具有四类故障可修系统解的存在惟一性

研究了具有四类故障且有两个热备器 (Warm Standby)的可修系统模型 .首先对用微分——积分方程描述的模型转换为 6维空间的积分方程形式 ,运用泛函分析 Banach空间下的算子理论 ,证明了此系统非负解的存在惟一性     

由常规故障和临界人为错误引起系统故障的可修复系统动态解的最优控制

研究了由两个运行部件和一个储备部件并且具有常规故障和临界人为错误的随机模型,故障系统的修复时间是任意分布的.先把系统方程的解转化为Volterra 积分方程的形式,证明了系统方程中正解的存在唯一性,再以泛数指标泛函作为衡量系统可控性的标准,研究该系统的最优控制问题.     

具有临界和非临界人为故障的人-机系统解的存在唯一性及半离散化

研究了具有临界和非临界人为故障率,且修复时间任意分布的可修复的人-机系统模型.利用初等方法将系统转换为8维Banach空间下的Volterra积分方程,得到系统非负解存在且唯一.并讨论了系统解的逼近.     

一类非线性含有时滞的资产发展方程的解

给出了带有时滞的中性技术进步的资产投资模型,此模型为含有非局部和时滞边界条件的分布参数系统.运用泛函分析和积分方程理论,证明了系统解的存在性与唯一性,得到系统解的解析表达式.     

两不同部件并联可修系统动态解的最优控制

针对修复时间服从任意分布的两不同部件并联可修系统的模型,把系统方程的解转化为Volterra积分方程的形式,用范数指标函数作为衡量控制变量的标准,以及系统在某一时刻T的最优控制问题.     

马氏环境下带干扰Cox风险模型的罚金折现期望函数

研究了马氏环境下带干扰的Cox风险模型.首先给出了罚金折现期望函数满足的积分方程,然后给出了破产概率,破产前瞬时盈余、破产赤字的分布及各阶矩所满足的积分方程.最后给出当索赔额服从指数分布且理赔强度为两状态时的破产概率的拉普拉斯变换.     

非线性非完整系统Vacco动力学方程的积分方法*

本文给出积分非线性非完整系统Vacco动力学方程的积分方法.首先,将Vacco动力学方程表示为正则形式和场方程形式;然后,分别用梯度法,单分量法和场方法积分相应完整系统的动力学方程,并加上非完整约束对初条件的限制而得到非线性非完整系统Vacco动力学方程的解.     

具有尺度结构和时滞的种群系统遍历性与最优控制

研究带有时滞的尺度结构种群模型,它是一类包含全局反馈的偏泛函积分微分方程.利用特征线方法确立了状态系统的适定性,借助积分方程和积分变换证明了系统的强遍历性:种群各尺度类别的个体数量占总量之比渐近于常数,与初始分布无关.运用非线性分析中的切锥法锥理论描述了最优策略的结构,证实了最优策略的存在唯一性.     

Smoluchowski方程的对称与显式解析解

研究了一类带齐次核函数的偏微分一积分Smoluchowski方程.利用发展了的李群分析方法给出了带齐次核函数的Smoluchowski方程的决定方程的通解、对称、最优子李代数系统、约化的常微分—积分方程、群不变解和显式解析解.     

索赔次数为复合Poisson-Geometric过程的常利率风险模型的罚金函数

讨论了常利率下索赔次数为复合Poisson-Geometric过程的风险模型的罚金函数,得到了罚金函数的期望所满足的积分方程,并由所得到的积分方程推出了破产概率所满足的积分方程,初始盈余为0时,得到了罚金函数的期望及破产概率的精确解.     

Possibly non-unital operator system structures on a possibly non-unital function system

In this paper, we first give the definition of possibly non-unital function system, which is a characterization of the self-adjoint subspace of the space of continuous functions on a compact Hausdorff space with the induced order and norm structure. Similar to operator system case, we define the unitalization of a possibly non-unital function system. Then we construct two possibly non-unital operator system structures on a given possibly non-unital function system, which are the analogues of minimal and maximal operator spaces on a normed space. These two structures have many interesting relations with the minimal and maximal operator system structures on a given function system.     

A Positive and Monotone Numerical Scheme for Volterra-Renewal Equations with Space Fluxes

We study a numerical method for solving a system of Volterra-renewal integral equations with space fluxes, that represents the Chapman-Kolmogorov equation for a class of piecewise deterministic stochastic processes. The solution of this equation is related to the time dependent distribution function of the stochastic process and it is a non-negative and non-decreasing function of the space. Based on the Bernstein polynomials, we build up and prove a non-negative and non-decreasing numerical method to solve that equation, with quadratic convergence order in space.     

具有预警功能的可修复系统

研究了一个具有预警功能的可修复系统．通过选取空间和定义系统算子,将模型方程转化成为了抽象Cauchy问题．然后利用算子半群理论证明了系统解的存在唯一性与指数稳定性．另外,当风险系数趋于无穷时,这种系统逼近于一种具有弱解的模型系统,利用这个性质可得出相应结论并给出了数值仿真例子．     

Fixed Point Theorems of the Iterated Function Systems

In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of generalized metric space, which is also extensively applied in topological dynamic system.     

A completeness criterion for a double power system with degenerate coefficients

We consider a double power system with degenerate coefficients. Under certain conditions we obtain a completeness criterion for this system in the Lebesgue function space.     

Reich-type iterated function systems

In this paper, we introduce the concept of Reich-type iterated function system and prove the existence and uniqueness of the attractor of such a system. Moreover, we study the properties of the canonical projection from the code space onto the attractor of such a system. We also present an iterated function system consisting of continuous Reich contractions having more than one attractor.     

On the dynamics of capital accumulation across space

We solve an optimal growth model in continuous space, continuous and bounded time. The optimizer chooses the optimal trajectories of capital and consumption across space and time by maximizing an objective function with both space and time discounting. We extract the corresponding Pontryagin conditions and prove their sufficiency. We end up with a system of two parabolic differential equations with the corresponding boundary conditions. We propose a simple numerical set-up to simulate PDE systems which we employ to study the roles of initial capital and technology distributions over space in various scenarios.     

Robust Approximate Zeros in Banach Space

We extend Smale’s concept of approximate zeros of an analytic function on a Banach space to two computational models that account for errors in the computation: first, the weak model where the computations are done with a fixed precision; and second, the strong model where the computations are done with varying precision. For both models, we develop a notion of robust approximate zero and derive a corresponding robust point estimate. A useful specialization of an analytic function on a Banach space is a system of integer polynomials. Given such a zero-dimensional system, we bound the complexity of computing an absolute approximation to a root of the system using the strong model variant of Newton’s method initiated from a robust approximate zero. The bound is expressed in terms of the condition number of the system and is a generalization of a well-known bound of Brent to higher dimensions.      

THE VLASOV-MAXWELL-FOKKER-PLANCK SYSTEM WITH RELATIVISTIC TRANSPORT IN THE WHOLE SPACE

In this paper, we consider the Vlasov-Maxwell-Fokker-Planck system with relativistic transport in the whole space. The global solutions to this system near the relativistic Maxwellian are constructed and the optimal time decay rate of global solutions are also obtained by an approach by combining the compensating function and energy method.