具有Brézis伪单调算子的广义拟变分不等式解的存在性

利用有限维空间上变分不等式解的存在性理论,讨论了带有Brézis伪单调算子的广义变分不等式在一般拓扑空间上解的存在性,及广义拟变分不等式在局部凸Hausdorff拓扑向量空间上解的存在性.     

关于平面Bonnesen型不等式与第2类完全椭圆积分的注记

利用欧氏平面R2中凸域的几何不等式和Bonnesen型不等式给出第2类完全椭圆积分的一些上界和下界估计.     

Global Attractors for a Class of Pattern Formation Equations

A class of pattern formation equations is treated, the existence of its global attractor is considered and some estirnates of its dimension are given. This sort of pattern formation equations relate to turbulence phenomenon in chemistry and combustion, so it is of great physical importance. Besides, its important theoretical value lies in that the equation contains differential operator of the fourth order in space. The global attractor exists after a series sophisticated estimates by the means of interpolation inequity and embedding theorems in sobolev spaces. Furthermore, some estimates on its fractal dimension are given.     

Guaranteed Cost Control of a Class of Linear Stochastic Systems on the Basis of Robust Analysis

This paper discusses the guaranteed cost control of a class of linear stochastic systems on the research of uncertain linear systems.The authors give the definition of this linear stochastic systems' guaranteed cost control,by using Ito formula and linear matrix inequality,combined its square-stability,under the supposition of the square stability of this kind of linear stochastic system,gets the accordingly guaranteed cost control condition.The conclusion is,if the linear stochastic system is square-stability,then its guaranteed cost control exists.Finally,the problem of designing a optimal guaranteed cost control can be turned into a convex optimal problem.     

MINIMAX INEQUALITY FOR VECTOR-VALUED FUNCTION

Minimax inequality is proposed in this paper.The minimax inequality for affinecontinuous vector-valued mapping is established.A kind of the minimax inequality for set-valuedmapping is derived.     

不确定关联时滞大系统的分散鲁棒稳定控制器设计

对一类具有数值界不确定性关联时滞大系统,应用线性矩阵不等式(LMI)方法研究使其分散稳定化的鲁棒控制器设计问题.给出了其存在分散鲁棒稳定化控制器的充分条件,在此基础上,通过求解一凸优化问题,指出了具有较小反馈增益的分散稳定化状态反馈控制律的设计方法.仿真示例说明了该方法的应用.     

概率方法在其它数学问题中的应用

通过概率论的思想方法来解决其它数学领域中的问题,如:组合恒等式、不等式的证明,级数、积分和极限等,得出一个一般的概率思想方法.     

农村居民收入不均等分解:基于辽宁农户数据的实证分析

为深入研究农村居民的收入不均等状况及其影响因素，本文利用基尼系数和泰尔指数2个指标值测度了辽宁省农村居民收入不均等总体状况，并对农村居民收入不均等进行了要素分解（收入来源分解）和地区分组分解，通过这2种分解以揭示收入不均等的微观状况，和收入不均等问题的实质，在以上分析的基础上阐述本研究的政策涵义。     

多值非扩张映射的广义平衡问题的不动点解

在巴拿赫空间中引入一种迭代算法,并证明了此算法强收敛到多值非扩张映射的不动点集与广义平衡问题解集的公共元素,推广了以前的结论.     

平面上几个对偶 Brunn-Minkowski 不等式

对于平面中具有二阶光滑边界的凸体，给出了一个与之对偶的星体，称之为曲率星体。并且用积分几何与凸几何的方法，得到了该星体的一些性质及其相关的几何不等式。