bluuebunny/crossref_metadata_2025_split huggingface dataset:
Spherical curves and quadratic relationships for special functions
Authors: Mehlum Even , Wimp Jet 
Published: February 2009

AbstractWe show that the position vector of any 3-space curve lying on a sphere satisfies a third-order linear (vector) differential equation whose coefficients involve a single arbitrary function A(s). By making various identifications of A(s), we are led to nonlinear identities for a number of higher transcendental functions: Bessel functions, Horn functions, generalized hypergeometric functions, etc. These can be considered natural geometrical generalizations of sin2t + cos2t = 1. We conclude with some applications to the theory of splines.
Splitting least squares and collocation procedures for two-point boundary value problems
Authors: Locker John , Prenter P. M. 
Published: February 2009

AbstractLet L, T, S, and R be closed densely defined linear operators from a Hubert space X into X where L can be factored as L = TS + R. The equation Lu = f is equivalent to the linear system Tv + Ru = f and Su = v. If Lu = f is a two-point boundary value problem, numerical solution of the split system admits cruder approximations than the unsplit equations. This paper develops the theory of such splittings together with the theory of the Methods of Least Squares and of Collocation for the split system. Error estimates in both L2 and L∞ norms are obtained for both methods.
Critical point behaviour of the diffusion length for radiative transfer
Authors: Grant I. F. , McKellar B. H. J. 
Published: February 2009

AbstractCritical point behaviour of the diffusion length γ for the solutions of the radiative transfer equation deep in a homogenous medium is studied. The Legendre expansion of the medium's phase function P(cos ψ) is taken to be an infinite series and is characterized by the parameters h0, h1h2,…. A characteristic equation for γ is given in terms of an infinite continued fraction. From this equation it is shown that as any one of the hn, say hp, approaches zero, the others being held constant, γ behaves as , where the critical exponent is found to be vp = ½ for all p = 0, 1, 2,….
Asymptotic location of nodal lines using geodesic theory
Authors: Mahony J. J. , Norbury J. 
Published: February 2009

AbstractThe asymptotic properties of solutions of the non-linear eigenvalue problem, associated with the homogeneoud Dirichlet problem forare investigated. Here f and g are smooth functions of position in a finite plane region with a smooth boundary. The results for the positive solution are well established, but knowledge of other branches of solutions is scarce. Here positive solutions are pieced together across lines partitioning the domain, and variational arguments are framed, as an effective means of locating the lines, so that the composite function is everywhere a solution of *. Heuristic arguments suggest strongly that there is a close relationship between the nodal lines of * and certain classes of weighted geodesic lines defined by the classical variational problem for the functionalwhich provides an effective basis for computation. Some results are proved but others remain conjectures. Analogous results are proved for the associated ordinary differential equation. The geometry of the solutions is surprisingly restricted when the coefficients are spatially variable. The arguments are extended to a class of reactive, diffusive systems. It is possible to predict the pattern of domains of different outcomes in terms of properties of the surface on which the reactions occur, without a knowledge of the chemical kinetics. The results appear to provide a basis for stringent testing of the postulated role of reactive-diffusive mechanisms in the formation of complex patterns in biological species.
Exact edge wave solutions for some generalised exponential shelf topographies
Authors: Louis J. P. , Clarke D. J. 
Published: February 2009

AbstractExact wave-height solutions are presented for trapped waves over two new three-parameter depth topographies. Dispersive properties are calculated for both a semi-infinite and a truncated convex exponential profile, as well as for a semi-infinite concave profile. The analysis in all three cases is general in that both horizontal divergence and rotational effects are included. These solutions may be used for either high-frequency edge wave or low-frequency shelf wave studies by taking appropriate limits (f → 0 for edge wave and ε = f2L2/gH ≪ 1 for shelf waves).
Optimal control in liver kinetics
Authors: Fink A. M. 
Published: February 2009

