bluuebunny/crossref_metadata_2025_split huggingface dataset:
Monotonicity properties of the zeros of Bessel functions
Authors: McCann Roger C. , Love E. R. 
Published: February 2009

AbstractLet jν, denote the first positive zero of Jν. It is shown that jν/(ν + α) is a strictly decreasing function of ν for each positive α provided ν is sufficiently large. For each α lowe bounds on ν are given to assure the monotonicity of jν/(ν + α). From this it is shown that jν > ν + j0 for all ν > 0, which is both simpler and an improvement on the well known inequality Jν ≥ (ν (ν + 2))1/2.
Approximate solutions for coupled moment equations
Authors: Winley Graham , Tognetti Keith 
Published: February 2009

AbstractIn studying the coupled differential equations for the moments of a stochastic process it is often found that the equation for thejth moment involves higher moments. The usual methods of “decoupling” such a system of equations to obtain estimates of the moments are surveyed and shown generally to result in a system of nonlinear simultaneous differential equations which may be readily solved by numerical methods.Often, estimates of the first and second moments are the main concern. In this case, two further assumptions reported in the literature can be used to simplify the system and avoid the expense of solving the nonlinear equations. These two techniques are evaluated and compared with a new technique. Two processes are analysed, one representing a chemical reaction and the other population growth.
Ray analysis and punching problems for stretched elastic plates
Authors: Moodie T. Bryant , Tait R. J. , Barclay D. W. 
Published: February 2009

AbstractThe present paper presents a ray analysis for a problem of technical importance in fragmentation studies. The problem is that of suddenly punching a circular hole in either isotropic or transversely isotropic plates subjected to a uniaxial tension field. The ray method, which involves only differentiation, integration, and simple algebra, is shown to be particularly useful in clarifying the propagation process of the resulting unloading waves and obtaining the attendant discontinuities of the various quantities involved. Numerical results obtained from the ray analysis are presented in graphical form and compared with those obtained by more elaborate schemes.
A note on the random walk model arising in double diffusion
Authors: Liyanage L. H. , Hill J. M. , Gulati C. M. 
Published: February 2009

AbstractThe discrete random walk problem for the unrestricted particle formulated in the double diffusion model given in Hill [2] is solved explicitly. In this model it is assumed that a particle moves along two distinct horizontal paths, say the upper path I and lower path 2. For i = 1, 2, when the particle is in path i, it can move at each jump in one of four possible ways, one step to the right with probability pi, one step to the left with probability qi, remains in the same position with probability ri, or exchanges paths but remains in the same horizontal position with probability si (pi + qi + ri + si = 1). Using generating functions, the probability distribution of the position of an unrestricted particle is derived. Finally some special cases are discussed to illustrate the general result.
Saddle point and duality in the optimization theory of convex set functions
Authors: Lai Hang-Chin , Yang Shu-Shih 
Published: February 2009

AbstractFor a set function G on an atomless finite measure space (X, , m), we define the subgradient, conjugate set of and conjugate functional of G. It is proved that a minimization problem of set function G has an optimal solution if and only if the Lagrangian on × L1(X, , m)has a saddle point (Ω0, f0) such thatwhere f0 is an element of the conjugate set (for the definition, see the later context).
Iterative solution of quasilinear parabolic equations by parabolic equations with constant coefficients
Authors: Lavery John E. 
Published: February 2009

AbstractA method for solving quasilinear parabolic equations of the typesthat differs radically from previously known methods is proposed. For each initial-boundary-value problem of one of these types that has boundary conditions of the first kind (second kind), a conjugate initial-boundary-value problem of the other type that has boundary conditions of the second kind (first kind) is defined. Based on the relations connecting the solutions of a pair of conjugate problems, a series of parabolic equations with constant coefficients that do not change step to step is constructed. The method proposed consists in calculating the solutions of the equations of this series. It is shown to have linear convergence. Results of a series of numerical experiments in a finite-difference setting show that one particular implementation of the proposed method has a smaller domain of convergence than Newton's method but that it sometimes converges faster within that domain.
Insulating circular rugs
Authors: Weir G. J. 
Published: February 2009

