bluuebunny/crossref_metadata_2025_split huggingface dataset:
A nonlinear singular perturbation problem on a semi-infinite interval
Authors: Shepherd J. J. 
Published: February 2009

AbstractWe consider a nonlinear singular perturbation problem on a semi-infinite interval, that is a generalization of the well-known Lagerstrom model equation intended to model low Reynolds number flow. By applying a Green's function method and the contraction mapping principle, we are able to obtain existence, uniqueness and asymptoticity results for this problem.
Inverse power law potentials about polygonal prisms and in polygonal cavities
Authors: Philip J. R. 
Published: February 2009

AbstractThe effects on adsorption of the geometry of the solid may be studied through calculations based on a (distance)−ε (ε> 3) intermolecular potential. This paper establishes the result that the potential due to an infinitely long polygonal homogeneous solid prism, at position r in the plane of its right section, is – . Here ρi = ∣ r − ri ∣, where the ri are the position vectors of the n vertices of the polygon, and θij are the angles r − ri makes with the two sides of the polygon which meet at vertex ri. The g's are exact functions of θij. They are, in general, integrals of associated Legendre functions, but they are elementary for ε an even integer. A similar result holds for the potential within an infinitely long polygonal prismatic cavity. The analysis involves a systematic superposition schema and the concept of a supplementary potential with datum within the solid at infinity. The cases ε = 6 and ε = 4 are treated in detail and illustrative solutions given for the following configurations: semi-infinite laminae, deep rectangular cracks, square prisms, square prismatic cavities and regular n-gonal prismatic cavities.
On tensor operators and characteristic identities for semi-simple Lie algebras
Authors: Gould M. D. 
Published: February 2009

AbstractTensor identities for finite dimensional representations of arbitrary semi-simple Lie algebras are derived and are applied to the construction of left-projection operators which project out the shift components of tensor operators from the left. The corresponding adjoint identities are also derived and are used for the construction of right-projection operators. It is also shown that, on a finite dimensional irreducible representation, these identities may be considerably reduced. Commutation relations between the shift tensors of a tensor operator are also computed in terms of the roots appearing in the tensor identities.
Existence of optimal controls for systems governed by second order linear parabolic partial delay-differential equations with first boundary conditions
Authors: Teo K. L. 
Published: February 2009

AbstractIn this paper, we consider a class of systems governed by second order linear parabolic delay-partial differential equations with first boundary conditions. Our main results are reported in Theorems 3.1 and 3.2. As in [9, Theorems 4.1 and 4.2], the coefficients and forcing terms of the system considered in Theorem 3.1 are linear in the control variables. On the other hand, the forcing terms of the system considered in Theorem 3.2 are allowed to be nonlinear in the control variables at the expense of dropping the control variables in the cost integrand.
Multivariable adaptive parameter and state estimators with convergence analysis
Authors: Moore J. B. , Ledwich G. 
Published: February 2009

AbstractThe convergence properties of a very general class of adaptive recursive algorithms for the identification of discrete-time linear signal models are studied for the stochastic case using martingale convergence theorems. The class of algorithms specializes to a number of known output error algorithms (also called model reference adaptive schemes) and equation error schemes including extended (and standard) least squares schemes. They also specialize to novel adaptive Kalman filters, adaptive predictors and adaptive regulator algorithms. An algorithm is derived for identification of uniquely parameterized multivariable linear systems.A passivity condition (positive real condition in the time invariant model case) emerges as the crucial condition ensuring convergence in the noise-free cases. The passivity condition and persistently exciting conditions on the noise and state estimates are then shown to guarantee almost sure convergence results for the more general adaptive schemes.Of significance is that, apart from the stability assumptions inherent in the passivity condition, there are no stability assumptions required as in an alternative theory using convergence of ordinary differential equations.
Doubling strategies for backgammon-like games
Authors: Tuck E. O. 
Published: February 2009

