Pointwise stabilization of strings with non‐linear feedback

We consider an initial and boundary value problem for a homogenous string subject to an internal pointwise control. The solution resulting from a non‐linear feedback is studied. We give various explicit decay estimates depending on the control position and the feedback non‐linearity. Copyright © 2004 John Wiley & Sons, Ltd.     

Low‐gain adaptive stabilization of semilinear second‐order hyperbolic systems

In this paper low‐gain adaptive stabilization of undamped semilinear second‐order hyperbolic systems is considered in the case where the input and output operators are collocated. The linearized systems have an infinite number of poles and zeros on the imaginary axis. The adaptive stabilizer is constructed by a low‐gain adaptive velocity feedback. The closed‐loop system is governed by a non‐linear evolution equation. First, the well‐posedness of the closed‐loop system is shown. Next, an energy‐like function and a multiplier function are introduced and the exponential stability of the closed‐loop system is analysed. Some examples are given to illustrate the theory. Copyright © 2004 John Wiley & Sons, Ltd.     

On the uniform decay for the Korteweg–de Vries equation with weak damping

The aim of this work is to consider the Korteweg–de Vries equation in a finite interval with a very weak localized dissipation namely the H^?1‐norm. Our main result says that the total energy decays locally uniform at an exponential rate. Our analysis improves earlier works on the subject (Q. Appl. Math. 2002; LX (1):111–129; ESAIM Control Optim. Calculus Variations 2005; 11 (3):473–486) and gives a satisfactory answer to a problem suggested in (Q. Appl. Math. 2002; LX (1):111–129). Copyright © 2007 John Wiley & Sons, Ltd.     

Memory and a priori best strategy in complex adaptive systems

We employ an agent‐based model to show that memory and the absence of an a priori best strategy are sufficient for self‐segregation and clustering to emerge in a complex adaptive system with discrete agents that do not compete over a limited resource nor contend in a winner‐take‐all scenario. An agent starts from a corner of a two‐dimensional lattice and aims to reach a randomly selected site in the opposite side within the shortest possible time. The agent is isolated during the course of its journey and does not interact with other agents. Time‐bound obstacles appear at random lattice locations and the agent must decide whether to challenge or evade any obstacle blocking its path. The agent is capable of adapting a strategy in dealing with an obstacle. We analyze the dependence of strategy‐retention time with strategy for both memory‐based and memory‐less agents. We derive the equality spectrum to establish the environmental conditions that favor the existence of an a priori best strategy. We found that memory‐less agents do not polarize into two opposite strategy‐retention time distributions nor cluster toward a center distribution. © 2004 Wiley Periodicals, Inc. Complexity 9: 41–46, 2004     

Evaluation of Polycation-Stabilized Lactate Oxidase in a Silica Sol–Gel as a Biosensor Platform

 Whereas glucose oxidase and related proteins are encapsulated readily in silica sol–gels, α-hydroxy enzymes such as lactate oxidase (LOx), are reported to be damaged by electrostatic interaction with these matrices. Based on a previous report, poly(ethyleneimine), PEI, was evaluated as a protecting compound under conditions suited to analytical measurements. With LOx and PEI co-encapsulated in a silica sol–gel, the enzyme retained 62% of its initial activity after 20 days. In the absence of PEI, activity was lost during the processing. Batch analytical measurements with enzyme-doped sol–gel yielded a linear response over the range 0.5–2.0 mM lactate and a detection limit of 0.03 mM lactate. Both simple incorporation of LOx in a silica sol–gel and an alternative protection method, blocking the ion-exchange sites on silica with La(III), failed. These negative results supported the hypothesis that the efficacy of PEI was related to its formation of a protective sheath around the enzyme. Author for correspondence. E-mail: coxja@muohio.edu Received July 29, 2002; accepted December 15, 2002 Published online May 19, 2003     

A floating-point genetic algorithm for solving the unit commitment problem

This paper proposes a floating-point genetic algorithm (FPGA) to solve the unit commitment problem (UCP). Based on the characteristics of typical load demand, a floating-point chromosome representation and an encoding–decoding scheme are designed to reduce the complexities in handling the minimum up/down time limits. Strategic parameters of the FPGA are characterized in detail, i.e., the evaluation function and its constraints, population size, operation styles of selection, crossover operation and probability, mutation operation and probability. A dynamic combination scheme of genetic operators is formulated to explore and exploit the FPGA in the non-convex solution space and multimodal objective function. Experiment results show that the FPGA is a more effective technique among the various styles of genetic algorithms, which can be applied to the practical scheduling tasks in utility power systems.     

仓库容量有限条件下的一类存贮管理模型

建立了一类仓库容量有限条件下存贮管理决策模型 ,给出最优存贮策略 .     

纯量反馈系统同时强镇定的充分条件

一个稳定的补偿器可同时镇定n个对象(同时强镇定)等价于一个补偿器(不一定稳定)同时镇定n 1个对象(同时镇定)．两个以上对象的同时强镇定和三个以上对象的伺时镇定是线性系统中一个急待解决的公开问题．文中所作的基本假定是所有的对象具有相同的简单不稳定零点，在此条件下给出了n个对象同时强镇定的一个充分条件．当仅有一个不稳定零点时．容易检验是否同时强镇定，否则仅需确定n个对象的不稳定零点并且判定由不稳定零点导出一个相应矩阵是正定的，就能判定n个对象同时强镇定．因此是一个易于检验的充分条件．文章同时给出了n个对象同时强镇定的算法，丰富了同时强镇定的充分条件．     

解约束优化问题的QP-free可行域方法

本文利用一个新的分片线性NCP函数提出一个新的可行的QP-free方法解非线性不等式约束优化问题.不同于其他的QP-free方法,这个方法只考虑在工作集中的约束函数,工作集是积极集的一个估计,因此子问题的维数不是满秩的.这个方法可行的并且不需假定严格互补条件、聚点的孤立性得到算法的全局收敛性,并且积极约束函数的梯度不要求线性独立的,其中由拟牛顿法得到的子矩阵不需要求一致正定性.     

Optimal Investment Strategies for an Insurer with SAHARA Utility

In this paper, we consider the optimal investment strategy which maximizes the utility of the terminal wealth of an insurer with SAHARA utility functions. This class of utility functions has non-monotone absolute risk aversion, which is more flexible than the CARA and CRRA utility functions. In the case that the risk process is modeled as a Brownian motion and the stock process is modeled as a geometric Brownian motion, we get the closed-form solutions for our problem by the martingale method for both the constant threshold and when the threshold evolves dynamically according to a specific process. Finally, we show that the optimal strategy is state-dependent.