The Z-transform and linear multistep stability

^** Email: mapjjc{at}maths.bath.ac.uk^*** Corresponding author. Email: ath{at}maths.bath.ac.uk^**** Email: hl{at}maths.bath.ac.uk This paper makes systematic use of control-theoretic methodssuch as the -transform, small-gain theorems and frequency-domainstability criteria in the analysis of the stability behaviourof linear multistep methods. Some of the results in Nevanlinna'swork are recovered and a number of new boundedness and asymptoticproperties of solutions of numerical schemes are obtained. Inparticular, we give a careful and detailed analysis of the nonlinearstability properties of strictly zero-stable methods.     

A unified framework for the numerical solution of general quadratic matrix equations

^** Email: vassilios.tsachouridis{at}ieee.org^*** Email: N.karcanias{at}city.ac.uk^**** Email: ixp{at}le.ac.uk Algebraic quadratic equations are special cases of a singlegeneralized algebraic quadratic matrix equation (GQME). Thispaper focuses on the numerical solution of the GQME using probability-1homotopy methods. A synoptic review of these methods and theirapplication to algebraic matrix equations is provided as background.A large variety of analysis and design problems in systems andcontrol are reported as special cases of the presented frameworkand some of them are illustrated via numerical examples fromthe literature.     

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.     

Optimal allocation of reliability tasks to mitigate faults during system development

^** Email: walter.johnston{at}baesystems.com^*** Email: j.quigley{at}strath.ac.uk^**** Email: lesley.walls{at}strath.ac.uk This paper considers reliability planning for a concept designfor a new system where a portfolio of possible reliability developmenttasks exists; the goal is to find a selection and sequence oftasks to achieve reliability targets subject to time constraintsat minimal cost. This is non-trivial given that each task potentiallycan expose several different weaknesses and each weakness potentiallycan be exposed by several different tasks. We use a Bayesianpoint process model to estimate the system reliability. Theprior distribution maps to a fault register and relates directlyto a set of potential engineering modifications.The likely impactof each task can be assessed using the point process model.An integer programming approach is used to sequence and scheduletasks under the constraint that contractual reliability requirementsmust be met. An illustrative example is provided and an extensionto system availability is proposed.     

On the numerical solution of involutive ordinary differential systems: enhanced linear algebra

^** Email: jukka.tuomela{at}joensuu.fi^*** Corresponding author. Email: arponen{at}maths.warwick.ac.uk^**** Email: villesamuli.normi{at}joensuu.fi We analyse some Runge–Kutta type methods for computing1D integral manifolds, i.e. solutions to ordin-ary differentialequations and differential-algebraic equations. We show thatwe can compute the solutions which respect all the constraintsof the problem reliably and reasonably quickly. Moreover, weshow that the so-called impasse points are regular points inour approach and hence require no special attention.     

An a posteriori error indicator for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations

^** Email: paul.houston{at}nottingham.ac.uk^*** Corresponding author. Email: ilaria.perugia{at}unipv.it^**** Email: schoetzau{at}math.ubc.ca We introduce a residual-based a posteriori error indicator fordiscontinuous Galerkin discretizations of H(curl; )-ellipticboundary value problems that arise in eddy current models. Weshow that the indicator is both reliable and efficient withrespect to the approximation error measured in terms of a naturalenergy norm. We validate the performance of the indicator withinan adaptive mesh refinement procedure and show its asymptoticexactness for a range of test problems.     

