bluuebunny/crossref_metadata_2025_split huggingface dataset:
Scoring with constraints
Authors: Osborne Michael R. 
Published: February 2009

AbstractThis paper considers the solution of estimation problems based on the maximum likelihood principle when a fixed number of equality constraints are imposed on the parameters of the problem. Consistency and the asymptotic distribution of the parameter estimates are discussed as n → ∞, where n is the number of independent observations, and it is shown that a suitably scaled limiting multiplier vector is known. It is also shown that when this information is available then the good properties of Fisher's method of scoring for the unconstrained case extend to a class of augmented Lagrangian methods for the constrained case. This point is illustrated by means of an example involving the estimation of a mixture density.
Solution of nonlinear equations and computation of multiple solutions of a simple reaction-diffusion equation
Authors: Swift Adrian , Balakrishnan Easwaran 
Published: February 2009

AbstractThe first part of this paper starts with a brief discussion of some methods for solution of nonlinear equations which have interested the first author over the last twenty years or so. In the second part we discuss a recent research involvement, the success of which relies heavily on the numerical solution of nonlinear equation systems. We briefly describe path-following methods and then present an application to a simple steady-state reaction-diffusion equation arising in combustion theory. Results for some regular geometric shapes are shown and compared with those from an approximate method.
Integral equation methods in inverse obstacle scattering
Authors: Kress Rainer 
Published: February 2009

AbstractIn this survey we consider a regularized Newton method for the approximate solution of the inverse problem to determine the shape of an obstacle from a knowledge of the far field pattern for the scattering of time-harmonic acoustic or electromagnetic plane waves. Our analysis is in two dimensions and the numerical scheme is based on the solution of boundary integral equations by a Nyström method. We include an example of the reconstruction of a planar domain with a corner both to illustrate the feasibility of the use of radial basis functions for the reconstruction of boundary curves with local features and to connect the presentation to some of the research work of Professor David Elliott.
The Lebesgue function for generalized Hermite-Fejér interpolation on the Chebyshev nodes
Authors: Byrne Graeme J. , Mills T. M. , Smith Simon J. 
Published: February 2009

AbstractThis paper presents a short survey of convergence results and properties of the Lebesgue function λm,n(x) for(0, 1, …, m)Hermite-Fejér interpolation based on the zeros of the nth Chebyshev polynomial of the first kind. The limiting behaviour as n → ∞ of the Lebesgue constant Λm,n = max{λm,n(x): −1 ≤ x ≤ 1} for even m is then studied, and new results are obtained for the asymptotic expansion of Λm,n. Finally, graphical evidence is provided of an interesting and unexpected pattern in the distribution of the local maximum values of λm,n(x) if m ≥ 2 is even.
Diagonal scaling of stiffness matrices in the Galerkin boundary element method
Authors: Ainsworth Mark , McLean Bill , Tran Thanh 
Published: February 2009

AbstractA boundary integral equation of the first kind is discretised using Galerkin's method with piecewise-constant trial functions. We show how the condition number of the stiffness matrix depends on the number of degrees of freedom and on the global mesh ratio. We also show that diagonal scaling eliminates the latter dependence. Numerical experiments confirm the theory, and demonstrate that in practical computations involving strong local mesh refinement, diagonal scaling dramatically improves the conditioning of the Galerkin equations.
Uniform convergence of the collocation method for Prandtl's Integro-differential equation
Authors: Capobianco M. R. , Criscuolo G. , Junghanns P. , Luther U. 
Published: February 2009

AbstractAn integro-differential equation of Prandtl's type and a collocation method as well as a collocation-quadrature method for its approximate solution is studied in weighted spaces of continuous functions.
Accelerated spectral refinement Part II: Cluster of eigenvalues
Authors: Alam Rafikul , Kulkarni Rekha P. , Limaye Balmohan V. 
Published: February 2009

