一类具时滞的Rayleigh型泛函微分方程反周期解的存在性

应用Leray Schauder不动点定理,研究了一类具时滞的Rayleigh型泛函微分方程： x″（t）＋f（x′（t））＋g（x（t-τ（t）））=e（t）的反周期解问题,得到了反周期解存在的新的结果。     

一类二阶具偏差变元的微分方程周期解

本文利用重合度理论研究一类二阶具偏差变元的微分方程x＇＇（t）+f（t,x（t）,x（t-τ0（t）））x＇（t）+β（t）g（x（t-τ1（t）））=p（t）的周期解问题,得到了存在周期解的新的结果.     

一类二阶中立型微分差分方程周期解的存在性

考虑如下二阶中立型微分差分方程的边值问题：{x(t-τ)-x(t-τ） f(t,x(t),x(t-τ）,x(t-2τ）=0 x(0)=x(2kτ），x（0）=x（2kτ）其中k是任意给定的正整数,τ 为正实数，利用含有偏差变元的变分结构及临界点理论，作给出了判定上述方程存在非平凡周期解的判定准则。     

具偏差变元的Rayleigh型p-Laplacian方程的周期解

研究了一类具偏差变元的Rayleigh型p-Laplacian方程（φp（x′（t）））′＋f（t,x′（t））＋g（t,x（t-τ（t）））=e（t）的周期解问题.利用拓扑度理论和一个先验估计,获得了一些新的结果,同时也改进并推广了已有文献中的一些结果.     

三阶泛函微分方程的周期解

利用Brouwer度理论得到了泛函微分方程x′″（t） ∑i=0^2[αix(i)(t) bix(i)(t-τi)] g1(x(t)) g2(x(t-τ））=p（t）存在2π周期解的充分性条件，推广了[1]中的有关结果．     

含有n个滞量的三维微分差分方程组周期解的存在性

本文研究含有n 个滞量的三维微分差分方程组x(t)=sum from i=1 to ∞(1/i)f[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)]y(t)=sum from i=1 to ∞(1/i)g[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)](τ_i>0)z(t)=sum from i=1 to ∞(1/i)h[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)]周期解的存在性,给出了方程组周期解周期的取值范围.推广并改进了文[1]的结果.     

方程a2x（t—τ）＋a1x（t—τ）＋a0x（t—τ）＋b2x（t）＋b1x（t）＋b0x（t）=δ的部分解讨论

讨论了方程a2x(t-τ）＋a1x(t-τ) a0x(t-τ) b2x(t) b1x(t) b0x(t)=δ的部分解。     

含反馈控制和参数的非线性泛函微分系统的正周期解的分析

我们研究下面具有反馈控制和参数的非线性微分系统的正周期解的存在性与不存在性：{dx/dt=-r（t）x（t）＋λF（t,xt,u（t-δ（t）））,du/dt=-h（t）u（t）＋g（t）x（t-σ（t））.在一定条件下通过应用Leggett．Williams不动点定理,证明该系统至少有三个正周期解;在另外的条件下,通过用反证法证明了该系统的正周期解不存在．     

一类非线性中立型时滞微分方程周期解的存在性

本文利用k-集压缩算子拓扑度抽象连续定理和某些分析技巧，研究了非线性中立型时滞微分方程x＇（t)=f(t,x(t-τ），x＇(t-τ) p(t)周期解的存在性。     

一类二阶混合型泛函微分方程多重周期解

本文利用变分原理和Z2不变群指标研究了二阶混合型泛函微分方程x"(t-τ) f(t,x(t),x(t-τ),x(t-2τ))=0和x"(t-r) λf1(t,x(t),x(t-τ),x(t-2τ))=x(t-τ)多重周期解．得出了有关新结果．     

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.     

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.     

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     

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     

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).     

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.     

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.