bluuebunny/crossref_metadata_2025_split huggingface dataset:
The fractional fourier transform and the wigner distribution
Authors: Mustard David 
Published: February 2009

AbstractThe Wigner distribution and many other members of the Cohen class of generalized phase-space distributions of a signal all share certain translation properties and the property that their two marginal distributions of energy density along the time and along the frequency axes equal the signal power and the spectral energy density. A natural generalization of this last property is shown to be a certain relationship through the Radon transform between the distribution and the signal's fractional Fourier transform. It is shown that the Wigner distribution is now distinguished by being the only member of the Cohen class that has this generalized property as well as a generalized translation property. The inversion theorem for the Wigner distribution is then extended to yield the fractional Fourier transforms.
Adaptive boundary-element methods for transmission problems
Authors: Carstensen Carsten , Stephan Ernst P. 
Published: February 2009

AbstractIn this paper we present an adaptive boundary-element method for a transmission prob-lem for the Laplacian in a two-dimensional Lipschitz domain. We are concerned with an equivalent system of boundary-integral equations of the first kind (on the transmission boundary) involving weakly-singular, singular and hypersingular integral operators. For the h-version boundary-element (Galerkin) discretization we derive an a posteriori error estimate which guarantees a given bound for the error in the energy norm (up to a multiplicative constant). Then, following Eriksson and Johnson this yields an adaptive algorithm steering the mesh refinement. Numerical examples confirm that our adaptive algorithms yield automatically good triangulations and are efficient.
Analytical and numerical studies of the Bonhoeffer van der Pol system
Authors: Barnes Belinda , Grimshaw Roger 
Published: February 2009

AbstractThe Bonhoeffer Van der Pol system is a planar autonomous nonlinear system of differential equations which has been invoked as a qualitative model of physiological states in a nerve membrane. It contains three independent parameters and previous work has only studied a small portion of the parameter space, that part which is thought to be of physiological relevance. Here we give a complete study of the full parameter space, using both theoretical results and numerical solutions.
Second method of Lyapunov and comparison principle for impulsive differential–difference equations
Authors: Bainov D. D. , Stamova I. M. 
Published: February 2009

AbstractIn the present paper questions related to stability and boundedness with respect to manifolds of solutions of impulsive differential-difference equations are considered. The investigations are carried out by means of piecewise-continuous functions which are analogues of the classical Lyapunov's functions. By means of a vectorial comparison equation and differential inequalities for piecewise-continuous functions, theorems are proved on stability and boundedness with respect to manifolds of solutions of impulsive differential-difference equations with impulse effect at fixed moments.
A programming model for student enrolment planning
Authors: Campbell L. H. 
Published: February 2009

AbstractThe problem of planning the annual intakes to a university course, in which there are capacity constraints on the total enrolment, so as to produce a steady transition into an eventual no-growth situation is formulated as a linear program. The special structure of the problem is exploited to find a particular, optimal solution and to show that the addition of integrality constraints on the intakes poses no additional difficulty. The usefulness of the proposed methods is illustrated with an example from the University of Adelaide.
Heat transfer in the thermal entrance region of a flat duct
Authors: Jones A. S. 
Published: February 2009

AbstractThe problem of heat transfer in a duct or tube for large values of the Péclet number has traditionally been solved by assuming that diffusion in the axial direction is negligible. This approach was used by Graetz [2] for the circular tube and by Prins et al [5] for the flat duct to obtain a series solution for downstream temperature field.Since these series converge very slowly in the neighbourhood of the origin, some other approach is necessary in the thermal entrance region. This was supplied by Lévêque [3] and extended by Mercer [4] who matched the Lévêque solution to the eigenfunction expansion.In all these solutions it was assumed that the axial diffusion of heat was negligible, but this assumption is invalid close to the discontinuity, since in this region the axial temperature gradient is large and the fluid velocity is small, so that axial diffusion plays an important role.In this paper, the assumptions implicit in Lévêque's solution are re-examined, and the correct approximation in the neighbourhood of the discontinuity as well as the solution which matches this into Lévêque's solution are presented. In the first of these solutions, diffusion is the only heat-transfer mechanism, while in the matching solution diffusion and convection are in balance.The corresponding solutions for the case of prescribed flux on the boundary are also considered.
On finite anti-plane shear for imcompressible elastic materials
Authors: Knowles James K. 
Published: February 2009

