自由亚交换群的直积的检验元素

设Sri(i=1,2,…,n)为秩ri的自由亚交换群,G=Sr1×Sr2…×Srn为自由亚交换群的直积,本文证明了G有检验元素的充分必要条件为ri=2(i=1,2,…,n)．同时,还证明了g=(g1,g2,…,gn)为G的检验元素的充分必要条件是:gi∈S′2-1(i= 1,2,…,n),且{g1,g2,…,gn}为独立集．此外,我们给出了一类具体的检验元素．     

有限生成自由代数FV（LK）（n）的自同构群（英文）

本文研究了自同构群AutLk和AutFV(LK)(n)的结构问题.利用了正交模格及其自同构群的直积分解方法,获得了正交模格Lk和自由代数FV(LK)(n)的自同构群的直积分解式.     

AUTOMORPHISM GROUP OF FINITELY GENERATED FREE ALGEBRAS FV(Lκ)(n)

本文研究了自同构群AutLκ和AutFV(LK)(n)的结构问题.利用了正交模格及其自同构群的直积分解方法,获得了正交模格Lκ和自由代数FV(LK)(n)的自同构群的直积分解式.     

关于(QU)型模糊拓扑群的直积

研究(QU)型模糊拓扑群族直积,证明了任意(QU)型模糊拓扑群族的直积仍是(QU)型模糊拓扑群;研究了(QU)型模糊拓扑群族直积的模糊单位元之重域基的结构,得到了(QU)型模糊拓扑群族直积的一些重要性质.     

Fuzzy子群的直积特征

自A.Rosenfeld 1971年提出fuzzy子群的概念以来,关于fuzzy代数结构方面的讨论正在逐步深入下去。对fuzzy子群直积的研究已有些文章,如文[1],[2]等。本文以文[2]给出的fuzzy子群的直积概念,在§2中研究了直积fuzzy子群的几个特征性质;在§3中得到了直积群G×G上的fuzzy子群可分解为群G上fuzzy子群直积的充分必要条件。作为推论,得到了群G×G上fuzzy正规子群可分解为群G上正规子群直积的充分必要条件。     

关于T-S模的直觉模糊群的直积特征

首先将T模、S模的概念推广,并研究了推广的T-S模的基本性质,进而分别定义了在对偶模意义下直觉模糊群的外直积与内直积.最后,证明了直觉模糊群的两种直积在一定条件下是同构的.     

自由正交模格FMOk(n)的自同构群

文章先利用自同构映射保有限并的性质研究了一般正交模格的次直积的自同构群与自同构群的次直积的关系,再用块置换的方法研究了MOk的自同构群的生成元集,由此得到自由正交模格FMOk(n)的自同构群的直积分解式,从而完全解决了FMOk(n)的自同构群的结构问题.     

对角方阵的变换群

在不改变对角方阵各行、各列、主对角线、次对角线的元素之集的条件下,其变换群是n次对称群S_n的直积S_n×S_n的子群,因对角拉丁方、对角拉丁方正交侣、幻方、高次幻方、加乘幻方均属此类方阵,本文对构作这类对象及研究它们的计数有重要意义.     

群代数作用遍历性的一点注记

证明了由自由群整数环上一类元素确定的代数作用的遍历性,计算了Heisenberg群因子中特定元素的Fuglede-Kadison行列式值.     

有限维线性空间上的极大线性变换群在几个线性空间上的群作用

群作用是研究群(特别是有限群)的一个外部方法.首先构作域上一有限维线性空间上的全线性变换半群的极大群,其次给出了三个群作用:极大群在其幺元的不动点子空间上的一个(自然的)群作用,两个极大群的(外)直积在两个极大群的幺元的不动点子空间的(外)直和上的一个群作用,两个极大群的(外)直积在两个极大群的幺元的不动点子空间之间的所有线性映射构成之集上的一个群作用.     

Test elements of direct sums and free products of free Lie algebras

We give a characterization of test elements of a direct sum of free Lie algebras in terms of test elements of the factors. In addition, we construct certain types of test elements and we prove that in a free product of free Lie algebras, product of the homogeneous test elements of the factors is also a test element.     

Descent from the form ring and buchsbaum rings

An element it of a finitely generated free Lie algebra L is a test element if any endomorphism of L fixing u is an automorphism. We prove that test elements of L are precisely those elements not contained in any proper retract of L. In addition we characterize retracts of free Lie algebras.     

Factoring an Infinite Abelian Group by Subsets

By a theorem of L. Rédei if a finite abelian group is a direct product of its subsets such that each subset has a prime number of elements and contains the identity element of the group, then at least one of the factors must be a subgroup. The content of this paper is that this result holds for certain infinite abelian groups, too. Namely, for groups that are direct products of finitely many Prüferian groups and finite cyclic groups of prime power order, belonging to pairwise distinct primes.     

