Sturm-Liouville边值问题解的非存在性、存在性和多重性结果

本文研究下述Sturm-Liouville边值问题利用Schauder不动点定理、上下解方法和Leray-Schauder映射度理论,获得了解的非存在性、存在性和多重性结果.其中一些是全新的结果,另一些则扩展、改进和完善了由Erbe,Wang,Hai,Lee和Lin所获得的结果.     

半线性椭圆方程的正解

本文用特征理论及上下解方法,证明了一类半线性椭圆方程边值问题的正解的存在性,同时给出了解的估计.     

一维p-拉普拉斯三个正解的存在性

考虑边值问题:(p(x'(t)))'+q(t)f(t,x(t),x'(t))=0,P>1,t∈[0,1],边值条件为x(0)=x(1)=0或x(0)=x'(1)=0．借助于一个新的不动点定理我们获得了存在至少三个正解的充分条件．问题的关键是非线性项f依赖于未知函数的一阶导数．最后,给出一个具体的例子．     

The method of fundamental solutions with eigenfunction expansion method for nonhomogeneous diffusion equation

In this article we describe a numerical method to solve a nonhomogeneous diffusion equation with arbitrary geometry by combining the method of fundamental solutions (MFS), the method of particular solutions (MPS), and the eigenfunction expansion method (EEM). This forms a meshless numerical scheme of the MFS‐MPS‐EEM model to solve nonhomogeneous diffusion equations with time‐independent source terms and boundary conditions for any time and any shape. Nonhomogeneous diffusion equation with complex domain can be separated into a Poisson equation and a homogeneous diffusion equation using this model. The Poisson equation is solved by the MFS‐MPS model, in which the compactly supported radial basis functions are adopted for the MPS. On the other hand, utilizing the EEM the diffusion equation is first translated to a Helmholtz equation, which is then solved by the MFS together with the technique of the singular value decomposition (SVD). Since the present meshless method does not need mesh generation, nodal connectivity, or numerical integration, the computational effort and memory storage required are minimal as compared with other numerical schemes. Test results for two 2D diffusion problems show good comparability with the analytical solutions. The proposed algorithm is then extended to solve a problem with irregular domain and the results compare very well with solutions of a finite element scheme. Therefore, the present scheme has been proved to be very promising as a meshfree numerical method to solve nonhomogeneous diffusion equations with time‐independent source terms of any time frame, and for any arbitrary geometry. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

A matricial extension of the Helson-Sarason theorem and a characterization of some multivariate linearly completely regular processes

We generalize the theorems of Helson-Szegö and Helson-Sarason for matricial measures. We study two-weighted inequalities for the Hilbert transform in [0, 2π] and in R and give a characterization for the positivity of the angle between past and future of multivariate weakly stationary stochastic processes, in the discrete and the continuous case. We also characterize the multivariate weakly stationary stochastic processes that are linearly completely regular and study the rate of convergence of the maximal correlation coefficient.     

非紧集合上的Brezis-Nirenberg定理

本文证明了在非紧集合上的Brezis-Nirenberg定理的结构仍然成立。     

Models for Stationary Max-Stable Random Fields

Models for stationary max-stable random fields are revisited and illustrated by two-dimensional simulations. We introduce a new class of models, which are based on stationary Gaussian random fields, and whose realizations are not necessarily semi-continuous functions. The bivariate marginal distributions of these random fields can be calculated, and they form a new class of bivariate extreme value distributions.     

功率GaAs MESFET小信号模型参数的提取（英）

采用非本征元件的参数作为本征元件参数函数的自变量的方法，求解MESFET小信号等效电路模型，并彩相对误差来构建目标函数。以FET在零偏置状态的非本征元件值作为初值，通过优化求得了热FET状态的本征元件值，S参数的计算值与实验值吻合得很好，S11的相对误差为0.09%,S12为1.1%,S21为0.08%，S22为 2.26%。该方法收敛快，精度高并且效率高，便于移植到微波器件CAD设计和模拟软件中。     

The Method of Fundamental Solutions: A Weighted Least-Squares Approach

We investigate the Method of Fundamental Solutions (MFS) for the solution of certain elliptic boundary value problems. In particular, we study the case in which the number of collocation points exceeds the number of singularities, which leads to an over-determined linear system. In such a case, the resulting linear system is over-determined and the proposed algorithm chooses the approximate solution for which the error, when restricted to the boundary, minimizes a suitably defined discrete Sobolev norm. This is equivalent to a weighted least-squares treatment of the resulting over-determined system. We prove convergence of the method in the case of the Laplace’s equation with Dirichlet boundary data in the disk. We develop an alternative way of implementing the numerical algorithm, which avoids the inherent ill-conditioning of the MFS matrices. Finally, we present numerical experiments suggesting that introduction of Sobolev weights improves the approximation. AMS subject classification (2000) 35E05, 35J25, 65N12, 65N15, 65N35, 65T50     

Generalized Derivations with Skew Nilpotent Values on Lie Ideals

This article gives characterizations of generalized derivations with skew nilpotent values on noncommutative Lie ideals of a prime ring. The results simultaneously generalize the ones of Herstein, Lee and Carini et al.