用差分代换研究实数域中多项式的半正定性

Study of multi-nomial semi-positive definiteness in real number field by the means of difference replacement

以逐次差分代换为依据,提出了多级差分代换平凡和非平凡以及绝对差分代换非平凡的概念;通过分情形讨论,将实数域中的多项式转化为正数域中的等价多项式集,从而实现用差分代换研究实数域中多项式半正定性的问题。

Based on gradual difference replacement, the definitions of multi-difference replacement non- triviality and absolute difference replacement non-triviality are put forward. Through situational discussion, we have converted the muhi-nomial in real number field into equivalent muhi-nomial set in positive number, thus we can study the muhi-nomial semi-positive definiteness in real number field by the means of difference replacement.