Lotka-Volterra模型全局指数稳定性和相应方程解的分岔

研究具有变系数的时滞Lottka-Volterra模型,证明该模型在适当的条件下存在正的平衡解,并给出了正平衡解指数稳定的充分条件,进一步讨论了模型(1)的相对退化形式的解产生Hopf分岔现象.     

一类非线性的经济系统控制模型的稳定性分析

用边界比较法讨论了以CE S生产函数作为反馈的定常经济系统控制模型的稳定性,该模型为含有非局部条件的分布参数系统.并且证明了非定常模型的平衡解是全局渐进稳定的.     

一类带立方源项的Keller-Segel模型时变解的整体性态

本文研究一类带立方源项的Keller-Segel模型在齐次Neumann初边值问题下时变解的整体性态.证明了整体解的存在性及一致有界性;在比率b_2~2+4b_1b_3/χ适当大的情况下,证得该模型的正常数平衡解(u_c,v_c)是全局渐近稳定的.     

具有自然年龄和染病年龄的SIQRS传染病模型的稳定性

研究一类具有自然年龄和染病年龄的年龄结构SIQRS传染病模型,在人口处于稳定状态的假设下,得到了阈值R1和R2.首先,通过将模型在无病平衡解处线性化,证明了当R1＜1时无病平衡解是局部渐近稳定的.其次,利用特征线法和Fatou引理,证明了当R2＜1时无病平衡解是全局渐近稳定的.最后,根据Volterra积分方程的相关知...     

粘性非等熵流体方程平衡解的稳定性

该文在三维空间中,研究Navier-Stokes-Poisson方程的平衡解及其非线性稳定性.当绝热指数4/3γ2时,利用约束变分的方法得到N-S-P方程的平衡解,并且证明该平衡解是非线性稳定的.当γ=4/3时,证明在一定条件下平衡解是不稳定的.     

一类糖酵解模型正平衡解的存在性分析

研究生化反应中具有代表性的一类糖酵解模型.运用先验估计讨论非常数正平衡解的不存在性,得到非常数正平衡解存在的必要条件.在常数平衡解Turing不稳定的基础上,利用度理论方法和解的先验估计,进一步给出非常数正平衡解存在的充分条件.     

投资控制模型解的渐近性质

本文利用初值比较法和边值比较法，讨论了投资系统解的渐适性质，得到了投资控制模型的平衡解是全局渐近稳定的．     

一类修正的Holling-Tanner捕食模型的持久性和全局渐近稳定性

研究了一类修正了捕食种群的功能反应函数的食饵-捕食Holling-Tanner扩散模型,在Neumman边界条件下,得到了模型持久性的一个充分条件,并且用比较原理和上下解方法证明了此模型唯一的正的常数平衡解是全局渐近稳定的.     

一类具有内部存储的非均匀恒化器模型的共存解

本文研究一类具有内部存储的非均匀恒化器模型正平衡解的存在性.由于模型中比率项的奇性,通常的线性化方法、分歧理论等均不适用.为克服比率项的奇性,首先建立模型正平衡解细致的先验估计,该估计表明模型的正平衡解含于一个特殊的锥内.然后借助于一类非线性特征值问题的主特征值及锥上的不动点指标理论给出了模型正平衡解存在的充分条件.     

一个趋化性模型非常数平衡解的存在性

对带两个趋化性参数的趋化性模型平衡解的存在性问题进行研究.在参数满足特定的条件下,应用局部分岔理论得到非常数平衡解的局部分岔结构,从而证明了该趋化性模型存在无穷多个非常数正平衡解.     

Efficiency consideration of generalized age replacement policy

Under the generalized age replacement policy, the system is replaced either at the predetermined age or upon failure if its corresponding repair time exceeds the threshold, whichever comes first. In this paper, we investigate the optimal choice of the pre‐determined preventive replacement age for a nonwarranted system, which minimizes the expected cost rate during the life cycle of the system from the customer's perspective under certain cost structures. Furthermore, we discuss several properties of such a generalized age replacement policy in comparison with the traditional age replacement policy. An efficiency, which represents the fractional time that the system is on, is defined under the proposed generalized age replacement policy and its monotonicity properties are investigated as well. The main objective of this study is to investigate the advantageous features of the generalized age replacement policy over the traditional age replacement policy with regard to the availability of the repairable system. Assuming that the system deteriorates with age, we illustrate our proposed optimal policies numerically and observe the impact of relevant parameters on the optimal preventive replacement age.     

Virtual age,is it real? ‐ Discussing virtual age in reliability context

Several settings, where the notion of virtual age is employed, are discussed. We argue that the age reduction imperfect repair modeling is often not sufficiently justified in practice, as it is not possible to execute repair in most of real situations that conforms with this model. On the other hand, a shock‐based virtual age model is suggested and justified via the probabilities of failures on shocks. The new notion of virtual age for degrading items is also introduced. We discuss how to recalculate virtual age after switching from one regime to another. Several examples illustrating different notions of virtual age are presented.     

