两类剩余幺半群

主要讨论了两类可换剩余幺半群的结构及其定定理，给出并证明了一些有关的等价条件和充分必要条件，然后证明了剩余运算满足消去律的充要条件。     

项重写系统和自由幺半群

项重写系统起源于数理逻辑,是理论计算机科学的重要组成部分.关于项重写系统的一个主要问题是描述一个重写系统是否具有汇合或终止等基本性质.本文首先将一个项重写系统与自由幺半群上的二元关系联系起来.然后,基于自由幺半群上的项重写系统,刻画了收敛项重写系统与自由幺半群的商截面之间的关系.作为应用,分别给出了由三个元素生成的Platic幺半群和中国幺半群的截面.     

剩余幺半群的商结构

本文首先定义了交换剩余幺半群Ｍ相对于其子半群Ｐ（Ｍ）的商结构Ｍ／Ｐ（Ｍ），然后研究了它的性质并给出了一些同构定理。     

特殊么半群上的Green等价

本文主要讨论有限特殊Ｃｈｕｒｃｈ－ＲｏｓｓｅｒＴｈｕｅ系统所表现的么半群上Ｇｒｅｅｎ等价的数量性质．证明每种Ｇｒｅｅｎ等价类都是正则集合，其个数或１或∞且多项式时间内可计算．同时获得一个关于有限特殊Ｔｈｕｅ系统描述能力的结论．     

幺半群的半直积及其同余

给出了两个幺半群的半直积是Ｃｌｉｆｆｏｒｄ半群的充要条件及其结构。并讨论了逆半群半直积的Ｇｒｅｅｎ关系、最小群同余和极大幂等元分离同余。     

可换幺半群的结构

关于“群”有各种各样的定义,本给出了有限幺半群成为群的一个条件。并对有限可换幺半群进行了讨论,通过对它的商集的研究,建立了有限可换幺半群与有限可换幺半群之间的关系,从而揭示了有限可换幺半群的结构。     

幺半群上的Rees矩阵半群的半格的结构

推广了Ｍ．Ｐｅｔｒｉｃｈ在文「１」中所用的方法，得到了幺半群上Ｒｅｅｓ矩阵半群的半格的一个结构定理，研究了单幂幺半群Ｒｅｅｓ矩阵半群的半格的性质并给出了矩形单幂幺半群的半格的若干等价刻划。     

一族具有正则幺半群的图

本文给出了一族具有正则自同态幺半群的图及相应的自同态计数公式。     

右消去幺半群、左正则带和左正则型A幺半群

本文利用右消去幺半群,左正则带建立了真左正则型A幺半群．在证明了任一左正则型A幺半群均有P－覆盖后,给出P－覆盖的结构．     

On the resolution of relative Thue equations

An efficient algorithm is given for the resolution of relative Thue equations. The essential improvement is the application of an appropriate version of Wildanger's enumeration procedure based on the ellipsoid method of Fincke and Pohst.

Recently relative Thue equations have gained an important application, e.g., in computing power integral bases in algebraic number fields. The presented methods can surely be used to speed up those algorithms.

The method is illustrated by numerical examples.

     

On the solutions of a parametric family of cubic Thue equations

In this paper, we solve a family of Diophantine equations associated with families of number fields of degree 3. In fact, we use Baker’s method find all solutions to the Thue equation

Structural Properties of Cubic Sets in Regular LA-semihypergroups

In this article we characterize the regular LA-semihypergroups in terms of $({\in }_{\Gamma },{\in }_{\Gamma }\vee q_{\Delta })$-cubic (left, right, two sided, bi, generalized bi, interior, quasi)-hyperideals of LA-semihypergroups. Meanwhile, some illustrative examples are given to show the rationality of the definitions popularized in the present paper.     

Properties of the Optimal Ellipsoids Approximating the Reachable Sets of Uncertain Systems

The ellipsoidal estimation of reachable sets is an efficient technique for the set-membership modelling of uncertain dynamical systems. In the paper, the optimal outer-ellipsoidal approximation of reachable sets is considered, and attention is paid to the criterion associated with the projection of the approximating ellipsoid onto a given direction. The nonlinear differential equations governing the evolution of ellipsoids are analyzed and simplified. The asymptotic behavior of the ellipsoids near the initial point and at infinity is studied. It is shown that the optimal ellipsoids under consideration touch the corresponding reachable sets at all time instants. A control problem for a system subjected to uncertain perturbations is investigated in the framework of the optimal ellipsoidal estimation of reachable sets.     

On Characterization of Monoids by Properties of Generators

Kilp and Knauer in(Comm. Algebra, 1992, 20(7), 1841–1856) gave characterizations of monoids when all generators in category of right S-acts(S is a monoid) satisfy properties such as freeness, projectivity, strong flatness, Condition(P), principal weak flatness, principal weak injectivity, weak injectivity, injectivity, divisibility, strong faithfulness and torsion freeness.Sedaghtjoo in(Semigroup Forum, 2013, 87: 653–662) characterized monoids by some other properties of generators including weak flatness, Condition(E) and regularity. To our knowledge,the problem has not been studied for properties mentioned above of(finitely generated, cyclic,monocyclic, Rees factor) right acts. In this article we answer the question corresponding to these properties and also f g-weak injectivity.     

Structural Properties of Homomorphism Dilation Systems

Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras, the authors explore a pure algebraic version of the dilation theory for linear systems acting on unital algebras and vector spaces. By introducing two natural dilation structures, namely the canonical and the universal dilation systems, they prove that every linearly minimal dilation is equiva...