Boundedness, global existence and continuous dependence for nonlinear dynamical systems describing physiologically structured populations

The paper is aimed as a contribution to the general theory of nonlinear infinite dimensional dynamical systems describing interacting physiologically structured populations. We carry out continuation of local solutions to maximal solutions in a functional analytic setting. For maximal solutions we establish global existence via exponential boundedness and by a contraction argument, adapted to derive uniform existence time. Moreover, within the setting of dual Banach spaces, we derive results on continuous dependence with respect to time and initial state.To achieve generality the paper is organized top down, in the way that we first treat abstract nonlinear dynamical systems under very few but rather strong hypotheses and thereafter work our way down towards verifiable assumptions in terms of more basic biological modelling ingredients that guarantee that the high level hypotheses hold.     

二阶中立型微分方程的区间振动准则

利用平均函数技巧 ,对二阶中立型微分方程 [a(t) (x(t) p(t)x(t-τ) )′]′ q(t)f[x(t) ,x(t-σ) ]g[x′(t) ]=0建立了一些区间振动准则 ,这些振动准则不同于已知依赖于整个区间 [t0 ,∞ )的性质的结果 ,而是仅依赖于 [t0 ,∞ )上的子区间列的性质     

Global existence for systems of wave equations with nonresonant nonlinearities and null forms

We consider the Cauchy problem for systems of nonlinear wave equations with different propagation speeds in three space dimensions. We prove global existence of small amplitude solutions for systems with some nonresonant nonlinearities which may depend on both of the unknowns and their derivatives. Our method here can be also adopted to treat the null forms.     

带非线性边界条件的热传导方程的整体解与爆破问题

本文考虑下面的带有非线性边界条件的热传导方程的整体解的存在性及爆破问题，给出平衡解的分岐结果及整体解存在的充要条件．     

Hopping of chaotic dynamics in a doubly resonant parametric oscillator

We study a doubly resonant optical parametric oscillator where the pump can feed two pairs of signal-idler modes. We assume the presence of gain at the pump frequency. We investigate the various oscillation states of interest, namely, when only the first pair oscillates with the other pair having null amplitudes and vice versa. We demonstrate the exchange of dynamics between the mode pairs when the relevant parameters of the cavity, namely, the phase mismatch factors or the decay rates switch because of fluctuations. The exchange of dynamics is shown to be independent of the nature of dynamics, i.e. independent of whether the motion isn-periodic or chaotic. We also investigate the case where both the pairs can exhibit chaotic dynamics though these states are difficult to realize because of fluctuations.     

非线性DEDS的周期时间部分合并配置与能稳性

对于具有状态反馈的非自治非线性DEDS,通过引入强连通系的最大能并子集,定义了周期时间部分合并配置和能稳性,给出了周期时间部分合并配置的一个充要条件以及能稳性的一个充分条件,前者推广了已有结果.     

一类非线性方程的激波解

该文是利用匹配条件讨论一类非线性方程激波解。得出了对应的激波解与边界条件的关系。     

储存环内电子冷却过程模拟

考虑储存环内离子的横向振荡和纵向振荡的运动特性,模拟了HIRFL-CSR内重离子束的电子冷却过程.给出了离子束的横向发射度和纵向动量散度随时间连续变化的图象,由此分析了电子束的空间电荷效应,冷却段色散函数和横向电子束温度对冷却过程快慢的影响.     

A Convex Envelope Formula for Multilinear Functions

Convex envelopes of multilinear functions on a unit hypercube arepolyhedral. This well-known fact makes the convex envelopeapproximation very useful in the linearization of non-linear 0–1programming problems and in global bilinear optimization. This paperpresents necessary and sufficient conditions for a convex envelope to be apolyhedral function and illustrates how these conditions may be used inconstructing of convex envelopes. The main result of the paper is a simpleanalytical formula, which defines some faces of the convex envelope of amultilinear function. This formula proves to be a generalization of the wellknown convex envelope formula for multilinear monomial functions.     

柱形量子点中的三阶极化率

利用量子力学的密度矩阵理论,在有效质量近似下，采用有限深势阱模型，导出了柱形量子点的三阶非线性极化率的解析表达式.通过数值计算，分析了GaAs/AlβGa1－βAs柱形量子点的三阶非线性极化率与量子点尺寸、掺杂浓度、入射光的频率和偏振方向等参量的关系.结果表明，三阶极化率峰值位置与这些参量密切相关，并且对于确定频率和偏振方向的入射光以及材料的掺杂浓度，存在与之相匹配的量子点尺寸，使三阶极化率达到极大，比体材料的相应值高出2个数量级以上.