群上同余

本引进了群上同余的概念，得到了群上的等价关系为群上同余的一个充分必要条件，并讨论了群上同余与群上正规子群之间的关系以及群上同余与群上同态之间的关系．     

多属性群决策算法及一致性分析研究

在多属性群决策中 ,集结群体意见之前必须先对群体的决策数据进行一致性分析 ,以确保群体作出的决策符合客观实际 .提出了群决策的三种三维层次模型 ;用欧几里得距离 ( Euclidean Distance)表示个人决策中方案的评价值 ;然后设置一致性指标值α,作为群体数据一致性的判断依据 ;提出了满足一致性基础上的一种群决策方法 ;最后用实例说明了算法的使用步骤 .     

Affinely Prime Dynamical Systems

This paper deals with representations of groups by "affine" automorphisms of compact,convex spaces,with special focus on "irreducible" representations:equivalently "minimal" actions.When the group in question is PSL(2,R),the authors exhibit a oneone correspondence between bounded harmonic functions on the upper half-plane and a certain class of irreducible representations.This analysis shows that,surprisingly,all these representations are equivalent.In fact,it is found that all irreducible affine representations of this group are equivalent.The key to this is a property called "linear Stone-Weierstrass"for group actions on compact spaces.If it holds for the "universal strongly proximal space"of the group (to be defined),then the induced action on the space of probability measures on this space is the unique irreducible affine representation of the group.     

Affinely Prime Dynamical Systems(Dedicated to Professor Haim Brezis on the occasion of his 70th birthday)

This paper deals with representations of groups by "affine" automorphisms of compact, convex spaces, with special focus on "irreducible" representations: equivalently"minimal" actions. When the group in question is P SL(2, R), the authors exhibit a oneone correspondence between bounded harmonic functions on the upper half-plane and a certain class of irreducible representations. This analysis shows that, surprisingly, all these representations are equivalent. In fact, it is found that all irreducible affine representations of this group are equivalent. The key to this is a property called "linear Stone-Weierstrass"for group actions on compact spaces. If it holds for the "universal strongly proximal space"of the group(to be defined), then the induced action on the space of probability measures on this space is the unique irreducible affine representation of the group.     

The admissibility of sporadic simple groups

In 1955 Hall and Paige conjectured that a finite group is admissible, i.e., admits complete mappings, if its Sylow 2-subgroup is trivial or noncyclic. In a recent paper, Wilcox proved that any minimal counterexample to this conjecture must be simple, and further, must be either the Tits group or a sporadic simple group. In this paper we improve on this result by proving that the fourth Janko group is the only possible minimal counterexample to this conjecture: John Bray reports having proved that this group is also not a counterexample, thus completing a proof of the Hall–Paige conjecture.     

Geometry of cotangent bundle of Heisenberg group

In this paper, the classification of left invariant Riemannian metrics on the cotangent bundle of the (2n+1)-dimensional Heisenberg group up to the action of the automorphism group is presented. Moreover, it is proved that the complex structure on this group is unique, and the corresponding pseudo-Kähler metrics are described and shown to be Ricci flat. It is known that this algebra admits an ad-invariant metric of neutral signature. Here, the uniqueness of such metric is proved.     

基于决策者风险偏好大数据分析的大群体应急决策方法

针对重大突发事件应急决策大群体成员的风险偏好复杂难测问题,提出了一种新的基于决策者风险偏好大数据分析的大群体应急决策方法。首先专家群体对突发事件进行快速响应,生成若干应急预案及其风险属性信息;其次,社会公众通过网络等渠道参与到应急决策中来并形成决策大群体,给出不同预案的偏好值;然后,利用证据推理算法得出公众对各预案的风险效用值,将预案风险效用值与预案偏好值加权组合,得到各个预案的大群体决策者的风险偏好值;最后,基于风险偏好值,利用大数据分析技术对大群体的风险偏好进行聚类识别,从中筛选出风险中立者组成新的应急决策群体,再次聚类得出应急决策群体的成员组成结构,以此为基础计算决策者权重和应急预案的最终效用值,得应急预案排序结果。最后通过算例分析验证了方法的有效性和可行性。     

关于群体决策的偏比映射

本文引进群体决策的决策个体和决策群体关于供选方案对的偏比度,以及偏比泛函概念.由此,定义了群体在供选方案集上的偏比映射,构造了相应的偏比公理系,并且建立了关于群体决策的偏比度分析的基本理论.最后,给出一个利用偏比映射进行群体排序的方法.特别是,文中表明,满足本文所提出的所有偏比公理的偏比映射是存在的.     

