用投影方法求耗散广义Hamilton约束系统的李群积分

针对耗散广义Hamilton约束系统．通过引入拉格朗日乘子和采用投影技术，给出了一种保持动力系统内在结构和约束不变性的李群积分法．首先将带约束条件的耗散Hamilton系统化为无约束广义Hamilton系统．进而讨论了无约束广义Hamilton系统的李群积分法，最后给出了广义Hamilton约束系统李群积分的投影方法．采用投影技术保证了约束的不变性，引入拉格朗日乘子后，在向约束流形投影时不会破坏原动力系统的李群结构．讨论的内容仅限于完整约束系统，通过数值例题说明了方法的有效性．     

通过同步实现从混沌到有序的转变

本文旨在研究连续的混沌系统是否存在“混沌＋混沌=有序”的现象．证明了两个双向耦合的连续混沌系统在一些情况下可产生有序的动力学行为．作为例子，通过选取适当的耦合参数使Lorenz系统以及Chen和Lee引入的混沌系统同步，进而对同步系统的动力学行为进行了理论分析和数值模拟．结果表明，逐渐改变参数，系统实现了从混沌到有序的过渡．     

谐和与有界噪声联合参激作用下的Visco-Elastic系统

研究了带visco-elastic项的非线性系统，在谐和与有界噪声联合参激作用下的响应和稳定性问题．用多尺度法分离了系统的快变项，并求出了系统的最大Liapunov指数和稳态概率密度函数，根据最大Liapunov指数可得系统解稳定的充分必要条件．讨论了系统的visco-elastic项对系统阻尼项和刚度项的贡献，给出了随机项和确定性参激强度等参数对系统响应影响的讨论．数值模拟表明该方法是有效的．     

飞艇姿态跟踪系统的研究

研究了具有参数不确定和外部干扰的飞艇姿态跟踪控制问题．飞艇姿态运动的数学模型为一个多输入／多输出不确定非线性系统，根据该系统的特点，采用了一个基于不确定项上界的鲁棒输出跟踪控制器设计方法，应用输入／输出反馈线性化法和李雅普诺夫方法，设计了飞艇姿态鲁棒控制律，它可确保系统输出按指数规律跟踪期望输出．该控制器设计简单，易于实现．仿真结果表明：即使系统存在不确定性和外界干扰，仍可在闭环系统中实现精确的姿态控制．     

一类带有扩散和时滞的捕食与被捕食模型的渐近性质

本文中，我们考虑一类带有扩散和时滞的捕食与被捕食系统．我们分析了系统的非负不变性，边界平衡点性质，全局渐近稳定性及永久持续生存性．在这一系统中，当时滞由0变到ro时，系统在平衡点附近发生Hopf分支．即当r增加通过临界值ro时，从正平衡点分支出周期解．     

有噪及无噪的时滞细胞神经网络稳定性分析

分析了一类时滞细胞神经网络（DCNN）系统在无噪声和有噪声干扰情况下的稳定性．首先针对确定性系统给出了一种简单且容易验证的全局指数稳定性条件，然后讨论了噪声干扰下系统的稳定性．当DCNN被外部噪声扰动时，系统是全局稳定的．重要的是，当系统被内在噪声扰动时，只要噪声总强度控制在一定范围内，系统是全局指数稳定的．鉴于随机共振现象在越来越多的非线性生物系统中被发现，这种稳定性具有重要意义．     

具有非单调功能反应和脉冲扰动的捕食系统的研究

研究捕食者具有非单调功能反应和周期脉冲扰动的捕食者一食饵系统，利用脉冲微分方程的Floquet理论和比较定理，得到了系统灭绝和持续生存的充分条件．最后，通过数值模拟阐明系统在周期脉冲扰动下的复杂性．     

关于刚体系统的单侧约束运动

本文研究了一大类刚体系统的单侧约束运动的局部和整体性质．主要结论是；局部地，这类系统的运动相当于某带过黎曼流形上的质点的运动；整体地，在能量守恒的假定下．这类系统相当于某带边黎曼流形上的台球系统．     

