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\title[abbreviated title ]{title}

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\author[M. Hojo]{Mayumi Hojo}

\address[M. Hojo]{??????????????, Japan}
\email{{\tt ????????@????}}

\author[W. Takahashi]{Wataru Takahashi}
\address[W. Takahashi]{????????, Taiwan}
\email{\tt ???????@???????}



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\begin{abstract}
???????????????
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\section{Introduction}

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Please change shape from  (1.1) to (1.2) or (1.3).\\


Please do not use the following style (textstyle).

\begin{equation}\label{sample}
    \begin{array}{ll}&\|x_t-p\|^2\\
 &=\langle x_t-w_t,x_t-p\rangle+\langle(I-\theta_tA)(S{\Lambda}^N_tS_rx_t-p),x_t-p\rangle
 +\theta_t[t\langle\gamma Vx_t-\mu Fp,x_t-p\rangle\\
 &~~~+\langle(I-t\mu F)S{\Lambda}^N_tS_rx_t-(I-t\mu F)p,x_t-p\rangle]+\theta_t\langle(I-A)p,x_t-p\rangle\\
 &\leq[1-\theta_t(\bar\gamma-1+t(\tau-\gamma l)]\|x_t-p\|^2
 -\frac{1-\theta_t(\bar\gamma-1+t\tau)}{2}[\lambda_{i,t}(2\eta_i-\lambda_{i,t})\|B_i{\Lambda}^{i-1}_tS_rx_t-B_ip\|^2\\
 &~~~+r(2\alpha-r)\|{\mathcal{A}}x_t-{\mathcal{A}}p\|^2]+\theta_t(t\|\gamma Vp-\mu Fp\|\|x_t-p\|+\|(I-A)p\|\|x_t-p\|),\end{array}
\end{equation}

\bigskip

Please use the following style (displaystyle).

\begin{equation}\label{1.2}
   \aligned
\|x_t-p\|^2 &=\langle x_t-w_t,x_t-p\rangle+\langle(I-\theta_tA)(S{\Lambda}^N_tS_rx_t-p),x_t-p\rangle
 \\&\quad+\theta_t[t\langle\gamma Vx_t-\mu Fp,x_t-p\rangle\\
&\quad+\langle(I-t\mu F)S{\Lambda}^N_tS_rx_t-(I-t\mu F)p,x_t-p\rangle]\\
&\quad+\theta_t\langle(I-A)p,x_t-p\rangle\\
 &\leq[1-\theta_t(\bar\gamma-1+t(\tau-\gamma l)]\|x_t-p\|^2\\
&\quad -\frac{1-\theta_t(\bar\gamma-1+t\tau)}{2}[\lambda_{i,t}(2\eta_i-\lambda_{i,t})\|B_i{\Lambda}^{i-1}_tS_rx_t-B_ip\|^2\\
&\qquad+r(2\alpha-r)\|{\mathcal{A}}x_t-{\mathcal{A}}p\|^2]\\&\quad+\theta_t(t\|\gamma Vp-\mu Fp\|\|x_t-p\|+\|(I-A)p\|\|x_t-p\|),
\endaligned\end{equation}

or
\begin{eqnarray}\label{1.3}
\|x_t-p\|^2 &=&\langle x_t-w_t,x_t-p\rangle+\langle(I-\theta_tA)(S{\Lambda}^N_tS_rx_t-p),x_t-p\rangle\nonumber\\
 &&+\theta_t[t\langle\gamma Vx_t-\mu Fp,x_t-p\rangle\nonumber\\
&&+\langle(I-t\mu F)S{\Lambda}^N_tS_rx_t-(I-t\mu F)p,x_t-p\rangle]\nonumber\\
&&+\theta_t\langle(I-A)p,x_t-p\rangle\nonumber\\
 &\leq&[1-\theta_t(\bar\gamma-1+t(\tau-\gamma l)]\|x_t-p\|^2\\
&& -\frac{1-\theta_t(\bar\gamma-1+t\tau)}{2}[\lambda_{i,t}(2\eta_i-\lambda_{i,t})\|B_i{\Lambda}^{i-1}_tS_rx_t-B_ip\|^2\nonumber\\
&&+r(2\alpha-r)\|{\mathcal{A}}x_t-{\mathcal{A}}p\|^2]\nonumber\\
&&+\theta_t(t\|\gamma Vp-\mu Fp\|\|x_t-p\|+\|(I-A)p\|\|x_t-p\|),\nonumber
\end{eqnarray}



\begin{thebibliography}{99}%Please arrange author's name in alphabetical order.

\bibitem{1} B. D. O. Anderson and J. B. Moore, {\it Linear optimal
control},  Prentice-Hall,  Englewood Cliffs, NJ, 1971.


\bibitem{2}S. Aubry and P.Y. Le Daeron, {\it The discrete
Frenkel-Kontorova model and its extensions I},  Physica D  {\bf 8} (1983), 381--422.

\bibitem{3} J. Baumeister, A. Leitao and G. N. Silva, {\it On
the value function for nonautonomous optimal control problem with
infinite horizon},  Systems Control Lett. {\bf 56}  (2007),  188--196.


\bibitem{4} J. Blot, {\it Infinite-horizon Pontryagin
principles without invertibility},  J. Nonlinear Convex Anal.
{\bf 10} (2009),  177--189.

\bibitem{5} J. Blot and P. Cartigny, {\it  Optimality in
infinite-horizon variational problems under sign conditions},
J. Optim. Theory Appl. {\bf 106} (2000),  411--419.








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