bluuebunny/crossref_metadata_2025 huggingface dataset:
The stability of a curved, heated boundary layer: linear and nonlinear problems
Authors: Watson C. E. , Otto S. R.
Published: February 2009

We consider the stability of high Reynolds number flow past a heated, curved wall. The influence of both buoyancy and curvature, with the appropriate sense, can render a flow unstable to longitudinal vortices. However, conversely each mechanism can make a flow more stable; as with a stable stratification or a convex curvature. This is partially due to their influence on the basic flow and also due to additional terms in the stability equations. In fact the presence of buoyancy in combination with an appropriate local wall gradient can actually increase the wall shear and these effects can lead to supervelocities and the promotion of a wall jet. This leads to the interesting discovery that the flow can be unstable for both concave and convex curvatures. Furthermore, it is possible to observe sustained vortex growth in stably stratified boundary layers over convexly curved walls. The evolution of the modes is considered in both the linear and nonlinear régimes.
Some problems about the representation of monotone operators by convex functions
Authors: Penot Jean-Paul , Zᾰlinescu Constantin
Published: February 2009

We answer a few questions raised by S. Fitzpatrick concerning the representation of maximal monotone operators by convex functions. We also examine some other questions concerning this representation and other ones which have recently emerged.
Cavities at atmospheric pressure behind two-dimensional bodies at an angle of attack
Authors: Haese P. M.
Published: February 2009

This paper presents an interior source method for the calculation of semi-infinite cavities behind two-dimensional bluff bodies placed at an angle of attack in a uniform stream. Aspects under consideration include the pressure distribution along the body, especially just ahead of the separation point, lift and drag forces, and how these quantities vary with the angle of attack. We include discussion of the physical conditions of separation, and identify critical angles of attack for which the cavitating flow past an airfoil may (a) become unstable, or (b) yield the greatest lift to drag ratio.
Elastic plastic analysis of shallow shells—a new approach
Authors: Mazumdar J. , Ghosh A. , Hewitt J. S. , Bhattacharya P. K.
Published: February 2009

A simple and efficient method for the analysis of the elastic-plastic bending of shallow shells is presented. The method is based upon the concept of contour lines of equal deflection on the surface of the shell, and uses Illyushin's theory of plastic deformation. As an illustration of the method, a technically interesting example of a shallow elliptic elastic dome is examined. Results are obtained for increasing loads and varying aspect ratios, and are illustrated graphically. The application of the method to other shell geometries is quite straightforward.
Hyperelliptic parametrisation of the generalised order parameter of the N = 3 chiral Potts model
Authors: Baxter R. J.
Published: February 2009

It has been known for some time that the Boltzmann weights of the chiral Potts model can be parametrised in terms of hyperelliptic functions. but as yet no such parametrisation has been applied to the partition and correlation functions. Here we show that for N = 3 the function S(tp) that occurs in the recent calculation of the order parameters can he expressed quite simply in terms of such a parametrisation.
Including ionisation in a simple model of single-bubble sonoluminescence
Authors: Munro Angus I. S. , Forbes Larry K.
Published: February 2009

A small gas bubble in a liquid, when driven by intense ultrasound, collapses and emits light in a process called Single-Bubble Sonoluminescence (SBSL). While the dynamics of driven bubbles are well studied, less is known of the physical conditions in the gas or whether it is necessary to include ionisation in simpler studies of bubble dynamics. In this study, a model was derived from Rayleigh-Plesset dynamics, a van der Waals equation of state and the first law of thermodynamics (including interfacial heat transfer and ionisation). Stronger model ionisation reduced the maximum collapse temperature, and altered other collapse characteristics. Chaotic parameter regions are proximal to, but not coincident with, known stable SL regions. Resonant behaviour was only markedly affected by ionisation close to these chaotic regions.
Guide expansions for the recursive parametric solution of polynomial dynamical systems
Authors: Duff G. F. D. , Leipnik R. B. , Pearce C. E. M.
Published: February 2009

Recursive parametric series solutions are developed for polynomial ODE systems, based on expanding the system components in series of a form studied by Weiss. Individual terms involve first-order driven linear ODE systems with variable coefficients. We consider Lotka-Volterra systems as an example.
Saddle point criteria and duality in multiobjective programming via an η-approximation method
Authors: Antczak Tadeusz
Published: February 2009

In this paper, Antczak's η-approximation approach is used to prove the equivalence between optima of multiobjective programming problems and the η-saddle points of the associated η-approximated vector optimisation problems. We introduce an η-Lagrange function for a constructed η-approximated vector optimisation problem and present some modified η-saddle point results. Furthermore, we construct an η-approximated Mond-Weir dual problem associated with the original dual problem of the considered multiobjective programming problem. Using duality theorems between η-approximation vector optimisation problems and their duals (that is, an η-approximated dual problem), various duality theorems are established for the original multiobjective programming problem and its original Mond-Weir dual problem.
Unsteady flow induced by a withdrawal point beneath a free surface
Authors: Stokes T. E. , Hocking G. C. , Forbes L. K.
Published: February 2009

