含时滞及迁移的Prey—Predator系统中大时滞对Hopf分支的作用机制

在本文中,我们研究了含时滞及迁移的Prey-Predator系统。在此我们指出,当迁移(扩散)系数满足某一限制时,随着时滞量增加,平衡态稳定性出现交替的变化,且相伴地出现Hopf分支的规律。     

由环的P-性质所确定的根

定义了环的Ｐ根Ｐ、弱拟Ｐ根Ｐｗ 和拟Ｐ根ＰＱ,证明它们均为Ａｍ ｉｔｓｕｒＫｕｒｏｓｈ 根且Ｐ＝ Ｐｗ 为特殊根,给出了Ｐ半单环的结构定理和Ｐ根的模刻划     

一个求解P*(k)水平线性互补问题精确极大互补解的不可行内点算法

Stoer,Wechs,和Mizuno最近提出了一个求解P*(k)水平线性互补问题的不可行内点算法,他们的算法能在有限不内得到问题的一个精确解,但是没有讨论算法的多项式复杂性.本文提出一个能得到P*(k)水平线性互补问题精确极大互补解的不可行内点算法,通过使用条件数和误差界理论,我们证明了所给算法是多项式有界的.     

新型节能BT下载协议的设计与验证

随着因特网普及,因上网而消耗的能源迅速上升,逐渐成为世界能源消耗的主要部分之一.这些能源绝大部分消耗在终端计算机上,包括用户的个人电脑和大型数据中心的服务器等.将重点考虑用户在P2P下载(如BT下载)中,因个人电脑必须处在长期工作状态而导致的能耗.我们设计了一种新型的BT下载协议,引入一种新的BT协议的网络结构,从而在不牺牲用户BT下载的速度的情况下,允许用户的个人电脑在一定时间内待机或关机,以此大量降低BT下载协议的能耗.对该协议用实验进行了验证,实验证明新型BT下载协议最高可以减少95%的能耗,同时还能缩短文件的平均下载时间.     

C(P)系对幺半群的刻画

设S是幺半群.本文介绍并研究了正则右系的一个推广.一个右S-系A称为C(P)系,如果A的所有循环子系满足条件(P).本文证明了右C(P)系形成了右S-系的一个新的类,同时,C(P)性质为幺半群同调分类研究提供了新思路.     

P2P保险的道德风险问题研究

伴随信息产业的快速发展和互联网保险的广泛运用,近几年来国际上出现了一种新型保险模式――P2P保险(Peer to Peer Insurance)。该模式基于互联网,通过聚集若干风险类型相似的投保人组建风险共担互助小组,风险互助小组成员间一般是亲戚、朋友等熟人关系。P2P保险形成的相互监督机制和声誉机制,可以较好地解决传统保险市场中存在的道德风险问题。本文利用经济学中的比较静态分析方法,研究了P2P保险的道德风险问题,并从理论上证明了在P2P保险模式下,投保人会倾向于更加努力防范风险以降低出险概率,道德风险问题可以得到有效缓解。     

鞅的P均方算子的Ф不等式

证明了鞅的P均方算子、P条件均方算子、P均方平削算子和P条件均方平削算子在qФ≥P和PФ≤P时鞅的一些Ф不等式，并讨论其中的不等式的系数的优良性．     

基于有限关注的P2P借贷市场监管模式:以百度为例

P2P借贷相对于传统金融中介具有向下整合闲散资金并降低交易成本的优势,在"互联网+"和"大众创业万众创新"的政策背景下能够有效倒逼传统金融中介改革,为创新企业提供资金.但目前行业仍存在严重的监管缺失问题,而银监会等政府部门监管缺乏法律授权,监管行为缺乏积极性.因此,提出了以《互联网信息搜索服务管理规定》为契机,通过监管百度对P2P的推广业务进而规范行业发展的思路,并论证了这种方法的有效性.百度搜索量对P2P用户投资行为的相关性分析表明,监管百度推广业务能有效阻碍问题平台获得用户,进而减少问题平台的产生及影响.     

