中立型对数种群模型的正周期解存在性

本文利用k-集压缩算子的拓朴度抽象连续定理和某些分析技巧,研究了一类中立型对数种群模型dN/dt=N(t)[r(t)-a(t)lnN(t-σ)-b(t)d/dtlnN(t-r)]的正周期解存在性问题。得到了正周期解存在性的新结果。     

一类二阶n-维中立型微分系统周期解问题

笔者利用重合度原理研究一类二阶n-维中立型微分系统(d2)/(dt2)(x(t)-Cx(t- ))+d/(dt)gradF(x(t))+gradG(x(t-τ(t)))=p(t)的周期解问题,得到了周期解存在性的新结果,推广了已有工作中相应的结论.     

多时滞中立型微分积分方程的周期解

研究了一类具有多个时滞的中立型微分积分方程x'(t)=∫tt-σ9(t,s,x(s))ds f(t,x(t-τ0),x'(t-τ1))周期解的存在性,得到了方程周期解存在的充分条件.所得结果体现了滞量σ对周期解存在性的影响.     

一个周期中立型对数种群模型

本文获得了周期中立型对数种群模型N(t)=N(t)(r(t)-α(t)log[N(t-σ)]-b(t)d/dtlog[N(t-r)])的周期正解的存在性及对所有正解的吸引性．     

一类高阶中立型泛函微分方程周期解的存在性

研究了一类高阶非线性中立型泛函微分方程x~((2n))(t)+cx~((2n))(t-τ)+f(x)x′+bx(t)+g(x(t-σ))=p(t)周期解的存在性,利用分析技巧结合重合度理论给出了该方程存在周期解的充分性定理.     

一类具时滞耗散型Duffing方程的周期解

利用Mawhin重合度理论研究了一类耗散型时滞Duffing方程ax″+f[x′(t-τ1(t))]+cx+g(x(t-τ2(t)))=p(t)周期解的存在性,得到了该方程2π周期解存在的充分性定理.     

一类时滞广义Lienard系统的概周期解的存在唯一性

运用二分性理论及不动点方法,研究一类时滞广义Lienard系统x″+[x~m(t-τ)+h(t)]x′+q(t)x+g(t,x(t-τ))=p(t).的概周期解的存在性和稳定性,得到广义Lienard系统的概周期解存在唯一性和稳定性的充分性定理.     

捕食模型正周期解存在性的一个注记

利用重合度理论中的延拓定理讨论了多滞量捕食模型(dN_1(t))/dt=N_1(t)[r_1(t)-a_(11)(t)N_1(t-τ_1(t))-a_(12)(t)N_2(t-τ_2(t))] (dN_2(t))/dt=N_2(t)[-r_2(t)+a_(21)(t)N_1(t-τ_3(t))]的正周期解的存在性,得到了保证上述系统周期解存在的一组时滞依赖的充分条件,补充和完善了已有学者的工作.     

一类具有偏差变元的高阶中立型Rayleigh方程周期解的存在性

利用重合度理论和不等式分析技巧,获得了一类具有偏差变元的高阶中立型Rayleigh方程(x(t)-cx(t-σ))~((m))+f(x'(t))+β(t)g(x(t-τ(t)))=p(t)周期解存在性的新的充分条件,有意义的是函数f(x)和非线性项前的系数β(t)可以变号.     

一类非线性中立型时滞微分方程周期解的存在性

本文利用抽象连续定理，研究了一类非线性时滞微分方程x′(t)=f(t，x(t)，x(t-τ)，x′(t-τ)) p(t)的周期解问题，并在滞量τ的不同范围内分别得到了周期解存在的充要条件。     

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.