bluuebunny/crossref_metadata_2025 huggingface dataset:
The modulation of short gravity waves by long waves or currents
Authors: Grimshaw R.
Published: February 2009

The modulation of short gravity waves by long waves or currents is described for the situation when the flow is irrotational and when the short waves are described by linearised equations. Two cases are distinguished depending on whether the basic flow can be characterised as a deep-water current, or a shallow-water current. In both cases the basic flow has a current which has finite amplitude, while in the first case the free surface slope of the basic flow can be finite, but in the second case is small. The modulation equations are the local dispersion relation of the short waves, the kinematic equation for conservation of wave crests and the wave action equation. The results incorporate and extend the earlier work of Longuet-Higgins and Stewart [10, 11].
The application of centre-manifold theory to the evolution of system which vary slowly in space
Authors: Roberts A. J.
Published: February 2009

In many physical problems, the system tends quickly to a particular structure, which then evolves relatively slowly in space and time. Various methods exist to derive equations describing the slow evolution of the particular structure; for example, the method of multiple scales. However, the resulting equations are typically valid only for a limited range of the parameters. In order to extend the range of validity and to improve the accuracy, correction terms must be found for the equations. Here we describe a procedure, inspired by centre-manifold theory, which provides a systematic approach to calculating a sequence of successively more accurate approximations to the evolution of the principal structure in space and time.

The formal procedure described here raises a number of questions for future research. For example: what sort of error bounds can be obtained, do the approximations converge or are they strictly asymptotic, and what sort of boundary conditions are appropriate in a given problem?
A method of accelerating stationary iterative methods for solving linear systems
Authors: Robinson G. K.
Published: February 2009

The speed of convergence of stationary iterative techniques for solving simultaneous linear equations may be increased by using a method similar to conjugate gradients but which does not require the stationary iterative technique to be symmetrisable. The method of refinement is to find linear combinations of iterates from a stationary technique which minimise a quadratic form. This basic method may be used in several ways to construct refined versions of the simple technique. In particular, quadratic forms of much less than full rank may be used. It is suggested that the method is likely to be competitive with other techniques when the number of linear equations is very large and little is known about the properties of the system of equations. A refined version of the Gauss-Seidel technique was found to converge satisfactorily for two large systems of equations arising in the estimation of genetic merit of dairy cattle.
Smoothness and conditioning in generalised smoothing spline calculations
Authors: Osborne M. R. , Prvan Tania
Published: February 2009

We consider a generalisation of the stochastic formulation of smoothing splines, and discuss the smoothness properties of the resulting conditional expectation (generalised smoothing spline), and the sensitivity of the numerical algorithms. One application is to the calculation of smoothing splines with less than the usual order of continuity at the data points.
A square-root fixed-interval discrete-time smoother
Authors: Prvan Tania , Osborne M. R.
Published: February 2009

The square-root fixed-interval discrete-time smoother has been used extensively in discrete recursive estimation since it was first developed by Rauch, Tung and Streibel [10]. Various people, for example Bierman [2], [3], have recognized the inherent instability in employing this kind of smoother in its original form; they have investigated implementing the recursion more stably. Bierman's paper [3] is one such contribution. In this paper we plan to present a more comprehensive development of Bierman's approach, and to show that this algorithm can be implemented more stably as a square-root smoother. Throughout this paper the fixed-interval discrete-time smoother will be referred to as the RTS smoother. Numerical results are given for the usual form of the RTS smoother, Bierman's algorithm and our square-root formulation of his algorithm. These confirm that the square-root formulation is more desirable than Bierman's algorithm, which performs better than the usual implementation of the RTS smoother.
Controllability of generalised dynamical systems with constrained control
Authors: Zhaolin Chen , Huimin Hong , Jifeng Zhang
Published: February 2009

The state controllability for generalised dynamical systems with constrained control is discussed in this paper. The main results of the paper are the following:

(1) a necessary and sufficient condition of the state controllability in the sense of control energy or amplitude constrained for generalised dynamical systems is obtained;

