bluuebunny/crossref_metadata_2025_split huggingface dataset:
Efficient multiple-term approximations for the generalised elliptic-type integrals
Authors: El-Gabali M. 
Published: February 2009

AbstractThe generalised elliptic-type integral Rμ(k, α, γ)where 0 ≤ k < 1, Re(γ) > Re(α) > 0, Re(μ) ≥ −0.5, is represented in terms of the Gauss hypergeometric function by Kalla, Conde and Hubbell [8]. In 1987, Kalla, Lubner and Hubbell derived a simple-structured single-term approximation for this function in the neighbourhood of k2 = 1 in some range of the parameters α, γ and μ. Another formula which complements the parameter range was recently derived by the author. In this paper a novel technique is used in deriving multiple-term efficient approximations (in the neighbourhood of k2 = 1) which may be considered as a generalisation to the concept of the single-term approximations mentioned above. Two non-overlapping expressions which almost cover the entire range of parameters (α, γ, μ) are derived. Closed-form solutions are obtained for single- and double-term approximations (in the neighbourhood of k2 = 1). Results show that the proposed technique is superior to existing approximations for the same number of terms. Our formulation has potential application for a wide class of special functions.
The allometric hypothesis when the size variable is uncertain: issues in the study of carcass composition by serial slaughter
Authors: Pleasants A. B. , Wake G. C. , Rae A. L. 
Published: February 2009

AbstractThe allometric hypothesis which relates the shape (y) of biological organs to the size of the plant or animal (x), as a function of the relative growth rates, is ubiquitous in biology. This concept has been especially useful in studies of carcass composition of farm animals, and is the basis for the definition of maintenance requirements in animal nutrition.When the size variable is random the differential equation describing the relative growth rates of organs becomes a stochastic differential equation, with a solution different from that of the deterministic equation normally used to describe allometry. This is important in studies of carcass composition where animals are slaughtered in different sizes and ages, introducing variance between animals into the size variable.This paper derives an equation that relates values of the shape variable to the expected values of the size variable at any point. This is the most easily interpreted relationship in many applications of the allometric hypothesis such as the study of the development of carcass composition in domestic animals by serial slaughter. The change in the estimates of the coefficients of the allometric equation found through the usual deterministc equation is demonstrated under additive and multiplicative errors. The inclusion of a factor based on the reciprocal of the size variable to the usual log - log regression equation is shown to produce unbiased estimates of the parameters when the errors can be assumed to be multiplicative.The consequences of stochastic size variables in the study of carcass composition are discussed.
An integrable fourth-order nonlinear evolution equation applied to surface redistribution due to capillarity
Authors: Tritscher Peter 
Published: February 2009

AbstractMembers of an hierarchy of integrable nonlinear evolution equations, related to the well-known linearizable diffusion equation which has the diffusivity form as the reciprocal of the square of the concentration, are adapted to derive a new integrable nonlinear equation which models the surface evolution of an arbitrarily-oriented theoretical anisotropic material by the concomitant action of evaporation-condensation and surface diffusion. The constitutive relations are explicitly formulated and these show that the theoretical anisotropic material behaves like a liquid crystal. The integrable nonlinear equation may be used to advantage as test cases for numerical schemes. Its form has many attributes of the nonlinear governing equation for an isotropic material. Closed-form solutions are constructed for the evolution of a ramped surface by concomitant evaporation-condensation and surface diffusion.
Internal solitary waves with stratification in density
Authors: Sha Huyun , Vanden-Broeck J.-M. 
Published: February 2009