The unsteady axisymmetric withdrawal from a fluid with a free surface through a point sink is considered. Results both with and without surface tension are included and placed in context with previous work. The results indicate that there are two critical values of withdrawal rate at which the surface is drawn directly into the outlet, one after flow initiation and the other after the flow has been established. It is shown that the larger of these values corresponds to the point at which steady solutions no longer exist.
A boundary value problem for second-order nonlinear difference equations on the integers
Authors: Dal F. , Guseinov G. Sh.
Published: February 2009

In this study, we are concerned with a boundary value problem (BVP) for nonlinear difference equations on the set of all integers Z. under the assumption that the left-hand side is a second-order linear difference expression which belongs to the so-called Weyl-Hamburger limit-circle case. The BVP is considered in the Hilbert space l2 and includes boundary conditions at infinity. Existence and uniqueness results for solution of the considered BVP are established.
Diversity sensitivity and multimodal Bayesian statistical analysis by relative entropy
Authors: Leipnik Roy B. , Pearce C. E. M.
Published: February 2009

A list of recognised social diversities is assembled, including those used in social action programmes in the USA. Responses to diversity are discussed and diversity sensitivity defined as the derivative of response with respect to a defining parameter of a diversity distribution. Rewards (or penalties) for diversity are listed also; sensitivities to the responses to the rewards for diversity are called diversity sensitivities of the second kind. The statistics of bimodal and multimodal distributions are discussed, including the parametric estimation of such distributions by mixtures of multivariate normal distributions. An example is considered in detail.
On Parrondo's paradox: how to construct unfair games by composing fair games
Authors: Key E. S. , Kłosek M. M. , Abbott D.
Published: February 2009

We construct games of chance from simpler games of chance. We show that it may happen that the simpler games of chance are fair or unfavourable to a player and yet the new combined game is favourable—this is a counter-intuitive phenomenon known as Parrondo's paradox. We observe that all of the games in question are random walks in periodic environments (RWPE) when viewed on the proper time scale. Consequently, we use RWPE techniques to derive conditions under which Parrondo's paradox occurs.
An algorithm for constructing biorthogonal multiwavelets with higher approximation orders
Authors: Shouzhi Yang
Published: February 2009

Given a pair of biorthogonal multiscaling functions, we present an algorithm for raising their approximation orders to any desired level. Precisely, let Φ(x) and (x) be a pair of biorthogonal multiscaling functions of multiplicity r, with approximation orders m and , respectively. Then for some integer s, we can construct a pair of new biorthogonal multiscaling functions Φnew(x) = [ΦT (x), φr+1 (x), φr+2(x),… φr+s(x)]T and new(x) = [ (x) T, r+1(x), r+2(x),… r+s(x)]T with approximation orders n (n > m) and ñ (ñ > ), respectively. In addition, corresponding to Φnew(x) and new(x) a biorthogonal multiwavelet pair ψnew(x) and new(x) is constructed explicitly. Finally, an example is given.
Computational models satisfying relative angle constraints for 2-dimensional segmented bodies
Authors: Munzir S. , Jennings L. S. , Koh M. T.
Published: February 2009

Planar hinged segmented bodies have been used to represent models of biomechanical systems. One characteristic of a segmented body moving under gravitational acceleration and torques between segments is the possibility that the body's segments spin through more than a revolution or past a natural limit, and a computational mechanism to stop such behaviour should be provided. This could be done by introducing angle constraints between segments, and computational models utilising optimal control are studied here. Three models to maintain angle constraints between segments are proposed and compared. These models are: all-time angle constraints, a restoring torque in the state equations and an exponential penalty model. The models are applied to a 2-D three-segment body to test the behaviour of each model when optimising torques to minimise an objective. The optimisation is run to find torques so that the end effector of the body follows the trajectory of a half-circle. The result shows the behaviour of each model in maintaining the angle constraints. The all-time constraints case exhibits a behaviour of not allowing torques (at a solution) which makes segments move past the constraints, while the other two show a flexibility in handling the angle constraints which is more similar to what occurs in a real biomechanical system.
The molecular weight distribution problem and reptation mixing rules
Authors: Anderssen R. S. , Westcott M.
Published: February 2009

Mixing rules model how the physical properties of a polymer, such as its relaxation modulusG(t), depend on the distributionw(m)of its molecular weightsm. They are of practical importance because, among other things, they allow estimates of the molecular weight distribution (MWD)w(m)of a polymer to be determined from measurements of its physical properties including the relaxation modulus. The two most common mixing rules are “single” and “double” reptation. Various derivations for these rules have been published. In this paper, a conditional probability formulation is given which identifies that the fundamental essence of “double” reptation is the discrete binary nature of the “entanglements”, which are assumed to occur in the corresponding topological model of the underlying polymer dynamics. In addition, various methods for determining the MWD are reviewed, and the computation of linear functionals of the MWD motivated and briefly examined.
A generalization of the Bernstein polynomials based on the q-integers
Authors: Phillips George M.
Published: February 2009

