Some Results Concerning Hereditary Algebras

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关于一个奇异积分的估计

In this note, we present some detail estimates for the integral ∫L^Ne(x^ky)x^(p-1)dx with general integer k, as well as a singular integral formed from it, which would be useful for some nonlinear additive problems of primes.     

Perturbation des Resolvantes Triangulaires et Balayage des Couples Excessifs

In this work, we start by developing an elementary potential theory associated to a triangular kernel. Then we study the perturbation of triangular resolvent, which enable us to characterize, with an elementary way, the excessive couples relatively to a triangular resolvent U. Finally, we study the balayage of U-surmedians couples and the triangular resolvents in duality.     

关于两个伪硬币问题的一些新结果

下面的问题被称为n个外观不可区分硬币的分组测试问题,每个硬币可以是伪硬币或是标准硬币.本文所涉及的问题是:已知一个由n个硬币组成的集合中有两个伪(较重的)硬币,用一台天平以最小的称重次数,从这n个硬币组成的集合中探测出两个伪(较重的)硬币. 我们构造了找出两个伪(较重的)硬币的两个算法,并且这两个算法是最优的.     

关于三个相同伪硬币问题的一些新结果

本文中,给定一台比较型测试装置和确切的三个相同伪硬币出现的信息,作者研究最小测试数的探求问题,这个最小测试数能从λ个有同样外观的硬币组成的集合中鉴别出三个相同的伪硬币,这里λ≥4.作者构造了对于无限多个λ值的一个最优鉴别分组测试算法,这个最优鉴别分组测试算法改进了To（s）ic的对于无限多个λ值的一个最优鉴别分组测试算法,也改进了Bo（s）njak的对于无限多个λ值的一个最优鉴别分组测试算法.作者还提出另一个鉴别分组测试算法,并且猜想这个算法是最优的.     

关于四个相同伪硬币问题的一些新结果

本文给定一台比较型测试装置和确切的四个相同伪硬币出现的信息,作者研究最小测试数的探求问题,这个最小测试数能从λ个有同样外观的硬币组成的集合中鉴别出四个相同的伪硬币,这里λ≥5.作者构造了一个鉴别四个相同伪硬币的测试算法,这个测试算法改进了Toic的一个测试算法,还修正了另外一个测试算法.     

Some Results Concerning the Estimation of Beta Distribution Parameters in PERT

The traditional method of estimating mean activity-time in PERT analysis, as a weighted average of the pessimistic, most likely and optimistic activity-times, is examined. Based on properties of the beta distribution, it is shown that there are theoretical grounds for using this estimate for a specified range of modal activity times. Finally, a simple refinement of the estimate is suggested when the modal value lies outside this range.     

空心球复合材料热弹性性质的一些精确结果

本文基于所提出的基体均匀场方法研究了空心球增强复合材料的热弹性性质·导出了均匀边界条件激发的局部热场和力学场量的关系，并进而得到了复合材料等效热弹性性质之间的精确关系·对于具有某种特定内外径比的空心球所构成的宏观各向同性复合材料，如果基体和空心球的热膨胀系数相同，可以证明其等效体积模量和线膨胀系可以精确地确定·     

Some Results Concerning a Class of Differential Equations with Piecewise Constant Argument

Under some conditions the asymptotic behavior of the solutions of a class of differential equations with piecewise constant argument is studied.     

Some Results behind Dividend Problems

We consider the basic dividend problem of the compound Poisson model with constant barrierstrategy.Some results concealed behind the dividend problem are made explicit in the present work.Differentmethods and some of which are firstly given in this paper.All these results presented certain direct relationshipbetween some important actuary variables in classical risk theory is also revealed.     

Some New Results on Strong Ergodicity

Coupling method is used to obtain the explicit upper and lower bounds for convergence rates in strong ergodicity for Markov processes. For one-dimensional diffusion processes and birth-death processes, these bounds are sharp in the sense that the upper one and the lower one are only different by a constant. This announcement is an outline of an original research paper “Convergence Rates in Strong Ergodicity for Markov Processes” that will appear in Stoch. Process. Their Appl.     

On Some Inequalities Concerning Rate of Growth of Polynomials

In this paper we consider a class of polynomials P(z) = a0+∑n v=t a v z v, t ≥ 1not vanishing in |z|k, k≥1 and investigate the dependence of max|z|=1|P(Rz)-P(rz)on max|z|=1|P(z)|, where 1 ≤ r R. Our result generalizes and refines some know polynomial inequalities.     

Some Results Concerning Convergence of Convolution Products of Probability Measures on Discrete Semigroups

Two types of conditions have been significant when considering the convergence of convolution products of nonidentical probability measures on groups and semigroups. The essential points of a sequence of measures have been useful in characterizing the supports of the limit measures. Also, enough mass eventually on an idempotent has proven sufficient for convergence in a number of structures. In this paper, both of these types of conditions are analyzed in the context of discrete non-abelian semigroups. In addition, an application to the convergence of nonhomogeneous Markov chains is given.     

关于π-局部群系的几个结果

本文做了两方面的工作：（１）给出了一个群属于π-局部群系的一些充要条件，推广了Ｇａｓｃｈｕｔｚ关于群的中心与Ｆｒａｔｔｉｎｉ子群关系的结果；（２）对满足π-齐次性条件的群统一到７π-局部群系上进行研究．     

关于Fuzzy拓扑线性空间的某些结果

本文给出了Ｆｕｚｚｙ拓扑线性空间的若干特征刻划，简化了判断Ｆｕｚｚｙ拓扑线性空间的条件，研究了Ｆｕｚｚｙ拓扑线性空间的层次结构，揭示了Ｆｕｚｚｙ拓扑线性空间与分明拓扑线性空间的内在联系，得到了Ｆｕｚｚｙ拓扑线性空间的“平移不变性”与“局部凸性”都是可截性质。     

On Some Results in Probabilistic Number Theory

The paper presents an overview of main methods and results of the value distribution problem of additive arithmetical functions.     

Certain Results Concerning the Iterative Function System

Invention of wavelets and fractals have revolutionized several areas of emerging technologies, especially image processing and scientific computing. The iterated function system [2-4,13,17,18,20,25,26,29], inverse problem of images [5,14-16] and wavelet-based numerical methods [6,7,10,19,22,23] are basic in-gredients of these exciting developments. The iterated function system and the collage theorem are among the basic mathematical tools which are consequences of the Banach contraction fixed point theorem. In one of the sections of this paper we have generalized these two theorems applying a generalization of the Banach contraction fixed point theorem due to Edelstein [11]. In the other section we have studied the inverse problem of images by the iterative function system with grey-level in the context of Besov space, extending a result of Forte and Vrscay [16].     

On Generalizations of Ostrowski Inequality and Some Related Results

Some generalizations of the Ostrowski inequality, the Milovanovi-Peari-Fink inequality, the Dragomir-Agarwal inequality and the Hadamard inequality are given.