bluuebunny/crossref_metadata_2025_split huggingface dataset:
Black holes and solitons of the quantized dispersionless NLS and DNLS equations
Authors: Pashaev Oktay K. , Lee Jyh-Hao 
Published: February 2009

AbstractThe classical dynamics of non-relativistic particles are described by the Schrödinger wave equation, perturbed by quantum potential nonlinearity. Quantization of this dispersionless equation, implemented by deformation of the potential strength, recovers the standard Schrödinger equation. In addition, the classically forbidden region corresponds to the Planck constant analytically continued to pure imaginary values. We apply the same procedure to the NLS and DNLS equations, constructing first the corresponding dispersionless limits and then adding quantum deformations. All these deformations admit the Lax representation as well as the Hirota bilinear form. In the classically forbidden region we find soliton resonances and black hole phenomena. For deformed DNLS the chiral solitons with single event horizon and resonance dynamics are constructed.
Numerical solitary wave interaction: the order of the inelastic effect
Authors: Marchant T. R. 
Published: February 2009

AbstractSolitary wave interaction is examined using an extended Benjamin-Bona-Mahony (eBBM) equation. This equation includes higher-order nonlinear and dispersive effects and is is asymptotically equivalent to the extended Korteweg-de Vries (eKdV) equation. The eBBM formulation is preferable to the eKdV equation for the numerical modelling of solitary wave collisions, due to the stability of its finite-difference scheme. In particular, it allows the interaction of steep waves to be modelled, which due to numerical instability, is not possible using the eKdV equation.Numerical simulations of a number of solitary wave collisions of varying nonlinearity are performed for two special cases corresponding to surface water waves. The mass and energy of the dispersive wavetrain generated by the inelastic collision is tabulated and used to show that the change in solitary wave amplitude after interaction is of O(α4), verifying previously obtained theoretical predictions.
Propagation of an electromagnetic soliton in a ferromagnetic medium
Authors: Veerakumar V. , Daniel M. 
Published: February 2009

AbstractWe study the propagation of electromagnetic waves (EMWs) in both isotropic and anisotropic ferromagnetic material media. As the EMW propagates through linear charge-free isotropic and anisotropic ferromagnetic media, it is found that the magnetic field and the magnetic induction components of the EMW and the magnetization excitations of the medium are in the form of solitons. However, the electromagnetic soliton gets damped and decelerates in the case of a charged medium. In the case of a charge-free nonlinear ferromagnetic medium we obtain results similar to those for the linear case.
On the geometry of the Painlevé V equation and a Bäcklund transformation
Authors: Schief W. K. 
Published: February 2009

AbstractIt is shown that an integrable class of helicoidal surfaces in Euclidean space E3 is governed by the Painlevé V equation with four arbitrary parameters. A connection with sphere congruences is exploited to construct in a purely geometric manner an associated Bäcklund transformation.
Inverse scattering for the matrix Schrödinger operator and Schrödinger operator on graphs with general self-adjoint boundary conditions
Authors: Harmer M. S. 
Published: February 2009

AbstractUsing a parameterisation of general self-adjoint boundary conditions in terms of Lagrange planes we propose a scheme for factorising the matrix Schrödinger operator and hence construct a Darboux transformation, an interesting feature of which is that the matrix potential and boundary conditions are altered under the transformation. We present a solution of the inverse problem in the case of general boundary conditions using a Marchenko equation and discuss the specialisation to the case of a graph with trivial compact part, that is, with diagonal matrix potential.
Global existence for the generalised 2D Ginzburg-Landau equation
Authors: Gao Hongjun , Kwek Keng-Huat 
Published: February 2009

AbstractGinzburg-Landau type complex partial differential equations are simplified mathematical models for various pattern formation systems in mechanics, physics and chemistry. Most work so far has concentrated on Ginzburg-Landau type equations with one spatial variable (1D). In this paper, the authors study a complex generalised Ginzburg-Landau equation with two spatial variables (2D) and fifth-order and cubic terms containing derivatives. Based on detail analysis, sufficient conditions for the existence and uniqueness of global solutions are obtained.
Nonresonance conditions and extremal solutions for first-order impulsive problems under weak assumptions
Authors: Franco Daniel , Pouso Rodrigo L. 
Published: February 2009

