Operator-norm inequalities and interpolated trace inequalities

In this article, we investigate some operator-norm inequalities related to some conjectures posed by Hayajneh and Kittaneh that are related to questions of Bourin regarding a special type of inequalities referred to as subadditivity inequalities. While some inequalities are meant to answer these conjectures, other inequalities present reverse-type inequalities for these conjectures. Then, we present some new trace inequalities related to Heinz means inequality and use these inequalities to prove some variants of the aforementioned conjectures.     

关于算子方程Nχ=δLχ解的若干研究

利用多重拓扑度的性质以及一些不等式研究了零指标的Predholm算子和L-全连续算子方程Nχ=δχ的解,获得若干新的结果,推广了一些重要结论,并将结果应用到一类二阶微分方程的边值问题中.     

On commutativity of near-rings with generalized derivations

In this paper we prove some theorems of commutativity for near-rings with generalized derivations. As a consequence of the results obtained, we generalize some published results. Also, we give some examples to show that some conditions in some results obtained are not redundant.     

关于一个奇异Dirichlet问题的注记

The Dirichlet problem to a second order differential equation with some singularities is studied. Some existence results are established to the problem which generalize some results recently obtained by D. O‘Regan by eliminating some superfluous constrains to the problem. Also, some new results have been proven which may provide more useful information for the study of the problem.     

Bell polynomials and binomial type sequences

This paper concerns the study of the Bell polynomials and the binomial type sequences. We mainly establish some relations tied to these important concepts. Furthermore, these obtained results are exploited to deduce some interesting relations concerning the Bell polynomials which enable us to obtain some new identities for the Bell polynomials. Our results are illustrated by some comprehensive examples.     

Scepticism,context and modal reasoning

I analyze some classical solutions of the skeptical argument and some of their week points (especially the contextualist solution). First I have proposed some possible improvement of the contextualist solution (the introduction of the explicit-implicit belief and knowledge distinction beside the differences in the relevance of some counter-factual alternatives). However, this solution does not block too fast jumps of the everyday context (where empirical knowledge is possible) into skeptical context (where empirical knowledge is impossible). Then I analyze some formal analogies between some modal arguments on the contingency of empirical facts (and the world as whole) and the skeptical arguments against empirical knowledge. I try to show that the skeptical conclusion “Empirical knowledge does not exist” is logically coherent with the thesis that they are empirical facts and that we have true belief on them. In order to do that without contradictions I have to accept a non-classical definition of knowledge: S knows that p:= S is not justified to allow that non-p. Knowledge and justified allowance function here as some pseudo-theoretical concepts which allow only some partial and conditional definitions by some “empirical” terms and logical conditions.     

FC-空间上的连续选择和邻近选择定理

给出了-些从仿紧拓扑空间到FC-空间的新的连续选择;也给出了-些从仿紧拓扑空间到局部FC-一致空间的新的邻近选择.这些结果改进且推广了-些近来的结论.     

ECO:a methodology for the enumeration of combinatorial objects

In this Paper, we illustrate a method (called the ECO method) for enumerating some classes of combinatorial objects. The basic idea of this method is the following: by means of an operator that performs a "local expansion" on the objects, we give some recursive constructions of these classes. We use these constructions to deduce some new funtional equations verified by classes' generating functions. By solving the functional equations, we enumerate the combinatorial objects according to various parameters. We show some applications of the method referring to some classical combinatorial objects, such as: trees, paths, polyminoes and permutations     

限制李三系的半单元

研究了限制李三系的半单元的一些重要性质,给出了若干个限制李三系是可换的条件,得到了限制李三系的有环面元基的几个条件,刻划了限制李三系的Frattini p-子系的一些性质.同时,研究了中心为零的所有元素是半单元的限制李三系的一些重要性质.     

高阶变系数泛函方程解的振动性

讨论了高阶变系数泛函微分方程解的振动性,并给出了这类高阶变系数函数方程解的若干新振动准则.结果推广了目前已有的某些结果.并且给出了在差分方程中的应用.     

