Sandbox

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wikitex

<wikitex refresh dpi="144"> \section*{Education} \begin{itemize} \item M.A. Media Design and Communication: Networked Media, Piet Zwart Institute, Willem de Kooning Academy, Rotterdam University, Netherlands, 2010--2012. \item M.A. Information Technologies, Faculty of Economic Informatics, Economic University of Bratislava, Slovakia, 1997--2002. \begin{itemize} \item \textit{Dissertation:} Electronic Business (Online Market in the Mirror of Chaos Theory). \end{itemize} \item Mass Media Communication, Faculty of Mass Media Communication, University of Cyril and Method in Trnava, Slovakia, 1999--2001. \end{itemize} </wikitex>

<wikitex> Let $Q$ be any finite set, and $\mathcal B=2^Q$ be the collection of the subsets of $Q$. Let $f:\mathcal B\rightarrow \mathbb R$ be a function assigning real numbers to the subsets of $Q$ and suppose $f$ satisfies the following conditions:

(i) $f(A)\ge 0$ for all $A\subseteq Q$, $f(\emptyset)=0$,
(ii) $f$ is monotone, i.e. if $A\subseteq B\subseteq Q$ then $f(A)\le f(B)$,
(iii) $f$ is submodular, i.e. if $A$ and $B$ are different subsets of $Q$ then
     $$f(A)+f(B)\ge f(A\cap B) + f(A\cup B).\eqno{(2)}$$


</wikitex>

<wikitex> $\frac{1}{\displaystyle1+\frac{1}{\displaystyle 1+\sqrt{5}}}$ </wikitex>

lua

<lua who="Sandbox"> function hello(s)

 return string.format("Hello, %s!", s)


end

print(hello(who)) </lua>