This paper is concerned with a generalization of the Bernstein polynomials in which the approximated function is evaluated at points spaced in geometric progression instead of the equal spacing of the original polynomials.
Approximate evaluation of integrals
Authors: Hosking Roger J.
Published: February 2009

Asymptotic and numerical analysis provides essential insight into the behaviour of Fourier integral solutions for the deflexion of an infinite continuously-supported flexible plate due to moving load. Thus we can define in detail how the plate deflexion depends upon the load speed, including (a) the wave patterns generated by a load moving steadily at various supercritical speeds; and (b) the time-dependent behaviour of the deflexion due to an impulsively-started load, where the two-dimensional response tends to a steady state except at the critical speed, when it grows continuously with time (in the absence of dissipation).
A variational approach to splines
Authors: Champion R. , Lenard C. T. , Mills T. M.
Published: February 2009

This is an expository paper in which we present an introduction to a variational approach to spline interpolation. We present a sequence of theorems which starts with Holladay's classical result concerning natural cubic splines and culminates in some general abstract results.
Aesthetic factors in geometric modelling
Authors: Pham Binh
Published: February 2009

CAD systems have traditionally catered for architectural and mechanical engineering designs which are somewhat constrained in scope. Problems concerning other types of design such as art design, industrial design or sculpting, where creativity and aesthetic factors play an important role, are not adequately addressed. These types of design require much more flexibility in both geometric modelling capability and user-machine interaction. This paper first gives a brief overview of recent work which deals with creative activities, and analyses important issues that need to be addressed in object representations for 3D creative activities. We then discuss a scheme to categorise and represent aesthetic factors in geometric modelling.
Derivative-type ascent formulas for kernels of some half-space Dirichlet problems
Authors: Bragg L. R.
Published: February 2009

Derivative-type ascent formulas are deduced for the kernels of certain half-space Dirichlet problems. These have the character of differentiation formulas for the Bessel functions but involve modifying variables after completing the differentiations. The Laplace equation and the equation of generalized axially-symmetric potential theory (GASPT) are considered in these. The methods employed also permit treating abstract versions of Dirichlet problems.
Conditions for permanence in well-known biological competition models
Authors: van Vuuren Jan H. , Norbury John
Published: February 2009

Reaction-diffusion systems are widely used to model the population densities of biological species competing for natural resources in their common habitat. It is often not too difficult to establish positive uniform upper bounds on solution components of such systems, but the task of establishingstrictly positiveuniform lower bounds (when they exist) can be quite troublesome. Two previously established criteria for the permanence (non-extinction and non-explosion) of solutions of general weakly-coupled competition-diffusion systems with diagonally convex reaction terms are used here as background to develop more easily verifiable and concrete conditions for permanence in various well-known competition diffusion models. These models include multi-component reaction-diffusion systems with (i) the by now classical Lotka-Volterra (logistic) reaction terms, (ii) higher order “logistic” interaction between the species, (iii) logistic-logarithmic reaction terms, (iv) Ayala-Gilpin-Ehrenfeld θ-interaction terms (which are used to modelDrosophilacompetition), (v) logistic-exponential interaction between the species, (vi) Schoener-exploitation and (vii) modified Schoener-interference between the species. In (i) a known condition for permanence (for the ODE-system) is recovered, while in (ii)–(vii) new criteria for permanence are established.
The best least squares approximation problem for a 3-parametric exponential regression model
Authors: Jukić D. , Scitovski R.
Published: February 2009

Given the data (pi, ti, fi), i = 1,…,m, we consider the existence problem for the best least squares approximation of parameters for the 3-parametric exponential regression model. This problem does not always have a solution. In this paper it is shown that this problem has a solution provided that the data are strongly increasing at the ends.
Bifurcation of positive solutions for a Neumann boundary value problem
Authors: Mays Laurence , Norbury John
Published: February 2009

Analytical, approximate and numerical methods are used to study the Neumann boundary value problem

− uxx + q2u = u2(1 + sin x), for 0 < x < π,

subject to ux(0) = 0, ux(π) = 0,

for q2 ∈ (0,∞). Asymptotic approximations to (1) are found for q2 small and q2 large. In the case where q2 is large u(x) ≈ 3qδ(x − π/2). When q2 = 0 we show that the only possible solution is u ≡ 0. However, there exist non-zero solutions for q2 > 0 as well as the trivial solution u ≡ 0. To O(q4) in the q2 small case u(x) = q2π(π + 2)−1, so that bifurcation occurs about the trivial solution branch u ≡ 0 at the first eigenvalue λ0 = 0 and in the direction of the first eigenfunction ξ0 = constant.

We obtain a bifurcation diagram for (1), which confirms that there exists a positive solution for q2 ∈ (0, 10). Symmetry-breaking bifurcations and blow-up behaviour occur on certain regions of the diagram. We show that all non-trival solutions to the problem must be positive.

