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author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/fancytooltips/examples |
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Diffstat (limited to 'macros/latex/contrib/fancytooltips/examples')
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diff --git a/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo.pdf b/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo.pdf Binary files differnew file mode 100644 index 0000000000..b1c5c66d96 --- /dev/null +++ b/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo.pdf diff --git a/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo.sin.table b/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo.sin.table new file mode 100644 index 0000000000..e1383fb5ff --- /dev/null +++ b/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo.sin.table @@ -0,0 +1,29 @@ +#Curve 0, 25 points +#x y type +0.00000 0.00000 i +0.26167 0.25869 i +0.52333 0.49977 i +0.78500 0.70683 i +1.04667 0.86576 i +1.30833 0.96575 i +1.57000 1.00000 i +1.83167 0.96617 i +2.09333 0.86656 i +2.35500 0.70795 i +2.61667 0.50115 i +2.87833 0.26023 i +3.14000 0.00159 i +3.40167 -0.25715 i +3.66333 -0.49839 i +3.92500 -0.70570 i +4.18667 -0.86496 i +4.44833 -0.96534 i +4.71000 -1.00000 i +4.97167 -0.96658 i +5.23333 -0.86735 i +5.49500 -0.70907 i +5.75667 -0.50253 i +6.01833 -0.26177 i +6.28000 -0.00319 i + + diff --git a/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo.tex b/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo.tex new file mode 100644 index 0000000000..e5361d82a5 --- /dev/null +++ b/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo.tex @@ -0,0 +1,278 @@ +%\documentclass{article} +\documentclass[envcountsect,t,10pt]{beamer} + +%\usetheme{Ilmenau} +%\usetheme{Marburg} +%\usetheme{PaloAlto} + +\setbeamertemplate{theorems}[numbered] +\usepackage{amsthm,amsmath,graphicx,color} + +\usepackage{tikz} +\PassOptionsToPackage{naturalnames}{hyperref} + +\newtheorem{remark}{Remark} +\def\dx{{\mathrm d}x} +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\usepackage[inactive]{fancytooltips} +\begin{document} + +\title{Fantytooltips demo} +\author{Robert Ma\v{r}\'ik} + +\maketitle +\section{Introduction} + +\begin{frame}{Content} + \tableofcontents +\end{frame} +\begin{frame} + \frametitle{What can you find in this file?} + \begin{itemize} + \item Demo (math fiction) which shows how the cooperation between + preview and fancytooltips package can be used to insert popup + previews for equations, theorems and definitions into a + presentation -- see for example Figure \ref{pic:sine} (move the + mouse to the blue mark). + \item Explanation how we achieved this behaviour. + \end{itemize} +\end{frame} + +\section{Math text example} + +\begin{frame}{Demo: Definitions} + \begin{definition}[Excellent number{\cite[citation only for testing]{D-1}}] + Let $n$ be positive integer. The number $n$ is said to be + \textit{excellent}, if the last digit of the number $\alpha$ + defined by the relation + \begin{equation} + \label{eq:excel} + \alpha = n^2 +\int_0^{2\pi}\sin x\dx + \end{equation} + equals $1$.\label{def:excellent-number} + \end{definition} + + {(Note that from \eqref{eq:excel} it follows that $\alpha$ is + integer, see \ref{eq:sin}.) } + + {\begin{definition}[Happy number] + Let $n$ be positive integer. The number $n$ is said to be + \textit{happy}, if the last digit of the number $n$ equals $1$. + \label{def:happy-number} + \end{definition}} + + {Citations are also extracted. See \cite{D,D-R,D-F,D-Rez}. You + \textit{have to} insert emtpy line after each \texttt{\textbackslash + bibitem} command. Ordinary \tooltip{tooltips}{hodnost} and + \tooltipanim{animations}{4}{28} also work.} + \end{frame} + +\begin{frame}{Demo: Example and comments} +\begin{example} + The number $1$ is both happy and excellent. The number $129$ is + excellent but not happy. This follows immediately from the + Definitions \ref{def:excellent-number} and \ref{def:happy-number}. +\end{example} +\begin{alertblock}{Fancytooltips comment} + Put the mouse pointer to the graphical symbol following definitions + numbers. You will see the definitions again. We can also refer to + equation, like this: \eqref{eq:excel}. Note that the same reference + has been used on previous slide and the tooltip has not been + attached, since the reference to \eqref{eq:excel} on the previous + page is at the same page as its target. +\end{alertblock} +\end{frame} + + +\begin{frame}{Demo: A picture} + \begin{figure} + \centering +\begin{tikzpicture}[domain=0:6.28] + \draw[->] (0,0) -- (7,0) node[right] {$x$}; + \draw[->] (0,-1.2) -- (0,1.2) node[above] {$f(x)$}; + \shadedraw[color=black,top color=blue,bottom color=red] + plot[id=sin] function{sin(x)}; +\end{tikzpicture} + \caption{Sine curve} + \label{pic:sine} + \end{figure} + + On one of the previous slides (in Definition \ref{def:excellent-number}) + we defined \textit{excellent} number in terms of the number $\alpha$ + defined by relation \eqref{eq:excel}. Below we introduce a simple + characterization in Theorem \ref{theorem}. +\end{frame} + +\begin{frame}{Demo: Newton--Leibniz theorem} + + \begin{theorem} + Let $f(x)$ be integrable in the sense of Riemann on $[a,b]$. Let + $F(x)$ be a function continuous on $[a,b]$ which is an + antiderivative of the function $f$ on the interval $(a,b)$. Then + \begin{equation*} + \int_a^bf(x)\dx=[F(x)]_a^b=F(b)-F(a) + \end{equation*} + holds.