fancytooltips 1.8 (18dec10)

git-svn-id: svn://tug.org/texlive/trunk@20781 c570f23f-e606-0410-a88d-b1316a301751

22 files changed, 887 insertions, 18 deletions

diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancy-preview b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancy-preview
index f9386225dc2..7fa28f5f20e 100644
--- a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancy-preview
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancy-preview
@@ -3,12 +3,21 @@
 
 FILENAME=$1
 
-COLOR="0.8,0.8,0.8"
-PREVIEW="\PreviewEnvironment{definice} \PreviewEnvironment{veta} \PreviewEnvironment{definition} \PreviewEnvironment{figure} \PreviewEnvironment{theorem} \setlength\PreviewBorder{5pt}"
+if [ "$COLOR" == "" ]; then
+   COLOR="0.8,0.8,0.8";
+fi
 
-FBOXLENGTHS="\fboxrule=5pt\fboxsep=10pt"
+if [ "$PREVIEW" == "" ]; then
+PREVIEW="\PreviewEnvironment{definice} \PreviewEnvironment{veta} \PreviewEnvironment{Theorem} \PreviewEnvironment{definition} \PreviewEnvironment{figure} \PreviewEnvironment{theorem} \setlength\PreviewBorder{5pt}";
+fi
 
-FANCYOPTIONS="mouseover,movetips"
+if [ "$FBOXLENGTHS" == "" ]; then
+    FBOXLENGTHS="\fboxrule=5pt\fboxsep=10pt";
+fi
+
+if [ "$FANCYOPTIONS" == "" ]; then
+    FANCYOPTIONS="mouseover,movetips";
+fi
 
 echo "--------------------------"
 echo "------ pdflatex ----------"
@@ -19,13 +28,13 @@ echo "------ pdflatex with preview.sty ----------"
 echo "-------------------------------------------"
 pdflatex "\AtBeginDocument{\usepackage[pdftex,active,tightpage,floats,displaymath]{preview} $PREVIEW \definecolor{backgroundcolor}{rgb}{$COLOR}\pagecolor{backgroundcolor}\definecolor{shadethmcolor}{rgb}{$COLOR} \definecolor{shaderulecolor}{rgb}{$COLOR}} \input $FILENAME.tex"
 
-grep '\\newlabel{' $FILENAME.aux | sed 's/newlabel/maplabelstoall/g' > $FILENAME.tmp
+grep '\\newlabel{' $FILENAME.aux > $FILENAME.tmp
 mv $FILENAME.pdf $FILENAME-tmp.pdf
 
 echo "----------------------------------------------"
 echo "------ pdflatex genearting tooltips ----------"
 echo "----------------------------------------------"
-pdflatex "\documentclass{minimal}\usepackage[papersize={5in,5in},margin=1pt]{geometry}\usepackage[createtips]{fancytooltips}\usepackage{color,graphicx}\begin{document} $FBOXLENGTHS\relax \definecolor{backgroundcolor}{rgb}{$COLOR}\gdef\savemaplabels#1#2#3#4{\xdef\temp{#2}} \def\maplabelstoall#1#2{\savemaplabels#2 \setbox0=\hbox{\colorbox{backgroundcolor}{\includegraphics[page=\temp]{$FILENAME-tmp.pdf}}}\pdfpagewidth=\wd0 \pdfpageheight=\ht0 \advance \pdfpageheight by \dp0 \copy0 \keytip{#1}\newpage} \input $FILENAME.tmp\end{document}"
+pdflatex "\documentclass{minimal}\usepackage[papersize={5in,5in},margin=1pt]{geometry}\usepackage[createtips]{fancytooltips}\usepackage{color,graphicx}\begin{document} $FBOXLENGTHS\relax \definecolor{backgroundcolor}{rgb}{$COLOR}\gdef\savemaplabels#1#2#3#4{\xdef\temp{#2}} \def\maplabelstoall#1#2{\savemaplabels#2 \setbox0=\hbox{\colorbox{backgroundcolor}{\includegraphics[page=\temp]{$FILENAME-tmp.pdf}}}\pdfpagewidth=\wd0 \pdfpageheight=\ht0 \advance \pdfpageheight by \dp0 \copy0 \keytip{#1}\newpage} \let\newlabel\maplabelstoall \input $FILENAME.tmp\end{document}"
 mv $FILENAME.tips minimal.tip
 
 echo "----------------------------------------------"
@@ -44,4 +53,3 @@ echo "----------------------------------------------"
 echo "------ pdflatex final compilation 4 ----------"
 echo "----------------------------------------------"
 pdflatex "\PassOptionsToPackage{active,filename=minimal,$FANCYOPTIONS}{fancytooltips}\input $FILENAME.tex"
-
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancy-preview-demo.pdf b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancy-preview-demo.pdf
index 9f171c2dffd..66640eef218 100644
--- a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancy-preview-demo.pdf
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancy-preview-demo.pdf
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancy-preview-demo.tex b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancy-preview-demo.tex
index 74489e6c986..f536293315e 100644
--- a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancy-preview-demo.tex
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancy-preview-demo.tex
@@ -11,7 +11,7 @@
 \usepackage{tikz}
 \PassOptionsToPackage{naturalnames}{hyperref}
 