The formal outer solution u = q2û appears to satisfy û = û2(1 + sin x), so that û ≡ 0 and û = (1 + sin x)−1 are possible limit solutions. However, in the non-trivial case ûx(0) = −1 and ûx(π) = 1; this means that û does not satisfy the boundary conditions required for a solution of (1). This behaviour usually implies that for q2 large a boundary layer exists near x = 0 (and one near x = π), which corrects the slope. However, we find no evidence for such a solution structure, and only find perturbations in the direction of a delta function about u ≡ 0. We show using the monotone convergence theorem for quadratic forms that the inverse of the operator on the left-hand side of (1) is strongly convergent as q2 → ∞. We show that strong convergence of the operator is sufficient to stop outer-layer behaviour occurring.
Vector Lyapunov functions and conditional stability for systems of impulsive differential-difference equations
Authors: Bainov D. D. , Stamova I. M.
Published: February 2009

By means of piecewise continuous vector functions, which are analogues of the classical Lyapunov functions and via the comparison method, sufficient conditions are found for conditional, stability of the zero solution of a system of impulsive differential-difference equations.
An application of Newton's method to differential and integral equations
Authors: Gutiérrez J. M. , Hernández M. A.
Published: February 2009

Newton's method is applied to an operator that satisfies stronger conditions than those of Kantorovich. Convergence and error estimates are compared in the two situations. As an application, we obtain information on the existence and uniqueness of a solution for differential and integral equations.
Refinements of some bounds in information theory
Authors: Matić M. , Pearce C. E. M. , Pečarić J.
Published: February 2009

Recently Dragomir and Goh have produced some interesting new bounds relating to entropy measures in information theory. We establish several refinements of their results.
Chaos in perturbed Lotka-Volterra systems
Authors: Christie J. R. , Gopalsamy K. , Li Jibin
Published: February 2009

Lotka-Volterra systems have been used extensively in modelling population dynamics. In this paper, it is shown that chaotic behaviour in the sense of Smale can exist in timeperiodically perturbed systems of Lotka-Volterra equations. First, a slowly varying threedimensional perturbed Lotka-Volterra system is considered and the corresponding unperturbed system is shown to possess a heteroclinic cycle. By using Melnikov's method, sufficient conditions are obtained for the perturbed system to have a transverse heteroclinic cycle and hence to possess chaotic behaviour in the sense of Smale. Then a special case involving a reduction to a two-dimensional Lotka-Volterra system is examined, leading finally to an application with a model for the self-organisation of macromolecules.
Extrapolation techniques and the collocation method for a class of boundary integral equations
Authors: Celorrio Ricardo , Sayas Francisco-Javier
Published: February 2009

In this paper we prove the existence of asymptotic expansions of the error of the spline collocation method applied to Fredholm integral equations of the first kind with logarithmic kernels. These expansions justify the use of Richardson extrapolation for the acceleration of convergence of the method. The results are stated and proven for a single equation, corresponding to the parameterization of a boundary integral equation on a smooth closed curve. As a byproduct we obtain the nodal superconvergence of the scheme. These results are then extended to smooth open arcs and to systems of integral equations. Finally we prove that such expansions also exist for the Sloan iteration of the numerical solution.
Fast diffusion with loss at infinity—additional solutions
Authors: Brown A.
Published: February 2009

The paper presents some additional solutions of the diffusion equation

for the case s = 2, m = −1, a case that was left open in a previous discussion. These solutions behave in a manner that is physically acceptable as the time, t, increases and as the radial coordinate, r, tends to infinity.
Towards numerically estimating Hausdorff dimensions
Authors: Stewart David E.
Published: February 2009

This paper gives a numerical method for estimating the Hausdorff-Besicovitch dimension where this differs from the fractal (or capacity or box-counting) dimension. The method has been implemented, and numerical results obtained for the set {1/n | n ∈ N} and the Cantor set. Comments about the practical use of the estimation algorithms are made.
Lipschitz stability of impulsive functional-differential equations
Authors: Bainov D. D. , Stamova I. M.
Published: February 2009

An initial value problem is considered for impulsive functional-differential equations. The impulses occur at fixed moments of time. Sufficient conditions are found for Lipschitz stability of the zero solution of these equations. An application in impulsive population dynamics is also discussed.
Asymptotic behaviour of a nonautonomous cooperative system
Authors: Hongliang Zhu , Jingan Cui
Published: February 2009

This paper considers a nonautonomous cooperative system, in which all the parameters are time-dependent and asymptotically approach periodic functions. We prove that under some appropriate conditions any positive solutions of the system asymptotically approach the unique positive periodic solution of the corresponding periodic system.
On a periodic mutualism model
Authors: Li Yongkun
Published: February 2009

Sufficient conditions are obtained for the existence of a globally attracting positive periodic solution of the mutualism model

where ri, Ki, αi ∈ C(R, R+) and αi > Ki, i = 1, 2, τi, σi ∈ C(R, R+), i = 1, 2, and ri, Ki, αi, τi, σi (i = 1, 2) and functions of period ω > 0.
An optimal linear filter for random signals with realisations in a separable Hilbert space
Authors: Howlett P. G. , Pearce C. E. M. , Torokhti A. P.
Published: February 2009

