bluuebunny/crossref_metadata_2025_split huggingface dataset:
Trajectory analysis and extrapolation in barrier function methods
Authors: Jittorntrum Krisorn , Osborne M. R. 
Published: February 2009

AbstractIt has been known for some time that if a certain non-degeneracy condition is satisfied then the successive solution estimates x(r) produced by barrier function techniques lie on a smooth trajectory. Accordingly, extrapolation methods can be used to calculate x(0). In this paper we analyse the situation further treating the special case of the log barrier function. If the non-degeneracy assumption is not satisfied then the approach to x(0) is like r½ rather than like r which would be expected in the non-degenerate case. A measure of sensitivity is introduced which becomes large when the non- degeneracy assumption is close to violation, and it is shown that this sensitivity measure is related to the growth of dix/dri with respect to i for fixed r small enough on the solution trajectory. With this information it is possible to analyse the extrapolation procedure and to predict the number of stages of extrapolation which are useful.
Asymptotic behaviour of a class of discontinuous difference equations
Authors: Fisher M. E. , Kloeden P. E. 
Published: February 2009

AbstractSufficient conditions for an equilibrium point to be an attractor or a global attractor are derived for a class of first-order difference equations which need not be continuous at the equilibrium point. These conditions involve Lyapunovlike functions which need not be continuous and are applied to the logistic equation with a piecewise continuous control.
Bifurcation and stability of periodic solutions from a zero eigenvalue
Authors: Landman K. A. 
Published: February 2009

AbstractA study is made of the branching of time periodic solutions of a system of differential equations in R2 in the case of a double zero eigenvalue. It is shown that the solution need not be unique and the period of the solution is large. The stability of these solutions is analysed. Examples are given and generalizations to larger systems are discussed.
A note on the solution of the one-dimensional unsteady equations of arterial blood flow by the method of characteristics
Authors: Forbes L. K. 
Published: February 2009

AbstractThe “Hartree hybrid method” has recently been employed in one-dimensional non-linear aortic blood-flow models, and the results obtained appear to indicate that shock-waves could only form in distances which exceed physiologically meaningful values. However, when the same method is applied with greater numerical accuracy to these models, the existence of a shock-wave in the vicinity of the heart is predicted. This appears to be contrary to present belief.
On the unsteady squeezing of a viscous fluid from a tube
Authors: Skalak F. M. , Wang C. Y. 
Published: February 2009

AbstractViscous fluid is squeezed out from a shrinking (or expanding) tube whose radius varies with time as (1 – βt)½. The full Navier–Stokes equations reduce to a non-linear ordinary differential equation governed by a non-dimensional parameterSrepresenting the relative importance of unsteadiness to viscosity. This paper studies the analytic solutions for large |S| through the method of matched asymptotic expansions. A simple numerical scheme for integration is presented. It is found that boundary layers exist near the walls for large |S|. In addition, flow reversals and oscillations of the velocity profile occur for large negativeS(fast expansion of the tube).
Existence theorems for optimal control of quasilinear parabolic partial differential equations
Authors: Nababan S. , Noussair E. S. 
Published: February 2009

AbstractThe question on existence of optimal controls for a system governed by quasilinear parabolic partial differential equations which is linear in the control variables is considered. It is shown that whenever the controls converge in the weak * topology of L∞, the corresponding solutions converge uniformly. Using this result and results on lower semi-continuity of integral functionals, existence theorems for optimal controls are proved.
Aspects of the kinetic equations for a special one-dimensional system
Authors: Evans J. W. 
Published: February 2009

AbstractSome initial value problems are considered which arise in the treatment of a one-dimensional gas of point particles interacting with a “hard-core” potential.Two basic types of initial conditions are considered. For the first, one particle is specified to be at the origin with a given velocity. The positions in phase space of the remaining background of particles are represented by continuous distribution functions. The second problem is a periodic analogue of the first.Exact equations for the delta-function part of the single particle distribution functions are derived for the non-periodic case and approximate equations for the periodic case. These take the form of differential operator equations. The spectral and asymptotic properties of the operators associated with the two cases are examined and compared. The behaviour of the solutions is also considered.
The problem of a rigid punch moving on a viscoelastic half-plane with inertial effects approximately included
Authors: Golden J. M. 
Published: February 2009

AbstractThe problem of an infinitely long rigid punch of uniform cross-section moving across a viscoelastic half-space at constant velocity, large enough so that inertial effects cannot be neglected, is examined and solved in various approximations. Frictional shear is assumed to exist between the punch and the half-space. The method, which is an extension of that developed in previous papers [6, 7], is applicable for any form of viscoelastic behaviour in the half-space. For the special case of discrete spectrum behaviour the method is described in detail. For the case where the punch is cylindrical and viscoelastic effects are small compared with elastic effects, explicit expressions are given for all quantities of interest, in particular the coefficient of hysteretic friction. A general Hilbert transform formula is derived in the appendix.
The structure of RI-invariant tweleve-tone rows
Authors: Fill James A. , Izenman Alan J. 
Published: February 2009