AbstractIn this work we shall study the existence of extremal solutions for an impulsive problem with functional-boundary conditions and weak regularity assumptions, not only on the right-hand side of the equation and on the functions that define the boundary conditions, but also on the impulse functions, which will be required to be nondecreasing, but not continuous as well, as is customary in the literature.Moreover, in order to prove one of our results we shall study a general impulsive linearproblem, giving a complete characterisation of resonance for it.
On some noncoercive variational inequalities containing degenerate elliptic operators
Authors: Le Vy Khoi 
Published: February 2009

AbstractWe are concerned with the solvability of variational inequalities that contain degenerate elliptic operators. By using a recession approach, we find conditions on the boundary conditions such that the inequality has at least one solution. Existence results of Landesman-Lazer type for a nonsmooth inequality and a resonance problem for a weightedp-Laplacian are discussed in detail.
On the condition number of integral equations in linear elasticity using the modified Green's function
Authors: Argyropoulos E. , Gintides D. , Kiriaki K. 
Published: February 2009

AbstractIn this work the modified Green's function technique for an exterior Dirichlet and Neumann problem in linear elasticity is investigated. We introduce a modification of the fundamental solution in order to remove the lack of uniqueness for the solution of the boundary integral equations describing the problems, and to simultaneously minimise their condition number. In view of this procedure the cases of the sphere and perturbations of the sphere are examined. Numerical results that demonstrate the effect of increasing the number of coefficients in the modification on the optimal condition number are also presented.
Effects of an axisymmetric rigid punch on a nonhomogeneous transversely isotropic half-space
Authors: Chaudhuri P. K. , Ray Subhankar 
Published: February 2009

AbstractElastic behaviour of a nonhomogeneous transversely isotropic half-space is studied under the action of a smooth rigid axisymmetric indentor. Hankel transforms of different orders have been used. It is observed that in contrast to a homogeneous medium, the pressure distribution in the contact region in a nonhomogeneous medium is not directly available, rather it is obtainable from the solution of a Fredholm integral equation. The integral equation is solved for a flat-ended punch and paraboloidal indentations for various values of the nonhomogeneity parameter, and the effects of nonhomogeneity in elastic behaviour on stresses have been shown graphically. The results of the associated homogeneous case are readily available from the results of the present study.
A certain class of generating functions involving bilateral series
Authors: Srivastava H. M. , Pathan M. A. , Bin-Saad M. G. 
Published: February 2009

AbstractThe authors derive a general theorem on partly bilateral and partly unilateral generating functions involving multiple series with essentially arbitrary coefficients. By appropriately specialising these coefficients, a number of (known or new) results are shown to follow as applications of the theorem.
Direction of vorticity and a new regularity criterion for the Navier-Stokes equations
Authors: Zhou Yong 
Published: February 2009

AbstractIn this paper, we prove a new regularity criterion in terms of the direction of vorticity for the weak solution to 3-D incompressible Navier-Stokes equations. Under the framework of Constantin and Fefferman, a more relaxed regularity criterion in terms of the direction of vorticity is established.
Impulsive control of rumours with two broadcasts
Authors: Belen Selma , Kaya C. Yalçin , Pearce C. E. M. 
Published: February 2009

AbstractIn this paper we introduce an impulsive control model of a rumour process. The spreaders are classified as subscriber spreaders, who receive an initial broadcast of a rumour and start spreading it, and nonsubscriber spreaders who change from being an ignorant to being a spreader after encountering a spreader. There are two consecutive broadcasts. The first starts the rumour process. The objective is to time the second broadcast so that the final proportion of ignorants is minimised. The second broadcast reactivates as spreaders either the subscriber stiflers (Scenario 1) or all individuals who have been spreaders (Scenario 2). It is shown that with either scenario the optimal time for the second broadcast is always when the proportion of spreaders drops to zero.
Duality for linear multiplicative programs
Authors: Scott Carlton H. , Jefferson Thomas R. 
Published: February 2009

