A marker method for the solution of the damped Burgers' equation

A new method for the solution of the damped Burgers' equation is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details. The marker method is applicable to a general class of nonlinear dispersive partial differential equations. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Approximation of Matrices and a Family of Gander Methods for Polar Decomposition

Two matrix approximation problems are considered: approximation of a rectangular complex matrix by subunitary matrices with respect to unitarily invariant norms and a minimal rank approximation with respect to the spectral norm. A characterization of a subunitary approximant of a square matrix with respect to the Schatten norms, given by Maher, is extended to the case of rectangular matrices and arbitrary unitarily invariant norms. Iterative methods, based on the family of Gander methods and on Higham’s scaled method for polar decomposition of a matrix, are proposed for computing subunitary and minimal rank approximants. Properties of Gander methods are investigated in details. AMS subject classification (2000) 65F30, 15A18     

Asymptotic expansions in sequential estimation for the first-order random coefficient autoregressive model: Regenerative approach

Edgeworth expansions for the distribution of a sequential least squares estimator in the random coefficient autoregressive (RCA) model are derived. The regenerative approach to second-order asymptotic analysis of Markov-type statistical models is developed.     

Limits of parallelism in explicit ODE methods

Numerical methods for ordinary initial value problems that do not depend on special properties of the system are usually found in the class of linear multistage multivalue methods, first formulated by J.C. Butcher. Among these the explicit methods are easiest to implement. For these reasons there has been considerable research activity devoted to generating methods of this class which utilize independent function evaluations that can be performed in parallel. Each such group of concurrent function evaluations can be regarded as a stage of the method. However, it turns out that parallelism affords only limited opportunity for reducing the computing time with such methods. This is most evident for the simple linear homogeneous constant-coefficient test problem, whose solution is essentially a matter of approximating the exponential by an algebraic function. For a given number of stages and a given number of saved values, parallelism offers a somewhat enlarged set of algebraic functions from which to choose. However, there is absolutely no benefit in having the degree of parallelism (number of processors) exceed the number of saved values of the method. Thus, in particular, parallel one-step methods offer no speedup over serial one-step methods for the standard linear test problem. Although the implication of this result for general nonlinear problems is unclear, there are indications that dramatic speedups are not possible in general. Also given are some results relevant to the construction of methods.Work supported in part by National Science Foundation grants DMS 89 11410 and DMS 90 15533 and by US Department of Energy grant DOE DEFG02-87ER25026. Work of the second author was completed while at the University of Illinois.     

大规模界约束优化的子空间截断牛顿法

给出了大规模界约束优化的一个子空间截断牛顿法。利用截断牛顿法修正非有效约束所对应的变量，用投影梯度法修正有效约束所对应的变量，文中证明了方法的整体收敛性，并对方法进行了数值试验，且与子空间有限内存拟牛顿法进行了数值比较。     

脑细胞激活素药物的化学成分分析

采用日本岛津LC-60A型高压液相色谱仪和美国P-E3030型原子吸收分光光度计，对该药进行了氨基酸、维生素和化学元素的含量测定。结果表明，该药含有18种氨基酸，不少于3种维生素和20几种化学元素，为进一步改进该药物的合理配制方法和临床应用提供了参考数据。     

On disjoint configurations in infinite graphs

For a graph A and a positive integer n, let nA denote the union of n disjoint copies of A; similarly, the union of ?₀ disjoint copies of A is referred to as ?₀A. It is shown that there exist (connected) graphs A and G such that nA is a minor of G for all n??, but ?₀A is not a minor of G. This supplements previous examples showing that analogous statements are true if, instead of minors, isomorphic embeddings or topological minors are considered. The construction of A and G is based on the fact that there exist (infinite) graphs G₁, G₂,… such that G_i is not a minor of G_j for all i ≠ j. In contrast to previous examples concerning isomorphic embeddings and topological minors, the graphs A and G presented here are not locally finite. The following conjecture is suggested: for each locally finite connected graph A and each graph G, if nA is a minor of G for all n ? ?, then ?₀A is a minor of G, too. If true, this would be a far‐reaching generalization of a classical result of R. Halin on families of disjoint one‐way infinite paths in graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 222–229, 2002; DOI 10.1002/jgt.10016     

First-passage times in a critical stochastic model

Average first-passage times for a single-variable stochastic model with a critical fixed point at the origin are computed by exact enumeration. The numerical measurements show excellent agreement with analytical results. The scaling function approaches the predicted asymptotic dependence.     

用区域分解算法结合蒙特卡罗法求坦克温度场和红外辐射出射度

本文将区域分解算法和蒙特卡罗法相结合，求坦克温度场和红外辐射出射度．采用蒙特卡罗法计算辐射传递系数，可以考虑界面的复杂辐射特性，如：镜反射、各向异性发射、各向异性反射等；可直接考虑界面的复杂几何特性，如:相互遮挡、太阳入射方向上的投影面积等．引入辐射传递系数，分离了计算的难点，使得在时间域（计算步骤）上能把整个问题分解为若干个子问题并行处理、在空间域（计算区域）上将坦克分解为若干个子区域，缩小计算规模，并可使用多个处理器并行计算；同时减轻了蒙特卡罗法编程的难度，缩短了计算时间．