Let u be a random signal with realisations in an infinite-dimensional vector space X and υ an associated observable random signal with realisations in a finite-dimensional subspace Y ⊆ X. We seek a pointwise-best estimate of u using a bounded linear filter on the observed data vector υ. When x is a finite-dimensional Euclidean space and the covariance matrix for υ is nonsingular, it is known that the best estimate û of u is given by a standard matrix expression prescribing a linear mean-square filter. For the infinite-dimensional Hilbert space problem we show that the matrix expression must be replaced by an analogous but more general expression using bounded linear operators. The extension procedure depends directly on the theory of the Bochner integral and on the construction of appropriate HilbertSchmidt operators. An extended example is given.
Seasonality and critical community size for infectious diseases
Authors: Cullen R. M. , Korobeinikov A. , Walker W. J.
Published: February 2009

The endemicity of infectious diseases is investigated from a deterministic viewpoint. Sustained oscillation of infectives is often due to seasonal effects which may be related to climatic changes. For example the transmission of the measles virus by droplets is enhanced in cooler, more humid seasons. In many countries the onset of cooler, more humid weather coincides with the increased aggregation of people and the seasonal effect can be exacerbated. In this paper we consider non-autonomous compartmental epidemiological models and demonstrate that the critical community size phenomenon may be associated with the seasonal variation in the disease propagation. This approach is applicable to both the prevaccination phenomenon of critical community size and the current goal of worldwide elimination of measles by vaccination.
Minimax control of an elliptic variational bilateral problem
Authors: Chen Qihong
Published: February 2009

This paper deals with a minimax control problem for semilinear elliptic variational inequalities associated with bilateral constraints. The control domain is not necessarily convex. The cost functional, which is to be minimised, is the sup norm of some function of the state and the control. The major novelty of such a problem lies in the simultaneous presence of the nonsmooth state equation (variational inequality) and the nonsmooth cost functional (the sup norm). In this paper, the existence conditions and the Pontryagin-type necessary conditions for optimal controls are established.
Sequential eigenfunction expansion for a problem in combustion theory
Authors: Al-Refai M. , Tam K. K.
Published: February 2009

A method of sequential eigenfunction expansion is developed for a semi-linear parabolic equation. It allows the time-dependent coefficients of the eigenfunctions to be determined sequentially and iterated to reach convergence. At any stage, only a single ordinary differential equation needs to be considered, in contrast to the Galerkin method which requires the consideration of a system of equations. The method is applied to a central problemin combustion theory to provide a definitive answer to the question of the influence of the initial data in determining whether the solution is sub- or super-critical, in the case of multiple steady-state solutions. It is expected this method will prove useful in dealing with similar problems.
A notion of local proper efficiency in the Borwein sense in vector optimisation
Authors: Jiménez B. , Novo V.
Published: February 2009

In this paper we define two types of proper efficient solutions in the Borwein sense for vector optimisation problems and we compare them with the notions of local Borwein, Ishizuka-Tuan, Kuhn-Tucker and strict efficiency. A sufficient condition for a proper solution is also proved.
Natural cubic element formulation and infinite domain modelling for potential flow problems
Authors: Mohr G. A. , Power A. S.
Published: February 2009

A simple formulation of a 9 df cubic Hermitian finite element for potential flow problems is given, using the interpolation of the BCIZ element and after Argyris, defining natural velocities parallel to the element sides. Consistent loads for body forces are also derived and it is shown that these are necessary to obtain accurate results when body forces are significant. Example problems include those of infinite domains for which simpleconditions at infinityare used.
An epidemic model for the transmission dynamics of HIV and another pathogen
Authors: Moghadas S. M. , Gumel A. B.
Published: February 2009

A five-dimensional deterministic model is proposed for the dynamics between HIV and another pathogen within a given population. The model exhibits four equilibria: a disease-free equilibrium, an HIV-free equilibrium, a pathogen-free equilibrium and a co-existence equilibrium. The existence and stability of these equilibria are investigated. A competitive finite-difference method is constructed for the solution of the non-linear model. The model predicts the optimal therapy level needed to eradicate both diseases.
Degree reduction of Béezier curves using constrained Chebyshev polynomials of the second kind
Authors: Ahn Young Joon
Published: February 2009

In this paper a constrained Chebyshev polynomial of the second kind with C1-continuity is proposed as an error function for degree reduction of Bézier curves with a C1-constraint at both endpoints. A sharp upper bound of the L∞ norm for a constrained Chebyshev polynomial of the second kind with C1-continuity can be obtained explicitly along with its coefficients, while those of the constrained Chebyshev polynomial which provides the best C1-constrained degree reduction are obtained numerically. The representations in closed form for the coefficients and the error bound are very useful to the users of Computer Graphics or CAD/CAM systems. Using the error bound in the closed form, a simple subdivision scheme for C1-constrained degree reduction within a given tolerance is presented. As an illustration, our method is applied to C1-constrained degree reduction of a plane Bézier curve, and the numerical result is compared visually to that of the best degree reduction method.
The dimension of attractors of nonautonomous partial differential equations
Authors: Caraballo T. , Langa J. A. , Valero J.
Published: February 2009