Differentiated service delivery in cooperative IP-based broadcast and mobile telecommunications networks

Email: angelo.centonza{at}brunel.ac.uk Corresponding author. Email: thomas.owens{at}brunel.ac.uk Email: john.cosmas{at}brunel.ac.uk^¶ Email: y.h.song{at}brunel.ac.uk Received on 26 November 2005. Accepted on 20 March 2007. The evolution of wireless systems has led recently to the deploymentof cooperative network infrastructures where networks basedon different technologies cooperate together to offer innovativeservices which the networks individually could not offer. Cooperativenetwork infrastructures are hybrid systems. Examples of hybridsystems are already in use in areas as diverse power systemsand locomotion systems. It is very important to apply efficientsystem management techniques to hybrid systems that produceadvantageous business case scenarios for each participatingsystem and efficient use of the available resources. In thispaper, scenarios are investigated where cooperation betweenan integrated project (IP)-based broadcast network and an IP-basedmobile telecommunications network has the potential to allowservices to be provided to mobile users which would not be economicalto offer over either an IP-based broadcast network or an IP-basedmobile telecommunications network alone. The paper presentsa novel technique for determining which network to use to deliversuch services at a given point in time. The application of thistechnique in appropriate scenarios has the potential to generateadditional income for both the IP-based broadcast network operatorand the IP-based mobile telecommunications network operatorin an infrastructure where the operators cooperate to offerinnovative services. The paper explains the construction ofutility functions for cooperative IP-based broadcast and mobiletelecommunications networks. These utility functions are thenused to provide results that enable the efficiency of the managementof the network to be assessed in terms of the utility volumegenerated by the innovative services provided.     

Asymptotic and numerical analysis of thermoelastic waves in an isotropic plate

^** Email: n.scott{at}uea.ac.uk This paper considers the propagation of a plane thermoelasticwave in an infinite homogeneous isotropic plate subjected toeither isothermal or thermally insulated traction-free boundaryconditions. The primary concerns are the derivation and numericalexamination of the dispersion relations along with the developmentof asymptotic models for the fundamental branches of the dispersionrelations. Thermal dissipation is also discussed.     

A priori and a posteriori analysis of non-conforming finite elements with face penalty for advection-diffusion equations

^** Corresponding author. Email: l.elalaoui{at}imperial.ac.uk^*** Email: ern{at}cermics.enpc.fr^**** Email: erik.burman{at}epfl.ch We analyse a non-conforming finite-element method to approximateadvection–diffusion–reaction equations. The methodis stabilized by penalizing the jumps of the solution and thoseof its advective derivative across mesh interfaces. The a priorierror analysis leads to (quasi-)optimal estimates in the meshsize (sub-optimal by order in the L²-norm and optimal in thebroken graph norm for quasi-uniform meshes) keeping the Pécletnumber fixed. Then, we investigate a residual a posteriori errorestimator for the method. The estimator is semi-robust in thesense that it yields lower and upper bounds of the error whichdiffer by a factor equal at most to the square root of the Pécletnumber. Finally, to illustrate the theory we present numericalresults including adaptively generated meshes.     

On a modified version of ILDM approach: asymptotic analysis based on integral manifolds

^** Email: vbykov{at}cs.bgu.ac.il^*** Email: goldfarb{at}cs.bgu.ac.il^**** Email: vladimir{at}bgumail.bgu.ac.il^***** Email: umaas{at}itt.mach.uni-karlsruhe.de Using the method of integral (invariant) manifolds, the intrinsiclow-dimensional manifolds (ILDM) method is analysed. This isa method for identifying invariant manifolds of a system's slowdynamics and has proven to be an efficient tool in modellingof laminar and turbulent combustion. It allows treating multi-scalesystems by revealing their hidden hierarchy and decomposingthe system dynamics into fast and slow motions. The performedanalysis shows that the original ILDM technique can be interpretedas one of the many possible realizations of the general framework,which is based on a special transformation of the original coordinatesin the state space. A modification of the ILDM is proposed basedon a new definition of the transformation matrix. The proposednumerical procedure is demonstrated on linear examples and highlynon-linear test problems of mathematical theory of combustionand demonstrates in some cases better performance with respectto the existing one.     

