bluuebunny/crossref_metadata_2025_split huggingface dataset:
Families of three-stage third order Runge-Kutta-Nyström methods for y″ = f (x, y, y′)
Authors: Chawla M. M. , Sharma S. R. 
Published: February 2009

AbstractIn this paper all three-stage third order (explicit) Runge-Kutta-Nyström (R-K-N) methods for y″ = f (x, y, y′) are presented. While determining particular methods we require that when these methods are applied to the test equation: y″ − (α + β) y ′ + αβy = 0, the measure of the relative error F, introduced by Rutishauser [4], should not deteriorate in the case of equal eigenvalues (β → α). Further, we require that when these methods are applied to special differential equations y″ = f(x, y) they should possess either of the two properties: (P1) a method remains of order three but is two-stage, (P2) a method remains three-stage but attains order four. We present new R-K-N methods which are stabilized in the sense of Ruthishauser [4] and which possess the property (P1). (There does not exist any three-stage third order R-K-N method which is stabilized and which possesses the property (P2).)
Reflection of oblique shock waves in incompressible elastic solids
Authors: Duszczyk B. , Kosinski S. , Wesolowski Z. 
Published: February 2009

AbstractUsing a semi-inverse method proposed by Wright the reflection of a finite elastic plane shock wave at a plane boundary of a special elastic incompressible material is examined. Three types of boundary conditions are considered. In the case of frictionless-rigid boundary the reflected wave is a single simple wave. For clamped boundary the solution indicates a possibility of irregular reflection as well. There is no reflection solution in the case of a free boundary.
On the general random walk formulation for diffusion in media with Diffusivities
Authors: Hill James M. , Hughes Barry D. 
Published: February 2009

AbstractA general discrete multi-dimensional and multi-state random walk model is proposed to describe the phenomena of diffusion in media with multiple diffusivities. The model is a generalization of a two-state one-dimensional discrete random walk model (Hill [8]) which gives rise to the partial differential equations of double diffusion. The same partial differential equations are shown to emerge as a special case of the continuous version of the present general model. For two states a particular generalization of the model given in [8] is presented which is not restricted to nearest neighbour transitions. Under appropriate circumstances this two-state model still yields the partial differential equations of double diffusion in the continuum limit, but an example of circumstances leading to a radically different continuum limit is presented.
The generalized Mayer theorem in the approximating Hamiltonian method
Authors: Bakulev A. P. , Bogolubov N. N. , Kurbatov A. M. 
Published: February 2009

AbstractWith the help of the generalized Mayer theorem we obtain an improved inequality for free energies of model and approximating systems, where only “connected parts” over the approximating Hamiltonian are taken into account. For a concrete system we discuss the problems of convergence of appropriate series of “connected parts ”.
Simple nonlinear dual control problems
Authors: Murray J. M. 
Published: February 2009

AbstractIn this paper we consider a simple, nonlinear optimal control problem with sufficient convexity to enable us to formulate its dual problem. Both primal and dual problems will include constraints on both the states and controls. The constraints in one problem may cause the “optimal” dual states to be discontinuous. However, we will look at conditions under which the presence of constraints does not force discontinuities and the optimal states and costates are absolutely continuous.
A non-linear difference equation with two parameters. II
Authors: Brown A. 
Published: February 2009

AbstractThe paper discusses solutions of period 4 for the difference equationwhere k and m are real parameters, with k > 0. For given values of k and m there are at most three solutions with period 4 and equations are set up to determine the elements of these solutions and the stability of each solution. Only real solutions are considered. The procedure that is used to find these solutions allows unstable solutions to be identified as well as stable solutions.In a previous paper, solutions of period 2 and period 3 were examined for this equation and there was evidence of anomalous behaviour in the way the stability intervals occurred. Some preliminary information about solutions of period 4 was mentioned in the discussion. The present paper provides more complete results, which confirm the anomalous behaviour and give a better idea of how the stability criterion changes for different families of solutions. These results are used to indicate the variety of behaviour that can be found for one-parameter systems by imposing suitable conditions on m and k.
Strong system equivalence (I)
Authors: Anderson B. D. O. , Coppel W. A. , Cullen D. J. 
Published: February 2009

AbstractStrong system equivalence is defined for polynomial realizations of a rational matrix. It is shown that any polynomial realization is strongly system equivalent to a generalized state-space realization, and two generalized state-space realizations are strongly system equivalent if and only if they are constant system equivalent.
Strong pseudo-convexity and symmetric duality in nonlinear programming
Authors: Mishra M.S. , Nanda S. , Acharya D. 
Published: February 2009

