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\begin{document}
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{\Large\bf
Scrambled eggs
}
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% AUTHORS - if all affiliations are the same, upper indices can be excluded
% AUTHORS - please underline the presenting author
{\large
\underline{
Richard Onion}$^{1,2}$, John Mushroom$^{1}$ and Terry Fish$^{2}$
}
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% AFFILIATION - required with address, email at least for corresponding author
{\small
$^{1}$ Charles University, Faculty of Food and Taste,\\
Malostransk\'{e} n\'{a}m. 25, 11800, Prague, Czech Republic\\
\texttt{\{onion, mushroom\}@food.mff.cuni.cz}\\
$^{2}$ Charles University, Faculty of Food and Taste,\\
Malostransk\'{e} n\'{a}m. 25, 11800, Prague, Czech Republic\\
\texttt{fish@food.mff.cuni.cz}
}
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% KEYWORDS - required
{\noindent\bf Keywords:} frying pan, pumping potato lemma, hard boiled eggs
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\subsection*{Introduction}
Scrambled eggs are useful if there is not much time, but hunger is still there~\cite{Luncheonmeat2009}. There is rising interests among scientists over the globe towards studies of their properties. It seems that there are connections to algorithmic cooking theory, algebraic digestive theory or convex taste optimization~\cite{Hunger1997}. This area is also suspected to solve food halting problem.
\subsection*{Basic properties}
There is in fact not much to say about scrambled eggs, however, there are some obvious observations, like
\begin{prop}
Let $\mathcal{E}_S$ be scrambled eggs system with maximum possible taste. Solving a problem of eating this system up is in $P$.
\end{prop}
We can in fact show that this can be done in sub-logarithmic time assuming no previous food being eaten sufficiently long ago.
\subsection*{Main results}
Let $\mathcal{E}_S$ be a scrambled eggs system. Let moreover there exists a matrix $A$ coding a system of the corresponding linear conditions. We would like to maximize its taste. This effort is represented by the following maximizing problem:
\begin{equation*}
\max\; \sum_{i,j=1}^n a_{ij}\mathcal{E}_S(i,j+n)
\mbox{ subject to } \mathcal{E}_S\succeq\ 0.
\end{equation*}
We have solved this problem using a hard-boiled eggs theorem producing a sub-optimal taste.
\subsubsection*{Acknowledgement}
Thanks the National Institute of Full Stomach and Department of Vegetable Cooking of the Academy of Science of the Carrot Republic for their kind support of this work.
% REFERENCES
\begin{thebibliography}{1}
\bibitem{Luncheonmeat2009}
R.E. Luncheonmeat, R.B. Beafeater, and M.J. Rumpsteak,
{\it Introduction to Meat Analysis},
Anti-Diet Publishing, Czech Republic, 2009.
% paper
\bibitem{Hunger1997}
J. Hunger and K. Thirsty,
A new polynomial time method to cook dinner,
{\it Journal of Modern Cuisine} 3(1):51--81, 1997.
\end{thebibliography}
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