AbstractA thin, partially insulating circular rug is placed on a uniform half space up through which a steady heat flow passes. The corresponding dual integral equations are solved using Tranter's method, finite Legendre transforms and Mellin-Bames contour integrals. An untabulated Bessel (or Stieltjes) transform similar to the discontinuous WeberSchafheitlin integral is evaluated, and a simple expression derived for the rug's surface temperature.
Steady states of the reaction-diffusion equations. Part II: Uniqueness of solutions and some special cases
Authors: Burnell J. G. , Lacey A. A. , Wake G. C. 
Published: February 2009

AbstractIn an earlier paper (Part I) the existence and some related properties of the solution to a coupled pair of nonlinear elliptic partial differential equations was considered. These equations arise when material is undergoing an exothermic chemical reaction which is sustained by the diffusion of a reactant. In this paper we consider the range of parameters for which the uniqueness of solution is assured and we also investigate the converse question of multiple solutions. The special case of the one dimensional shape of the infinite slab is investigated in full as this case admits to solution by integration.
On maximum principles for diffusion in the presence of three diffusion paths
Authors: Lee Alexander I. , Hill James M. 
Published: February 2009

AbstractThis note examines maximum principles for systems of parabolic partial differential equations describing diffusion in the presence of three diffusion paths. The particular system under consideration arises from a random walk model. For a more general system constraints on the various constants are given which guarantee maximum principles. Remarkably, the physical system arising from the random walk model automatically satisfies these constraints.
Non-linear optimization of the material constants in Ogden's stress-deformation function for incompressinle isotropic elastic materials
Authors: Twizell E. H. , Ogden R. W. 
Published: February 2009

AbstractIn previous papers, three terms have been included in Ogden's stress-deformation function for incompressible isotropic elastic materials. The material constants have been calculated by elementary methods and the resulting fits to sets of experimental data have been moderately good.The purpose of the present paper is to improve upon established correlation between theory and experiment by means of a systematic optimization procedure for calculating material constants. For purposes of illustration the Levenberg-Marquardt non-linear least squares optimization algorithm is adapted to determine the material constants in Ogden's stress-deformation function.The use of this algorithm for three-term stress-deformation functions improves somewhat on previous results. Calculations are also carried out in respect of a four-term stress-deformation function and further improvement in the fit is achieved over a large range of deformation.
Hearing the shape of an annular drum
Authors: Gottlieb H. P. W. 
Published: February 2009

AbstractThe asymptotic expansion for a spectral function of the Laplacian operator, involving geometrical properties of the domain, is demonstrated by direct calculation for the case of a doubly-connected region in the form of a narrow annular membrane. By utilizing a known formula for the zeros of the eigenvalue equation containing Bessel functions, the area, total perimeter and connectivity are all extracted explicitly.
Existence theorems for Segal quantization via spectral theory in Krein space
Authors: Broadbridge P. 
Published: February 2009

AbstractSegal's unitarizing complex structure J is shown, in the Fermi-Dirac case, to be the orthogonal component in the polar decomposition of the real skew adjoint generator of classical dynamics. It is proven that in the Bose-Einstein case, the classical symplectic dynamics cannot be unitarized unless the generator is similar to a real skew adjoint operator.With the classical Hamiltonian strictly positive, J is the pseudo-orthogonal component in the polar decomposition of the generator, using spectral theory in Krein space with indefinite metric. Thus, J can be expressed simply in terms of the projection E(0) onto the subspace of classical solutions with negative frequency. This complements the physicists' experience that conceptual difficulties arise when dynamically invariant separation of positive and negative frequency solutions is impossible.
Field of a charged particle in the presence of scalar meson fields in general relativity
Authors: Reddy D. R. K. , Rao V. U. M. 
Published: February 2009

