diff --git a/Kstmumu/Jakobian/beamerthemeSybila.sty b/Kstmumu/Jakobian/beamerthemeSybila.sty index 633f89e..d1c9d75 100644 --- a/Kstmumu/Jakobian/beamerthemeSybila.sty +++ b/Kstmumu/Jakobian/beamerthemeSybila.sty @@ -4,17 +4,17 @@ % Themes %------------------------------------------------------------------------------- -\useoutertheme{split} -%\useinnertheme{rounded} -\usefonttheme{structurebold} -\useoutertheme{shadow} - -\useinnertheme[shadow=true]{rounded} -% Solid \item symbols -\useinnertheme{circles} - -\setbeamertemplate{itemize items}[default] -\setbeamertemplate{enumerate items}[default] +\useoutertheme{split} +%\useinnertheme{rounded} +\usefonttheme{structurebold} +\useoutertheme{shadow} + +\useinnertheme[shadow=true]{rounded} +% Solid \item symbols +\useinnertheme{circles} + +\setbeamertemplate{itemize items}[default] +\setbeamertemplate{enumerate items}[default] %------------------------------------------------------------------------------- @@ -23,7 +23,7 @@ \beamertemplatenavigationsymbolsempty \beamertemplateheadempty -%\beamertemplateshadowblocks +\beamertemplateshadowblocks %------------------------------------------------------------------------------- % Own templates @@ -51,7 +51,7 @@ \vskip1em - + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} \usebeamerfont{date}\insertinstitute \end{beamercolorbox} @@ -80,10 +80,10 @@ %------------------------------------------------------------------------------- %\logo{\hspace*{0.6\textwidth}\includegraphics[width=1.8cm]{images/uzh.jpg}\hspace*{0.3cm}} -\logo{% - \includegraphics[width=1.8cm,keepaspectratio]{images/uzh.jpg}\hspace*{0.3cm}% +%\logo{% +% \includegraphics[width=1.8cm,keepaspectratio]{images/uzh.jpg}\hspace*{0.3cm}% % \includegraphics[height=0.6cm,keepaspectratio]{images/ifj.png}% -} +%} \newif\ifplacelogo \logo{\ifplacelogo \includegraphics[width=1.8cm,keepaspectratio]{images/uzh.jpg}\hspace*{0.3cm} \fi} % replace with your own command @@ -93,18 +93,18 @@ \setbeamercovered{dynamic} -%\definecolor{mygreen}{RGB}{51,80,255} -\definecolor{mygreen}{RGB}{0, 204,0} -\definecolor{mygreentitle}{RGB}{0, 170,0} -%\definecolor{lightgreen}{RGB}{218, 241, 241} -\definecolor{lightgreen}{RGB}{65,255,65} +%\definecolor{myblue}{RGB}{51,80,255} +\definecolor{myblue}{RGB}{0, 109, 182} +\definecolor{myblue_title}{RGB}{0, 139, 212} +%\definecolor{lightblue}{RGB}{218, 241, 241} +\definecolor{lightblue}{RGB}{177, 236, 236} \setbeamercolor{math text}{fg=white!0!black} % white -\setbeamercolor{title}{bg=mygreen, fg=black} -\setbeamercolor{frametitle}{bg=mygreentitle, fg=black} +\setbeamercolor{title}{bg=myblue, fg=black} +\setbeamercolor{frametitle}{bg=myblue_title, fg=black} \setbeamercolor{footline}{bg=black,fg=white} -\setbeamercolor{author in head/foot}{bg=lightgreen,fg=black} -\setbeamercolor{title in head/foot}{bg=mygreen, fg=black} +\setbeamercolor{author in head/foot}{bg=lightblue,fg=black} +\setbeamercolor{title in head/foot}{bg=myblue, fg=black} \setbeamercolor{block title}{bg=white!45!black} \setbeamercolor{block title example}{bg=white!45!black} \setbeamercolor{block title alerted}{bg=white!15!black} @@ -114,30 +114,24 @@ %\colorlet{shadedshaded}{black!10!bg} %\colorlet{blackshaded}{black!40!bg} +%------------------------------------------------------------------------------- +% Hacking colors +%------------------------------------------------------------------------------- -%------------------------------------------------------------------------------- -% Hacking colors -%------------------------------------------------------------------------------- - - -\colorlet{titleleft}{mygreen!100!black} -\colorlet{titleright}{mygreen!55!black} - -\setbeamercolor*{frametitle}{fg=black} - -\makeatletter -\pgfdeclarehorizontalshading[titleleft,titleright]{beamer@frametitleshade}{\paperheight}{% - color(0pt)=(titleleft); - color(\paperwidth)=(titleright)} -\makeatother - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\colorlet{titleleft}{myblue!100!black} +\colorlet{titleright}{myblue!55!black} + +\setbeamercolor*{frametitle}{fg=black} + +\makeatletter +\pgfdeclarehorizontalshading[titleleft,titleright]{beamer@frametitleshade}{\paperheight}{% + color(0pt)=(titleleft); + color(\paperwidth)=(titleright)} +\makeatother - - +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usecolortheme{whale} @@ -155,7 +149,7 @@ %------------------------------------------------------------------------------- \titlegraphic{ -\includegraphics[width=3.0cm]{images/uzh.jpg}\hspace*{0.3cm} +%\includegraphics[width=3.0cm]{images/uzh.jpg}\hspace*{0.3cm} %\includegraphics[height=0.9cm,keepaspectratio]{images/ifj.png}% } diff --git a/Kstmumu/Jakobian/images/2DZ2.png b/Kstmumu/Jakobian/images/2DZ2.png new file mode 100644 index 0000000..2fbe7b6 --- /dev/null +++ b/Kstmumu/Jakobian/images/2DZ2.png Binary files differ diff --git a/Kstmumu/Jakobian/images/LL_pdf.png b/Kstmumu/Jakobian/images/LL_pdf.png new file mode 100644 index 0000000..5b621ef --- /dev/null +++ b/Kstmumu/Jakobian/images/LL_pdf.png Binary files differ diff --git a/Kstmumu/Jakobian/images/LL_toys.png b/Kstmumu/Jakobian/images/LL_toys.png new file mode 100644 index 0000000..c06970d --- /dev/null +++ b/Kstmumu/Jakobian/images/LL_toys.png Binary files differ diff --git a/Kstmumu/Jakobian/images/P5.png b/Kstmumu/Jakobian/images/P5.png new file mode 100644 index 0000000..6a67ed9 --- /dev/null +++ b/Kstmumu/Jakobian/images/P5.png Binary files differ diff --git a/Kstmumu/Jakobian/mchrzasz.log b/Kstmumu/Jakobian/mchrzasz.log index 5d23d65..6bf93bb 100644 --- a/Kstmumu/Jakobian/mchrzasz.log +++ b/Kstmumu/Jakobian/mchrzasz.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2015.4.1) 9 JUL 2015 10:54 +This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2015.4.1) 10 JUL 2015 16:43 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -1100,10 +1100,198 @@ Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargthree' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargtwo' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargtwo' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargthree' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `subscript' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `superscript' on input line 24. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\mskip' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\to' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargthree' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargtwo' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargtwo' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargthree' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `subscript' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `superscript' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\ast' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\mskip' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargthree' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargtwo' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargtwo' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargthree' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\mu' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `subscript' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `superscript' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\mskip' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargthree' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargtwo' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargtwo' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\-command' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\myargthree' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\mu' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `subscript' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `superscript' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): +(hyperref) removing `\mskip' on input line 24. + + +Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 24. @@ -1562,15 +1750,9 @@ (Font) Font shape `OT4/cmss/m/sl' tried instead on input line 30. LaTeX Font Info: Font shape `OT4/cmss/m/it' in size <8> not available (Font) Font shape `OT4/cmss/m/sl' tried instead on input line 30. - - -File: images/uzh.jpg Graphic file (type jpg) - -Package pdftex.def Info: images/uzh.jpg used on input line 30. -(pdftex.def) Requested size: 85.35826pt x 26.54065pt. [1 -{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map} <./images/uzh.jpg>] +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] Package