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）.

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.

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.

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.

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.

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.

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.

The Multi-sensitivity and Topological Sequence Entropy of Dynamical System with Group Action

In this paper,we study the relationship between the multi-sensitivity and the topological maximal sequence entropy of dynamical systems for general group action.Furthermore,we also discuss the consistency of multi-sensitivity of a dynamical system(G■X)and its hyperspace dynamical system G■K(X).Moreover,we research the relationship between the multi-sensitivity of two dynamical systems and the multi-sensitivity of their product space dynamical system.Finally,we prove that if the topological sequence entropy of G■X vanishes,then so does that of its induced system G■M(X);if the topological sequence entropy of G■X is positive,then that of its induced system G■M(X)is infinity.

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 Nonexistence of Sensitive Commutative Group Actions on Dendrites

In this paper, using the integral method observed by Mai Jiehua recently, we show that no dendrite admits a sensitive commutative group action.

Finite Group Action and Gromov-Witten Invariants in Symplectic Four-Manifolds

Let a finite group act semi-freely on a closed symplectic four-manifold with a 2-dimensional fixed point set. Then we show that the relative Gromov-Witten invariants are the same as the invariants on the quotient set-up with respect to the fixed point set.

Stronger Versions of Sensitivity for Minimal Group Actions

We study several stronger versions of sensitivity for minimal group actions,including nsensitivity,thick n-sensitivity and blockily thick n-sensitivity,and characterize them by the regionally proximal relation.

The nonexistence of sensitive commutative group actions on graphs

In this paper,we observe a special kind of continuous functions on graphs.By estimating the integrals of these functions,we prove that there are no sensitive commutative group actions on graphs.Furthermore,we consider a 1-dimensional continuum composed of a spiral curve and a circle and show that there exist sensitive homeomorphisms on it,which answers negatively a question proposed by Kato in 1993.

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

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

LOOP GROUP ACTIONS AND THE RIBAUCOUR TRANSFORMATIONS FOR FLAT LAGRANGIAN SUBMANIFOLDS

The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a purely algebraic algorithm. At the same time, it is shown that such Ribaucour transformation always comes with a permutability formula.

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.

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.

Group actions on treelike compact spaces

We show that group actions on many treelike compact spaces are not too complicated dynamically.We first observe that an old argument of Seidler(1990)implies that every action of a topological group G on a regular continuum is null and therefore also tame.As every local dendron is regular,one concludes that every action of G on a local dendron is null.We then use a more direct method to show that every continuous group action of G on a dendron is Rosen thal represent able,hence also tame.Similar resul ts are obtained for median pretrees.As a related result,we show that Helly's selection principle can be extended to bounded monotone sequences defined on median pretrees(for example,dendrons or linearly ordered sets).Finally,we point out some applications of these results to continuous group actions on dendrites.

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.

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。