AbstractWe solve a minimization problem in liver kinetics posed by Bass, et al., in this journal, (1984), pages 538–562. The problem is to choose the density functions for the location of two enzymes, in order to minimize the concentration of an intermediate form of a substance at the outlet of the liver. This form may be toxic to the rest of the body, but the second enzyme renders it harmless. It seems natural that the second enzyme should be downstream from the first. However, we can show that the minimum problem is sometimes solved by an overlap of the supports of the two density functions. Even more surprising is that, for certain forms of the kinetic functions and high levels of transformation of the first enzymatic reaction, some of the first enzyme should be located downstream from all the second enzyme. This suggests that the first reaction should be relatively slow.
Existence and regularity results for Maxwell's equations in the quasi-static limit
Authors: Carey A. L. , O'Brien D. M. 
Published: February 2009

AbstractWe prove the existence of solutions of Maxwell's equations for a conducting medium whose constitutive parameters are piecewise constant on R3, and then examine the convergence of these solutions in the quasi-static limit in which displacement currents are neglected. Secondly, we examine the regularity of the limiting solution and the sense in which the classical boundary conditions hold, namely, continuity of the tangential electric field and the normal current density.
Ship bows with contiunous and splashless flow attachment
Authors: Madurasinghe M. A. D. , Tuck E. O. 
Published: February 2009

AbstractIn two-dimensional bow-like flows past a semi-infinite body, one must in general expect a free-surface discontinuity, in the form of a splash or spray jet. However, there is numerical evidence that special body shapes do exist for which this splash is absent. In this study, we first establish conditions on the geometry of the bow in order that it should be splash-free at zero gravity, by solving the mathematical problem exactly. We then obtain solutions for finite non-zero gravity, by solving a non-linear integral equation numerically. A class of splashless body geometries with a downward directed segment at the extreme of the bow, to which the free surface attaches tangentially, is demonstrated in detail.
Boundary value control problems involving the bessel differential operator
Authors: Werner K.-D. 
Published: February 2009

AbstractIn this paper, we consider the hyperbolic partial differential equation wrr = wrr + 1/r wr − ν2 /r2w, where v ≥ 1/2 or ν = 0 is aprameter, with the Dirichlet, Neumann and mixed boundary conditions. The boundary controllability for such problems is investigated. The main resutl is that all “finite energy” intial states can be steered to the zero state in time T, using a control f ∈ L2 (0, T), provided T > 2. Furthermore, necessary conditions for controllability are also presented.
On the dynamic analysis of a Leontief model with fixed capitial
Authors: Woods J. E. 
Published: February 2009

AbstractIn Convex Structures and Economic Theory, Nikaideo analysed, inter alia, a circulating capital Leontief model where final demand could exhibit either proportional or non-proporaitonal growth. This paper extends his analsis to a fixed capital modee. Analogues of Nikaido's results are derived for the closed model and for the open model under blaanced grwoth. However, the results obtained here for the open model with unbalanced growth are weaker than Nikaido's.
Ordinary and partial difference equations
Authors: Potts Renfrey B. 
Published: February 2009

AbstractOrdinary difference equations (OΔE's), mostly of order two and three, are derived for the trigonometric, Jacobian elliptic, and hyperbolic functions. The results are used to derive partial difference equations (PΔE's) for simple solutions of the wave equation and three nonlinear evolutionary partial differential equations.
Oscilations of higher-order neutral equations
Authors: Ladas G. , Sficas Y. G. 
Published: February 2009

AbstractSufficient conditions are given for the occurrence of various types of asymptotic behaviour in the solution of a class of n th order neutral delay differential equations. The conditions are in the form of certain inequalities amongst the constants involved in the definition of the differential equations, and specify either oscillatory behavior, or asymptotic divergence, or solutions which converge to zero.
What is invexity?
Authors: Ben-Israel A. , Mond B. 
Published: February 2009

AbstractRecently it was shown that many results in Mathematical Programming involving convex functions actually hold for a wider class of functions, called invex. Here a simple characterization of invexity is given for both constrained and unconstrained problems. The relationship between invexity and other generalizations of convexity is illustrated. Finally, it is shown that invexity can be substituted for convexity in the saddle point problem and in the Slater constraint qualification.
On stability and stationary points in nonlinear optimization
Authors: Guddat J. , Jongen H. Th. , Rueckmann J. 
Published: February 2009