AbstractOptimal strategies are obtained for two-player games with an alternating staek doubling option. A complete two-parameter analysis is provided for games that must end within two moves, and a recursive procedure then enables a solution for games of any number of moves. Examples are given of relevance to extureme end games in backgammon.
Some pure radiation filds in general relativity
Authors: Akabari R. P. , Dave U. K. , Patel L. K. 
Published: February 2009

AbstractA Demianski-type metric investigated in connection with Einstein's field equations corresponding to pure radiation fields. With aid of complex vectorical formalism, a general solution of these fiel equations is obtained. The solution is algebraically spcial. A particular case of the solution is considered which includes many known solutions; among them are the raiationg versions of some of Kinnersley's solutions.
A scheduling problem with a simple graphical solution
Authors: Beecham A. F. , Hurley A. C. 
Published: February 2009

AbstractIt is shown that a problem which arose in the scheduling of two simultaneous competitions between a number of golf clubs may be reduced to that of 4- colouring the edges of a certain bipartite graph which has 4 edges meeting at each vertex. This colouring problem is solved by an analysis in terms of directed cycles, which is simple to carry through in a practical case and is easily extended to the problem with 4 replaced by 2m. The more general colouring problem with 4 replaced by any positive integer is solved by relating it to the marriage problem enunciated by Philip Hall and to the latin multiplication technique of Kaufmann but, in practical applications, this approach involves severe computational difficulties.
On a nonlinear hydromagnetic convection under a rotational constraint
Authors: Riahi N. 
Published: February 2009

AbstractNonlinear hydromagnetic convection in a horizontal layer of fluid rotating about the vertical axis is investigated using the mean field approximation. The boundary layer method is used assuming large Rayleigh number R for different ranges of the Chandrasekhar number Q and the Taylor number Ta. The heat flux F is determined for the value of the horizontal wave number α which maximizes F. It is shown that, for certain regions of the parameter space (R, Q, Ta), F and α change discontinuously for Ta greater than some critical value (given R and Q). Thus, for Ta about this critical value, wave numbers and heat fluxes of two different values will be predicted simultaneously. Also, for certian regions of the parameter space, the field can facilitate convection, but rotation can facilitate convection only for sufficiently large Ta.
On the influence of the initial data in a combustion problem
Authors: Tam K. K. 
Published: February 2009

AbstractThe combustion of a material can be modelled by two coupled parabolic partial differential equations for the temperature and concentration of the material. This paper deals with properties of the solution of these equations inside a cylinder or a sphere and under given initial conditions. Bounds for the variation of the temperature with the initial conditions are first established by considering a decoupled form of the equations. Then the coupled system is used to obtain approximate expressions for the temporal evolution of temperature and concentration.
Geometric programming with probabilistic decision variables
Authors: Jefferson T. R. , Scott C. H. 
Published: February 2009

AbstractHere we consider a particular class of stochastic geometric programs in which the randomness occurs in the decision variables. Specifically we analyse a program in which we specify a joint normal probability for the dicision variables and require the constraint set to be satisfied in the chance constrained mode. A numerical example is given to illustrate the approach.
Poisoning-induced exchange of steady states in a catalytic chemical reactor
Authors: Do D. D. , Weiland R. H. 
Published: February 2009

AbstractSlow catalyst poisoning can result in the sudden failure of a chemical reactor operating isothermally with substrate-inhibited kinetics. At failure, a satisfactory steady state is exchanged for one of low conversion. The method of matched asymptotic expansions is used to give a detailed description of the exchange process in the phase plane. The structure of the jump is ascertained by separate asymptotic expansions across two adjoining transition regions in which the independent variables contain unknown shifts.
Solution of a general homogeneous linear difference equation
Authors: Singh V. N. 
Published: February 2009

In Section 3, since relation (6) is valid only for n ≥ 2r, the condition n ≥ r in relation (9) should be replaced by n ≥ 2r. When r ≤ n ≤ 2r − 1, relation (9) still holds but now relations (6) and (7) should be replaced, respectively, by the relationsandthe asterisk again denoting omission of the last column. The proof of (9) for r ≤ n ≤ 2r − 1 is exactly similar to its proof for n ≥ 2r.
The kernel of a rule of approximate integration
Authors: Loxton J. H. , Sanders J. W. 
Published: February 2009