AbstractLinear multiplicative programs are an important class of nonconvex optimisation problems that are currently the subject of considerable research as regards the development of computational algorithms. In this paper, we show that mathematical programs of this nature are, in fact, a special case of more general signomial programming, which in turn implies that research on this latter problem may be valuable in analysing and solving linear multiplicative programs. In particular, we use signomial programming duality theory to establish a dual program for a nonconvex linear multiplicative program. An interpretation of the dual variables is given.
Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. III The inhibiting effect of an inert species
Authors: Nelson M. I. 
Published: February 2009

AbstractWe extend an investigation into the static and dynamic multiplicity exhibited by the reaction of a fuel/air mixture in a continuously stirred tank reactor by considering the effect of adding a chemically inert species to the reaction mixture. The primary bifurcation parameter is taken to be the fuel fraction as this is the most important case from the perspective of fire-retardancy. We show how the addition of the inert species progressively changes the steady-state diagrams and flammability limits. We also briefly outline how heat-sink additives can be incorporated into our scheme.
A robust linearisation scheme for a nonlinear elliptic boundary value problem: Error estimates
Authors: Slodička Marian 
Published: February 2009

AbstractWe consider a nonlinear second-order elliptic boundary value problem in a bounded domain Ω ⊂ RN with mixed boundary conditions. The solution is found via linearisation. We design a robust and efficient approximation scheme. Error estimates for the linearisation algorithm are derived in L2(Ω), H1(Ω) and L∞(Ω) spaces under the minimal regularity assumptions of the exact solution.
Robust H∞ stabilisation with definite attenuance of an uncertain impulsive switche system
Authors: Xu Honglei , Liu Xinzhi , Teo Kok Lay 
Published: February 2009

AbstractIn this paper, we study the problem of robust H∞ stabilisation with definite attenuance for a class of impulsive switched systems with time-varying uncertainty. A norm-bounded uncertainty is assumed to appear in all the matrices of the state model. An LMI-based method for robust· H∞ stabilisation with definite attenuance via a state feedback control law is developed. A simulation example is presented to demonstrate the effectiveness of the proposed method.
Ramaswami's duality and probabilistic algorithms for determining the rate matrix for a structured GI/M/1 Markov chain
Authors: Hunt Emma 
Published: February 2009

AbstractWe show that Algorithm H* for the determination of the rate matrix of a block-GI/M/1 Markov chain is related by duality to Algorithm H for the determination of the fundamental matrix of a block-M/G/1 Markov chain. Duality is used to generate some efficient algorithms for finding the rate matrix in a quasi-birth-and-death process.
Sharp integral inequalities based on general Euler two-point formulae
Authors: Pečarić J. , Perić I. , Vukelić A. 
Published: February 2009

AbstractWe consider a family of two-point quadrature formulae, using some Euler-type identities. A number of inequalities, for functions whose derivatives are either functions of bounded variation, Lipschitzian functions orR-integrable functions, are proved.
Point-joint coordinate formulation for the dynamic analysis of generalised planar linkages
Authors: Attia Hazem Ali 
Published: February 2009

AbstractThis paper presents a two-step formulation for the dynamic analysis of generalised planar linkages. First, a rigid body is replaced by a dynamically equivalent constrained system of particles and Newton's second law is used to study the motion of the particles without introducing any rotational coordinates. The translational motion of the constrained particles represents the general motion of the rigid body both translationally and rotationally. The simplicity and the absence of any rotational coordinates from the final form of the equations of motion are considered the main advantages of this formulation. A velocity transformation is then used to transform the equations of motion to a reduced set in terms of selected relative joint variables. For an open-chain, this process automatically eliminates all of the non-working constraint forces and leads to efficient integration of the equations of motion. For a closed-chain, suitable joints should be cut and some cut-joint constraint equations should be included. An example of a closed-chain is used to demonstrate the generality and efficiency of the proposed method.
Plane poloidal-toroidal decomposition of doubly periodic vector fields. Part 2. The Stokes equations
Authors: McBain G. D. 
Published: February 2009

