欧氏空间E^n中Pedoe不等式推广  

Generalizations of n-dimensional Pedoe inequality in euclidean space E^n

作　　者：王文[1,2] 杨世国[1] 

机构地区：[1]合肥师范学院数学系,安徽合肥230601 [2]安徽大学数学科学学院,安徽合肥230039

出　　处：《中国科学技术大学学报》2012年第11期913-919,共7页JUSTC

基　　金：高等学校博士学科点专项科研基金(20113401110009);合肥师范学院校级自然科学研究一般项目(2012kj11);安徽省高校自然科学基金(KJ2011B133;20120904646)资助

摘　　要：应用距离几何的理论与方法,先证明了欧氏空间中n维单形的几个几何不等式,然后建立了加强形式的涉及两个单形棱长的n维Pedoe不等式和彭-常不等式以及k-n型Pedoe不等式和彭-常不等式.另外还建立了一个重要不等式.Using the theory and method of distance geometry, some geometric inequalities for n-dimensional simplexes were proved in Euclidean space E^n, from which the n-dimensional Pedoe inequality and Peng- Chang＇s inequality involving the edge-lengths of two simplexes were generalized. In addition, the k-n type Pedoe inequality and Peng-Chang＇s inequality in Euclidean space were generalized. Finally, a new inequality for an n-dimensional simplex in Euclidean space was obtained.

关 键 词：欧氏空间 单形 棱长 体积 PEDOE不等式 

分 类 号：O184[理学—数学]