AbstractIt is well known that the trapezoidal rule of quadrature is exact for linear functions on [0, 1], and easy to see that it is exact for functions of the form f = l+g where l is linear and g is odd about ½. Not so well known is an example of a continuous function for which the trapezoidal rule is exact but which does not have this form. In this paper we show that if the trapezoidal rule is exact for f then f has the form above provided it has either absolutely convergent Fourier series or continuous second derivative. We consider one-sided versions in which the approximate integrals are non-negative, and also characterize those sequences arising as the approximate integrals of a function with absolutely convergent Fourier series.
Invariance properties of Schoenberg's tone row system
Authors: Fill James A. , Izenman Alan J. 
Published: February 2009

AbstractThis paper organizes in a systematic manner the major features of a general theory ofm-tone rows. A special case of this development is the twelve-tone row system of musical composition as introduced by Arnold Schoenberg and his Viennese school. The theory as outlined here applies to tone rows of arbitrary length, and can be applied to microtonal composition for electronic media.
A modified barrier function method with improved rate of convergence for degenerate problems
Authors: Jittorntrum Krisorn , Osborne M. R. 
Published: February 2009

AbstractIn a previous paper the authors have shown that the classical barrier function has anO(r) rate of convergence unless the problem is degenerate when it reducesO(r½). In this paper a modified barrier function algorithm is suggested which does not suffer from this problem. It turns out to have superior scaling properties which make it preferable to the classical algorithm, even in the nondegenerate case, if extrapolation is to be used to accelerate convergence.
An algorithm for solving the restricted least squares problem
Authors: Clark David 
Published: February 2009

AbstractThis paper presents an algorithm to solve the least squares problem when the parameters are restricted to be non-negative. The algorithm is based on the branch and bound method which has been suggested for this problem, and shares with it the property that an unrestricted least squares subproblem is solved at each step. However, improvements have been made to the branching rules by making use of the convexity of the problem, and the Kuhn–Tucker conditions are used to test for optimality. The resulting algorithm becomes essentially iterative in nature, and linearity of the number of subproblems solved can be shown under assumptions which have always been observed in practice.
Uniform estimation of the eigenvalues of Sturm–Liouville problems
Authors: Paine John , de Hoog Frank 
Published: February 2009

AbstractThe perturbation of the eigenvalues of a regular Sturm–Liouville problem in normal form which results from a small perturbation of the coefficient function is known to be uniformly bounded. For numerical methods based on approximating the coefficients of the differential equation, this result is used to show that a better bound on the error is obtained when the problem is in normal form. A method having a uniform error bound is presented, and an extension of this method for general Sturm–Liouville problems is proposed and examined.
Solution of a general homogeneous linear difference equation
Authors: Singh V. N. 
Published: February 2009

AbstractSolutions of a homogeneous (r + 1)-term linear difference equation are given in two different forms. One involves the elements of a certain matrix, while the other is in terms of certain lower Hessenberg determinants. The results generalize some earlier results of Brown [1] for the solution of a 3-term linear difference equation.
The one-dimensional gas-lubricated slider bearing
Authors: Shepherd J. J. 
Published: February 2009

AbstractUnder the appropriate physical hypotheses, the problem of determining the pressure distribution in a gas-filled slider bearing becomes a singular perturbation problem as Λ, the bearing number, tends to infinity. This paper extends the results of an earlier one by the author to consider the case where the film profile has jump discontinuities in slope at points interior to the bearing. Application of the methods of general singular perturbation theory establishes the appropriate existence-uniqueness results for this problem, and a means is devised by which uniformly valid asymptotic approximations to the pressure distribution may be obtained for large values of Λ.
Singularity subtraction in the numerical solution of integral equations
Authors: Anselone P. M. 
Published: February 2009

