中山大学学报自然科学版 ›› 2011, Vol. 50 ›› Issue (1): 27-30.

• 研究论文 • 上一篇    下一篇

联系两个n维单形的不等式及应用

杨世国1,钱 娣2   

  1. (1.合肥师范学院数学系,安徽 合肥 230061;2.安徽大学数学科学学院,安徽 合肥 230039)
  • 收稿日期:2010-01-11 修回日期:1900-01-01 出版日期:2011-01-25 发布日期:2011-01-25
  • 通讯作者: 钱娣

Inequalities for Two nDimensional Simplexes with Applications

YANG Shiguo 1,QIAN Di 2   

  1. (1.Department of Mathematics, Hefei Teachers College, Hefei 230061, China;2.School of Mathematics Sciences, Anhui University, Hefei 230039, China)
  • Received:2010-01-11 Revised:1900-01-01 Online:2011-01-25 Published:2011-01-25

摘要: 利用距离几何的理论与方法,研究了欧氏空间En中涉及两个单形棱长和体积的几何不等式问题,建立了涉及两个n维单形棱长与体积的两个几何不等式,推广了En中n维Pedoe不等式和彭-常不等式。

关键词: 欧氏空间, 单形, 棱长, 体积, 不等式

Abstract: Using the theory and method of distance geometry, the problems about geometric inequalities for the edgelengths and volumes of two n dimensional simplexes in the Euclidean space E-n are studied. Two geometric inequalities for the edgelengths and volumes of two n dimensional simplexes are established,and the n dimensional Pedoe inequality and PengChang inequality are improved.

Key words: Euclidean space, simplex, edge-length, volume, circumradius, inequality

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