THE DUAL BRUNN-MINKOWSKI INEQUALITIES FOR STAR DUAL OF MIXED INTERSECTION BODIES

In this article, some dual Brunn-Minkowski inequalities are established for star dual of mixed intersection bodies with respect to the harmonic p-combination and p-radial linear combination.     

Orlicz混合相交体

本文研究了Orlicz混合相交体及其性质.利用几何分析方法提出了Orlicz混合相交体的概念,获得了Orlicz混合相交体算子的连续性和仿射不变性.通过积分方法和Steiner对称,建立了Orlicz混合相交体的仿射等周不等式.     

截面体与凸体的包含测度

本文建立了E^n中的凸体与其位似体的包含测度的相等关系，同时给出了凸体Minkowski和的包含测度的估计。最后证明了E^3中的关于原点对称的旋转椭球与其截面体相似的充要条件是K为以原点为心的球。     

On an analytic generalization of the Busemann-Petty problem

In this paper, we establish an extension of the connections between an analytic generalization of the Busemann-Petty problem and the positive definite distributions. Our results show that the structure of the positive definite distributions in Rn is closely related to the analytic generalization of the Busemann-Petty problem which was posed by Koldobsky.     

Aleksandrov-Fenchel不等式及应用

本文运用Aleksandrov-Fenchel不等式,首先推广了Lutwak,Bonnesen和Fenchel等建立的三个有用的定理,这三个定理在解决某些唯一性问题中扮演着重要角色.然后,把这些结果从一般的混合体积和投影体推广到混合投影体的极和混合仿射表面积上,获得了一些较理想的结果.     

SOME INEQUALITIES ABOUT DUAL MIXED VOLUMES OF STAR BODIES

The authors establish some inequalities about the dual mixed volumes of star bodies in R^n. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symmetric functions of positive reals.     

混合投影体的极与混合相交体的Aleksandrov-Fenchel 不等式的稳定性

引进了多个几何体(主要是凸体(Convex body)和星体(Star body)) 相似``偏差'的一个度量方法, 从而推广了已有的相似``偏差'度量方法.并在此度量下,利用Rⁿ 中Hölder不等式的一个加强获得了文献[1]建立的混合投影体的极的Aleksandrov-Fenchel不等式和文献[2]建立的混合相交体的Aleksandrov-Fenchel不等式的稳定性版本.     

一般对偶混合体积不等式(英文)

本文研究了星体的对偶仿射均质积分问题.利用H(o)lder不等式和Blaschke-Santaló不等式.获得了一般对偶均质积分的Minkowski不等式,Brunn-Minkowski不等式以及定理3.从而不等式推广了文献[7]的结果.     

LOOMIS-WHITNEY'S INEQUALITY ABOUT MIXED BODY

In this article,the authors establish two theorems for mixed body,which are the generalizations of the well-known Loomis-Whitney's inequality.     

THE DUAL MIXED METHOD FOR AN UNILATERAL PROBLEM

In this paper, the dual mixed method for an unilateral problem, which is the simplified modelling of scalar function for the friction-free contact problem, is considered. The dual mixed problem is introduced, the existence and uniqeness of the solution of the problem are presented, and error bounds O(h^3/4 ) and O(h^3/2 ) are obtained for the dual mixed finite element approximations of Raviart-Thomas elements for k= 0 and k= 1 respectively.     

Cross -sections of star bodies and dual mixed volumes

In this paper, we establish an extension of Funk's section theorem. Our result has the following corollary: If is a star body in whose central -slices have the same volume (with appropriate dimension) as the central -slices of a centered body , then the dual quermassintegrals satisfy , for any , with equality if and only if . The case that is a centered body implies Funk's section theorem.

     

A NEW SELF-ADAPTIVE ITERATIVE METHOD FOR GENERAL MIXED QUASI VARIATIONAL INEQUALITIES

The general mixed quasi variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due to the presence of nonlinear term. It is well known that the variational inequalities involving the nonlinear term φ are equivalent to the fixed point problems and resolvent equations. In this article, the authors use these alternative equivalent formulations to suggest and analyze a new self-adaptive iterative method for solving general mixed quasi variational inequalities. Global convergence of the new method is proved. An example is given to illustrate the efficiency of the proposed method.     

On intersection and mixed intersection bodies

Duals of the basic projection and mixed projection inequalities are established for intersection and mixed intersection bodies.      

Brunn-Minkowski inequality for mixed intersection bodies

Dual of the Brunn-Minkowski inequality for mixed projection bodies are established for mixed intersection bodies.     

求解广义混合单调变分不等式的预解算子方法

1引言设R~n表示n维欧式空间,‖·‖和＜,＞分别表示R~n中的范数和内积,K为R~n中的非空闭凸集,(?)是R~n到R∪{ ∞)的算子．对于给定的非线性算子T,g：R~n→R~n,考虑下面的广义混合变分不等式,记为GMVI：求u∈R~n满足(Tu)~T(g(v)-g(tu)) (?)(g(v))-(?)(g(u))(?)0,(?)g(v)∈R~n．(1)假如(?)是R~n中非空闭凸集K的指标集,即,(?)(u)≡I_k(u)=(?)．此时GMVI等价于下面的广义变分不等式：求u∈R~n,g(u)∈K满足     

弹性接触问题的对偶混合有限元分析

１．引言用混合有限元方法求解弹性力学问题,其优点在于可同时求解位移和应力．力学问题的混合变分形式是混合有限元方法的基础．对于弹性接触问题,文献［６］给出了一种混合变分形式,以及相应的混合有限元分析（也可见［１０］）．其混合变分形式是直接从位移交分方程和Ｈｏｏｋ方程导出的,获得了应力ａ在Ｌ２（Ω）而位移、在Ｈ１（Ω）的一个闭凸子集上求解的混合变分问题．本文在［９］中提出的混合变分形式的基础上,再引入另一个Ｌａｐｒａｎｇｅ乘子,获得了三重组混合变分形式．它能同时求解物体内点的应力,位移和接触边界上的…     

INEQUALITIES FOR Lp-MIXED CURVATURE IMAGES

Lutwak, Yang, and Zhang posed the notion of Lp-curvature images and established several Lp analogs of the affne isoperimetric inequality. In this article, the notion of Lp-mixed curvature images is introduced, Lp-curvature images being a special case. The properties and Lp analogs of the affne isoperimetric inequality are established for Lp-mixed curvature images.     

On dual quermassintegrals of mixed intersection bodies

In this paper, it is shown that a family of inequalities involving mixed intersection bodies holds. The Busemann intersection inequality is the first of this family. All of the members of this family are strengthened versions of classical inequalities between pairs of dual quermassintegrals of a star body.     

EFFECTIVE STABILITY FOR NEARLY INTEGRABLE MAPPINGS WITH INTERSECTION PROPERTY

We consider a nearly integrable mapping with a fixed twist frequency. Under the intersection property and Diophantine condition we prove that the mapping possesses effective stability. In particular, the mapping considered may have different dimensions of action-angle variables in our case.     

On the Dual Orlicz Mixed Volumes

In this paper, the authors define a harmonic Orlicz combination and a dual Orlicz mixed volume of star bodies, and then establish the dual Orlicz-Minkowski mixed-volume inequality and the dual Orlicz-Brunn-Minkowksi inequality.