关于多项式连续性的Newton多胞型充分条件
On Newton-polytope-type sufficiency conditions for coercivity of polynomials
摘要：
我们确定了新的充分条件一般多元多项式$f\in\mathbb{R}[x]$，这是表示在其牛顿多面体在无穷远，其中包括一个系统的仿射线性不等式的多项式系数的空间中。通过改进已有的一类gem非正则多项式的非正则性的必要条件，给出了回路多项式非正则性的一个刻画，推广了已有的关于这类多项式非正则性的结果.对于已经存在的充分条件包含一个描述，涉及一组投影操作，我们确定了一个等价的描述，涉及一个单一的正项不等式。这使得它们更容易应用，因此从实践的角度来看也更具吸引力。我们将我们的结果与现有的文献，我们用几个例子来说明我们的结果。
英文摘要：
We identify new sufficiency conditions for coercivity of general multivariate polynomials $f\in\mathbb{R}[x]$ which are expressed in terms of their Newton polytopes at infinity and which consist of a system of affine-linear inequalities in the space of polynomial coefficients. By sharpening the already existing necessary conditions for coercivity for a class of gem irregular polynomials we provide a characterization of coercivity of circuit polynomials, which extends the known results on this well studied class of polynomials. For the already existing sufficiency conditions for coercivity which contain a description involving a set projection operation, we identify an equivalent description involving a single posynomial inequality. This makes them more easy to apply and hence also more appealing from the practical perspective. We relate our results to the existing literature and we illustrate our results with several examples.
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