AbstractField equations for coupled gravitational and zero mass scalar fields in the presence of a point charge are obtained with the aid of a static spherically symmetric conformally flat metric. A closed from exact solution of the field equations is presented which may be considered as describing the field of a charged particle at the origin surrounded by the scalar meson field in a flat space-time.
Scattering analysis and synthesis of wave trains
Authors: Sobey R. J. , Colman E. J. 
Published: February 2009

AbstractThe Zakharov-Shabat scattering transform is an exact solution technique for the nonlinear Schrödinger equation, which describes the time evolution of weakly nonlinear wave trains. Envelope soliton and uniform wave train solutions of the nonlinear Schrödinger equation are separable in scattering transform space. The scattering transform is a potential analysis and synthesis technique for natural wave trains. Discrete versions of the direct and inverse scattering transform are presented, together with proven algorithms for their numerical computation from typical ocean wave records. The consequences of discrete resolution are considered.
The generation of surface waves by an intense cyclone
Authors: Viera F. , Buchwald V. T. 
Published: February 2009

AbstractAssuming a travelling oscillating pressure source model, this paper sets out to investigate the observation of surface gravity waves generated by a cyclone moving with constant speed v. It is shown that when the source frequency is near the critical resonant value g/4ν, large amplitude waves may be generated. There is some agreement with observations of waves from cyclone Pam of February, 1974.
Surface-wave interaction with a deeply submerged circular duct
Authors: Miles John W. 
Published: February 2009

AbstractThe interaction of a surface wave of angular frequency ω with a deeply submerged, vertical open-mouthed, circular duct of radius a is considered. The resulting boundary- value problem is solved by the Wiener-Hopf technique. The pressure-amplification factor (the ratio of the complex amplitude of the pressure in the depths of the duct to that of the incident wave in the plane of the mouth) is determined in closed form as a function of the dimensionless wave number K = ω2a/g.
Interaction of internal waves in a continuous thermocline model
Authors: Hung N. T. , Maslowe S. A. 
Published: February 2009

AbstractWeak nonlinear interactions are studied for systems of internal waves when the Brunt-Väisälä frequency is proportional to sech z, where z = 0 is the centre of the thermocline. Explicit results expressed in terms of gamma functions have been obtained for the interaction coefficients appearing in the amplitude evolution equations. The cases considered include resonant triads as well as second and third harmonic resonance. In the non-resonant situation, the Stokes frequency correction due to finite-amplitude effects has been computed and the extension to wave packets is outlined. Finally, the effect of a mean shear on resonant interactions is discussed.
Low Reynolds number flow in a heated tube of varying section
Authors: Bestman A. R. 
Published: February 2009

AbstractIn this paper we study the effect of forced and free convection heat transfer on flow in an axisymmctric tube whose radius varies slowly in the axial direction. Asymptotic series expansions in terms of a small parameter ∈, which is a measure of the radius variation, are obtained for the velocity components, pressure and temperature on the assumption that the Reynolds number (R) is of order one. The effect of the free convection parameter or Grashof number (G) on the axial velocity, temperature distribution, shear stress and heat flux at the wall are discussed quantitatively for a locally constricted tube.
The propagation of small amplitude long waves on the surface of superfluid helium
Authors: Johnson R. S. 
Published: February 2009