The concept of nonautonomous (or cocycle) attractors has become a proper tool for the study of the asymptotic behaviour of general nonautonomous partial differential equations. This is a time-dependent family of compact sets, invariant for the associated process and attracting “from –∞”. In general, the concept is rather different to the classical global attractor for autonomous dynamical systems. We prove a general result on the finite fractal dimensionality of each compact set of this family. In this way, we generalise some previous results of Chepyzhov and Vishik. Our results are also applied to differential equations with a nonlinear term having polynomial growth at most.
Periodic solutions of a two-species ratio-dependent predator-prey system with time delay in a two-patch environment
Authors: Zhang Zhengqiu , Wang Zhicheng
Published: February 2009

By using the continuation theorem of coincidence degree theory, a sufficient condition is obtained for the existence of a positive periodic solution of a predator-prey diffusion system.
Global attractivity of a class of delay differential equations with impulses
Authors: Liu Yuji , Zhang Binggen
Published: February 2009

In this paper, we study the global attractivity of the zero solution of a particular impulsive delay differential equation. Some sufficient conditions that guarantee every solution of the equation converges to zero are obtained.
On some switching inequalities of Brenner and Alzer
Authors: Pearce C. E. M. , Pečarić J.
Published: February 2009

We consider some general switching inequalities of Brenner and Alzer. It is shown that Brenner's Theorem B below does not hold in general without further conditions. A simple proof is given of Alzer's Corollary D.
Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. II Diabatic operation
Authors: Nelson M. I. , Sidhu H. S.
Published: February 2009

We extend an investigation into the bifurcation phenomena exhibited by an oxidation reaction in an adiabatic reactor to the case of a diabatic reactor. The primary bifurcation parameter is the fuel fraction; the inflow pressure and inflow temperature are the secondary bifurcation parameters. The inclusion of heat loss in the model does not change the static steady-state bifurcation diagram; the organising centre is a pitchfork singularity for both the adiabatic and diabatic reactors. However, unlike the adiabatic reactor, Hopf bifurcations may occur in the diabatic reactor. We construct the degenerate Hopf bifurcation curve by determining the double-Hopf locus. When the steady-state and degenerate Hopf bifurcation diagrams are combined it is found that there are 23 generic steady-state diagrams over the parameter region of interest. The implications of these structures from the perspective of flammability in the CSTR are discussed.
Conservation laws for second-order parabolic partial differential equations
Authors: Van Brunt B. , Pidgeon D. , Vlieg-Hulstman M. , Halford W. D.
Published: February 2009

Conservation laws for partial differential equations can be characterised by an operator, the characteristic and a condition involving the adjoint of the Fréchet derivatives of this operator and the operator defining the partial differential equation. This approach was developed by Anco and Bluman and we exploit it to derive conditions for second-order parabolic partial differential equations to admit conservation laws. We show that such partial differential equations admit conservation laws only if the time derivative appears in one of two ways. The adjoint condition, however, is a biconditional, and we use this to prove necessary and sufficient conditions for a certain class of partial differential equations to admit a conservation law.
An investigation into the effects of heat transfer on the motion of a spherical bubble
Authors: Harris P. J. , Al-Awadi H. , Soh W. K.
Published: February 2009

This paper investigates the effect of heat transfer on the motion of a spherical bubble in the vicinity of a rigid boundary. The effects of heat transfer between the bubble and the surrounding fluid, and the resulting loss of energy from the bubble, can be incorporated into the simple spherical bubble model with the addition of a single extra ordinary differential equation. The numerical results show that for a bubble close to an infiniterigid boundary there are significant differences in both the radius and Kelvin impulse of the bubble when the heat transfer effects are included.
The limiting ideal theory for shear-index cohesionless granular materials
Authors: Cox G. M. , Hill J. M.
Published: February 2009

To model cohesionless granular flow using continuum theory, the usual approach is to assume the cohesionless Coulomb-Mohr yield condition. However, this yield condition assumes that the angle of internal friction is constant, when according to experimental evidence for most powders the angle of internal friction is not constant along the yield locus, but decreases for decreasing normal stress component σ from a maximum value of π/2. For this reason, we consider here the more general yield function which applies for shear-index granular materials, where the angle of internal friction varies with σ. In this case, failure due to frictional slip between particles occurs when the shear and normal components of stress τ and σ satisfy the so-called Warren Spring equation (|τ|/c)n = 1 − (σ/t), where c, t and n are positive constants which are referred to as the cohesion, tensile strength and shear-index respectively, and experimental evidence indicates for many materials that the value of the shear-index n lies between 1 and 2. For many materials, the cohesion is close to zero and therefore the notion of a cohesionless shear-index granular material arises. For such materials, a continuum theory applying for shear-index cohesionless granular materials is physically plausible as a limiting ideal theory, and any analytical solutions might provide important benchmarks for numerical schemes. Here, we examine the cohesionless shearindex theory for the problem of gravity flow of granular materials through two-dimensional wedge-shaped hoppers, and we attempt to determine analytical solutions. Although some analytical solutions are found, these do not correspond to the actual hopper problem, but may serve as benchmarks for purely numerical schemes. The special analytical solutions obtained are illustrated graphically, assuming only a symmetrical stress distribution.
Maximising output from oil reservoirs without water breakthrough
Authors: Lucas S. K.
Published: February 2009

