The Convergence of Operator Approximations at Turning Points

Present address: Department of Mathematics, University of Reading, Reading RG6 2AX. We consider the convergence of solution curves of approximationsto parameter-dependent operator equations of the form G(, x)= 0. Provided G_x(, x) remains non-singular this problem is cateredfor by a simple extension to standard theory. In this paper,however, attention is concentrated on solution curves throughcertain singular points (⁰, x⁰), and the main result is thatconvergence depends on consistency and stability results forthe linear eigenvalue problem G_x(⁰, x⁰)0 = 0.     

Pointwise Stabilization for a Chain of Coupled Vibrating Strings

For the system representing a chain of coupled vibrating strings,we show that the associated semigroup satisfies the assumptionof spectrum-determined growth, and hence obtain conditions forenergy to decay strongly or exponentially. We examine in detailthe three-string case, and our results include those obtainedby others for the two-string case. Permanent address: Beijing Institute of Information and Control,Beijing, China.     

Estimating vaccine coverage by using computer algebra

Email: altmannd{at}rki.deEmail: altmann{at}mathematik.hu-berlin.de The approach of N Gay for estimating the coverage of a multivalentvaccine from antibody prevalence data in certain age cohortsis complemented by using computer aided elimination theory ofvariables. Hereby, Gay's usage of numerical approximation canbe replaced by exact formulae which are surprisingly nice, too.     

Numerical stabilization of polynomial and matrix

Email: jdhan{at}sia.cn Email: zhjiang{at}sia.cn Corresponding author Email: nyy{at}sia.cn Received on March 6, 2006; Accepted on September 4, 2006 In this paper, the conception of numerical stabilization, whichis related to mantissa digits of computer and dimensions ofsystem, is described; and several strategies for the numericalstabilization of polynomial and matrix are presented.     

Multiple criteria models for evaluation of competitive bids

Email: slliu{at}mail.east.net.cnAuthor for correspondence Email: mskklai{at}cityu.edu.hkEmail: sywang{at}iss02.iss.ac.cn In this paper, two general bidding systems are proposed to aidan owner to select one contractor based on multiple-attributedecision making models. They are named the general multiple-attributelower-bidder system and the general multiple-attribute average-bid system and are an extension (and refreshment) of the multiparameterbidding system and the average-bid method, respectively. Thepreference of the owner over the criteria (or attributes) relevantto construction work award is incorporated into the two newsystems if necessary and required by the owner. The values ofthe attributes (excluding the cost) required to be determinedby the owner in the multiparameter bidding system are not necessarilydetermined in the general multiple-attribute lower-bidder system.This reduces the burden to the owner. The two new bidding systemsare demonstrated via an example, and are compared with the multiparameterbidding system and the average-bid method. The comparisons showthat the preference of the owner in regard to the attributesrelevant to selection of contractors has a significant effecton bid evaluation. The two new systems preserve the form ofthe competitive bidding concept and can easily be applied topractice.     

Estimates of the region of attraction of continuous-time cascade systems

Xiao-Song Yang Department of Mathematics, Huazhong University of Science and Technology Wuhan, Hubei 430074, People's Republic of China Huimin Li Departments of Mathematics and Control and Engineering, Huazhong University of Science and Technology Wuhan, Hubei 430074, People's Republic of China Corresponding author. Email: yangxs{at}cqupt.edu.cn Received on May 1, 2006; Accepted on October 6, 2006 In this paper, we first present some new sufficient conditionsfor global asymptotic stability of continuous-time cascade systems.Then, we give some detailed results on the region of attractionof continuous-time cascade systems. Some examples are presentedto illustrate these results.     

Necessary conditions for infinite-horizon Volterra optimal control problems with time delay

Email: csfvega{at}dm.uba.ar Received on August 17, 2006; Accepted on September 8, 2007 Necessary conditions are proved for optimal control problemsinvolving an infinite horizon and terminal conditions at infinitywhose states are governed by Volterra integral equations withnon-linear time delay.     

Error estimates for the finite-element solution of an elliptic singularly perturbed problem

e-mail:ang{at}am.uni-erlangen.de The paper deals with an upwind discretization of finite-volume-typefor singularly perturbed elliptic boundary value problems. Stability,inverse monotonicity and convergence are considered. The mainobjective is to pursue the dependence of the error estimateon the perturbation parameter.     

Dual-based optimization of cyclic four-day workweek scheduling

Email: hesham{at}ccse.kfupm.edu.sa An optimization method is presented for the cyclic labour days-offscheduling problem, in which workers are given three consecutivedays off per week. This method does not include linear or integerprogramming, and it does not assume that the costs of differentdays-off work patterns are equal. The dual problem is firstsolved to determine the minimum workforce size. Then, the dualsolution is used to determine days-off assignments that minimizethe total labour cost. By requiring only simple manual calculations,the new method eliminates the need for linear or integer programmingsoftware.     

