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.     

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.     

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。     

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.     

多元统计分析在课堂教学质量评价元中的应用

为了确保课堂教学质量评价体系的科学性,我们必须对它进行元评价,在元评价过程中,使用α法计算评价的信度,用因子分析评价的效度,是检验评价体系可信和有效程度的重要方法。     

System of generalized resolvent equations with corresponding system of variational inclusions

The purpose of this paper is to introduce a new system of generalized resolvent equations with corresponding system of variational inclusions in uniformly smooth Banach spaces. We establish an equivalence relation between system of generalized resolvent equations and system of variational inclusions. The iterative algorithms for finding the approximate solutions of system of generalized resolvent equations are proposed. The convergence of approximate solutions of system of generalized resolvent equations obtained by the proposed iterative algorithm is also studied.      

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.     

Approach to the stabilization of unstable periodic solutions of autonomous systems of partial differential equations

We suggest an approach to the stabilization of unstable periodic solutions of autonomous systems of partial differential equations based on the introduction of a derivative system in which each periodic solution of the original system is stationary. By using the introduction of an additional space into the derivative system, we suggest to stabilize its stationary solution corresponding to a periodic solution of the original system. This approach permits effectively obtaining a complete ordered set of functions corresponding to an unstable cycle of the original system. We consider an example of stabilization of an unstable cycle in the Kuramoto-Tsuzuki system.     

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.     

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.     

Generalizations of the concept of marginal synchronization of chaos

Generalizations of the concept of marginal synchronization between chaotic systems, i.e. synchronization with zero largest conditional Lyapunov exponent, are considered. Generalized marginal synchronization in drive–response systems is defined, for which the function between points of attractors of different systems is given up to a constant. Auxiliary system approach is shown to be able to detect this synchronization. Marginal synchronization in mutually coupled systems which can be viewed as drive–response systems with the response system influencing the drive system dynamics is also considered, and an example from solid-state physics is analyzed. Stability of these kinds of synchronization against changes of system parameters and noise is investigated. In drive–response systems generalized marginal synchronization is shown to be rather sensitive to the changes of parameters and may disappear either due to the loss of stability of the response system, or as a result of the blowout bifurcation. Nonlinear coupling of the drive system to the response system can stabilize marginal synchronization.     

一类五次Hamilton系统平面相图的拓扑分类

该文研究一类五次的哈密顿系统. 通过对其系数的分析、计算给出它所有可能的平面相图的拓扑类型. 从而为对它们的扰动系统的研究提供条件.     

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.     

Evaluating the effects of distribution centres on the performance of vendor-managed inventory systems

This paper evaluates the effects of the distribution centre (DC) in a vendor-managed inventory (VMI) system comprising one manufacturer, one DC and n retailers. Adopting the order-up-to-level (OUL) replenishment policy, the system aims to maximize the overall system profit. We propose a model to evaluate the system performance by considering the scale of the distribution network, influential cost factors, demand distribution, planning horizon, and facility locations. From the viewpoint of a supply chain, we examine the DC’s effects on the system in terms of net profit. Our findings reveal that the DC has effects on demand variance and system profit, and there are some dominant factors that affect the overall system performance. The DC may lead to different system performance under a variety of cost factors, and in some situations, the DC may negatively affect system performance. We also suggest some innovative uses of the DC’s location to help enhance system performance.     

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．     

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.     

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.     

Charpit System of Partial Differential Equations with Algebraic Constraints

In this paper the Charpit system of partial differential equations with algebraic constraints is considered. So, first the compatibility conditions of a system of algebraic equations and also of the Charpit system of partial differential equations are separately considered. For the combined system of equations of both types sufficient conditions for the existence of a solution are found. They lead to an algorithm for reducing the combined system to a Charpit system of partial differential equations of dimension less than the initial system and without algebraic constraints. Moreover, it is proved that this system identically satisfies the compatibility conditions if so does the initial system.     

非线性控制系统的梯度扩张的能达性

研究了仿射非线性控制系统的梯度扩张系统.利用非线性控制系统的微分几何理论,通过计算梯度扩张系统的输出函数沿着输入向量场和系统向量场的李导数,讨论仿射非线性控制系统的梯度扩张系统的能达性分布,研究了非线性控制系统和它的梯度扩张系统的能达性之间的关系,证明了如果梯度扩张系统是能达的,则原非线性控制系统也是能达的.     

考虑n中连续取k失效准则的树状系统可靠性求解方法

树状网络系统在管道运输,网络通信中较为常见,对其进行可靠性评估对系统设计及优化具有重要意义。针对树状冗余系统,在n中连续取k失效准则下,通过有限马尔可夫嵌入法并对其进行变形,研究了树状系统可靠性求解方法。本文对树状系统建模加以定义,提出了基于层数参数,层-节点向量,父-子节点矩阵三元参数的树状系统表示方法,研究了变形有限马尔可夫嵌入法的树状系统n中连续取k失效准则下的可靠性求解方法,给出了三个数值算例应用并分析了算法的运算复杂度。最后,本文对比讨论了基于概率母函数法的树状系统在n中连续取k准则下系统可靠性求解方法的研究,得出结论本文算法针对树状冗余系统n中连续取k失效准则下系统可靠性求解应用范围更广,求解效率较高。