三次自催化模型的整体解

该文利用重要不等式及能量积分方法首先得到了解的初等的先验估计．然后利用线性半群的有关性质及精细计算得到了解的最大模估计，从而证明了两类三次自催化模型在Dirichlet边界条件下整体解的存在性，并进而证明了第一类模型的最大吸引子的存在性．     

The stationary solution of a one-dimensional bipolar quantum hydrodynamic model

In this paper, we consider the existence and uniqueness of stationary solution to the bipolar quantum hydrodynamic model in one dimensional space with general non-constant doping profile. The existence of the stationary solution is proved by Leray-Schauder fixed-point theorem and a crucial truncation technique is used to derive the positive upper and lower bounds of the stationary solution. The uniqueness of the stationary solution is shown by a delicate energy estimate.     

Wallis公式的精致化

证明了∫_0~(π/2)sin~αxdx(α→+∞)渐进展开式的存在性,并给出了展开式系数的递推公式,进而得到了((2n-1)!!)/((2n)!!)/((2n)!!)的渐进展开式和精致化的Wallis公式.在精致化的Wallis公式中取到1/n~m项,对π的逼近精度可达O(1/(n~(m+1))),比原来的Wallis公式的精度大为提高.     

Doubly nonlinear evolution equations with non-monotone perturbations

The local (in time) existence of strong solutions to Cauchy problems for doubly nonlinear abstract evolution equations with non-monotone perturbations in reflexive Banach spaces is proved under appropriate assumptions, which allow the case where solutions of the corresponding unperturbed problem may not be unique. To prove the existence, a couple of approximate problems are introduced and delicate limiting procedures are discussed by using various tools from convex analysis and the Kakutani-Ky Fan fixed point theorem. Furthermore, an application of the preceding abstract theory to a nonlinear PDE is also given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A density-dependent chemotaxis-haptotaxis system modeling cancer invasion

This paper deals with a chemotaxis-haptotaxis model of cancer invasion of tissue, initially proposed by Chaplain and Lolas. The model consists of three reaction-diffusion-taxis partial differential equations describing interactions between cancer cells, matrix degrading enzymes, and the host tissue. The equation for cell density includes two bounded nonlinear density-dependent chemotactic and haptotactic sensitivity functions. In the presence of logistic damping, we prove the global existence of a unique classical solution to this model by some delicate a priori estimate techniques.     

Global Existence and Asymptotic Behavior for the 3D Compressible Non–isentropic Euler Equations with Damping

We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.     

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR THE 3D COMPRESSIBLE NON–ISENTROPIC EULER EQUATIONS WITH DAMPING

We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.     

On the minimal Keller–Segel system with logistic growth

This paper applies a delicate method which is inspired by Deuring (1987) and is different from those of Winkler (2010) and Yang et al. (2015) to show the known conclusion: The weak chemotactic effect can ensure the global existence and boundedness of the solutions of the minimal Keller–Segel model with logistic growth in any dimensional cases. Moreover, we obtain the explicit uniform-in-time upper bound for the global solution. It is noted that the method used in the paper may be employed to study other chemotaxis systems.     

连串反应中控制火焰的耦合GKS-CGL方程组解的极限行为

本文考虑连串反应中控制火焰的耦合广义Kuramoto Sivashinsky-Ginzburg Landau(GKS-CGL)方程组的周期初值问题,主要研究其解在系数g→0和δ→0时的极限行为.首先,采用Galerkin方法,通过构造一系列精细的先验估计,得到GKS-CGL方程组周期初值问题整体光滑解的存在唯一性.其次,利用一致有界估计证得GKS-CGL方程组极限解收敛,并给出解的收敛率估计.     

Limit cycles in a generalized Gause-type predator–prey model

We study the problem of the existence of limit cycles for a generalized Gause-type predator–prey model with functional and numerical responses that satisfy some general assumptions. These assumptions describe the effect of prey density on the consumption and reproduction rates of predator. The model is analyzed for the situation in which the conversion efficiency of prey into new predators increases as prey abundance increases. A necessary and sufficient condition for the existence of limit cycles is given. It is shown that the existence of a limit cycle is equivalent to the instability of the unique positive critical point of the model. The results can be applied to the analysis of many models appearing in the ecological literature for predator–prey systems. Some ecological models are given to illustrate the results.