N(2,2,0)代数的稳定化子与同余分解

为了深入研究N(2,2,0)代数的代数结构,首先利用代数的推理方法进一步研究了N(2,2,0)代数的稳定化子,改进了以前学者的部分结果,然后利用稳定化子建立了一种同余关系,给出了N(2,2,0)代数的同余分解,证明了其商代数仍是N(2,2,0)代数,并获得了自然同态下一类逆像的代数结构和性质.     

全序幂等元剩余格

研究了全序幂等元剩余格,给出了全序幂等元剩余格的另一种新的构造方法,并且得到了这类剩余格的结构定理,推广了相关文献的结论．     

Harnack and HWI inequalities on infinite-dimensional spaces

In this paper, the dimensional-free Harnack inequalities are established on infinite-dimensional spaces. More precisely, we establish Harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhlenbeck semigroup on the abstract Wiener space. As an application, we establish the HWI inequality on the abstract Wiener space, which contains three important quantities in one inequality, the relative entropy “H”, Wasserstein distance “W”, and Fisher information “I”.     

The global attractor of a non-local PDE model with delay for population dynamics in ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In this paper, we consider a non-local PDE model with delay for population dynamics in ℝ ⁿ . First, we prove the existence and uniqueness of weak solutions under some suitable decayed assumptions on non-local term at infinity. Then, we obtain the global attractor by proving ω-limit compactness property of the solution operator semigroup.     

Congruence triples on regular semigroups and their generalizations

In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by using the equivalences on S/ℒ, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup.     

半线性抛物方程在L2p空间中全局吸引子的存在性

本文研究了半线性抛物方程所生成的半群{S（t）}t≥0的吸引子的存在性.利用文献[1]中证明吸引子正则性的思想,分别得到半群{S（t）}t≥0在L^2p（Ω）空间中具有一个有界吸收集和一个全局吸引子.     

INVERSE COEFFICIENT PROBLEMS FOR PARABOLIC HEMIVARIATIONAL INEQUALITIES

This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained.     

基于格半群的有限状态自动机的同态

本文研究了格值有限状态自动机(LFSA)的同态和强同态及其性质.利用强同态概念,在格值有限状态自动机的状态集上建立了一种等价关系,得到了格值有限状态自动机的商自动机,证明了商自动机与强同态像自动机同构.     

具有一种故障类型的二相关单元冗余系统的指数稳定性

利用C_0-半群理论证明了具有一种故障类型的二相关单元冗余系统非负解的存在惟一性,并研究了相应算子的谱特征,通过分析本质谱界经过紧扰动后的变化,得到了系统动态解以指数形式收敛于稳态解.最后,给出几个数值模拟的例子用来说明本文的意义所在.     

关于内射模的P-平坦性

通过引用P-平坦模的定义,引入了右IPF环的概念,推广了右IF环的概念,这对研究IF环及QF环具有重要的作用,同时对右IPF环的性质作了一些刻画,得到了右IPF环的若干个等价命题;最后,用P-平坦模及右IPF环推出了正则环的一些等价条件．