伴有边界摄动二阶非线性系统的奇摄动

讨论了伴有边界摄动的含积分算子的二阶非线性微分方程组边界问题的奇摄 适当的假设条件下,通过对角化技巧,证明了解的存在,并估计的余项。     

伴有边界摄动的Volterra型积分微分方程组的奇摄动

讨论了伴有边界摄动的二阶非线性Volterra型积分微分方程组的奇摄动.在适当的条件下,利用对角化技巧证明了解的存在性,构造出解的渐近展开式并给出余项的一致有效估计.     

具有边界摄动的非线性反应扩散方程奇摄动问题

研究了具有边界摄动的非线性反应扩散方程奇摄动问题．在适当的条件下,利用微分不等式理论,讨论了问题解的渐近性态．     

具有边界摄动弱非线性反应扩散方程的奇摄动

在适当的条件下研究了一类具有边界摄动的非线性反应扩散方程奇摄动初始边值问题.首先,借助正规摄动方法,得到了原问题的外部解.其次,利用伸长变量和幂级数展开理论,构造了解的初始层项.然后,利用微分不等式理论,研究了初始边值问题解的渐近性态.最后,利用一些相关的不等式,讨论了原问题解的存在、唯一性及其一致有效的渐近估计.     

一类具有摄动边界的弱非线性反应扩散方程

研究了具有摄动边界的非线性反应扩散方程的问题.在适当的条件下,利用微分不等式理论,讨论了问题的渐近解.     

THE NONLINEAR SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH BOUNDARY PERTURBATION

The nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied.     

具有边界摄动的非线性奇摄动椭圆型问题(英文)

研究了一类具有边界摄动的非线性奇摄动椭圆型问题.并证明了边值问题解的渐近展开的一致有效性.     

一类具有边界摄动的奇摄动问题

利用渐近理论,讨论了一类具有边界摄动的奇摄动问题.在适当的条件下,得出了这类问题解的存在性条件及其渐近解, 并将所得的结果应用于一类壁面波的传播问题.     

一类奇摄动方程组的边值问题

其中ρ为自变量,θ,s为ρ的未知函数,且均已无量纲化;0相似文献   

一类奇摄动椭圆方程在摄动区域上的渐近解

研究了一类具有摄动边界的非线性椭圆方程摄动问题.经过极坐标变换,在适当的条件下,通过构建近似解以及校正项,利用上下解方法和微分不等式理论得到了解的渐近性态,并通过实际例子进行了验证.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.