AbstractThis paper presents an efficient method for generating the class of all twelve-tone rows which are transpositions of their own retrograde-inversions. It is shown here that the members of this class can be obtained from a subclass of those rows whose first six notes are ascending and whose first note is C. The number of twelve-tone rows in this subclass is 192, and a complete listing is given in an appendix to this paper. The theory as developed here can be applied to tone rows having any even number of notes.
Stability of large-scale systems with lagged interconnections
Authors: Kloeden P. E. 
Published: February 2009

AbstractThe aggregation-decomposition method is used to derive sufficient conditions for the uniform stability, uniform asymptotic stability and exponential stability of the null solution of large-scale systems described by functional differential equations with lags appearing only in the interconnections. The free subsystems are described by ordinary differential equations for which converse theorems involving Lyapunov functions exist and thus enable the sufficient conditions to be expressed in terms of Lyapunov functions rather than the more complicated Lyapunov functionals.
Equilibrium states of a Bose gas with repulsive interactions
Authors: Bratteli Ola , Robinson Derek W. 
Published: February 2009

AbstractWe consider infinite volume limit Gibbs states of a nonrelativistic quantum Bose gas consisting of one species of spinless particles with positive interaction potentials. The finite volume reduced density matrices are dominated by the corresponding matrices for the noninteracting gas, and as a consequence all infinite volume limit states are regular, locally normal, and analytic on the appropriate CCR algebra. For sufficiently short range repulsive two-body interactions, the cyclic vector associated with the limit state is separating for the σ-weak closure of the algebra in the associated representation.
The optimum processing of clipped signals: An approach based on minimum signal distortion
Authors: Keats R. G. , Cooper Joan 
Published: February 2009

AbstractThe minimization of signal distortion was one approach applied successfully in the theory of optimum signal detection for arrays [3]. The processors considered operated on the input as received.In some applications it is desirable to clip the received signal before processing and the problem of optimum processing of such clipped signals then arises. Several approaches to this problem are being studied, but the present paper is concerned with that based on minimum signal distortion.
A theoretical investigation of an asymmetric planing hull at infinite Froude number
Authors: Casling E. M. 
Published: February 2009

AbstractThe extent to which an asymmetric low-aspect-ratio flat ship is wetted when planing at infinite Froude number is investigated, with emphasis placed on its relationship with the shape of the hull. Two cases are considered. First the hull is assumed to have two laterally-asymmetric leading edges and, secondly, the hull is assumed to be yawed sufficiently for one of the leading edges to become a trailing edge. In the first case, the relationship involves a pair of coupled integral equations, but in the second case there is a complication by the occurrence of hull-wake interaction.
On the evolution of shock-waves in mathematical models of the aorta
Authors: Forbes L. K. 
Published: February 2009

AbstractThe one-dimensional, non-linear theory of pulse propagation in large arteries is examined in the light of the analogy which exists with gas dynamics. Numerical evidence for the existence of shock-waves in current one-dimensional blood-flow models is presented. Some methods of suppressing shock-wave development in these models are indicated.
On error bounds in strong approximations for eigenvalue problems
Authors: Kulkarani R. P. , Limaye B. V. 
Published: February 2009

AbstractSome corrections of error bounds obtained by Chatelin and Lemordant for the first three terms of the asymptotic case of a strong approximation are given. The error bounds for the approximations of order 2 in the Galerkin method are compared with the Rayleigh quotients constructed with the eigenvectors in the Sloan method. A numerical experiment is also carried out.
Mean flows generated by a progressing water wave packert
Authors: Grimshaw R. 
Published: February 2009

AbstractEquations are derived which describe the evolution of the mean flow generated by a progressing water wave packet. The effect of friction is included, and so the equations are subject to the boundary conditions first derived by Longuet-Higgins [10]. Solutions of the equations are obtained for a wave packet of finite length, and also for a uniform wave train. The latter solution is compared with experiments.
Love's integral and other relations between solutions to mixed boundary-value problems in potential theory
Authors: England A. H. 
Published: February 2009

AbstractIn a paper published in 1949, E. R. Love [10] found an integral relation between a separated solution (in oblate spheroidal coordinates) to a particular mixed boundary-value problem and a solution to the same problem using an integral representation. This note examines further representations of the same type which occur in some simple two and three-dimensional potential problems.
A formal comparison of methods proposed for the numerical solution of first kind integral equations
Authors: Anderssen R. S. , Prenter P. M. 
Published: February 2009

