高维单形的Janic'R R型不等式的加强形式

Strengthening Form of Janic''s R R Type Inequality on the High Dimensional Simplex

给出了高维单形的Jani'c R R型不等式的加强形式:∑1≤i<j≤n+1a2ij/(rirj)≥n2(n-1)2(R/(nr))2/(n(n-1))≥n2(n-1)2,等号成立的充要条件是Ω为正侧单形.

The strengthening forms of Janic＇s R R type inequalities on the high dimensional simplex are given：∑1≤i〈j≤n＋1 aij^2/（rirj）≥n^2（n-a）^2（R/（nr））^2/（n（n-1））≥n^2（n-1）^2 and the sufficient and necessary condition for the equalities is that Ω is canonical simplex.