-\usepackage[inactive]{fancytooltips}
+\usepackage[inactive,blur=0.6, fixcolor]{fancytooltips}
 
 \newtheorem{remark}{Remark}
 \def\dx{{\mathrm d}x}
@@ -194,7 +194,7 @@
  \section{Short howto}
  \begin{frame}
    \frametitle{How to create a presentation with pdf\LaTeX}
-   Creating tooltips is easy. Simply follow these steps.
+%   Creating tooltips is easy. Simply follow these steps.
    \begin{itemize}
    \item Create presentation with your favorit presentation package,
      such as
@@ -211,16 +211,19 @@
        \texttt{\textbackslash FancyHook}
      \end{quote}
      after \texttt{\textbackslash begin\{document\}}.
-   \item Use the script \texttt{fancy-preview} to compile the
+   \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}
-     either in Linux terminal or inside
-     \href{http://www.mingw.org/wiki/MSYS}{\color{blue}MSYS} on
-     Windows.
-   \item You may want to customize the script \texttt{fancy-preview}
-     (colors, options for fancytooltips, etc.)
+     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}
 
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancypreview.bat b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancypreview.bat
new file mode 100755
index 00000000000..fd28f80f10c
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview/fancypreview.bat
@@ -0,0 +1,46 @@
+@echo off
+
+set FILENAME=%1
+
+set COLOR=0.8,0.8,0.8
+set PREVIEW=\PreviewEnvironment{definice} \PreviewEnvironment{veta} \PreviewEnvironment{definition} \PreviewEnvironment{figure} \PreviewEnvironment{theorem} 
+
+set FBOXLENGTHS=\fboxrule=5pt\fboxsep=10pt
+
+set FANCYOPTIONS=mouseover,movetips
+
+echo "--------------------------"
+echo "------ pdflatex ----------"
+echo "--------------------------"
+pdflatex %1.tex 
+echo "-------------------------------------------"
+echo "------ pdflatex with preview.sty ----------"
+echo "-------------------------------------------"
+pdflatex "\AtBeginDocument{\usepackage[pdftex,active,tightpage,floats,displaymath]{preview} %PREVIEW% \definecolor{backgroundcolor}{rgb}{%COLOR%}\pagecolor{backgroundcolor}\definecolor{shadethmcolor}{rgb}{%COLOR%} \definecolor{shaderulecolor}{rgb}{%COLOR%}} \input %1.tex"
+
+
+findstr /b "\newlabel" %1.aux > %1.tmp
+copy %1.pdf %1-tmp.pdf
+
+echo "----------------------------------------------"
+echo "------ pdflatex genearting tooltips ----------"
+echo "----------------------------------------------"
+pdflatex "\documentclass{minimal}\usepackage[papersize={5in,5in},margin=1pt]{geometry}\usepackage[createtips]{fancytooltips}\usepackage{color,graphicx}\begin{document} %FBOXLENGTHS%\relax \definecolor{backgroundcolor}{rgb}{%COLOR%}\gdef\savemaplabels#1#2#3#4{\xdef\temp{#2}} \def\maplabelstoall#1#2{\savemaplabels#2 \setbox0=\hbox{\colorbox{backgroundcolor}{\includegraphics[page=\temp]{%1-tmp.pdf}}}\pdfpagewidth=\wd0 \pdfpageheight=\ht0 \advance \pdfpageheight by \dp0 \copy0 \keytip{#1}\newpage} \let\newlabel\maplabelstoall \input %1.tmp\end{document}"
+
+echo "----------------------------------------------"
+echo "------ pdflatex final compilation 1 ----------"
+echo "----------------------------------------------"
+pdflatex "\PassOptionsToPackage{active,filename=minimal,%FANCYOPTIONS%}{fancytooltips}\input %1.tex"
+echo "----------------------------------------------"
+echo "------ pdflatex final compilation 2 ----------"
+echo "----------------------------------------------"
+pdflatex "\PassOptionsToPackage{active,filename=minimal,%FANCYOPTIONS%}{fancytooltips}\input %1.tex"
+echo "----------------------------------------------"
+echo "------ pdflatex final compilation 3 ----------"
+echo "----------------------------------------------"
+pdflatex "\PassOptionsToPackage{active,filename=minimal,%FANCYOPTIONS%}{fancytooltips}\input %1.tex"
+echo "----------------------------------------------"
+echo "------ pdflatex final compilation 4 ----------"
+echo "----------------------------------------------"
+pdflatex "\PassOptionsToPackage{active,filename=minimal,%FANCYOPTIONS%}{fancytooltips}\input %1.tex"
+
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/LDF.jpg b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/LDF.jpg
new file mode 100644
index 00000000000..b0cb5963ba6
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/LDF.jpg
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/README b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/README
new file mode 100644
index 00000000000..467c7fd0fdc
