摘要
设 n维 Euclid空间 En(n≥ 2 )中单形 Ω(A)的顶点集为 A={ A0 ,A1,… ,An} .,Ω(A)内任一点 P至侧面 { A0 ,A1,… ,An} \{ Ai}的距离为 di(i=0 ,1,… ,n) ,Ω(A)的外接超球半径和内切超球半径分别为 R、r,记C( n,α) =(2 (n+ 1 2 ) + (n+ 1) 2α- (n+ 1) α) / 4 (n+ 12 ) ) α(α≥ 1) ,本文建立了涉及Ω (A)内一点的不等式∑0≤ i<j≤ n1(didj) α≥ C( n,α)12 a +((n+ 12 ) - Cn,αn2 aR2α ,并推广了文献 [2 - 3]的结果 .
Let Ω(A)={A 0,A 1,...,A n}denote an n-dimensional simplex in the n-dimen-sional Euclidean space E n with vertices A 0,A 1,...,A n and of volume V.R and r the radii of circum scribed and inscribed hyperspheres of Ω(A),respectively,and let Ω i=A 0,A 1,...,A n)\{A i} be a facet of Ω(A) which lies in a hyperplance π i(i=0,1,2,...,n) and let d i be the distance form and interior point P of Ω(A) to π i(i=0,1,2,...,n). we established the following inequality,Which are generalizations in 2-3: JB(∑JB)DD(X0≤i<j≤nDD)SX(1(d id j) αSX)≥SX(C (n,α)1 2αSX)+SX(((SX(Bn+12SX))-C n,αn 2αR 2αSX), Where C (n,α)=(2(JB(n+1 KG*22JB))+(n+1) 2α-(n+1) α)/4(SX(Bn+12SX))) α(α≥1), and equality holds if and only if Ω(A) is regular and the point P in the centre of Ω(A).
出处
《数学理论与应用》
2002年第2期47-52,共6页
Mathematical Theory and Applications