Alternate strip-based substructuring algorithms for elliptic PDEs in two dimensions

^** Email: angela.mihai{at}strath.ac.uk^*** Email: alan.craig{at}durham.ac.uk The alternate strip-based substructuring algorithms are efficientpreconditioning techniques for the discrete systems which arisefrom the finite-element approximation of symmetric ellipticboundary-value problems in 2D Euclidean spaces. The new approachis based on alternate decomposition of the given domain intoa finite number of strips. Each strip is a union of non-overlappingsubdomains and the global interface between subdomains is partitionedas a union of edges between strips and edges between subdomainsthat belong to the same strip. Both scalability and efficiencyare achieved by alternating the direction of the strips. Thisapproach generates algorithms in two stages and allows the useof a two-grid V cycle. Numerical estimates illustrate the behaviourof the new domain decomposition techniques.     

Explicit stability conditions for time-discrete vector Lur'e-type systems

^** Email: gilmi{at}cs.bgu.ac.il^*** Email: rmedina{at}ulagos.cl Non-linear discrete-time Lur'e-type systems are considered.Explicit stability conditions are suggested. They are formulatedin terms of the determinants of characteristic polynomials.Moreover, an estimate for the region of attraction of the zerosolution is derived.     

An adaptive boundary element method for the exterior Stokes problem in three dimensions

^** Email: vjervin{at}clemson.edu^*** Email: norbert.heuer{at}brunel.ac.uk We present an adaptive refinement strategy for the h-versionof the boundary element method with weakly singular operatorson surfaces. The model problem deals with the exterior Stokesproblem, and thus considers vector functions. Our error indicatorsare computed by local projections onto 1D subspaces definedby mesh refinement. These indicators measure the error separatelyfor the vector components and allow for component-independentadaption. Assuming a saturation condition, the indicators giverise to an efficient and reliable error estimator. Also we describehow to deal with meshes containing quadrilaterals which arenot shape regular. The theoretical results are underlined bynumerical experiments. To justify the saturation assumption,in the Appendix we prove optimal lower a priori error estimatesfor edge singularities on uniform and graded meshes.     

Modelling a baseball game to optimise pitcher substitution strategies incorporating handedness of players

^** Email: hirotsu.nobuyoshi{at}jiss.naash.go.jp^*** Email: m.wright{at}lancaster.ac.uk This paper proposes a method for identifying the optimal strategyfor substituting players in a baseball game, taking into considerationthe handedness of players, which is one of the main factorsin terms of managerial decision-making for substitution. Usinga Markov chain model, we incorporate the effect of the handednessof players by introducing the concept of the defensive earnedrun average as a measure of the defensive ability of pitchersand calibrating the batting probabilities of players dependingon their handedness. We then develop a dynamic programming formulationincluding the effect of the handedness of players. This methodis illustrated using a match based on the real line-ups of theColorado Rockies and the San Francisco Giants in the NationalLeague of Major League Baseball, especially focusing on theintroduction of a relief pitcher in consideration with his handedness.     

Solving parallel machines scheduling problems with sequence-dependent setup times using variable neighbourhood search

^** Corresponding author. Email: mahdi{at}dcc.ufmg.br^*** Email: martin{at}dcc.ufmg.br^**** Email: mateus{at}dcc.ufmg.br^***** Email: pardalos{at}ufl.edu Variable neighbourhood search (VNS) is a modern metaheuristicbased on systematic changes of the neighbourhood structure withina search to solve optimization problems. The aim of this paperis to propose and analyse a VNS algorithm to solve schedulingproblems with parallel machines and sequence-dependent setuptimes, which are of great importance on the industrial context.Three versions of a greedy randomized adaptive search procedurealgorithm are used to compare with the proposed VNS algorithmto highlight its advantages in terms of generality, qualityand speed for large instances.     

Robust constrained linear regulator problem

^** Email: mesquine{at}ucam.ac.ma^*** Email: a.benlamkadem{at}ucam.ac.ma The robust constrained state and control regulator problem isconsidered. Necessary and sufficient conditions of positiveinvariance are established. A linear programming approach ispresented in order to construct, for an uncertain constrainedlinear system, a stabilizing linear state feedback control.The control law transfers asymptotically to the origin any initialstate belonging to a given set, while constraints on the stateand the control vectors are respected.     

