单形内顶角的不等式及其应用

AN INEQUALITY FOR THE INSIDE VERTEX ANGLES OF A SIMPLEX AND ITS APPLICATIONS

本文首先给出了单形内顶角的概念，建立了单形内顶角的不等式，以此为基础可得到涉及单形体积的两个不等式。

Def init ion Let P be any inside point of an n-dimensional simplex:A_0A_1...A_n in E￣n,and the identidy vector which its direction is same as be ε_i(i=0,1,...,n).If D_i=G(ε_0,ε_1,..., ε_(i-1),ε_(i+1),...,ε_n)where G(ε_0,ε_1,...,ε_(i-1),ε_(i+1),...,ε_n)is the Gram determinant of vectors ε_0, ε_1,...,ε_(i-1),ε_(i+1),...,ε_n, then a_i=arc be called the inside vertex angle of simplex which its vertex is P(i=0,1,...,n).An inequality for the insjde vertex angles of simplex and two other inegualities for volume of simplex are given In this paper.