热传导问题的一种近似解法

本文在给定的精度要求下,利用多项式及Fourier级数,给出了求热传导方程Cauchy问题在某处的近似解的方法,并把此方法推广成为求解任一有界域上满足给定精度要求的近似解的方法。     

Integral operators with Green's function type kernel

A variant of the Nyström method based on Simpson's rule is presented. This is designed to deal with integral operators with kernels k(s, t) that are not continuous along the diagonal s = t. A complete analysis is carried out, generalizations for other interpolatory quadrature rules are proposed; also a variant using Gaussian quadrature is considered and examples are given.     

On the use of loss functions in the changepoint problem

Summary We consider a sequence of independent random variables whose densities depend on a parameter which is subject to a change at an unknown time point. A Bayesian decision-theoretic approach is used to obtain an optimal choice of changepoint. The exponential and multivariate normal models are analyzed, and some numerical examples are given.     

A new simplicial variable dimension algorithm to find equilibria on the product space of unit simplices

A new simplicial variable dimension restart algorithm is introduced to solve the nonlinear complementarity problem on the product spaceS of unit simplices. The triangulation which underlies the algorithm differs from the triangulations ofS used thus far. Moreover, the number of rays along which the algorithm can leave the arbitrarily chosen starting point is much larger. More precisely, there is a ray leading from the starting point to each vertex ofS. In caseS is the product ofn one-dimensional unit simplices the alogrithm is similar to the octahedral algorithm onR ⁿ having 2 ⁿ rays. Also, the accuracy of an approximate solution in the terminal simplex of the algorithm is in general better than for the other algorithms onS. Computational results will show that the number of iterations for the new algorithm is much less. The examples concern the computation of equilibria in noncooperative games, exchange economies and trade models. This author is financially supported by the Netherlands Organisation for the Advancement of Pure Research (ZWO), Grant 46-98. This research is part of the VF-program “Equilibrium and Disequilibrium in Demand and Supply” which has been approved by the Netherlands ministry of education and sciences.     

Q-superlinear convergence of the iterates in primal-dual interior-point methods

Sufficient conditions are given for the Q-superlinear convergence of the iterates produced by primal-dual interior-point methods for linear complementarity problems. It is shown that those conditions are satisfied by several well known interior-point methods. In particular it is shown that the iteration sequences produced by the simplified predictor–corrector method of Gonzaga and Tapia, the simplified largest step method of Gonzaga and Bonnans, the LPF+ algorithm of Wright, the higher order methods of Wright and Zhang, Potra and Sheng, and Stoer, Wechs and Mizuno are Q-superlinearly convergent. Received: February 9, 2000 / Accepted: February 20, 2001?Published online May 3, 2001     

On reductions for the Steiner Problem in Graphs

Several authors have demonstrated how reductions can be used to improve the efficiency with which the Steiner Problem in Graphs can be solved. Previous reduction algorithms have been largely ad hoc in nature. This paper uses a theory of confluence to show that, in many cases, all maximal reduction sequences are equivalent, gaining insights into the design of reduction algorithms that obtain a maximum degree of reduction.     

EXISTENCE AND UNIQUENESS THEOREMS FOR HIGHER-ORDER BOUNDARY VALUE PROBLEMS

An existence and uniqueness of solutions for boundary value problemsandare established, by employing a priori estimates for all solutions and the Schau-der fixed point theorem. Some of these results extend earlier results due toUsmani(1979), Yang(1988), and Pei(1997).     

A note on the spectrum of an upper triangular operator matrix

Let be a upper triangular operator matrix acting on the Banach space . We investigate the set of the operators for which , where denotes the spectrum.

     

New methods for calculating the dew/bubble curves of classical model fluids

We describe two new methods for locating the dew/bubble curves of fluids. One is a numerical method and the other an analytical method based on the use of series expansions. The utility of these two methods is illustrated by application to a simple one-component fluid model and to several model polydisperse fluids. The numerical method is based on a new geometric representation of the equilibrium conditions-similar in spirit to the geometric representations often used for solving the equilibrium conditions of pure fluids. Our calculations show that the series-expansion technique can be quite effective at producing accurate representations of the phase boundaries.