Lie Groups Actions on Non Orientable <i>n</i>-Dimensional Complex Manifolds

Analytic atlases on can be easily defined making it an n-dimensional complex manifold. Then with the help of bi-Möbius transformations in complex coordinates Abelian groups are constructed making this manifold a Lie group. Actions of Lie groups on differentiable manifolds are well known and serve different purposes. We have introduced in previous works actions of Lie groups on non orientable Klein surfaces. The purpose of this work is to extend those studies to non orientable n-dimensional complex manifolds. Such manifolds are obtained by factorizing with the two elements group of a fixed point free antianalytic involution of . Involutions h(z) of this kind are obtained linearly by composing special Möbius transformations of the planes with the mapping . A convenient partition of is performed which helps defining an internal operation on and finally actions of the previously defined Lie groups on the non orientable manifold are displayed.

THE SYSTEMS WITH ALMOST BANACH-MEAN EQUICONTINUITY FOR ABELIAN GROUP ACTIONS

In this paper,we present the concept of Banach-mean equicontinuity and prove that the Banach-,Weyl-and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent.Furthermore,we obtain that the topological entropy of a transitive,almost Banach-mean equicontinuous dynamical system of Abelian group action is zero.As an application of our main result,we show that the topological entropy of the Banach-mean equicontinuous system under the action of an Abelian groups is zero.

CHAOTIC GROUP ACTIONS

It is proved that there is no chaotic group actions on any topological space with free arc.In this paper the chaotic actions of the group like G×F ,where F is a finite group,are studied.In particular,under a suitable assumption,if F is a cyclic group,then the topological space which admits a chaotic action of Z×F must admit a chaotic homeomorphism.A topological space which admits a chaotic group action but admits no chaotic homeomorphism is constructed.

FUNDAMENTAL GROUPS OF CLOSED POSITIVELY CURVED MANIFOLDS WITH ALMOST DISCRETE ABELIAN GROUP ACTIONS

Let M be a closed n-manifold of positive sectional curvature. Assume that M admits an effective isometrical T1× Zpk-action with p prime. The main result of the article n＋1 for n 〉 5, then there exists a positive constant p（n）, is that ifk=lforn=3or k〉 n＋1/4 for n≥5,then there exists a positive constant p（n）,depending only on n, such that π1 （M） is cyclic if p ≥ p（n）.

Group Structure of Stabilizer of 2×2 Matrix under Similarity Action

This paper determines the group structure of stabilizer of 2×2 matrix under similarity action over arbitrary field. Then, the cardinal number of any orbit is calculated over finite field.

Group Action on Fuzzy Modules

In this article, we introduce the notion of fuzzy G-module by defining the group action of G on a fuzzy set of a Z-module M. We establish the cases in which fuzzy submodules also become fuzzy G-submodules. Notions of a fuzzy prime submodule, fuzzy prime G-submodule, fuzzy semi prime submodule, fuzzy G-semi prime submodule, G-invariant fuzzy submodule and G-invariant fuzzy prime submodule of M are introduced and their properties are described. The homomorphic image and pre-image of fuzzy G-submodules, G-invariant fuzzy submodules and G-invariant fuzzy prime submodules of M are also established.

The p.q.-Baer Property of Fixed Rings under Finite Group Action

A ring R is called right principally quasi-Baer (simply, right p.q.-Baer) if the right annihilator of every principal right ideal of R is generated by an idempotent. For a ring R, let G be a finite group of ring automorphisms of R. We denote the fixed ring of R under G by RG. In this work, we investigated the right p.q.-Baer property of fixed rings under finite group action. Assume that R is a semiprime ring with a finite group G of X-outer ring automorphisms of R. Then we show that: 1) If R is G-p.q.-Baer, then RG is p.q.-Baer;2) If R is p.q.-Baer, then RG are p.q.-Baer.

ON DENSITY OF SMOOTH ELEMENTS FOR AN ACTION OF AN AMENABLE GROUP

The aim of this paper is to prove the problem 2.2.2 in Bratteli's paper, It is proved that the problem is true for amenable group action.

