F幂群的分类

文[1]首次提出了F幂群的概念,并讨论了F幂群的基本结构及同态问题。本文讨论F幂群的分类,并构造各类子群列和正规子群列。     

幂群的结构及其相互关系

§1 预备知识为了使本文自成一体,先介绍一些必备的定义和定理。定义1.1 设G是一个群,在(G)\{}中引入代数运算:A·B={a·b|a∈A,b∈B}。如果一个非空集族((G)\{(}对上运算作成群,我们称为G上幂群,其单位元用E来表示。定义1.2 设为幂群,若e∈E,其中e为G中单位元,则称为G的正则幂群。定理1.1 如果为G上的一个幂群,用|A|表示A的元素个数,则     

幂群的结构与分类

完整地研究了各种幂群的结构，对幂群进行了分类，并构造了各类的子群列和正规子群列。     

Fuzzy幂群

文［１］讨论了代数结构的提升问题，提出了幂群的概念。模糊数学的发展要求各种数学结构不但要由论域向其幂集上提升，而且还要求向模糊幂集上提升，在更广泛的意义下讨论其结构问题，本文首先提出Ｆｕｚｚｙ幂群的概念，讨论了Ｆｕｚｚｙ幂群的结构及其同态问题。     

幂群所诱导的L—Fuzzy幂群

本文在幂群［１］的基础上，提出了幂群所诱导的Ｌ－Ｆｕｚｚｙ幂群、Ｌ－Ｆｕｚｚｙ幂群的λ－截、次幂群等一系列概念，并给出了幂群与其诱导的Ｌ－Ｆｕｚｚｙ幂群、λ截集群间的次同态、同态等关系。     

点态化Fuzzy幂群的转移定理

从F uz zy点的角度来研究F uz zy幂群,建立F uz zy幂群的转移定理,然后通过转移定理将分明幂群的许多概念和结论直接转到F uz zy幂群,揭示了F uz zy幂群与分明幂群的关系。     

Fuzzy幂群与Fuzzy商群的相互关系

In this paper,we extend the concept of fuzzy quotient groups.The structures of fuzzy power groups and fuzzy quotient groups are discussed.The relationship between fuzzy power groups and fuzzy quotient groups are considered.     

幂群与序关系

设Ｇ为非ｍｏｎｏｉｄａｌ群，Ｅ是它的正规子集，满足Ｅ²＝Ｅ并且１_Ｇ∈／Ｅ．利用Ｅ作为正锥，可以在Ｇ上定义一个偏序，并且Ｇ成为一个偏序群．这样就可以利用这个序关系同时研究群Ｇ以及Ｇ上的以Ｅ为单位元的幂群．当Ｅ是极大子半群时，得到Ｇ的一个结构定理；在Ｇ是格序群的条件下，Ｇ上的幂群Γ可以膨胀为一个拟商群．     

循环群上幂群的结构

This paper gives some further research on the basic of paper[2].The theorem of paper[2] is improved and proved here.considering the limitations of this theorem,we prove isomorphic theorem of structure of hypergroup with no.condition.At last,we show some of its application through some examples.     

点态化的模糊幂群

文献[1]提出了点态化Fuzzy集的概念,本文利用文献[1]中定义的Fuzzy点来研究Fuzzy幂群的性质和结构.得到了一些有关Fuzzy幂群的新结果.     

广义幂群及其构造

引入了广义核和广义幂群的概念，刻画了广义幂群的结构，并给出了广义幂群的构造定理。     

正规幂环和一致幂环

文[1]首次提出了HX环（幂环）的概念,文[2]探索了幂环的性质和结构,本文类似于幂群的研究,提出了正规幂环和一致幂环的概念,研究了它们的结构和它们之间的关系,对它们进行了分类,并讨论了它们的交与和,从而构造了它们的子环链和理想链。     

模糊自动机的强连通性及群自动机

为了更好地研究模糊自动机的结构和性质,采用代数的方法,在传统的模糊有限状态自动机的基础上,通过定义状态集合为代数群的自动机,讨论了这一类自动机的连通性和正则性,这丰富了模糊自动机理论．     

直觉模糊正规子群与直觉模糊商群

在直觉模糊子群的基础上 ,引入直觉模糊正规子群与直觉模糊商群概念 ,并讨论了它们的一些性质 ,最后研究了群同态下 ,直觉模糊正规子群的对应关系     

分配格中模糊理想诱导的模糊幂格

在模糊幂格讨论基础上,给出了由分配格中模糊理想诱导的两种模糊幂格.     

A novel of fuzzy PSS based on new objective function in multimachine power system

This article proposed a new control strategy based on Takagi–Sugeno fuzzy model for deceasing the power system oscillation. This controller is based on the parallel distributed compensation structure, the stability of the whole closed‐loop model is provided using a general Lyapunov‐Krasovski functional. Also, in this article, a new objective function has been considered to test the proposed Fuzzy Power System Stabilizer in different load conditions which increase the system damping after the system undergoes a disturbance. So, for testing the effectiveness of the proposed controller, the damping factor, damping ratio, and a combination of the damping factor and damping ratio were analyzed and compared with the proposed objective function. The effectiveness of the proposed strategy has been used over 16 machine 68 bus power system. The eigenvalue analysis and nonlinear time domain simulation results proof the effectiveness of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 288–298, 2016     

Diameter of a direct power of a finite group

We present two conjectures concerning the diameter of a direct power of a finite group. The first conjecture states that the diameter of Gⁿ with respect to each generating set is at most n(|G|?rank(G)); and the second one states that there exists a generating set 𝒜, of minimum size, for Gⁿ such that the diameter of Gⁿ with respect to 𝒜 is at most n(|G|?rank(G)). We will establish evidence for each of the above mentioned conjectures.