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\newtheorem{theorem}{Theorem}
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\author{ { Author 1} \\ \small{University 1} \and
{ Author 2} \\ \small{University 2} \and
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%\author{Author 1}
%\address[Author 1]{Department of Mathematics,
%hdjfhb, bfh, PO Box 70377, San Juan, Puerto Rico 00936}
%\email{author1@gmail.com}
%\author{Author 2}
%\address[Author 2]{Department of Mathematics,
%hdjfhb, bfh, PO Box 70377, San Juan, Puerto Rico 00936}
%\email{author1@gmail.com}
%\author{Author 3}
%\address[Author 3]{Department of Mathematics,
%hdjfhb, bfh, PO Box 70377, San Juan, Puerto Rico 00936}
%\email{author1@gmail.com}
\date{July 37 2013}
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\begin{abstract}
We prove ...
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\section{Introduction}
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A finite sequence of real numbers $\{d_0,d_1,\ldots,d_m\}$ is said to be {\it unimodal} if there
exists an index $0\leq r\leq m$, called the $mode$ of the sequence such that $d_j$ increases
up to $j=r$ and decreases from then on, that is, $d_0\leq d_1\leq\cdots\leq d_r$ and
$d_r\geq d_{r+1}\cdots\geq d_m$. Details can be found in \cite{BM}.
\begin{example} The following polynomial is unimodal with mode $3$:
$$5 + 8x + 10x^2 + 50x^3 + 27x^4 + 13x^5$$
\end{example}
\begin{definition}
The sequence $\{d_0,d_1,\ldots,d_m\}$ is said to be \textit{logarithmically concave}
(or {\bf log-concave} for short) if $d_{j+1}d_{j-1}\leq d_j^2$ for $1\leq j\leq m-1$.
\end{definition}
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\section{Algebra Background}
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Our research concerns a special case of a conjecture of B.Sturmfels of \cite{ST}.
A group action of any finite group $G$ forms a ring $k[x_1,\ldots,x_n]^G$.
The Reynolds operator is defined as in \cite{CLS} by
\begin{equation}
x=1
\end{equation}
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Something
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We begin this section with the following result.
\begin{theorem}\label{alabel}
$2 \not=1.$
\end{theorem}
\begin{Proof}
In the real numbers
\begin{eqnarray}
1+2 & = & 3 \nonumber \\
2+2+1 & \not= & 1 \label{boberias} \\
2 & < & 3
\end{eqnarray}
Using (\ref{boberias}) we can prove Theorem \ref{alabel}. See the Latex files to see how to do the add the references to theorems and equations.
\end{Proof}
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\section{Acknowledgements}
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We would like to thank XXXXX.
This work was conducted at the 2013 MSRI-UP and supported by the National Security Agency (NSA) grant H-98230-13-1-0262 and the National Science Foundation (NSF) grant 1156499.
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% Bibliography.
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\begin{thebibliography}{aaaa}
\bibitem {CLS} D. Cox, J. Little, \& D. O'Shea, \textit{Ideals,
Varieties and Algorithms}, 2nd Ed., Springer-Verlag, New York,
1997.
\bibitem {BM} G. Boros \& V. Moll , \textit{A sequence of unimodal polynomials},
Jour. Math. Anal. Appl., \textbf{237} , 272-287, 1999.
\bibitem {ST} B. Sturmfels, \textit{Gr\"obner Bases and Convex Polytopes},
American Mathematics Society, Providence, RI, 1996.
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