bluuebunny/crossref_metadata_2025_split huggingface dataset:
On waves due to small oscillations of a vertical plate submerged in deep water
Authors: Mandal B. N. 
Published: February 2009

AbstractThis paper is concerned with surface water waves produced by small oscillations of a thin vertical plate submerged in deep water. Green's integral theorem in the fluid region is used in a suitable manner to obtain the amplitude for the radiated waves at infinity. Particular results for roll and sway of the plate, and for a line source in the presence of a fixed vertical plate, are deduced.
On neutral-delay two-species Lotka-Volterra competitive systems
Authors: Kuang Y. 
Published: February 2009

AbstractThe qualitative behavior of positive solutions of the neutral-delay two-species Lotka-Volterra competitive system with several discrete delays is investigated. Sufficient conditions are obtained for the local asymptotic stability of the positive steady state. In fact, some of these sufficient conditions are also necessary except at those critical values. Results on the oscillatory and non-oscillatory characteristics of the positive solutions are also included.
On lognormal random variables: I-the characteristic function
Authors: Leipnik Roy B. 
Published: February 2009

AbstractThe characteristic function of a lognormal random variable is calculated in closed form as a rapidly convergent series of Hermite functions in a logarithmic variable. The series coefficients are Nielsen numbers, defined recursively in terms of Riemann zeta functions. Divergence problems are avoided by deriving a functional differential equation, solving the equation by a de Bruijn integral transform, expanding the resulting reciprocal Gamma function kernel in a series, and then invoking a convergent termwise integration. Applications of the results and methods to the distribution of a sum of independent, not necessarily identical lognormal variables are discussed. The result is that a sum of lognormals is distributed as a sum of products of lognormal distributions. The case of two lognormal variables is outlined in some detail.
Determination of a control parameter in a parabolic partial differential equation
Authors: Cannon J. R. , Lin Yanping , Wang Shingmin 
Published: February 2009

AbstractThe authors consider in this paper the inverse problem of finding a pair of functions (u, p) such thatwhere F, f, E, s, αi, βi, γi, gi, i = 1, 2, are given functions.The existence and uniqueness of a smooth global solution pair (u, p) which depends continuously upon the data are demonstrated under certain assumptions on the data.
Determination of a controllable set for a controlled dynamic system
Authors: Peng Shige , Yong Jiongmin 
Published: February 2009

AbstractThe controllable set of a controlled ordinary differential dynamic system to a given set is defined. Under certain reasonable conditions, the controllable set is characterised by a level set of the unique viscosity solution to some Hamilton-Jacobi-Bellman equation. The result is used to determine the asymptotic stable set of nonlinear autonomous differential equations.
Uncertainty principles invariant under the fractional Fourier transform
Authors: Mustard David 
Published: February 2009

AbstractUncertainty principles like Heisenberg's assert an inequality obeyed by some measure of joint uncertainty associated with a function and its Fourier transform. The more groups under which that measure is invariant, the more that measure represents an intrinsic property of the underlying object represented by the given function. The Fourier transform is imbedded in a continuous group of operators, the fractional Fourier transforms, but the Heisenberg measure of overall spread turns out not to be invariant under that group. A new family is developed of measures that are invariant under the group of fractional Fourier transforms and that obey associated uncertainty principles. The first member corresponds to Heisenberg's measure but is generally smaller than his although equal to it in special cases.
Some boundary-value problems for nonlinear (N) diffusion and pseudo-plastic flow
Authors: Atkinson C. , Champion C. R. 
Published: February 2009

AbstractIn this article, exact and approximate techniques are used to obtain parameters of interest for two problems involving differential equations of power-law type. The first problem is related to non-linear steady-state diffusion, and is investigated by means of a hodograph transformation and an approximation using a path-independent integral. The second problem involves Poiseuille flow of a pseudo-plasticfluid, and a path-independent integral is derived which yields an exact result for the geometry under consideration.
Control of a surface of discontinuity in continuous thickness
Authors: Barton N. G. , Li C.-H. , Spencer S. J. 
Published: February 2009