AbstractVarious problems related to the propagation of small amplitude long waves on the surface of superfluid helium (helium II), usually called third sound, are studied on the basis of the appropriate governing equations. The two-fluid continuum model due to Landau is considered, with the effects of healing and relaxation incorporated, and viscosity, heat conduction and compressibility terms retained. The helium vapour is treated as a classical (Newtonian) compressible gas and the exact jump conditions across the liquid/vapour interface are employed. These liquid, vapour and jump equations constitute the exact problem although, in an effort to reduce the complexity of the equations, a simplified set of ‘model’ surface boundaiy conditions is also introduced. This full set of equations is non-dimensionalised taking care that all physical parameters are defined using only the undisturbed depth of the layer as the appropriate length scale. The ratio depth/wave-lenght (δ) is then a separate parameter as is the wave amplitude/depth ratio (ɛ). The limit which corresponds to the wave under discussion is then ɛ, δ → 0 with all the other parameters fixed.A number of analyses are presented, four of which describe various aspects of the linearised theory and two examine the nature of the far-field nonlinear problem. Using the simplified surface boundary conditions we discuss in turn: the wave motion in the absence of healing: the rôle of a second wave speed leading to a wave hierarchy; and the effects of healing. The final linearised problem makes use of the full vapour model, but again the healing terms are ignored. This latter analysis suggests that if the upper boundary of the vapour is sufficiently close to the liquid surface then third sound is suppressed.The complexity of the equations, particularly when the nonlinear terms are to be examined, is such that the incompressible limit is now taken in the absence of both healing and relaxation. Imposing the physically realistic limiting process (ɛ, δ → 0) we show that the only equation valid in the far-field is the Burgers equation. However, we also demonstrate that allowing the other parameters to be functions of e (which is not physically realisable in practice) it is easy to derive, for example, the Korteweg-de Vries equation.
On a complementarity problem associated with nondifferentiable programming
Authors: Craven B. D. , Mond B. , Parida J. 
Published: February 2009

AbstractThis paper deals with the question of the existence of a solution to the stationary-point problem corresponding to a given nonlinear nondifferentiable program. An existence theorem for the stationary-point problem is presented under some convexity and regularity conditions on the functions involved, which also guarantee an optimal solution to the nonlinear program.
solutions of period three for a non-linear difference equation
Authors: Brown A. 
Published: February 2009

AbstractThe paper uses the factorisation method to discuss solutions of period three for the difference equationwhich has been proposed as a simple mathematical model for the effect of frequency dependent selection in genetics. Numerical values are obtained for the critical values of a at which solutions of period three first appear. In addition, the interval in which stable solutions are possible has been determined. Exact solutions are given for the case a = 4 and these have been used to check the results.
Delayed responses and stability in two-species systems
Authors: Gopalsamy K. 
Published: February 2009

AbstractIt is shown that if intraspecific self-regulating negative feedback effects are strong enough such that a nontrivial steady state of a two species system is locally asymptotically stable, then time delays in the positive feedback as well as in other interspecific interactions cannot destabilise the system and hence delay induced instability leading to persistent oscillations is impossible whatever the magnitude of the time delays. A method is also proposed for an estimate of decay rate of perturbations.
On the design of mortgages and the need for indexation
Authors: Gair F. C. 
Published: February 2009

AbstractThere is a well-recognized need for a mortgage instrument that will operate satisfactorily in the presence of a volatile inflation. This paper analyses a large class of mortgages—the ‘continuous mortgage’ (CM)—as a basis for such design. In particular, it is shown that the real (inflation-adjusted) payment stream is exponentially sensitive to changes in the real interest rate. Consequently to realize a satisfactory design, the mortgage must be indexed by assigning the real interest rate. Then, under appropriate restraints, the CM offers a continuum of satisfactory mortgage designs.
An observation problem for the Bessel differential operator
Authors: Werner K.-D. 
Published: February 2009

AbstractIn this paper, the parabolic partial differential equation ut = urr + (1/r)ur − (v2/r2)u, where v ≥ 0 is a parameter, with Dirichlet, Neumann, and mixed boundary conditions is considered. The final state observability for such problems is investigated.
The diffraction of long elastic waves by elliptic cylindrical cavities
Authors: Buchwald V. T. , Cong T. Tran 
Published: February 2009

