Moment stability of fractional stochastic evolution equations with Poisson jumps

Fractional differential equations have wide applications in science and engineering. In this paper, we consider a class of fractional stochastic partial differential equations with Poisson jumps. Sufficient conditions for the existence and asymptotic stability in pth moment of mild solutions are derived by employing the Banach fixed point principle. Further, we extend the result to study the asymptotic stability of fractional systems with Poisson jumps. An example is provided to illustrate the effectiveness of the proposed results.     

Approximate controllability of semilinear partial functional differential systems

In this paper, we study the approximate controllability of semilinear neutral functional-differential systems and impulsive functional-differential systems with finite delay. Since the considered equations admit nonlinear terms involving spatial derivatives, the fraction power theory and α-norm is used to discuss the problem so that the established results can be applied to them. An example is provided to illustrate the application of the obtained results. This work is supported by NNSF of China (No. 10671069) and Shanghai Leading Academic Discipline Project (No. B407).     

正则语言的一个特征

Myhill-Nerode定理利用等价关系描述了正则语言的一个重要特征,它是有限自动机理论中的一个经典、优美的结果。为了将Myhill-Nerode定理推广到更一般的情形,引入了有限自动机M上的状态转移半群和Σ*上的M-半群,讨论了其若干性质。在此基础上,将Myhill-Nerode定理中的等价关系一般化,给出了正则语言的一个新的特征定理,Myhill-Nerode定理成为该定理的一个推论。讨论了正则语言的最一般的特征,提出了有待进一步研究的问题。     

一种泛逻辑代数系统

文[3]给出了理想状态(广义相关系数h=0.5,广义自相关系数k=0.5)下泛逻辑的形式演绎系统B,证明了此系统是可靠的。该文提出理想状态下(h=k=0.5)泛逻辑学对应的代数系统-UB代数,给出它的一系列性质。证明了UB代数是一个交换剩余半群;进一步证明了U B代数与M V代数、正规FI代数是等价的。     

Some properties of topological pressure of a semigroup of continuous maps

Based on the work of Ma and Wu,[9 Ma D, Wu M. Topological pressure and topological entropy of a semigroup of maps. Discrete Contin Dyn Syst. 2011;31:545–557.[Crossref], [Web of Science ®] , [Google Scholar]] some equivalent definitions of topological pressure of a semigroup of continuous maps are given and several of their basic properties are provided by using separated sets and spanning sets. We also answer an open problem of Bi? and Urbański.[19 Bi? A, Urbański M. Some remarks on topological entropy of a semigroup of continuous maps. Cubo. 2006;8:63–71. [Google Scholar]] That is, letting f_i, i = 2, … , k, be homeomorphisms acting on a compact metric space, G₁ = {id_X, f₂, … , f_k}, G^{? 1}₁ = {id_X, f^{? 1}₂, …, f_k^{? 1}} and letting G and G^?1 denote the semigroups generated by G₁ and G^{? 1}₁, respectively, we give an example showing that the topological entropy of G does not equal the topological entropy of G^?1.     

非线性SKG型耦合方程组的Cauchy问题

考虑多维非线性Schrodinger-Klein-Gordon型耦合方程组的Cauchy问题,采用算子半群方法和先验估计技巧,证明了该问题整体强解的存在唯一性,并讨论了解的光滑性.     

矩形半环的分配格

借助半群的理论及观点引入并研究了加法半群为矩形群的半环及加法半群为纯正群的半环,即纯正半环和矩形半环.并通过对矩形半环及纯正半环的结构和性质的分析与研究,给出了这两类半环的若干性质,从而给出了矩形半环的分配格的定义.最后研究了矩形半环的分配格与坚固分配格,即对这类半环坚固框架的刻画,得到了一些有趣的新结果.     

半群代数k[A]中理想交集的生成元的算法

半群代数k[A]中Groebner基有许多性质,继续对其进行研究,并将其用于解决k[A]中两个理想交集的生成元问题.     

Admissibility of Linear Systems in Banach Spaces

In this paper, infinite-time p-admissibility of unbounded operators is introduced and the Co-semigroup characterization of the infinite-time p-admissibility of unbounded observation operators is given. Moreover, the analogous result for the infinite-time p-admissibility of unbounded control operators is presented.