一个供应链系统的可靠性模型的适定性分析

供应链系统是一个复杂的动态系统,许多影响因素的存在,使得供应链系统具有强烈的随机性,从而直接影响供应链系统的可靠性,我们通过分析供应链系统的状态之间的转移关系,引入增补变量法,用偏微分方程组建立了供应链系统的可靠性模型,并对该模型系统解的存在唯一性进行了讨论和证明.     

加权演化的港口网络模型的研究

港口系统的发展、演化对国民经济的繁荣发展起着至关重要的作用,因此如何定量地描述港口系统的发展、演化规律也就显得尤为关键,由此出发,从整体论的角度把港口系统作为一个整体来进行系统研究,利用复杂网络的特性,提出了一个真实的随时间演化的港口系统发展、演化模型,该模型能够有效地再现实际港口系统的一些统计特性,这些特性对于了解港口系统的运行状态和对于港口容错能力的优化将具有十分重要的意义.     

具有F性质系统的拓扑熵和熵维数的关系

对于紧度量空间上的Lipschitz系统,拓扑熵中存在一个经典的上界,即拓扑熵小于等于熵维数和Lipschitz常数的对数的乘积.提出了一类具有F性质的系统,该系统是一类比Lipschitz系统和H(o)lder系统更为一般的系统,最后得到系统(X,f)具有F性质时Ghys猜想成立的充要条件.     

拓扑系统的紧性和分离性

考察拓扑系统的两种紧性——空间式紧和locale式紧,给出紧性的若干刻画,讨论了两种紧性的相互关系,证明了拓扑系统的两种紧性都是拓扑空间紧性的良好推广,说明了紧拓扑系统的闭子拓扑系统、有限和系统以及积系统仍是紧拓扑系统。最后在拓扑系统中考察了紧性加强分离性的问题,得到了紧,(强)T2拓扑系统为(强)T3,(强)T4拓扑系统等结论,并用理想收敛刻画了拓扑系统的强T2分离性。     

复杂系统的一般数学框架(Ⅰ)

复杂系统的基本和最简单的结构就是网络.根据这一思想,本系列论文拟发展一套处理复杂系统的新数学框架.本文详细论述了系统的概念、一般描述方法:系统=(硬部,软部,环境)和局整关系,包括子系统、元素与系统的关系和系统与系统的关系;给出了系统运算的基本法则;简要论述了系统的软、硬部之间的诱导转化.     

基础L*系统的一种扩张——Lukasiewicz系统

研究模糊命题演算的形式演绎系统 L *和 Lukasiewicz命题演算系统 Lu,提出基础系统L *—— BL *系统 ,证明 BL *系统的一种扩张与 Lukasiewicz系统之间的等价性 ,从而为 L *系统和BL *系统提供了一个应用实例。     

基础模糊命题演算系统BL~*的改进系统

基础模糊命题演算系统BL*是一个和基础命题演算系统BL相对独立的命题演算系统。命题演算系统L*是系统BL*的扩张,但不是系统BL的扩张。通过对系统BL*及其它模糊命题演算系统的研究,本文对BL*系统进行了修正,进一步改进了BL*系统中的公理体系。     

不含混沌真子系统的Li-Yorke混沌

研究了一类Li-Yorke混沌系统,该系统没有真子系统是Li-Yorke混沌的,我们称之为混沌极小系统.本文证明混沌极小系统是拓扑传递的,而且该系统每个非空开集都包含一个不可数混乱集.混沌极小系统不一定是极小的,本文构造了一个这样的反例.特别地,我们考察了线段连续自映射,指出该类系统都不是混沌极小的,线段上混沌极小子系统的存在性和该系统有正熵是等价的.     

具有止步和中途退出的两不同服务台的可修排队

研究了等待空间有限的两服务台可修排队系统,其中一个服务台可能故障.到达的顾客可能进入系统也可能不进入系统(止步),进入系统的顾客可能因等待的不耐烦而中途退出.利用马尔可夫过程的方法建立了系统稳态概率满足的方程组,通过分块矩阵推导出了系统稳态概率向量的迭代计算公式,由此得到了系统各项性能指标的计算公式.最后,给出了一些数值结果.     

关于计时事件图的同步性

计时事件图可用于通信、制造等系统的建模、分析、控制和优化.运用极大加代数方法研究计时事件图的同步性.对自治系统,在极大子系统之间添加时间限制来得到系统的同步,并给出同步系统的一些性质和系统同步的最短周期时间.对非自治系统,通过因果反馈得到系统的同步性,并给出较短的周期时间.     

Systems of Quotients of Lie Triple Systems

In this article, we introduce the notion of system of quotients of Lie triple systems and investigate some properties which can be lifted from a Lie triple system to its systems of quotients. We relate the notion of Lie triple system of Martindale-like quotients with respect to a filter of ideals and the notion of system of quotients, and prove that the system of quotients of a Lie triple system is equivalent to the algebra of quotients of a Lie algebra in some sense, and these allow us to construct the maximal system of quotients for nondegenerate Lie triple systems.     

