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.     

Quasistatic Thermoviscoelastic Frictional Contact Problem with Damped Response

We analyze a problem which describes the frictional contact between a thermoviscoelastic body and a rigid foundation. The process is assumed to be quasistatic and the contact is modeled by a general normal damped response condition with friction law and heat exchange. Then we present a variational formulation of the problem, which is set in an abstract form as a system of evolution equations for the displacements and temperature. We establish the existence and uniqueness of the weak solution, using general results on evolution equations with monotone operators and fixed point arguments. Finally, we study the continuous dependence of the solution with respect to the initial data and contact conditions.     

Numerical Approximation of the Elastic-Viscoplastic Contact Problem with Non-matching Meshes

Summary.  This work deals with the approximation of a time dependent variational inequality modelling the unilateral contact problem of elastic-viscoplastic bodies in a bidimensional context. The problem is approximated in the space variable with nonconforming finite element methods which allow the handling of nonmatching meshes on the contact zone. Several error estimates are established and the corresponding numerical experiments are achieved. Received Febuary 7, 2001 / Revised version received August 14, 2002 / Published online October 29, 2002 Mathematics Subject Classification (1991): 73T05     

带裂纹十次对称二维准晶平面弹性的无摩擦接触问题

借助经典平面弹性复变函数方法,研究了单个刚性凸基底压头作用下,带任意形状裂纹十次对称二维准晶半平面弹性的无摩擦接触问题.利用十次对称二维准晶位移、应力的复变函数表达式,带任意形状裂纹的准晶半平面弹性无摩擦接触问题被转换为可解的解析函数复合边值问题,进而简化成一类可解的Riemann边值问题.通过求解Riemann边值问题,得到了应力函数的封闭解,并给出了裂纹端点处应力强度因子和压头下方准晶体表面任意点处接触应力的显式表达式.从压头下方接触应力的表达式可以看出,接触应力在压头边缘和裂纹端点处具有奇异性.当忽略相位子场影响时,该文所得结论与弹性材料对应结果一致.数值算例分别给出了单个平底刚性压头无摩擦压入带单个垂直裂纹和水平裂纹的十次对称二维准晶下半平面的结果.该文所得结论为准晶材料的应用提供了理论参考.     

The Dynamic Response of a Problem Solving Group

A study was made of information flows within a medium sized company producing ‘one off’, high technology products. The investigation provided evidence that the delay to the progress of information introduced by ‘problem solving’ groups could be described in a mathematical form. These findings were supported by subsequent analysis which suggests ways in which both project completion times and the expenditure of man-hours on a project can be better predicted.     

Damped Oscillatory Integrals and the Boundedness Problem for Maximal Operators

Let S ⊂ ℝR ^{n +1} be a real-analytic hypersurface with surface measure dσ, and let ψ be a smooth nonnegative compactly supported cutoff function. Consider the surface measure dμ _q = ψ|Λ(X)|^q dσ, where Λ(X) is a damping factor determined by the matrices of the first and second fundamental forms of the surface. We show that its Fourier transform decays for large |ξ| as O (|ξ|^−(1/2+ε)), ε > 0, provided that q > 3/2. We also consider applications involving maximal operators associated with means of functions over hypersurfaces.__________Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 39, No. 2, pp. 70–74, 2005Original Russian Text Copyright © by I. A. Ikromov     

Analyticity and Dynamic Behavior of a Damped Three-Layer Sandwich Beam

Using the Riesz basis approach, we study a sandwich beam that is composed of an outer stiff layer and a compliant middle layer. The dynamic behavior and analyticity of the system are obtained based on a detailed spectral analysis and Riesz basis generation. As a consequence, the analyticity of the solution and the exponential stability of the system are concluded. This work was supported by the National Natural Science Foundation of China, Program for New Century Excellent Talents in the Universities of China and by the National Research Foundation of South Africa.     

一类有时间窗口约束的多资源动态调度模型与方法

含时间窗口的多资源调度，是一个包括资源分配和时间窗口分配的两阶段优化过程。在初始调度方案执行过程中，由于新的任务需求的到达，需要对初始方案进行调整．以使整个调度方案最优。本针对这种情况，分析了该问题中的主要约束条件．建立了含时间窗口的多资源动态调度模型，给出了一种启发式迭代修改求解方法；并以含时间窗口的多机调度问题为例．对模型和算法进行了验证。     

A Problem of Normal Form in Natural Deduction

Recently Ekman gave a derivation in natural deduction such that it either contains a substantial redundant part or else is not normal. It is shown that this problem is caused by a non‐normality inherent in the usual modus ponens rule.     

