Some geometric properties of successive difference substitutions  

作　　者：HOU XiaoRong XU Song SHAO JunWei 

机构地区：[1]School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China [2]Faculty of Science, Ningbo University, Ningbo 315211, China

出　　处：《Science China(Information Sciences)》2011年第4期778-786,共9页中国科学（信息科学）（英文版）

基　　金：supported by the National Basic Research Porgram of China (Grant No. 2004CB318000);the National Natural Science Foundation of China (Grant Nos. 10571095, 61074189)

摘　　要：This paper provides a new, geometric perspective to study successive difference substitutions, and proves that the sequence of the successive difference substitution sets is not convergent. An interesting result that a given k-dimensional rational hyperplane can be transformed to a k-dimensional coordinate hyperplane of new variables by finite steps of successive difference substitutions is presented. Moreover, a sufficient condition for the sequence of the successive difference substitution sets of a form being not terminating is obtained. That is, a class of polynomials which cannot be proved to be positive semi-definite by the successive difference substitution method axe obtained.This paper provides a new, geometric perspective to study successive difference substitutions, and proves that the sequence of the successive difference substitution sets is not convergent. An interesting result that a given k-dimensional rational hyperplane can be transformed to a k-dimensional coordinate hyperplane of new variables by finite steps of successive difference substitutions is presented. Moreover, a sufficient condition for the sequence of the successive difference substitution sets of a form being not terminating is obtained. That is, a class of polynomials which cannot be proved to be positive semi-definite by the successive difference substitution method axe obtained.

关 键 词：successive difference substitutions nonnegativity decision of forms Barycentric subdivision 

分 类 号：O177.2[理学—数学] TP391.72[理学—基础数学]