一类非线性SEIR传染病模型的全局稳定性

研究了一类具有一般形式非线性发生率g(S)h(I)的SEIR传染病模型.利用Liapunov函数方法,证明了当R_0≤1时,无病平衡点P_0在G内全局渐近稳定,疾病最终消失.利用周期轨道稳定性和Poincare-Bendixson性质理论,证明了当R_01时,地方病平衡点P~*在G的内部全局渐近稳定,疾病流行形成地方病.     

一类具有非线性发生率的传染病模型的稳定性

建立和研究一类具有非线性发生率的传染病模型,得到该模型基本再生数R_0的表达式,运用Lyapunov函数和第二加性复合矩阵理论证明了当R_0<1时无病平衡点全局渐近稳定,此时疾病消失,当R_0>1时地方病平衡点全局渐近稳定,此时疾病在人群中流行.     

本原环的Grothendieck群

设R为本原环,对应的忠实既约模为T,且soc(R)≠R,设R=R/soc(R).在文中证明了以下结果: (1)K_o(R)→K_o(R)是满同态,且当soc(R)≠0时,N=Ker(K_o(R)→K_o(R))是由[T]∈K_o(R)生成的循环子群. (2)若soc(R)=0,则存在一个本原环R_1,soc(R_1)≠0,使得R是R_1的同态象,且K_o(R_1)≌K_o(R)⊕N,其中N=Ker(K_o(R_1)→K_o(R))是由[T]∈K_o(R_t)生成的循环子群.     

一类高维种群动力系统的持续性

§1.引言 对于下述形式的Kolmogorov系统: x_i=x_if_i(x_1,x_2,…x_n),i=1,2…,n, (1.1)其中x_i=dx_i(t)/dt,x_i(t)表示种群x_i在时刻t时的种群密度,X=(x_1,x_2,…,x_n)∈R_ ~n,f_i(x)∈C~1(R_ ~n),这里R_ ~n={X|x_i≥0,i∈N},而N={1,2,…,n},R_ ~(n,0)={X|x_i>0,i∈N},在条件X(0)={x_1(0),x_2(0),…,x_n(0)}∈R_ ~(n,0)下,如果对一切i∈N:有lim sup_(t→∞)x_i(t)>0成立,称系统(1.1)弱持续生存;若liminf_(t→∞)x_i(t)>0成     

紧性在迁移方程中的应用

在L_1空间上研究了板几何中具抽象边界条件下各向异性、连续能量、非均匀介质的迁移方程,证明了方程相应的迁移算子产生C_0半群(V(t))_(t≥0)的Dysonphillips展开式的第9阶余项R_9(t)是弱紧的,从而得到了该C_0半群(V(t))_(t≥0)和streaming算子B生成的C_0半群(U(t))_(t≥0)有相同的本质谱型.     

一类潜伏期和染病期均传染的SEIQR模型的全局稳定性

研究一类潜伏期和染病期均传染的SEIQR传染病模型,得到疾病流行与否的阈值R_0.运用Lyapunov函数方法、LaSalle不变性原理及第二加性复合矩阵理论证明了当R_0≤1时无病平衡点全局渐近稳定,当R_01时地方病平衡点全局渐近稳定.     

广义Bergman空间上的紧复合算子

首先证明广义Bergman空间A_(N,α)~p,(α-n-1,p0)上的复合算子C_φ的有界性和紧性是不依赖于p的,进而证明了若对某个q0和-n-1βα,C_φ在A_(N,β)~α上有界,则C_φ在A_(N,α)~p,α(α-n-1,p0)上是紧的当且仅当lim|z|→1-1-(|z|~2/1-|φ(1)|~2)=0.     

一种梅毒模型的稳定性分析

根据人类感染梅毒的方式建立了一种新的数学模型,整个人口被分成四个组:注射吸毒者,女性性工作者,性工作者的客人以及MSM人群.通过对模型的研究和分析得到了模型的基本再生数R_0,还进一步研究了平衡点的存在性和稳定性,当R_01时,无病平衡点是全局渐近稳定的,疾病将会被消除;当R_0 1时,疾病是一致持续的而且给出了地方病平衡点全局渐近稳定的充分性条件,疾病将持续流行.     