Often in oil reservoirs a layer of water lies under the layer of oil. The suction pressure due to a distribution of oil wells will cause the oil-water interface to rise up towards the wells. Given a particular distribution of oil wells, we are interested in finding the flow rates of each well that maximise the total flow rate without the interface breaking through to the wells. A method for finding optimal flow rates is developed using the Muskat model to approximate the interface height, and a version of the Nelder-Mead simplex method for optimisation. A variety of results are presented, including the perhaps nonintuitive result that it is better to turn off some oil wells when they are sufficiently close to one another.
Memory, market stability and the nonlinear cobweb theorem
Authors: Gaffney J. M. , Pearce C. E. M.
Published: February 2009

Carlson has shown that if the predicted price in the linear cobweb model is taken as the average of all previous actual prices, then stability results independently of parameter values provided only that the demand–curve gradient is less than that of the supply curve. This result has subsequently been generalised by Manning and by Holmes and Manning. We investigate the robustness of their results.
Positive solutions of singular nonlinear Sturm-Liouville boundary value problems
Authors: Sun Yan , Liu Lishan , Cho Yeol Je
Published: February 2009

By using fixed point index theory, we present the existence of positive solutions for a Sturm-Liouville singular boundary value problem with at least one positive solution. Our results significantly extend and improve many known results even for non-singular cases.
Non-adiabatic combustion waves for general Lewis numbers: wave speed and extinction conditions
Authors: McIntosh A. C. , Weber R. O. , Mercer G. N.
Published: February 2009

This paper addresses the effect of general Lewis number and heat losses on the calculation of combustion wave speeds using an asymptotic technique based on the ratio of activation energy to heat release being considered large. As heat loss is increased twin flame speeds emerge (as in the classical large activation energy analysis) with an extinction heat loss. Formulae for the non-adiabatic wave speed and extinction heat loss are found which apply over a wider range of activation energies (because of the nature of the asymptotics) and these are explored for moderate and large Lewis number cases—the latter representing the combustion wave progress in a solid. Some of the oscillatory instabilities are investigated numerically for the case of a reactive solid.
An affine scaling interior point backtracking algorithm for nonlinear constrained optimisation
Authors: Zhu Detong
Published: February 2009

In this paper we propose a new affine scaling interior trust region algorithm with a nonmonotonic backtracking technique for nonlinear equality constrained optimisation with nonnegative constraints on the variables. In order to deal with large problems, the general full trust region subproblem is decomposed into a pair of trust region subproblems in horizontal and vertical subspaces. The horizontal trust region subproblem in the algorithm is defined by minimising a quadratic function subject only to an ellipsoidal constraint in a null tangential subspace and the vertical trust region subproblem is defined by the least squares subproblem subject only to an ellipsoidal constraint. By adopting Fletcher's penalty function as the merit function, combining a trust region strategy and a nonmonotone line search, the mixing technique will switch to a backtracking step generated by the two trust region subproblems to obtain an acceptable step. The global convergence of the proposed algorithm is proved while maintaining a fast local superlinear convergence rate, which is established under some reasonable conditions. A nonmonotonic criterion is used to speed up the convergence progress in some highly nonlinear cases.
Singular perturbation methods for a class of initial and boundary value problems in multi-parameter classical digital control systems
Authors: Krishnarayalu M. S.
Published: February 2009

A stable linear time-invariant classical digital control system with several widely different small coefficients multiplying the lowest functions is considered. It is formulated as a multi-parameter singularly perturbed system. Perturbation methods are developed for both initial and boundary value problems based on asymptotic expansions of the perturbation parameters. The approximate solution consists of an outer solution and a number of boundary layer correction solutions equal to the number of initial conditions lost in the process of degeneration. An example is provided for illustration.
Nonlinear-cobweb dynamics in the approach to equilibrium
Authors: Gaffney J. M. , Pearce C. E. M.
Published: February 2009

We discuss some propositions of Holmes and Manning relating to the evolution of price in a cobweb market approaching equilibrium. We find in particular that the detailed behaviour of the linear model is quite typical of nonlinear cobweb models.
Spectral refinement using a new projection method
Authors: Kulkarni Rekha P. , Gnaneshwar N.
Published: February 2009