AbstractThis paper is concerned with deformations corresponding to antiplane shear in finite elastostatics. The principal result is a necessary and sufficient condition for a homogeneous, isotropic, incompressible material to admit nontrivial states of anti-plane shear. The condition is given in terms of the strain energy density characteristic of the material and is illustrated by means of special examples.
The initial dispersion of soluble matter in three-dimensional flow
Authors: Barton N. G. 
Published: February 2009

AbstractThe dispersion of a passive solute in three-dimensional flow is examined for short times after the injection of solute. If the diffusivity is constant, the solute at first diffuses isotropically about the fluid particle originally coincident with the injection point whilst, at longer times, the effect of diffusion across a velocity shear becomes more important. An asymptotic expansion is derived for the concentration of solute at small times after its injection into the fluid flow and the use of the theory is illustrated for three representative flows. Some critical remarks on the applicability and limitations of the results conclude the note.
Characterizations of optimality for continuous convex mathematical programs. Part I. Linear constraints
Authors: Scott C. H. , Jefferson T. R. 
Published: February 2009

AbstractRecently we have developed a completely symmetric duality theory for mathematical programming problems involving convex functionals. Here we set our theory within the framework of a Lagrangian formalism which is significantly different to the conventional Lagrangian. This allows various new characterizations of optimality.
A-topology for Minkowski space
Authors: Nanda Sribatsa 
Published: February 2009

AbstractWe consider in this paper a topology (which we call the A-topology) on Minkowski space, the four-dimensional space–time continuum of special relativity and derive its group of homeomorphisms. We define the A-topology to be the finest topology on Minkowski space with respect to which the induced topology on time-like and light-like lines is one-dimensional Euclidean and the induced topology on space-like hyperplanes is three- dimensional Euclidean. It is then shown that the group of homeomorphisms of this topology is precisely the one generated by the inhomogeneous Lorentz group and the dilatations.
Propagation properties in scattering theory
Authors: Robinson Derek W. 
Published: February 2009

AbstractGeneralizations of the Green-Lanford-Dollard theorem on scattering into cones and Ruelle-Amerin-Georgescu theorem characterizing bound states and scattering states are derived. The first is shown to be an easy consequence of the Kato-Trotter theorem on semi-group convergence whilst the latter is corollary of Wiener's version of the mean ergodic theorem.
Asymmetric bifurcation
Authors: Rosenblat S. 
Published: February 2009

AbstractA study is made of a non-linear diffusion equation which admits bifurcating solutions in the case where the bifurcation is asymmetric. An analysis of the initial-value problem is made using the method of multiple scales, and the bifurcation and stability characteristics are determined. It is shown that a suitable interpretation of the results can lead to determination of the choice of the bifurcating solution adopted by the system.
The diffraction of elastic waves by small cylindrical cavities
Authors: Buchwald V. T. 
Published: February 2009

The note added in proof on p. 495 should read:The author has discovered that R. P. Kanwal (J. Math. Phys. 44 (1965), 273–283) proposed a technique similar to the one in this paper. Unfortunately, Kanwal's scheme implies that the elastostatic problem can be reduced generally to the solution of Laplace's equation, a result which is well-known to be incorrect.
The complete symmetry group of a forced harmonic oscillator
Authors: Leach P. G. L. 
Published: February 2009