AbstractLong periodic waves propagating in a closed channel are considered. The fluid consists of two layers of constant densities separated by a layer in which the density varies continuously. The numerical results of Vanden-Broeck and Turner [8] are extended. It is shown that their solutions are particular members of a family of solutions. Solutions are selected by requiring that the streamfunction takes values on the upper and lower walls which are consistent with a uniform stream far upstream. The new solutions are qualitatively similar to those of Vanden-Broeck and Turner [8]. In particular, there are periodic waves characterized by a train of ripples at their troughs. It is shown numerically that these waves approach solitary waves with oscillatory tails as their wavelength increases. Moreover special solutions for which the amplitude of the ripples is almost zero are identified. Such solutions without ripples were previously found for solitary waves with surface tension.
Some high-order zero-finding methods using almost orthogonal polynomials
Authors: Brent Richard P. 
Published: February 2009

AbstractSome multipoint iterative methods without memory, for approximating simple zeros of functions of one variable, are described. For m > 0, n ≧ 0, and k satisfying m + 1 ≧ k > 0, there exist methods which, for each iteration, use one evaluation of f, f′, … f(m) followed by n evaluations of f(k), and have order of convergence m + 2n + 1. In particular, there are methods of order 2(n + 1) which use one function evaluation and n + 1 derivative evaluations per iteration. These methods naturally generalize the known cases n = 0 (Newton's method) and n = 1 (Jarratt's fourth-order method), and are useful if derivative evaluations are less expensive than function evaluations. To establish the order of convergence of the methods we prove some results, which may be of independent interest, on orthogonal and “almost orthogonal” polynomials. Explicit, nonlinear, Runge-Kutta methods for the solution of a special class of ordinary differential equations may be derived from the methods for finding zeros of functions. The theoretical results are illustrated by several numerical examples.
On air flow over free surfaces of stationary water
Authors: Tuck E. O. 
Published: February 2009

AbstractA correspondence is established between flows of air above stationary water, and flows of water below air at atmospheric pressure. Flows in the latter category are well studied, and all such hydrodynamic flows can be “turned upside-down” to generate flows of air in which the free surface deforms under gravity, due to a balance between aerodynamic and hydrostatic pressures. Examples are given of some exact inverse solutions, and a general semi-inverse approach is outlined for numerical solutions via an integral formulation.
Analytic solution of the linearized shallow-water wave equations for certain continuous depth variations
Authors: Clements D. L. , Rogers C. 
Published: February 2009

AbstractThe linear long-wave equations with (and without) small ground motion are considered. The governing equations are represented in a matrix from and transformations are sought which reduce the system to (for example) a form associated with the conventional wave equation. Integration of the system is then immediate. It is shown that such a reduction may be acheived provided the variation in water depth is specified by certain multi-parameter forms.
Spectral resolution of the identity for matrices of elements of a lie algebra
Authors: Green H. S. 
Published: February 2009

AbstractThis is an application of the characteristic identity satisfied by matrices whose elements are also elements of a semi-simple Lie algebra. Generalized eigenvectors are determined for matrices consisting of generators of GL(n), O(n) and Sp(n), and it is shown how to resolve the identity into idempotents constructed from such eigenvectors. By this means rather general functions of the matrices may be defined. It is also shown how to determine traces of such functions, in terms of the invariants of the Lie algebra.
Fast local convergence with single and multistep methods for nonlinear equations
Authors: Abbott James P. , Brent Richard P. 
Published: February 2009

AbstractMethods which make use of the differential equation ẋ(t) = −J(x)−1f(x), where J(x) is the Jacobian of f(x), have recently been proposed for solving the system of nonlinear equations f(x) = 0. These methods are important because of their improved convergence characteristics. Under general conditions the solution trajectory of the differential equation converges to a root of f and the problem becomes one of solving a differential equation. In this paper we note that the special form of the differential equation can be used to derive single and multistep methods which give improved rates of local convergence to a root.
Concentric circular misfit and a circular arc crack in an infinite isotropic elastic plate
Authors: Bhargava R. D. , Narayan Ram 
Published: February 2009