AbstractThe framework for accelerated spectral refinement for a simple eigenvalue developed in Part I of this paper is employed to treat the general case of a cluster of eigenvalues whose total algebraic multiplicity is finite. Numerical examples concerning the largest and the second largest multiple eigenvalues of an integral operator are given.
Lattice vibrations with Rayleigh dissipation
Authors: Boyd J. N. , Raychowdhury P. N. 
Published: February 2009

AbstractWe approximate a linear array of coupled harmonic oscillators as a symmetric circular array of identical masses and springs. The springs are taken to possess mass distributed along their lengths. We give a Lagrangian formulation of the problem of finding the natural frequencies of oscillation for the array. Damping terms are included by means of the Rayleigh dissipation function. A transformation to symmetry coordinates as determined by the group of rotations of the circle uncouples the equations of motion.
On the solution of the problem of scattering of surface water waves by a sharp discontinuity in the surface boundary conditions
Authors: Chakrabarti A. 
Published: February 2009

AbstractClosed-form analytical expressions are derived for the reflection and transmission coefficients for the problem of scattering of surface water waves by a sharp discontinuity in the surface-boundary-conditions, for the case of deep water. The method involves the use of the Havelock-type expansion of the velocity potential along with an analysis to solve a Carleman-type singular integral equation over a semi-infinite range. This method of solution is an alternative to the Wiener-Hopf technique used previously.
On the solution of a class of second-order quasi-linear PDEs and the Gauss equation
Authors: Selvaratnam A. R. , Vlieg-Hulstman M. , van-Brunt B. , Halford W. D. 
Published: February 2009

AbstractGauss' Theorema Egregium produces a partial differential equation which relates the Gaussian curvature K to components of the metric tensor and its derivatives. Well-known partial differential equations (PDEs) such as the Schrödinger equation and the sine-Gordon equation can be derived from Gauss' equation for specific choices of K and coördinate systems. In this paper we consider a class of Bäcklund Transformations which corresponds to coördinate transformations on surfaces with a given Gaussian curvature. These Bäcklund Transformations lead to the construction of solutions to certain classes of non-linear second order PDEs of hyperbolic type by identifying these PDEs as the Gauss equation in some coördinate system. The possibility of solving the Cauchy Problem has also been explored for these classes of equations.
Smoothly attaching bow flows with constant vorticity
Authors: McCue S. W. , Forbes L. K. 
Published: February 2009

AbstractThe free surface flow of a finite depth fluid past a semi-infinite body is considered. The fluid is assumed to have constant vorticity throughout and the free surface is assumed to attach smoothly to the front face of the body. Numerical solutions are found using a boundary integral method in the physical plane and it is shown that solutions exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a comer is also considered. Vorticity is included in the flow and it is shown that the behaviour of the solutions is qualitatively the same as that found in the problem described above.
Early quasi-steady electro-magnetic fields about conducting surfaces
Authors: Weir Graham J. 
Published: February 2009

AbstractStep changes in current through either grounded or ungrounded wires lying on the surface of a uniformly conducting half-space produce image current sources within the surface the conductor. This image current is effectively the only source term for initial changes in ∂1Bz, Ex and Ey. The general steady state electric and magnetic field components resulting from steady currents flowing through either grounded or ungrounded wires of finite length lying on the surface of a uniform half- space are derived. Then the operators mapping these steady fields into the early values of ∂tBz, Ex and Ey on or above the conducting half-plane resulting from instantaneously stopping the current flow through the wires are derived.
On monotonicity and superadditivity properties of the entropy function
Authors: Dragomir S. S. , Goh C. J. 
Published: February 2009

AbstractWe apply superadditivity and monotonicity properties associated with the Jensen discrete inequality to derive relationships between the entropy function of a probability vector and a renormalized arbitrary sub-vector. The results are extended to cover other entropy measures such as joint entropy, conditional entropy and mutual information.
Determining rotational deformity in broken forearms
Authors: Stokes Y. M. 
Published: February 2009

