关于调和级数的一些不等式

本文在改进Ｅｕｌｅｒ－Ｍｅｃｌａｕｒｉｎ求和公式的基础上，建立调和级数的一般不等式，并对若干经典不等式作出改进．     

有关常数项级数的几个典型例题

通过实例考察常数项级数收敛和发散时一般项的一些特点,并讨论级数不满足比值判别法、根值判别法或莱布尼茨定理的条件时的收敛性问题.     

无穷级数与无穷乘积

通过构造新的级数以研究原来级数通项的极限性质,从而得到其敛散性.该方法在精细判别和无穷乘积研究有重要有用.     

不等式证明的幂级数方法

以部分国内外数学竞赛题为例说明幂级数方法在证明不等式方面的应用.     

Some Inequalities for Tree Martingales

In this paper we study tree martingales and proved that if 1≤α,β〈∞,1≤p〈∞ then for every predictable tree martingale f=（ft,t∞T）and E[σ^（P）（f）]〈∞,E[S^（P）（f）]〈∞,it holds that ‖（St^（p）（f）,t∈T）‖M^α∞≤Cαβ‖f‖p^αβ,‖（σt^（p）（f）,t∈T）‖M^α,β‖f‖P^αβ,where Cαβ depends only on α and β.     

Some Inequalities for Two Simplices

In this paper, we establish some inequalities for two n-dimensional simplices in the n-dimensional Euclidean space E ⁿ .     

关于有限与无限级数的新的反演级数关系及应用

Some new series inversion formulas of the general form.     

Certain Classes of Infinite Series

 The authors evaluate some interesting families of infinite series by analyzing known identities involving generalized hypergeometric series. Several special cases of the main results are shown to be related to earlier works on the subject.     

Certain Classes of Infinite Series

 The authors evaluate some interesting families of infinite series by analyzing known identities involving generalized hypergeometric series. Several special cases of the main results are shown to be related to earlier works on the subject. Received 16 December 1996; in revised form 21 May 1997     

Statistical Convergence of Infinite Series

In this paper we use the notion of statistical convergence of infinite series naturally introduced as the statistical convergence of the sequence of the partial sums of the series. We will discuss some questions related to the convergence of subseries of a given series.     

无穷级数引入的教学设计

给出针对无穷级数引入的一种教学设计.以趣味故事作为实例引入,通过对π的计算这个实际问题的讲解,让学生抓住概念的本质,并对无穷级数的应用有一个初步的了解,从而对无穷级数有一个总体的认识.在教学过程中,步步引导,全程既具有趣味性又具有启发性.     

Some Dido-type Inequalities

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Some Dido-type Inequalities

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一类算子迹的不等式

将一个算子迹的不等式进行加细,并获得了一个新的算子迹不等式.     

On Some Inequalities for Poisson Networks

A stationary Poisson hyperplane process in R^d induces a random network of (d-2)-flats, each of which is the intersection of two hyperplanes of the process. It is known that the intensity of the induced (d-2)-flat process divided by the square of the intensity of the original hyperplane process is maximal in the isotropic case. An integral-geometric formula for elliptic spaces is presented, from which the mentioned extremum property and related inequalities for superpositions of stationary Poisson hyperplane processes are derived.     

Some Hardy-Type Inequalities

In this paper, some new Hardy-type inequalities involving many functions are obtained. These on the one hand generalize and on the other hand improve some existing results by Isumi and Isumi, Levinson, and Pachpatte on this famous type of inequalities.     

Steckin-Marchard-Type Inequalities for Some Durrmeyer Operators

In this paper, we will derive some Steckin-Marchard-type inequalities for Bernstein-Durrmeyer and Szasz-Durrmeyer operators.     

Steckin-Marchard-Type Inequalities for Some Durrmeyer Operators

In this paper, we will derive some Steckin-Marchard-type inequalities for Bernstein-Durrmeyer and Szasz-Durrmeyer operators.     

Some Area-Diameter Inequalities for Two-Dimensional Lattices

We obtain some inequalities concerning area and diameter of planar convex sets verifying the assumptions of Minkowski's Theorem, establishing the best possible upper bounds for the ratio A/D, (0,2], and for A/D when some lattice points are included.