Wolff's Inequality for Radially Nonincreasing Kernels and Applications to Trace Inequalities

We extend Th. Wolff's inequality to a general class of radially decreasing convolution kernels. As an application we obtain characterizations of nonnegative Borel measures on R ⁿ such that the trace inequality holds for every f in L ^p (dx).     

两个反三角平均的Schur凸性及不等式链

关于张帆,钱伟茂所定义的四个反三角函数平均,利用Hermite-Hadamard不等式证得其中两个反三角平均:Marcsin(a,b)分别是Schur-凸,Schur-几何凸,Schur-调和凸;Marctan(a,b)分别是Schur-凹,Schur-几何凸,Schur-调和凸,并结合凸函数理论得出若干不等式链.     

Ostrowski不等式的改进及其应用

通过对Ostrowski不等式的改进,扩大了Ostrowski积分公式的适用范围,将该积分公式应用于数值积分推广了经典的中点积分公式、梯形积分公式和Simpson积分公式,同时得到相应的最佳误差限,并给出了具体的数值应用.     

Talagrand's T_2-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations

We establish Talagrand's T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type's approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction-Diffusion equations are provided.     

Talagrand＇s T2-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations

Abstract We establish Talagrand’s T₂-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type’s approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction-Diffusion equations are provided. * Project supported by the Yangtze Scholarship Program.     

一个推广的Hilbert不等式及应用

This paper gives a new generalization of Hilbert's inequality with a best constant factor involving theβfunction. An applications, we consider the equivalent form and some particular results.     

On a Refinement of Hardy-Hilbert's Inequality and Its Applications

§1. Introduction If p＞1, 1p+1q=1, an≥0, bn≥0, and 0＜∑∞n=1-λapn＜∞, 0＜∑∞n=1-λbqn＜∞ (λ=0,1), then∑∞m=1-λ∑∞n=1-λambnm+n+λ＜πsin(π/p)∑∞n=1-λapn1/p∑∞n=1-λbqn1/q,(1.1)where the constant π／sinπp is best possible for λ=0, or 1. For λ=0,1, (1.1) is named of HardyHilberts inequality, which is important in analysis and applications (see ［1］, Chapt. 9). On (1.1) for λ=0, by estimating a weight coefficient, Xu［2］ gave a refinement as∑∞m=1∑∞n=1ambnm+n＜∑∞n=…     

柯西-布涅柯夫斯基不等式在优化中的应用

本文给出了柯西—布涅柯夫斯基不等式在非线性规划中应用的两个例子．     

关于双曲空间中n维Pedoe不等式及应用

本文应用距离几何的理论与方法,研究了双曲空间中n维单形的几何不等式问题,建立了双曲空间中涉及两个单形棱长的n维Pedoe不等式和彭-常不等式,由此获得双曲空间n维单形的一些新的不等式.     

关于双曲函数的Huygens型不等式及应用

给出了关于双曲函数的Huygens型不等式,并得到了双曲函数的Wilker型不等式的加强.定义了一类新的Seiffert型平均,给出两个有关不等式.     

Some Applications of a Polynomial Inequality to Global Optimization

In this paper, we use the Ehlich-Zeller-Gärtel inequality to derive an algorithm for finding the global minima of polynomials over hyperrectangles as well as to provide a bounding method for the branch-and-bound algorithm. The latter application of the inequality results in an improved algorithm which gives simultaneously a decreasing upper bound and an increasing lower bound for the global minimum at each iteration. The algorithm can be used also to find the Lipschitz constant of a polynomial.     

两平面凸域的对称混合等周不等式

设K_k(k=i,j)为欧氏平面R~2中面积为A_k,周长为P_k的域,它们的对称混合等周亏格(symmetric mixed isoperimetric deficit)为σ(K_i,K_j)=P_i~2P_j~2-16π~2A_iA_j.根据周家足,任德麟(2010)和Zhou,Yue(2009)中的思想,用积分几何方法,得到了两平面凸域的Bonnesen型对称混合不等式及对称混合等周不等式,给出了两域的对称混合等周亏格的一个上界估计.还得到了两平面凸域的离散Bonnesen型对称混合不等式及两凸域的对称混合等周亏格的一个上界估计,并应用这些对称混合(等周)不等式估计第二类完全椭圆积分.     

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.     

Hajek-Renyi-type Inequality for a Class of Random Variable Sequences and Its Applications

In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.     

对算术-几何不等式的两种推广与改进

将关于一组正数的加权算术-几何不等式推广为关于两组正数的改进型加权算术-几何不等式,其思路可为部分已有结论提供新的证明方法.突破关于自然对数的加权算术-几何不等式对具体函数的依赖,给出并证明了关于对数凸函数的加权算术-几何不等式.     

一个逆向Hilbert型不等式的推广及其应用

引入独立参数A及应用改进的Euler-Maclaurin求和公式以估算权系数,给出了—个具有最佳常数因子的逆向Hilbert型不等式的推广．作为应用,考虑了它的等价形式．     

关于“对数和”不等式在信息论中应用的一个注记

利用对数和不等式,在一般情形下证明了信息论中的两个基本定理,由此指出有关教材相应方法的局限性并给予了推广.     

一个新的有两对共轭指数并在全平面积分的Hilbert型不等式

引入二对共轭指数,应用权函数的方法,给出一个新的有最佳常数因子并在全平面积分的Hilbert型不等式,同时考虑了对应的等价式.     

关于一个Hilbert类积分不等式的推广及应用

本文引入单参数，对一个积分型Hilbert类不等式作具有最佳常数 推广。作为应用，建立它的等价形式。     

关于高维单形的一个不等式及应用

本文推广文献 [1 ]的结果 ,获得 En中关于单形的一个不等式 ( 1 ) ,并由此导出 En中面型的彭——常不等式 [5] ( 7)和涉及 n维单形 ∑A内任一点的两个几何不等式 ( 9) ,( 1 0 ) .