广义Sierpinski集

本文考察了包括平面上的各种广义 Cantor集 ,Sierpinski集和包括某些连续不可微曲线在内的广义 Sierpinski集 .由相似变换 ,导出了它们的级数表达式 ,并利用它和字符串空间的对应关系 ,计算出它们的Hausdorff维数     

前缘弯掠斜流转子叶顶间隙流动特性数值分析

本文对前缘弯掠斜流转子叶顶间隙内的流动特性进行了数值分析。结果表明:叶顶间隙气流与主流发生卷吸而生成泄漏涡。泄漏涡作用的区域具有较低的压力分布。在叶片通道内,泄漏涡沿着与转子旋向相反的方向朝相邻叶片的压力面移动。大间隙时的泄漏涡比小间隙时强烈。低流量时泄漏涡的作用区域比高流量时大。在各种流量特性下,叶顶尾缘近吸力面区域都存在着二次间隙流。     

矩阵方程AXB=D的最小二乘Hermite解及其加权最佳逼近

本中,我们讨论了矩阵方程AXB=D的最小二乘Hermite解,通过运用广义奇异值分解(GSVD)，获得了解的通式。此外,对于给定矩阵F，也得到了它的加权最佳逼近表达式。     

On the structure of the optimal server control for fluid networks

This paper derives the optimal trajectories in a general fluid network with server control. The stationary optimal policy in the complete state space is constructed. The optimal policy is constant on polyhedral convex cones. An algorithm is derived that computes these cones and the optimal policy. Generalized Klimov indices are introduced, they are used for characterizing myopic and time-uniformly optimal policies.Received: November 2004 / Revised: February 2005The research of this author has been supported by the project ‘‘Stochastic Networks’’ of the Netherlands Organisation for Scientific Research NWO.     

Geometric quadrisection in linear time, with application to VLSI placement

We consider the following problem: given a set of points in the plane, each with a weight, and capacities of the four quadrants, assign each point to one of the quadrants such that the total weight of points assigned to a quadrant does not exceed its capacity, and the total distance is minimized.

This problem is most important in placement of VLSI circuits and is likely to have other applications. It is NP-hard, but the fractional relaxation always has an optimal solution which is “almost” integral. Hence for large instances, it suffices to solve the fractional relaxation. The main result of this paper is a linear-time algorithm for this relaxation. It is based on a structure theorem describing optimal solutions by so-called “American maps” and makes sophisticated use of binary search techniques and weighted median computations.

This algorithm is a main subroutine of a VLSI placement tool that is used for the design of many of the most complex chips.     

The Best Lower Bound for the Permanent of a Correlation Matrix of Rank Two

If 1≤k≤n, then Cor(n,k) denotes the set of all n×n real correlation matrices of rank not exceeding k. Grone and Pierce have shown that if A∈Cor (n, n-1), then per(A)≥n/(n-1). We show that if A∈Cor(n,2), then , and that this inequality is the best possible.     

A grid‐free upwind relaxation scheme for inviscid compressible flows

A new grid‐free upwind relaxation scheme for simulating inviscid compressible flows is presented in this paper. The non‐linear conservation equations are converted to linear convection equations with non‐linear source terms by using a relaxation system and its interpretation as a discrete Boltzmann equation. A splitting method is used to separate the convection and relaxation parts. Least squares upwinding is used for discretizing the convection equations, thus developing a grid‐free scheme which can operate on any arbitrary distribution of points. The scheme is grid free in the sense that it works on any arbitrary distribution of points and it does not require any topological information like elements, faces, edges, etc. This method is tested on some standard test cases. To explore the power of the grid‐free scheme, solution‐based adaptation of points is done and the results are presented, which demonstrate the efficiency of the new grid‐free scheme. Copyright © 2005 John Wiley & Sons, Ltd.     

矩阵对角相似的图论判别法

本文证明了任意两个ｎ阶复矩阵Ａ和Ｂ为对角相似的充要条件是：它们有相同的伴随有向图，并且以此有向图为基础有向图，以Ａ和Ｂ的对应非零元素比值为弧权值的赋权有向图满足“无向圈平衡条件”。我们还给出了矩阵对角相似条件在非负矩阵谱理论研究中的一个应用。     

具有奇异值分解性质的代数

设F为一个域,R为一个带有对合的F-代数,如果R上每一个矩阵都有奇异值分解(简称SVD),则称R为一个有SVD性质的F-代数.本文指出:R为一个有SVD性质的F-代数的充要条件是:R同构于R~+,或R~+上二次扩域,或R~+上四元数体((-1,-1)/R~+),其中R~+为R的对称元集合,并且R~+为一个Galois序闭域.