AbstractA formal framework is constructed for the comparison of different stabilization techniques, such as Wiener filtering, regularization, Courant's method and Landweber–Strand iterations, for the solution of first kind integral equations. It is shown that, when they are applied to convolution equations, all these methods can be reinterpreted as Wiener filters. This equivalence is then used to derive some specific results about regularization, Courant's method and Landweber–Strand iteration.
Subsonic potential flow past a circle and the transonic controversy
Authors: Van Dyke M. D. , Guttmann A. J. 
Published: February 2009

AbstractThe Mach-number series expansion of the potential function for the two-dimensional flow of an inviscid, compressible, perfect, diatomic gas past a circular cylinder is obtained to 29 terms. Analysis of this expansion allows the critical Mach number, at which flow first becomes locally sonic, to be estimated as M* = 0.39823780 ± 0.00000001. Analysis also permits the following estimate of the radius of convergence of the series for the maximum velocity to be made: Mc = 0.402667605 ± 0.00000005, though we have been unable to determine the nature of the singularity of M = Mc. Since Mc exceeds M* by some 1.1%, it follows that this particular “airfoil” can possess a continuous range of shock-free potential flows above the critical Mach number. This result hopefully resolves a 70-year old controversy.
Thermal ignition in a reactive slab with unsymmetric boundary temperatures
Authors: Tam K. K. , Chapman P. B. 
Published: February 2009

AbstractThe problem of thermal ignition in a reactive slab with unsymmetric temperatures equal to 0 and T is considered. Steady state upper and lower solutions are constructed. It is found that T plays a critical role. Results similar to the case with symmetric boundary temperatures are expected when T is small. When T is sufficiently large, there is only one steady state upper or lower solution. The time dependent problem is then considered. Phenomena suggested by studying the upper and lower steady state solutions are confirmed.
On a two lag differential delay equation
Authors: Braddock R. D. , van den Driessche P. 
Published: February 2009

AbstractThe non-linear differential difference equation of the formis investigated. This equation, with constant coefficients, is used to model the population level,N, of a single species, and incorporates two constant time lagsT2>T1> 0; for example, regeneration and reproductive lags. The linear equation is investigated analytically, and some linear stability regions are described. The special case in which the two delay terms are equally important in self damping,B = C, is investigated in detail. Numerical solutions for this case show stable limit cycles, with multiple loops appearing whenT2/T1is large. These may correspond to splitting of major peaks in population density observations.
On interpreting the sums of asymptotic series of positive terms
Authors: Drummond J. E. 
Published: February 2009

AbstractFour different kinds of positive asymptotic series are identified by the limiting ratio of successive terms. When the limiting ratio is 1 the series is unsummable. When the ratio tends rapidly to a constant, whether greater or less than 1, the series is easily summed. When the ratio tends slowly to a constant not equal to 1 the series is compared with a binomial model which is then used to speed the convergence. When the ratio increases linearly, a limiting binomial and an exponential integral model are both used to speed convergence. The two resulting model sums are consistent and in this case are complex numbers. Truncation at the smallest term is found to be unreliable in the second case, invalid in the third case, and the exponential integral is used to produce a significantly improved truncation in the third case. A divergent series from quantum mechanics is also examined.
Moving boundary problems in the flow of liquid through porous media
Authors: Lacey A. A. 
Published: February 2009

AbstractThe movement of the interface between two immiscible fluids flowing through a porous medium is discussed. It is assumed that one of the fluids, which is a liquid, is much more viscous than the other. The problem is transformed by replacing the pressure with an integral of pressure with respect to time. Singularities of pressure and the transformed variable are seen to be related.Some two-dimensional problems may be solved by comparing the singularities of certain analytic functions, one of which is derived from the new variable. The implications of the approach of a singularity to the moving boundary are examined.
On the explosion of chain-thermal reactions
Authors: Ayeni R. O. 
Published: February 2009

AbstractA chain reaction of oxygen (reactant) and hydrogen (active intermediary) with mtrosyl chloride (sensitizer) as a catalyst may be modelled mathematically as a non-isothermal reaction. In this paper we present an asymptotic analysis of a spatially homogeneous model of a non-isothermal branched-chain reaction. Of particular interest is the so-called explosion time and we provide an upper bound for it as a function of the activation energy which can vary over all positive values. We also establish a bound on the temperature when the activation energy is finite.
Converging factors for some asymptotic moment series that arise in numerical quadrature
Authors: Sidi Avram 
Published: February 2009

