Inclusion measures of convex bodies （ Ⅰ ）

In this paper, the relations between inclusion measures of different bodies related to convex body K and the inclusion measure of convex body K itself were obtained.     

凸体的包含测度(Ⅱ)

In this paper,several inequalities for inclusion measures of convex bodies were obtained.The inclusion measure was proved to have concavity by considering the property of relative inner parallel body.     

凸体的包含测度(Ⅰ)

1 Introduction In [1] ,Zhang established certain geometric inequa-lities by considering the inclusion measure of a convexfigure containedin a convex body.Theyrelated thein-clusion measure to the mixed volumes of convex bo-dies ,and gave sharp lower and up…     

一类特殊点、线段的包含测度

本文讨论了由各种特殊图形蜕化为点或直线的包含测度的一般公式。由此通过比较它们蜕化为同一图形结果上的差异,从本质上加深认识包含测度的意义。     

一类特殊点、线段的包含测度

本文讨论了由各种特殊图形蜕化为点或直线的包含测度的一般公式。由此通过比较它们蜕化为同一图形结果上的差异,从本质上加深认识包含测度的意义。     

R~3上相交线偶与凸体相交的几何概率问题

利用在平面中建立的凸体的双弦幂积分理论,研究了空间中凸体的双弦幂积分的一些性质,并在此基础上,讨论了空间上相交线偶与凸体相交这一几何概率问题。     

R^3上相交线偶与凸体相交的几何概率问题

利用在平面中建立的凸体的双弦幂积分理论,研究了空间中凸体的双弦幂积分的一些性质,并在此基础上,讨论了空间上相交线偶与凸体相交这一几何概率问题。     

凸性与广义凸性综述(1)

对庞大的凸性家族给予轮廓性描述,以期引起同仁对各种非常规凸性研究的关注.本文第一节简述通常凸性概念及其在不等式理论方面的几个简单应用,第二节简介几何凸性、对数凸性、指数凸性及其与通常凸性之间的相互关系;第三节介绍集合与函数的理想凸性;第四节简介由笔者首创的积分凸性及其进展.     

弱对数凸(凹)函数及其应用

本文给出了弱对数凸(凹)函数的一些等价条件,得到了Adamovi■不等式的推广形式.     

Firey linear combinations of convex bodies

For convex bodies, the Firey linear combinations were introduced and studied in several papers. In this paper the mean width of the Firey linear combinations of convex bodies is studied, and the lower bound of the mean width of the Firey linear combinations of convex body and its polar body is given.     

Asymptotic properties of two affine invariants for 1-unconditonal convex bodies

Let K be a 1-unconditional convex bodies in Euclidean spaces.We study the asymptotic properties of two affine invariants m2（K） and S2（K） for a random simplex inside K.As an application,we discuss the asymptotic properties of two affine invariants m2（Bpn ） and S2（Bpn ）,where Bpn = {x ∈ Rn ： ‖x‖ p 1}.     

Asymptotic properties of two affine invariants for 1-unconditional convex bodies

Let K be a 1-unconditional convex bodies in Euclidean spaces. We study the asymptotic properties of two affine invariants m2(K) and S2(K) for a random simplex inside K. As an application, we discuss the asymptotic properties of two affine invariants m2(Bnp) and S2(Bnp), where Bnp = {χ∈ Rn: ‖χ‖p ≤ 1}.     

正多边形与平行线网相交的Buffon概率

目的:研究了正多边形与平行线网相交的Buffon概率问题.方法:利用几何体的运动测度的比值.结果:求得了正三边形和正四边形的Buffon概率.结论:通过对这两类特殊几何体上得出的结论,推广得出了正多边形的Buffon概率的一般公式.     

单形的径向平均体

In this paper, it is proved that the radial pth mean body RpK（p 〉 0） is homothetic to the difference body DK when K is a simplex, Furthermore, the equality Rp（Rq） = Rq（Rp） is established when p 〉 0 and q 〉 0. It is also proved the Brunn-Minkowski inequality of radial pth mean body of simplex and uniqueness property.     

凸体p-非对称度的稳定性

证明了凸体p-非对称度在其最大最小值处的稳定性定理,其中关于1-非对称度在最小值1处的结论是该文的主要贡献。     

凸几何分析简介

本文概述了凸几何分析的发展历程与研究现状,主要代表人物以及我国数学家在这方面的工作.