AbstractIn this note, the weak duality theorem of symmetric duality in nonlinear programming and some related results are established under weaker (strongly Pseudo-convex/strongly Pseudo-concave) assumptions. These results were obtained by Bazaraa and Goode [1] under (stronger) convex/concave assumptions on the function.
Surface mounted heat flux sensors
Authors: Weir G. J. 
Published: February 2009

AbstractThe dual integral equations describing heat flow about a circular Heat Flux Sensor on the surface of a layered medium are derived and discussed, together with the extent to which the Heat Flux Sensor measures the heat flow which would occur in the absence of a Heat Flux Sensor. An asymptotic analysis provides new analytical results supporting those derived previously by numerical methods.It is suggested that some properties of the general problem of a Heat Flux Sensor on the surface of a multiply-layered medium can be approximated by a lumped-parameter model depending on only four non-dimensional numbers: namely, two non-dimensional linear heat transfer coefficients, and essentially two non-dimensional thermal resistances. Some support for the lumped parameter model is provided.
Force distribution along a slender body straddling an interface
Authors: Fulford G. R. , Blake J. R. 
Published: February 2009

AbstractLine distributions of Stokes flow singularities are used to model the flow around a slender body which is straddling a flat interface between two viscous fluids. Motion of the slender body parallel to the interface and normal to the interface is considered where the axis of symmetry of the slender body is always perpendicular to the undisturbed interface. Asymptotic approximations to the force distributions on the slender body are evaluated and the relative contributions of that part of the slender body in one fluid to the force distribution in the other fluid and of the interface interaction to the force distribution are examined. It is observed that a shielding region exists about the interface which is due to the interaction with that part of the slender body in the other fluid. Finally, for parallel motion, the first order interface deformation is calculated.
Airfoils moving in air close to a dynamic water surface
Authors: Grundy I. H. 
Published: February 2009

AbstractSteady potential flow about a thin wing, flying in air above a dynamic water surface, is analysed in the asymptotic limit as the clearance-to-length ratio tends to zero. This leads to a non-linear integral equation for the one-dimensional pressure distribution beneath the wing, which is solved numerically. Results are compared with established “rigid-ground” and “hydrostatic” theories. Short waves lead to complications, including non-uniqueness, in some parameter ranges.
Parseval's integral and the Jacobi expansions in series of Bessel fuinctions
Authors: Lekner John 
Published: February 2009

AbstractThe sumsare shown to approximate J0 (z); the error terms are series in higher order Bessel functions, leading with J2M (z). Similar sums approximate J1(z). These sums may be looked on as extensions of the Jacobi expansions for cos z and sin z in series of Bessel functions. They become numerically useful for M > |z|.
Expansion formulae for general triple hypergeometric series
Authors: Mohd Ch. Wali , Qureshi M. I. 
Published: February 2009

AbstractThe main object of present paper is to obtain a finite summation of Srivastava's general triple hypergeometric series in terms of Kampé de Fériet's double hypergeometric series. A number of finite sums of Kampé de Fériet's double hypergeometric polynomials in terms of different kinds of single hypergeometric polynomials of higher order, are obtained. Some known results of Manocha and Sharma [9], [10], Munot [11], Pathan [12], Qureshi [15], Qureshi and Pathan [16] and Srivastava [26] are deduced as special cases. A result of Pathan [13, page 316 (1.2)] is also corrected here.
The foliage density equation revisited
Authors: Miller John Boris 
Published: February 2009

AbstractThe foliage density equation is the means by which the foliage density g in a leaf canopy, as a function of the angle of inclination of the leaves, is to be estimated from discrete data gathered using photometric methods or point quadrats. It is an integral equation relating f, a function of angle estimated from measurements, to the unknown function g. The explicit formula for g is known and depends upon f and its first three derivatives; the operator f →, g is unbounded, and the problem is ill posed.In this paper we give the form of g when f is a trigonometric polynomial, extending earlier results due to J. R. Philip. This provides a means of estimating g without directly estimating the derivatives of f from numerical data. To assess the reliability of the method we discuss the convergence of Fourier series representations of f and g.
Criticality dependence on data and parameters for a problem in combustion theory
Authors: Tam K. K. 
Published: February 2009

AbstractA central problem in the theory of combustion, consisting of a nonlinear parbolic equation together with initial and boundary conditions, is considered. The influence of the initial and boundary data examined. In the main part of the study, a two-step linearization is developed such that the interesting features of the original problem are given by the solution of a non-liner and ordinary differential equation. Approximate solutions are obtained and upper and lower solutions are used to assess the validity of the approximations. Whenever possible, results are compared with those obtained previously and there is good agreement in all cases.
A note on nondifferentiable symmetric duality
Authors: Craven B. D. 
Published: February 2009