The p.q.-Baer Property of Skew Group Rings under Finite Group Action

In this paper, Let R is a ring, G be a finite group of ring automorphisms of R. R*G denote the skew group ring of R under G. We investigate the right p.q.-Baer property of skew group rings under finite group action, Assume that R is a semiprime ring with a finite group G of X-outer ring automorphisms of R, then 1) R*G is p.q.-Baer if and only if R is G-p.q.-Baer;2) if R is p.q.-Baer, then R*G is p.q.-Baer.

Personalized Action Rules for Side Effects Object Grouping

There have been multiple techniques to discover action-rules, but the problem of triggering those rules was left exclusively to domain knowledge and domain experts. When meta-actions are applied on objects to trigger a specific rule, they might as well trigger transitions outside of the target action rule scope. Those additional transitions are called side effects, which could be positive or negative. Negative side effects could be devastating in some domains such as healthcare. In this paper, we strive to reduce those negative side effects by extracting personalized action rules. We proposed three object-grouping schemes with regards to same negative side effects to extract personalized action rules for each object group. We also studied the tinnitus handicap inventory data to apply and compare the three grouping schemes.

Lattice of Finite Group Actions on Prism Manifolds

The set of finite group actions (up to equivalence) which operate on a prism manifold M, preserve a Heegaard Klein bottle and have a fixed orbifold quotient type, form a partially ordered set. We describe the partial ordering of these actions by relating them to certain sets of ordered pairs of integers. There are seven possible orbifold quotient types, and for any fixed quotient type we show that the partially ordered set is isomorphic to a union of distributive lattices of a certain type. We give necessary and sufficent conditions, for these partially ordered sets to be isomorphic and to be a union of Boolean algebras.

Chemospecific and Regioselective Ethereal Methyl-Oxygen Bond Cleavage Behavior of Aroylated Dimethoxynaphthalenes by Combined Action of AlCl₃and Aroyl Group

AlCl3-mediated cleavage of ethereal methyl–oxygen bond in aroylated 2,7-dimethoxynaphthalene compounds proceeds chemospecifically and regioselectively. The ethereal bond at the β(2)-position of 1-monoaroylated 2,7-dimethoxynaphthalene is cleaved readily and predominantly against the β(7)-position, whereas scission of β-ethereal bonds of 1,8-diaroylated 2,7-dimethoxynaphthalene hardly undergoes like the non-aroylated mother frame compound of 2,7-dimethoxynaphthalene.

Differential Representations of SO(4) Dynamical Group

In this paper we present systematic differential representations for the dynamical group SO(4).Theserepresentations include the left and the right differential representations and the left and the right adjoint differentialrepresentations in both the group parameter space and its coset spaces.They are the generalization of the differentialrepresentations of the SO(3) rotation group in the Euler angles.These representations may find their applications in thestudy of the physical systems with SO(4) dynamical symmetry.

A Contribution to the DLF-Theory: On Singularities of the SU(2,2)-Action in U(1,1)

Segal’s chronometric theory is based on a space-time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is realized as the Lie group with a causal structure defined by an invariant Lorentzian form on u(1,1). Two Lie groups G, GF are introduced as representations of SU(2,2): they are related via conjugation by a certain matrix Win Gl(4). The linear-fractional action of G on D is well-known to be global, conformal, and it plays a crucial role in the analysis on space-time bundles carried out by Paneitz and Segal in the 1980’s. This analysis was based on the parallelizing group U(2). In the paper, singularities’ general (“geometric”) description of the linear-fractional conformal GF-action on F is given and specific examples are presented. The results call for the analysis of space-time bundles based on U(1,1) as the parallelizing group. Certain key stages of such an analysis are suggested.