\label{th:NL} + \end{theorem} +\end{frame} + +\begin{frame}{Demo: Integral term equals zero} + \begin{remark} + It is easy to see that + \begin{equation} + \label{eq:sin} + \int_0^{2\pi}\sin x\dx=0. + \end{equation} + Really, direct computation based on Newton-Leibniz Theorem + \ref{th:NL} shows + \begin{align*} + \int_0^{2\pi}\sin x\dx&=[\cos x]_0^{2\pi}\\ + &=\cos(2\pi)-\cos 0\\ + &=0. + \end{align*} + (see also Figure \ref{pic:sine}) + \end{remark} +\end{frame} + +\begin{frame} + \frametitle{Demo: Main result} + \begin{theorem}[Characterization of excellent numbers] + The positive integer $n$ is + \tooltip{excellent}{def:excellent-number} if and only if the last + digit of the number $n$ is either $1$ or $9$. + \label{theorem} + \end{theorem} + +\begin{alertblock}{Fancytooltips comment} + Since we used {\color{red}\texttt{\textbackslash + label\{def:excellent-number\}}} in the Definition + \ref{def:excellent-number}, we can insert a tooltip to the word + excellent by using command{\color{red} \texttt{\textbackslash + tooltip\{excellent\}\{def:excellent-number\}}}. In this case the + tooltip is activated by hovering the text, not the soap. This is the + default behavior of fancytooltips. +\end{alertblock} + +\end{frame} + +\begin{frame} + \frametitle{Demo: Corollary} + \begin{theorem}[Relationship between happy and excellent numbers] + Each \tooltip*{happy}{def:happy-number} number is + \tooltip{excellent}{def:excellent-number}. + \end{theorem} + +\begin{alertblock}{Fancytooltips comment} + The ``happy'' tooltip is created by + \texttt{\color{red}\textbackslash + tooltip*\{happy\}\{def:happy-number\}}. The starred version causes + that the active button is not attached to the text, but is attached + to the mark. The ``excellent'' tooltip is created by + \texttt{\color{red}\textbackslash + tooltip\{excellent\}\{def:excellent-number\}} and hence, the blue soap is + inactive and the text active. +\end{alertblock} +\end{frame} + +\section{How it works} +\begin{frame} + \frametitle{How it works} + \begin{itemize} + \item We compile the presentation in an ordinary way to get correct + labels and references. + \item We compile the presentation with preview package and extract + displayed equations, theorems, definitions and floats (tables and + figures). + \item We create a new document which contains those parts extracted + in the previous step, which have a label inside. + \item We compile the presentation again with redefined \texttt{ref} + macro. This macro inserts the popup using fancytooltips package. + \end{itemize} +\end{frame} + +% \section{Short howto} +% \begin{frame} +% \frametitle{How to create a presentation with pdf\LaTeX} +% % Creating tooltips is easy. Simply follow these steps. +% \begin{itemize} +% \item Create presentation with your favorit presentation package, +% such as +% \href{http://www.ctan.org/tex-archive/help/Catalogue/entries/acrotex-web.html}{\color{blue}web}, +% \href{http://www.ctan.org/tex-archive/macros/latex/contrib/pdfscreen/}{\color{blue}pdfscreen} +% or +% \href{http://www.ctan.org/tex-archive/help/Catalogue/entries/beamer.html}{\color{blue}beamer}. +% \item In Linux use the script \texttt{fancy-preview} to compile the +% presentation again, i.e. if your file is filename.tex run +% \begin{quote}\upshape\color{darkgreen} +% \texttt{bash fancy-preview filename} +% \end{quote} +% On Windows use (still experimental) +% \begin{quote}\upshape\color{darkgreen} +% \texttt{fancypreview.bat filename} +% \end{quote} +% \item You may want to customize the variables in the script +% \texttt{fancy-preview} or batch file +% \texttt{fancypreview.bat} (colors, options for fancytooltips, +% etc.) +% \end{itemize} +% \end{frame} + +% \begin{frame} +% \frametitle{How to create a presentation with dvips} +% \begin{itemize} +% \item This work-flow should still work with dvips, but has been not +% tested, since it +% requires Acrobat Professional which is not available on author's +% platform (\texttt{Linux}). Moreover, the compilation cannot be +% done automatically, due to the post-processing in Acrobat. You +% are encouraged to try it by yourselves. Report success of problems +% to the authors email, please. +% \item Basically follow the instructions for pdf\LaTeX{} users. +% \item You have to customize the script \texttt{fancy-preview} +% \begin{itemize} +% \item Replace \texttt{pdflatex} by \texttt{latex} +% \item Add commands which convert \texttt{minimal.ps} into +% \texttt{minimal.pdf} +% \item Extract the number of pages of the file +% \texttt{minimal.pdf} and pass it as an argument to the +% fancytooltips package. (You may use \texttt{pdftk} or +% \texttt{pdflatex} for this task.) +% \end{itemize} +% \item Remember that you have post-process the resulting +% \texttt{ps} file as described in manual for fancytooltips +% package. +% \end{itemize} +% \end{frame} + + +\begin{frame} + \frametitle{That's all. } + Any problem? Send a \textit{minimal example} to the author of the + package. +\end{frame} + +\begin{thebibliography}{10} +\bibitem{D-1} {K. Nowak}, A remark on \dots , Opuscula Math. {\bf 26} + (2004), 25--31. + +\bibitem{D} {R. Stuchlik}, Perturbations of \dots , + J. Math. Anal. Appl. {\bf 23} (19986), 4--44. + +\bibitem{D-F} {O. Stuchlik}, Half-linear oscillation criteria: + Perturbation in term involving derivative, Nonlinear Anal. {\bf 73} + (2010), 3756--3766. + +\bibitem{D-R} {T. Topas}, Half-linear Differential Equations, + North-Holland Mathematics Studies 202, Elsevier, 2005. + +\bibitem{D-Rez} {K. Ulrich}, Oscillation and nonoscillation of + perturbered half-linear Euler differential equations, + Publ. Math. Debrecen {\bf 1} (2000). + + +\end{thebibliography} + + +\end{document} + diff --git a/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo2.pdf b/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo2.pdf Binary files differnew file mode 100644 index 0000000000..46f911f1a1 --- /dev/null +++ b/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo2.pdf diff --git a/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo2.tex b/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo2.tex new file mode 100644 index 0000000000..a756a44090 --- /dev/null +++ b/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo2.tex @@ -0,0 +1,691 @@ +\documentclass{article} + +\let\rmdefault\sfdefault +\def\modra#1{{\color{blue}\bm{#1}}} +\def\cervena#1{{\color{red}\bm{#1}}} +\def\separuj{\par\smallskip\hrule\kern 0.5pt\hrule \smallskip} +\def\separujB{\par\hrule\kern 0.5pt\hrule} + +\newenvironment{block}{}{} +\usepackage{amsfonts,amsmath,amsthm,url,bm} +\usepackage{fancybox} +\usepackage{mathpazo} +\usepackage[latin2]{inputenc} +\usepackage[IL2]{fontenc} + + +\newtheorem{theorem}{Theorem} +\newtheorem{corollary}{Corollary} +\newtheorem{lemma}{Lemma} +\newtheorem{Theorem}{Theorem} +\def\theTheorem{\Alph{Theorem}} +\theoremstyle{definition} +\newtheorem{definition}{Definition} +\newtheorem{remark}{Remark} + +\sloppy +\everymath{\displaystyle} +\usepackage[pdftex,nodirectory]{web} +\def\titlepageTrailer{} +\margins{.15in}{.15in}{12pt}{.15in} % left,right,top, bottom +\screensize{4.5in}{6in} % web.sty dimensions + +\parindent 0 pt + +\usepackage{mdwlist} +\usepackage{eso-pic} +\definecolor{mygreen}{RGB}{120,190,20} +\definecolor{mygreen}{RGB}{10,80,40} +\definecolor{webgreen}{RGB}{10,80,40} +\definecolor{seda}{gray}{0.31} +\definecolor{webgreen}{RGB}{120,190,20} +\AddToShipoutPicture{\hbox to 0 pt{\hbox to \paperwidth{\color{mygreen}\vrule +width 0.5em height\paperheight\color{black}%\hskip -0.5 em +\hskip 0 pt plus 1 fill +\raise 1 pt\hbox {\normalfont\tiny \color{gray}\textbf{CDDEA 2010, Rajecké Teplice} (\thepage/12)} +\hskip 0 pt plus 1 fill +}}}% + +\def\qed{} + +\def\lambdamin{\lambda_{\text{\rm{min}}}} +\def\lambdamax{\lambda_{\text{\rm{max}}}} + +\makeatletter\let\over\@@over\makeatother +\def\theenumi{\roman{enumi}} +\def\labelenumi{\textrm{\upshape{(\theenumi)}}} +\def\konst{\textrm{const}} +\def\div{\mathop{\hbox{\rm div}}} +\def\meas{\mathop{\hbox{\rm meas}}} +\def\sgn{\mathop{\hbox{\rm sgn}}} +\def\laplac{\Delta} +\def\R{\mathbb{R}} +\def\N{\mathbb{N}} +\def\dxi{\,\mathrm{d}\xi\,} +\def\dx{\,\mathrm{d}x\,} +\def\dS{\,\mathrm{d}\sigma\,} +\def\dt{\,\mathrm{d}t\,} +\def\dT{\,\mathrm{d}T\,} +\def\du{\,\mathrm{d}u\,} +\def\ds{\,\mathrm{d}s\,} +\def\dr{\,\mathrm{d}r\,} +\def\dphi{\,\mathrm{d}\phi\,} +\newcommand{\duxi}{\frac{\partial u}{\partial x_i}} +\newcommand{\derxi}{{\partial\over\partial x_i}} +\newcommand{\pnorm}[1]{\|#1\|_p } +\newcommand{\qnorm}[1]{\|#1\|_q } +\newcommand\diver{\mathop{\rm div}} +\let\hat\widehat +\let\tilde\widetilde +\let\~\tilde + +\let\phi\varphi + +\def\vyplnekA{\leaders\hrule height 0.8pt\hfill} +\def\vyplnekB{\leaders\hrule height 6 pt depth -5.2pt\hfill} +\def\nadpis#1\par{\medbreak \hbox to \hsize{{\color{mygreen}\vyplnekA\ {\textsc{#1}}\vyplnekB}}\par\medbreak} + + +%\def\vec#1{\boldsymbol{#1}} +\def\norm#1{\left\Vert#1\right\Vert} +\def\x{\norm{x}} +\def\w{\norm{\vec{w}}} +\def\a{{\alpha}} +\def\aa{{\alpha-1}} +\def\at{{a\leq\x\leq t}} +\def\o{\omega_n} +\def\O{\Omega} +\def\c{\cdot} +\def\const{\hbox{const}} +\def\eps{\varepsilon} +\let\epsilon\varepsilon +\interdisplaylinepenalty 50 +\setcounter{tocdepth}{1} + +\raggedbottom +\let\rmdefault\sfdefault + +\usepackage{graphicx} +\usepackage{multicol} + +\def\ss#1#2{\left\langle#1,#2\right\rangle} + + +\makeatletter +\renewcommand\maketitle +{% + \thispagestyle{empty}% + \null\bigskip\bigskip + \ifeqforpaper\vspace*{2\baselineskip}% + \else + \vbox to\titleauthorproportion\textheight\bgroup% + \fi + \noindent\makebox[\linewidth]{\parbox{\linewidth}% + {\bfseries\color{\webuniversity@color}\ifeqforpaper\large\fi + \centering\webuniversity}}\par\ifeqforpaper\else\minimumskip\fi + \vspace{\stretch{1}}% + \noindent\makebox[\linewidth]{% + \parbox{\hproportionwebtitle\linewidth}% + {\bfseries\color{\webtitle@color}\ifeqforpaper\Large\else + \large\fi\centering\webtitle}}\par\ifeqforpaper + \vspace{2\baselineskip}\else\minimumskip\vspace{\stretch{1}}\fi + \noindent\makebox[\linewidth]{% + \parbox{\hproportionwebauthor\linewidth}% + {\bfseries\color{\webauthor@color}\ifeqforpaper + \large\fi\centering\webauthor}} + \ifeqforpaper\else + \egroup % end of \vbox for title and author + \fi\bigskip + \optionalpagematter + \par\vspace{\stretch{1}} + \ifx\web@directory@option y\webdirectory\fi + \par\ifeqforpaper\else\minimumskip\fi\vspace{\stretch{1}} + \vfill\noindent\begingroup + \trailerFontSize\titlepageTrailer\par\endgroup + \newpage +} + +\makeatother + +\pagestyle{empty}% + +%\usepackage[inactive]{fancytooltips} +\begin{document} + +\def\TooltipRefmark{\hbox{\ \ }} +\def\TooltipExtratext{\hbox{\ \ }} + + \title{Conjugacy criteria for half-linear ODE \\in theory of PDE\\ with + generalized $p$-Laplacian\\ and mixed powers\\[15pt]} + +\author{Robert Ma\v r\'\i k\\[6mm]Dpt. of Mathematics\\ Mendel University\\Brno, CZ + } + +\date{} + +\maketitle + +\begin{equation} + \begin{aligned} + \div\left(A(x)\norm{\nabla y}^{p-2}\nabla y\right)&+ \ss{\vec + b(x)}{\norm{\nabla y}^{p-2}\nabla y}\\&+ + c(x)|y|^{p-2}y+\sum_{i=1}^m c_i(x)|y|^{p_i-2}y=e(x), + \end{aligned} +\tag{E} +\end{equation} +\begin{itemize} +\item $x=(x_1,\ldots,x_n)_{i=1}^n\in\R^n$, $p>1$, $p_i>1$, +\item $A(x)$ is elliptic $n\times n$ matrix with differentiable + components, $c(x)$ and $c_i(x)$ are H\"older continuous functions, + $\vec b(x)=\bigl(b_1(x),\ldots,b_n(x)\bigr)$ is continuous + $n$-vector function, +\item $\nabla=\left({\partial \over\partial + x_1},\ldots,{\partial \over\partial + x_n}\right)_{i=1}^n$ and $\div={\partial \over\partial + x_1}+\cdots+{\partial \over\partial + x_n}$ is are the usual nabla and divergence operators, +\item $q$ is a conjugate + number to the number $p$, i.e., $q=\frac p{p-1}$, +\item $\ss{\cdot}{\cdot}$ is the usual scalar product in $\R^n$, + $\Vert{\cdot}\Vert$ is the usual norm in $\R^n$, $\Vert A\Vert + =\sup\left\{\Vert Ax\Vert: x\in \R^n \text{ with } \Vert x\Vert + =1\right\}=\lambdamax$ is the spectral norm +\item \textbf{solution} of \eqref{eq:E} in $\Omega\subseteq \R^n$ is a +differentiable function $u(x)$ such that $A(x)\Vert\nabla +u(x)\Vert^{p-2}\nabla u(x)$ is also differentiable and $u$ satisfies +\eqref{eq:E} in $\Omega$ +\item $ S(a)=\{x\in\R^n: \Vert x\Vert =a\}$, \\$ + \Omega(a)=\{x\in\R^n:a\leq \Vert x\Vert \}$, \\$ + \Omega(a,b)=\{x\in\R^n:a\leq\Vert x\Vert \leq b\}$ +\end{itemize} + +\newpage + +% \begin{equation} +% {\shadowbox{$\div\Bigl(A(x)\Vert\nabla u\Vert^{p-2}\nabla u\Bigr) + \ss{\vec b(x)}{\Vert\nabla u\Vert^{p-2}\nabla u}+c(x)|u|^{p-2}u=0$}} \tag{E} +% \end{equation} + +\nadpis {Concept of oscillation for ODE} + +\begin{equation} + u''+c(x)u=0 \label{eq1} +\end{equation} + +\begin{itemize} +\item Equation \eqref{eq1} is oscillatory if each solution has + infinitely many zeros in $[x_0,\infty)$. +\item Equation \eqref{eq1} is oscillatory if each solution has a zero $[a,\infty)$ + for each $a$. +\item Equation \eqref{eq1} is oscillatory if each solution has + conjugate points on the interval $[a,\infty)$ for each $a$. +\item All definition are equivalent (no accumulation of zeros and + Sturm separation theorem). +\item Equation is oscillatory if $c(x)$ is large enough. Many + oscillation criteria are expressed in terms of the integral + $\int^\infty c(x)\dx$ (Hille and Nehari type) +\item There are oscillation criteria which can detect oscillation even + if $\int^\infty c(x)\dx$ is extremly small. These criteria are in + fact series of conjugacy criteria. +\end{itemize} + +\newpage +\nadpis Equation with mixed powers + +\begin{equation} + \label{eq:Sun} + (p(t)u')'+c(t)u+\sum_{i=1}^m c_i(t)|u|^{\alpha _i}\sgn u=e(t) +\end{equation} +where $\alpha_1>\cdots >\alpha_m>1>\alpha_{m+1}>\cdots>\alpha_n>0$. +\begin{Theorem}[Sun,Wong (2007)] +\label{theorem:sun_wong} + If for any $T\geq 0$ there exists $a_1$, $b_1$, $a_2$, $b_2$ such + that $T\leq a_1<b_1\leq a_2<b_2$ and + \begin{equation*} + \begin{cases} + c_i(t)\geq 0& t\in[a_1,b_1]\cup[a_2,b_2],\ i=1,2,\dots,n\\ + e(x)\leq 0& t\in[a_1,b_1]\\ + e(x)\geq 0& t\in[a_2,b_2] + \end{cases} + \end{equation*} + and there exists a continuously differentiable function $u(t)$ + satisfying $u(a_i)=u(b_i)=0$, $u(t)\neq 0$ on $(a_i,b_i)$ and + \begin{equation}\label{eq:SW} + \int_{a_i}^{b_i}\left\{p(t)u'^2(t)-Q(t)u^2(t)\right\}\dt\leq 0 + \end{equation} + for $i=1,2$, where + \begin{equation*} + Q(t)=k_0|e(t)|^{\eta_0}\prod_{i=1}^m\Bigl(c_i^{\eta_i}(t)\Bigr)+c(t), + \end{equation*} + $k_0=\prod_{i=0}^m\eta_i^{-\eta_i}$ and $\eta_i$, $i=0,\dots,n$ are + positive constants satisfying +% \begin{equation*} +$ \sum_{i=1}^m\alpha_i\eta_i=1\quad\text{and}\quad \sum_{i=0}^m\eta_i=1$, +% \end{equation*} + then all solutions of \eqref{eq:Sun} are oscillatory. +\end{Theorem} + + + +\newpage +\nadpis {Concept of oscillation for linear PDE} + +\begin{equation} + \Delta u+c(x)u=0 \label{eq2} +\end{equation} + +\begin{itemize} +\item Equation \eqref{eq2} is \textit{oscillatory} if every solution + has a zero on $\{x\in\R^n: \norm x\geq a\}$ for each $a$. +\item Equation \eqref{eq2} is \textit{nodally oscillatory} if every + solution has a nodal domain on $\{x\in\R^n: \norm x\geq a\}$ for + each $a$. +\item Both definition are equivalent (Moss+Piepenbrink). +\end{itemize} + + +\nadpis {Concept of oscillation for half-linear PDE} + +\begin{equation} + \div\Bigl(\norm{\nabla u}^{p-2}\nabla u\Bigr)+c(x)|u|^{p-2}u=0 \label{eq3} +\end{equation} + +\begin{itemize} +\item Essentialy the same approach to oscillation as in linear case +\item The equivalence between two oscillations is open problem. +\end{itemize} + + +% \newpage +% \nadpis Riccati substituion + +% If $u$ is a positive solution of the equation +% \begin{equation}\label{eq:linODE} +% u''+c(x)u=0, +% \end{equation} then the function +% $w=\frac{u'}{u}$ is a solution of the Riccati type differential equation +% \begin{equation} +% w'+c(x)+|w|^2=0.