平稳序列中的一些结果

平稳过程预报方法相继在气象、水文、黑子预报、地震……上有一定应用,都需用资料估计相关函数,估计出的相关函数不一定是正定的,因此有时计算出奇怪的结果,预报误差为负数,或预报出的数值数量级过大,这才引起我们研究本文的问题。 R_0 R_1 … R_m R_1 R_0 … R_(m-1) …………………………设R_0,R_1,…,R_m为一串实数,称 R_m R_(m-1) … R_0 为实对称的平稳矩阵。本文的问题是设R_0,R_1,…,R_(n-1)对应的平稳矩阵为正定的,问R_n满足什么条件,使R_0,R_1,…,R_(n-1),R_n对应的平稳矩阵为非负定的,得到的结果是:R_n必须在闭区间[q_(n-1)-V_(n-1),q_(n-1)+V_(n-1)]中,q_(n-1),V_(n-1)是实常数,有清楚的概率论意义,V_(n-1)是熟知的子报误差,q_(n-1)的引入可能是新的,还把这基本结果应用于宽平稳N重马尔柯夫过程,退化时,R_N,R_(N+1),…均取上述可取值之闭区间之边点。非退化时,均取其可取值之闭区间之中点。     

无限区间上二阶离散问题的正解

在本文中,通过运用离散的Arzel\''{a}-Ascoli引理和锥上的不动点定理,我们讨论了无限区间上二阶离散Sturm-Liouville边值问题$$\left\{\begin{array}{l}\Delta^{2}u(x-1)=f(x,u(x),\Delta u(x-1)),~~x\in\mathbb{N},\\ u(0)-a\Delta u(0)=B,~~\Delta u(\infty)=C\end{array}\right.$$ 正解的存在性,其中$\Delta u(x)=u(x+1)-u(x)$是前向差分算子,$\mathbb{N}=\{1,2,\ldots,\infty\}$且$f:\mathbb{N}\times\mathbb{R_{+}}\times\mathbb{R_{+}}\to\mathbb{R_{+}}$连续,$a>0, B, C$ 为非负实数,$\mathbb{R_{+}}=[0,+\infty)$, $\Delta u(\infty)=\lim_{x\rightarrow\infty}\Delta u(x)$.     

Quantized Riemann surfaces and semiclassical spectral series for a non-self-adjoint Schrödinger operator with periodic coefficients

We consider a non-self-adjoint Schrödinger operator describing the motion of a particle in a one-dimensional space with an analytic potential iV (x) that is periodic with a real period T and is purely imaginary on the real axis. We study the spectrum of this operator in the semiclassical limit and show that the points of its spectrum asymptotically belong to the so-called spectral graph. We construct the spectral graph and evaluate the asymptotic form of the spectrum. A Riemann surface of the particle energy-conservation equation can be constructed in the phase space. We show that both the spectral graph and the asymptotic form of the spectrum can be evaluated in terms of integrals of the pdx form (where x ∈31 ?/T? and p ∈, ? are the particle coordinate and momentum) taken along basis cycles on this Riemann surface. We use the technique of Stokes lines to construct the asymptotic form of the spectrum.     

Spectrum and pseudospectrum of non-self-adjoint Schrödinger operators with periodic coefficients

We consider the pseudospectrum of the non-self-adjoint operator $$\mathfrak{D} = - h^2 \frac{{d^2 }}{{dx^2 }} + iV(x)$$ , where V(x) is a periodic entire analytic function, real on the real axis, with a real period T. In this operator, h is treated as a small parameter. We show that the pseudospectrum of this operator is the closure of its numerical image, i.e., a half-strip in ?. In this case, the pseudoeigenfunctions, i.e., the functions ?(h, x) satisfying the condition $$\left\| {\mathfrak{D}\varphi - \lambda \varphi } \right\| = O(h^N ), \left\| \varphi \right\| = 1, N \in \mathbb{N}$$ , can be constructed explicitly. Thus, it turns out that the pseudospectrum of the operator under study is much wider than its spectrum.     

