Existence and Uniqueness of Solutions to Random Impulsive Differential Systems

The existence and uniqueness in mean square of solutions to certain random impulsive differentialsystems is discussed in this paper.Cauchy-Schwarz inequality,Lipschtiz condition and techniques in stochasticanalysis are employed in achieve the desired results.     

The Petty Projection Inequality for Lp-Mixed Projection Bodies

Recently, Lutwak, Yang and Zhang posed the notion of Lp-projection body and established the Lp-analog of the Petty projection inequality. In this paper, the notion of Lp-mixed projection body is introduced--the Lp-projection body being a special case. The Petty projection inequality, as well as Lutwak＇s quermassintegrals （Lp-mixed quermassintegrals） extension of the Petty projection inequality, is established for Lp-mixed projection body.     

一类混合型Szàsz-Beta算子的强逆不等式(英文)

In this paper,a strong converse inequality of type B in terms of a new Kfunctional Kλα f,t2(0 < α < 2,0 ≤ λ ≤ 1) for certain mixed Szász-Beta operators is given.By this inequality,the converse theorem can be obtained for the operators.     

Existence of Solutions to Generalized Vector Quasi-variational-like Inequalities with Set-valued Mappings

In this paper, we introduce and study a class of generalized vector quasivariational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. We use the maximal element theorem with an escaping sequence to prove the existence results of a solution for generalized vector quasi-variational-like inequalities without any monotonicity conditions in the setting of locally convex topological vector space.     

广义非线性隐似变分不等式

A new class of generalized nonlinear implicit variational-like inequality problems （for short, GNIVLIP） in the setting of locally convex topological vector spaces is introduced and studied in this paper. Under suitable conditions, some existence theorems of solutions for （GNIVLIP） are presented by using some fixed point theorems.     

Two Theorems on Volume and Dihedral Angles of a n—dimensional Simplex

In this paper,we obtain thorem 1 on volum of a n-dimensional simplex and theorem 2 on dihedral angles of a simplex.Besides.We obtain Vasic inequality in E^n and its extension.The results in this paper contain and improve the results in paper[1]、[2]、[3]、[4].     

An Simple Elementary Proof for the Inequality dn〈3^n

In this paper, by using a variation of the Chebyshev＇s method, we present a very simple, elementary proof of an inequality which has applications in number theory.     

Moment inequality and Hölder inequality for BSDEs

Under the Lipschitz and square integrable assumptions on the generator g of BSDEs, this paper proves that if g is positively homogeneous in （y, z） and is decreasing in y, then the Moment inequality for BSDEs with generator g holds in general, and if g is positively homogeneous and sub-additive in （y, z）, then the HSlder inequality and Minkowski inequality for BSDEs with generator g hold in general.     

链环的零度和符号差的不等式估计

An inequality estimate of signature and nullity for links and those for its satelites has been given in this paper,which is an improvement of the result obtained by Japanese mathematician Tetsuo Shibuya.     

Solvability of Navier-Stokes equations with leak boundary conditions

The time-dependent Navier-Stokes equations with leak boundary conditions are investigated in this paper. The equivalent variational inequality is derived, and the weak and strong solvabilities of this variational inequality are obtained by the Galerkin approximation method and the regularized method. In addition, the continuous dependence property of solutions on given initial data is establisbed, from which the strong solution is unique.     

REFINEMENTS OF THE FAN－TODD‘S INEQUALITIES

51. IntroductionIn recent years, refinements or interpolations have played an important role on severaltypes of inequalities with new results deduced as a consequence. Please refer to the papers[2, 8, 9, 12], etc. The aim of this paper is to furnish refinements of the Cauchy's and Bessel'sinequalties as shown in Section 2, and also refinements of the Fan-Todd's inequality and theFan-Todd's determinantal inequality in Sections 3 and 4, with an improved condition forequality derived.First of…     

关于几个新不等式

本文利用Redheffer不等式,Jordan不等式和Jensen不等式给出了一些新的不等式作为应用推广了文[1]的一个结果。     

REFINEMENTS OF THE FAN-TODD'S INEQUALITIES

Refinements to inequalities on inner product spaces are presented. In this respect, inequalities dealt with in this paper are: Cauchy's inequality, Bessel's inequality, Fan-Todd's inequality and Fan-Todd's determinantal inequality. In each case, a strictly increasing function is put forward, which lies between the smaller and the larger quantities of each inequality. As a result, an improved condition for equality of the Fan-Todd's determinantal inequality is deduced.     

Two new forms of half-discrete Hilbert inequality

In this paper, we introduce two new forms of the half-discrete Hilbert inequality. The first form is a sharper form of the half-discrete Hilbert inequality and is related to Hardy inequality. In the second one, we give a differential form of this inequality.     

三大著名不等式的拓广与深化

利用一个分式型的双向积分不等式 ,将 H lder不等式、H.Minkowski不等式、Schl milch不等式(幂平均不等式 )三大世界著名不等式进行拓广与深化 ,使对此问题的研究更具深刻性、系统性 .     

The dual difference Aleksandrov–Fenchel inequality

Recently, a dual Minkowski inequality and a dual Brunn–Minkowski inequality for volume differences were established. Following this, in this paper we establish a dual Aleksandrov–Fenchel inequality for dual mixed volume differences which generalizes several recent results.     

Hlder不等式和Minkowski不等式的推广

本文利用变分方法对多个变元的不含变元导数的Holder不等式和Minkowski不等式进行了推广．此种方法的主要意义不在于证明传统的不等式，而在于发现新的不等式．     

关于离散Karamata不等式及其应用

本文获得了著名Karamata不等式的离散形式，利用这个结果推广了Newton不等式，应用推广的Newton不等式将张景中和杨路在[1]所得的几何不等式加以推广。     

Hlder不等式和Minkowski不等式的推广

本文利用变分方法对多个变元的不含变元导数的H■lder不等式和Minkowski不等式进行了推广．此种方法的主要意义不在于证明传统的不等式,而在于发现新的不等式．     

类似Hilbert不等式的一些新不等式的推广

本文推广了 Pachpatte在文 [1 ]中给出的类似 Hilbert不等式的一些新不等式 .