具有脉冲效应和综合害虫控制的捕食系统

本文通过生物控制和化学控制提出了具有周期脉冲效应与害虫控制的捕食系统. 系统保护天敌避免灭绝,在一些条件下可以使害虫灭绝.就是说当脉冲周期小于某一临界值时,存在全局稳定害虫灭绝周期解.脉冲周期增大大于临界值时,平凡害虫灭绝周期解失去稳定性并产生正周期解,利用分支理论来研究正周期解的存在性.进而,利用李雅普诺夫函数和比较定理确定了持续生存的条件.     

参数依赖时滞的Nicholson生态模型的稳定性和分支

研究了参数依赖时滞的Nicholson生态模型的稳定性和分支问题.利用几何分析方法和摄动法,给出了系统唯一正平衡态的稳定性和Hopf分支存在条件,得到了分支周期解的近似解析表达式和周期解稳定性判别式,通过若干实例验证了理论分析和数值计算的一致性.     

具有饱和反应率和阶段时滞结构的害虫生物防治模型

考虑了一个害虫和天敌都有阶段结构及具有饱和反应率的阶段时滞脉冲捕食者-食饵模型,利用人工周期定量地投放有病的害虫和天敌去治理害虫.借助脉冲时滞微分方程的相关理论和方法获得易感害虫根除周期解全局吸引的充分条件以及天敌与易感害虫可以共存且易感害虫的密度可以控制在经济危害水平之下的充分条件.我们的结论为现实的害虫管理提供了可靠的策略依据.     

一类具有非线性脉冲的捕食与被捕食系统的定性分析

实际的害虫控制策略由于受到资源有限、种群密度的影响,具有饱和效应或非线性特征.因此,该文对一类具有非线性脉冲控制策略的捕食与被捕食模型进行了全局定性分析.利用脉冲微分方程中的Floquet理论和比较方法,得到模型的天敌根除周期解全局渐近稳定的充分条件,通过分支理论,得到非平凡周期解存在性的条件,数值模拟验证了具有非线性脉冲的模型具有非常复杂的动态行为.     

具脉冲两阶段结构的自治SIS传染病模型

讨论了具有脉冲两阶段结构的自治SIS传染病模型,得到了该模型无病周期解存在性和稳定性的充分条件,并利用分支理论研究了正周期解的存在性.     

害虫治理的病毒感染模型

研究了食饵受病毒感染且捕食者具有Beddington-DeAngelis功能性反应的生态流行病模型,此模型考虑的是脉冲释放病毒颗粒和自然天敌. 利用Floquet乘子理论、小振幅扰动技巧和比较定理证明了害虫根除周期解的全局渐近稳定性以及系统持续生存的充分条件.结论为现实的害虫管理提供了有效的策略依据.     

一类具有阶段结构和时滞的捕食模型的稳定性及Hopf分支(英文)

研究一类具有阶段结构和时滞的捕食模型.通过特征方程分别分析了正平衡点和边界平衡点的局部稳定性,到了系统Hopf分支存在的充分条件.通过规范型理论和中心流型定理,给出了确定Hopf分支方向和分支周期解的稳定性的计算公式.     

一类具有抑制剂和质载的非均匀恒化器模型的共存解

研究了一类具有抑制剂和质载的非均匀恒化器模型.首先,采用锥映射上不动点指标理论得到了物种共存的充分条件.然后,根据度理论及摄动理论,研究了模型正平衡态解的唯一性和稳定性.结果表明当抑制剂的影响充分大时,模型存在唯一的渐近稳定的共存解.最后,利用比较原理和一致持续理论研究了系统的长时行为,并采用数值模拟的方法对所得结论进行了验证和补充.     

带有疾病、分段常数变量的捕食-被捕食系统的稳定性和分支行为

本文研究一类带有疾病和分段常数变量的捕食-被捕食模型的稳定性和分支行为.首先通过计算得到捕食-被捕食模型对应的差分模型,利用线性稳定性理论讨论边界和正平衡点局部渐近稳定的充分条件.其次将食饵种群的出生率作为分支参数,使用分支理论研究差分模型在边界和正平衡点处产生鞍结点分支、翻转分支、Neimark-Sacker分支、Neimark-Sacker分支、鞍结点-Neimark-Sacker分支、鞍结点-翻转分支和翻转-Neimark-Sacker分支的充分条件.最后数值模拟验证理论分析的正确性,并展示模型复杂的动力学性态.     

一类具有时滞和Holling Ⅲ型功能性反应的捕食模型的稳定性和Hopf分支

研究一类具有时滞和Holling Ⅲ型功能性反应的捕食模型的稳定性和Hopf分支.以滞量为参数,得到了系统正平衡点的稳定性和Hopf分支存在的充分条件,给出了确定Hopf分支方向和分支周期解的稳定性的计算公式.     