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/README
@@ -0,0 +1,21 @@
+Run the script compile.sh to compile the presentation.
+
+You get the file slides.pdf with my talk from the conferrence
+CDDE in Rajecke Teplice 2010. The file includes invisible buttons
+which follow some links to numbered equations or theorem-like
+environments. More preciselly: if the link points to an object which
+is not present on the current page, then moving the cursor behind the
+link opens the preview of the theorem or equation. Clicking the link
+jumps to the page with this object, as usual.
+
+The important lines from slides.tex which are used to get this behavior are
+\usepackage[inactive]{fancytooltips} before \begin{document} and 
+\FancyHook \def\TooltipRefmark{\hbox{\ \ }} \def\TooltipExtratext{\hbox{\ \ }}
+after \begin{document}.
+
+You get also the file marik.pdf -- a version of the presentation which does
+not have extra features, use as a solution if the main file with the
+presentation behaves wrong on the PC which is used for presentation
+(JavaScript capable browser is necessary).
+
+
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/complie.sh b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/complie.sh
new file mode 100644
index 00000000000..ccb09e965d2
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/complie.sh
@@ -0,0 +1,17 @@
+#!/bin/bash
+#
+
+COLOR="1,1,0.5"
+
+pdflatex slides
+pdflatex slides
+cp slides.pdf marik.pdf
+
+source fancy-preview slides
+
+
+#pdflatex "\AtBeginDocument{\usepackage{pdfpages}}\AtEndDocument{\includepdf[pages=1-12,nup=4x3, delta = 6 10]{a.pdf}}\PassOptionsToPackage{active,filename=minimal,$FANCYOPTIONS}{fancytooltips}\input $FILENAME.tex"
+
+pdflatex "\AtBeginDocument{\usepackage{pdfpages}}\AtEndDocument{\newpage \AddToShipoutPicture{\hbox to 0 pt{\hbox to \paperwidth{\color{mygreen}\vrule width \paperwidth height\paperheight}}}\null\bigskip\bigskip\lineskip 12 pt\parindent 0 pt \input multido.tex \multido{\i=1+1}{12}{\leavevmode\href{\jobname.pdf\#page.\i}{\fboxsep=0pt\colorbox{white}{\includegraphics[width=0.23\hsize,page=\i]{marik.pdf}}}\hfill\penalty 0}}\PassOptionsToPackage{active,filename=minimal,$FANCYOPTIONS}{fancytooltips}\input $FILENAME.tex"
+
+#cp slides.pdf marik-slides.pdf
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/fancy-preview b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/fancy-preview
new file mode 100644
index 00000000000..7fa28f5f20e
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/fancy-preview
@@ -0,0 +1,55 @@
+#!/bin/bash
+#
+
+FILENAME=$1
+
+if [ "$COLOR" == "" ]; then
+   COLOR="0.8,0.8,0.8";
+fi
+
+if [ "$PREVIEW" == "" ]; then
+PREVIEW="\PreviewEnvironment{definice} \PreviewEnvironment{veta} \PreviewEnvironment{Theorem} \PreviewEnvironment{definition} \PreviewEnvironment{figure} \PreviewEnvironment{theorem} \setlength\PreviewBorder{5pt}";
+fi
+
+if [ "$FBOXLENGTHS" == "" ]; then
+    FBOXLENGTHS="\fboxrule=5pt\fboxsep=10pt";
+fi
+
+if [ "$FANCYOPTIONS" == "" ]; then
+    FANCYOPTIONS="mouseover,movetips";
+fi
+
+echo "--------------------------"
+echo "------ pdflatex ----------"
+echo "--------------------------"
+pdflatex $FILENAME.tex 
+echo "-------------------------------------------"
+echo "------ pdflatex with preview.sty ----------"
+echo "-------------------------------------------"
+pdflatex "\AtBeginDocument{\usepackage[pdftex,active,tightpage,floats,displaymath]{preview} $PREVIEW \definecolor{backgroundcolor}{rgb}{$COLOR}\pagecolor{backgroundcolor}\definecolor{shadethmcolor}{rgb}{$COLOR} \definecolor{shaderulecolor}{rgb}{$COLOR}} \input $FILENAME.tex"
+
+grep '\\newlabel{' $FILENAME.aux > $FILENAME.tmp
+mv $FILENAME.pdf $FILENAME-tmp.pdf
+
+echo "----------------------------------------------"
+echo "------ pdflatex genearting tooltips ----------"
+echo "----------------------------------------------"
+pdflatex "\documentclass{minimal}\usepackage[papersize={5in,5in},margin=1pt]{geometry}\usepackage[createtips]{fancytooltips}\usepackage{color,graphicx}\begin{document} $FBOXLENGTHS\relax \definecolor{backgroundcolor}{rgb}{$COLOR}\gdef\savemaplabels#1#2#3#4{\xdef\temp{#2}} \def\maplabelstoall#1#2{\savemaplabels#2 \setbox0=\hbox{\colorbox{backgroundcolor}{\includegraphics[page=\temp]{$FILENAME-tmp.pdf}}}\pdfpagewidth=\wd0 \pdfpageheight=\ht0 \advance \pdfpageheight by \dp0 \copy0 \keytip{#1}\newpage} \let\newlabel\maplabelstoall \input $FILENAME.tmp\end{document}"
+mv $FILENAME.tips minimal.tip
+
+echo "----------------------------------------------"