\label{eq:riceq} +% \end{equation} + + +% \textbf{Remark:} In fact +% \begin{equation} +% w'+c(x)+|w|^2\leq 0\label{eq:RICineq} +% \end{equation} +% is sufficient in proofs of nonexistence of positive (nonoscillatory) +% solution \eqref{eq:linODE}, since solvability of \eqref{eq:RICineq} +% implies solvability of \eqref{eq:riceq}. + + +% \nadpis Transforming ODE result (nonexistence of positive solution) +% into PDE + +% \null + +% \vskip -3\baselineskip + +% \null + +% % The method used to prove most of oscillation criteria for half-linear PDE +% \begin{enumerate*} +% \item Suppose by contradiction that the PDE possesses positive +% (eventually positive) solution. +% \item Using transformation +% % \begin{equation*} +% $ \vec w(x)= +% \frac{\Vert \nabla u(x)\Vert ^{p-2}\nabla u(x)}{|u(x)|^{p-2}u(x)} +% $ +% % \end{equation*} +% convert positive solutions of +% \begin{equation*} +% \div\Bigl(\Vert\nabla u\Vert^{p-2}\nabla u\Bigr)+c(x)|u|^{p-2}u=0 +% \end{equation*} +% into +% \begin{equation}\label{5RIC} +% \div \vec w+c(x) +(p-1)\ss{\vec w}{\frac{\nabla u(x)}{u(x)}}=0. +% \end{equation} +% \item Integrating \eqref{5RIC} over spheres and using standard tools +% derive a Riccati type inequality of the form \eqref{eq:RICineq} and +% proceed as in the ODE case. +% \end{enumerate*} + +\newpage + +\null +\kern-2\baselineskip + +\begin{equation} + \begin{aligned} + \div\left(A(x)\norm{\nabla y}^{p-2}\nabla y\right)&+ \ss{\vec + b(x)}{\norm{\nabla y}^{p-2}\nabla y}\\&+ + c(x)|y|^{p-2}y+\sum_{i=1}^m c_i(x)|y|^{p_i-2}y=e(x), + \end{aligned} +\tag{E} +\end{equation} + +\nadpis Detection of oscillation from ODE + +% Oscillation of partial differential equation can be detected from +% oscillation of ordinary differential equation. +\begin{Theorem}[O. Do\v sl\'y (2001)] \label{rad} +% Let +% \begin{align*} +% % \~a(r)={1\over \omega_nr^{n-1}}\int_{S(r)}a(x)\dS\\ +% \hat c(r)={1\over \omega_nr^{n-1}}\int_{S(r)}c(x)\dS. +% \end{align*} +Equation +\begin{equation} +\div(\Vert\nabla u\Vert^{p-2}\nabla u)+c(x)|u|^{p-2}u=0\label{eq:E-non-damp} +\end{equation} +is oscillatory, if the ordinary differential equation + \begin{equation} + \label{hl} + \Bigl( r^{n-1}|u'|^{p-2}u'\Bigr)'+r^{n-1}\left(\frac{1}{\omega_n r^{n-1}}\int_{S(r)}\, c(x) \,\dx\right)|u|^{p-2}u=0 + \end{equation} +is oscillatory. +The number $\omega_n$ is the surface area of the unit sphere in $\R^n$. +\end{Theorem} + +J. Jaro\v s, T. Kusano and N. Yoshida proved independently similar +result (for $A(x)=a(\Vert x\Vert )I$, $a(\cdot)$ differentiable). + +\nadpis {Our aim} + +\begin{itemize*} +\item Extend method used in Theorem \ref{theorem:sun_wong} to + \eqref{eq:E}. Derive a general result, like Theorem B. +\item Derive a result which does depend on more general expression, + than the mean value of $c(x)$ over spheres centered in the origin. +% Is it possible to detect oscillation in such an extreme case as +% $\int_{S(||x||)}\modra{c(x)}\dS=0$? +\item Remove restrictions used by previous authors (for example Xu (2009) + excluded the possibility $p_i>p$ for every $i$). + % S(r)}\cervena{\lambdamax(x)}}$ plays a crucial role in the linear + % case and $\boxed{\rho(r)\geq \max_{x\in S(r)}\cervena{\frac{\Vert + % {A(x)}\Vert ^p_F}{\lambdamin^{p-1}(x)}}}$ plays similar role + % if $p>1$. This phenomenon can be observed also in other + % oscillation criteria than Theorems B and C. We know that + % $\rho(r)\geq \lambda(r)$. Why such a discrepancy appears? +\end{itemize*} + +\newpage +\begin{equation} + \begin{aligned} + \div\left(A(x)\norm{\nabla y}^{p-2}\nabla y\right)&+ \ss{\vec + b(x)}{\norm{\nabla y}^{p-2}\nabla y}\\&+ + \modra{c(x)|y|^{p-2}y}+\cervena{\sum_{i=1}^m c_i(x)|y|^{p_i-2}y}=\cervena{e(x)}, + \end{aligned} +\tag{E} +\label{eq:E} +\end{equation} + +\nadpis Modus operandi + +\begin{itemize} +\item Get rid of terms $\sum_{i=1}^m c_i(x)|y|^{p_i-2}y$ and $e(x)$ + (join with $c(x)|y|^{p-2}y$) and convert the problem into + \begin{equation*} + \div\left(A(x)\norm{\nabla y}^{p-2}\nabla y\right)+ \ss{\vec + b(x)}{\norm{\nabla y}^{p-2}\nabla y}+\modra{C(x)|y|^{p-2}y}=0. + \end{equation*} +\item Derive Riccati type inequality in $n$ variables. +\item Derive Riccati type inequality in $1$ variable. +\item Use this inequality as a tool which transforms results from ODE + to PDE. +\end{itemize} + + +\newpage + +Using generalized AG inequality $\sum \alpha _i\geq +\prod\left(\frac{\alpha_i}{\eta_i}\right)^{\eta_i}$, if $\alpha_i\geq +0$, $\eta_i>0$ and $\sum \eta_i=1$ we eliminate the right-hand side and terms with mixed powers. + + + +\begin{lemma}\label{lemma:est1} + Let either $y>0$ and $e(x)\leq 0$ or $y<0$ and $e(x)\geq 0$. Let + $\eta_i>0$ be numbers satisfying $\sum_{i=0}^m{\eta_i}=1$ and + $\eta_0+\sum_{i=1}^m p_i\eta_i=p$ and let $c_i(x)\geq 0$ for every + $i$. Then + \begin{equation*}%\label{eq:est1} + \frac{1}{|y|^{p-2}y}\left(-e(x)+\sum_{i=1}^m c_i(x)|y|^{p_i-2} y\right)\geq C_1(x), + \end{equation*} + where + \begin{equation} + \label{eq:C1} + C_1(x):=\left|\frac{e(x)}{\eta_0}\right|^{\eta_0} + \prod_{i=1}^m\left(\frac{c_i(x)}{\eta_i}\right)^{\eta_i}. + \end{equation} +\end{lemma} + + + +%\begin{remark} +\textbf{Remark:} The numbers $\eta_i$ from Lemma \ref{lemma:est1} exist, if $p_i>p$ for some $i$. +%\end{remark} + +% The following lemma is a modification of Lemma \ref{lemma:est1} in +% the case $e(x)\equiv 0$. + +\begin{lemma}\label{lemma:est10} + Suppose $c_i(x)\geq 0$. Let $\eta_i>0$ be numbers satisfying + $\sum_{i=1}^m{\eta_i}=1$ and $\sum_{i=1}^m p_i\eta_i=p$. Then + \begin{equation*}%\label{eq:est10} + \frac{1}{|y|^{p-2}y}\sum_{i=1}^m c_i(x)|y|^{p_i-2}y\geq C_2(x), + \end{equation*} + where + \begin{equation} + \label{eq:C2} + C_2(x):=\prod_{i=1}^m\left(\frac{c_i(x)}{\eta_i}\right)^{\eta_i} + \end{equation} +\end{lemma} + +% \begin{remark} +\textbf{Remark:} The numbers $\eta_i$ from Lemma \ref{lemma:est10} +exist iff $p_i>p$ for some $i$ and $p_j<p$ for some $j$. +% \end{remark} + + +\newpage +% \begin{lemma}\label{lemma:ineq_cal} +% The following inequalities hold for $a\geq 0$ and $x>0$. +% \begin{enumerate} +% \item If $\alpha<\beta$ and $b>0$, then $b-ax^\alpha\geq -x^\beta \left(\frac{a(\beta-\alpha)}{b\beta}\right)^{\frac\beta\alpha} \frac{b\alpha}{\beta-\alpha}$ +% \label{pa} +% \item If $\alpha>\beta$ and $b\geq0$, then $ax^\alpha+b\geq x^\beta \left(\frac{a(\alpha-\beta)}{b\beta}\right)^{\frac\beta\alpha} \frac{b\alpha}{\alpha-\beta}$ +% \label{pb} +% \end{enumerate} +% \end{lemma} + +% Another possibility how to remove the right hand side and terms with +% mixed powers is available if we rewrite +% \begin{equation*} +% \frac{1}{|y|^{p-2}y}\left(-e(x)+\sum_{i=1}^m c_i(x)|y|^{p_i-2}y\right) +% \end{equation*} +% into the form +% \begin{equation*} +% \sum_{i=1}^m \left(c_i(x)|y|^{p_i-p}-\frac{\epsilon_i e(x)}{|y|^{p-2}y} \right), \quad \epsilon_i>0, \quad \sum_{i=1}^m\epsilon_i=1 +% \end{equation*} +% study the family of min/max problems +% for terms in this sum. + +% \bigskip + +% \begin{lemma}\label{lemma:estimate2} +% Let $e(x)<0$ and $y>0$. Then +% \begin{equation*}%\label{eq:estimate2} +% \sum_{i=1}^m c_i(x)|y|^{p_i-p}-\frac{e(x)}{|y|^{p-2}y} +% \geq C_3(x), +% \end{equation*} +% where +% \begin{multline} +% \label{eq:C3} +% C_3(x):=\sum_{i\in I_1} +% \left(\left[\frac{[c_i(x)]_+(p_i-p)}{\epsilon_i|e(x)|(p-1)}\right]^{(p-1)/(p_i-1)}\frac{\epsilon_i|e(x)|(p_i-1)}{p_i-p}\right)\\ +% - \sum_{i\in I_2}\left(\left[\frac{[-c_i(x)]_+(p-p_i)}{\epsilon_i|e(x)|(p-1)}\right]^{(p-1)/(p_i-1)}\frac{\epsilon_i|e(x)|(p_i-1)}{p-p_i}\right), +% \end{multline} +% $I_1=\{i\in[1,m]\cap \N:p_i>p\}$ and $I_2=\{i\in[1,m]\cap \N:p_i<p\}$, +% $\epsilon_i>0$, $\sum_{i=1}^m\epsilon_i=1$. Moreover, if +% $I_2=\{\}$, then the inequality $e(x)<0$ can be relaxed to +% $e(x)\leq 0$. +% \end{lemma} + + + +% \newpage +\begin{lemma}\label{lemma:cC} + Let $y$ be a solution of \eqref{eq:E} which does not have zero on + $\Omega$. Suppose that there exists a function + $C(x)$ such that + \begin{equation*} + C(x)\leq c(x)+\sum_{i=1}^m c_i(x)|y|^{p_i-p}-\frac{e(x)}{|y|^{p-2}y} +% \label{ineq:C} + \end{equation*} + Denote $\vec w(x)=A(x)\frac{\norm{\nabla y}^{p-2}\nabla + y}{|y|^{p-2}y}$. The function $\vec w(x)$ is well defined on + $\Omega$ and satisfies the inequality + \begin{equation} + \label{eq:RIC} + \div \vec w+(p-1)\Lambda(x) \norm{\vec w}^q+\ss{\vec w}{A^{-1}(x)\vec b(x)}+C(x)\leq 0 + \end{equation} + where + \begin{equation}\label{eq:Lambda} + \Lambda(x)= + \begin{cases} + \lambda_{{\max}}^{1-q}(x)& % \text{ for } + 1<p\leq 2,\\ + \lambda_{{\min}}\lambda_{\max}^{-q}(x)& % \text{ for } + p>2. + \end{cases} + \end{equation} + \end{lemma} + +\begin{lemma}\label{lemma:alpha} + Let \eqref{eq:RIC} hold. Let $l>1$, $l^*=\frac{l}{l-1}$ be two + mutually conjugate numbers and $\alpha \in C^1(\Omega,\R^+)$ be + a smooth function positive on $\Omega$. Then + \begin{multline*} + % \label{eq:RIC2} + \div (\alpha(x)\vec w)+ (p-1)\frac {\Lambda(x)\alpha^{1-q}(x)}{l^*} + \norm{\alpha(x)\vec w}^q\\ + -\frac{l^{p-1}\alpha(x)}{ p^p \Lambda^{p-1}(x)}\norm{A^{-1}(x)\vec b(x)-\frac{\nabla \alpha(x)}{\alpha(x)}}^p +\alpha(x)C(x)\leq 0 + \end{multline*} + holds on $\Omega$. If $\norm{A^{-1}\vec b-\frac{\nabla + \alpha}\alpha}\equiv 0$ on $\Omega$, then this inequality holds + with $l^*=1$. +\end{lemma} + +\newpage +\begin{theorem}\label{lemma:radialODE} + Let the $n$-vector function $\vec w$ satisfy inequality + \begin{equation*} + \div \vec w+C_0(x)+(p-1)\Lambda_0(x)\norm{\vec w}^q\leq 0 + \end{equation*} + on $\Omega(a,b)$. Denote $\tilde C(r)=\int_{S(r)}C_0(x)\dS$ and + $\tilde R(r)=\int_{S(r)}\Lambda_0^{1-p}\dS$. Then + the half-linear ordinary differential equation + \begin{equation*}%\label{eq:radialODE} + \left(\tilde R(r) |u'|^{p-2}u\right)'+\tilde C(r) |u|^{p-2}u=0, + \qquad {}'=\frac{\mathrm{d}}{\dr} + \end{equation*} + is disconjugate on $[a,b]$ and it possesses solution which has no + zero on $[a,b]$. +\end{theorem} + +\begin{theorem}\label{th1} + Let $l>1$. Let $l^*={1}$ if $\norm{\vec b}\equiv 0$ and + $l^*=\frac{l}{l-1}$ otherwise. Further, let $c_i(x)\geq 0$ for every + $i$. Denote + \begin{equation*}%\label{eq:tildeR} + \tilde R(r)=(l^*)^{p-1}\int_{S(r)}\Lambda^{1-p}(x)\dS + \end{equation*} + and + \begin{equation*} + \tilde C(r)=\int_{S(r)}c(x)+C_1(x)-\frac{l^{p-1}}{ p^p \Lambda^{p-1}(x)}\norm{A^{-1}(x)\vec b(x)}^p\dS, + \end{equation*} + where $\Lambda(x)$ is defined by \eqref{eq:Lambda} and $C_1(x)$ is + defined by \eqref{eq:C1}. + + Suppose that the equation + \begin{equation*}%\label{eq:th1} + \left(\tilde R(r)|u'|^{p-2}u'\right)'+\tilde C(r) |u|^{p-2}u=0 + \end{equation*} + has conjugate points on $[a,b]$. + + If $e(x)\leq 0$ on $\Omega(a,b)$, then equation \eqref{eq:E} has no + positive solution on $\Omega(a,b)$. + + If $e(x)\geq 0$ on $\Omega(a,b)$, then equation \eqref{eq:E} has no + negative solution on $\Omega(a,b)$. +\end{theorem} + +\begin{theorem}[non-radial variant of Theorem \ref{th1}]\label{th1a} + Let $l>1$ and let $\Omega\subset\Omega(a,b)$ be an open domain with + piecewise smooth boundary such that $\meas(\Omega \cap S(r))\neq 0$ + for every $r\in[a,b]$. Let $c_i(x)\geq 0$ on $\Omega$ for every + $i$ and let $\alpha(x)$ be a function which is + positive and continuously differentiable on $\Omega$ and vanishes on + the boundary and outside $\Omega$. Let $l^*=1$ if $\norm{A^{-1}\vec + b-\frac{\nabla \alpha}{\alpha}}\equiv 0$ on $\Omega$ and + $l^*=\frac{l}{l-1}$ otherwise. In the former case suppose also that + the integral + \begin{equation*} + \int_{S(r)}\frac{\alpha(x)}{ \Lambda^{p-1}(x)}\norm{A^{-1}(x)\vec b(x)-\frac{\nabla\alpha(x)}{\alpha(x)}}^p\dS + \end{equation*} + which may have singularity on $\partial \Omega$ if + $\Omega\neq\Omega(a,b)$ is convergent for every $r\in[a,b]$. Denote + \begin{equation*} + \tilde R(r)=(l^*)^{p-1}\int_{S(r)}\alpha(x)\Lambda^{1-p}(x)\dS + \end{equation*} + and + \begin{equation*} + \tilde C(r)=\int_{S(r)}{\cervena{\alpha(x)}}\left(c(x)+C_1(x)-\frac{l^{p-1}}{ p^p \Lambda^{p-1}(x)}\norm{A^{-1}(x)\vec b(x)-\frac{\nabla\alpha(x)}{\alpha(x)}}^p\right)\dS, + \end{equation*} + where $\Lambda(x)$ is defined by \eqref{eq:Lambda} and $C_1(x)$ is + defined by \eqref{eq:C1} and suppose that equation + \begin{equation*} + \left(\tilde R(r)|u'|^{p-2}u'\right)'+\tilde C(r) |u|^{p-2}u=0 + \end{equation*} + has conjugate points on $[a,b]$. + + If $e(x)\leq 0$ on $\Omega(a,b)$, then equation \eqref{eq:E} has no + positive solution on $\Omega(a,b)$. + + If $e(x)\geq 0$ on $\Omega(a,b)$, then equation \eqref{eq:E} has no + negative solution on $\Omega(a,b)$. +\end{theorem} + +\newpage + +\begin{theorem}\label{th2} + Let $l$, $\Omega$, $\alpha(x)$, $\Lambda(x)$ and $\tilde R(r)$ be + defined as in Theorem \ref{th1a} and let $c_i(x)\geq 0$ and + \cervena{$e(x)\equiv 0$} on $\Omega(a,b)$. Denote + \begin{equation*} + \tilde C(r)=\int_{S(r)}\alpha(x)\left(c(x)+C_2(x)-\frac{l^{p-1}}{ p^p \Lambda^{p-1}(x)}\norm{A^{-1}(x)\vec b(x)-\frac{\nabla \alpha(x)}{\alpha(x)}}^p\right)\dS, + \end{equation*} + where $C_2(x)$ is defined by \eqref{eq:C2}. + If the equation %\eqref{eq:th1} + \begin{equation*} + \left(\tilde R(r)|u'|^{p-2}u'\right)'+\tilde C(r) |u|^{p-2}u=0 + \end{equation*} + has conjugate points on $[a,b]$, then every solution of equation + \eqref{eq:E} has zero on $\Omega(a,b)$. +\end{theorem} + +\bigskip\bigskip\bigskip +{\rightskip 2cm +\leftskip 2cm + +Similar theorems can be derived also for estimates of terms +with mixed powers based on different methods than AG inequality % (for example +% \eqref{eq:C3}) +(see R. M., Nonlinear Analysis TMA 73 (2010)). + +} + +\end{document} + + + diff --git a/macros/latex/contrib/fancytooltips/examples/fancytooltips-example.pdf b/macros/latex/contrib/fancytooltips/examples/fancytooltips-example.pdf Binary files differnew file mode 100644 index 0000000000..8413b6fc27 --- /dev/null +++ b/macros/latex/contrib/fancytooltips/examples/fancytooltips-example.pdf diff --git a/macros/latex/contrib/fancytooltips/examples/fancytooltips-example.tex b/macros/latex/contrib/fancytooltips/examples/fancytooltips-example.tex new file mode 100644 index 0000000000..292f6cbf3e --- /dev/null +++ b/macros/latex/contrib/fancytooltips/examples/fancytooltips-example.tex @@ -0,0 +1,55 @@ +\documentclass{article} + +\usepackage[pdftex,designiii]{web} + +\usepackage[filename=tooltipy,movetips,mouseover]{fancytooltips} + +\let\rmdefault\sfdefault + +\usepackage[shadein]{shadethm} + +\newshadetheorem{definition}{Definition} + +\usepackage{graphicx} + +\definecolor{bkg}{rgb}{1,0.9,0.9} +\def\Message#1{\colorbox{bkg}{ + \begin{minipage}{1\linewidth} + \smallskip + #1 + \smallskip + \end{minipage} + }} +\begin{document} + + +\parindent 0 pt + +\Message{ +\begin{itemize} +\item