AbstractThis paper examines the control of an interface between a suspension of sedimenting particles in liquid and a bed of dense-packed particles at the bottom of the suspension. The problem arises in the operation of continuous thickeners (e.g. in mineral processing) and is here mathematically described by a first order inhomogeneous partial differential equation for the concentration C(x, t) of particles. The controlled variable is the height H* of the bed, and the control variables are the volume fluxes injected at the feed level and removed at the bed. A strategy to control the interface is devised, and control is confirmed and demonstrated by a series of numerical experiments.
Exact solutions for redistribution by nonlinear convection-diffusion
Authors: Philip J. R. 
Published: February 2009

AbstractThe nonlinear convection-diffusion equation has been studied for 40 years in the context of nonhysteretic water movement in unsaturated soil. We establish new similarity solutions for instantaneous sources of finite strength redistributed by nonlinear convection-diffusion obeying the dimensionless equation ∂θ/∂t = ∂ (θm ∂θ/∂z) − θm+1 ∂θ/∂z (m ≥ 0). For m = 0 (Burgers’ equation) solutions involve the error function, and for m = 1 Airy functions. Problems 1, 2, and 3 relate, respectively, to the regions 0 ≤ z ≤ ∞, –∞ ≤ z ≤ ∞, and –∞ ≤ z ≤ 0. Solutions for m = 0 have infinite tails, but for m > 0 and finite t, θ > 0 inside, and θ = 0 outside, a finite interval in z. At the slug boundary, θ(z) is tangential to the z-axis for 0 < m < 1; and it meets the axis obliquely for m = 1 and normally for m > 1. Illustrative results are presented. For Problems 1 and 2 (but not 3) finiteness of source strength sets an upper bound on Θ0, the similarity “concentration” at z = 0. The magnitude of convection relative to diffusion increases with Θ0; and apparently the dynamic equilibrium between the two processes, implied by the similarity solutions, ceases to be possible when Θ0 is large enough.
Exact solutions to nonlinear diffusion-convection problems on finite domains
Authors: Sander G. C. 
Published: February 2009

AbstractNew exact solutions are presented for nonlinear diffusion and convection on a finite domain 0 ≤ z ≤ 1. These solutions are developed for the conditions of constant fluxes at both boundaries z = 0 and z = 1. In particular, solutions for the flux QL at the lower boundary z = 1, being a multiple of the flux Qs at the surface z = 0, (that is QL = aQs, where a = constant), are presented. Solutions for any constant, a, are given for an initial condition which is independent of space z. For the special cases (i) a = 1, and (ii) Qs = 0 and hence QL = 0, solutions are given for an initial condition which has an arbitrary dependence on z.
The effect of conductivity on hotspots
Authors: Smyth N. F. 
Published: February 2009

AbstractIn industrial applications of microwave heating, it has been observed that rather than the heating taking place uniformly, regions of high temperature, called hot-spots, tend to form. Depending on the industrial application, these can be either desirable or undesirable, and hence a theoretical understanding of the properties of the material that lead to hotspot formation is necessary. It has been shown in previous studies that hotspot formation is a product of the nonlinear dependence of microwave energy absorption by the material on temperature. It is shown in the present work that the conductivity of the material can have a significant effect on hotspot formation and can, if large enough, stop a hotspot from forming.
Nonlinearly constrained optimal control problems
Authors: Teo K. L. , Wong K. H. 
Published: February 2009

AbstractIn a paper by Teo and Jennings, a constraint transcription is used together with the concept of control parametrisation to devise a computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type. The aim of this paper is to extend the results to a more general class of constrained optimal control problems, where the problem is also subject to terminal equality state constraints. For illustration, a numerical example is included.
Numerical solution of an evolution equation with a positive-type memory term
Authors: McLean W. , Thomée V. 
Published: February 2009

