一类比率依赖种群模型在常数收获下的分岔

利用微分方程定性理论以及规范型理论研究了一类具有常数收获项的生物模型.首先,考虑常数收获项对该模型非负平衡点的影响,讨论平衡点的稳定性情况.其次,选取常数收获项作为参数,给出系统存在鞍结点分岔、Hopf分岔以及极限环的充分条件.进一步地,考虑双参数分岔,给出系统存在余维2的Bogdanov-Takens分岔的充分条件.结果表明,由于添加了常数收获项,系统具有丰富的动力学行为.最后,通过数值仿真验证了所得结果的正确性.     

Optimal dividend strategies in the diffusion model with stochastic return on investments

This paper studies the optimal dividend problem in the diffusion model with stochastic return on investments. The insurance company invests its surplus in a financial market. More specially, the authors consider the case of investment in a Black-Scholes market with risky asset such as stock. The classical problem is to find the optimal dividend payment strategy that maximizes the expectation of discounted dividend payment until ruin. Motivated by the idea of Thonhauser and Albrecher (2007), we take the lifetime of the controlled risk process into account, that is, the value function considers both the expectation of discounted dividend payment and the time value of ruin. The authors conclude that the optimal dividend strategy is a barrier strategy for the unbounded dividend payment case and is of threshold type for the bounded dividend payment case.     

保险公司的最优再保险和红利分配

本文将讨论保险公司的最优再保险和分红策略。其中风险由复合泊松过程描述了,相应的盈余过程（ｓｕｒｐｌｕｓ ｐｒｏｃｅｓｓ）是一个跳跃过程。对这一跳跃过程最优控制问题,我们应用动态规划原理得到了积分－微分（ｉｎｔｅｇｒｏ－ｄｉｆｆｅｒｅｎｔｉａｌ）形式的ＨＪＢ方程。由于此方程的解析解较难得到,我们将采用近似方法,将模型在时间和状态空间上分别离散化,将离散最优控制问题的解作为连续模型的近似。     

复合最优模型微粒群优化算法研究及应用

针对微粒群算法全局最优(Gbest)模型收敛速度快、局部搜索能力强、鲁棒性差,局部最优(Lbest)模型全局搜索能力强、鲁棒性好、收敛速度慢的特点,提出了一种结合全局最优和局部最优两基本模型特点的复合最优模型微粒群优化算法。用4个Benchmarks函数进行了测试,实验结果表明,与微粒群算法的两种基本模型相比,该复合模型算法能有效提高算法的收敛速度及全局搜索能力。最后将算法应用于一个非线性系统模型的辨识,辨识结果验证了该算法的有效性。     

A note on the model reference adaptive control of linear parabolic systems with constant coefficients

The problem of constructing a model reference adaptive control law for an uncertain 1-dimensional parabolic system with one constant coefficient is considered in this paper. Adaptive control law are obtained by Lyapunov redesign method. The energy method for parabolic systems and the Agmon’s inequality are applied in the analysis, which leads to a stronger result than that of Hong and Bentsman (Automatica, 1994).     

需求随机情形下时效性物品的随机存储策略

针对具有固定存储寿命、并且批量补充与批量随机需求情形下一类时效性产品的随机存储问题，应用排队论的思想和方法给出了其排队论模型，将状态概率方程组转化为可用数学软件求解的形式并给出了一般的算法，从而在货物需求强度已知的情况下可以得到近似最优的货物补充强度，最后给出实际算例，得到了三种情况下近似最优的货物补充强度。     

带有弹药参数的军事系统模型的建立与分析

采用微分方程建立战争模型是一种常用的方法。但是现有的模型通常用于说明某些战术模式,对战术以外的参数没有考虑,而这些参数可能影响到战争的进程。采用高维微分线性方程组建立了包含人员 弹药参数情况的战术模型,拟对其它参数对战争的影响进行分析。分析结果表明,战争的进程不一定会简单地沿着Lanchester模型进展,其它因素也会影响到战争的发展方向。本模型的结论也适用于包含人员 食物参数情况的战术模型。     

耐用品动态古诺模型的建立及分析

依据耐用品的市场容量随着时间发生变化的特点,对多个企业同时博弈的动态古诺模型进行修正,建立了适用于耐用品市场的动态古诺模型,并得到新的产量均衡解.通过与合作情形下的最优产量解的比较与分析,得到非合作情形下的产量均衡解和合作情形下的最优产量解都随着阶段数的增加而单调下降,并且前者依旧劣于后者等结论.     

易变质性产品生产商和销售商库存协调模型

本文基于如下假定:1)生产商的生产率为有限值且采取两阶段生产供贷模式;2)生产的产品具有易变质性.在此假定下,建立了单生产商单销售商生产销售协调模型.讨论了如何利用价格折扣策略来激励销售商的订货行为.在保证销售商利润不减的前提下,给出了求解使得生产商利润达到最大化的最优价格折扣算法,同时给出了生产商的最优供给批量和销售商的最优订货批量.最后,用数值实例来验证模型的求解过程.     

统计平衡状态下复合系统的维修理论及其优化设计

为防止产品性能退化或为了降低产品失效的概论,在统计平衡状态下讨论了复合系统(串联-并联系统,并联-串联系统,表决-串联系统,旁联-串联系统)的预防维修措施的维修理论,并给出了系统中单元的冗余数及维修人员数的最优设计方法。列举多个算例,对这些算例进行比较表明,所提出的整数规划算法非常有效。     

Global stability for a heroin model with age-dependent susceptibility

This paper considers global asymptotic properties for an age-structured model of heroin use based on the principles of mathematical epidemiology where the incidence rate depends on the age of susceptible individuals. The basic reproduction number of the heroin spread is obtained. It completely determines the stability of equilibria. By using the direct Lyapunov method with Volterra type Lyapunov function, the authors show that the drug-free equilibrium is globally asymptotically stable if the basic reproduction number is less than one, and the unique drug spread equilibrium is globally asymptotically stable if the basic reproduction number is greater than one.     