Under suitable hypotheses on the function f, the two constrained minimization problems:are well known each to be dual to the other. This symmetric duality result is now extended to a class of nonsmooth problems, assuming some convexity hypotheses. The first problem is generalized to:in which T and S are convex cones, S* is the dual cone of S, and ∂y denotes the subdifferential with respect to y. The usual method of proof uses second derivatives, which are no longer available. Therefore a different method is used, where a nonsmooth problem is approximated by a sequence of smooth problems. This duality result confirms a conjecture by Chandra, which had previously been proved only in special cases.
Nonlinear model reference adaptive control
Authors: Skowronski J. M. 
Published: February 2009

AbstractThe known linear model reference adaptive control (MRAC) technique is extended to cover nonlinear and nonlinearizable systems (several equilibria, etc) and used to stabilize the system about a model. The method proposed applies the same Liapunov Design Technique but avoids the classical error equation. Instead it operates in the product of the state spaces of plant and model, aiming at convergence to a diagonal set. Control program, Liapunov functions and adaptive law are specified. The case is illustrated on a two-degrees of freedom robotic manipulator.
Ziebur's matrix equation for population growth
Authors: Brown A. 
Published: February 2009

AbstractThe paper examines a matrix equation given by Ziebur [6] for the growth of a population in which the birth-rate and death-rate are age-dependent. For convenience the population was sub-divided into four age groups, with the same birth-rate and death-rate for individuals in a particular group, and the matrix equation relates the numbers in each sub-division in consecutive years. This avoids delay terms and makes it easier to modify the growth equation but it is shown that the form suggested by Ziebur for the transition matrix leads to some difficulties.
Two infinite-Froude-number cusped free-surface flows due to a submerged line source or sink
Authors: Collings I. L. 
Published: February 2009

AbstractSolutions are found to two cusp-like free-surface flow problems involving the steady motion of an ideal fluid under the infinite-Froude-number approximation. The flow in each case is due to a submerged line source or sink, in the presence of a solid horizontal base.
A note on the singularities in the theory of water waves with an inertial surface
Authors: Mandal B. N. , Kundu Krishna 
Published: February 2009

AbstractThis note is concerned with the derivation of velocity potentials describing the generation of infinitesimal gravity waves in a motionless liquid with an inertial surface composed of uniformly distributed floating particles, due to fundamental line and point sources with time-dependent strengths submerged in a liquid of finite constant depth.
The finite-section approximation for integral equations on the half-line
Authors: de Hoog Frank , Sloan Ian H. 
Published: February 2009

AbstractIntegral equations on the half line are commonly approximated by the finite-section approximation, in which the infinite upper limit is replaced by a positive number β. A novel technique is used here to rederive a number of classical results on the existence and uniqueness of the solution of the Wiener-Hopf and related equations, and is then extended to obtain existence, uniqueness and convergence results for the corresponding finite-section equations. Unlike the methods used in the recent work of Anselone and Sloan, the present methods are constructive, and result in explicit asymptotic bounds for the error introduced by the finite-section approximation.
On the continuity of the Wiener-Hopf factorization operation
Authors: Green Michael , Anderson Brian D.O. 
Published: February 2009

AbstractThe problem of passing from an L∞ function to a Wiener-Hopf factorization is considered. It is shown that a small L∞ perturbation which does not change the factorization indices will lead to small Lp (1 < p < ∞) perturbations in the Wiener-Hopf factors, but can lead to large L∞ perturbations, unless the derivatives are controlled during the perturbation.
On the uniqueness of solitary Rossby waves
Authors: Kloeden P. E. 
Published: February 2009

AbstractThe explicit solitary Rossby wave solutions found by Larichev, Reznik and Berestov are shown to be unique for the model equations considered, in the sense that there are no other antisymmetric wave solutions which are not of these forms. This is done by adapting arguments used by Amick and Fraenkel to show the uniqueness of the Hill's vortex solution. It is based on the maximum principle and the domain folding method of Gidas, Ni and Nirenberg, and involves showing that the function ψ/y is radially symmetric, where ψ is the streamfunction of a solitary wave and y the horizontal cartesian coordinate perpendicular to the x-axis, along which the waves move at steady positive speed. This argument is also used to show the uniqueness of the well-known explicit solutions for cylindrical vortices. The result does not apply directly to rider solutions of Flierl et al., which are not antisymmetric, but it does restrict the possible rider solutions that can form because of their association with particular antisymmetric solutions.
Finite element error estimates for subsonic flow
Authors: Chow S. S. , Carey G. F. 
Published: February 2009