AbstractTo assess rotational deformity in a broken forearm, an orthopaedic surgeon needs to determine the amount of rotation of the radius from one or more two-dimensional x-rays of the fracture. This requires only simple first-year university mathematics — rotational transformations of ellipses plus a little differential calculus — which yields a general formula giving the rotation angle from information obtained from an x-ray. Preliminary comparisons with experimental results are excellent. This is a practical problem that may be useful to motivate the teaching of conic sections.
Global attractivity of the periodic Kolmogorov system
Authors: Wen Xianzhang , Wang Zhicheng 
Published: February 2009

AbstractWe study a periodic Kolmogorov model with m predators and n prey. By means of the comparison theorem and a Liapunov function, a set of easily verifiable sufficient conditions that guarantee the existence, uniqueness and global attractivity of the positive periodic solution is obtained. Finally, some suitable applications are given to illustrate that the conditions of the main theorem are feasible.
Examples of the nonexistence of a solution in the presence of upper and lower solutions
Authors: Habets Patrick , Pouso Rodrigo L. 
Published: February 2009

AbstractStandard results for boundary value problems involving second-order ordinary differential equations ensure that the existence of a well-ordered pair of lower and upper solutions together with a Nagumo condition imply existence of a solution. In this note we introduce some examples which show that existence is not guaranteed if no Nagumo condition is satisfied.
A new trust region method for nonsmooth equations
Authors: Yang Y. F. 
Published: February 2009

AbstractWe propose a new trust region algorithm for solving the system of nonsmooth equations F(x) = 0 by using a smooth function satisfying the Jacobian consistency property to approximate the nonsmooth function F(x). Compared with existing trust region methods for systems of nonsmooth equations, the proposed algorithm possesses some nice convergence properties. Global convergence is established and, in particular, locally superlinear or quadratical convergence is obtained if F is semismooth or strongly semismooth at the solution.
Inequalities for the beta function of n variables
Authors: Alzer Horst 
Published: February 2009

AbstractWe present various inequalities for Euler's beta function of n variables. One of our theorems states that the inequalitieshold for all xi ≥ (i = 1,… n; n ≥ 3) with the best possible constants an = 0 and bn = 1 − 1/(n − 1)!. This extends a recently published result of Dragomir et al., who investigated (*) for the special case n = 2.
A flat ship theory on bow and stern flows
Authors: Zhu Songping , Zhang Yinglong 
Published: February 2009

AbstractAn analytical solution of a two-dimensional bow and stern flow model based on a flat ship theory is presented for the first time. The flat ship theory is a counterpart to Michell's thin ship theory and leads to a mixed initial-boundary value problem, which is usually difficult to solve analytically. Starting from the transient problem, we shall first show that a steady state is attainable at the large time limit. Then the steady problem is solved in detail by means of the Wiener-Hopf technique and closed-form far-field results are obtained for an arbitrary hull shape. Apart from providing a better understanding of the underlying physics, the newly found analytical solution has shed some light on solving a longtime outstanding problem in the engineering practice of ship building, the optimisation of hull shape.
Derivation of the probability density function for ultimate muscle pH in slaughtered animals
Authors: Pleasants A. B. , Wake G. C. , Daly C. C. 
Published: February 2009

AbstractWe consider the form of the probability density function for the ultimate muscle pH in slaughtered animals. Muscle pH in slaughtered animals is dependent on a biochemical process which forms lactic acid from the breakdown of glycogen stored in the muscle at slaughter. The relationship between glycogen and muscle pH after slaughter is expressed as a pair of coupled differential equations. The solution of this system for the equilibrium muscle pH as time → ∞ gives the form of the probability density for the ultimate muscle pH. When the initial density for the muscle glycogen is normal, the density for the ultimate muscle pH is shown to be approximately a mixed normal density.
Numerical algorithms for constrained maximum likelihood estimation
Authors: Li Z. F. , Osborne M. R. , Prvan T. 
Published: February 2009