AbstractWe continue our study of the adaptation from spherical to doubly periodic slot domains of the poloidal-toroidal representation of vector fields. Building on the successful construction of an orthogonal quinquepartite decomposition of doubly periodic vector fields of arbitrary divergence with integral representations for the projections of known vector fields and equivalent scalar representations for unknown vector fields (Part 1), we now present a decomposition of vector field equations into an equivalent set of scalar field equations. The Stokes equations for slow viscous incompressible fluid flow in an arbitrary force field are treated as an example, and for them the application of the decomposition uncouples the conservation of momentum equation from the conservation of mass constraint. The resulting scalar equations are then solved by elementary methods. The extension to generalised Stokes equations resulting from the application of various time discretisation schemes to the Navier-Stokes equations is also solved.
Symmetry analysis of rotating fluid
Authors: Fakhar K. , Chen Zu-Chi , Ji Xiaoda 
Published: February 2009

AbstractThe machinery of Lie theory (groups and algebras) is applied to the unsteady equations of motion of rotating fluid. A special-function type solution for the steady state is derived. It is then shown how the solution generates an infinite number of time-dependent solutions via three arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.
Existence of seamount steady vortex flows
Authors: Emamizadeh B. , Bahrami F. 
Published: February 2009

AbstractIn this paper we will study a feature of a localised topographic flow. We will prove existence of an ideal fluid containing a bounded vortex, approaching a uniform flow at infinity and passing over a localised seamount. The domain of the fluid is the upper half-plane and the data prescribed is the rearrangement class of the vorticity field.
On constant-sign periodic solutions in modelling the spread of interdependent epidemics
Authors: Agarwal Ravi P. , O'Regan Donal , Wong Patricia J. Y. 
Published: February 2009

AbstractWe consider the following model that describes the spread of n types of epidemics which are interdependent on each other:Our aim is to establish criteria such that the above system has one or multiple constant-sign periodic solutions (u1, u2, …, un), that is, for each 1 ≤ i ≤ n, ui, is periodic and θiui ≥ 0 where θi, ε (1, −1) is fixed. Examples are also included to illustrate the results obtained.
Generalisation of a corrected Simpson's formula
Authors: Pečarić J. , Franjić I. 
Published: February 2009

AbstractThe results obtained by A. J. Roberts and N. Ujević in a recent paper are generalised. A number of inequalities for functions whose derivatives are either functions of bounded variation or Lipschitzian functions or R-integrable functions are derived. Also, some error estimates for the derived formulae are obtained.
On the low frequency asymptotics for the 2-D electromagnetic transmission problem
Authors: Anestopoulos C. N. , Argyropoulos E. E. 
Published: February 2009

AbstractWe examine the transmission problem in a two-dimensional domain, which consists of two different homogeneous media. We use boundary integral equation methods on the Maxwell equations governing the two media and we study the behaviour of the solution as the two different wave numbers tend to zero. We prove that as the boundary data of the general transmission problem converge uniformly to the boundary data of the corresponding electrostatic transmission problem, the general solution converges uniformly to the electrostatic one, provided we consider compact subsets of the domains.
Stability analysis of resource-consumer dynamic models
Authors: Hari Rao V. Sree , Sekhara Rao P. Raja 
Published: February 2009

AbstractA nutrient-consumer model involving a distributed delay in material recycling and a discrete delay in growth response has been analysed. Various easily verifiable sets of sufficient conditions for global asymptotic stability of the positive equilibrium solution of the model equations have been obtained and the length of the delay in each case has been estimated.
Optimal control on an infinite domain
Authors: Craven B. D. 
Published: February 2009