+echo "------ pdflatex final compilation 1 ----------"
+echo "----------------------------------------------"
+pdflatex "\PassOptionsToPackage{active,filename=minimal,$FANCYOPTIONS}{fancytooltips}\input $FILENAME.tex"
+echo "----------------------------------------------"
+echo "------ pdflatex final compilation 2 ----------"
+echo "----------------------------------------------"
+pdflatex "\PassOptionsToPackage{active,filename=minimal,$FANCYOPTIONS}{fancytooltips}\input $FILENAME.tex"
+echo "----------------------------------------------"
+echo "------ pdflatex final compilation 3 ----------"
+echo "----------------------------------------------"
+pdflatex "\PassOptionsToPackage{active,filename=minimal,$FANCYOPTIONS}{fancytooltips}\input $FILENAME.tex"
+echo "----------------------------------------------"
+echo "------ pdflatex final compilation 4 ----------"
+echo "----------------------------------------------"
+pdflatex "\PassOptionsToPackage{active,filename=minimal,$FANCYOPTIONS}{fancytooltips}\input $FILENAME.tex"
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/marik.pdf b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/marik.pdf
new file mode 100644
index 00000000000..68173ab4216
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/marik.pdf
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/slides.pdf b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/slides.pdf
new file mode 100644
index 00000000000..00ee4fbf751
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/slides.pdf
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/slides.tex b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/slides.tex
new file mode 100644
index 00000000000..1efe048f81c
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancy-preview2/slides.tex
@@ -0,0 +1,716 @@
+\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}
+
+\makeatletter
+\def\@shadowbox#1{%
+  \setbox\@fancybox\hbox{\fbox{\color{black}#1}}%
+  \leavevmode\vcenter{%
+    \offinterlineskip
+    \dimen@=\shadowsize
+    \advance\dimen@ .5\fboxrule
+    \hbox{\color{mygreen}\copy\@fancybox\kern-.5\fboxrule\lower\shadowsize\hbox{%
+      \vrule \@height\ht\@fancybox \@depth\dp\@fancybox \@width\dimen@}}%
+    \vskip-\dimen@
+    \moveright\shadowsize\vbox{\color{mygreen}%
+      \hrule \@width\wd\@fancybox \@height\dimen@}}}
+
+\makeatother
+
+\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
+\raise -2pt\hbox to 0 pt{\hss \includegraphics[width=1.2cm]{LDF.jpg}}}}}%
+
+\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}
+
+\FancyHook
+\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}
+  \shadowbox{$\begin{aligned}
+    \div\left(A(x)\norm{\nabla y}^{p-2}\nabla y\right)&+ \ss{\vec
+      b(x)}{\norm{\nabla y}^{p-2}\nabla y}\\&+
+    c(x)|y|^{p-2}y+\sum_{i=1}^m c_i(x)|y|^{p_i-2}y=e(x),
+  \end{aligned}$}
+\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}
+  \shadowbox{$\begin{aligned}
+    \div\left(A(x)\norm{\nabla y}^{p-2}\nabla y\right)&+ \ss{\vec
+      b(x)}{\norm{\nabla y}^{p-2}\nabla y}\\&+
+    c(x)|y|^{p-2}y+\sum_{i=1}^m c_i(x)|y|^{p_i-2}y=e(x),
+  \end{aligned}$}
+\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}
+  \shadowbox{$\begin{aligned}
+    \div\left(A(x)\norm{\nabla y}^{p-2}\nabla y\right)&+ \ss{\vec
+      b(x)}{\norm{\nabla y}^{p-2}\nabla y}\\&+
+    \modra{c(x)|y|^{p-2}y}+\cervena{\sum_{i=1}^m c_i(x)|y|^{p_i-2}y}=\cervena{e(x)},
+  \end{aligned}$}
+\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}
+
+% % \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}
+% \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}
+
+
+\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/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-dvips.pdf b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-dvips.pdf
index 89d2065cba2..9297d5016ec 100644
--- a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-dvips.pdf
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-dvips.pdf
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-dvips.tex b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-dvips.tex
index 6175a2c0180..0118a55c2c6 100644
--- a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-dvips.tex
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-dvips.tex
@@ -3,6 +3,7 @@
 \usepackage{color}
 \usepackage[dvips,designiii]{web}
 \usepackage[display]{texpower}
+\let\pdfsavepos\undefined
 \usepackage[dvips,filename=tooltipy,movetips,pages=28]{fancytooltips}
 