AbstractThe complete symmetry group of a forced harmonic oscillator is shown to be Sl(3, R) in the one-dimensional case. Approaching the problem through the Hamiltonian invariants and the method of extended Lie groups, the method used is that of time-dependent point transformations. The result applies equally well to the forced repulsive oscillator and a particle moving under the influence of a coordinate-free force. The generalization to na-dimensional systems is discussed.
A “constant of the motion” for the geodesic deviation equation
Authors: Dolan P. , Choudhury P. , Safko J. L. 
Published: February 2009

AbstractIn this short paper, it is shown that the geodesic deviation equation admits a “constant of the motion” and so can be solved exactly. We also derive an expression for the energy E of relative motion between two freely falling test particles. We can infer that, in general, E will not be a linear superposition of kinetic and potential energies.
A discrete random walk model for diffusion in media with double diffusivity
Authors: Hill James M. 
Published: February 2009

AbstractDiffusion in the presence of high-diffusivity paths is an important issue of current technology. In metals, high-diffusivity paths are identified with dislocations, grain boundaries, free surfaces and internal microcracks. In pourous media such as rocks, fissures provide a system of high-flow paths. Recently, based on a continuum approach, these phenomena have been modelled, resulting in coupled systems of partial differential equations of parabolic type for the concentrations in bulk and in the high-diffusivity paths. This theory assumes that each point of the medium is simultaneously occupied by more than one diffusion or flow path. Here a simple discrete random walk model of diffusion in a medium with double diffusivity is given.
The effect of a submerged barrier on the natural freqencies and radiation damping of a shallow basin connected to open water
Authors: Tuck E. O. 
Published: February 2009

AbstractA theory is provided for the natural seiching frequencies and radiative decay rates for a shallow-water basin whose connection to open water is restricted by a submerged wall or reef. The transition from an essentially-open basin to a closed basin, as the aperture reduces to zero, is discussed using a matching procedure. Graphs of frequencies and damping factors as functions of aperture size are obtained for idealized two-dimensional shelf configurations, involving a constant-depth shallow basin connected to constant-depth, but not necessarily shallow, open water.
Extended optima and equilibria for continuous games. I. General results
Authors: Gates D. J. , Westcott M. 
Published: February 2009

AbsrtactIn this, the first of three papers, we examine conditions, derived previously, which specify the equilibrium solutions of an adjustment process for N players engaged in a game with continuous (in fact, continuously differentiable) payoff functions, where each player's strategy is to choose a single real number. It is equivalent to the basic form of quantity-variation competition between N firms. The conditions are related to a new optimum which takes account of the ability of firms, or coalitions of firms, to discipline another firm that tries to increase its own profit. Closely related optima are also introduced and analysed. The new optima occupy N-dimensional regions in the strategy space, and contain the optima of Cournot, Pareto, von-Neumann and Morgenstern, and Nash as special cases.
Non-classical integrals of Bessel functions
Authors: Stuart S. N. 
Published: February 2009

AbstractCertain definite integrals involving spherical Bessel functions are treated by relating them to Fourier integrals of the point multipoles of potential theory. The main result (apparently new) concernswhere l1, l2 and N are non-negative integers, and r1 and r2 are real; it is interpreted as a generalized function derived by differential operations from the delta function δ(r1 − r2). An ancillary theorem is presented which expresses the gradient ∇2nYlm(∇) of a spherical harmonic function g(r)YLM(Ω) in a form that separates angular and radial variables. A simple means of translating such a function is also derived.
The boundary integral equation method with application to certain stress concentration problems in elasticity
Authors: Rizzo F. J. , Shippy D. J. 
Published: February 2009

AbstractThe essential aspects of the Boundary Integral Equation Method for the numerical solution of elliptic type boundary value problems are presented. A numerical example for a stress concentration problem in classical elasticity in three dimensions is given along with several examples for a class of scalar problems in elastic torsion of non-cylindrical bars. Some discussion and criticism of the method itself and in comparison with widely used field methods is also presented.
Two-dimensional resonators with small openings
Authors: Bigg G. R. , Tuck E. O. 
Published: February 2009