Robust tube-based MPC of constrained piecewise affine systems with bounded additive disturbances

In this article, we propose a robust tube-based MPC formulation for a class of hybrid systems, namely autonomously switched PWA systems, with bounded additive disturbances. The term tube-based refers to those control techniques whose objective is to maintain all possible trajectories of the uncertain system inside a tube which is a set around the nominal (or reference) system trajectory, that is free from disturbances. Common methods in tube-based control systems consider an error dynamical system as the difference between the state of the nominal system and the state of the perturbed system. However, this definition of the error dynamical system leads to a complicated switched affine system for PWA systems. Therefore, we use a new notion of the reference system similar to the nominal system except that the switching between the various modes of the PWA system is driven by the state of the real system. Using this reference system instead of the nominal system leads us to an error dynamical system that can be modeled as a switched linear system. We employ a switched linear controller to stabilize this error system under arbitrary switching. This auxiliary controller forces the states of the uncertain system to remain in a tube confined to the invariant set around the state of the reference system. We add new constraints and tighten some other constraints of the nominal hybrid MPC for the reference system, in order to ensure convergence of the uncertain system and to guarantee robust exponential stability of the closed-loop system.     

一类不同可靠度部件非单调关联系统的最优设计

本文对航天系统中应用广泛的一类典型的非单调关联系统（ｎ中取ｒ至ｓ系统）进行了可靠性分析,比较了目前对系统进行可靠度计算的几种方法的优劣,详细研究了给定ｒ,ｓ及不同部件可靠度ｐ_ｉ的情况下,使系统效益达到最高的条件ｎ值的最优配置问题,并结合国外某类航天系统工程中的计算机集成系统给出了一个数值例子,并用面向 Ｗｉｎｄｏｗｓ的 ＶＢ６． ０实现了一个图形交互的求解系统最优配置和系统可靠度的软件．     

Finite-dimensional representation of delay systems

It is shown that given a state delayed system, one can construct a finite-dimensional system whose partial state replicates the response of the delay system up to a small solution of the homogeneous delay system. Thus, in the absence of small solutions, the response of the delay system can be exactly replicated by a finite-dimensional system. reserved.     

Optimal burn-in for maximizing reliability of repairable non-series systems

Burn-in is a manufacturing process applied to products to eliminate early failures in the factory before the products reach the customers. Various methods have been proposed for determining an optimal burn-in time of a non-repairable system or a repairable series system, assuming that system burn-in improves all components in the system. In this paper, we establish the trade-off between the component reliabilities during system burn-in and develop an optimal burn-in time for repairable non-series systems to maximize reliability. One impediment to expressing the reliability of a non-series system is in that successive failures during system burn-in cannot be described precisely because a failed component is not detected until the whole system fails. For approximating the successive failures of a non-series system during system burn-in, we considered two types of repair: minimal repair at the time of system failure, and repair at the time of component or connection failure. The two types of repair provide bounds on the optimal system burn-in time of non-series systems.     

Bifurcation of limit cycles at the equator

This paper studies center conditions and bifurcation of limit cycles from the equator for a class of polynomial differential system of order seven. By converting real planar system into complex system, we established the relation of focal values of a real system with singular point quantities of its concomitant system, and the recursion formula for the computation of singular point quantities of a complex system at the infinity. Therefore, the first 14 singular point quantities of a complex system at the infinity are deduced by using computer algebra system Mathematica. What’s more, the conditions for the infinity of the real system to be a center or 14 degree fine focus are derived, respectively. A system of order seven that bifurcates 12 limit cycles from the infinity is constructed for the first time.     

交通运输系统协调发展理论与模型研究

提出了交通运输系统协调度的评价分析模型.从系统论的观点出发,提出了交通运输系统协调理论的概念,探讨了交通运输系统随时间而不断演化变迁的规律,给出了交通运输系统协调发展基本步骤;并根据协调学原理,讨论了交通运输系统的协调性问题,提出了系统协调发展模型,对交通运输子系统内部及子系统之间及系统整体的协调发展问题进行了研究,探讨了交通运输可持续发展的系统协调管理过程,为进一步研究交通运输系统的可持续发展奠定了基础.     

Singularity Structure of Third-Order Dynamical Systems. II

The singularity structure of the solutions of a general third-order system, with polynomial right-hand sides of degree less than or equal to two, is studied about a movable singular point. An algorithm for transforming the given third-order system to a third-order Briot–Bouquet system is presented. The dominant behavior of a solution of the given system near a movable singularity is used to construct a transformation that changes the given system directly to a third-order Briot–Bouquet system. The results of Horn for the third-order Briot–Bouquet system are exploited to give the complete form of the series solutions of the given third-order system; convergence of these series in a deleted neighborhood of the singularity is ensured. This algorithm is used to study the singularity structure of the solutions of the Lorenz system, the Rikitake system, the three-wave interaction problem, the Rabinovich system, the Lotka–Volterra system, and the May–Leonard system for different sets of parameter values. The proposed approach goes far beyond the ARS algorithm.     

Bifurcation of limit cycles at the equator for a class of polynomial differential system

In this paper, center conditions and bifurcation of limit cycles from the equator for a class of polynomial system of degree seven are studied. The method is based on converting a real system into a complex system. The recursion formula for the computation of singular point quantities of complex system at the infinity, and the relation of singular point quantities of complex system at the infinity with the focal values of its concomitant system at the infinity are given. Using the computer algebra system Mathematica, the first 14 singular point quantities of complex system at the infinity are deduced. At the same time, the conditions for the infinity of a real system to be a center and 14 order fine focus are derived respectively. A system of degree seven that bifurcates 13 limit cycles from the infinity is constructed for the first time.     

有两种修复方法的复杂可修复系统解的渐近稳定性

讨论了两种修复方法的系统解的渐近稳定性.证明了系统在Banach空间中生成正压缩c0半群,系统的非负稳定解恰是系统算子0本征值对应的本征向量,系统算子的谱点均位于复平面的左半平面且在虚轴上除0外无谱.