不确定线性时滞中立系统的鲁棒无源控制

研究了带有中立和离散滞后的不确定中立系统的鲁棒无源控制．设计了使不确定时滞中立系统鲁棒稳定和无源的状态反馈控制器．通过线性矩阵不等式和Lyapunov函数，在系统的时间滞后和不确定参数范数有界的约束条件下，给出了系统无源稳定的条件和期望的状态反馈控制器的表达式．最后给出的数值例子说明了设计方法的有效性．     

具有连续时滞和功能性反应的非自治竞争系统的持续生存

本文利用Lyapunov-Razumikhin理论讨论了具有连续时滞和Ⅱ类功能性反应的非自治扩散竞争系统．此系统有两个种群n个斑块，其中一个种群可以在n个斑块中自由扩散，另一种群被限定在一斑块中不能扩散．当系数满足一定的条件时，证明了系统是持续生存的，此外，给出了该系统的一周期解全局吸引的充分条件．     

Partially isometric dilations of noncommuting -tuples of operators

Given a row contraction of operators on a Hilbert space and a family of projections on the space that stabilizes the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries that satisfy natural relations. For a fixed row contraction the set of all dilations forms a partially ordered set with a largest and smallest element. A key technical device in our analysis is a connection with directed graphs. We use a Wold decomposition for partial isometries to describe the models for these dilations, and we discuss how the basic properties of a dilation depend on the row contraction.

     

A Dynamic Frictional Contact Problem with Normal Damped Response

We consider a mathematical model which describes the frictional contact between a viscoelastic body and a reactive foundation. The process is assumed to be dynamic and the contact is modeled with a general normal damped response condition and a local friction law. We present a variational formulation of the problem and prove the existence and uniqueness of the weak solution, using results on evolution equations with monotone operators and a fixed point argument. We then introduce and study a fully discrete numerical approximation scheme of the variational problem, in terms of the velocity variable. The numerical scheme has a unique solution. We derive error estimates under additional regularity assumptions on the data and the solution.     

A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge

This paper considers a two-stage distribution problem of a supply chain that is associated with a fixed charge. Two kinds of cost are involved in this problem: a continuous cost that linearly increases with the amount transported between a source and a destination, and secondly, a fixed charge, that incurs whenever there exists a transportation of a non-zero quantity between a source and a destination. The objective criterion is the minimisation of the total cost of distribution. A genetic algorithm (GA) that belongs to evolutionary search heuristics is proposed and illustrated. The proposed methodology is evaluated for its solution quality by comparing it with the approximate and lower bound solutions. Thus, the comparison reveals that the GA generates better solution than the approximation method and is capable of providing solution either equal or closer to the lower bound solution of the problem.     

Kripke submodels and universal sentences

We define two notions for intuitionistic predicate logic: that of a submodel of a Kripke model, and that of a universal sentence. We then prove a corresponding preservation theorem. If a Kripke model is viewed as a functor from a small category to the category of all classical models with (homo)morphisms between them, then we define a submodel of a Kripke model to be a restriction of the original Kripke model to a subcategory of its domain, where every node in the subcategory is mapped to a classical submodel of the corresponding classical model in the range of the original Kripke model. We call a sentence universal if it is built inductively from atoms (including ? and ⊥) using ∧, ∨, ?, and →, with the restriction that antecedents of → must be atomic. We prove that an intuitionistic theory is axiomatized by universal sentences if and only if it is preserved under Kripke submodels. We also prove the following analogue of a classical model‐consistency theorem: The universal fragment of a theory Γ is contained in the universal fragment of a theory Δ if and only if every rooted Kripke model of Δ is strongly equivalent to a submodel of a rooted Kripke model of Γ. Our notions of Kripke submodel and universal sentence are natural in the sense that in the presence of the rule of excluded middle, they collapse to the classical notions of submodel and universal sentence. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence of a solution for two phase flow in porous media: The case that the porosity depends on the pressure

In this paper we prove the existence of a solution of a coupled system involving a two phase incompressible flow in the ground and the mechanical deformation of the porous medium where the porosity is a function of the global pressure. The model is strongly coupled and involves a nonlinear degenerate parabolic equation. In order to show the existence of a weak solution, we consider a sequence of related uniformly parabolic problems and apply the Schauder fixed point theorem to show that they possess a classical solution. We then prove the relative compactness of sequences of solutions by means of the Fréchet-Kolmogorov theorem; this yields the convergence of a subsequence to a weak solution of the parabolic system.     

