Radon不等式的新推广

利用Ho。lder不等式、Young不等式、Chebyshev不等式、幂平均不等式建立Radon不等式的指数推广形式,得到一个具有广泛应用价值的不等式.指出文[7]中给出的关于Radon不等式的推广结果是错误的,并在本文中作了修正.     

关于Veljan-Korchmaros不等式的改进及应用

推广了Veljan—Korchmaros不等式，并应用它推广了n维Euler不等式．     

非线性互补问题的一种全局收敛的显式光滑Newton方法

本针对Po函数非线性互补问题，给出了一种显式光滑Newton方法，该方法将光滑参数μ进行显式迭代而不依赖于Newton方向的搜索过程，并在适当的假设条件下，证明了算法的全局收敛性。     

关于Van Der Corput不等式双参数推广的改进

梳理了有关Van Der Corput不等式的研究成果与方法,并对Van Der Corput不等式的双参数推广作了进一步改进,建立了更强的推广式,它优于现有的相关结论.     

Rado不等式的多参数推广及应用

给出Rado不等式的多参数推广形式,并运用该结果建立Popoviciu不等式的推广形式.     

Milloux不等式精简形式的推广及应用

主要讨论了Milloux不等式的精简形式的推广问题,借助代数体函数的第二基本定理,得到了关于代数体函数的精简形式的Milloux不等式的一般形式,推广了Milloux不等式的精简形式的结论,并由此得到了关于代数体函数及其导数的涉及拟Borel例外值的性质,推广了亚纯函数的相关性质.     

复矩阵的亚半正定性

复亚半正定矩阵是 Hermite正定阵的推广 ,研究了它的 Kronecker积、Hadamard积和行列式理论 ,将实对称阵的 Schur定理、华罗庚定理、Minkowski不等式、Ky-Fan不等式、Ostrowski-Taussky不等式推广到了一类非 Hermite复矩阵上 ,扩大了 Minkowski不等式的指数范围 ,削弱了华罗庚不等式的条件 .     

E^n中Euler不等式的推广与改进

设n维欧氏空间En中n维单形Ω的外接球半径为R，内切球半径为r，M．S．Klamkin［1］获得了En中之Euler不等式R≥nr，本文给出了上述Euler不等式的几个推广与改进。     

亚半正定矩阵的广义Minkowski不等式的隔离

利用张晗方建立的推广的Hlder不等式和李炯生给出的关于Ostrowskii-Taussky不等式的新刻划,建立了亚半正定矩阵的广义Minkowski不等式的一种隔离,修正并推广了已有结论.     

关于耦合反应扩散系统解的整体存在性

利用对偶性技巧及Hoelder不等式，证明了一类耦合反应扩散系统解的整体存在性，推广了相关结果．     

Moment inequalities for the partial sums of random variables

This paper discusses the conditions under which Rosenthal type inequality is obtained from M-Z-B type inequality. And M-Z-B type inequality is proved for a wide class of random variables. Hence Rosenthal type inequalities for some classes of random variables are obtained.     

Hardy-Hilbert积分不等式的改进

通过引入带参数的指数积分并利用Bernoulli不等式以及改进了的Hlder不等式,对Hardy-Hilbert积分不等式作了有意义改进.特别,当p=2时,得到了经典的Hilbert积分不等式的一个很强的结果.     

On Variance and Covariance for Bounded Linear Operators

In this paper we initiate a study of covariance and variance for two operators on a Hilbert space, proving that the c-v (covariance-variance) inequality holds, which is equivalent to the Cauchy-Schwarz inequality. As for applications of the c-v inequality we prove uniformly the Bernstein-type inequalities and equalities, and show the generalized Heinz-Kato-Furuta-type inequalities and equalities, from which a generalization and sharpening of Reid's inequality is obtained. We show that every operator can be expressed as a p-hyponormal-type, and a hyponormal-type operator. Finally, some new characterizations of the Furuta inequality are given. Received April 9, 2000, Revised July 20, 2000, Accepted August 8, 2000     

Quasi Lp-Intersection Bodies

The purpose of this paper is to generalize the notion of intersection bodies to that of quasi Lp-intersection bodies. The Lp-analogs of the Busemann intersection inequality and the Brunn- Minkowski inequality for the quasi Lp-intersection bodies are obtained. The Aleksandrov Fenchel inequality for the mixed quasi Lp-intersection bodies is also established.     

反向Dresher不等式

配合使用Houlder不等式和Minkowski不等式,得到了反向Dresher不等式。     

Generalization of a sharp Hölder's inequality and its application

In this paper, we generalize Hu Ke's sharpness of Hölder's inequality. As application, the obtained result is used to improve the well-known Opial-Olech inequality.     

一个改进的Hardy-Hilbert不等式

通过建立权系数的不等式,得到一个改进的Hardy-Hilbert不等式.     

Cauchy-Schwarz不等式的一些反向及改进

在一些附加条件下给出内积空间的Cauchy-Schwarz不等式的反向不等式及其改进,利用所得结果得到一个新的积分型Kantorovich不等式,并获得关于函数的Fourier系数的两个不等式.     

Hardy-Hilbert重级数定理的一个改进

利用Gram矩阵的正定性和Bernoulli不等式得到Holder不等式的一个加强的结果.由此建立了Hardy-Hilbert重级数定理的一个改进.特别,当p=2时,得到了经典的Hilbert重级数定理的一个很强的结果.     

Mass-Capacity Inequalities for Conformally Flat Manifolds with Boundary

In this paper we prove a mass-capacity inequality and a volumetric Penrose inequality for conformally flat manifolds, in arbitrary dimensions. As a by-product of the proofs, capacity and Aleksandrov-Fenchel inequalities for mean-convex Euclidean domains are obtained. For each inequality, the case of equality is characterized.