hyperref Warning: Option `pdfauthor' has already been used, (hyperref) setting the option has no effect on input line 31. @@ -1588,7 +1770,7 @@ ] [5 -] +] File: images/Fl_AFb.png Graphic file (type png) @@ -1597,50 +1779,59 @@ [6 <./images/Fl_AFb.png>] - -File: images/Fl_boundry.png Graphic file (type png) + +File: images/2DZ2.png Graphic file (type png) + +Package pdftex.def Info: images/2DZ2.png used on input line 118. +(pdftex.def) Requested size: 338.02072pt x 84.3233pt. - -Package pdftex.def Info: images/Fl_boundry.png used on input line 113. -(pdftex.def) Requested size: 261.19826pt x 224.3927pt. - -Overfull \vbox (9.9315pt too high) detected at line 113 +Overfull \hbox (30.73085pt too wide) in paragraph at lines 118--118 + [] [] [7 - <./images/Fl_boundry.png>] -File: images/2D.png Graphic file (type png) + <./images/2DZ2.png>] +File: images/LL_pdf.png Graphic file (type png) - -Package pdftex.def Info: images/2D.png used on input line 122. -(pdftex.def) Requested size: 261.19826pt x 106.93678pt. + +Package pdftex.def Info: images/LL_pdf.png used on input line 135. +(pdftex.def) Requested size: 162.60638pt x 114.1604pt. + +File: images/LL_toys.png Graphic file (type png) + + +Package pdftex.def Info: images/LL_toys.png used on input line 135. +(pdftex.def) Requested size: 162.60638pt x 114.1604pt. [8 - <./images/2D.png>] - -File: images/2DZ.png Graphic file (type png) - -Package pdftex.def Info: images/2DZ.png used on input line 132. -(pdftex.def) Requested size: 261.19826pt x 106.82155pt. + <./images/LL_pdf.png> <./images/LL_toys.png>] + +File: images/P2.png Graphic file (type png) + +Package pdftex.def Info: images/P2.png used on input line 154. +(pdftex.def) Requested size: 153.57483pt x 130.04822pt. + + +File: images/cast.png Graphic file (type png) + +Package pdftex.def Info: images/cast.png used on input line 154. +(pdftex.def) Requested size: 153.57483pt x 153.57141pt. + +Overfull \vbox (7.11024pt too high) detected at line 154 + [] [9 - <./images/2DZ.png>] -File: images/P2.png Graphic file (type png) - - -Package pdftex.def Info: images/P2.png used on input line 152. -(pdftex.def) Requested size: 153.57483pt x 130.04822pt. - -File: images/cast.png Graphic file (type png) - - -Package pdftex.def Info: images/cast.png used on input line 152. -(pdftex.def) Requested size: 153.57483pt x 153.57141pt. + <./images/P2.png> <./images/cast.png (PNG copy)>] + +File: images/P5.png Graphic file (type png) + +Package pdftex.def Info: images/P5.png used on input line 166. +(pdftex.def) Requested size: 261.19826pt x 174.68065pt. [10 - <./images/P2.png> <./images/cast.png (PNG copy)>] + <./images/P5.png>] \tf@nav=\write6 \openout6 = `mchrzasz.nav'. @@ -1650,27 +1841,26 @@ \tf@snm=\write8 \openout8 = `mchrzasz.snm'. -Package atveryend Info: Empty hook `BeforeClearDocument' on input line 163. -Package atveryend Info: Empty hook `AfterLastShipout' on input line 163. - -(./mchrzasz.aux) -Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 163. -Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 163. +Package atveryend Info: Empty hook `BeforeClearDocument' on input line 176. +Package atveryend Info: Empty hook `AfterLastShipout' on input line 176. + (./mchrzasz.aux) +Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 176. +Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 176. Package rerunfilecheck Info: File `mchrzasz.out' has not changed. (rerunfilecheck) Checksum: D41D8CD98F00B204E9800998ECF8427E;0. -Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 163. +Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 176. ) Here is how much of TeX's memory you used: 18871 strings out of 493304 - 326733 string characters out of 6139872 - 418881 words of memory out of 5000000 - 21785 multiletter control sequences out of 15000+600000 + 326765 string characters out of 6139872 + 419963 words of memory out of 5000000 + 21786 multiletter control sequences out of 15000+600000 48363 words of font info for 137 fonts, out of 8000000 for 9000 957 hyphenation exceptions out of 8191 - 49i,32n,59p,424b,633s stack positions out of 5000i,500n,10000p,200000b,80000s -{/usr/share/texlive/texmf-dist/fonts/enc/dvips/pl/plms.enc}{/usr/share/texliv -e/texmf-dist/fonts/enc/dvips/pl/plmi.enc}{/usr/share/texlive/texmf-dist/fonts/e -nc/dvips/pl/plrm.enc}{/usr/share/texlive/texmf-dist/fonts/enc/dvips/pl/plme.enc + 49i,32n,59p,424b,631s stack positions out of 5000i,500n,10000p,200000b,80000s +{/usr/share/texlive/texmf-dist/fonts/enc/dvips/pl/plmi.enc}{/usr/share/texliv +e/texmf-dist/fonts/enc/dvips/pl/plrm.enc}{/usr/share/texlive/texmf-dist/fonts/e +nc/dvips/pl/plme.enc}{/usr/share/texlive/texmf-dist/fonts/enc/dvips/pl/plms.enc } -Output written on mchrzasz.pdf (10 pages, 317176 bytes). +Output written on mchrzasz.pdf (10 pages, 315116 bytes). PDF statistics: - 205 PDF objects out of 1000 (max. 8388607) + 206 PDF objects out of 1000 (max. 8388607) 145 compressed objects within 2 object streams 20 named destinations out of 1000 (max. 500000) 90 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/Kstmumu/Jakobian/mchrzasz.pdf b/Kstmumu/Jakobian/mchrzasz.pdf index 2e16b6e..d063755 100644 --- a/Kstmumu/Jakobian/mchrzasz.pdf +++ b/Kstmumu/Jakobian/mchrzasz.pdf Binary files differ diff --git a/Kstmumu/Jakobian/mchrzasz.synctex.gz b/Kstmumu/Jakobian/mchrzasz.synctex.gz index a8b9f28..7a83534 100644 --- a/Kstmumu/Jakobian/mchrzasz.synctex.gz +++ b/Kstmumu/Jakobian/mchrzasz.synctex.gz Binary files differ diff --git a/Kstmumu/Jakobian/mchrzasz.tex b/Kstmumu/Jakobian/mchrzasz.tex index 619da04..8e05f36 100644 --- a/Kstmumu/Jakobian/mchrzasz.tex +++ b/Kstmumu/Jakobian/mchrzasz.tex @@ -21,15 +21,15 @@ \usetheme{Sybila} \title[Jacobian for $\PBzero \to \PKstar \Pmuon \APmuon$]{Jacobian for $\PBzero \to \PKstar \Pmuon \APmuon$ \\ proposed solution} -\author{Marcin Chrz\k{a}szcz$^{1}$} -\institute{$^1$~University of Zurich} +\author{$\PBzero \to \PKstar \Pmuon \APmuon$ team} +%\institute{$^1$~University of Zurich} \date{\today} \begin{document} % --------------------------- SLIDE -------------------------------------------- \frame[plain]{\titlepage} -\author{Marcin Chrz\k{a}szcz{~}} -\institute{(UZH)} +\author{$\PBzero \to \PKstar \Pmuon \APmuon$ team} +%\institute{(UZH)} % ------------------------------------------------------------------------------ % --------------------------- SLIDE -------------------------------------------- \begin{frame}\frametitle{Introduction} @@ -104,37 +104,39 @@ \includegraphics[width=0.85\textwidth]{images/Fl_AFb.png} \end{frame} - \begin{frame}\frametitle{Toys} -\begin{itemize} -\item I am rejecting the non-physical regions: - -\end{itemize} -\includegraphics[width=0.85\textwidth]{images/Fl_boundry.png} -\end{frame} - - + \begin{frame}\frametitle{Toys} \begin{itemize} \item Now how does the new space look like. \item Important to take into account the boundary as without all my theorems fall down. +\item The white point is the value from which the toy was generated. \end{itemize} -\includegraphics[width=0.85\textwidth]{images/2D.png} -\end{frame} - - - -\begin{frame}\frametitle{Toys ZOOM} +\begin{center} +\includegraphics[width=1.1\textwidth]{images/2DZ2.png} + +\end{center} +\end{frame} + + + +\begin{frame}\frametitle{Re parametrization of pdf} \begin{itemize} -\item Now how does the new space look like. -\item Important to take into account the boundary as without all my theorems fall down. +\item Re parametrization of the pdf gives exactly the same answer as toys taking into account the jacobian: \end{itemize} -\includegraphics[width=0.85\textwidth]{images/2DZ.png} -\end{frame} - - - \begin{frame}\frametitle{Toys Conclusions} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.9\textwidth]{images/LL_pdf.png} +\column{2.5in} +\includegraphics[width=0.9\textwidth]{images/LL_toys.png} +\end{columns} + + + +\end{frame} + +\begin{frame}\frametitle{Toys Conclusions} \begin{itemize} -\item One needs to take into account the Jacobian! +\item Jakobian give the same answer as does the parametrization of pdf. \item The most probable value agrees perfectly. \item The confidence belt can be transformed analytically even :) \item There is one hack here: one cannot look at $P_2$ stand alone any more: @@ -151,6 +153,17 @@ \end{frame} + \begin{frame}\frametitle{Why so sinuous?} +\begin{itemize} +\item This is how we should advertise the $P^{\prime}_{5}$: + +\end{itemize} +\includegraphics[width=0.85\textwidth]{images/P5.png} + + + + +\end{frame}