite{Pontryagin-1964} (for definitions and main properties
see \cite[Part 3]{Lyapunov-1892}).

 Text text text text text text text text
text text text text text text text text text text text text text
text text text text text text text text text text text text text.
This Information for Manuscript Preparation is valid starting
November 2018.

In the case of non-observance of these  rules of manuscript
preparation a manuscript will not be considered.

 The
manuscript should have references in {\bf Roman script}.

\vskip5mm

{\bf Acknowledgement.}
Authors thank Name whose critical revision of the paper
allows to improve it essentially.

\renewcommand{\refname}{\normalsize \rm \centerline{REFERENCES}}
\vskip1cm
\begin{thebibliography}{9}


\bibitem{Lyapunov-1892} A.M. Lyapunov, The general problem of the stability of motion. 1892.
Kharkov Mathematical Society, Kharkov, 251~p. (in Russian). %
%[Original '����� ������ ��� ������������ ������i�. ���������i�% �.��������. �����i� ������������ ��������������� ��������. ��������. ��������i� ������������. 1892.'].

\bibitem{Pontryagin-1964} L. S. Pontryagin, On zeros of some .... functions. Izv. AN SSSR. Ser. Matem., -- 1942. -- {\bf 6}. -- P.~115--134.

\bibitem{Chueshov-2015} I.D. Chueshov, Dynamics of quasi-stable dissipative systems, Springer, 2015. --  390~p. %%ISBN: 978-3-310-22902-7; 978-3-319-22903-4.
DOI:
\href{http://dx.doi.org/10.1007/978-3-319-22903-4}{10.1007/978-3-319-22903-4}

\bibitem{Visnyk-2015-ukr} �.B.�uthor, Title of the paper, Visnyk of V.N.Karazin Kharkiv National University, Ser. ``Mathematics, Applied Mathematics and Mechanics''. -- 2015. -- {\bf 81}. -- P.~91--99.
(in Ukrainian).
%[Original '����� �.�. ����� �����, ³���� ����������� ������������� ������������ ����� �.�. �������, ���� �����������, ��������� ���������� �  �������. -- 2015. -- {\bf 81}. -- C.~91--99.]

\bibitem{Visnyk-2015-en} A.�.Author, Title of the paper, Visnyk of V.N.Karazin Kharkiv National University, Ser. ``Mathematics, Applied Mathematics and Mechanics''. -- 2015. -- {\bf 81}. -- P.~52--59.

\end{thebibliography}%}


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\abstractS{F.\,F.\,Author, S.\,S.\,Author, L.\,L.\,Author. {\bf Title of the paper in English.} %
Text of the extended abstract in English (NOT~LESS~THAN~1800
SYMBOLS, taking into account the keywords) ... text of the extended
abstract  ... text of the extended abstract ... text of the extended
abstract ...  text of the extended abstract ... text of the extended
abstract ... text of the extended abstract in English, text of the
extended abstract (NOT~LESS~THAN~1800 SYMBOLS, taking into account the keywords) ...
text of the extended annotation ... text of the extended annotation ... text of the extended annotation  ... text of the extended annotation ... text of the extended annotation ... text of the extended annotation  ... 
text of the extended annotation ... text of the extended annotation ... text of the extended annotation ...
text of the extended annotation ... text of the extended annotation  (NOT~LESS~THAN~1800 SYMBOLS, taking
into account the keywords). 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\\
{\it Keywords:} word1; word2; word3.}

\noindent
\begin{tabbing}%
Article history: \=Received: 15 February 2018; Final form: 15 May
2018; \\
 \>Accepted: 18 July 2018.
\end{tabbing}

 \end{document}
