聚合物单晶生长的三维相场模拟研究

利用元胞自动机方法与相场模型的结合建立新型三维模拟相场模型.同时,为模拟真实的、三维的高分子结晶的过程,采用元胞自动机方法离散方程,且元胞几何形状的选取符合真实聚合物晶格扩散方式的物理规律,以及新建立的相场模型套用间规聚丙烯的实验参数.利用该模型模拟了多种三维立方体或者薄层的晶体形貌及其相互之间的演化过程,包括正方形、长方形、菱形、六边形、多层单晶等.通过模拟结果与真实形貌作对比来证明所建立的相场模型真实可靠性.     

基于HMM的机载设备状态健康评估方法研究

针对机载设备的状态健康评估问题,采用隐马尔科夫模型(HMM)对其进行性能退化程度的评估。首先引入状态条件概率矢量对HMM进行不确定性改进,并推导了其表达式;其次以状态条件概率比值为基础,给出了机载设备状态等级量化分值的计算方法,并据此设计了机载设备状态健康评估流程。最后以飞机发动机温控放大器为例进行仿真验证,结果表明上述方法能够给出直观、准确的状态评估结果。     

大型砂尘风洞中砂尘浓度测量与控制方法的研究

砂尘浓度指标严重影响砂尘风洞试验效果;在大型砂尘风洞中准确的测量及有效的控制砂尘浓度是砂尘风洞设备研制中的两个关键问题;针对动态试验工况环境中浓度传感器标定的问题,分析了浓度测量时标定参数与风速和浓度的关系,使用模型树算法建立了三者之间的关系模型,以此模型来预测各种动态情况下的标定参数;针对复杂环境下浓度动态控制问题,采用专家PID算法,提出了多回路控制系统结构和专家规则;工程实践表明该测量和控制方法满足了动态试验环境的需求,取得了良好效果;模型树算法和专家PID系统能有效的解决动态工况下砂尘浓度的测量与控制问题。     

A new approach to constant term identities and Selberg-type integrals

Selberg-type integrals that can be turned into constant term identities for Laurent polynomials arise naturally in conjunction with random matrix models in statistical mechanics. Built on a recent idea of Karasev and Petrov we develop a general interpolation based method that is powerful enough to establish many such identities in a simple manner. The main consequence is the proof of a conjecture of Forrester related to the Calogero–Sutherland model. In fact we prove a more general theorem, which includes Aomoto's constant term identity at the same time. We also demonstrate the relevance of the method in additive combinatorics.     

具有固定时滞的经济周期模型的动态分析

在经济活动中,投资行为和资本存量存在一定的时滞效应,这会影响经济周期模型的动态行为,进而使得投资政策对经济的稳定调整复杂化.考虑到资本存量的预期时间以及投资时滞对经济活动的影响,采用Hopf分岔理论,研究具有固定时滞的经济周期模型的均衡点的稳定性以及形成经济周期的条件.研究发现,投资过程中的投资时滞,以及投资决策中对于资本存量的预测时间构成经济周期产生的诱因;同时可通过政府投资政策调整达到预期均衡目标,这对保持经济周期稳定及经济政策制定有一定的指导作用.     

二阶离散隐马尔科夫模型的严格定义及等价性质

隐马氏模型作为一种具有双重随机过程的统计模型,具有可靠的概率统计理论基础和强有力的数学结构,已被广泛应用于语音识别、生物序列分析、金融数据分析等领域.由于传统的一阶隐马氏模型无法表示更远状态距离间的依赖关系,就可能会忽略很多有用的统计特征,故有人提出二阶隐马氏模型的概念,但此概念并不严格.本文给出二阶离散隐马尔科夫模型的严格定义,并研究了二阶离散隐马尔科夫模型的两个等价性质.     

Pseudo almost periodic dynamics of delay Nicholson's blowflies model with a linear harvesting term

In this paper, we investigate a class of delay Nicholson's blowflies model with a linear harvesting term, new criteria for the existence and convergence dynamics of positive pseudo almost periodic solutions are established by using the fixed point method and the properties of pseudo almost periodic function, together with constructing suitable Lyapunov functionals. The obtained results extend previously known results, and they also partially answer an open problem proposed by L. Berezansky et al. Finally, an example with simulation is presented to demonstrate the effectiveness of theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

On global stability of an HIV pathogenesis model with cure rate

In this paper, applying both Lyapunov function techniques and monotone iterative techniques, we establish new sufficient conditions under which the infected equilibrium of an HIV pathogenesis model with cure rate is globally asymptotically stable. By giving an explicit expression for eventual lower bound of the concentration of susceptible CD4⁺ T cells, we establish an affirmative partial answer to the numerical simulations investigated in the recent paper [Liu, Wang, Hu and Ma, Global stability of an HIV pathogenesis model with cure rate, Nonlinear Analysis RWA (2011) 12 : 2947–2961]. Our monotone iterative techniques are applicable for the small and large growth rate in logistic functions for the proliferation rate of healthy and infected CD4⁺ T cells. Copyright © 2014 John Wiley & Sons, Ltd.     

Consequences of weak Allee effect on prey in the May–Holling–Tanner predator–prey model

In this work, a modified Holling–Tanner predator–prey model is analyzed, considering important aspects describing the interaction such as the predator growth function is of a logistic type; a weak Allee effect acting in the prey growth function, and the functional response is of hyperbolic type. Making a change of variables and time rescaling, we obtain a polynomial differential equations system topologically equivalent to the original one in which the non‐hyperbolic equilibrium point (0,0) is an attractor for all parameter values. An important consequence of this property is the existence of a separatrix curve dividing the behavior of trajectories in the phase plane, and the system exhibits the bistability phenomenon, because the trajectories can have different ω ? limit sets; as example, the origin (0,0) or a stable limit cycle surrounding an unstable positive equilibrium point. We show that, under certain parameter conditions, a positive equilibrium may undergo saddle‐node, Hopf, and Bogdanov–Takens bifurcations; the existence of a homoclinic curve on the phase plane is also proved, which breaks in an unstable limit cycle. Some simulations to reinforce our results are also shown. Copyright © 2015 John Wiley & Sons, Ltd.