MID-FACETS OF A SIMPLEX  

作　　者：李小燕[1,2] 何斌吾[1,3] 冷岗松[1] 

机构地区：[1]Department of Mathematics, Shanghai University, Shanghai 200436, P.R.China [2].Department of Mathematics, Hunan Normal University, Changsha 410081, P.R.China [3]Department of Mathematics, Hunan University of Science and Technology, Yueyang 414000, P.R.China

出　　处：《应用数学和力学》2004年第6期621-626,共6页Applied Mathematics and Mechanics

基　　金：theNationalNaturalScienceFoundationofChina (10 2 710 71)

摘　　要：The mid-facet of a simplex in n-dimensional Euclidean space which was introduced quite recently is an important geometric element. An analytic expression for the mid-facet area of a simplex is firstly given. In order to obtain the expression,the exterior differential method was presented. Furthermore, the properties of the mid-facets of a simplex analogous to median lines of a triangle (such as for all mid-facets of a simplex,there exists another simplex such that its edge-lengths equal to these mid-facets area respectively, and all of the mid-facets of a simplex have a common point) were proved. Finally, by applying the analytic expression, a number of inequalities which combine edge-lengths, circumradius, median line, bisection area and facet area with the mid-facet area for a simplex were established.The mid_facet of a simplex in n_dimensional Euclidean space which was introduced quite recently is an important geometric element. An analytic expression for the mid_facet area of a simplex is firstly given. In order to obtain the expression,the exterior differential method was presented. Furthermore, the properties of the mid_facets of a simplex analogous to median lines of a triangle (such as for all mid_facets of a simplex,there exists another simplex such that its edge_lengths equal to these mid_facets area respectively, and all of the mid_facets of a simplex have a common point) were proved. Finally, by applying the analytic expression, a number of inequalities which combine edge_lengths, circumradius, median line, bisection area and facet area with the mid_facet area for a simplex were established.

关 键 词：单形 中面 中线 GRASSMANN代数 几何不等j 

分 类 号：O184[理学—数学]