This paper presents three theorems concerning stability and stationary points of the constrained minimization problem:In summary, we provethat, given the Mangasarian-Fromovitz constraint qualification (MFCQ), the feasible setM[H, G] is a topological manifold with boundary, with specified dimension; (ℬ) a compact feasible setM[H, G] is stable (perturbations ofHandGproduce homeomorphic feasible sets) if and only if MFCQ holds;under a stability condition, two lower level sets offwith a Kuhn-Tucker point between them are homotopically related by attachment of ak-cell (kbeing the stationary index in the sense of Kojima).
Green manure and nitrogenous fertilizer—a two-sector optimal-growth model
Authors: Mustard David 
Published: February 2009

AbstractA continuous-time model of a two-sector trading economy with a finitely-saturating production function and constant population is constructed. To apply it to the farm-economy problem of optimal trading of cereal for chemical nitrogenous fertilizer and of optimal allocation of land for green manure the special assumptions are made of similar technologies in both sectors and of a nitrogen-capital loss proportional to the cereal production. Optimal-control theory is applied to get the pair of controls that maximizes an infinite-horizon integral of utility of consumption. The analysis of the model is shown to reduce to that of the Ramsey-Koopmans one-sector neoclassical model of optimal growth. Calculations of the feedback control and optimal time-paths for the standardized dimensionless model are tabulated for a range of 7 utility functions of constant elasticity of marginal utility of magnitude 1 to 4 and of production functions of degree 2 to 4. Two particular analytic solutions are given. The application of the results both to the farm-economy model and to the Ramsey-Koopmans model is illustrated.
On partly bilateral and partly unilateral generating functions
Authors: Pathan M. A. , Yasmeen  
Published: February 2009

AbstractThe purpose of this work is to begin the development of a theory of generating functions that will not only include the generating functions which are partly bilateral and partly unilateral but also provide a set of expansions, by taking successive partial derivatives with respect to one of the variables of the generating relations. Our starting point is a result of Exton [4] on associated Laguerre polynomials whose application gives certain generating functions of the polynomials of Jacobi and Appell, and functions of n variables of Lauricella.
The long jump record revisited
Authors: de mestre Neville 
Published: February 2009

AbstractA mathematical model is presented in which the long Jump is treated as the motion of a projectile under gravity with slight drag. The first two terms of a perturbation solution are obtained and are shown to be more accurate than earlier approximate analytical solutions. Results from the perturbation analysis are just as accurate as results from various numerical schemes, and require far less computer time.The model is modified to include the observation that a long-jumper's centre of mass is forward of his feet at take-off and behind his feet on landing.The modified model is used to determine the take-off angle for the current world long jump record, resulting in several interesting observations for athletic coaches.
Closed form solution to some mixed boundary value problems for a charged sphere
Authors: Fabrikant V. I. 
Published: February 2009

AbstractA new method is described which allows an exact solution in a closed form to the following non-axisymmetric mixed boundary-value problem for a charged sphere: arbitrary potential values are given at the surface of a spherical segment while an arbitrary charge distribution is prescribed on the rest of the sphere. The method is founded on a new integral representation of the kernel of the governing integral equation. Several examples are considered. All the results are expressed in elementary functions. Some further applications of the method are discussed. No similar result seems to have been published previously.
A heuristic method for the determination of a Hamiltonian circuit in a graph
Authors: Karmakar Sudhangshu B. 
Published: February 2009

AbstractA heuristic methodology for the identification of a circuit passing through all the vertices only once in a graph is presented. The procedure is based upon defining a normal form of a matrix and then transforming the adjacency matrix into its normal form. For a class of graphs known to be Hamiltonian, it is conjectured that this methodology will identify circuits in a small number of steps and in many cases merely by observation.
Necessary and sufficient condition for oscillations of neutral differential equations
Authors: Kulenović M. R. S. , Ladas G. , Meimaridou A. 
Published: February 2009

