涉及单形内点的几何不等式

建立了涉及n维单形内点的两个几何不等式，作为其特例得到n维Euler不等式的推广。     

单形中的两个几何不等式(英文)

给出了n维欧氏空间中关于单形的n-1维体积与单形内部任意一点到所对界面的距离的两个不等式.     

Inequalities for a Simplex and an Interior Point

We establish some inequalities for the inradius, circumradius and distances between an interior point and facets of an n-simplex, and prove a recursion inequality for the radii of the circumscribed spheres of an n-simplex and its facets.     

关于内接单形的不等式及其应用

应用解析方法和几何不等式理论研究了n维欧氏空间E~n中涉及n维单形Ω_n与其内接单形Ω′_n的几何不等式的问题,建立了涉及单形Ω_n及其内接单形Ω′_n的外接球半径与高线的一类几何不等式,作为其特例得到了著名的n维Euler不等式的一些推广.     

关联单形和一点的一类几何不等式

本文建立联系单形和一动点的几个新颖不等式,并提出几个有待进一步讨论的猜想.     

有关度量加的几个几何不等式

本文利用代数的方法建立了一个与距离几何中度量加单形的体积和外接超球半径有关的几何不等式,作为其应用,由此可以导出一系列重要的几何不等式.在文末还给出了“广义度量加”的概念,并提出若干猜想供进一步研究.     

有关度量加单形宽度的不等式

本文利用距离几何理论和解析不等式的技巧,研究了度量加单形的宽度度量估计,建立了有关度量加单形宽度之间的几个几何不等式.     

关于n维单形的几个几何不等式

建立了关于n维单形的几个几何不等式,并给出了它们的一些应用.     

三论切点单形的不等式

本文给出了单形与其切点单形关于外接球半径等不变量之间的两个关系式．     

关于单形的几个不等式及其应用

Using theory of distance geometry and analytic method, the problem on relations about the volumes of some simplices is studied, and some new inequalities for the volumes of simplices are established. As special cases, an inequality for the volume of the pedal simplex of a simplex and other inequalities for simplices are gotten.     

Some Inequalities for Two Simplices

In this paper, we establish some inequalities for two n-dimensional simplices in the n-dimensional Euclidean space E ⁿ .     

Notes on Two Geometric Inequalities for a Finite Set of Points

Two geometric inequalities for a finite set of points were established in Geom. Dedicata 62 (1996), 157--160. In this paper, we point out a computational mistake in that paper, and give corrections to two geometric inequalities.     

涉及两个单形的几何不等式

本文建立了涉及两个单形一个几何不等式,并应用它得到单形的一些几何不等式。     

n维欧氏空间En中Child不等式的推广

利用几何不等式理论与解析方法,研究了n维欧氏空间En中n维单形的内点到各顶点的距离与到各侧面距离之间的关系,获得相关的几个几何不等式,推广了Child不等式．     

关于切点单形的两个不等式

Definition Let A_i(i=1,2,…,n+1) be the vertex of a simplex Σ_A in n-dimen-sional Euclidean space Eⁿ and A_i′ be the tangent points which the inscribed sphere of Σ_A is tangent to the side face of Σ_A, then the simplex with the tangent points as vertexes is called the tangent points simplex.     

n维欧氏空间E~n中Child不等式的推广

利用几何不等式理论与解析方法,研究了n维欧氏空间En中n维单形的内点到各顶点的距离与到各侧面距离之间的关系,获得相关的几个几何不等式,推广了Child不等式.     

球面空间中的一类几何不等式

本文首先给出n维球面空间的正弦定理,其次得到了一类几何不等式及其应用(即文中的推论)。     

Proximal Point Algorithms for General Variational Inequalities

This paper presents a unified framework of proximal point algorithms (PPAs) for solving general variational inequalities (GVIs). Some existing PPAs for classical variational inequalities, including both the exact and inexact versions, are extended to solving GVIs. Consequently, several new PPA-based algorithms are proposed. M. Li was supported by NSFC Grant 10571083 and SRFDP Grant 200802861031. L.Z. Liao was supported in part by grants from Hong Kong Baptist University and the Research Grant Council of Hong Kong. X.M. Yuan was supported in part by FRG/08-09/II-40 from Hong Kong Baptist University and NSFC Grant 10701055.     

An Inequality for the Pedal Simplex

In this paper, we improve an inequality on the volume of the pedal simplex.