AbstractThe singularity subtraction technique described by Kantorovich and Krylov in [11] is designed to reduce or overcome the effect of a weakly singular kernel in the numerical solution of integral equations. First, the equation is rearranged in such a way that the singularity of the kernel is at least partially cancelled by the smoothness of the solution, and then numerical integration is applied. We present convergence results and error bounds under general conditions on the nature of the singularity and the numerical integration procedure. Numerical examples demonstrate the benefit of the singularity subtraction technique.
The properties of solutions of weakly singular integral equations
Authors: Vainikko G. , Pedas A. 
Published: February 2009

AbstractWe examine the differential properties of the solution of the linear integral equation of the second kind, whose kernel depends on the difference of arguments and has an integrable singularity at the point zero. The derivatives of the solution of the equation have singularities at the end points of the domain of integration, and we derive precise estimates for these singularities.
A piecewise polynomial approximation to the solution of an integral equation with weakly singular kernel
Authors: Vainikko G. , Uba P. 
Published: February 2009

AbstractWe construct collocation methods with an arbitrary degree of accuracy for integral equations with logarithmically or algebraically singular kernels. Superconvergence at collocation points is obtained. A grid is used, the degree of non-uniformity of which is in good conformity with the smoothness of the solution and the desired accuracy of the method.
The iterated projection solution for the Fredholm integral equation of second kind
Authors: Chatelin Françoise , Lebbar Rachid 
Published: February 2009

AbstractWe are concerned with the solution of the second kind Fredholm equation (and eigenvalue problem) by a projection method, where the projection is either an orthogonal projection on a set of piecewise polynomials or an interpolatory projection at the Gauss points of subintervals.We study these cases of superconvergence of the Sloan iterated solution: global superconvergence for a smooth kernel, and superconvergence at the partition points for a kernel of “Green's function” type. The mathematical analysis applies for the solution of the inhomogeneous equation as well as for an eigenvector.
Collocation methods for two dimensional weakly singular integral equations
Authors: Graham Ivan G. 
Published: February 2009

AbstractGiven a Fredhoim integral equation of the second kind, which is defined over a certain region ⊆ R2, we define and , two different numerical approximations to its solution, using the collocation and iterated collocation methods respectively. We describe without proof some known results concerning the general convergence properties of and when the kernel and solution of the integral equation are smooth. Then, we prove rigorously order of convergence estimates for and which are applicable in the practically siginificant case when is a rectangle, and the kernel of the integral equation is weakly singular. These estimates are illustrated by the numerical solution of a two dimensional weakly singular equation which arises in electrical engineering.
The extension of generalized cross-validation to a multi-parameter class of estimators
Authors: O'Brien D. M. , Holt J. N. 
Published: February 2009

AbstractThe method of generalized cross-validation (GCV) provides a good value for the “ridge” regularization parameter for an ill-conditioned linear system, such as the system produced by discretization of a Fredholm integral equation of the first kind. In this note we apply GCV to a wider class of estimators than the one parameter ridge estimators. We observe that the expected values of the parameter mean-square error, the predictive mean-square error, and the GCV function are simultaneously minimized over this new class, so we accept the minimizer of the GCV function as the best computable estimator. We present a simple algorithm for computing this estimator from the data, so that a numerical search is not needed.
Stability analysis of Runge–Kutta methods applied to a basic Volterra integral equation
Authors: Baker Christopher T. H. , Wilkinson Joan C. 
Published: February 2009

AbstractOur purpose in this paper is to display the stability analysis of Runge–Kutta methods applied to a Volterra integral equation of a simple form. As prerequisite we define, and then develop the structure of, the class of Runge–Kutta methods considered. The test equation is taken as the “;basic” equation ; the simple form of this equation permits ready insight into features which are more obscure when considering (as elsewhere [1], [2], [6]) equations of a more complicated form. Due to the structure of the methods and the nature of the test equation, the stability analysis reduces to the study of recurrence relations of the form Фk + 1 = MФ k + γk (k = 0, 1, 2, …) which are common in stability discussions in numerical analysis.
A convergence theorem for singular integral equations
Authors: Elliott David 
Published: February 2009