AbstractA homogeneous isotropic infinite elastic plate contains a circular cavity and a circular arc crack symmetrically situated about thex-axis. The cavity and crack are concentric but are of different radii. A circular inhomogeneity of radius slightly larger than that of the cavity is inserted into the cavity; thus generating a system of stresses in the outer material as well as in the inhomogeneity. The elastic field in the inhomogeneity and in the outer material outside the inhomogeneity is evaluated in this paper.
Contact problem of an elastic plug in an elastic region
Authors: Steven G. P. 
Published: February 2009

AbstractThe contact problem investigated in this paper may be more fully described as a three dimensional elastic body with a circular hole through it; inside this tunnel is press fitted a solid elastic plug of finite length. Shear stresses are taken to be absent along the contact interface.An influence coefficient technique is used to model the governing integral equation. For the elastic region the displacement influence coefficients due to bands of constant pressure are determined using a numerical quadrature on Fourier integrals. However, the plug, being of finite length, requires the superposition of two separate solutions to boundary value problems before the displacement influence coefficients can be determined.Contact pressure distributions are presented for a sample of parameter variations and also for a case where hydrostatic pressure is present in the tunnel in the elastic region. Despite both components being elastic the imposition of a constant interference displacement along the interface still gives rise to the characteristic singularity in contact pressure at the edges of contact due to the strain discontinuity at these points.
A transformation of Cooke's treatment of some triple integral equations
Authors: Love E. R. , Clements D. L. 
Published: February 2009

AbstractThe reduction of an important class of triple integral equations to a pair of simultaneous Fredholm equations has been carried out by Cooke [1]. In this paper, Cooke's equations are transformed to new uncoupled Fredholm equations which, for certain important cases, are shown to be simpler than Cooke's and also superior for the purposes of solution by iteration.
A programming problem with anLpnorm in the objective function
Authors: Mond Bertram , Schechter Murray 
Published: February 2009

AbstractWe consider a programming problem in which the objective function is the sum of a differentiable function and thepnorm ofSx, whereSis a matrix andp> 1. The constraints are inequality constraints defined by differentiable functions. With the aid of a recent transposition theorem of Schechter we get a duality theorem and also a converse duality theorem for this problem. This result generalizes a result of Mond in which the objective function contains the square root of a positive semi-definite quadratic function.
Nonlinear least squares — the Levenberg algorithm revisited
Authors: Osborne M. R. 
Published: February 2009

AbstractOne of the most succesful algorithims for nonlinear least squares calculations is that associated with the names of Levenberg, Marquardt, and Morrison. This algorithim gives a method which depends nonlinearly on a parameter γ for computing the correction to the current point. In this paper an attempt is made to give a rule for choosing γ which (a) permits a satisfactory convergence theorem to be proved, and (b) is capable of satisfactory computer implementation. It is beleieved that the stated aims have been met with reasonable success. The convergence theorem is both simple and global in character, and a computer code is given which appears to be at least competitive with existing alternatives.
On the stability of differential-difference equations
Authors: Braddock R. D. , Van Den Driessche P. 
Published: February 2009

AbstractThe local properties of non-linear differential-difference equations are investigated by considering the location of the roots of the eigen-equation derived from the lineraised approximation of the original model. A general linear system incorporating one time delay is considered and local stability results are obtained for cases in which the coefficient matrices satisfy certain assumptions. The results have applications to recent Biological and Economic models incorporating time lags.
Effect of static magnetic field on the helical flow of incompressible cholesteric liquid crystal between two coxial circular cylinders having rotational and axial velocities
Authors: Paria G. , Sharma A. K. 
Published: February 2009

AbstractThe paper investigates the effect of a static magnetic field on the helical flow of an incompressible cholestenc liquid crystal with director of unit magnitude between two coaxial circular cylinders rotating with different angular velocities about their common axis and moving with different axial velocities. At low shear rates with a weak magnetic field in the axial direction, the axial velocity, the angular velocity and the orientation of molecules between the two cylinders have been obtained. It is found that the magnetic field has influenced the orientation of molecules while the axial velocity and the angular velocity remain uneffected by the magnetic field.
Properties of propagation of quantum spin systems
Authors: Robinson Derek W. 
Published: February 2009