AbstractConsider the neutral delay differential equationwhere p ∈ R, τ ≥ 0, q1 > 0, σ1 ≥ 0, for i = 1, 2, …, k. We prove the following result.Theorem. A necessary and sufficient condition for the oscillation of all solutions of Eq. (1) is that the characteristic equationhas no real roots.
A computational method for free time optimal control problems, with application to maximizing the range of an aircraft-like projectile
Authors: Teo K. L. , Jepps G. , Moore E. J. , Hayes S. 
Published: February 2009

AbstractA class of non-standard optimal control problems is considered. The non-standard feature of these optimal control problems is that they are of neither fixed final time nor of fixed final state. A method of solution is devised which employs a computational algorithm based on control parametrization techniques. The method is applied to the problem of maximizing the range of an aircraft-like gliding projectile with angle of attack control.
On the analysis of joint production
Authors: Woods J. E. 
Published: February 2009

AbstractIt is well known that n-process, n-commodity (or square), models of productive single-product industries have positive solutions to their price and quantity systems if the rates of profit and growth lie in appropriate non-negative intervals. On the other hand, negative prices and quantities can occur in formal solutions of models of square, productive, multiple-product industries even when the rates of profit and growth are less than their respective maximum positive values. It is shown in this paper that these differences can be attributed to the presence in joint production of dominance, in either row or column versions. Results on positive solutions to the price (respectively, quantity) system are derived in terms of the absence of column (respectively, row) dominance of the net output matrix. As the concepts of row and column dominance are defined in terms of linear inequalities, the basic mathematical results to be applied are theorems of the alternative.
Eigenvalues of the Laplacian for the third boundary value problem
Authors: Zayed E. M. E. 
Published: February 2009

AbstractThe spectral function , where are the eigenvalues of the two-dimensional Laplacian, is studied for a variety of domains. The dependence of θ(t) on the connectivity of a domain and the impedance boundary conditions is analysed. Particular attention is given to a doubly-connected region together with the impedance boundary conditions on its boundaries.
Properties of short-crested waves in water of finite depth
Authors: Marchant T. R. , Roberts A. J. 
Published: February 2009

AbstractShort-crested waves are defined as propagating surface gravity waves which are doubly-periodic in the horizontal plane. Linearly, the short-crested wave system we consider occurs when two progressive wavetrains of equal amplitude and frequency are propagating at an angle to each other.Solutions are calculated via a computer-generated perturbation expansion in wave steepness. Harmonic resonance affects the solutions but Padé approximants can be used to estimate wave properties such as maximum wave steepness, frequency, kinetic energy and potential energy.The force exerted by waves being reflected by a seawall is also calculated. Our results for the maximum depth-integrated onshore wave force in the standing wave limit are compared with experiment. The maximum force exerted on a seawail occurs for a steep wave in shallow water incident at an oblique angle. Results are given for this maximum force.
Reflection from a water waves from a vertical vortex sheet in water of finite depth
Authors: McKee W. D. , Tesoriero F. 
Published: February 2009

AbstractThe reflection-transmission properties of water waves obliquely incident upon a vortex sheet in water of finite depth are studied. The problem is reduced to that of solving two integral equation. An accurate Galerkin solution is obtained which supports the use of the “variational method” in water wave problems that has recently been questioned by Kirby and Dalyrmple.
Integro-differential equations for the self-organisation of liver zones by competitive exclusion of cell-types
Authors: Bass L. , Bracken A. J. , Holmåker K. , Jefferies B. R. F. 
Published: February 2009

