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\noindent {\footnotesize The Extended Abstracts of \\
The 3$^{\rm rd}$ Seminar on Operator Theory and its Applications\\
8-9$^{\rm th}$ March 2017, Ferdowsi University of Mashhad, Iran}\\[1.00in]
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\title[Synchronization for uncertain chaotic neural networks]{Synchronization for uncertain chaotic neural networks with mixed time delays}
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\author[Babaei Tehrani, Jamshidian, Zanjani]{Ghasem Babaei Tehrani$^1$, Amir Ali Jamshidian$^1$\Speaker and Akbar Zanjani$^2$}
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\authorsaddresses{$^1$ Department of Pure Mathematics, Ferdowsi University
of Mashhad, P. O. Box 1159, Mashhad 91775, Iran;\\ Centre of
Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi
University of Mashhad, Mashhad, Iran.\\
javadi@um.ac.ir; jamshid@member.ams.org\\
\vspace{0.5cm} $^2$ Department of Mathematics, Faculty of
Mathematics and Statistics, University of Birjand, Birjand, Iran.\\
zanjani@bu.ac.ir}
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\subjclass[2010]{Primary 47A55; Secondary 39B52, 34K20, 39B82.}
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% keywords; Note that the number of keywords must be at least 3 items and at most 5 items.
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\keywords{Hilbert space, local cohomology, semi-Fredholm operator
(at least 3 and at most 5 items).}
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% Abstract of your extended abstract
% Note: the abstract should be 200 words or less with no reference number therein.
%The speaker is responsible for the proper formatting his/her talk by using the style
%file of the booklet of abstracts.
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\begin{abstract}
Here please insert your abstract. The abstract should be 200 words
or less with no reference number therein and should contain the main
result of the talk. The speaker is responsible for the proper
formatting of his/her talk by using the style file of the booklet of
abstracts.
\end{abstract}
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\maketitle
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\section{Introduction}
The number of pages of the extended abstract
should have 3-4 pages. Papers prepared in less than 3 pages, more
than 4 pages or out of the style of the meeting will be
returned.
You can use Photoshop for converting eps to jpg. A sample for
inserting a jpg file is the following (use winedit and directly
produce pdf not dvi):
% \includegraphics[scale=1.75]{BJMA.jpg}
Here you should state the introduction, preliminaries and your
notation. Authors are required to state clearly the contribution of
the extended abstract and its significance in the introduction.
There should be some survey of relevant literature.
\subsection{Instructions for speakers}
While you are preparing your extended abstract, please take care of
the following:\\
\textbf{Before submitting your extended abstract to the
meeting, please rename its tex file by using your name and the
names of your coauthors, e.g. Jamshidian-BabaeiTehrani.tex\\}
\textbf{\begin{enumerate}
\item MSC2010: Primary only one item; and Secondary at most 3 items.\\
\item Key words: At least 3 items and at most 5 items.\\
\item Authors: Full names, mailing addresses and emails of all authors.\\
\item Margins: A long formula should be broken into two or more lines. Empty spaces in the text should be removed.\\
\item Tags (Formula Numbers): Use $\backslash \text{\tt label\{A\}}$ and $\backslash \text{\tt eqref\{A\}}$. Remove unused tags.\\
\item Acknowledgement: At the end of extended abstract but preceding to References, if there is any\\
\item References: Use $\backslash \text{\tt cite\{H\}}$ to refer to the specific book or paper [2], whose bibitem code is $\backslash \text{\tt bibitem\{H\}}$ . Remove unused references. References should be listed in the alphabetical order according to the surnames of the first author at the end of the extended abstract and should be cited in the text as, e.g., [2] or [3, Theorem 4.2], etc.\\
\item Abbreviations: Abbreviations of titles of periodicals or books should be given by using Math. Reviews, see Abbreviations of names of serials or MRLookup at\\
http://www.ams.org/mrlookup.
\end{enumerate}}
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\section{Main results}
The following is an example of a lemma.
\begin{lemma} Assume that $K$ is
an arbitrary field, $GL(n,K)$ is a linear group of dimension $n$
over $K$, $n$ is a positive integer.
\begin{itemize}
\item [\rm{(a)}]~ If $G$ is a locally nilpotent subgroup of $GL(n,K)$, then $G$ has no proper
conjugately dense subgroups;
\item [\rm{(b)}]~ If $G$ is a locally solvable subgroup of $GL(n,K)$, then $G$ has
no proper conjugately dense subgroups.
\end{itemize}
\end{lemma}
%---------------------------------------------------------------------------------------%
Here is an example of a table.
\begin{table}[ht]
\small
\caption{Your table's caption}\label{eqtable}
\begin{tabular}{ccc}
\hline
% after \\: \hline or \cline{col1-col2} \cline{col3-col4} ...
col1 & col2 & col3 \\
\hline
4 & 5 & 6 \\
7 & 8 & 9 \\
\hline
\end{tabular}
\end{table}
This is an example of a matrix
\begin{equation*}
\begin{bmatrix}
1 & -2 \\
3 & 5
\end{bmatrix}
\end{equation*}
The following is an example of an example.