一类具免疫应答和非线性感染函数的时滞HIV-1感染模型的全局稳定性

考虑到HIV-1感染过程中免疫反应和非线性感染函数,建立了一类具有三个分布时滞的HIV-1感染动力学模型.得到了关于病毒感染的基本再生数R0和CTLs免疫反应的基本再生数R1 ＜R0.通过构造Lyapunov泛函证明了系统具有阈值动力学性质,即当R0≤1时,系统存在全局渐近稳定的无感染平衡点;当R1≤1＜R0时,系统出...     

On Crawley Modules

A curve Xis said to be of type (iV, γ) if it is an iV-sheeted covering of a curve of genus γ with at least one totally ramified point. A numerical semigroup His said to be of type (iV, γ) if it has γ positive multiples of Nin [N, 2N_J] such that its γth element is 2Nγ and (2γ+1)NεH. If the genus of X is large enough and N is prime, X is of type (TV, γ) if and only if there is a point P6 X such that the Weierstrass semigroup at P is of type (N, γ) (this generalizes the case of double coverings of curves). Using the proof of this result and the Buchweitz's semigroup, we can construct numerical semigroups that cannot be realized as Weierstrass semigroups although they might satisfy Buchweitz's criterion     

DNS of a Turbulent Channel Flow with Streamwise Rotation - Study of the Reverse Effect of the Cross Flow

Modeling of rotating turbulent flows is a major issue in engineering applications. In this work a turbulent channel flow rotating about the streamwise direction is presented. The theory is based on the investigations of [3] employing Lie group analysis. It was found that a cross flow in spanwise direction is induced. A series of direct numerical simulations (DNS) has been conducted for both different rotation rates and different Reynolds numbers to validate the cross flow. In addition some new interesting effects were observed. The averaged profile ū₃ of the cross flow is formed like a ‘S’ that means it exhibits a triple zero-crossing which denotes regions of reverse flow. Alaso a reverse effect is seen which means that for small rotation rates up to Ro=10 the spanwise mean velocity profiles increase and at rotation number Ro=14 this effect appears to reverse. Both effects were observed at two different Reynolds numbers Re = 180 and Re = 270. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

正态AR(1)模型参数极大似然估计的精确解

本文对正态ＡＲ（１）模型，当Ｒ０已知，且时，证明了极大似然估计存在，但不唯一，这与Ｒ０，Ｒ１两个参数整体求极大似然估计的结果有本质上的不同，同时还研究了极大似然估计（）的数学特性与解析表达式．     

The upper semicontinuity of the solution maps in vector implicit quasicomplementarity problems of type R0

In this paper, we introduce and study several kinds of vector implicit quasicomplementarity problems of type Ro and give some necessary and sufficient conditions for the upper semicontinuity of the solution maps of these problems, respectively.     

媒体报道对一类具有潜伏期的传染病控制的影响

针对媒体报道产生的信息对一类具有潜伏期的传染病控制的影响问题,建立了一类带时滞的传染病模型.计算得到模型的基本再生数R_0并证明了当R0<1时,无病平衡点局部渐近稳定.通过分析模型正平衡点处对应的特征方程,得到了模型在正平衡点处稳定的条件,给出了正平衡点处会出现Hopf分支的临界条件并得到相关结论.     

具有线性脉冲的周期捕食系统的持久性

研究具有HollingIV功能性反应和脉冲的周期捕食食饵系统．找到了影响该系统动力学行为的阈值Ro．证明了当Ro〈1时,该系统的食饵灭绝周期解是局部渐近稳定的;当R0〉1时,该系统的食饵灭绝周期解变得不稳定且食饵将一致持久．     

On observability and stability in infinite-dimensional linear systems

It seems to be generally known (Ref. 1) that, in the case of finite-dimensional systems, the state stability properties of the system may be inferred from the output stability properties if the system is completely observable.In the case of infinite observable systems, the notion of observability generalizes in two distinct ways, weak and strong notions. The above-mentioned stability properties remain true only for the case of strong observability.This research was partially supported by the Bat-Sheva de Rothschild Fund for Advancement of Science and Technology.