Asymptotics for Certain Harmonic Functions and the Martin Compactification on the Quaternionic Heisenberg Group

In this paper, we make the asymptotic estimates of the heat kernel for the quaternionic Heisenberg group in various cases. We also use these results to deduce the asymptotic estimates of certain harmonic functions on the quaternionic Heisenberg group. Moreover a Martin compactification of the quaternionic Heisenberg group is constructed, and we prove that the Martin boundary of this group is homeomorphic to the unit ball in the quaternionic field.     

On A-Critical nilpotent groups

It is useful to consider a critical structure of a class of groups. For example, the results on minimal non-nilpotent group, and on minimal non-p-nilpotent group, have been widely used in group theory. In this paper, we analyze the critical structure of a class of groups, which admit an operator group.     

Generalized group actions in a global setting

We study generalized group actions on differentiable manifolds in the Colombeau framework, extending previous work on flows of generalized vector fields and symmetry group analysis of generalized solutions. As an application, we analyze group invariant generalized functions in this setting.     

Cubulating random groups in the square model

Our main result is that for densities < 3/10 a random group in the square model has the Haagerup property and is residually finite. Moreover, we generalize the Isoperimetric Inequality to some class of non-planar diagrams and, using this, we introduce a system of modified hypergraphs providing the structure of a space with walls on the Cayley complex of a random group. Then we show that the natural action of a random group on this space with walls is proper, which gives the proper action of a random group on a CAT(0) cube complex.     

A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP

In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the Lp-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.     

Ordering groups constructively

The existence of a linear order on a group that is compatible with the group structure generally requires transfinite methods. However, this can be circumvented by concentrating on the consistency of a suitable propositional theory. To this end, we work with Scott’s multiple-conclusion entailment relations to describe the positive cones of a group. The commutative case then leads to a constructive version of Levi’s theorem that an Abelian group be orderable if and only if it is torsion-free. Subsequently, Cederquist and Coquand’s fundamental theorem of entailment relations prompts a finitary version of Sikora’s theorem.     

基于模糊二元运算的直觉模糊群

为了使直觉模糊群也具有经典的结构,首先给出经典集合G的一种直觉模糊二元运算,利用这种直觉模糊二元运算定义了直觉模糊群,讨论这种直觉模糊群的一些性质,并给出直觉模糊群的两种等价定义。由于直觉模糊群具有和群一样经典的结构,因此,使直觉模糊代数的深入研究有了充分的理论基础。     

Lie gradings on associative algebras

In this paper we apply the method of functional identities to the study of group gradings by an abelian group G on simple Lie algebras, under very mild restrictions on the grading group or the base field of coefficients.     

On continuation of a topology from a system of generators of a group to a topology on the group

In this paper we establish conditions under which a topology is continued from a subset of a group to a topology on the group coordinated with the group operation.     

历届全国大学生数学建模竞赛专科组赛题的模糊综合评价

建立了在针对每一个待评方案的决策者数量不相等的情况下的多层次多属性模糊综合群决策模型,在对历届全国大学生数学建模竞赛专科组24个赛题进行重点调查的基础上,应用该模型对这些赛题进行了综合评价,评价结果验证了模型的有效性和可行性.     

分子格半群

在本文中，作者在格半群上引入了半群元和理想元的概念，使得半群（理想）和ＴＬ－Ｆｕｚｚｙ半群（理想）是其特例。在分子格半群上引入了群元和正规群元等概念，在更高的层次上统一了群和Ｌ－Ｆｕｚｚｙ群。