CEO年龄、公司治理与海外并购——来自我国沪深股市的经验数据(2009~2014)

本研究基于高阶理论、委托代理理论和最优契约理论,运用沪深两市上市公司在2009~2014年的海外并购数据,对CEO年龄以及与CEO紧密相关的公司治理对企业海外并购决策进行了实证研究。实证结果表明:(1)CEO年龄整体上与企业海外并购决策负相关,说明年纪越大的CEO越不倾向于进行海外并购,越年轻的CEO则越倾向于实施海外并购。在年龄组Ⅰ(<=40岁)中,CEO年龄与企业海外并购决策在5%的水平上显著负相关,说明在年龄小于等于40岁的CEO中,也就是处于青年成熟期的CEO越倾向于实施海外并购;处于中年稳健期(年龄组Ⅲ,49~55岁)的CEO,随着管理经营经验的不断累积,年龄越大越倾向于实施海外并购。(2)在公司治理对海外并购决策的影响方面,股权集中度与海外并购决策正相关,股权集中程度越高就越容易进行海外并购;CEO持股比例与海外并购决策负相关,CEO持股比例越高,CEO越不会做出海外并购决策。     

A common age effect model for the mortality of multiple populations

We introduce a model for the mortality rates of multiple populations. To build the proposed model we investigate to what extent a common age effect can be found among the mortality experiences of several countries and use a common principal component analysis to estimate a common age effect in an age–period model for multiple populations. The fit of the proposed model is then compared to age–period models fitted to each country individually, and to the fit of the model proposed by Li and Lee (2005).Although we do not consider stochastic mortality projections in this paper, we argue that the proposed common age effect model can be extended to a stochastic mortality model for multiple populations, which allows to generate mortality scenarios simultaneously for all considered populations. This is particularly relevant when mortality derivatives are used to hedge the longevity risk in an annuity portfolio as this often means that the underlying population for the derivatives is not the same as the population in the annuity portfolio.     

On the Asymptotic Behaviour of Age Distributions in Manpower Systems

The literature on supply models for manpower planning shows that an important consideration is the size of the discrepancy between the age or length of service distribution of the population and the age distribution which would be reached if present policies were continued indefinitely. In the present paper we study the asymptotic behaviour of the age distribution in any manpower system. An application to a decision problem in a university system is given.     

Calibrating Gompertz in reverse: What is your longevity-risk-adjusted global age?

This paper develops a computational framework for inverting Gompertz–Makeham mortality hazard rates, consistent with compensation laws of mortality for heterogeneous populations, to define a longevity-risk-adjusted global (L-RaG) age. To illustrate its salience and possible applications, the paper calibrates and presents L-RaG values using country data from the Human Mortality Database (HMD). Among other things, the author demonstrates that when properly benchmarked, the longevity-risk-adjusted global age of a 55-year-old Swedish male is 48, whereas a 55-year-old Russian male is closer in age to 67. The paper also discusses the connection between the proposed L-RaG age and the related concept of Biological age, from the medical and gerontology literature. Practically speaking, in a world of growing mortality heterogeneity, the L-RaG age could be used for pension and retirement policy. In the language of behavioral finance and economics, a salient metric that adjusts chronological age for longevity risk might help capture the public’s attention, educate them about lifetime uncertainty and induce many of them to take action — such as working longer and/or retiring later.     

A multivariate time series approach to projected life tables

The method of mortality forecasting proposed by Lee and Carter describes a time series of age‐specific log‐death rates as a sum of an independent of time age‐specific component and a bilinear term in which one of the component is a time‐varying factor reflecting general change in mortality and the second one is an age‐specific parameter. Such a rigid model structure implies that on average the mortality improvements for different age groups should be proportional, regardless of the calendar period: a single time factor drives the future death rates. This paper investigates the use of multivariate time series techniques for forecasting age‐specific death rates. This approach allows for relative speed of decline in the log death rates specific to the different ages. The dynamic factor analysis and the Johansen cointegration methodology are successfully applied to project mortality. The inclusion of several time factors allows the model to capture the imperfect correlations in death rates from 1 year to the next. The benchmark Lee–Carter model appears as a special case of these approaches. An empirical study is conducted with the help of the Johansen cointegration methodology. A vector‐error correction model is fitted to Belgian general population death rates. A comparison is performed with the forecast of life expectancies obtained from the classical Lee–Carter model. Copyright © 2009 John Wiley & Sons, Ltd.     

Stochastic Comparison of Age-Dependent Block Replacement Policies

The age-dependent block replacement policy is a modified block replacement policy with an age limit for preventive replacements. Under this policy, any failed component is repaired, but only the components whose ages exceed a fixed age limit are replaced preventively at the scheduled maintenance times. Using the compensator method, we compare stochastically the failure counting processes of the age-dependent block replacement policies with different parameters, and show that the age-dependent block replacement policy, although cost effective, leads to more failures than the age and block replacement policies. AMS 2000 Subject Classification 60K10     

PROTECTING A FOREST AGAINST FIRE: OPTIMAL PROTECTION PATTERNS AND HARVEST POLICIES

A model for determining the optimal level of expenditure on fire protection for a forest, through time, is developed. The model requires the specification of a function relating the probability of fire at a given age to the current level of expenditure. Use of the Pontryagin Maximum Principle enables the determination of the optimal protection schedule for a single rotation with a fixed cutting age. The optimal cutting age and protection schedule for an ongoing succession of stands on a site can be determined numerically by an iterative technique.