Stock loan valuation under a regime-switching model with mean-reverting and finite maturity

<正> Stock loans are business contracts between borrowers and lenders in which the borroweruses shares of stock as collateral for the loan.Since the value of the collateral is subject to wide andfrequent price swings,valuing such a transaction behaves more like an option pricing problem thana debt valuation problem.This paper will list,prove,and analyze formulas for stock loan valuationwith finite horizon under various stock models,including classical geometric Brownian motion,meanreverting,and two-state regime-switching with both mean-reverting and geometric Brownian motionstates.Numerical examples are reported to illustrate the results.     

不确定计划数的轧制批量计划的模型和算法

根据热轧生产工艺将热轧生产批量计划归结为不确定车辆数的车辆路径问题 (VRP) ,考虑了轧制计划中钢板宽度的反跳和相同宽度钢板的总长度约束 ,在轧制作业计划数不确定的情况下 ,把组批和排序有机地结合起来 ,并用遗传算法和禁忌搜索算法相结合的混合算法对问题进行求解 ,实验结果表明算法获得的最好解、平均负荷率和计算成本都比较令人满意 .     

The ANOVA-type inference in linear mixed model with skew-normal error

Linear mixed effect models with skew-normal errors and distribution-free random effects are considered. The ANOVA-type F-tests are proposed to test the significance of random effects and the hypothesis on fixed effects of interest, respectively. Both tests are proved to be exact F-tests under this model, and the exact confidence interval for fixed effects of interest is derived. Simulation results are given to study the powers of ANOVA-type tests.     

Nonlinear Langevin model with product stochasticity for biological networks: The case of the Schnakenberg model

Langevin equation is widely used to study the stochastic effects in molecular networks, as it often approximates well the underlying chemical master equation. However, frequently it is not clear when such an approximation is applicable and when it breaks down. This paper studies the simple Schnakenberg model consisting of three reversible reactions and two molecular species whose concentrations vary. To reduce the residual errors from the conventional formulation of the Langevin equation, the authors propose to explicitly model the effective coupling between macroscopic concentrations of different molecular species. The results show that this formulation is effective in correcting residual errors from the original uncoupled Langevin equation and can approximate the underlying chemical master equation very accurately.     

System optimization model of adoption of a new infrastructure with multi-resource and multi-demand sites

This study develops a conceptual system optimization model of adoption of a new infrastructure technology with multiple resource sites and multiple demand sites. With the model, this paper analyzes how the distance, spillover effect, demand, initial investment cost, and learning rate influence the adoption of the new infrastructure technology and presents optimization results of the model in different scenarios. The main findings of the study are: from the perspective of system optimization, (1) different distances among different resource-demand pairs will result in different adoption time of a new infrastructure; (2) technological spillover among different resource-demand pairs will accelerate the adoption of a new infrastructure; (3) it is hard to say that higher demand will pull faster adoption of a new infrastructure, and the optimal time of adopting of a new infrastructure is very sensitive to its technological learning rate.     

具有多种市场形态的多主体股市演化动力机制

股票市场呈现出的多种波动形态,对其内在机制的探讨备受学者和业界的关注.建立多主体股市演化模型,并抽象出一个常微分方程系统描述其核心动力机制.对该系统的定性分析和数值实验表明,受交易主体模仿学习倾向、价格追踪倾向和交易策略转移倾向等市场环境参数影响,模型呈现出基础价值均衡、非基础价值均衡、周期和混沌等市场形态.     

The data envelopment analysis model with intersection form production possibility set

The data envelopment analysis (DEA) model is used to evaluate the relative economic efficiency of a given set of decision making units (DMUs). In this paper, the DEA production possibility set is transferred from the conventional sum form into the intersection form which is represented by a linear inequality system. Although it is time consuming to obtain the intersection form of the production possibility set, it suggests a new angle to investigate the properties of DMUs and to extend the DEA research further beyond the efficiency measurement. Following the intersection form, the analytical formula of the efficiency indicator and projection is given. Various aspects of technical efficiency, returns to scale and evidence of congestion of the DMUs are studied. The relationship between the weak DEA efficiency and the weak Pareto solution is discussed. Finally, a procedure for DMU grouping is proposed to help the decision makers for better resource reallocation and strategy adjustment.     

助飞声诱饵对抗声自导鱼雷数学模型及其仿真

如何使用某型助飞声诱饵对抗声自导鱼雷是水面舰艇水下防御作战中的重要问题之一。首先建立了使用某型助飞声诱饵对抗声自导鱼雷的数学模型,即舰艇的规避机动及声诱饵的发射参数模型,然后对声诱饵的发射参数和舰艇的生存概率进行了仿真计算,并对仿真结果进行了分析,最后得出有关作战使用的几点结论,对装备的作战使用具有重要意义。     

Estimation of a subset of regression coefficients of interest in a model with non-spherical disturbances

This paper considers the estimation of a subset of regression coefficients in a linear regression model with non-spherical disturbances, when other regression coefficients are of no interest. A family of estimators is considered and its asymptotic distribution is derived. This proposed family of improved estimators is compared with the usual unrestricted FGLS estimator, and dominance conditions are obtained with respect to risk under quadratic loss as well as the Pitman nearness criterion. The results of a numerical simulation are presented to illustrate the risk performance of various estimators.