LIE GROUP INTEGRATION FOR CONSTRAINED GENERALIZED HAMILTONIAN SYSTEM WITH DISSIPATION BY PROJECTION METHOD

For the constrained generalized Hamiltonian system with dissipation, by introducing Lagrange multiplier and using projection technique, the Lie group integration method was presented, which can preserve the inherent structure of dynamic system and the constraint-invariant. Firstly, the constrained generalized Hamiltonian system with dissipative was converted to the non-constraint generalized Hamiltonian system, then Lie group integration algorithm for the non-constraint generalized Hamiltonian system was discussed, finally the projection method for generalized Hamiltonian system with constraint was given. It is found that the constraint invariant is ensured by projection technique, and after introducing Lagrange multiplier the Lie group character of the dynamic system can't be destroyed while projecting to the constraint manifold. The discussion is restricted to the case of holonomic constraint. A presented numerical example shows the effectiveness of the method.

On the Structure of the Augmentation Quotient Group for Some Non-abelian p-groups

In this paper, we study the basis of augmentation ideals and the quotient groups of finite non-abelian p-group which has a cyclic subgroup of index p, where p is an odd prime, and k is greater than or equal to 3. A concrete basis for the augmentation ideal is obtained and then the structure of its quotient groups can be determined.

Multiplicative Jordan Decomposition in Integral Group Ring of Group K_8×C_5

In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hales A W,Passi I B S and Wilson L E in the paper 'The multiplicative Jordan decomposition in group rings II.

Towards Interaction,Communication and Integration of Ethnic Groups with Commonality:A Comparison of Inner Mongolia,Guangxi and Ningxia Autonomous Region

One crucial measure of strengthening and advancing the Party's work on ethnic affairs in the new era is to promote interaction,communication and integration of various ethnic groups,so as to enhance commonality.Entering the new era,Inner Mongolia,Guangxi and Ningxia have achieved remarkable results in encouraging interaction,communication and integration of various ethnic groups.By comparatively analyzing successes of the three autonomous regions through the perspective of promoting commonality,this article summarizes the following strategic revelations:1)we should comprehensively implement the Party's ethnic policies and ensure theactual implementation of mutual interaction,mutual communication and mutual integration of ethnic groups;2)we should proactively promote the substantial progress of the economy,so as to provide solid material foundation for mutual interaction,mutual communication and mutual integration of ethnic groups;3)we should facilitate activities that promote ethnic unity and progress,so that the promotion of interaction,communication and mutual integration of ethnic groups can be seen,be felt and gain actual outcomes;4)we should take measures that suit to local conditions and explore all-round embedding mechanisms in order to foster the ethos for mutual interaction,mutual communication and mutual integration of ethnic groups;5)we should make every effort to forge a strong sense of community for the Chinese nation and orient precisely to the cause of encouraging mutual interaction,mutual communication and mutual integration of ethnic groups.

Structure of augmentation quotients of finite homocyclic abelian groups

Let G be a finite abelian group and its Sylow p-subgroup a direct product of copies of a cyclic group of order p r , i.e., a finite homocyclic abelian group. Let Δ n (G) denote the n-th power of the augmentation ideal Δ(G) of the integral group ring ?G. The paper gives an explicit structure of the consecutive quotient group Q n (G) = Δ n (G)/Δ n+1(G) for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups.

Coleman Automorphisms of Holomorphs of Finite Abelian Groups

Let K be a finite abelian group and let H be the holomorph of K. It is shown that every Coleman automorphism of H is an inner automorphism. As an immediate consequence of this result, it is obtained that the normalizer property holds for H.

Integrated Groups and Smooth Distribution Groups

In this paper, we prove directly that α-times integrated groups define algebra homomorphisms. We also give a theorem of equivalence between smooth distribution groups and α-times integrated groups.

The Stable Behavior of the Augmentation Quotients of the Groups of Order p^5, I

In this article we describe the stable behavior of the augmentation quotients Qn （G） for the groups G of order p^5 with even numbers of generators, where p is an odd prime.

Class-Preserving Coleman Automorphisms of Finite Groups with Prescribed Centralizers

Let G be a finite group. It is proved that any class-preserving Coleman automorphism of G is an inner automorphism whenever G belongs to one of the following two classes of groups： （1） CN-groups, i.e., groups in which the centralizer of any element is nilpotent; （2） CIT-groups, i.e., groups of even order in which the centralizer of any involution is a 2-group. In particular, the normalizer conjecture holds for both CN-groups and CIT-groups. Additionally, some other results are also obtained.

Conjugacy Classes of Torsion in 4×4 Integral Symplectic Group

A complete list of representatives of conjugacy classes of torsion in 4×4 integral symplectic group is given in this paper. There are 55 distinct such classes and each torsion element has order of 2, 3, 4, 5, 6, 8, 10 and 12.

GENERALIZED INTUITIONISTIC FUZZY HYBRID CHOQUET AVERAGING OPERATORS

In this study a new hybrid aggregation operator named as the generalized intuitionistic fuzzy hybrid Choquet averaging（GIFHCA） operator is defined.Meantime,some desirable properties are studied, and several important cases are examined.Furthermore,we define the generalized Shapley GIFHCA （GS-GIFHCA） operator,which does not only overall consider the importance of elements and their ordered positions,but also globally reflect the correlations among them and their ordered positions.In order to simplify the complexity of solving a fuzzy measure,we further define the generalizedλ-Shapley GIFHCA（GλS-GIFHCA） operator.

L^p-L^q Estimates for a Class of Pseudo-Differential Equations and Their Applications

This paper is concerned with the L^p-L^q estimates of the solutions for a class of pseudodifferential equations under some suitable degenerate assumptions. As applications, these estimates can be used to show that a generalized Schroedinger operator with some integrable potential generates a fractionally integrated group in L^p（R^n）.