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diff --git a/Master/texmf-dist/source/latex/elsarticle/contrib/mytool.tex b/Master/texmf-dist/source/latex/elsarticle/contrib/mytool.tex deleted file mode 100644 index f0c6f841739..00000000000 --- a/Master/texmf-dist/source/latex/elsarticle/contrib/mytool.tex +++ /dev/null @@ -1,83 +0,0 @@ -\Clear{426.79134pt}{% -\let\la\lambda -\noindent\textbf{Remark 3.}\enspace -We remark that; when the ratio $h/\la$ tends to 0, the expression $\la -L(r,s)=-(s-r)/(4\left(\frac{h}{\la}\right)^2+(r-s)^2)$ tends to -$1/(r-s)$ which is a singular function. This means that the expression -$\la L(r,s)$ is not well behaved for the small values of -$h/\la$. Consequently, for the solution to converge, the integrals of -(10) and (11) must be evaluated with a large number of -nodes. In our numerical applications (cf. section 5), we -use 100 nodes to evaluate these integrals. With the smallest value of -$h/\la=0.02$, the convergence is good with $N=20$. -} -\Clear{426.79134pt}{% -\noindent\textbf{Theorem 2.}\enspace\itshape -For system (8), consensus can be achieved with -$\|T_{\omega z}(s)\|_{\infty}<\gamma$ if there exist a symmetric -positive definite - matrix $P\in \mathcal{R}^{(n-1)\times (n-1)}$ and a scalar $\mu>0$ satisfying -\setcounter{equation}{9} -\begin{eqnarray}\label{10} -\Gamma=\begin{bmatrix} --\bar{L}^TP-P\bar{L}+U_1^TU_1+\mu \bar{E}&PU_1^TE_1&PU_1^T\\ -E_1^TU_1P&-\mu I&0\\ U_1P&0&-\gamma^2I\end{bmatrix}<0, -\end{eqnarray} -where $\bar{L}=U_1^TLU_1$ and $\bar{E}=U_1^TE_2^TE_2U_1.$ -} -\Clear{426.79134pt}{% -\noindent\textbf{Proof of Theorem 2.}\enspace Proof follows -straightforward from Lemma 3 and Theorem 1. However, it should be -emphasized that all possible $\bar{L}_{\sigma(t)}$ should share a -common Lyapunov function $V(\delta)=\delta^T(t)P\delta(t)$ (see -the proof of Lemma 3 in Appendix A). \hfill$\square$ -} -\Clear{426.79134pt}{% - \begin{enumerate}[1.] - \item The enumerate environment starts with an optional - argument `1.' so that the item counter will be suffixed - by a period. - \item If you provide parentheses to the number, the - output will have only one parentheses for all the item - counters. - \item You can use `(a)' for alphabetical counter and '(i)' for - roman counter. - \begin{enumerate}[a)] - \item Another level of list with alphabetical counter. - \item One more item before we start another. - \begin{enumerate}[(i)] - \item This item has roman numeral counter. - \item Another one before we close the third level. - \end{enumerate} - \item Third item in second level. - \end{enumerate} - \item All list items conclude with this step. -\end{enumerate} -} -\Clear{284.52756pt}{% -\lmrgn=4em - \begin{enumerate}[Step 1.] - \item This is the first step of the example list. -\item Obviously this is the second step. -\item The final step to wind up this example. - \end{enumerate} -} -\Clear{284.52756pt}{% -\centering - {\ttfamily\bs includegraphics[width=3in,angle=45]\lb - tiger.pdf\rb}\\ - \hspace*{-1cm} - \includegraphics[width=3in,angle=45,origin=c]{tiger.pdf}\\ - \raggedright - \textbf{Fig.~1.}~~More details on the usage of {\ttfamily\bs - includegraphics} can be found in the \textsf{grfguide.ps} of the - \LaTeX{} documentation. -} -\Clear{426.79134pt}{% -\raggedright -\begin{enumerate}[{[1]}] -\item Knuth, D.E., \emph{TeX: The Program}, Computers \& -Typesetting; B., 1995, Addisson-Wesley Publishing Co., Inc., New -York. -\end{enumerate} -} |