AbstractThe acoustic response of a two-dimensional nearly-closed cavity to an excitation through a small opening is examined, using the method of matched asymptotic expansions. The Helmholtz mode of vibration is discussed using a low-frequency expansion of the velocity potential in the cavity interior. The variation in frequency and magnitude of the resonator response is explored, both for the Helmholtz and the natural-frequency modes.
A trace formula for schrödinger operators with step potentials
Authors: O'Brien D. M. 
Published: February 2009

AbstractThis paper shows how to compute the trace of G(T) – G(T0), where G is an infinitely differentiable function with compact support, and where T and T0 are one-dimensional Schrödinger operators on (−∞, ∞) with potentials q and q0. It is assumed that q0 is a simple step potential and that q decays exponentially to q0. The trace is expressed in terms of the reflection and transmission coefficients for the scattering of plane waves by the potential q.
Detection of Hamiltonian circuits in a directed graph
Authors: Karmakar Sudhangshu B. 
Published: February 2009

AbstractA simple algebraic method is presented to determine the necessary condition for the existence of a Hamiltonian circuit in a directed graph of n vertices. A search procedure is then introduced to identify any or all of the existing Hamiltonian circuits. The procedure is based upon finding a set of edges which will then be candidates for being parts of circuits of length n at any vertex of the graph.
The temporal evolution of a system in combustion theory
Authors: Tam K. K. 
Published: February 2009

AbstractA model governing the combustion of a material is considered. The model consists of two non-linear coupled parabolic equations with initial and boundary conditions. An approximation for the rate of reactant consumption is made to enable the system to the treated by laplace transform. Three simple geometries are considered; namely, an infinite slab, an infinite circular and a sphere. The results obtained are then compared with numerical solutions for spme specific values of the parameters. There is good agreement over time duration for which numerical work was performed.
On Charwat's theory of motion of tracers in planar vortex flows
Authors: Leipnik R. B. 
Published: February 2009

AbstractThe motion of small, near neutrally buoyant tracers in vortex flows of several types is obtained on the basis of Charwat's mathematical model, which is highly non-linear.The solution method in the non-degenerate case expresses the squared orbital radius r2 as a product AA*, where the complex number A satisfies a second-order linear differential ‘factor equation’, generally with variable coefficients. The angular coordinate is expressed in terms of log(A*/A). Solid-type rotation and sinusoidally perturbed solid-type rotation correspond respectively to constant coefficients and sinusoidal coefficients. The former exactly yields a scalloped spiral tracer motion; the latter yields unstable tracer motion as t → ∞ except when the perturbing frequency and amplitude are rather specially related to the flow and tracer parameters. Free vortex motion is somewhat degenerate for this solution method but can be partially analyzed in terms of solutions of a generalized Emden–Fowler equation. The method can be used for other planar flow problems with a symmetry axis.
On the generation of water waves at an inertial surface
Authors: Rhodes-Robinson P. F. 
Published: February 2009

AbstractIn this paper we develop the Laplace-transform method to solve initial-value problems for the velocity potential describing the generation of infinitesimal capillary-gravity waves in a motionless liquid with an inertial surface composed of uniformly distributed floating particles. The two principal problems considered are the forced motions due to a submerged wave source and an immersed vertical plane wave-maker, which begin to operate in a time-dependent manner at a given instant. The transformed potentials are calculated using techniques similar to those which are effective in traditional time-harmonic problems with a free surface. The steady-state development in the time-harmonic example taken demonstrates the existence of outgoing progressive waves under any inertial surface, in contrast to the case of no surface tension when such waves cannot propagate under an inertial surface that is too heavy. The solution is also noted of the Cauchy-Poisson problem for the free motion flowing an intial elevation of the inertial surface, which is obtained by the same method.
Linear functionals of foliage angle density
Authors: Anderssen R. S. , Jackett D. R. 
Published: February 2009