AbstractError estimates are derived for a finite element analysis of plane steady subsonic flows described by the full potential equation. The analysis is based on the use of the theory of variational inequalities to accomodate the subsonic flow constraint and leads to a suboptimal estimate relative to that obtained for linear potential flow. We then consider an alternative dual formulation of the problem and obtain an optimal estimate subject to reasonable regularity assumptions.
The solution of some integral equations
Authors: Ahner John F. , Lowndes John S. 
Published: February 2009

AbstractAlgorithms are developed by means of which certain connected pairs of Fredholm integral equations of the first and second kinds can be converted into Fredholm integral equations of the second kind. The methods are then used to obtain the solutions of two different sets of triple integral equations tht occur in mixed boundary value problems involving Laplace' equation and the wave equation respectively.
Observables in modular field thoey
Authors: Kleeman R. 
Published: February 2009

AbstractThe observables of modular quantisation are studied from the point of view of locality. Such a study allows identification of possible Hamiltonians and also enables us to generalize the fundamental trilinear commutation relations of parafield theory. A comparison of modular field theory with a normal U(m) gauge theory, begun in an earlier publication, is completed with the conclusion that the two are equivalent except that the former has certain restrictions on its observables.
Determining statistical dominance by linear programming
Authors: Drynan Ross G. 
Published: February 2009

AbstractThis note generalises the necessary and sufficient conditions for one act to be dominated by another when the two acts available to the decision maker have outcomes contingent on discrete states of nature whose probabilities of occurrence are known only to the extent of linear partial information. The generalisation relates to the dominance of an act by a set of acts. The presentation is in terms of general vector dominance, of which statistical dominance is only a particular case.
Eigenvalues of the Laplacian for rectilinear regions
Authors: Gottlieb H. P. W. 
Published: February 2009

AbstractFrom a knowledge of the eigenvalue spectrum of the Laplacian on a domain, one may extract information on the geometry and boundary conditions by analysing the asymptotic expansion of a spectral function. Explicit calculations are performed for isosceles right-angle triangles with Dirichlet or Neumann boundary conditions, yielding in particular the corner angle terms. In three dimensions, right prisms are dealt with, including the solid vertex terms.
Stable continuous orthonormalisation techniques for linear boundary value problems
Authors: van Loon P. M. , Mattheij R. M. M. 
Published: February 2009

AbstractAn investigation is made of a hybrid method inspired by Riccati transformations and marching algorithms employing (parts of) orthogonal matrices, both being decoupling algorithms. It is shown that this so-called continuous orthonormalisation is stable and practical as well. Nevertheless, if the problem is stiff and many output points are required the method does not give much gain over, say, multiple shooting.
Necessary conditions for a mathematical programming problem with set and cone constraints
Authors: Nagahisa Youji 
Published: February 2009

AbstractThis paper is devoted to the derivation of a necessary condition of F. John type which must be satisfied by a solution of a mathematical programming problem with set and cone constraints. The necessary condition is applied to an optimisation problem defined on functional spaces with inequality state constraints. Furthermore a pseudo open mapping theorem is developed in the course of proving the main theorem.
On algorithms for generalised smoothing splines
Authors: Osborne M. R. , Prvan Tania 
Published: February 2009

AbstractRecently, considerable interest has been shown in the connection between smoothing splines and a particular class of stochastic processes. Here the connection with an equivalent class of least squares problems is used to develop algorithms, and properties of the solution are examined. We give an estimate of the condition number of the solution process and compare this with an estimate for the condition number of the Reinsch algorithm in its conventional implementation.
Potential of several arbitrarily located disks
Authors: Fabrikant V. I. 
Published: February 2009

AbstractThe electrostatic field of a set of arbitrarily located circular disks is considered. A set of governing integral equations is derived by a new method. It is shown that some integral characteristics can be found without solving the integral equations. The upper and lower bounds for the total charge are found from a set of linear algebraic equations whose coefficients are defined by simple geometric characteristics of the system. Examples considered show sufficient sharpness of the estimations.
Mean flow induced by the viscous critical layer in a stratified fluid
Authors: Smyth Noel 
Published: February 2009

AbstractThe evolution of the critical layer in a viscous, stratified fluid is examined in the limit of large Richardson and Reynolds numbers. A source far above the critical layer and of amplitude ɛ is turned on at t = 0 and the behaviour of both the steady state and transients is found. Viscosity dominates over nonlinearity in the critical layer for , Re being an appropriately defined Reynolds number. Wave amplitudes are found to grow as the critical layer is approached, then decay rapidly due to the action of viscosity in a critical layer of O((Re)−1/3) around the critical level. The critical layer acts as a source of vorticity, which diffuses into the outer flow, resulting in an induced mean flow of . This induced mean flow causes the critical level to move towards the incoming wave.