A Viscoelastic Sliding Contact Problem with Normal Compliance,Unilateral Constraint and Memory Term

Mediterranean Journal of Mathematics - We consider a mathematical model which describes the equilibrium of a viscoelastic body in frictional contact with a moving foundation. The contact is modeled...     

对提早响应问题的再考察

本文将非标准分析应用于信号分析中的提早响应问题,证明提早响应产生于付里叶分析过程而不是产生于信号传输过程.这一例子表明标准分析对于实证科学是不完备的.     

Existence and Regularity for Dynamic Viscoelastic Adhesive Contact with Damage

A model for the dynamic process of frictionless adhesive contact between a viscoelastic body and a reactive foundation, which takes into account the damage of the material resulting from tension or compression, is presented. Contact is described by the normal compliance condition. Material damage is modelled by the damage field, which measures the pointwise fractional decrease in the load-carrying capacity of the material, and its evolution is described by a differential inclusion. The model allows for different damage rates caused by tension or compression. The adhesion is modelled by the bonding field, which measures the fraction of active bonds on the contact surface. The existence of the unique weak solution is established using the theory of set-valued pseudomonotone operators introduced by Kuttler and Shillor (1999). Additional regularity of the solution is obtained when the problem data is more regular and satisfies appropriate compatibility conditions.     

带客户协同分仓的动态车辆路径问题研究

随着互联网商业迭代的不断深化,越来越多的企业倾向于从商品前置视角解决配送距离与配送时效性的矛盾。为此,本文研究基于客户协同分仓备货的动态车辆调度问题(Dynamic Vehicle Routing Problem with Inventory Synergetic Customer, DVRP-ISC),设计考虑区域分异特征的协同分仓客户选择方法,建立多阶段动态配送网络优化模型。鉴于研究问题的特殊性,设计多阶段两级网络协同配送路径优化算法;最后,以仿真算例、自定义算例集和基准算例,验证所提模型和算法性能及其拓展性。     

考虑外包的单产品再制造批量决策

在已有动态批量决策问题的基础上,考虑了再制造与外包这两个因素建立了单产品的再制造批量决策模型。对考虑外包的单产品再制造批量决策问题最优解的性质进行了讨论,在此基础上利用动态规划的思想给出了时间复杂性为O(T4)的算法,并用C++实现了本算法,实验表明本算法是有效的。     

A Note on a Two-dimensional Dynamic Programming Problem

A two-dimensional dynamic programming problem is posed. By relaxing some of the restraints on the problem it is reduced to a standard dynamic programming problem. Results are quoted from a particular case study.     

A Dynamic Programming Algorithm for the κ-Haplotyping Problem

The Minimum Fragments Removal （MFR） problem is one of the haplotyping problems： given a set of fragments, remove the minimum number of fragments so that the resulting fragments can be partitioned into k classes of non-conflicting subsets. In this paper, we formulate the κ-MFR problem as an integer linear programming problem, and develop a dynamic programming approach to solve the κ-MFR problem for both the gapless and gap eases.     

投资组合问题的动态规划方法

关于投资组合问题,Markowitz的均值-方差模型奠定了理论基础。近年来出现了许多简化模型,多目标线性规划模型是其中之一,但是这种线性化方法不便于处理非线性的交易费,本文建立一种动态规划模型和递推算法。     

A Preference Order Dynamic Program for a Knapsack Problem with Stochastic Rewards

In this paper, we extend the knapsack problem to include more realistic situations by treating the rewards (or values) associated with each item included in the solution as random variables with distributions that are known (or may be estimated) rather than known integers, as in the usual formulation. We propose a dynamic programming solution methodology where the usual real-valued return function is replaced by a preference ordering on the distributions of returns from the items selected. In addition to extending previous solutions to the knapsack problem, we demonstrate the selection of a preference ordering criterion and illustrate the conditions required of the ordering to guarantee optimality of the procedure. A sample problem is shown to demonstrate the algorithm, and results of computational experience with 459 problems of varying sizes and parameters are presented.