基于公共因子扩展的因子分析的EM算法

在一般因子分析模型的基础上,假设连续的潜在向量(公共因子)与另一观察随机向量有关,并假定是一个多元线性回归模型,对由此扩展的因子分析模型进行分析.主要通过EM算法给出模型中参数的估计.文中给出了它的详细推导过程.     

三元对称形式的Schur分拆与不等式的可读证明

本文给出了一类三元对称形式(即对称齐次多项式)的一种分拆法,即将此类多项式表示成一类特定形式的正半定对称形式的线性组合,介绍分拆算法．并由此而给出了三元对称形式半正定的一个充分条件．     

广义混合隐拟h变分不等式的解的存在性与算法

本文在Hilbert空间中,引入了一类广义混合隐拟h变分不等式.运用变分原理,给出了广义混合隐拟h变分不等式逼近解的迭代算法,证明了这类变分不等式解的存在性定理,同时,得到迭代序列的收敛性.并改进和推广了[6~8]一些已知结果.     

Approximation of the steepest descent direction for the O-D matrix adjustment problem

In this paper, a method to approximate the directions of Clarke's generalized gradient of the upper level function for the demand adjustment problem on traffic networks is presented. Its consistency is analyzed in detail. The theoretical background on which this method relies is the known property of proximal subgradients of approximating subgradients of proximal bounded and lower semicountinuous functions using the Moreau envelopes. A double penalty approach is employed to approximate the proximal subgradients provided by these envelopes. An algorithm based on partial linearization is used to solve the resulting nonconvex problem that approximates the Moreau envelopes, and a method to verify the accuracy of the approximation to the steepest descent direction at points of differentiability is developed, so it may be used as a suitable stopping criterion. Finally, a set of experiments with test problems are presented, illustrating the approximation of the solutions to a steepest descent direction evaluated numerically. Research supported under Spanish CICYT project TRA99-1156-C02-02.     

Ising模型的并行计算

以Ising模型为例,介绍有关格点系统的Monte Carlo数值模拟并行算法的设计和编程,并给出在本组建造的PC集群式高性能并行计算系统上的测量结果.本文的结果对格点量子色动力学的大规模数值模拟研究有一定的参考价值     

ON THE BOTTLENECK CAPACITY EXPANSION PROBLEMS ON NETWORKS

This article considers a class of bottleneck capacity expansion problems. Such problems aim to enhance bottleneck capacity to a certain level with minimum cost. Given a network G(V, A, C) consisting of a set of nodes V= {v1,v2,…,vn},a set of arcs A ■ {(vi, vj) | i=1,2,…, n;j=1,2,…,n} and a capacity vector C. The component cij of C is the capacity of arc (vi ,vj). Define the capacity of a subset A' of A as the minimum capacity of the arcs in A, the capacity of a family F of subsets of A is the maximum capacity of its members. There are two types of expanding models. In the arc-expanding model, the unit cost to increase the capacity of arc (vi, vj) is wij. In the node-expanding model, it is assumed that the capacities of all arcs (vi,vj) which start at the same node vi should be increased by the same amount and that the unit cost to make such expansion is wi. This article considers three kinds of bottleneck capacity expansion problems (path, spanning arborescence and maximum flow) in both expanding models. For each kind of expansion problems, this article discusses the characteristics of the problems and presents several results on the complexity of the problems.     

Modeling of one-dimensional smoldering of polyurethane in microgravity conditions

Results are presented from a model of forward smoldering combustion of polyurethane foam in microgravity. The transient one-dimensional numerical-model is based on that developed at the University of Texas at Austin. The conservation equations of energy, species, and mass in the porous solid and in the gas phases are numerically solved. The solid and the gas phases are not assumed to be in thermal or in chemical equilibrium. The chemical reactions modeled consist of foam oxidation and pyrolysis reactions, as well as char oxidation. The model has been modified to account for new polyurethane kinetics parameters and radial heat losses to the surrounding environment. The kinetics parameters are extracted from thermogravimetric analyses published in the literature and using Genetic Algorithms as the optimization technique. The model results are compared with previous tests of forward smoldering combustion in microgravity conducted aboard the NASA Space Shuttle. The model calculates well the propagation velocities and the overall smoldering characteristics. Direct comparison of the solution with the experimental temperature profiles shows that the model predicts well these profiles at high temperature, but not as well at lower temperatures. The effect of inlet gas velocity is examined, and the minimum airflow for ignition is identified. It is remarkable that this one-dimensional model with simplified kinetics is capable of predicting cases of smolder ignition but with no self-propagation away from the igniter region. The model is used for better understanding of the controlling mechanisms of smolder combustion for the purpose of fire safety, both in microgravity and normal gravity, and to extend the unique microgravity data to wider conditions avoiding the high cost of space-based experiments.     

High‐order upwind compact scheme and simulation of turbulent premixed V‐flame

A high‐order accurate upwind compact difference scheme with an optimal control coefficient is developed to track the flame front of a premixed V‐flame. In multi‐dimensional problems, dispersion effect appears in the form of anisotropy. By means of Fourier analysis of the operators, anisotropic effects of the upwind compact difference schemes are analysed. Based on a level set algorithm with the effect of exothermicity and baroclinicity, the flame front is tracked. The high‐order accurate upwind compact scheme is employed to approximate the level set equation. In order to suppress numerical oscillations, the group velocity control technique is used and the upwind compact difference scheme is combined with the random vortex method to simulate the turbulent premixed V‐flame. Distributions of velocities and flame brush thickness are obtained by this technique and found to be comparable with experimental measurement. Copyright © 2005 John Wiley & Sons, Ltd.     

基于超声波测量技术的颗粒尺寸分布模型的研究

提出了一种利用单颗粒背向散射信号来进行粒径分布估算的超声波测量技术,系统阐述了其 理论基础及基本工作原理。被测颗粒的散射信号幅度与它在探测区中的位置、颗粒尺寸和形状有关。 通过理论分析,建立了一个可用于描述散射信号幅度概率分布与颗粒系尺寸分布之间关系的数学模 型,对该模型的反演计算便可得到颗粒系的尺寸分布信息。为了避免求解过程中的病态系数矩阵问 题,将模型求解转化成了易于解决的最优化问题。仿真实例结果验证了该技术的可行性。     

计算数学与科学工程计算及其在中国的若干发展 (迎接ICM2002特约文章)

本文论述了计算数学与科学工程计算的重要性，回顾了近50年来这一学科在中国的发展，特别是冯康的杰出贡献，介绍了国家重点基础研究发展规划相关项目的研究课题。