A relation for general and inverse semigroups

The relation in the title is S defined by

关于循环子半群的结构与数量问题及拟环的特征与结构

彻底解决了所有循环半群及其子群的结构和数量问题,并讨论了拟群分解问题,同时,对群论基本定理作了部分推广,并给出了定理的另一部分不可推广的反例,最后,建立了一类特殊环－拟环。     

Gaussian estimates and regularized groups

We show that if a bounded analytic semigroup on satisfies a Gaussian estimate of order and is the generator of its consistent semigroup on , then generates a -regularized group on where . We obtain the estimate of () and the -independence of , and give applications to Schrödinger operators and elliptic operators of higher order.

     

Separability and the Twisted Frobenius Bimodule

This paper begins with an introduction to -Frobenius structure on a finite-dimensional Hopf subalgebra pair. In Section 2 a study is made of a generalization of Frobenius bimodules and -Frobenius extensions. Also a special type of twisted Frobenius bimodule which gives an endomorphism ring theorem and converse is studied. Section 3 brings together material on separable bimodules, the dual definitions of split and separable extension, and a theorem of Sugano on endomorphism rings of separable bimodules. In Section 4, separable twisted Frobenius bimodules are characterized in terms of data that generalizes a Frobenius homomorphism and a dual base. In the style of duality, two corollaries characterizing split -Frobenius and separable -Frobenius extensions are proven. Sugano"s theorem is extended to -Frobenius extensions and their endomorphism rings. In Section 5, the problem of when separable extensions are Frobenius extensions is discussed. A Hopf algebra example and a matrix example are given of finite rank free separable -Frobenius extensions which are not Frobenius in the ordinary sense.     

包络半群与拓扑动力学中的接近关系

运用包络半群的理论，对接近关系中一个重要定理给出了一个简单证明．作为这一定理的应用，我们得到接近关系可乘性的一个结果．并且对另一种接近关系，也得到一个结果．这两个定理减弱了Ｃｌａｙ在这一领域中两个定理的条件．     

紧拓扑半群上概率测度卷积序列的极限性质

本文讨论紧拓扑半群上概率测度卷积序列的若干重要极限性质．在第１节中，我们讨论测度集的代数结构与其支撑集代数结构的关系．第２节的定理１，通过支撑集的代数结构给出组合收敛测度序列的一个极限定理．在定理２中我们讨论独立同分布时的情形，建立了一类紧半群上的Ｋａｗａｄａ－Ｉｔ型结果．这些定理推广了紧群、紧交换半群、紧Ｌ－Ｘ半群上一些相应的结论．     

一类Schrodinger方程的周期解和谱方法

本文利用半群理论讨论了一类非线性非自共轭Ｓｃｈｒｏｄｉｎｇｅｒ方程周期初边值解的存在唯一性，以及它的Ｆｏｕｒｉｅｒ谱方法的可解性，稳定性和收敛性     

Global solutions of the Boltzmann equation on a lattice

The nonlinear Boltzmann equation with a discretized spatial variable is studied in a Banach space of absolutely integrable functions of the velocity variables. Conservation laws and positivity are utilized to extend weak local solutions to a global solution. This is shown to be a strong solution by analytic semigroup techniques.Supported by National Science Foundation Grant ENG-7515882.