关于Mn*-半群

本文研究了全体n阶矩阵关于乘法和转置构成的*-半群,给出了*-子半群的概念证明了Mn存在*-正则子半群、*-逆子半群、*-子群.证明了对于任意正整数n,如果一个集合S的元素个数为n2+1则可以定义乘法和*运算把S变成正则*-半群,而且S是一个逆半群.

On Subsemi-Ideal Rings

In this note we introduce a new ideal called subsemi-ideal of a ring R. We obtain a necessary and sufficient condition for a group ring to be a subsemi ideal ring.

Finite Groups with only S-seminormal or Selfnormal Subgroups

In this note the author studies such a finite group in which each subgroup is either Sseminormal or selfnormal and characterizes this kind of finite groups.Moreover,the main results in[1] and [2] can be obtained by the conclusion in this note.

Attractor for a Fourth-order Equation in the Whole Line

This paper studies the long time behavior of the following Cauchy problem δu/δt＋σδ^4u/δx^4＋ru＋uδu/δx=f,x∈R,t〉0,The authors prove the existence of global attractor by showing the corresponding operator semigroup is asymptotically compact.

The Semigroup Characterizations of Positive Implicative BCK-algebras

Adjoint semigroups of BCI algebras were introduced by Huang [1] and some of its important properties were obtained. In this paper,some characterizations of positive implicative BCK algebras are given by discussing the adjoint semigroups. Moreover,the semigroup differences between positive BCK algebras and implicative BCK algebras are discussed,and some semigroup characterizations of implicative BCK algebras are given.

关于弱正则*—N(2,2,0)代数的若干结果

引入了弱正则 *— N (2 ,2 ,0 )代数的概念 ,着重探讨了弱正则 *— N (2 ,2 ,0 )代数的投射集 P(S)及 Q* (S)的性质 ,得到了投射集构成群的一个必要条件 ;证明了在弱正则 *— N (2 ,2 ,0 )代数中 ,每一个幂等元集都是投射集。

The Qualitative Analysis of a Solution of a Series Maintenance System with Two Components

In this paper, firstly we study the series ma intenance system with two components, obtain its exsistence and uniqueness of a dynamic state nonnegative solution by strongly continuous semigroups of operator s theory. Then we prove that 0 is the eigenvalue of the system’s host operators, a nd finally we study the eigenvector of the eigenvalue 0.

The Spectrum of High Rank Differential Operators of the C_0 Semigroups

In this paper,the author study the spectrum of high rank differential operators T (n) (t) of C 0 Semigroup T(t) ,given an approach to construct the spectral set opetator T (n) (t) ,and discussed the relation between the spectral points of both T (n) (t) and infinitesimal generator A of T(t) .

Fuzzy Ordered Filters in Implicative Semigroups

We fuzzify the concept of ordered filter in implicative negatively partially ordered semigroups and study its properties.

Notes on the Heat Diffusion Semigroup in a Riemannian Manifold

In this paper, the properties of the heat diffusion semigroup {e^(t△)}_(t≥0) generated by the Hodge-deRham operator in a Riemannian manifold are discussed.

The Spectrum of High Rank Differential Operators of the C0 Semigroups

In this paper,the author study the spectrum of high rank differential operators T (n) (t) of C 0 Semigroup T(t) ,given an approach to construct the spectral set opetator T (n) (t) ,and discussed the relation between the spectral points of both T (n) (t) and infinitesimal generator A of T(t) .

Properties of Fuzzy M-Semigroups with t-Norms

In this papr, we introduce the notion ofT-fuzzy M-subsemigroups of M-semigroups by using a t-norm T and obtain some interesting properties. Further we show that the direct product of a T-fuzzy M-subsemigroup of R and a fuzzy M-subsemigroup of S is a T-fuzzy M-subsemigroup of M, Moreover, we prove that T-fuzzy M-subsemigroup of M is exhibited as the direct product of T-fuzzy M-subsemigroups of R and S respectively.

Influence of s-Semipermutability of Some Subgroups of Prime Power Order on Structure of Finite Groups

A subgroup H of a finite group G is called semipermutable if it is permutable with every subgroup K of G with （｜H｜ ｜K｜） = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with （p, ｜H｜） = 1. In this paper, we investigate the influence of s-semipermutablity of some subgroups of prime power order of a finite group on its supersolvablility.

Intuitionistic (S,T)-Fuzzy M-Subsemigroups of an M-Semigroup

Intuitionistic fuzzy sets are generalized fuzzy sets which were first introduced by Atanassov in 1986. In this paper, we introduce the concept of intuitionistic fuzzy M-subsemigroups of an M-semigroup M with respect to an s-norm S and a t-norm T on in-tuitionistic fuzzy sets and study their properties. In particular, intuitionistic （S,T）-direct products of M-semigroups are considered and some recent results of fuzzy M-subsemigroups of M-semigroups obtained by Zhan and Tan^[21] are extended and generalized to intuitionistic （S, T）-fuzzy M-subsemigroups over M-semigroups.

Linear Operators Strongly Preserving M-P Inverses of Matrices over Some Antinegative Commutative Semirings

Let S be an antinegative commutative semiring having no zero divisions or finite general Boolean Algebra and μ(S) the set of n×n matrices over S. In this paper we characterize the structure of the senigroup n,(S) of linear operators on μn,(S) that strongly preserve the M-P inverses of matrices.

The characterization of a class of quantum Markov semigroups and the associated operator-valued Dirichlet forms based on Hilbert C~*-module l_2(A)

We characterize A-linear symmetric and contraction module operator semigroup{Tt}t∈R+L(l2(A)),where A is a finite-dimensional C-algebra,and L(l2(A))is the C-algebra of all adjointable module maps on l2(A).Next,we introduce the concept of operator-valued quadratic forms,and give a one to one correspondence between the set of non-positive definite self-adjoint regular module operators on l2(A)and the set of non-negative densely defined A-valued quadratic forms.In the end,we obtain that a real and strongly continuous symmetric semigroup{Tt}t∈R+L(l2(A))being Markovian if and only if the associated closed densely defined A-valued quadratic form is a Dirichlet form.

ASYMPTOTIC PROPERTY OF THE TIME-DEPENDENT SOLUTION OF A RELIABILITY MODEL

We discuss a transfer line consisting of a reliable machine, an unreliable machine and a storage buffer. This transfer line can be described by a group of partial differential equations with integral boundary conditions. First we show that the operator corresponding to these equations generates a positive contraction C0-semigroup T(t), and prove that T(t) is a quasi-compact operator. Next we verify that 0 is an eigenvalue of this operator and its adjoint operator with geometric multiplicity one. Last, by using the above results we obtain that the time-dependent solution of these equations converges strongly to their steady-state solution.

TENSOR PRODUCT OF SEMIGROUPSAND THE EQUATION AC-CB=Q

Properties for tensor products of semigroups are considered and the solutions of the equationAC - CB = Q are discussed. Results obtained in this paper considerably generalize thoseobtained in [9].

WELL-POSEDNESS OF THE MODEL DESCRIBING A REPAIRABLE,STANDBY,HUMAN & MACHINE SYSTEM

By using the strong continuous semigroup theory of linear operators we prove the existence of a unique positive time-dependent solution of the model describing a re-pairable, standby, human & machine system.

Regular Congruence Classes of Ordered Semigroups

The aim of this paper is to determine the subset of an ordered semigroup S that can serve as a class of some regular congruences on S. The results on semigroups without order given in [5] can be obtained as consequences.