On the Minimum of a Polynomial Function on a Basic Closed Semialgebraic Set and Applications
给出了基本闭半代数集的紧致连通分支上多项式函数非零最小值的一个显式代数度上界和绝对值下界，并推广到非紧致情形，进而得到两个不相交连通分支的分离下界。
We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is not zero. We also present extensions of these results to noncompact situations. As an application, we obtain a lower bound for the separation of two disjoint connected components of basic closed semialgebraic sets, when at least one of them is compact.