AbstractKnowledge about the foliage angle density g(α) of the leaves in the canopy of trees is crucial in foresty mangement, modelling canopy reflectance, and environmental monitoring. It is usually determined from observations of the contact frequency f(β) by solving a version of the first kind Fredholm integral equation derived by Reeve (Appendix in Warren Wilson [22]). However, for inference purposes, the practitioner uses functionals defined on g(α), such as the leaf area index F, rather than g(α) itself. Miller [12] has shown that F can be computed directly from f(β) without solving the integral equation. In this paper, we show that his result is a special case of a general transformation for linear functionals defined on g(α). The key is the existence of an alternative inversion formula for the integral equation to that derived by Miller [11].
Galerkin's method for boundary integral equations on polygonal domains
Authors: Chandler G. A. 
Published: February 2009

AbstractA harmonic function in the interior of a polygon is the double layer potential of a distribution satisfying a second kind integral equation. This may be solved numerically by Galerkin's method using piecewise polynomials as basis functions. But the corners produce singularities in the distribution and the kernel of the integral equation; and these reduce the order of convergence. This is offset by grading the mesh, and the orders of convergence and superconvergence are restored to those for a smooth boundary.
Growth and oscillation properties of solutions of a fourth order linear difference equation
Authors: Hooker John W. , Patula William T. 
Published: February 2009

AbstractFor the fourth-order linear difference equation Δ4un−2 = bn un, with bn > 0 for all n, generalized zeros are defined, following Hartman [5], and two theorems are proved concerning separation of zeros of linearly independent solutions. Some preliminary results deal with non-oscillation and asymptotic behavior of solutions of this equation for various types of initial conditions. Finally, recessive solutions are defined, and results are obtained analogous to known results for recessive solutions of second-order difference equations.
An inexact Levenberg-Marquardt method for large sparse nonlinear least squres
Authors: Wright S. J. , Holt J. N. 
Published: February 2009

AbstractA method for solving problems of the form is presented. The approach of Levenberg and Marquardt is used, except that the linear least squares subproblem arising at each iteration is not solved exactly, but only to within a certain tolerance. The method is most suited to problems in which the Jacobian matrix is sparse. Use is made of the iterative algorithm LSQR of Paige and Saunders for sparse linear least squares.A global convergence result can be proven, and under certain conditions it can be shown that the method converges quadratically when the sum of squares at the optimal point is zero.Numerical test results for problems of varying residual size are given.
End effects in a two dimensional potential problem for closely spaced rectangular plates
Authors: Barton N. G. 
Published: February 2009

AbstractThis paper presents a conformal mapping solution of Laplace's equation in the two dimensional region exterior to two rectangular plates or electrodes at different potentials. Plates with finite and semi-infinite lengths are considered separately and particular emphasis is placed upon the case when the separation between the plates is small. The key results of the paper are expressions for the integral of the square of the normal field along the mid-line between the plates. This integral is of importance in certain gaseous conductor experiments that are sufficiently accurate for a consideration of end effects to be necessary. For small gaps, the dominant end correction to the integral is linear with the gap width. It is also shown that, for small gaps, the simplified (semi-infinite) geometry gives essentially the same value for the integral as the full (finite plate length) geometry.
An uncoupling procedure for a class of coupled linear partial differential equations
Authors: McNabb A. 
Published: February 2009

AbstractA Fredholm operator exists which maps the solutions of a system of linear partial differential equations of the form ∂u/∂t = DLu + Au coupled by a matrix A onto those solutions of a similar system coupled by a matrix B which have the same initial values. The kernels of this operator satisfy a hyperbolic system of equations. Since these equations are independent of the linear partial differential operator L, the same operator serves as a mapping for a large class of equations. If B is chosen diagonal, the solutions of a coupled system with matrix A may be obtained from the uncoupled system with matrix B.