%---------------------------------------------------------------------------------------%
\begin{example}
Let $D_{\infty}=\cong {\mathbb Z}_2*{\mathbb Z}_2$ be
the infinite dihedral group. Then
$$M^{(2)}(D_{\infty})\not\cong M^{(2)}({\mathbb Z}_2)\oplus M^{(2)}({\mathbb Z}_2).$$
\end{example}
%---------------------------------------------------------------------------------------%
The following is an example of a theorem and a proof. Please note how to refer to a formula.
%---------------------------------------------------------------------------------------%
\begin{theorem}\label{maintheorem}
If ${\bf B}$ is an open ball of a real inner product space
${\mathcal X}$ of dimension greater than $1$, then there exist
additive mappings $T: {\mathcal X}\to {\mathcal Y}$ and $b:{\mathbb
R}_+\to {\mathcal Y}$ such that $f(x) = T(x) + b\left (\|x\|^2\right
)$ for all $x\in {\bf B}\setminus \{0\}$.
\end{theorem}
%---------------------------------------------------------------------------------------%
\begin{proof}
First note that if $f$ is a generalized Jensen mapping with
parameters $t=s \geq r $, then
\begin{align}\label{additive}
f(\lambda(x+y))&=\lambda f(x) + \lambda f(y)\nonumber\\
&\leq \lambda (f(x) + f(y))\nonumber\\
&= f(x) + f(y)
\end{align}
for some $\lambda \geq 1$ and all $x, y\in {\bf B}\setminus \{0\}$
such that $x \perp y$.
\medskip
\noindent \underline{\rm Step (I)- the case that f is odd:} Let $x
\in {\bf B} \setminus \{0\}$. There exists $y_0 \in {\bf B}
\setminus \{0\}$ such that $x \perp y_0$, $x + y_0 \perp x - y_0$.
We have
\begin{eqnarray*}
f(x)&=& f(x)- \lambda\, f\left ( \frac{x+y_0}{2\, \lambda}\, \right
) -
\lambda \, f\left ( \frac{x-y_0}{2\, \lambda}\, \right )\\
&&+ \, \lambda \, f\left ( \frac{x+y_0}{2\, \lambda}\, \right ) -
\lambda^2\, f\left ( \frac{x}{2\, \lambda^2}\, \right ) - \lambda^2
\, f\left (
\frac{y_0}{2\, \lambda^2}\, \right )\\
&=& 2\, \lambda^2 \, f\left ( \frac{x}{2\, \lambda^2}\, \right ).
\end{eqnarray*}
\medskip
\noindent \underline{\rm Step (II)- the case that f is even:} Using
the same notation and the same reasoning as in the proof of Theorem
\ref{maintheorem}, one can show that $f(x)=f(y_0)$ and the mapping $Q:
{\mathcal X}\to {\mathcal Y}$ defined by $Q(x) : = (4\lambda^2)^n
f((2\lambda^2)^{-n}x)$ is even orthogonally additive.
\medskip
Now the result can be deduced from Steps (I) and (II) and
\eqref{additive}.
\end{proof}
%---------------------------------------------------------------------------------------%
\bigskip
\section*{Acknowledgement} Acknowledgements could be placed at the end
of the text but precede the references.
\hspace{1in}
\fbox{\scriptsize{\textbf{Please cite your relevant papers but at
most total 5 papers/books.}}}
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% References
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\bibliographystyle{amsplain}
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% Please cite your relevant papers but at most total 5 papers/books.
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\begin{thebibliography}{5}
\bibitem{haag1} U. Haagerup, \textit{Solution of the similarity problem for cylic representations
of $C^*$-algebras}, Ann. of Math. 118 (1983), no. 2, 215--240.
\bibitem{H} A.A. Jamshidian, \textit{\v{C}ebyshev inequality}, Linear Multilinear Algebra, arXiv:1154.1464v2 (to appear).
\bibitem{J-J} M. Mirzavaziri and M. S. Moslehian, \textit{Automatic continuity of $\sigma$-derivations in $C^*$-algebras}, Proc. Amer. Math. Soc. \textbf{134} (2006), no. 11, 3319--3327.
\bibitem{MUR} V.S. Ryabenkii and S.V. Tsynkov, \textit{A theoretical introduction to numerical analysis}, Chapman \& Hall/CRC, Boca Raton, FL, 2007.
\bibitem{RAS} J. Mi\'lov\'c, \textit{Lie symmetries of systems of second-order linear ordinary differential equations}, Nonlinear analysis, 239--267, Springer Optim. Appl., 65, Springer, New York, 2011.
\end{thebibliography}
\end{document}