C^n单位球上的R-q值Dirichlet型函数

本文研究了Cn单位球上的Rademacher-q余型值的Dnμ函数,利用鞅论和Banach空间几何学的知识,将标量值Dnμ空间函数空间的结果推广到Rademacher-q余型值.Dnμ函数空间上来,并且刻划了Rademacher-q余型空间.     

Cauchy-Stieltjes积分和面积平均p叶函数

本文研究由Cauchy-Stieltjes积分形成的函数空间Fα.首先给出这个空间的一个等价定义,然后研究面积平均p叶函数的对数函数和这个函数空间的关系,最后对单叶函数的情形做进一步的讨论.根据这种研究,我们得到了有界单叶函数的系数增长估计,这是目前最好的结果.     

度量测度空间中Sobolev类Banach空间值函数的刻画（英文）

本文研究了在指标是无穷大时欧式空间情形下Sobolev函数类理论和指标是有限常数时度量空间下Sobolev类Banach空间值函数理论.利用Banach空间理论和位势理论的方法,得到了在指标是无穷大时度量测度空间中Sobolev类Banach空间值函数的各种刻画,进而比较了该Sobolev类与对应的Lipschitz类和Hajlasz-Sobolev类.所获结果推广了欧式空间和度量测度空间中Sobolev函数类相应的结论.     

四元数值函数空间L~1上有界右线性算子的积分表示

基于复Hilbert空间上丰富的算子理论,四元数函数空间与复值函数空间的区别和联系,将讨论四元数值函数空间L~1上有界右线性算子的积分表示.     

整函数空间AH-Ω中的可除性问题

本文给出了一个解决整函数空间AH-Ω中可除性问题的系统方法.利用次调和函数和加权函数系以及AH-Ω空间中函数的Phragm∈n-“ndel甜性质,刻划了可除空间中函数和加权系的特性,并给出了若干等价的判别条件.     

Weighted estimates for commutators of higher dimensional Hardy operators

得到了由加权Lipschitz函数(或加权CMO函数)和n维Hardy算子生成的交换子在一些函数空间的有界性,例如加权Lebesgue空间,加权Herz型空间.     

广义函数空间上Drygas型函数方程的稳定性

在广义函数空间上重新定义了Drygas型函数方程的稳定性,然后利用高斯变换将广义函数空间上的函数方程稳定性转换为R~(n+1)空间上的光滑函数方程的稳定性.在求得正则化的函数方程稳定性后,利用广义函数与正则化函数间的关系给出在广义函数空间上的Drygas型函数方程的Hyers-Ulam-Rassias型稳定性.     

Dirichlet空间中的正交函数

主要考虑了Dirichlet空间中的正交函数.主要结论表明单位圆盘中的一个解析自映射是Dirichlet空间中的正交函数,当且仅当其所对应的计数函数是本质径向的;当且仅当其所对应的诱导测度是径向的.作为主要结论的一个应用,给出了单位圆盘上的单叶解析函数和闭单位圆盘上的解析函数是Dirichlet空间中正交函数的完全刻画.     

g函数,弱基g函数和空间的度量化

函数刻画广义度量空间，最早可追溯至Heath和Hodel的工作. 近些年来，Nagat a和一些拓扑学者利用g函数系统地研究了度量化问题. 该文引入弱基g函数的概念，利用它给出拓扑空间度量化的一些等价刻画, 推广了前人的相关工作. 证明了拓扑空间X可以度量化，当且仅当X有弱基g函数满足条件(1)和(7).     

超空间上k-正则函数及其相关函数的性质

本文首先给出了超空间上高阶Cauchy-Pompeiu公式,然后由超空间上微分算子之间的缠绕关系,分别讨论了正则函数和k-正则函数及调和函数和k-调和函数之间的关系.最后,得到超空间上Cauchy-Riemann型方程.     

Improving the accuracy of solutions of the linear second kind volterra integral equations system by using the taylor expansion method

This paper presents a new and an efficient method for determining solutions of the linear second kind Volterra integral equations system. In this method, the linear Volterra integral equations system using the Taylor series expansion of the unknown functions transformed to a linear system of ordinary differential equations. For determining boundary conditions we use a new method. This method is effective to approximate solutions of integral equations system with a smooth kernel, and a convolution kernel. An error analysis for the proposed method is provided. And illustrative examples are given to represent the efficiency and the accuracy of the proposed method.     