Cosserat Parameter Identification within the Frame of the Discrete Element Method

One of the main challenges using the Discrete Element Method is that there is no direct compliance to the well known continuum parameters such as elastic moduli. In this article we show how homogenization procedures using representative volume elements composed of discrete particles lead to Cosserat continua. Simulating a shear test with discrete elements it becomes obvious, that the evolving microstructure is mainly composed of contact chains that form triangles and quadrilaterals. For these contact chains we set up contact energies in normal and shear directions and combine those to derive the effective energy of the material. By comparison of this energy to a Cosserat energy we can derive formulas for the Lamé and Cosserat parameters. They are now only dependent on the interaction energies and radii of the particles. To show the validity of our assumptions and derivations we present some discrete element simulations of shear tests. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reaching the minimum ideal in a finite semigroup

We introduce the depth parameters of a finite semigroup, which measure how hard it is to produce an element in the minimum ideal when we consider generating sets satisfying some minimality conditions. We estimate such parameters for some families of finite semigroups, and we obtain an upper bound for wreath products and direct products of two finite (transformation) monoids.     

构造任意非协调四边形单元的新模式

通过对Q4元增加一个非协调高阶项．构造了一类新的非协调四边形单元，并证明由此产生的单元对任意四边形网格通过Irons分片检查和广义分片检查，且形状函敷不依赖于单元本身．QM5是其中的一个特例．数值结果表明，该类单元有很好的收敛效果．     

Test elements in pro-<Emphasis Type="Italic">p</Emphasis> groups with applications in discrete groups

Let G be a group. An element g ∈ G is called a test element of G if for every endomorphism ? : G → G, ?(g) = g implies ? is an automorphism. We prove that for a finitely generated profinite group G, g ∈ G is a test element of G if and only if it is not contained in a proper retract of G. Using this result we prove that an endomorphism of a free pro-p group of finite rank which preserves an automorphic orbit of a nontrivial element must be an automorphism. We give numerous explicit examples of test elements in free pro-p groups and Demushkin groups. By relating test elements in finitely generated residually finite-p Turner groups to test elements in their pro-p completions, we provide new examples of test elements in free discrete groups and surface groups. Moreover, we prove that the set of test elements of a free discrete group of finite rank is dense in the profinite topology.     

Efficient linear solvers for incompressible flow simulations using Scott‐Vogelius finite elements

Recent research has shown that in some practically relevant situations like multiphysics flows (Galvin et al., Comput Methods Appl Mech Eng, to appear) divergence‐free mixed finite elements may have a significantly smaller discretization error than standard nondivergence‐free mixed finite elements. To judge the overall performance of divergence‐free mixed finite elements, we investigate linear solvers for the saddle point linear systems arising in ((P_k)^d,P _k‐1^disc) Scott‐Vogelius finite element implementations of the incompressible Navier–Stokes equations. We investigate both direct and iterative solver methods. Due to discontinuous pressure elements in the case of Scott‐Vogelius (SV) elements, considerably more solver strategies seem to deliver promising results than in the case of standard mixed finite elements such as Taylor‐Hood elements. For direct methods, we extend recent preliminary work using sparse banded solvers on the penalty method formulation to finer meshes and discuss extensions. For iterative methods, we test augmented Lagrangian and \begin{align*}\mathcal{H}\end{align*} ‐LU preconditioners with GMRES, on both full and statically condensed systems. Several numerical experiments are provided that show these classes of solvers are well suited for use with SV elements and could deliver an interesting overall performance in several applications.© 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Domain Decomposition Preconditioners for Discontinuous Galerkin Discretizations of Compressible Fluid Flows

In this article we consider the application of Schwarz-type domain decomposition preconditioners to the discontinuous Galerkin finite element approximation of the compressible Navier-Stokes equations. To discretize this system of conservation laws, we exploit the (adjoint consistent) symmetric version of the interior penalty discontinuous Galerkin finite element method. To define the necessary coarse-level solver required for the definition of the proposed preconditioner, we exploit ideas from composite finite element methods, which allow for the definition of finite element schemes on general meshes consisting of polygonal (agglomerated) elements. The practical performance of the proposed preconditioner is demonstrated for a series of viscous test cases in both two- and three-dimensions.     

A sand surface element for efficient modeling of residual stress in castings

This article describes a method to efficiently predict residual stresses in foundry castings. We replace explicit modeling of the sand mold during stress analysis by using a locally applied boundary condition element. Methods are given for assigning appropriate values to the individual elements, and we present several example problems. In these test problems, we also evaluate several constitutive models for the sand. We find that plastic strains and displacements in the casting do not depend strongly on the sand constitutive model. Further, the stress states produced, when using the new surface elements, are generally in good agreement with those found using a full mold. The computational advantages of the new element are demonstrated.