AbstractThis paper describes a SQP-type algorithm for solving a constrained maximum likelihood estimation problem that incorporates a number of novel features. We call it MLESOL. MLESOL maintains the use of an estimate of the Fisher information matrix to the Hessian of the negative log-likelihood but also encompasses a secant approximation S to the second-order part of the augmented Lagrangian function along with tests for when to use this information. The local quadratic model used has a form something like that of Tapia's SQP augmented scale BFGS secant method but explores the additional structure of the objective function. The step choice algorithm is based on minimising a local quadratic model subject to the linearised constraints and an elliptical trust region centred at the current approximate minimiser. This is accomplished using the Byrd and Omojokun trust region approach, together with a special module for assessing the quality of the step thus computed. The numerical performance of MLESOL is studied by means of an example involving the estimation of a mixture density.
Existence of optimal controls for semilinear elliptic equations without Cesari-type conditions
Authors: Lou Hongwei 
Published: February 2009

AbstractOptimal control problems governed by semilinear elliptic partial differential equations are considered. No Cesari-type conditions are assumed. By proving an existence theorem and the Pontryagin maximum principle of optimal “state-control” pairs for the corresponding relaxed problems, we establish an existence theorem of optimal pairs for the original problem.
A two-sided iterative method for computing positive definite solutions of a nonlinear matrix equation
Authors: El-Sayed Salah M. 
Published: February 2009

AbstractIn several recent papers, a one-sided iterative process for computing positive definite solutions of the nonlinear matrix equationX+A*X−1A=Q, whereQis positive definite, has been studied. In this paper, a two-sided iterative process for the same equation is investigated. The novel idea here is that the two sequences obtained by starting at two different values provide (a) an interval in which the solution is located, that is,Xk≤X≤Ykfor allkand (b) a better stopping criterion. Some properties of solutions are discussed. Sufficient solvability conditions on a matrixAare derived. Moreover, when the matrixAis normal and satisfies an additional condition, the matrix equation has smallest and largest positive definite solutions. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm.
The solution and the stability of a nonlinear age-structured population model
Authors: Norhayati  , Wake G. C. 
Published: February 2009

AbstractWe consider an age-structured population model achieved by modifying the classical Sharpe-Lotka-McKendrick model, incorporating an overcrowding effect or competition for resources term. This term depends on the whole population rather than on any specific age group, in the case of overcrowding or limitation of resources. We investigate the solutions for arbitrary initial conditions. We consider the existence of a steady age distribution and its stability and are able to determine this for a simple illustrative case. If the non-trivial steady age distribution is unstable, there is a critical initial population size beyond which the population explodes. This watershed is independent of the shape of the initial age distribution.
On the influence of wall properties in the peristaltic motion of micropolar fluid
Authors: Muthu P. , Rathish Kumar B. V. , Chandra Peeyush 
Published: February 2009

AbstractWe carry out a study of the peristaltic motion of an incompressible micropolar fluid in a two-dimensional channel. The effects of viscoelastic wall properties and micropolar fluid parameters on the flow are investigated using the equations of the fluid as well as of the deformable boundaries. A perturbation technique is used to determine flow characteristics. The velocity profile is presented and discussed briefly. We find the critical values of the parameters involving wall characteristics, which cause mean flow reversal.
A unified presentation of generalised Voigt functions
Authors: Kamarujjama M. 
Published: February 2009

AbstractVoigt functions occur frequently in a wide variety of problems in several diverse fields of physics. This paper presents a unified study of generalised Voigt functions. In particular, some expansions of unified Voigt functions are given in terms of the original functions. Some deductions from these representations are obtained which give us an opportunity to underline the special rôle of the associated generating functions.
Decomposition method for solving a nonlinear business cycle model
Authors: Deeba Elias , Dibeh Ghassan , Khuri Suheil , Xie Shishen 
Published: February 2009