Properties of Suborbits of the Dihedral Group D_nActing on Ordered Subsets

A group action on a set is a process of developing an algebraic structure through a relation defined by the permutations in the group and the elements of the set. The process suppresses most of the group properties, emphasizing the permutation aspect, so that the algebraic structure has a wider application among other algebras. Such structures not only reveal connections between different areas in Mathematics but also make use of results in one area to suggest conjectures and also prove results in a related area. The structure (G, X) is a transitive permutation group G acting on the set X. Investigations on the properties associated with various groups acting on various sets have formed a subject of recent study. A lot of investigations have been done on the action of the symmetric group Sn on various sets, with regard to rank, suborbits and subdegrees. However, the action of the dihedral group has not been thoroughly worked on. This study aims at investigating the properties of suborbits of the dihedral group Dn acting on ordered subsets of ?X={1,2,...,N}. The action of Dn on X[r], the set of all ordered r-element subsets of X, has been shown to be transitive if and only if n = 3. The number of self-paired suborbits of Dn acting on X[r] has been determined, amongst other properties. Some of the results have been used to determine graphical properties of associated suborbital graphs, which also reflect some group theoretic properties. It has also been proved that when G = Dn acts on ordered adjacent vertices of G, the number of self-paired suborbits is n + 1 if n is odd and n + 2 if n is even. The study has also revealed a conjecture that gives a formula for computing the self-paired suborbits of the action of Dn on its ordered adjacent vertices. Pro-perties of suborbits are significant as they form a link between group theory and graph theory.

The Orbital Graph of Primitive Group with Socle A7 ×A7

In this paper, we mainly study the orbital graphs of primitive groups with the socle A7 x A7 which acts by diagonal action. Firstly, we calculate the element conjugate classes of A7, then we discuss the stabilizer of two points in A7. Finally, according to the relation between suborbit and orbital, we obtain the orbitals, and determine the orbital graphs.

基于深度学习的群体动作识别综述

不同于传统的简单动作识别,群体动作识别需要理解场景中由若干人物的单人动作和他们之间的交互动作构成的复杂语义.近年来,群体动作识别在公共安全监控、体育视频分析和社会角色理解等领域的研究与应用引起了学者们的广泛关注.但是现有能够帮助学者们快速了解研究概况的中文文献很少且用于归纳和分析的依据较为笼统.为此,本文旨在综述近十年来基于深度学习的群体动作识别的研究进展.首先,本文介绍了群体动作识别的问题与定义,总结了现有解决方案的核心流程和该研究的关键挑战.然后,本文针对现有研究中的两个核心内容,即个体动作特征的提取及其关联建模,对现有文献作出了归纳与分析.具体而言,本文介绍并总结了群体动作研究中常用的人体行为特征,并将现有关联建模类型归纳为三类,即线性关联、序列关联和图关联.此外,本文还列举了现有的十二种可用于群体动作研究的视频数据集,并在三个常用数据集上对目前流行的方法进行了对比与分析.最后,本文研判了几个更具挑战的未来研究趋势.综上,本文剖析了群体动作识别的核心研究思路及未来研究趋势,有助于相关研究人员快速了解群体动作识别的研究概况.

群作用下逆极限空间的G-平均跟踪性和G-链传递

为了研究群作用下逆极限空间的G-平均跟踪性和G-链传递的动力学性质,利用原空间和逆极限空间之间的关系,得到以下结果:自映射f具有G-平均跟踪性与移位映射σ具有G-平均跟踪性是等价条件;自映射f是G-链传递与移位映射σ是G-链传递是等价条件。

A Note on the Entropy for Heisenberg Group Actions on the Torus

In this paper,the entropy of discrete Heisenberg group actions is considered.Let α be a discrete Heisenberg group action on a compact metric space X.Two types of entropies,h and h(α)are introduced,in which h is defined in Ruelle’s way and h(α) is defined via the natural extension of α.It is shown that when X is the torus and α is induced by integer matrices then h is zero and h(α) can be expressed via the eigenvalues of the matrices.

论证券特别代表人诉讼中和解的选择退出权

健全证券特别代表人诉讼中的和解机制,是完善我国现代资本市场司法制度的时代性议题。投资人在证券群体性诉讼中享有退出和解的权利,也是全球性的一种法治共识。在比较法视野上,和解退出机制具有差异性、权利性与普遍性的特征。其中,美国证券集团诉讼和解的经验表明,投资人的选择退出权虽极少被行使,却是投资人不可或缺的权利,并承载着美国程序正义的理念。对此,我国证券特别代表人诉讼退出和解机制的完善也需要借鉴比较法上的经验,确保和解程序的代表性。具体而言,应从限制和解金额、完善和解通知与听证程序、强化司法监督三方面着手,探寻我国选择退出机制的改良方案。