作物害虫天敌微生物系统的动力学研究

以棉田生态系统能量流动分析为基础,建立了作物害虫天敌微生物的种群动力学模型,对作物害虫天敌微生物系统进行了初步的研究.对系统的能量流动使用微分方程进行了模拟,并对系统正平衡点的存在性及局部渐近稳定性给出了相关条件.最后使用MATLAB软件对模型进行了动态模拟,对正平衡点的存在性条件和稳定性进行了验证.     

棉田生态系统时滞动力学模型及其应用

以棉田生态系统能量流动分析为基础,建立了作物-害虫-天敌-微生物的时滞种群动力学模型,利用泛函微分方程理论对该系统进行了持久性和稳定性研究,对系统解的正性、持久性、正平衡点的存在性及全局渐近稳定性给出了相关条件,证明该系统的时滞是无害时滞.最后使用MATLAB软件对模型进行了动态模拟,对正平衡点的存在性条件和稳定性进行了验证.     

具有时滞的捕食食饵共生模型的稳定性分析

以棉蚜、蚂蚁、瓢虫的种间关系为生物背景,建立了具有时滞的捕食-食饵-共生的系统模型,利用时滞微分方程定性理论,研究了该系统的正性、持久性和各平衡点的局部渐近稳定性,探讨了棉蚜和蚂蚁的发育历期对种群系统的影响.研究结果表明:棉蚜发育历期对种群系统有影响,当发育历期大于16天的时候,种群系统会出现周期性振荡.最后利用Mathematica软件对各个种群的变化给出了数值模拟.旨在通过研究系统的稳定性条件,对棉田生态系统的生物防治提供一定的理论依据.     

一类云杉蚜虫与其天敌相互作用模型的动态特性

使用微分方程理论研究了一类云杉蚜虫与其天敌在相互作用过程中所呈现的动态性质,分别得到了云杉蚜虫与其天敌之间达到稳定平衡状态和在平衡点附近出现hop f分支的条件,并给出了在何种条件下这两个种群的存量会发生周期变动.     

一个具有时滞和阶段结构的捕食-被捕食模型

研究一个具有时滞和阶段结构的捕食者-食饵模型.通过构造适当的Lyapunov泛函,讨论了该模型的正平衡点和非负边界平衡点的全局吸引性,从而得到了保证该生态系统永久持续生存与绝灭的充分性条件.     

一类比率型功能性反应捕食模型的稳定性分析

研究了一类具有比率型功能性反应的捕食模型,对模型进行了定性和稳定性分析,讨论了模型唯一正平衡点的存在条件,以及模型各个平衡点的性态.得到了各个平衡点全局渐近稳定的充分条件.通过绘制模型的相轨线,分析轨线的走向得到了原点全局渐近稳定的条件,并证明了模型不存在非平凡正周期解的条件,通过构造Lyapunov函数得到了模型的唯一正平衡点是全局渐近稳定的结论.     

具有时滞的单种群扩散模型的全局稳定性

该文研究了一类具有时滞的单种群扩散模型, 利用同伦技术得到了模型存在正平衡点. 在适当的条件下证明了系统是一致持续的, 获得了系统的正平衡点的局部和全局稳定性的充分条件.     

一类基于集合种群网络的传染病模型研究

研究了一类基于集合种群网络的传染病模型.针对在疾病传播过程中,随着染病者数量的增加,被感染的人数会达到饱和,研究了带有饱和发生率的传染病模型,建立了不同集合种群之间扩散模式,并分析了模型动力学的性态,给出了无病平衡点及其稳定性和正平衡点的存在性.最后用数值模拟验证了理论结果的正确性.     

具有常数迁入率和非线性传染率βI~pS~q的SI模型分析

对一种具有种群动力和非线性传染率的传染病模型进行了研究,建立了具有常数迁入率和非线性传染率βI~pS~q的SI模型.与以往的具有非线性传染率的传染病模型相比,这种模型引入了种群动力,也就是种群的总数不再为常数,因此,该类模型更精确地描述了传染病传播的规律.还讨论了模型的正不变集,运用微分方程稳定性理论分析了模型平衡点的存在性及稳定性,得出了疾病消除平衡点和地方病平衡点的全局渐进稳定的充分条件.进一步的,得出了在某些参数范围内会出现Hopf分支现象,并对上述模型进行了生物学讨论.     

带比例功能反应函数食物链交错扩散模型的整体解

本文研究了带有比例功能反应函数食物链交错扩散模型整体解的存在性和正平衡点的稳定性.利用能量方法和Gagliardo-Nirenberg型不等式,获得了该模型整体解的存在性和一致有界性,同时通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的充分条件.     

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.     

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.     

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.     

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.     

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