Control consolidation with a threshold: an algorithm

Email: ariane.chapelle{at}ulb.ac.be Corresponding author. Email: aszafarz{at}ulb.ac.be Received on 14 October 2005. Accepted on 21 November 2006. Besides multiple voting rights, board representation and shareholders’monitoring, control tunnelling over firms can be reached throughpyramids, cross-ownership and other complex features. This phenomenonis frequent in Europe and Asia. However, the theoretical literaturehas not yet converged towards a well-defined and robust measurementof integrated control that takes into account the thresholdfor control as applied in practice. Based on graph theory, thispaper aims at filling this gap and proposes a new algorithmfor evaluating the control tunnelling exerted by the firms’ultimate shareholders. Then, the paper discusses the variousforms of control existing next to voting shares, like multiplevoting rights, board representation and active monitoring, beforesuggesting ways to include them into the modelling of control.     

Controllability and observability of impulsive hybrid dynamic systems

Corresponding author, Email: cbsoh{at}auto.eee.ntu.ac.sg This paper considers the controllability and observability ofhybrid dynamic systems with impulsive switching of the otherwisecontinuously evolving state. It derives necessary and sufficientconditions for impulsive hybrid dynamic systems to be controllableand observable.     

Direct approximation of observer error linearization for nonlinear forced systems

Email: klaus{at}roebenack.de In this paper, we discuss a generalization of the extended Luenbergerobserver. Our approach can be interpreted as an approximateerror linearization. The design procedure which is formulatedin terms of Lie derivatives and Lie brackets can easily be implementedusing computer algebra software.     

End Conditions for Interpolatory Quintic Splines

Present address: Department of Mathematics, University of Tabriz, Tabriz, Iran. Accurate end conditions are derived for quintic spline interpolationat equally spaced knots. These conditions are in terms of availablefunction values at the knots and lead to O(h⁶) convergence uniformlyon the interval of interpolation.     

A Simple Proof for a Spectral Factorization Theorem

It is shown using simple methods that the transform Z(z), z C, of the coefficient sequence of the Wold decomposition ofany full-rank wide-sense stationary purely non-deterministicstochastic process satisfies (i) Z(z) H² (D) and (ii) Z^–1(z) H(D). Further it is shown that all spectral factors satisfying(i) and (ii) are equal up to right multiplication by orthogonalmatrices, and that among these the normalized (Z(0) =I) spectralfactors are equal to the transform of the Wold decomposition.An elementary proof of Youla's Theorem is then given togetherwith a simple proof that the rows of a Cholesky factor of abanded block Toeplitz matrix converge to the coefficients ofa stable matrix polynomial. Computer and Automation Institute of the Hungarian Academyof Sciences, Budapes, Hungary.     

Computation and parametrization of periodic and connecting orbits

Email: g.moore{at}ma.ic.ac.uk or na.gmoore New algorithms for the computation of periodic and connectingorbits of autonomous differential equations are developed. Previousmethods have parametrized these curves by the independent timevariable, but our procedure is based on the canonical arclengthparametrization.     

Post-processing with computable error bounds for the finite element approximation of a nonlinear heat conduction problem

Email: ain{at}mcs.le.ac.uk Email: D.Kelly{at}unsw.edu.au^* Email: I.Sloan{at}unsw.edu.au^** Email: swang{at}cs.curtin.edu.au It is shown how the finite element approximation of a nonlinearheat conduction problem may be post-processed to yield enhancedapproximations to the solution and the flux at any point inthe domain. Sharp computable bounds on the accuracy of the post-processedapproximations are derived. A criterion is identified for guidingadaptive refinements of the finite element discretization. Anumerical example is given illustrating the theoretical results.     

Time optimal control of retarded parabolic systems

Email: skrakowi{at}usk.pk.edu.pl Received on June 15, 2005; Accepted on July 12, 2006 In this paper, the time-optimal control problem for parabolicsystems in which time lags appear in the integral form bothin the state equation and in the Neumann boundary conditionis presented. The particular properties of the optimal controlare discussed.     

A semi-Markov maintenance model with credit rating application

Email: g.damico{at}unich.it Received on 6 December 2006. Accepted on 2 April 2008. The impact of a preventive rating maintenance policy on therating process is investigated through the definition of a semi-Markovmaintenance model with imperfect repair at random times. Theresults allow us to study the rating migrations process in thetransient and the asymptotic case.     

An analysis of the coupling of finite-element and Nystrm methods in acoustic scattering

In this paper we analyze the use of a combined Nystrm and finite-elementprocedure for approximating the scattered time-harmonic acousticfield produced when an incident wave interacts with a boundedinhomogeneity. The coupling technique uses a smooth artificialboundary and explicitly decouples the integral equation andfinite-element computations. We prove convergence of the method.One highlight of this analysis is that we prove Sobolev spaceerror estimates for the Nystrm scheme (which is usually analyzedin Hlder spaces). We also present some numerical results. E-mail: kirsch{at}am.uni-erlangen.de E-mail: monk{at}math.udel.edu