具有拟周期外力的非自治时滞发展方程的近似惯性流形

该文研究了一类具有拟周期外力的非自治时滞发展方程, 通过延伸相平面将非自治系统转化为自治系统, 再证明相应的自治系统的时滞惯性流形的存在性, 并在时滞惯性流形的基础上构造了非自治发展方程的近似惯性流形.     

具时滞Lotka-Volterra互惠系统的全局吸引性

利用Ｌｉａｐｕｎｏｖ泛函方法，讨论了具时滞非自治Ｌｏｔｋａ Ｖｏｌｔｅｒｒａ互惠系统周期正解的全局 吸引性，推广了文［１］已知相关结果．     

具无限时滞的周期系统的持久性与正周期解

本文利用比较定理,控制收敛定理和积分平均的方法,讨论一类具有无限时滞的非自治,非卷积的捕食者-食饵系统的一致持久性和正周期解.     

具无限时滞的周期系统的持久性与正周期解

本文利用比较定理,控制收敛定理和积分平均的方法,讨论一类具有无限时滞的非自治,非卷积的捕食者-食饵系统的一致持久性和正周期解。     

非自治的具有阶段结构和时滞的捕食系统的动力学行为

本文研究了一个非自治的具有阶段结构和时滞的捕食-食饵模型.利用比较原理获得了系统持久性的条件,在假设系统为周期系统的条件下通过构造Liapunov函数证明了正周期解的存在唯一性和全局渐近稳定性.     

具有连续时滞和比率型功能反应的竞争系统的正周期解的存在性

本文利用重合度理论中的延拓定理讨论了具有连续时滞和比率型功能反应的非自治扩散竞争系统的正周期解的存在性,得到了正周期解存在的充分条件。     

具有限时滞的非自治三种群扩散捕食系统的周期解

主要讨论了具有限时滞的非自治三种群扩散捕食系统的周期解的存在性.方法是运用Yoshizawa型周期解定理的推广,得出该系统至少有一个ω周期解.     

一类具有时滞及反馈控制的非自治非线性比率依赖食物链模型

该文研究了一类具有时滞和反馈控制的三种群非线性非自治比率依赖的食物链模型.首先,基于时滞微分不等式理论,提出了一些新的分析方法,并构造了一个合适的李亚普诺夫函数.其次,得到了系统正解的持久性和全局吸引性的充分条件.第三,利用理论分析和不动点理论,讨论了相应的周期系统,建立了周期系统正周期解的存在性、唯一性和稳定性的充分...     

一类具有时滞和比率依赖的竞争扩散系统

研究了一类具有时滞和基于比率的两种群非自治竞争扩散系统.利用比较原理证明了系统在适当条件下是一致持久的;利用B row er不动点原理和构造Lyapunov泛函,得到了系统存在唯一全局渐近稳定周期正解的充分条件.     

非自治时滞微分系统的周期解

本文将一类非自治时滞微分方程变换为等价的哈密顿系统.这样求解此时滞微分系统可以等价于求解相应的哈密顿系统.运用Floquet变换和辛变换方法,建立了此类微分系统多重周期解的存在性定理,此结果推广了先前文献中的一些结果.     

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.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

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.     

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.     

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