有限组两个完全同向单形的广义加权度量加  

Generalized weighted metric addition of finite groups of two dead synclastic n-dimensional simplexes

作　　者：马统一[1] 

机构地区：[1]河西学院数学系,甘肃张掖734000

出　　处：《纯粹数学与应用数学》2008年第3期566-575,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(10671117);甘肃省教育厅科研基金(0709-03)

摘　　要：利用广义Menger度量嵌入定理,推广了关于两组两个完全同向n维单形"广义度量加"的概念,提出了关于有限组两个完全同向n维单形的"广义加权度量加"的概念,并运用距离几何理论同矩阵不等式结合的方法,证明了几个涉及"广义加权度量加"的几何不等式,它们进一步推广了杨路和张景中关于Alexander猜想的结果,这些结论蕴含近期诸多文献的主要结果.By using the generalized Menger metric embedding theory, we extended the definition of the generalized metric addition which two groups of two dead synclastic simplexes, the definition is introduced of the generalized weighted metric addition which finite groups of two dead synclastic simplexes. In addition, by means of the method of the distance geometry theory and rectangle inequality, it was given that some geometry inequalities of the generalized weighted metric addition, which includ the main result of Yang and Zhang on Alexander conjecture. This conclusion include some main results of the resent articles.

关 键 词：n维Euclidean空间 完全同向单形 广义Menger度量嵌入定理 Sylvester-blumenthal矩阵 广义加权度量加 

分 类 号：O184[理学—数学]