Révision 246 CSL17/preliminaries.tex
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\end{definition}
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Bellantoni showed the following result: |
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\begin{theorem}[\cite{BellantoniThesis, Bellantoni95}]\label{thm:mubc}
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$\mubc =\fph$. Furthermore, for $i\geq 1$, $\mubc^{i-1} = \fphi{i}$.
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\end{theorem}
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\medskip
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\noindent
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\textbf{Some computational properties of $\mubc$ programs.}
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We will need some bounds for $\mubc$ functions that we use later on;
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all of this material is from \cite{bellantoni1995fph}.
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In what follows we will recall some of the intermediate results and state a slightly stronger result that directly follows from \cite{bellantoni1995fph}.
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%
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%\medskip
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%\noindent
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%\textbf{Some computational properties of $\mubc$ programs.}
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At the same time these results give us access to bounds for $\mubc$ functions that we use later on.
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\begin{definition}
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A function $f(\vec u; \vec x)$ is \textit{polymax bounded} if there exists a polynomial $q$ such that,
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