N维单形中Jain R.R.型分式不等式的稳定性  

Stability on the Jani R.R.type fractional inequalities of an N-Simplex

作　　者：张垚[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,湖南长沙410081

出　　处：《湖南文理学院学报（自然科学版）》2008年第3期1-4,8,共5页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：湖南省教育厅科研基金资助项目(00C064);湖南省自然科学基金资助项目(06JJ1034)

摘　　要：引入两个单形之间的一种新度量,使得全体n维单形集合成为一个度量空间,应用这种度量方法,证明了涉及n维单形体积、高和单形内点到侧面距离的Jani R.R.型分式不等式的稳定性,这些结论是对应的几何不等式的推广和加强.The definition of a metric between any two n-simplexes was put forward such that the set of all n-simplexes was a metric space. By this metric method, the stability was proven on Janic R.R.type factional inequalities concerning to the volume, altitude and the distance from an interior point to the side facet for an n-simplex. These conclusions are the generalization and strengthening of corresponding geometric inequalities.

关 键 词：稳定性 N维单形 不等式 体积 高 单形内点到侧面的距离 

分 类 号：O184[理学—数学]