%
% Test-slides
%
% remember to use 
%    latex AND dvipdf
%
% pdflatex alone does NOT WORK!
%

\documentclass[final, colorBG, pdf, accumulate, slideColor, sdu]{prosper}

\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{xspace}
\usepackage{pifont}

\usepackage{url}
\usepackage{amsmath}
\usepackage{amssymb}

% Titlepage
\title{%
    Slides using \\ \LaTeX{} and Prosper}
\author{%
    Jens Svalgaard Kohrt \\
    \url{http://imada.sdu.dk/~svalle/} 
}
\institution{%
    Department of Mathematics and Computer Science \\
    University of Southern Denmark, Denmark
}
\slideCaption{Test Slides}


\begin{document}
% ----------------------------------------------------------------------
% -                                                                    -
% -   Test Slides for SDU-Prosper                                      -
% -                                                                    -
% ----------------------------------------------------------------------
\maketitle

% -------------------------------------------------------------- SLIDE -
\begin{slide}{One Page}

  Usually on-line algorithms are compared using the compe\-ti\-tive ratio
  \[
     R(A) = \sup_I \frac{A(I)}{O(I)}
  \]

  We can also use other measures:
  \[
    {\ldots} 
  \]

\end{slide}
% ----------------------------------------------------------------------

% ======================================================================
%
\part{Part \#2}
%
% ======================================================================


% -------------------------------------------------------------- SLIDE -
\overlays{2}{
\begin{slide}{Two Slides on the Same Page}
  
  PRE uses
  \[
    M =  \max \left\{ \beta ~\frac Pm , \beta ~ p_{\max} \right\} = \beta~O(\sigma)
  \]%
  \onlySlide*{1}{
  where
  \[
    \beta = \frac{\theta^m}{\theta^m-1}, ~~ \theta = \frac{m}{m-1}
  \]%
  }\onlySlide*{2}{%

    MPRE uses %
    \[
      M' =  \max \left\{
        \beta ~\frac Pm , \frac{m-\beta}{m-1} p_{\max} + \frac{\beta-1}{m-1} P
      \right\} 
      \le M
    \]
    
    Both algorithms are optimal.
  }
\end{slide}}
% ----------------------------------------------------------------------

\end{document}