AbstractWe study the numerical solution of an initial-boundary value problem for a Volterra type integro-differential equation, in which the integral operator is a convolution product of a positive-definite kernel and an elliptic partial-differential operator. The equation is discretised in space by the Galerkin finite-element method and in time by finite differences in combination with various quadrature rules which preserve the positive character of the memory term. Special attention is paid to the case of a weakly singular kernel. Error estimates are derived and numerical experiments reported.
Optimal shape design for a nozzle problem
Authors: Butt R. 
Published: February 2009

AbstractIn this paper, a gradient method is developed for the optimal shape design in a nozzle problem described by variational inequalities. It is known that this method can be used for the optimal shape design for systems described by partial differential equations (Pironneau [6]); it is used here for differential inequalities by taking limits of the expression resulting from an approximations scheme. The computations are done by the finite element method; the gradient of the criteria as a function of the coordinates nodes is computed, and the performance criterion is then minimised by the gradient method.
Numerical computation of symmetry-breaking bifurcation points
Authors: Attili B. S. 
Published: February 2009

AbstractWe consider symmetry-breaking bifurcation points which arise in parameter-dependent nonlinear equations of the form f(x, λ) = 0. These types of bifurcation points are connected to pitchfork bifurcation points. A direct method is used to compute such points. Multiple shooting is used to discretise the two-point boundary-value problems to obtain a finite-dimensional problem.
On generalised convex mathematical programming
Authors: Jeyakumar V. , Mond B. 
Published: February 2009

AbstractThe sufficient optimality conditions and duality results have recently been given for the following generalised convex programming problem:where the funtion f and g satisfyfor some η: X0 × X0 → ℝnIt is shown here that a relaxation defining the above generalised convexity leads to a new class of multi-objective problems which preserves the sufficient optimality and duality results in the scalar case, and avoids the major difficulty of verifying that the inequality holds for the same function η(. , .). Further, this relaxation allows one to treat certain nonlinear multi-objective fractional programming problems and some other classes of nonlinear (composite) problems as special cases.
A model of the injection moulding process
Authors: Whale J. , Fowkes N. , Hocking G. , Hill D. 
Published: February 2009

AbstractThis paper is concerned with the injection moulding process, in which hot molten plastic is injected under high pressure into a thin cold mould. Assuming that the velocity and temperature profiles across the mould maintain their shape, a simple steady state model to describe the behaviour of a Newtonian fluid during the filling stage is developed. Various phenomena of the process are examined, including the formation of a layer of solid plastic along the walls of the mould, and the relationship between the flux of liquid plastic through the mould and the average pressure gradient along the mould. In any given situation, it is shown that there is a range of pressures and injection temperatures which will give satisfactory results.
A note on American options with varying exercise price
Authors: Dewynne J. N. , Wilmott P. 
Published: February 2009

AbstractWe examine the valuation of American options in a discrete time setting where the exercise price is known a priori but varies with time. (This is in contrast with the classical Black-Scholes [2] analysis, which lies in a continuous time framework and with constant exercise price.) In particular we consider a time series of exercise prices which are themselves a realisation of the share price random walk — that of the previous year, say.
Chaos in an anharmonic oscillator
Authors: Christie J. R. , Gopalsamy K. 
Published: February 2009

AbstractUsing Melnikov's method, the existence of chaotic behaviour in the sense of Smale in a particular time-periodically perturbed planar autonomous system of ordinary differential equations is established. Examples of planar autonomous differential systems with homoclinic orbits are provided, and an application to the dynamics of a one-dimensional anharmonic oscillator is given.
The temporal stability of a developing jet: a model problem
Authors: Stott Jillian A. K. , Denier James P. 
Published: February 2009

