Irregularities of distribution with respect to strips

Summary A lower bound is established for the strip discrepancy of a broad class of point distributions. The bound implies unbounded strip discrepancy for equally weighted point distributions under favorable conditions. The methods of proof use notions from integral geometry.     

Mathematical modeling of flows through inelastic porous solids

We propose a framework, based on classical mixture theory, to describe the isothermal flow of an incompressible fluid through a deformable inelastic porous solid. The modeling of the behavior of the inelastic solid takes into account changes in the elastic response due to evolution in the microstructure of the material. We apply the model to a compression layer problem. The mathematical problem generated by the model is a free boundary problem.     

Multilevel preconditioners for a quadrature Galerkin solution of a biharmonic problem

Efficient multilevel preconditioners are developed and analyzed for the quadrature finite element Galerkin approximation of the biharmonic Dirichlet problem. The quadrature scheme is formulated using the Bogner–Fox–Schmit rectangular element and the product two‐point Gaussian quadrature. The proposed additive and multiplicative preconditioners are uniformly spectrally equivalent to the operator of the quadrature scheme. The preconditioners are implemented by optimal algorithms, and they are used to accelerate convergence of the preconditioned conjugate gradient method. Numerical results are presented demonstrating efficiency of the preconditioners. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

Adaptive Algorithm for Constrained Least-Squares Problems

This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss–Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd–Omojokun trust-region method and the Powell damped BFGS line search method.     

The mapping properties of the radiosity operator along an edge

In this article we study the radiosity operator along an edge between two adjacent half‐planes. First we show that the radiosity operator is invertible in a whole scale of anisotropic Sobolev spaces. In the absence of any shadows we are able to derive regularity properties of the solution, which depend only on the angle between the half‐planes, the reflectivity coefficients and the right‐hand side. This work can be considered as a supplement to the article of Rathsfeld (Mathematical Methods in the Applied Sciences 1999; 22 : 217–241). Copyright © 2002 John Wiley & Sons, Ltd.     

Stability Properties of Feynman's Operational Calculus for Exponential Functions of Noncommuting Operators

Stability properties of Feynman's operational calculus are addressed in the setting of exponential functions of noncommuting operators. Applications of some of the stability results are presented. In particular, the time-dependent perturbation theory of nonrelativistic quantum mechanics is presented in the setting of the operational calculus and application of the stability results of this paper to the perturbation theory are discussed.     

拆边法求最短路径

本文利用局部比较法 ,在图中定义子图、无效路径、以及可去边 .利用推导的有关定理 ,拆去可去边 ,利用最短路径相同的等价性 ,达到化简图 ,从而求出最短路径     

A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP

In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the Lp-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.     

Integral Inequalities and Global Solutions of Semilinear Evolution Equations

A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality.     

最速下降规则不失为一可用规则

本从统计意义上平均迭代次数的观点出发，指出求解线性规划的最速下降规则是可取的，好用的。