AbstractThe method of asymptotic matching introduced by Buchwald [I] is adapted to the case of the diffraction of plane longitudinal and shear waves by cylindrical cavities with elliptic cross-sections. It is assumed that the dimensions of the cross section are small compared with the wavelength of the incident waves. Asymptotic formulae for the scattered wave potentials are obtained.The method is valid when the cavity reduces to a two-dimensional stress free crack whose length is small compared with the wavelength. Formulae for the scattered waves, and for the stress-concentrations at the crack tips are obtained.
New algorithms for discrete-time optimal control problems
Authors: Nedeljković Nikola B. 
Published: February 2009

AbstractThe paper presents new demonstrably convergent first-order iterative algorithms for unconstrained discrete-time optimal control problems. The algorithms, which solve the linear-quadratic problem in one iterative step, are particularly suited for solving nonlinear problems with linear constraints via penalty function methods. The proofs of the reduction of cost at each iteration and convergence of the algorithms are provided.
Solutions of period four for a non-linear difference equation
Authors: Brown A. 
Published: February 2009

AbstractThe paper extends earlier work by using the factorisation method to discuss solutions of period four for the difference equationThis equation was suggested by R. M. May as a simple mathematical model for the effect of frequency-dependent selection in genetics. It is shown that for a given value of the parameter, a, the identification of solutions of period four can be reduced to finding real roots for a polynomial equation of degree eight. The appropriate values of xn follow from a quartic equation. By splitting up the problem in this way it becomes relatively straightforward to determine the critical values of a at which the various solutions of period four first appear and to discuss the stability of these solutions. Intervals of stability are tabulated in the paper.
Unsteady waves on an open two layer fluid
Authors: Sharp P. W. 
Published: February 2009

AbstractThe evolution of small amplitude waves on an open two layer fluid is investigated. The spatially periodic surface and interface displacements are represented as Fourier series with time dependent coefficients, for which evolution equations with all significant quadratic interactions included, are derived. Solutions to these equations are found analytically for a small number of harmonics, and numerically for a larger number of harmonics. Two numerical solutions are given to illustrate the evolution properties.
Notes on Sraffa's fixed capital model
Authors: Woods J. E. 
Published: February 2009

AbstractThis paper considers a single-product industries, fixed capital model discussed briefly by Sraffa in Chaapter X if his book. The analysis is elementary, being based on the direct calculation of a certain martrix inverse. This generalises the approach adopted for circulating capital models. It also demonstrates that common economic and mathematical frameworks exist for both circulating and fixed capital models.
Eigenvalues of the Laplacian with Neumann boundary conditions
Authors: Gottlieb H. P. W. 
Published: February 2009

AbstractVarious grometrical properties of a domain may be elicited from the asymptotic expansion of a spectral function of the Laplacian operator for that region with apporpriate boundary conditions. Explicit calculations, using analytical formulae for the eigenvalues, are performed for the cases fo Neumann and mixed boundary conditions, extending earlier work involving Dirichet boundary conditions. Two- and three-dimensional cases are considered. Simply-connected regions dealt with are the rectangle, annular sector, and cuboid. Evaluations are carried out for doubly-connected regions, including the narrow annulus, annular cylinder, and thin concentric spherical cavity. The main summation tool is the Poission summation formula. The calculations utilize asymptotic expansions of the zeros of the eigenvalue equations involving Bessel and related functions, in the cases of curved boundaries with radius ratio near unity. Conjectures concerning the form of the contributions due to corners, edges and vertices in the case of Neumann and mixed boundary conditions are presented.
A canonical form and solution for the matrix Riccati differential equation
Authors: Leipnik R. B. 
Published: February 2009

AbstractA canonical form of the self-adjoint Matrix Riccati Differential Equation with constant coefficients is obtained in terms of extremal solutions of the self-adjoint Matrix Riccati Algebraic (steady-state) Equations. This form is exploited in order to obtain a convenient explicit solution of the transient problem. Estimates of the convergence rate to the steady state are derived.