AbstractThe principal result of this paper states sufficient conditions for the convergence of the solutions of certain linear algebraic equations to the solution of a (linear) singular integral equation with Cauchy kernel. The motivation for this study has been the need to provide a convergence theory for a collocation method applied to the singular integral equation taken over the arc (−1, 1). However, much of the analysis will be applicable both to other approximation methods and to singular integral equations taken over other arcs or contours. An estimate for the rate of convergence is also given.
The optimum processing of clipped signals: an approach based an a likelihood ratio statistic
Authors: Keats R. G. , Frost Winifred , Dobson Annette 
Published: February 2009

AbstractThe likelihood ratio approach to the detection of small signals in the presence of noise is investigated in the case where the available data have been clipped. The statistic obtained is the ratio of orthant probabilities and appears intractable; accordingly an approximation to this statistic is developed by truncating an appropriate Taylor expansion. Approximations are obtained for the mean and variance of this modified statistic and compared with those obtained from computer simulations.
The existence of Hadley convective regimes of atmospheric motion
Authors: Dutton John A. , Kloeden Peter E. 
Published: February 2009

AbstractThe solutions of the equations describing deep global convection on a rotating planet are discussed. The existence of generalized steady axisymmetric solutions is established. It is then shown that these are classical solutions when the heat source is sufficiently smooth. The solutions are shown to be unique when the heating is sufficiently weak and asymptotically stable when the shear is sufficiently small. Finally, the application of these results to Earth's atmosphere is discussed, with eddy viscosity replacing molecular viscosity.
Static plane-symmetric solution of a scalar-tensor theory of gravitation
Authors: Reddy D. R. K. , Rao V. U. M. 
Published: February 2009

AbstractVacuum field equations in a scalar-tensor theory of gravitation, proposed by Ross, are obtained with the aid of a static plane-symmetric metric. A closed form exact solution to the field equations in this theory is presented which can be considered as an analogue of Taub's empty space-time in Einstein's theory.
The effect of an enclosed air cavity on a rectangular drum
Authors: Gottlieb H. P. W. 
Published: February 2009

AbstractThe effect of an enclosed air cavity on the natural vibration frequencies of a rectangular membrane is investigated. The modes specified by an even integer are not affected. For the odd-odd modes, the frequency equation is found via a Green's function formulation and is solved to first order in a parameter representing the effect of the cavity of the rectangular drum. The frequencies are raised, with the fundamental being most affected. In the case of degeneracies, each degenerate mode contributes to the frequency shift, but the degeneracy itself is not broken to first order.
Stability of plane Couette flow for high Reynolds number
Authors: Davis G. B. , Morris A. G. 
Published: February 2009

AbstractExperimental evidence shows that plane Couette flow becomes unstable when the Reynolds number R reaches certain critical values. Linear stability theory does not predict these observations and has been unable to locate these instabilities. A Chebyshev/QR numerical technique is used to investigate much higher values of R than those previously tested. In particular, values of R up to 108 are confidently tested, whereas previously values of R up to only 2 × 104 have been considered.
Rapidly-convergent methods for evaluating elliptic integrals and theta and elliptic functions
Authors: Fenton J. D. , Gardiner-Garden R. S. 
Published: February 2009

AbstractThe expressions for elliptic integrals, elliptic functions and theta functions given in standard reference books are slowly convergent as the parameter m approaches unity, and in the limit do not converge. In this paper we use Jacobi's imaginary transformation to obtain alternative expressions which converge most rapidly in the limit as m → 1. With the freedom to use the traditional formulae for m ≤ ½ and those obtained here for m ≥ ½, extraordinarily rapidly-convergent methods may be used for all values of m; no more than three terms of any series need be used to ensure eight-figure accuracy.