On Super Hamiltonian Semigroups

The concept of super hamiltonian semigroup is introduced. As a result, the structure theorems obtained by A. Cherubini and A. Varisco on quasi commutative semi-groups and quasi hamiltonian semigroups respectively are extended to super hamiltonian semigroups.     

在可交换四元数空间中的双曲方程的特征边值问题

讨论了一阶和二阶双曲复方程的特征边值问题.对其中两种线性方程,分别在不同的情况下获得通解和可解条件.而对于拟线性的二阶双曲复方程,证明了解的存在性和唯一性.     

On Polynomial Functions over Finite Commutative Rings

Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained.     

Sparse generalized Fourier transforms

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast. Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant matrix. By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method. A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are preserved. AMS subject classification (2000)  43A30, 65T99, 20B25     

C^＊—模理论的若干结果

本文把代数结构与分析体系结合起来，运用同调的方法，较系统地确定了A上C^*－模的部分理论，这里A为复数域C上的交换C^*－代数。即不仅定义了与C^*－模有关的某些新概念，而且还得到了有关C^*－模的若干结果。     

On idempotents of a class of commutative rings

Abstract

In the present work, a procedure for determining idempotents of a commutative ring having a sequence of ideals with certain properties is presented. As an application of this procedure, idempotent elements of various commutative rings are determined. Several examples are included illustrating the main results.     

图表追踪的一种机器实现方法

交换图表追踪法是同调代数中一种重要的证明方法.本文提出了一种基于前推的交换图表追踪的机器实现方法,它可以证明同调代数中一系列基于交换图的定理.该方法从定理的结论出发,通过构造辅助元素以及对辅助元素进行推导,能在有限步内给出定理的证明.本文提出的前推方法已经在Java开发平台上实现,同调代数中的五引理、九引理、蛇引理等的证明都可以由我们的程序自动产生.     

广义分布参数系统的状态反馈稳定性问题(1)

关于系统的状态反馈稳定性问题的研究一直是现代控制理论研究的重要问题之一.广义分布参数系统是比分布参数系统更广的一类系统,在研究复合材料热导体中的温度分布等问题时会出现这样的系统.本文讨论了H ilbert空间中一阶广义分布参数系统的状态反馈稳定性问题.应用泛函分析及线性算子半群理论的方法给出了使闭环广义分布参数系统渐进稳定的充要条件,充分条件及状态反馈的构造性表达式.这对研究广义分布参数系统的状态反馈稳定性问题具有重要的理论价值.     

Associated primes of graded components of local cohomology modules

The -th local cohomology module of a finitely generated graded module over a standard positively graded commutative Noetherian ring , with respect to the irrelevant ideal , is itself graded; all its graded components are finitely generated modules over , the component of of degree . It is known that the -th component of this local cohomology module is zero for all > 0$">. This paper is concerned with the asymptotic behaviour of as .

The smallest for which such study is interesting is the finiteness dimension of relative to , defined as the least integer for which is not finitely generated. Brodmann and Hellus have shown that is constant for all (that is, in their terminology, is asymptotically stable for ). The first main aim of this paper is to identify the ultimate constant value (under the mild assumption that is a homomorphic image of a regular ring): our answer is precisely the set of contractions to of certain relevant primes of whose existence is confirmed by Grothendieck's Finiteness Theorem for local cohomology.

Brodmann and Hellus raised various questions about such asymptotic behaviour when f$">. They noted that Singh's study of a particular example (in which ) shows that need not be asymptotically stable for . The second main aim of this paper is to determine, for Singh's example, quite precisely for every integer , and, thereby, answer one of the questions raised by Brodmann and Hellus.