AbstractIn this paper we present a Kaleckian-type model of a business cycle based on a nonlinear delay differential equation. A numerical algorithm based on a decomposition scheme is implemented for the approximate solution of the model. The numerical results of the underlying equation show that the business cycle is stable.
Some remarks on a Neumann boundary value problem arising in fluid dynamics
Authors: Torres Pedro J. 
Published: February 2009

AbstractIt is proved that the Neumann boundary value problem, which Mays and Norbury have recently connected with a certain fluid dynamics equation, has a positive solution for any positive value of a particular parameter. Uniform bounds for the solutions and symmetry on a given range of the parameter are also introduced. The proofs include Krasnoselskii's classical fixed-point theorem on cones of a Banach space and basic comparison techniques.
Rumours with general initial conditions
Authors: Belen Selma , Pearce C. E. M. 
Published: February 2009

AbstractAn analysis is made of the Daley-Kendall and Maki-Thompson rumour models starting from general initial proportions of ignorants, spreaders and stiflers in the population. We investigate as a function of the initial conditions the composition of the final population when the rumour has run its course.
Harvesting in a two-prey one-predator fishery: a bioeconomic model
Authors: Kar T. K. , Chaudhuri K. S. 
Published: February 2009

AbstractA multispecies harvesting model with interference is proposed. The model is based on Lotka-Volterra dynamics with two competing species which are affected not only by harvesting but also by the presence of a predator, the third species. In order to understand the dynamics of this complicated system, we choose to model the simplest possible predator response function in which the feeding rate of the predator increases linearly with prey density. We derive the conditions for global stability of the system using a Lyapunov function. The possibility of existence of a bioeconomic equilibrium is discussed. The optimal harvest policy is studied and the solution is derived in the equilibrium case using Pontryagin's maximal principle. Finally, some numerical examples are discussed.
Performance of various BFGS implementations with limited precision second-order information
Authors: Byatt D. , Coope I. D. , Price C. J. 
Published: February 2009

AbstractThe BFGS formula is arguably the most well known and widely used update method for quasi-Newton algorithms. Some authors have claimed that updating approximate Hessian information via the BFGS formula with a Cholesky factorisation offers greater numerical stability than the more straightforward approach of performing the update directly. Other authors have claimed that no such advantage exists and that any such improvement is probably due to early implementations of the DFP formula in conjunction with low accuracy line searches.This paper supports the claim that there is no discernible advantage in choosing factorised implementations (over non-factorised implementations) of BFGS methods when approximate Hessian information is available to full machine precision. However the results presented in this paper show that a factorisation strategy has clear advantages when approximate Hessian information is available only to limited precision. These results show that a conjugate directions factorisation outperforms the other methods considered in this paper (including Cholesky factorisation).
Efficiency and generalised convexity in vector optimisation problems
Authors: Sach Pham Huu , Lee Gue Myung , Kim Do Sang 
Published: February 2009

AbstractThis paper gives a necessary and sufficient condition for a Kuhn-Tucker point of a non-smooth vector optimisation problem subject to inequality and equality constraints to be an efficient solution. The main tool we use is an alternative theorem which is quite different to a corresponding result by Xu.
Oscillation of symplectic dynamic systems
Authors: Bohner Martin , Došlý Ondřej 
Published: February 2009

AbstractWe investigate oscillatory properties of a perturbed symplectic dynamic system on a time scale that is unbounded above. The unperturbed system is supposed to be nonoscillatory, and we give conditions on the perturbation matrix, which guarantee that the perturbed system becomes oscillatory. Examples illustrating the general results are given as well.
Existence of solutions of third-order functional problems with nonlinear boundary conditions
Authors: Cabada Alberto , Heikkilä Seppo 
Published: February 2009

AbstractIn this paper some existence results for third-order differential equations with nonlinear boundary value conditions are derived. Functional dependence in the data is allowed. In the proofs we use the method of upper and lower solutions, Schauder's fixed point theorem and results from Cabada and Heikkilä on third-order differential equations with linear and nonfunctional initial-boundary value conditions.