有关n维单形几个不等式的稳定性

J4 ›› 2011, Vol. 46 ›› Issue (2): 117-122.

有关n维单形几个不等式的稳定性

杨世国¹,王文²,钱娣²,潘娟娟²

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:2009-12-24 出版日期:2011-02-16 发布日期:2011-03-30
通讯作者: 王文(1985- ),男，硕士研究生，主要从事距离几何研究. Email: wangwen0811@163.com
作者简介:杨世国(1952- ),男,教授,主要从事距离几何研究. Email: yangsg@hftc.edu.cn
基金资助:
国家自然科学基金资助项目(60671051);安徽省高校省级重点基金资助项目(KJ2009A45)

The stability of some inequalities for a simplex

YANG Shi-guo1, WANG Wen2, QIAN Di2, PAN Juan-juan2

1. Department of Mathematics, Hefei Normal University, Hefei 230061, Anhui, China;
2. School of Mathematics Sciences, Anhui University, Hefei 230039, Anhui, China

Received:2009-12-24 Online:2011-02-16 Published:2011-03-30

摘要/Abstract

摘要：

利用距离几何的理论与方法研究了欧氏空间中n维单形的几个几何不等式的稳定性,从两个单形的“偏正”度量证明了n维单形四个重要几何不等式的稳定性,并给出这些几何不等式的稳定性版本。

关键词: 单形;外接球半径;内切球半径;旁切球半径;稳定性

Abstract:

Using the theory and method of distance geometry, the problems of stability of some geometric inequalities for an n-dimensional simplex in the Euclidean space is studied. From the deviation regular metric of two simplexes, the stabilities of four important geometric inequalities of an n-dimensional simplex are proved, and the stability versions of these geometric inequalities for a simplex are given.

Key words: simplex; circum-radius; in-radius; radius of escribed ball; stability

杨世国1,王文2,钱娣2,潘娟娟2. 有关n维单形几个不等式的稳定性[J]. J4, 2011, 46(2): 117-122.

YANG Shi-guo1, WANG Wen2, QIAN Di2, PAN Juan-juan2. The stability of some inequalities for a simplex[J]. J4, 2011, 46(2): 117-122.

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