Use Acrobat Reader or Adobe Acrobat to view this file, please. +\item The blue texts are covered by an active button. If you \textbf{move mouse over} one of + these buttons, tooltip appears. If you move your mouse out or if you + close the page, the tooltip disappears. +\item The first links are tooltips, the fifth one is animated tooltip. +\item The tooltips appears with the left down corner at the mouse + cursor, or at least as close as possible. +\end{itemize} +} + +\begin{definition} + This is definition of \tooltip{rank}{2}. +\end{definition} + + +\begin{definition} + This is \tooltip{definition}3 of \tooltip{derivative}{1}. Filler + text. Filler text. Filler text. Filler text. Filler text. Filler text. Filler text. Filler text. Filler text. Filler text. + \tooltip{derivative}{1}. +\end{definition} + + +This is a geometric \tooltipanim{idea}{4}{28} which is behind the +definition of derivative. + +\end{document} diff --git a/macros/latex/contrib/fancytooltips/examples/pics/tecna2.pdf b/macros/latex/contrib/fancytooltips/examples/pics/tecna2.pdf Binary files differnew file mode 100644 index 0000000000..b4f69baa0f --- /dev/null +++ b/macros/latex/contrib/fancytooltips/examples/pics/tecna2.pdf diff --git a/macros/latex/contrib/fancytooltips/examples/pics/tooltipy.pdf b/macros/latex/contrib/fancytooltips/examples/pics/tooltipy.pdf Binary files differnew file mode 100644 index 0000000000..ba14c364dc --- /dev/null +++ b/macros/latex/contrib/fancytooltips/examples/pics/tooltipy.pdf diff --git a/macros/latex/contrib/fancytooltips/examples/pics/tooltipy.tex b/macros/latex/contrib/fancytooltips/examples/pics/tooltipy.tex new file mode 100644 index 0000000000..3900839282 --- /dev/null +++ b/macros/latex/contrib/fancytooltips/examples/pics/tooltipy.tex @@ -0,0 +1,103 @@ +\documentclass{article} +% \usepackage[czech]{babel} +% \usepackage[IL2]{fontenc} + +\pagestyle{empty} +\usepackage[createtips]{fancytooltips} + +\usepackage{fancybox} +\parindent 0 pt + +\usepackage{color} +\definecolor{gray}{rgb}{0.8, 0.8, 0.8} +\definecolor{lightblue}{rgb}{0.7, 0.7, 1} +\definecolor{lightgreen}{rgb}{0.7, 1, 0.7} + +\usepackage{multido,graphicx} +\usepackage[papersize={5in,5in},margin=1pt]{geometry} +\long\def\stranka#1#2{ +\setbox0=\hbox{\begin{minipage}{2in} +\fboxsep 0 pt +\color{red} +\shadowbox{{\fboxsep 4pt\colorbox{yellow} + {\begin{minipage}{\linewidth} + \color{black}#2 + \end{minipage}}}} +\end{minipage}\ \ \ \ } +\pdfpagewidth=\wd0 +\pdfpageheight=\ht0 +\advance \pdfpageheight by \dp0 +\copy0 +\keytip{#1} + \newpage +} + +\long\def\strankaB#1#2{ +\setbox0=\hbox{\fboxsep 0 pt +\color{red} +\shadowbox{{\fboxsep 4pt\colorbox{yellow} + {\color{black}#2 + }}}} +\pdfpagewidth=\wd0 +\pdfpageheight=\ht0 +\advance \pdfpageheight by \dp0 +\copy0 +\keytip{#1} + \newpage +} + + +\def\definice#1{ + \begin{center} + \colorbox{gray}{\begin{minipage}{0.9\linewidth} #1 + \end{minipage}} + \end{center} +} +\def\vyuziti#1{ + \begin{center} + \colorbox{lightblue}{\begin{minipage}{0.9\linewidth} #1 + \end{minipage}} + \end{center} +} +\def\vypocet#1{ + \begin{center} + \colorbox{lightgreen}{\begin{minipage}{0.9\linewidth} #1 + \end{minipage}} + \end{center} +} + + +\begin{document} + +\stranka{derivace}{ \definice{The \textbf{derivative} is the limit + $$\lim_{h\to0}\frac{f(x+h)-f(x)}h,$$ if this limit exists as a finite number.} \vyuziti{ The derivative + has important applications in physics as a rate of change and as a + linear approximation.} \vypocet{The derivative can be evaluated + using appropriate formulas}} + +\stranka{hodnost}{ \definice{\textbf{Rank} is a maximal number of + linearly independent rows in a matrix.} \vyuziti{Rank can be used + to prove or disprove linear independence of vectors and it also + appears in the Frobenius Theorem.} \vypocet{To find the rank of a + matrix, you have to convert this matrix into row echelon form.}} + +\strankaB{definition}{???} + +\pdfpageheight=0pt + +\pdfpagewidth=0pt + +\def\obrazek#1{% +\setbox0=\hbox{\color{red}% + \fboxsep 0 pt{\shadowbox{{\color{black}\includegraphics[width=3.5in, + page=#1,viewport= 0 57 350 230,clip]{tecna2.pdf}}}}} +\pdfpagewidth=\wd0 +\pdfpageheight=\ht0 +\advance \pdfpageheight by \dp0 +\copy0 +\newpage} + + +\multido{\i=1+1}{25}{\obrazek{\i}} + +\end{document} diff --git a/macros/latex/contrib/fancytooltips/examples/pics/tooltipy.tips b/macros/latex/contrib/fancytooltips/examples/pics/tooltipy.tips new file mode 100644 index 0000000000..d0f37ddb0e --- /dev/null +++ b/macros/latex/contrib/fancytooltips/examples/pics/tooltipy.tips @@ -0,0 +1,3 @@ +\tooltipname{derivace}{1} +\tooltipname{hodnost}{2} +\tooltipname{definition}{3} diff --git a/macros/latex/contrib/fancytooltips/examples/readme b/macros/latex/contrib/fancytooltips/examples/readme new file mode 100644 index 0000000000..7054e948d6 --- /dev/null +++ b/macros/latex/contrib/fancytooltips/examples/readme @@ -0,0 +1,5 @@ +Compile the examples as follows + +pdflatex fancytooltips-example.tex (2 times) +fancy-preview fancy-preview-demo --tooltips=pics/tooltipy --fancy_options=preview +fancy-preview fancy-preview-demo2
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