AbstractIn this work the asymptotic behavior of the partial sums of the divergent asymptotic moment series, where μiare the moments of the weight functionsw(x) =xαe−x, α > −1, andw(x) =xαEm(x), α > −1,m+ α > 0, on the interval [0, ∞), is analyzed. Expressions for the converging factors are derived by the author for the infinite range integraswithw(x) as given above.
Steady states of the reaction-diffusion equations. Part 1: Questions of existence and continuity of solution branches
Authors: Burnell J. G. , Lacey A. A. , Wake G. C. 
Published: February 2009

AbstractWhen material is undergoing an exothermic chemical reaction which is sustained by the diffusion of a reactant, the steady-state regime is governed by a coupled pair of nonlinear elliptic partial differential equations with linear boundary conditions. In this paper we consider questions of existence of solutions to these equations. It is shown that, with the exception of the special case in which the mass-transfer is uninhibited on the boundary, a solution always exists, whereas in this special case a solution exists only for sufficiently low values of the exothermicity. Bounds are established for the solutions and the occurrence of minimal and maximal solutions is shown for some cases. Finally the behaviour of the solution set with respect to one of the parameters is studied.
Solution of general inhomogeneous linear difference equations
Authors: Van Hoa H. 
Published: February 2009

AbstractThe general solution of the rth inhomogeneous linear difference equation is given in the formThe coefficients , i = 2, …, r, and b(n−r)(n) can be evaluated from n values , k = 0, …, n − 1, which santisfy an rth order homogenous linear difference equation. In the rth order homogeneous case and if n ≥ 2r, the method requires the evaluation of r determinants of successive orders n − 2r + 1, n − 2r + 2, …, n − r. If r ≤ n ≤ 2r − 1, only n − r determinants are required, with orders varying from 1 to n − r. In the second order ihnomogenous case, can be evaluated from a continued fraction amd a simple product.
Some elementary exact channel flows
Authors: de Mestre Neville , Pakes Trevor 
Published: February 2009

AbstractNew polynomial solutions of the Navier-Stokes equations for steady uni-directional flow of viscous incompressible fluid, with a free surface, down inclined channels of specialized cross-section are considered. An inverse method is uded to obtain the geometrical shape of the channel by equating the polynomials solution to zero (i.e. the no-slip condition) and thence determining the boundary shape.
Cyclic gravity waves in deep water
Authors: Bryant P. J. 
Published: February 2009

AbstractNumerical evidence is presented for the existence of unsteady periodic gravity waves of large height in deep water whose shape changes cyclically as they propagate. It is found that, for a given wavelength and maximum wave height, cyclic waves with a range of cyclic periods exist, with a steady wave of permanent shape being an extreme member of the range. The method of solution, using Fourier transforms of the nonlinear surface boundary conditions, determines the irrotational velocity field in the water and the water surface displacement as functions of space and time, from which properties of the waves are demonstrated. In particular, it is shown that cyclic waves are closer to the point of wave breaking than are steady permanent waves of the same wave height and wavelength.
Water waves, nonlinear Schrödinger equations and their solutions
Authors: Peregrine D. H. 
Published: February 2009

AbstractEquations governing modulations of weakly nonlinear water waves are described. The modulations are coupled with wave-induced mean flows except in the case of water deeper than the modulation length scale. Equations suitable for water depths of the order the modulation length scale are deduced from those derived by Davey and Stewartson [5] and Dysthe [6]. A number of ases in which these equations reduce to a one dimensional nonlinear Schrödinger (NLS) equation are enumerated.Several analytical solutions of NLS equations are presented, with discussion of some of their implications for describing the propagation of water waves. Some of the solutions have not been presented in detail, or in convenient form before. One is new, a “rational” solution describing an “amplitude peak” which is isolated in space-time. Ma's [13] soli ton is particularly relevant to the recurrence of uniform wave trains in the experiment of Lake et al.[10].In further discussion it is pointed out that although water waves are unstable to three-dimensional disturbances, an effective description of weakly nonlinear two-dimensional waves would be a useful step towards describing ocean wave propagation.
The anti-cyclonic shear wave: a new geophysical wave
Authors: Hughes Roger L. 
Published: February 2009

AbstractA new type of first baroclinic mode wave which propagates on an anti-cyclonic vorticity field in identified. It is of the vorticity class of waves which contains Rossby waves amongst others. This anti-cyclonic shear wave is produced by pressure variations distorting the vertical stratification in such a manner that the associated vortex stretching generates the velocity variation required for Bernoulli compatibility with the initial pressure variation. The wave travels at a speed characteristic of particles within the undisturbed shear flow and is a low frequency and low wavenumber wave, In the present study this wave is considered in the presence of a wark anti-cyclonic shear.