AbstractUsing an estimate on the group velocity we give an independent proof of the existence of time translations for a large class of short range interactions. We demonstrate that these systems satisfy a strong form of causal propagation and that space-time algebras in suitable space-like directions are disjoint. Finally we derive criteria for dispersion of the interaction in terms of the algebraic density of the orbit of local subalgebras under the evolution or under the associated group of shifts. In this sense the Heisenberg and X-Y models are dispersive but the Ising model is not.
Convergence of degenerate-kernel methods
Authors: Sloan Ian H. 
Published: February 2009

AbstractAdditional convergence results are given for the approximate solution in the space L2(a, b) of Fredholm integral equations of the second kind, y = f + Ky, by the degenerate-kernel methods of Sloan, Burn and Datyner. Convergence to the exact solution is provided for a class of these methods (including ‘method 2’), under suitable conditions on the kernel K, and error bounds are obtained. In every case the convergence is faster than that of the best approximate solution of the form yn = Σnan1u1, where u1, …, un are the appropriate functions used in the rank-n degenerate-kernel approximation. In addition, the error for method 2 is shown to be relatively unaffected if the integral equation has an eigenvalue near 1.
Similarity solutions of the steady state cosmic-ray equation of transport
Authors: Webb G. M. 
Published: February 2009

AbstractSimilarity solutions of the steady-state equation of transport for the distribution functionF0of cosmic rays in the interplanetary region are obtained by theuse of transformation groups. The solutions are derived in detail for a spherically-symmetric model of the interplanetary region with an effective radial diffusion coefficient κ = κ0(p)rbwithrthe heliocentric radial distance.pthe particle momentum, κ0(p) an arbitary function ofp, and the solar wind velocity is radial and of constant speed V. Solutions for which the similarity variable η is a function ofronly are also derived; these are of particular impoartance when theF0is specified on a boundary of given radius. Non spherically-symmetric solutions can also be obtained by group methods and examples of such solutions are listed, without derivation, for the equation of transport incorporating the effects of anisotropic diffusion (diffusion coefficient κ1in the radial direction and κ2normal to it). The solutions are the most extensive steady-state analytic solutions yet obtained, and contain previous analytic solutions as special cases.
On the asymptotic solution of an elliptic interior layer problem
Authors: Barton N. G. 
Published: February 2009

AbstractAn interior layer problem posed by an elliptic partial differential equation of the type ε∇2φ - x∂φ/∂y = f(x, y, ε), 0 < ε ≪ 1, is investigated. This equation arises, for example, in the theory of rotating fluids and the important feature of the problem is an interior layer of width O(ε1/3) in which the solution has a relatively large magnitude.The paper considers the simplest case which involves an interior layer, that is, where the domain is rectangular and f(x, y, ε) = εA for A constant. A leading approximation is derived and it is shown to be asymptotic to the exact solution in nearly all of the domain as ε → 0. The error estimates are derived using an a priori estimate for the solution of elliptic equations and a technique which optimizes the estimates is introduced. The applicability and limitations of the estimation technique are discussed briefly.
The numerical solution of stochastic differential equations
Authors: Kloeden P. E. , Pearson R. A. 
Published: February 2009

AbstractA method is proposed for the numerical solution of Itô stochastic differential equations by means of a second-order Runge–Kutta iterative scheme rather than the less efficient Euler iterative scheme. It requires the Runge–Kutta iterative scheme to be applied to a different stochastic differential equation obtained by subtraction of a correction term from the given one.
The stability of continental shelf waves I. Side band instability and long wave resonance
Authors: Grimshaw R. 
Published: February 2009

