表面粗糙度光纤传感器研究

基于光在粗糙表面的散射原理,利用时间延迟技术,设计了一种快速、非接触测量表面粗糙度的光纤传感器。与同类传感器相比,成本低,系统误差小。     

A strong variational algorithm for delay systems

In this paper, we present a convergent extension of the first-order strong-variational algorithm by Mayne and Polak (Ref. 1) for solving optimal control problems with control constraints to delay systems. Although the algorithm is similar to the one presented in Ref. 1, the proof of convergence is different, since the differential dynamic techniques used by Mayne and Polak are not applicable.This work forms part of the author's PhD Dissertation and was conducted at the Imperial College of Science and Technology under a studentship awarded by the UK Science and Engineering Research Council. This assistance is gratefully acknowledged. The author also wishes to thank Dr. R. B. Vinter for his encouragement and help.     

A singular perturbation analysis with applications to delay differential equations

We prove an approximation result for the solutions of a singularly perturbed, nonautonomous ordinary differential equation which has interesting applications to problems in higher dimensions. Here our result is applied to a singularly perturbed, delay differential equation with state dependent time-lags (i.e., aninfinite dimensional problem). We find a new dynamical system (also in infinite dimensions), which describes, in a certain sense, the dynamics of our delay equations for very small values of the singular parameter.     

基于时滞效应的随机微分投资与比例再保险博弈

金融市场不断发展,激烈的市场竞争使得相对绩效比较在保险机构的业绩评估中占据越来越重要的地位。考虑历史业绩对公司决策的影响,引入时滞效应,研究时滞效应对具有竞争关系公司之间最优投资策略和最优再保险策略的影响。运用随机最优控制和微分博弈理论,针对Cramér-Lundberg模型,得到了均衡投资和再保险策略,给出了值函数的显式解;然后进一步针对近似扩散过程,求得指数效用下均衡投资策略和比例再保险策略的显式表达。通过数值算例,分析了最优均衡策略随模型各重要参数的动态变化。结论显示:保险公司在决策时是否将时滞信息纳入考虑之中将大大影响其投资和再保险行为。保险公司考虑较早时间财富值越多,其投资再保险行为就表现得越趋向于保守和谨慎;与之相反,如果保险公司对行业间的竞争越看重,其投资再保险策略就越倾向于冒险和激进。     

延迟效应影响下的产学研协同创新知识共享研究

在高校和企业组成的产学研协同创新知识共享体系中,考虑成员的知识共享策略均存在延迟效应时的影响,构建了基于双延迟效应的动态微分模型。运用极大值原理,得到了协同创新主体在集中和分散两种决策下的最优知识共享策略、最优收益和体系的知识水平。研究发现:延迟时间的存在对高校和企业的知识共享策略具有负面效应,且均低于发生即时效应的情形;集中式决策并不总是优于分散式决策,两个延迟时间在满足一定的条件时,选择集中式决策为最优,否则双方企业将追求自身利益最大化而选择分散式决策;分散决策下,利润分配比例达到一定条件时,企业才愿意为高校提供补贴。且高校的知识共享延迟时间增加时,企业将提高该补贴比例。补贴比例越大,高校的知识共享水平越高,但对企业的知识共享策略没有影响。     

考虑多种类型缺陷的软件可靠性模型研究

本文提出一种考虑多种类型缺陷的软件可靠性模型,并构建了缺陷检测和剔除两个过程的模型。具体分类情况,可以根据模型的检验方法(拟合准则和预测有效性度量)和模型复杂度来具体决定,如果有测试人员的分类建议或者分类数据,可以结合模型共同决定。为了说明问题,本文给出四种类型缺陷的具体模型,并对实际数据集进行了拟合。通过模型比较,验证了多种类型缺陷模型的有效性。最后,通过构建软件最优发布时间策略对模型进行了应用。研究结果为软件开发和测试提供了理论参考。     

Propagation dynamics of a nonlocal periodic organism model with non-monotone birth rates

This work is concerned with a nonlocal reaction–diffusion system modeling the propagation dynamics of organisms owning mobile and stationary states in periodic environments. We establish the existence of the asymptotic speed of spreading for the model system with monotone birth function via asymptotic propagation theory of monotone semiflow, and then discuss the case for non-monotone birth function by using the squeezing technique. In terms of the truncated problem on a finite interval, we apply the method of super- and sub-solutions and the fixed point theorem combined with regularity estimation and limit arguments to obtain the existence of time periodic traveling waves for the model system without quasi-monotonicity. The non-existence proof is to use the results of the spreading speed. Finally, as an application, we study the spatial dynamics of the model with the birth rate function of Ricker type and numerically demonstrate analytic results.     

Global nonexistence for logarithmic wave equations with nonlinear damping and distributed delay terms

This paper is concerned with global nonexistence of solutions for a logarithmic wave equation with nonlinear damping and distributed delay terms. Due to the simultaneous presence of nonlinear damping and logarithmic source terms, we have difficulty in use of the concavity method. Applying the energy estimates, we show the global nonexistence of solutions with not only non-positive initial energy but also positive initial energy.     

Flocking of Multi-particle Swarm with Group Coupling Structure and Measurement Delay

We investigate the flocking conditions of a group coupling system with time delays, in which the communication between particles includes inter-group and intra-group interactions, and the time delay comes from the theory of moving object observation. As an effective model, we introduce a system of nonlinear functional differential equations to describe its dynamic evolution mechanism. By constructing two differential inequalities on velocity and velocity fluctuation from a continuity argument, and using the Lyapunov functional approach, we present some sufficient conditions for the existence of asymptotic flocking solutions to the coupling system, in which an upper bound of the delay allowed by the system is quantitatively given to ensure the emergence of flocking behavior. All results are novel and can be illustrated by using some specific numerical simulations.