In this paper we consider two spectral refinement schemes, elementary and double iteration, for the approximation of eigenelements of a compact operator using a new approximating operator. We show that the new method performs better than the Galerkin, projection and Sloan methods. We obtain precise orders of convergence for the approximation of eigenelements of an integral operator with a smooth kernel using either the orthogonal projection onto a spline space or the interpolatory projection at Gauss points onto a discontinuous piecewise polynomial space. We show that in the double iteration scheme the error for the eigenvalue iterates using the new method is of the order of , where h is the mesh of the partition and k = 0, 1, 2,… denotes the step of the iteration. This order of convergence is to be compared with the orders in the Galerkin and projection methods and in the Sloan method. The error in eigenvector iterates is shown to be of the order of in the new method, in the Galerkin and projection methods and in the Sloan method. Similar improvement is observed in the case of the elementary iteration. We show that these orders of convergence are preserved in the corresponding discrete methods obtained by replacing the integration by a numerical quadrature formula. We illustrate this improvement in the order of convergence by numerical examples.
Non-Newtonian conducting fluid flow and heat transfer due to a rotating disk
Authors: Attia Hazem A. , Ahmed Mohamed E. S.
Published: February 2009

The steady flow of an incompressible viscous non-Newtonian electrically conducting fluid and heat transfer due to the rotation of an infinite disk are studied considering the Hall effect. The effects of an externally applied uniform magnetic field, the Hall current, and the non-Newtonian fluid characteristics on the velocity and temperature distributions as well as the heat transfer are considered. Numerical solutions of the nonlinear equations which govern the magnetohydrodynamics (MHD) and energy transfer are obtained over the entire range of the physical parameters.
Optimal Hamiltonian completions and path covers for trees, and a reduction to maximum flow
Authors: Franzblau D. S. , Raychaudhuri A.
Published: February 2009

A minimum Hamiltonian completion of a graph G is a minimum-size set of edges that, when added to G, guarantee a Hamiltonian path. Finding a Hamiltonian completion has applications to frequency assignment as well as distributed computing. If the new edges are deleted from the Hamiltonian path, one is left with a minimum path cover, a minimum-size set of vertex-disjoint paths that cover the vertices of G. For arbitrary graphs, constructing a minimum Hamiltonian completion or path cover is clearly NP-hard, but there exists a linear-time algorithm for trees. In this paper we first give a description and proof of correctness for this linear-time algorithm that is simpler and more intuitive than those given previously. We show that the algorithm extends also to unicyclic graphs. We then give a new method for finding an optimal path cover or Hamiltonian completion for a tree that uses a reduction to a maximum flow problem. In addition, we show how to extend the reduction to construct, if possible, a covering of the vertices of a bipartite graph with vertex-disjoint cycles, that is, a 2-factor.
Exponential decay rate of the energy of a Timoshenko beam with locally distributed feedback
Authors: Shi Dong-Hua , Feng De-Xing
Published: February 2009

The problem of the energy exponential decay rate of a Timoshenko beam with locally distributed controls is investigated. Consider the case in which the beam is nonuniform and the two wave speeds are different. Then, using Huang's theorem and Birkhoff's asymptotic expansion method, it is shown that, under some locally distributed controls, the energy exponential decay rate is identical to the supremum of the real part of the spectrum of the closed loop system. Furthermore, explicit asymptotic locations of eigenfrequencies are derived.
Two-point formulae of Euler type
Authors: Matić M. , Pearce C. E. M. , Pečarić J.
Published: February 2009

An analysis is made of quadratureviatwo-point formulae when the integrand is Lipschitz or of bounded variation. The error estimates are shown to be as good as those found in recent studies using Simpson (three-point) formulae.
An M/G/l queueing system with fixed feedback policy
Authors: Choi Bong Dae , Kim Bara
Published: February 2009

We consider a single server queueing system where each customer visits the queue a fixed number of times before departure. A customer on his j th visit to the queue is defined to be a class-j -customer. We obtain the joint probability generating function for the number of class-j-customers and also obtain the Laplace-Stieltjes transform for the total response time of a customer.
IVORY IN EARLY MODERN CEYLON: A CASE STUDY IN WHAT DOCUMENTS DON’T REVEAL
Authors: Chaiklin Martha
Published: February 2009

In Sri Lanka elephants are endangered and ivory carving, as an art, is dead. Sri Lanka was once famous for the number and quality of its elephants, whose tusks were carved and exported since ancient times. Although Sri Lanka became, successively, a pivotal outpost for the Portuguese, Dutch and English, details about the Ceylonese ivory trade appear in trade documents only rarely. And yet, if information is not to be found there, does that mean ivory trade did not occur? Trade documents, after all, do not tell the whole story. Smugglers, illegal traders, big game hunters and plantation owners all played a part in the disappearance of elephants and its corollary, the ivory trade. When archival evidence is viewed in combination with physical evidence and the anecdotes of visitors and residents, it becomes evident that ivory remained an integral part of trade and crafts in Ceylon well into the last century.