隐马尔可夫模型在语音识别中的应用

隐马尔可夫模型 (HMM)的基本技术是语音识别中较为成功的算法 .主要是它具有较强的对时间序列结构的建模能力 .本文首先深入浅出地介绍了 HMM的基本技术和一个基于 HMM的孤立词语音识别系统的构成方法 ,其次 ,基于 HMM尚存有一些缺陷 ,造成语音识别能力较弱 ,为此本文又进一步阐述了语音识别应用中的几种改进的 HMM系统及目前的热点方法—— HMM与 ANN构成的混合网络     

颗粒随机分布复合材料热传导问题均匀化方法的理论分析

针对区域内颗粒随机分布复合材料的热传导问题给出了一种均匀化理论计算温度场.首先根据复合材料的特性以及通过用多尺度方法预测复合材料热传导参数的要求定义了一些基本的概率空间,然后结合材料的物理特性做合理的假设得到了在整个随机复合材料区域上的期望温度场与均匀化温度场之间的一种理论估计,从而说明了此均匀化温度场可以作为预测此类随机颗粒分布复合材料期望温度场的理论基础.     

Global attracting set,exponential stability and stability in distribution of SPDEs with jumps

A novel approach to the global attracting sets of mild solutions for stochastic functional partial differential equations driven by Lévy noise is presented. Consequently, some new sufficient conditions ensuring the existence of the global attracting sets of mild solutions for the considered equations are established. As applications, some new criteria for the exponential stability in mean square of the considered equations is obtained. Subsequently, by employing a weak convergence approach, we try to establish some stability conditions in distribution of the segment processes of mild solutions to stochastic delay partial differential equations with jumps under some weak conditions. Some known results are improved. Lastly, some examples are investigated to illustrate the theory.     

Three Dimensional Interface Problems for Elliptic Equations

The author studies the structure of solutions to the interface problems for second order linear elliptic partial differential equations in three space dimension.The set of singular points consists of some singular lines and some isolated singular points.It is proved that near a singular line or a singular point,each weak solution can be decomposed into two parts,a singular part and a regular part.The singular parts are some finite sum of particular solutions to some simpler equations,and the regular parts are bounded in some norms,which are slightly weaker than that in the Sobolev space H~2.     

EXISTENCE OF SOLUTIONS TO NONLINEAR TWO POINTS BOUNDARY VALUE PROBLEMS OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we obtain some criteria for the existence of solutions to nonli-near two-point boundary value problems by constructing some Liapunov func-tions, and we give some examples for our results to this problem in the end.     

On linear spaces and matroids of arbitrary cardinality

In this paper, we study linear spaces of arbitrary finite dimension on some (possibly infinite) set. We interpret linear spaces as simple matroids and study the problem of erecting some linear space of dimension n to some linear space of dimension n + 1 if possible. Several examples of some such erections are studied; in particular, one of these erections is computed within some infinite iteration process.Dedicated to the memory of Gian-Carlo Rota     

随机环境中马氏链的状态性质

本文研究了随机环境中马氏链的状态性质, 利用乘积空间的正则本质性和不可约性得到了随机环境中马氏链弱常返的充分条件.得到了随机环境中马氏链弱常返的充分条件.     

An application to the MKZ-operators of generalized convexity on ECT-systems

We analyze some relations between classical convexities and some generalized convexities. The results are applied to obtain some new shape preserving properties of the Meyer-König and Zeller operators.     

On the Green Function of the Annulus

Using the Gegenbauer polynomials and the zonal harmonics functions we give some representation formula of the Green function in the annulus. We apply this result to prove some uniqueness results for some nonlinear elliptic problems.     

On CLARKSON's Inequalities and Interpolation

We consider some elementary proofs of local versions of CLARKSON 's inequalities and point out the fact that these inequalities can be generalized to hold for a much wider class of parameters. In particular it is easy to generalize our interpolation proof in various ways to higher dimensions. We point out explicitely some examples of such generalizations and we also prove some corresponding global versions. In this elementary way we obtain both new proofs of some previous results of this kind and also some new complements, unifications and further generalizations of these results.