具有Beddington-DeAngelis型功能反应函数的阶段结构捕食-食饵模型

讨论了捕食者和食饵都具有阶段结构的捕食食饵模型.考虑到捕食者梭皮龟捕获食饵水母时彼此之间的干扰效应,用到了Beddington-DeAngelis型功能反应函数,食饵水母的幼年为水螅体,捕食者梭皮龟仅以成年水母为食.运用渐近系统理论得到了模型边界平衡点的全局渐近稳定性,运用一致持久生存理论得到了捕食者的一致持久性.最后,运用数值模拟的方式不仅验证了定性理论分析的结果,同时显示了捕食者之间适当的干扰可以有效控制水母种群的数量.     

比率依赖型捕食者-食饵系统行波解的存在性

本文讨论一类比率依赖型捕食者 -食饵系统的反应扩散方程组 .首先 ,我们证明了时间周期定常解的存在性和稳定性 .其次 ,我们给出了扩散引起正常数平衡解失稳的条件 .最后 ,我们证明了比率依赖型捕食者 -食饵系统行波解的存在性和渐近性 .     

一类具有Allee影响的捕食者-食饵扩散系统研究

讨论一类具有Allee影响的捕食者-食饵扩散模型解的整体性态.通过线性化方法和Lyapunov泛函方法分别证明了该模型正平衡点的局部渐近稳定性和全局渐近稳定性.     

一类捕食者—食饵系统的时间周期解的存在性与稳定性

本文讨论一类捕食者－食饵系统的反应扩散方程组,运用分歧理论,隐函数定理以及渐近开展的方法,获得了共存周期解的存在性与稳定性的结果。     

一类具有脉冲效应、Ivlev型功能性反应的两捕食者-食饵系统的持久性与稳定性

研究了一捕食者均具有Ivlev型功能性反应,另一捕食者具有HollingⅢ型功能性反应的捕食系统.利用脉冲微分方程比较定理和Floque乘子理论,证明了食饵灭绝的全局渐近稳定性和两捕食者-食饵持续生存的充分条件.此后,通过数值模拟来验证结论的正确性.     

一类具有交叉扩散捕食者-食饵系统的时间周期解的存在性与稳定性

本文讨论一类具有交叉扩散效应的捕食者-食饵系统的反应扩散方程组的时间周期解的存在性与稳定性．运用分歧理论、隐函数定理以及渐近展开的方法,获得了共存周期解的存在性与稳定性的结果．     

捕食者食饵均染病的入侵反应扩散捕食系统中扩散的作用

研究了捕食者食饵均染病的入侵反应扩散捕食系统.利用特征值方法和构造Lyapunov函数,获得了入侵扩散对正常数平衡解的影响, 当入侵扩散系数充分大时, 导致平衡态失稳.进一步, 利用拓扑度方法, 证明了在一定条件下入侵扩散系数很大, 自扩散充分小时, 有非常数正平衡解存在.     

一类具有分段常数变量的三维食饵捕食者系统的稳定性和分支行为

本文研究一类具有分段常数变量的三维食饵-捕食者系统的稳定性和分支行为,该系统由一个捕食者和两个食饵构成,其中一个食饵可由捕食者对另一个食饵的捕食行为中获益.首先通过计算得到三维食饵-捕食者系统对应的差分模型,其次通过选择合适的参数讨论边界和正平衡点的存在性,进而利用线性稳定性理论讨论平衡点局部渐近稳定的充分条件.将两个食饵种群的出生率以及最大环境容纳量作为分支参数,使用分支理论研究差分模型在平衡点处产生翻转分支、Neimark-Sacker分支、折-翻转分支和1:2共振分支的充分条件.最后通过数值模拟验证了理论分析的正确性.     

具次线性功能反应函数的食饵-捕食者模型的定性分析

本文研究了一类食饵具常数存放且功能反应函数为次线性函数的食饵-捕食者模型.利用常微分方程定性理论和稳定性理论的分析方法,获得了一些平衡点全局渐近稳定,极限环存在唯一的充分条件.     

具有Holling-II型功能反应和交叉扩散的捕食-食饵模型正平衡解的存在性和不存在性

本文主要研究一类在齐次Dirichlet边界条件下带交叉扩散的Holling-II型捕食者-食饵模型正平衡解的存在性, 其中两个交叉扩散系数分别代表食饵远离捕食者的趋势和捕食者追逐食饵的趋势. 应用不动点指标理论得到了正平衡解存在的充分条件, 并进一步研究了正平衡解不存在的条件.     

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.