Cycle factors in strongly connected local tournaments

A digraph without loops, multiple arcs and directed cycles of length two is called a local tournament if the set of in-neighbors as well as the set of out-neighbors of every vertex induces a tournament. A digraph is 2-connected if the removal of an arbitrary vertex results in a strongly connected digraph.In 2004 and 2005, Li and Shu investigated the structure of strongly connected, but not 2-connected tournaments. Using their structural results they were able to give sufficient conditions for a strongly connected tournament T to have complementary cycles or a k-cycle factor, i.e. a set of k vertex disjoint cycles that span the vertex set of T.Inspired by the articles of Li and Shu we develop in this paper the structure necessary for a strongly connected local tournament to be not cycle complementary. Using this structure, we are able to generalize and transfer various results of Li and Shu to the class of local tournaments.     

Bifurcation points for a reaction-diffusion system with two inequalities

We consider a reaction-diffusion system of activator-inhibitor or substrate-depletion type which is subject to diffusion-driven instability. We show that obstacles (e.g. a unilateral membrane) for both quantities modeled in terms of inequalities introduce a new bifurcation of spatially non-homogeneous steady states in the domain of stability of the trivial solution of the corresponding classical problem without obstacles.     

Acoustic limit for the Boltzmann equation in the whole space

This paper is devoted to the following rescaled Boltzmann equation in the acoustic time scaling in the whole space

(0.1)     

Convergence of the Klein-Gordon equation to the wave map equation with magnetic field

This paper is devoted to the proof of the convergence from the modulated cubic nonlinear defocusing Klein-Gordon equation with magnetic field to the wave map equation. More precisely, we discuss the nonrelativistic-semiclassical limit of the modulated cubic nonlinear Klein-Gordon equation with magnetic field where the Planck's constant ?=ε and the speed of light c are related by c=ε−α for some α?1. When α=1 the limit wave function satisfies the wave map with one extra term coming from the magnetic field. However, α>1, the effect of the magnetic filed disappears and the limit is the typical wave map equation only.     

NZ‐flows in strong products of graphs

We prove that the strong product G₁? G₂ of G₁ and G₂ is ?₃‐flow contractible if and only if G₁? G₂ is not T? K₂, where T is a tree (we call T? K₂ a K₄‐tree). It follows that G₁? G₂ admits an NZ 3 ‐flow unless G₁? G₂ is a K₄ ‐tree. We also give a constructive proof that yields a polynomial algorithm whose output is an NZ 3‐flow if G₁? G₂ is not a K₄ ‐tree, and an NZ 4‐flow otherwise. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 267–276, 2010     

A perturbation solution for long wavelength thermoacoustic propagation in dispersions

In thermoacoustic scattering the scattered field consists of a propagating acoustic wave together with a non-propagational “thermal” wave of much shorter wavelength. Although the scattered field may be obtained from a Rayleigh expansion, in cases where the particle radius is small compared with the acoustic wave length, these solutions are ill-conditioned. For this reason asymptotic or perturbation solutions are sought. In many situations the radius of the scatter is comparable to the length of the thermal wave. By exploiting the non-propagational character of the thermal field we obtain an asymptotic solution for long acoustic waves that is valid over a wide range of thermal wavelengths, on both sides of the thermal resonance condition. We show that this solution gives excellent agreement with both the full solution of the coupled Helmholtz equations and experimental measurements. This treatment provides a bridge between perturbation theory approximations in the long wavelength limit and high frequency solutions to the thermal field employing the geometric theory of diffraction.     

Analysis of the dynamics of a delayed HIV pathogenesis model

In this paper, considering full Logistic proliferation of CD4⁺ T cells, we study an HIV pathogenesis model with antiretroviral therapy and HIV replication time. We first analyze the existence and stability of the equilibrium, and then investigate the effect of the time delay on the stability of the infected steady state. Sufficient conditions are given to ensure that the infected steady state is asymptotically stable for all delay. Furthermore, we apply the Nyquist criterion to estimate the length of delay for which stability continues to hold, and investigate the existence of Hopf bifurcation by using a delay τ as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the main results.     

Brown运动增量在H(o)lder范数下关于(r,p)-容度的泛函极限定理

利用Brown运动在H\"older 范数下关于$(r,p)$-容度的大偏差,证明了Brown运动增量在H\"older范数下关于$(r,p)$-容度的泛函极限定理.     

弱化希尔伯特第16问题及其研究现状

V.I.Arnold多次提出如下问题:对于给定的自然数n≥2,所有n次多项式1-形式,沿一切可能的m≥3次闭代数曲线族的阿贝尔积分的孤立零点的最大个数Z(m,n)=?由Poincare-Pontryagin定理可知,当阿贝尔积分不恒为零时,A(n)=Z(n+1,n)给出n次Hamilton系统在n次多项式扰动下从原有周期环域分支出极限环的最大个数,因此Arnold把这个问题称为弱化的希尔伯特第16问题.30多年来,对此问题的研究取得了一定进展,也遇到了很大困难.本文拟对这个问题和相关研究工作做一个粗浅的介绍.     

Logistic映射三周期轨道分支值确定

运用分支函数的方法研究了Logistic映射出现稳定三周期点的参数窗口,借助软件Singular 2.0.3运用多元多项式的Grobner基并结合严格局部分析的方法给出Logistic映射出现稳定三周期点时的参数值范围,最后数值模拟方法对所得的结果进行了验证,并指出伪轨现象.