Ritz and harmonic Ritz values and the convergence of FOM and GMRES

The Ritz and harmonic Ritz values are approximate eigenvalues, which can be computed cheaply within the FOM and GMRES Krylov subspace iterative methods for solving non‐symmetric linear systems. They are also the zeros of the residual polynomials of FOM and GMRES, respectively. In this paper we show that the Walker–Zhou interpretation of GMRES enables us to formulate the relation between the harmonic Ritz values and GMRES in the same way as the relation between the Ritz values and FOM. We present an upper bound for the norm of the difference between the matrices from which the Ritz and harmonic Ritz values are computed. The differences between the Ritz and harmonic Ritz values enable us to describe the breakdown of FOM and stagnation of GMRES. Copyright © 1999 John Wiley & Sons, Ltd.     

Diversity and Popularity in Organizations and Communities

This paper examines social groupings whose structure depends only on the distribution of ability to attract attention. When people‘s attention is a scarce resource, those individuals who are rated highest by a large number of other individuals will have to ration their attention, resulting in constraints on the social structure of the group. The incidence of popular individuals by that definition reflects the extent to which individuals agree on who their highest-rated colleague is. We propose three basic distributions or ways to generate the matrix of perceived ability so as to yield popularity profiles that can be parametrically adjusted to match observations. We demonstrate that each of these assumption sets leads to a slightly different correlation between the value of the assumption‘s parameter and the set of observable popularity patterns. Since popularity, in real life, often determines such things as power, centrality, over-utilization and perhaps reduced accessibility, having more realistic ways of representing it is important for modeling and understanding virtual organizations and communities.     

Polytopes and arrangements: Diameter and curvature

We introduce a continuous analogue of the Hirsch conjecture and a discrete analogue of the result of Dedieu, Malajovich and Shub. We prove a continuous analogue of the result of Holt and Klee, namely, we construct a family of polytopes which attain the conjectured order of the largest total curvature.     

Navier and Stokes meet Poincare and Dulac

This paper surveys various precise (long-time) asymptotic results for the solutions of the Navier-Stokes equations with potential forces in bounded domains. It turns out that the asymptotic expansion leads surprisingly to a kind of Poincare-Dulac normal form of the Navier-Stokes equations. We will also discuss some related results and a few open issues.     

Singular quasilinear and Hessian equations and inequalities

We solve the existence problem in the renormalized, or viscosity sense, and obtain global pointwise estimates of solutions for quasilinear and Hessian equations with measure coefficients and data, including the following model problems:

     

Lebesgue测度等测包及其应用

利用Lebesgue测度的等测内核和等测外包讨论内外测度的一系列性质,给出外测度有限可加的一个充要条件,该条件改进了原有外测度有限可加性相关问题的结果.     

Dual and triple equations and q-orthogonal polynomials

In this paper, we solve dual and triple sequences involving q-orthogonal polynomials. We also introduce and solve a system of dual series equations when the kernel is the q-Laguerre polynomials. Examples are included.     

Proper and Unit Trapezoid Orders and Graphs

We show that the class of trapezoid orders in which no trapezoid strictly contains any other trapezoid strictly contains the class of trapezoid orders in which every trapezoid can be drawn with unit area. This is different from the case of interval orders, where the class of proper interval orders is exactly the same as the class of unit interval orders.     

Vertex- and edge-minimal and locally minimal graphs

Given a family of graphs , a graph is called edge-minimal (vertex-minimal) if for every subgraph (induced subgraph) G^′ of G; furthermore, G is called locally edge-minimal (locally vertex-minimal) if whenever G^′ is obtained from G by deleting an edge (a vertex). Similarly, the concepts of minimality and local minimality are introduced for directed graphs (digraphs) and, more generally, for partially ordered sets.For example, by the Strong Perfect Graph Theorem, the only vertex-minimal graphs with χ>ω are odd holes and anti-holes. In contrast, the only locally vertex-minimal graphs with χ>ω are partitionable graphs. Somewhat surprisingly, there are infinitely many non-trivial perfect graphs that are locally edge-minimal and -maximal simultaneously. In other words, such a graph is perfect but it becomes imperfect after any edge is deleted from or added to it.In this paper we consider vertex- and edge-minimal and locally minimal graphs in the following families: (i) perfect and imperfect graphs, (ii) graphs with χ=ω and with χ>ω, (iii) digraphs that have a kernel and kernel-free digraphs, and finally, (iv) vertex-minimal complementary connected d-graphs.     

Crossings and nestings of matchings and partitions

We present results on the enumeration of crossings and nestings for matchings and set partitions. Using a bijection between partitions and vacillating tableaux, we show that if we fix the sets of minimal block elements and maximal block elements, the crossing number and the nesting number of partitions have a symmetric joint distribution. It follows that the crossing numbers and the nesting numbers are distributed symmetrically over all partitions of , as well as over all matchings on . As a corollary, the number of -noncrossing partitions is equal to the number of -nonnesting partitions. The same is also true for matchings. An application is given to the enumeration of matchings with no -crossing (or with no -nesting).