In the fourth chapter the paper discusses the following relation between the least group congruences on the e - unitary inverse semigroup and the semidirect product : moreover we describe the following structure of the semidirect product of two e - unitary semigroups by mcalistertriple : T ny 、 tys陀xdt op这佯的关系；以及通过me人hater三元组刻划了e酉逆半群的半直积的如下的结构： sx 。
By this means , we get the descriptions of semidirect products to be strongly - inverse semigroup , clifford quasi - regular semigroup , strongly - e - unitary inverse semigroup and e - unitary inverse semigroup . for strongly - e - unitary inverse semigroup , we define it in the third chapter 主要给出了保持半直积的封闭性的充要条件，某些半直积的结构以及半直积上的某些同余与半群上的这类同余之间的关系
This paper discusses the semidirect products of two semigroups in the range of - regular semigroups . giving necessary and sufficient conditions for the semidirect products of two semigroups with strong left - inverse semigroups . providing a new method to the study of the structures of semigroups 在-正则半群范围内讨论半群的半直积.给出了两个半群的半直积为强左-逆半群的充要条件,给半群结构的研究提供了一种新的方法
This dissertation proves that formation of entanglement is smaller than mutual information . as a by - product , this dissertation also proves that there does not exist this kind of quantum state whose nearest separable state is the product of its two reduced density matrices except the state whose classical correlation is zero 证明了结构纠缠小于互信息，同时证明了对于任意的量子态(除了经典关联为0的态) ，它的两个约化密度矩阵的直积不可能为它的最近分离态。
In this dissertation , we characterize the congruences on a strong semilattice of semigroups by the congruences on those semigroups and prove that a sublattice of the direct product of the lattices of congruences on those semigroups is isomorphic to a sublattice of the lattice of congruences on the strong semilattice of semigroups 本文，我们主要利用一族半群上的同余刻划其强半格上的同余，并讨论这族半群的同余格的直积的子格与其强半格上的同余子格的关系。
First , according to the definition of strong distributive lattice of semirings , we define the pseudo - strong distributive lattice semiring s and the pseudo - direct product , and we prove that the pseudo - direct product that we just define is a semiring , then we prove that s is the pseudo - sub direct product of d and s / 9 首先根据半环的强分配格的定义，定义了伪强分配格半环和一个斗格半环r与任一半环t的伪直积，证明了我们所定义的伪直积是一个半环，并且证明了s是d与s的伪次直积。
What we do at this aspect are : firstly , we describe the permutation symmetry of the structure of some special networks and the corresponding attractor sets with some geometric graphs in euclidean space , which are called attractors graph and geometrized structure graph of the networks respectively ; the geometrizing conditions are also given ; we study the dynamical behavior of the networks using the geometrized structure graph and attractors graph of the network ; moreover , we propose an approach to construct a big - size network with some small - size network with symmetry by the method of direct - sum , direct - produce and semidirect - produce . we also study the dynamical properties " relation between the big - size network and the small - size networks . all those results will provide some theoretical basis for designing a special large - scale network 本文在这方面所做的工作如下：首次将一些特殊网络的结构和吸引子集的置换对称性用三维欧氏空间中的一些几何图来表示，分别称之为几何结构图和吸引子图；给出了网络对称性的几何化条州即相应的对称性群为可迁群） ：并惜助网络的几何结构图和吸弓吁图分析网络的动力学性质；此外，我们提出了用简单的具有一定对称性的小网络按照群的直和、半直积和直积的方式组合成较大的网络的方法，探讨了这些小网络和所组成的大网络的一些动力学性质的关系，如稳定态的个数、各稳定态的回忆性质等，为较大网络的设计提供一些理论依据。
In the second section , we structure a kind of semirings , namely semidirect product of semirings , and prove an isomorphic theorem of semidirect products . in the third section , we give the characterizations of the relations of all kinds of regular semirings and introduce the concept of pseudo - inverse and the necessary and sufficient conditions of pseudo - invertible element . in the fourth section , we define an equivalence relation on the cartersian product of commutative semiring and its multiplicative subset 第二部分，先构造一类半环，半环半直积，然后证明半直积的同构定理第三部分，刻划了半环各类正则元之间关系，引入伪逆的定义，给出了可伪逆元素的充要条件第四部分，在交换半环和乘法集的卡氏积上定义等价关系，进而构造了一类交换半环：分式半环
As examples , a - tautologies and f - tautologies in lattice valued logic systems 1 - 4p ( x ) and l6p ( x ) are discussed in detail . ( 2 ) a kind of calculus method that is used to determine the truth - values of propositional logic formulae by means of the dynamic neural networks is proposed . it is not necessary that the formulae be simplified into normal form 本文分析讨论了基于格蕴涵代数直积的格值逻辑系统中的-重言式和f -重言式，作为两个实例，详细讨论了两个格值逻辑系统l _ 4p ( x )和l _ 6p ( x )中的重言式和f -重言式的结构。
2 . the structure of the lattice implication sub - algebra which generated from a subset , and the product of lattice implication algebra were studied . the necessary condition was given of a lattice implication algebra which can be decomposed into lattice implication algebra ' s product . it is proved that lattice h implication algebra is a boole ring with a unit 2 、对格蕴涵代数中由一子集生成的格蕴涵子代数的结构及格蕴涵代数的直积进行了研究，给出了一格蕴涵代数可分解成一族格蕴涵代数直积的必要条件，证明了格h蕴涵代数是一有单位元的布尔环。