AbstractThe temporal instability of a developing swirling incompressible jet is considered. The jet development (in the streamwise direction) is modelled by combining a near-field and far-field approximation to the jet velocity profile into a one parameter family of basic velocity fields. The single parameter in the jet velocity field then allows us to model the radial spreading of the jet and the decay of swirl observed experimentally. Two distinct modes of instability of this model profile are found. The first is that found from a stability analysis of a fully developed swirling jet in the far field whilst the second is relevant to a “top-hat” jet with an imposed rigid body rotation. We demonstrate that the effect of azimuthal swirl is to destabilise both modes of instability. Additionally our results suggest that the near-nozzle modes of instability will dominate; indeed the growth rates of these modes are significantly larger than those found from previous studies of a fully developed jet in the far-field region.
Similarity solutions for a quasilinear parabolic equation
Authors: Guo Jong-Sheng 
Published: February 2009

AbstractIn this paper, we use an ordinary differential equation approach to study the existence of similarity solutions for the equationu1= Δ(uα) + θu–βin Rn× (0, ∞) where β > 0, θ ∈ [0, 1}, andn≥ 1. This includes the slow diffusion equation when α > = 1, and the standard heat equation when α = 1, and the fast diffusion equation when 0 < α < 1. We prove that there are forward self-similar solutions for this equation with initial data of the formc|x|p, wherep= 2/(α + β) if θ = 1;p≥ 0 and 2 + (1 – α)p> 0 if θ = 0, for some positive constantc.
Long wavelength vortices in time-periodic flows
Authors: Bassom Andrew P. , Blennerhassett P. J. 
Published: February 2009

AbstractThe linear stability properties are examined of long wavelength vortex modes in two time-periodic flows. These flows are the motion which is induced by a torsionally oscillating cylinder within a viscous fluid and, second, the flow which results from the sinusoidal heating of an infinite layer of fluid. Previous studies concerning these particular configurations have shown that they are susceptible to vortex motions and linear neutral curves have been computed for wavenumbers near their critical value. These computations become increasingly difficult for long wavelength motions and here we consider such modes using asymptotic methods. These yield simple results which are formally valid for small wavenumbers and we show that the agreement between these asymptotes and numerical solutions is good for surprisingly large wavenumbers. The two problems studied share a number of common features but also have important differences and, between them, our methods and results provide a basis which can be extended for use with other time-periodic flows.
Solution of a Schrödinger equation by iterative refinement
Authors: Kulkarni Rekha P. , Limaye Balmohan V. 
Published: February 2009

AbstractA simple eigenvalue and a corresponding wavefunction of a Schrödinger operator is initially approximated by the Galerkin method and by the iterated Galerkin method of Sloan. The initial approximation is iteratively refined by employing three schemes: the Rayleigh-Schrödinger scheme, the fixed point scheme and a modification of the fixed point scheme. Under suitable conditions, convergence of these schemes is established by considering error bounds. Numerical results indicate that the modified fixed point scheme along with Sloan's method performs better than the others.
On a model for interference between searching insect parasites
Authors: Pollett P. K. 
Published: February 2009

AbstractThe purpose of this paper is to study a stochastic model which assesses the effect of mutual interference on the searching efficiency in populations of insect parasites. By looking carefully at the assumptions which govern the model, I shall explain why the searching efficiency is of the same order as the total number, N, in the population, a conclusion which is consistent with the predictions of population biologists; previous studies have reached the conclusion that the efficiency is of order . The major results of the paper establish normal approximations for the distribution of the numbers of active parasites. These are valid at all stages of the process, in particular the non-equilibrium phase, where explicit analytic formulae for the state-probabilities are unavailable.
Existence of nonoscillatory solutions of first order nonlinear neutral equations
Authors: Wudu Lu 
Published: February 2009

