Generalized Halanay inequalities for dissipativity of Volterra functional differential equations

This paper is concerned with the dissipativity of theoretical solutions to nonlinear Volterra functional differential equations (VFDEs). At first, we give some generalizations of Halanay's inequality which play an important role in study of dissipativity and stability of differential equations. Then, by applying the generalization of Halanay's inequality, the dissipativity results of VFDEs are obtained, which provides unified theoretical foundation for the dissipativity analysis of systems in ordinary differential equations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs), Volterra delay-integro-differential equations (VDIDEs) and VFDEs of other type which appear in practice.     

Controllability of series connections of arbitrarily many linear systems

In this paper we study the controllability of series connections of arbitrarily many linear systems. As the main result, we completely determine the controllability and the possible controllability indices of a system obtained by a special series connection of arbitrarily many linear systems.     

Different choices of scaling in homogenization of diffusion and interfacial exchange in a porous medium

Several choices of scaling are investigated for a coupled system of parabolic partial differential equations in a two‐phase medium at the microscopic scale. This system may be regarded as modelling a reaction–diffusion problem, the Stokes problem of single‐phase flow of a slightly compressible fluid or as a heat conduction problem (with or without interfacial resistance), for example. It is shown that, starting with the same problem on the microscopic scale, different choices of scaling of the diffusion coefficients (resp. permeability or conductivity) and the interfacial‐exchange coefficient lead to different types of macroscopic systems of equations. The characterization of the limit problems in terms of the scaling parameters constitutes a modelling tool because it allows to determine the right type of limit problem. New macroscopic models, not previously dealt with, arise and, for some scalings, classical macroscopic models are recovered. Using the method of two‐scale convergence, a unified approach yielding rigorous proofs is given covering a very broad class of different scalings. Copyright © 2008 John Wiley & Sons, Ltd.     

The attractor of an equation of Tricomi's type

Consider the attractor A of an equation of pendulum type with friction driven by a constant torque. The results of M. Levi and also obtained independently by Q. Min, S. Xian, and Z. Jinyan show that if the friction coefficient is larger than a certain bound then A is homeomorphic to the circle. We shall study the bifurcation diagram of a particular class of equations of pendulum type and show that the bounds obtained before are optimal.     

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented. The authors were supported by PRONEX - CNPq / FAPERJ E-26 / 171.164/2003 - APQ1, FAPESP (Grants 2001/04597-4, 2002/00094-0, 2003/09169-6, 2002/00832-1 and 2005/56773-1) and CNPq.     

On the Analysis of the Virtual Waiting Time in Open Queueing Networks

The model of an open queueing network in heavy traffic has been developed. These models are mathematical models of computer networks in heavy traffic. A limit theorem has been presented for the virtual waiting time of a customer in heavy traffic in open queueing networks. Finally, we present an application of the theorem—a reliability model from computer network practice.     

Aircraft and crew scheduling for fractional ownership programs

Fractional aircraft ownership programs, where individuals or corporations own a fraction of an aircraft, have revolutionized the corporate aviation industry. Fractional management companies (FMC) manage all aspects of aircraft operations enabling the owners to enjoy the benefits of private aviation without the associated responsibilities. We describe here the development of a scheduling decision support tool for a leading FMC. We present mathematical models, exact and heuristic solution methods. Our computational results using real and randomly generated data indicate that these models are quite effective in finding optimal or near-optimal solutions. The first phase of the implementation of one of these models at the FMC led to a significant improvement in effective utilization of the aircraft, reduction of costs due to reduced empty moves, and hence increased profits.     

Novel designed polymer–acyclovir conjugates with linker‐controlled drug release and hepatoma cell targeting

To develop designed polymer–drug conjugates, where the rate of drug liberation and hepatoma cell targeting function could be rationally and widely controlled, we facilely synthesized a series of novel, galactose‐functionalized polymer–acyclovir conjugates with different linkers and first reported the effect of the linker structure including the type of acyclovir‐linked bond (an ester bond or an amide bond) and relative length of the linker between acyclovir and the polymer main chain on release rate and targeting ability of conjugates. In vitro release studies showed that the cumulative released acyclovir from these polymer–acyclovir conjugates was between 24 and 65% in pH 1.2 glycine solution after 7 days. The ester bond more easily underwent hydrolysis than the amide bond. The longer the relative linker length was, the faster the acyclovir was released. The cell recognition experiments visualized using confocal laser scanning microscopy exhibited that the resultant galactose‐functionalized polymer–acyclovir conjugates had evident targeting to hepG2 cells, and targeting ability was also in connection with the relative length of linker. By choosing appropriate linker, cellular internalization of acyclovir could be well achieved. We consider these results to be helpful for the design of multifunctional polymeric prodrugs, in which the required release rate and targeting ability could be rationally controlled by predetermined molecular architecture. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 117–126, 2008     

Superiority of zoom lens coupling in designing a novel X-ray image detector

We design a novel X-ray image detector by lens coupling a Gd2O2S:Tb intensifying screen with a high performance low-light-level (L3,which often means luminescence less than 10-3 Lux) image intensifier.Different coupling effects on imaging performance between zoom lens and fix-focus lens are analyzed theoretically.In experiment,for designing a detector of 15-inch visual field,the system coupled by zoom lens is of 12.25-1p/cm resolution,while the one with fix-focus lens is 10 lp/cm.The superiority of zoom lens is validated.It is concluded that zoom lens preserves the image information better than fix-focus lens and improves the imaging system's performance in this design,which is referential to the design of other optical imaging systems.     

Labeling algorithm for the shortest path problem with turn prohibitions with application to large-scale road networks

In real road networks, the presence of no-left, no-right or no U-turn signs, restricts the movement of vehicles at intersections. These turn prohibitions must be considered when calculating the shortest path between a starting and an ending point in a road network. We propose an extension of Dijkstra’s algorithm to solve the shortest path problem with turn prohibitions. The method uses arc labeling and a network structure with low memory requirements. We compare the proposed method with the dual graph approach in a set of randomly generated networks and Bogotá’s large-scale road network. Our computational experiments show that the performance of the proposed method is better than that of the dual graph approach, both in terms of computing time and memory requirements. We co-developed a Web-based decision support system for computing shortest paths with turn prohibitions that uses the proposed method as the core engine.