线性无量纲化方法对比及反向指标正向化方法

线性无量纲化方法的对比及反向指标的正向化方法都是综合评价的重要研究内容。从指标差异信息的角度,以TOPSIS、基于街区距离的TOPSIS和线性加权综合法为例,基于理论推导和实证分析对比了常用的线性无量纲化方法,并提出了两种反向指标正向化方法。研究发现,对于线性加权综合法和TOPSIS,不同线性无量纲化方法下同一指标归一化极差的不同是导致排序结果存在差异的关键因素;本文提出的反向指标正向化方法,不仅可以保证正向化前后TOPSIS、基于街区距离的TOPSIS的评价值不变,也可以实现反向指标正向化后线性加权综合法与基于街区距离的TOPSIS在排序目的上的等效性。最后,本文提出了线性无量纲化方法和反向指标正向化方法的应用建议。     

On the solution of the finite moment problem

In this work we propose a method to obtain the normal solution of the finite moment problem both in the absence and in the presence of linear boundary constraints. The method gives the normal solution as a linear combination of Jacobi polynomials and furnishes its coefficients in terms of the moments. A number of examples are given to illustrate the strength of the method.     

n阶常系数非齐次线性微分方程的降阶解法

给出一阶线性非齐次微分方程的积分因子解法,避免了常数变易法带来的不便和不自然;给出,n阶常系数非齐次线性微分方程的降阶解法,可以看出,高阶常系数线性非齐次微分方程最终都可以归结为求解一阶线性微分方程,从而避免了待定系数法求非齐次方程特解的繁琐,并最终说明了一般微积分教材中只给出两种类型常系数非齐次线性微分方程的待定系数解法的原因．     

Application of the Lanczos algorithm for solving the linear systems that occur in continuation problems

We study the Lanczos method for solving symmetric linear systems with multiple right‐hand sides. First, we propose a numerical method of implementing the Lanczos method, which can provide all approximations to the solution vectors of the remaining linear systems. We also seek possible application of this algorithm for solving the linear systems that occur in continuation problems. Sample numerical results are reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Effects of the material gradation on the SIFs of a crack in a 2-D FGM plate under thermal shock

Crack analysis of linear coupled thermoelasticity in two-dimensional, isotropic, non-homogeneous and linear elastic functionally graded materials subjected to thermal shock is performed by using a boundary-domain element method. The material parameters are assumed to be continuous functions of the spatial coordinates. Fundamental solutions of linear coupled thermoelasticity for the corresponding isotropic, homogeneous and linear elastic solids in Laplace-transformed domain are applied in the boundary-domain integral formulation. A collocation method is implemented for the numerical solution. Numerical examples for an exponential gradation of the material parameters are presented and discussed. The influences of the material gradation on the stress intensity factors are investigated. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A primal interior point method for the linear semidefinite programming problem

The linear semidefinite programming problem is examined. A primal interior point method is proposed to solve this problem. It extends the barrier-projection method used for linear programs. The basic properties of the proposed method are discussed, and its local convergence is proved.     

Numerical approximation of the spectra of Phan-Thien Tanner liquids

The linear stability of the linear Phan-Thien Tanner (PTT) fluid model is investigated for plane Poiseuille flow. The PTT model involves parameters that can be used to fit shear and extensional data, which makes it suitable for describing both polymer solutions and melts. The base flow is determined using a Chebyshev-tau method. The linear stability equations are also discretized using Chebyshev approximations to furnish a generalized eigenvalue problem. The spectrum is shown to comprise a continuous part and a discrete part. The theoretical and numerical results are validated for the UCM and Oldroyd-B models, which are special cases of the PTT model, by comparing with results in the literature. It is demonstrated that the linear extensional and elasticity parameters considered. The computational efficiency and accuracy of the numerical method are also investigated.     

Laplace transform for the solution of higher order deformation equations arising in the homotopy analysis method

A new analytic approach for solving nonlinear ordinary differential equations with initial conditions is proposed. First, the homotopy analysis method is used to transform a nonlinear differential equation into a system of linear differential equations; then, the Laplace transform method is applied to solve the resulting linear initial value problems; finally, the solutions to the linear initial value problems are employed to form a convergent series solution to the given problem. The main advantage of the new approach is that it provides an effective way to solve the higher order deformation equations arising in the homotopy analysis method.     

A parallelization of the simplex method

This paper presents a parallelization of the simplex method for linear programming. Current implementations of the simplex method on sequential computers are based on a triangular factorization of the inverse of the current basis. An alternative decomposition designed for parallel computation, called the quadrant interlocking factorization, has previously been proposed for solving linear systems of equations. This research presents the theoretical justification and algorithms required to implement this new factorization in a simplex-based linear programming system.