AbstractConsider the nonlinear neutral equationwhere pi(t), hi(t), gj(t), Q(t) Є C[t0, ∞), limt→∞hi(t) = ∞, limt→∞gj(t) = ∞ i Є Im = {1, 2, …, m}, j Є In = {1, 2, …, n}. We obtain a necessary and sufficient condition (2) for this equation to have a nonoscillatory solution x(t) with limt→∞ inf|x(t)| > 0 (Theorems 5 and 6) or to have a bounded nonoscillatory solution x(t) with limt→∞ inf|x(t)| > 0 (Theorem 7).
Reduction of second order linear dynamical systems, with large dissipation, by state variable transformations
Authors: Leipnik R. B. 
Published: February 2009

AbstractLinear dynamical systems of the Rayleigh form are transformed by linear state variable transformations , where A and B are chosen to simplify analysis and reduce computing time. In particular, A is essentially a square root of M, and B is a Lyapunov quotient of C by A. Neither K nor C is required to be symmetric, nor is C small. The resulting state-space systems are analysed by factorisation of the evolution matrices into reducible factors. Eigenvectors and eigenvalues are determined by these factors. Conditions for further simplification are derived in terms of Kronecker determinants. These results are compared with classical reductions of Rayleigh, Duncan, and Caughey, which are reviewed at the outset.
Flow caused by a point sink in a fluid having a free surface
Authors: Forbes Lawrence K. , Hocking Graeme C. 
Published: February 2009

AbstractThe flow caused by a point sink immersed in an otherwise stationary fluid is investigated. Low Froude number solutions are sought, in which the flow is radially symmetric and possesses a stagnation point at the surface, directly above the sink. A small-Froude-number expansion is derived and compared with the results of a numerical solution to the fully nonlinear problem. It is found that solutions of this type exist for all Froude numbers less than some maximum value, at which a secondary circular stagnation line is formed at the surface. The nonlinear solutions are reasonably well predicted by the small-Froude-number expansion, except for Froude numbers close to this maximum.
Comparison principles for impulsive parabolic equations with applications to models of single species growth
Authors: Erbe L. H. , Freedman H. I. , Liu X. Z. , Wu J. H. 
Published: February 2009

AbstractThis paper establishes some maximum and comparison principles relative to lower and upper solutions of nonlinear parabolic partial differential equations with impulsive effects. These principles are applied to obtain some sufficient conditions for the global asymptotic stability of a unique positive equilibrium in a reaction-diffusion equation modeling the growth of a single-species population subject to abrupt changes of certain important system parameters.
On certain new and exact solutions of the Emden-Fowler equation and Emden equation via invariant variational principles and group invariance
Authors: Bhutani O. P. , Vijayakumar K. 
Published: February 2009

AbstractAfter formulating the alternate potential principle for the nonlinear differential equation corresponding to the generalised Emden-Fowler equation, the invariance identities of Rund [14] involving the Lagrangian and the generators of the infinitesimal Lie group are used for writing down the first integrals of the said equation via the Noether theorem. Further, for physical realisable forms of the parameters involved and through repeated application of invariance under the transformation obtained, a number of exact solutions are arrived at both for the Emden-Fowler equation and classical Emden equations. A comparative study with Bluman-Cole and scale-invariant techniques reveals quite a number of remarkable features of the techniques used here.
Numerical study of Fisher's equation by a Petrov-Galerkin finite element method
Authors: Tang S. , Weber R. O. 
Published: February 2009

AbstractFisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by a Petrov-Galerkin finite element method. The results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are determined by the system itself and are independent of the initial values. Comparing with other studies, the numerical scheme used in this paper is satisfactory with regard to its accuracy and stability. It has the advantage of being much more concise.
A mathematical analysis of wind effects on a long-jumper
Authors: de Mestre Neville 
Published: February 2009

AbstractA perturbation model is used to predict the distance jumped by a long-jumper for a range of tailwinds and headwinds. The zeroth-order approximation is based on gravity being the only force present, the effects of drag and lift only being included in the first-order corrections. The difference in predicted distances produced by the zeroth and first-order approximations is less than 2% for headwinds or tailwinds upto 4 ms−1. Most increases or decreases due to wind are caused by changes in the run-up speed, and consequently the take-off angle and speed.