AbstractContinental shelf waves are examined for side band instability. It is shown that a modulated shelf wave is described by a nonlinear Schrödinger equation, from which the stability criterion is derived. Long shelf waves are stable to side band modulations, but as the wavenumber is increased there are regions of instability (in wavenumber space). A change of stability occurs at each long wave resonance, defined by the condition that the group velocity of the shelf wave equals a long wave speed. Equations describing the long wave resonance are derived.
Translations as gauge transformations
Authors: Smrz P. K. 
Published: February 2009

AbstractA local description of space and time in which translations are included in the group of gauge transformations is studied using the formalism of fibre bundles. It is shown that the flat Minkowski space–time may be obtained from a non-flat connection in a de Sitter structured fibre bundle by choosing at least two different cross-sections. The interaction terms in the covariant derivative of a Dirac wave function that correspond to translations may be interpreted as the mass term of the Dirac equation, and then the two cross-sections (gauges) correspond to the description of a fermion and antifermion respectively.
The deformation of rubber cylinders and tubes by rotation
Authors: Chadwick P. , Creasy C. F. M. , Hart V. G. 
Published: February 2009

AbstractA detailed analytical and numerical study is made of the deformation of highly elastic circular cylinders and tubes produced by steady rotation about the axis of symmetry. Explicit results are obtained through the use of Ogden's strain–energy function for incompressible isotropic elastic materials which, as well as being analytically convenient, is capable of reproducing accurately the observed isothermal behaviour of vulcanized rubber over a wide range of deformations. The three problems of steady rotation considered here concern (i) a tube shrink-fitted to a rigid spindle, (ii)an unconstrained tube, and (iii) a solid cylinder. In each case a set of restictions on the material constans appearing in the strain–energy function is stated which ensures that a tubular of cylindrical shape-preserving deformation exists for all angular spees and that, for problems (i) and (iii), there is no other solution. In connection with problems (ii) and (iii) values of the material constans are also given which correspond to the bifuraction or non-existence of soultions. Enegry consideration are used to determine the local stability of the various solutions obtained.
On a direct method for the determination of an exact invariant for the time-dependent harmonic oscillator
Authors: Leach P. G. L. 
Published: February 2009

AbstractAn exact invariant is found for the one-dimensional oscillator with equation of motion . The method used is that of linear canonical transformations with time-dependent coeffcients. This is a new approach to the problem and has the advantage of simplicity. When f(t) and g(t) are zero, the invariant is related to the well-known Lewis invariant. The significance of extension to higher dimension of these results is indicated, in particular for the existence of non-invariance dynamical symmetry groups.
Generalized shear deformations for isotropic incompressible hyperelastic materials
Authors: Hill James M. 
Published: February 2009

AbstractFor isotropic incompressible hyperelastic materials the single function characterizing generalized shear deformations or as they are sometimes called anti-plane strain deformations must satisfy two distinct partial differential equations. Knowles [5] has recently given a necessary and sufficient condition for the strain–energy function of the material which if satisfied ensures that the two equations have consistent solutions. It is shown here for the general material not satisfying Knowles' criterion that the only possible consistent solution of the two partial differential equations are those which are already known to exist for all strain–energy functions. More general types of generalized shear deformations for such meterials are shown to exist only for special or restricted form ot the strain-energy function. In derving these results we also obtain an alternative derivation of Knowles' criterion.
Supercritical flow of an ideal fluid over a spillway
Authors: Collings I. L. , Grimshaw R. 
Published: February 2009

AbstractThe irrotational flow of an incompressible, inviscid fluid over a spiliway is considered. The reciprocal ε of the Froude number is taken to be small and the method of matched asymptotic expansions is applied. The bed of the spillway is horizontal far upstream and makes an angle α with the horizontal far downstream. The inner expansion is valid upstream and over the spillway, but is invalid far downstream. The outer expansion which is valid downstream fails to satisfy the upstream conditions. Unknown constants in the outer expansion are determined by the matching and composite expansions obtained.