AbstractA model is developed for the seif-organisation of zones of enzymatic activity along a liver capillary (hepatic sinusoid) lined with cells of two types, which contain different enzymes and compete for sites on the wall of the sinusoid. An effectively non-local interaction between the cells arises from local consumption of oxygen from blood flowing throug1 the sinusoid, which gives rise to gradients of oxygen concentration in turn influencing rates of division and of death of the two cell-types. The process is modelled by a pair of coupled non-linear integro-differential equations for the cell-densities as functions of time and position along the sinusoid. Existence of a unique, bounded, non-negative solution of the equations is proved, for prescribed initial values. The equations admit infinitely many stationary solutions, but it is shown that all except one are unstable, for any given set of the model parameters. The remaining solution is shown to be asymptotically stable against a large class of perturbations. For certain ranges of the model parameters, the asymptotically stable stationaxy solution has a zonal structure, with cells of one type located entirely upstream of cells of the other type, and with jump discontinuities in the cell densities at a certain distance along the sinusoid. Such sinusoidal zones can account for zones of enzymatic activity observed in the intact liver. Exceptional cases are found for singular choices of model parameters, such that stationary cell-densities cannot be asymptotically stable individually, but together form an asymptotically stable set. Certain mathematical questions are left open, notably the behaviour of large deviations from stationary solutions, and the global stability of such solutions. Possible generalisations of the model are described.
A spot welding reliability problem
Authors: Rumsewicz M. , Taylor P. 
Published: February 2009

AbstractWhen multiple operators are connected to a single power source which is not large enough to simultaneously supply all users, interference can take place. This paper considers two models of a spot welding station which differ in the method of resolving interference between users. In the first model the system is allowed to become overloaded and the consequent deterioration in weld quality is accepted. In the second model any request which will overload the system is rejected. Expressions are found for (a) the proportion of poor quality welds in the first model and (b) the probability of operators being rejected in the second model. Numerical results are given which indicate how small the power supply can be made for a typical welding shop while keeping interference at a minimal level.
Impaired flow multi-index transportation problem with axial constraints
Authors: Bandopadhyaya Lakshmisree , Puri M. C. 
Published: February 2009

AbstractThis paper studies the impairing of flows in multi-index transportation problem with axial constraints. For any curtailed flow, the problem is shown to be equivalent to a standard axial sum problem, whose solution can be obtained by known methods. The equivalence is established only for specially defined solutions (referred to as M-feasible solutions) of the standard problem. It is also proved that an optimal solution of the impaired flow problem corresponds to such an M-feasible solution.
Interction of a short-wave field with a dominant long wave in deep water: derivation form Zakharov's spectral formulation
Authors: Craik A. D. D. 
Published: February 2009

AbstractThe leading-order interaction of short gravity waves with a dominant long-wave swell is calculated by means of Zakharov's [7] spectral formulation. Results are obtained both for a discrete train of short waves and for a localised wave packet comprising a spectrum of short waves.The results for a discrete wavetrain agree with previous work of Longuet-Higgins & Stewart [5], and general agreement is found with parallel work of Grimshaw [4] which employed a very different wave-action approach.
Some remarks on a quasi-steady-state approximation of the Navier-Stokes equation
Authors: Cannon John R. , Knightly George H. 
Published: February 2009

AbstractA quasi-steady-state apprcncimation to the Navier-Stokes equation is the corresponding equation with nonhomogeneous forcing term f(x, t), but with the term Vt deleted. For solutions that are zero on the boundary, the difference z between the solution of the Navier-Stokes equation and the solution of this quasi-steady-state approximation is estimated in the L2 norm ║z║ with respect to the spatial variables. For sufficiently large viscosity or sufficiently small body force f, the inequalityholds for 0 < t ≤ T and certain real numbres C, β > 0.
Waves below first cutoff in a duct
Authors: Davidson Rodney F. 
Published: February 2009

AbstractThe two-dimensional Helmholtz equation is studied for an infinite region with two semi-infinite plates extending to infinity in opposite directions and a finite duct in the overlapping region. The solution technique leads to coupled Wiener-Hopf equations, and subsequently to an infinite set of simultaneous linear equations. As an example, an asymptotic expansion is calculated and graphed for the case when the duct length divided by duct width is large enough to ensure damping of all but the zero mode wave in the duct.