AbstractFor an optimal control problem with an infinite time horizon, assuming various terminal state conditions (or none), terminal conditions for the costate are obtained when the state and costate tend to limits with a suitable convergence rate. Under similar hypotheses, the sensitivity of the optimum to small perturbations is analysed, and in particular the stability of the optimum when the infinite horizon is truncated to a large finite horizon. An infinite horizon version of Pontryagin's principle is also obtained. The results apply to various economic models.
Analysis of the Michaelis-Menten mechanism in an immobilised enzyme reactor
Authors: Nelson M. I. , Chen X. D. , Sexton M. J. 
Published: February 2009

AbstractWe investigate the behaviour of a reaction described by Michaelis-Menten kinetics in an immobilised enzyme reactor (IER). The IER is treated as a well-stirred flow reactor, with the restriction that bounded and unbounded enzyme species are constrained to remain within the reaction vessel. Our aim is to identify the best operating conditions for the reactor.The cases in which an iminobilised enzyme reactor is used to either reduce pollutant emissions or to synthesise a product are considered. For the former we deduce that the reactor should be operated using low flow rates whereas for the latter high flow rates are optimal. It is also shown that periodic behaviour is impossible.
A comparison principle and stability for large-scale impulsive delay differential systems
Authors: Liu Xinzhi , Shen Xuemin , Zhang Yi 
Published: February 2009

AbstractThis paper studies the stability of large-scale impulsive delay differential systems and impulsive neutral systems. By developing some impulsive delay differential inequalities and a comparison principle, sufficient conditions are derived for the stability of both linear and nonlinear large-scale impulsive delay differential systems and impulsive neutral systems. Examples are given to illustrate the main results.
Sufficient global optimality conditions for multi-extremal smooth minimisation problems with bounds and linear matrix inequality constraints
Authors: Huy N. Q. , Jeyakumar V. , Lee G. M. 
Published: February 2009

AbstractIn this paper, we present sufficient conditions for global optimality of a general nonconvex smooth minimisation model problem involving linear matrix inequality constraints with bounds on the variables. The linear matrix inequality constraints are also known as “semidefinite” constraints which arise in many applications, especially in control system analysis and design. Due to the presence of nonconvex objective functions such minimisation problems generally have many local minimisers which are not global minimisers. We develop conditions for identifying global minimisers of the model problem by first constructing a (weighted sum of squares) quadratic underestimator for the twice continuously differentiable objective function of the minimisation problem and then by characterising global minimisers of the easily tractable underestimator over the same feasible region of the original problem. We apply the results to obtain global optimality conditions for optinusation problems with discrete constraints.
A comparison of two- and three-variable models for combustion in sealed containers
Authors: Trenham Claire E. , Forbes Larry K. 
Published: February 2009

AbstractThis paper analyses a model for combustion of a self-heating chemical (such as pool chlorine), stored in drums within a shipping container. The system is described by three coupled nonlinear differential equations for the concentration of the chemical, its temperature and the temperature within the shipping container. Self-sustained oscillations are found to occur, as a result of Hopf bifurcation. Temperature and concentration profiles are presented and compared with the predictions of a simpler two-variable approximation for the system. We study the period of oscillation and its variation with respect to the ambient temperature and the reaction parameter. Nonlinear resonances are found to exist, as the solution jumps between branches having different periods.
Robust guaranteed cost control for descriptor systems with Markov jumping parameters and state delays
Authors: Fu Yan-Ming , Wu Di , Duan Guang-Ren 
Published: February 2009

AbstractThis paper deals with robust guaranteed cost control for a class of linear uncertain descriptor systems with state delays and jumping parameters. The transition of the jumping parameters in the systems is governed by a finite-state Markov process. Based on stability theory for stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost controllers is derived. In terms of the LMI (linear matrix inequality) approach, a linear state feedback controller is designed to stochastically stabilise the given system with a cost function constraint. A convex optimisation problem with LMI constraints is formulated to design the suboptimal guaranteed cost controller. A numerical example demonstrates the effect of the proposed design approach.