Construction of a CPA contraction metric for periodic orbits using semidefinite optimization

A Riemannian metric with a local contraction property can be used to prove existence and uniqueness of a periodic orbit and determine a subset of its basin of attraction. While the existence of such a contraction metric is equivalent to the existence of an exponentially stable periodic orbit, the explicit construction of the metric is a difficult problem.In this paper, the construction of such a contraction metric is achieved by formulating it as an equivalent problem, namely a feasibility problem in semidefinite optimization. The contraction metric, a matrix-valued function, is constructed as a continuous piecewise affine (CPA) function, which is affine on each simplex of a triangulation of the phase space. The contraction conditions are formulated as conditions on the values at the vertices.The paper states a semidefinite optimization problem. We prove on the one hand that a feasible solution of the optimization problem determines a CPA contraction metric and on the other hand that the optimization problem is always feasible if the system has an exponentially stable periodic orbit and the triangulation is fine enough. An objective function can be used to obtain a bound on the largest Floquet exponent of the periodic orbit.     

Partnership formation based on multiple traits

A model of partnership formation based on two traits, called beauty and character, is presented. There are two classes of individual and partners must be of different classes. Individuals prefer prospective partners with a high beauty measure and of a similar character. This problem may be interpreted as e.g. a job search problem in which the classes are employer and employee, or a mate choice problem in which the classes are male and female. Beauty can be observed instantly. However, a costly date (or interview) is required to observe the character of a prospective partner. On observing the beauty of a prospective partner, an individual decides whether he/she wishes to date. During a date, the participants observe each other’s character and then decide whether to form a pair. Mutual acceptance is required both for a date to occur and pair formation. On finding a partner, an individual stops searching. Beauty has a continuous distribution on a finite interval, while character ‘forms a circle’ and has a uniform distribution. Criteria based on the concept of a subgame perfect Nash equilibrium are used to define a symmetric equilibrium of this game. It is argued that this equilibrium is unique. When dating costs are high, this equilibrium is a block separating equilibrium as in more classical formulations of two-sided job search problems. However, for sufficiently small dating costs the form of this equilibrium is essentially different.     

覆盖数不超过3的图上渡河问题

1000多年前,英国著名学者Alcuin曾提出一个古老的渡河问题,即狼、羊和卷心菜的渡河问题。2006年,Prisner把该问题推广到任意的冲突图上,考虑了一类情况更一般的渡河运输问题。所谓冲突图是指一个图G=(V,E),这里V代表某些物品的集合,V中的两个点有边连结当且仅当这两个点是冲突的,即在无人监管的情况下不允许留在一起的点。图G=(V,E)的一个可行运输方案是指在保证不发生任何冲突的前提下,把V的点所代表的物品全部摆渡到河对岸的一个运输方案。图G的Alcuin数定义为它存在可行运输方案时所需船的最小容量。本文讨论了覆盖数不超过3的连通图的Alcuin数,给出了该类图Alcuin数的完全刻画。     

Computing lower and upper bounds for a large-scale industrial job shop scheduling problem

In this paper we present a case study from the lighting industry concerned with the scheduling of a set of job families each representing the production of a particular end-item in a given quantity. It is a job shop type problem, where each job family has a number of routing alternatives, and the solution has to respect batching and machine availability constraints. All jobs of the same job family have a common release date and a common due date, and they differ only in size. The objective is to minimize the total tardiness of the job families, rather than that of individual jobs. We propose a two-phase method based on solving a mixed-integer linear program and then improving the initial solution by tabu search. We evaluate our method on real-world as well as generated instances.