The number of powers of 2 in a representation of large even integers II

It is proved that for any integerk≥ 54 000, there isN _k >0 depending onk only such that every even integer ≥N _k is a sum of two odd prime numbers andk powers of 2. Project partially supported by RGC Research Grant (No.HKU 7122/97P) and Post-Doctoral Fellowship of the University of Hong Kong.     

Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

Equivalence of variational inequality problems to unconstrained minimization

In this paper we propose a class of merit functions for variational inequality problems (VI). Through these merit functions, the variational inequality problem is cast as unconstrained minimization problem. We estimate the growth rate of these merit functions and give conditions under which the stationary points of these functions are the solutions of VI. This work was supported by the state key project “Scientific and Engineering Computing”.     

CPL冷凝单管融化过程的双倒易边界元分析

1引言CPL（毛细泵两相流回路）能传输较高的热负荷，而且不需要循环泵、阀门等运动部件，重量轻可靠性好；在飞行器热控制方面有很好的应用前景[1]。CPL在恶劣的空间环境中运行，需要防止工作介质出现冷冻，为此，我们已经用解析[2]和数值的方法[3]进行了初步的分析，得到了一些可供工程设计参考应用的结果。另外，在恶劣的空间环境中，如果出现冻结，需要融化起动，热管的安全设计需要研究它的融化特性，以确保热管在空间能正常运行。双倒易边界元方法用Laplace基本解[4]，通过对一类偏微分方程两侧进行转化，将它全部转化为纯边界积分…     

关于混合型多项式Hammerstein积分方程正解迭代求法

本文给出了混合型多项式Ｈａｍｍｅｒｓｔｅｉｎ积分方程正解的迭代求法，并将所得结果应用到二阶非线性常微分方程的边值问题     

A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS_N) methods applied to the radiative transfer equation in the discrete ordinates (S_N) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S_N problems by using the LTS_N method. We show some numerical experiments for a typical model problem.     

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR NONLINEAR HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

The singularly perturbed boundary value problem for nonlinear higher order ordinary differential equation involving two small parameters has been considered. Under appropriate assumptions, for the three cases:ε/μ2→0(μ→0),μ2/ε→0 (ε→0) andε=μ2, the uniformly valid asymptotic solution is obtained by using the expansion method of two small parameters and the theory of differential inequality.     

VRPTW的扰动恢复及其TABU SEARCH算法

本文对带时间窗的车辆路线安排扰动恢复问题进行了讨论,分析了各种可能的扰动:增加减少客户,时间窗、客户需求及路线可行性的扰动,构造了扰动模型.利用禁忌搜索算法对问题进行求解,同时通过对模型参数重新设置,得到了多个满足要求的不同的解,这样使解更具有实际可行性和有效性.     

The destabilizing effect of boundary slip on Bénard convection

We investigate the influence of slip boundary conditions on the onset of Bénard convection in an infinite fluid layer. It is shown that the critical Rayleigh number is a decreasing function of the slip length, and therefore boundary slip is seen to have a destabilizing effect. Chebyshev‐tau and compound matrix formulations for solving the eigenvalue problem are presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Isotopic families of contact manifolds for elliptic PDE

A test for a function to be a solution of an elliptic PDE is given in terms of extensions, as solutions, from the boundaries inside the domains belonging to an isotopic family. It generalizes a result of Ehrenpreis for spheres moved along a straight line.