Anisotropic norms of dirichlet kernels and some other trigonometric polynomials

In the paper new estimates of anisotropic norms for trigonometric polynomials are obtained. Translated fromMatematischeskie Zametki, Vol. 67, No. 5, pp. 686–701, May, 2000.     

A Kind of Generalization of the Curve Type Node Configuration in R^S（S 〉 2）

A kind of generalization of the Curve Type Node Configuration is given in this paper,and it is called the generalized node configuration CTNCB in RS(S＞2).The related multivariate polynomial interpolation problem is discussed.It is proved that the CTNCB is an appropriate node configuration for the polynomial space PSn (S＞2).And the expressions of the multivariate Vandermonde determinants that are related to the Odd Curve Type Node Configuration in R2 are also obtained.     

Carleman estimates and unique continuation property for the anisotropic differential-operator equations

The unique continuation theorems for the anisotropic partial differential-operator equations with variable coeffcients in Banach-valued Lp-spaces are studied.To obtain the uniform maximal regularity and the Carleman type estimates for parameter depended differential-operator equations,the suffcient conditions are founded.By using these facts,the unique continuation properties are established.In the application part,the unique continuation properties and Carleman estimates for finite or infinite systems of quasielliptic partial differential equations are studied.     

复函数Cauchy微分中值定理的推广

以分割区域D为基础将解析函数与共轭解析函数的微分中值定理推广到高阶形式.     

A mesh-free numerical method for solution of the family of Kuramoto-Sivashinsky equations

In this paper, radial basis function (RBFs) based mesh-free method is implemented to find numerical solution of the Kuramoto-Sivashinsky equations. This approach has an edge over traditional methods such as finite-difference and finite element methods because it does not require a mesh to discretize the problem domain, and a set of scattered nodes in the domain of influence provided by initial data is required for the realization of the method. The accuracy of the method is assessed in terms of the error norms L₂,L_∞, number of nodes in the domain of influence, free parameter, dependent parameter RBFs and time step length. Numerical experiments demonstrate accuracy and robustness of the method for solving a class of nonlinear partial differential equations.     

Wavelet formulation of the polarizable continuum model

The first implementation of a wavelet discretization of the Integral Equation Formalism (IEF) for the Polarizable Continuum Model (PCM) is presented here. The method is based on the application of a general purpose wavelet solver on the cavity boundary to solve the integral equations of the IEF‐PCM problem. Wavelet methods provide attractive properties for the solution of the electrostatic problem at the cavity boundary: the system matrix is highly sparse and iterative solution schemes can be applied efficiently; the accuracy of the solver can be increased systematically and arbitrarily; for a given system, discretization error accuracy is achieved at a computational expense that scales linearly with the number of unknowns. The scaling of the computational time with the number of atoms N is formally quadratic but a N^1.5 scaling has been observed in practice. The current bottleneck is the evaluation of the potential integrals at the cavity boundary which scales linearly with the system size. To reduce this overhead, interpolation of the potential integrals on the cavity surface has been successfully used. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

平面三次Pythagorean-Hodograph Hyperbolic曲线

本文基于Pythagorean-hodograph (PH)曲线和代数双曲线的良好几何特性,构造了Pythagorean-Hodograph Hyperbolic (PH-H)曲线,并给出了PH-H曲线的定义以及相应性质.同时,分别利用Hyperbolic基函数和Algebraic Hyperbolic (AH) B\''ezier基函数,得到了平面三次AH B\''ezier曲线为PH曲线的两个不同的充要条件.此外,三次PH-H曲线也被用于求解具有确定解的$G^1$ Hermite插值问题.文中给出了具体实例来说明我们的方法.     

构造二元向量值有理插值函数的一种新方法

At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 （0 〈 dl ≤ m） and d2 （0 ≤ d2≤ n）, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.     

Error estimates for some quadrature rules with maximal trigonometric degree of exactness

In this paper, we give error estimates for quadrature rules with maximal trigonometric degree of exactness with respect to an even weight function on ( ? π,π) for integrand analytic in a certain domain of complex plane. Copyright © 2013 John Wiley & Sons, Ltd.     

n维散乱数据带自然边界条件多元多项式样条插值

考虑n维散乱数据Hermit-Birkhoff型插值问题,在使给定的目标泛极小的条件下,构造了一种带自然边界条件的多元多项式样条函数插值方法.重点研究了插值问题解的特征,存在唯一性和构造方法,并讨论了收敛性及误差,最后给出了一些数值算例对方法进行验证.