 \let\rmdefault\sfdefault
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-min-dvips.pdf b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-min-dvips.pdf
index a6bef916fe5..c1cf1e47ac1 100644
--- a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-min-dvips.pdf
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-min-dvips.pdf
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-min.pdf b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-min.pdf
index 644145b75c1..553c9497a70 100644
--- a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-min.pdf
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example-min.pdf
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example.pdf b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example.pdf
index 87b0b714a88..13d1cd00be3 100644
--- a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example.pdf
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example.pdf
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example.tex b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example.tex
index 8c2eced4c46..54803a48643 100644
--- a/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example.tex
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/fancytooltips-example.tex
@@ -4,8 +4,7 @@
 \usepackage[display]{texpower}
 \usepackage[pdftex,designiii]{web}
 
-\usepackage[filename=tooltipy,movetips]{fancytooltips}
-
+\usepackage[filename=tooltipy,movetips,mouseover,blur]{fancytooltips}
 
 \let\rmdefault\sfdefault
 
@@ -54,7 +53,7 @@
 \end{definice}
 
 \pause
-This is a geometric \tooltipanim{idea}{4}{28} which is behind the
+This is a geometric \tooltipanim*{idea}{4}{28} which is behind the
 definition of derivative.
 
 
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/tooltipy.pdf b/Master/texmf-dist/doc/latex/fancytooltips/examples/tooltipy.pdf
index 3dbafbc7290..38dff9a25f3 100644
--- a/Master/texmf-dist/doc/latex/fancytooltips/examples/tooltipy.pdf
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/tooltipy.pdf
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/examples/tooltipy.tips b/Master/texmf-dist/doc/latex/fancytooltips/examples/tooltipy.tips
new file mode 100644
index 00000000000..d0f37ddb0e7
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/fancytooltips/examples/tooltipy.tips
@@ -0,0 +1,3 @@
+\tooltipname{derivace}{1}
+\tooltipname{hodnost}{2}
+\tooltipname{definition}{3}
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/fancytooltips.pdf b/Master/texmf-dist/doc/latex/fancytooltips/fancytooltips.pdf
index edb3df37b5c..67c2776591d 100644
--- a/Master/texmf-dist/doc/latex/fancytooltips/fancytooltips.pdf
+++ b/Master/texmf-dist/doc/latex/fancytooltips/fancytooltips.pdf
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/README b/Master/texmf-dist/doc/latex/fancytooltips/readme
index e525d19663e..e525d19663e 100644
--- a/Master/texmf-dist/doc/latex/fancytooltips/README
+++ b/Master/texmf-dist/doc/latex/fancytooltips/readme
diff --git a/Master/texmf-dist/doc/latex/fancytooltips/tip.pdf b/Master/texmf-dist/doc/latex/fancytooltips/tip.pdf
index 993649d3577..e45dec7da58 100644
--- a/Master/texmf-dist/doc/latex/fancytooltips/tip.pdf
+++ b/Master/texmf-dist/doc/latex/fancytooltips/tip.pdf