Parallel variable neighbourhood search algorithms for job shop scheduling problems

^** Email: msevkli{at}fatih.edu.tr^*** Corresponding author. Email: mehmetaydin{at}acm.org, mehmet.aydin{at}beds.ac.uk Variable neighbourhood search (VNS) is one of the most recentmetaheuristics used for solving combinatorial optimization problemsin which a systematic change of neighbourhood with a local searchis carried out. However, as happens with other metaheuristics,it takes a long time to reach some useful solutions while solvingsome sort of hard combinatorial problems such as job shop scheduling(JSS). Parallelization is one of the most considerable policiesto overcome this matter. In this paper, firstly, a number ofVNS algorithms are examined for JSS problems and then four differentparallelization policies are taken into account to determineefficient parallelization for VNS algorithms. The experimentationreveals the performance of various VNS algorithms and the efficiencyof policies to follow in parallelization. In the end, the unilateral-ringtopology, a noncentral parallelization method, is found as themost efficient policy.     

A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems

^** Email: emmanuil.georgoulis{at}mcs.le.ac.uk^*** Email: al{at}maths.strath.ac.uk We consider a variant of the hp-version interior penalty discontinuousGalerkin finite element method (IP-DGFEM) for second-order problemsof degenerate type. We do not assume uniform ellipticity ofthe diffusion tensor. Moreover, diffusion tensors of arbitraryform are covered in the theory presented. A new, refined recipefor the choice of the discontinuity-penalization parameter (thatis present in the formulation of the IP-DGFEM) is given. Makinguse of the recently introduced augmented Sobolev space framework,we prove an hp-optimal error bound in the energy norm and anh-optimal and slightly p-suboptimal (by only half an order ofp) bound in the L² norm (the latter, for the symmetric versionof the IP-DGFEM), provided that the solution belongs to an augmentedSobolev space.     

On the stability of swelling porous elastic soils with fluid saturation by one internal damping

^** Email: wangjc{at}graduate.hku.hk^*** Email: bzguo{at}iss.ac.cn This article addressed the stabilization of a system of 1D swellingporous elastic soils with fluid saturation. The system is describedby strongly coupled vibrating fluid and solid elastic materials.Using Riesz basis approach, we show that the whole system canbe exponentially stabilized by only one internal viscous dampingwith variable feedback gain imposed in the fluid part, whichis sharp contrast with the same effect by two dampings in existingliterature. Moreover, the explicit asymptotic expressions ofhigh eigenfrequencies exhibit clearly how this one damping canaffect the another part of solid vibration.     

Reimbursement systems and regional inpatient allocation: a non-linear optimisation model

^** Email: marion.rauner{at}univie.ac.at^*** Email: georg.schneider{at}univie.ac.at^**** Email: kurt.heidenberger{at}univie.ac.at This study presents a non-linear optimisation model for investigatingthe optimal allocation of both budgets and inpatients with differenttreatments among hospitals within a geographic region such asVienna. The objective function maximises the overall qualityof treatment provided by regional hospitals. We compare theeffects of two different reimbursement systems—fixed versusvariable budgets—on optimal allocation strategies. Thecombination of modelling ideas from hospital location-allocationmodels and economic models to solve such a problem is new accordingto the literature. We found that fixed budgets outperformedvariable budgets as fewer Euros had to be invested for an incrementalunit of quality of care provided in most of the policy scenariosanalysed. Regional demand and supply patterns for differenttreatments affect the decision makers' choice of the most suitablereimbursement system. In our illustrative example, two hospitalsappeared inefficient regardless of the reimbursement system.Vienna policy makers are currently considering restructuringthese hospitals. They plan to merge one with nearby hospitalsand transform the other into a nursing home.