(2) a control function u(t) is constructed such that

a) u(t) satisfies constrained energy or amplitude condition,

b) the state driven by u(t) moves from an arbitrary x(0−) = x0 to x(T(x0)) = 0,

c) the trajectory driven by u(t) has no impulsive behaviour within (0, T(x0)].
Travelling wave solutions for rich flames of reactive suspensions
Authors: Tam K. K.
Published: February 2009

The modelling of the combustion of dust suspensions leads to a nonlinear eigenvalue problem for a system of ordinary differential equations defined over an infinite interval. The equations contain a number of parameters. In this study, the shooting method is used to prove the existence of a solution. Linearisation is then used to provide an approximate solution, from which an estimate of the eigenvalue and its dependence on the given parameters can be obtained.
Radiating Demianski-type metrics and the Einstein-Maxwell fields
Authors: Patel L. K. , Akabari R. P. , Dave U. K.
Published: February 2009

A Demianski-type metric is investigated in connection with the Einstein-Maxwell fields. Using complex vectorial formalism, some exact solutions of Einstein-Maxwell field equations for source-free electromagnetic fields plus pure radiation fields are obtained. The radiating Demianski solution, the Debney-Kerr-Schild solution and the Brill solution are derived as particular cases.
A note on the free surface induced by a submerged source at infinite Froude number
Authors: King A. C. , Bloor M. I. G.
Published: February 2009

The free surface due to a submerged source in a fluid of finite depth at infinite Froude number is reconsidered. A conformal transformation technique is used to formulate this problem as an integral equation for the free-surface angle. An elementary solution is found for the equation, which results in a closed form expression for the free-surface elevation. Comparison is made with previous numerical solutions.
Some asymptotic spectral formulae for the eigenvalues of the Laplacian
Authors: Zayed E. M. E.
Published: February 2009

In this paper we shall derive some asymptotic formulae for spectra of the third boundary value problem in Rn, n = 2 or 3, linked with variation of a positive function entering the boundary conditions. Further results may be obtained.
A boundary integral method for contaminant transport in two adjacent porous media
Authors: Landman K. A.
Published: February 2009

The problem of transient two-dimensional transport by diffusion and advection of a decaying contaminant in two adjacent porous media is solved using a boundary-integral method. The method requires the construction of appropriate Green's functions. Application of Green's theorem in the plane then yields representations for the contaminant concentration in both regions in terms of an integral of the initial concentration over the region's interior and integrals along the boundaries of known quantities and the unknown interfacial flux between the two adjacent media. This flux is given by a first-kind integral equation, which can be solved numerically by a discretisation technique. Examples of contaminant transport in fractured porous media systems are presented.
Flux ratios for biological membranes and reciprocity theorems for linear operators
Authors: Bracken A. J. , Holmåker K. , Maloney L. V. , Bass L.
Published: February 2009

The constancy in time of the ratio of unidirectional tracer fluxes, passing in opposite directions through a membrane that has transport properties varying arbitrarily with the distance from a boundary face, has been established recently for successively more sophisticated mathematical models of tracer transport within the membrane. Such results are important in that, when constancy is not observed experimentally, inferences can be drawn about the dimensionality of distributions of transport properties of the membrane. The known theoretical results are shown here to follow from much more general theorems, valid for a wide class of models based on linear-operator equations, including elliptic and hyperbolic partial differential equations as well as the essentially parabolic equations of interest in membrane transport problems. These theorems have the general character of “reciprocity theorems” known for a long time in other areas, such as mechanics, acoustics and elasticity. The general results obtained here clarify the conditions on membrane properties under which constancy of a flux ratio can be expected. In addition, flux ratio theorems of a new type are proved to hold under suitable conditions, for the normal components of flux vectors at points on either side of a membrane, as distinct from previously established theorems for total fluxes through membrane faces. Possible new experiments are suggested by the analysis.
Exact solutions of nonlinear evolution equations of the AKNS class
Authors: Chan W. L. , Zheng Yu-Kun
Published: February 2009

The problem of obtaining explicit and exact solutions of soliton equations of the AKNS class is considered. The technique developed relies on the construction of the wave functions which are solutions of the associated AKNS system; that is, a linear eigenvalue problem in the form of a system of first order partial differential equations. The method of characteristics is used and Bäcklund transformations are employed to generate new solutions from the old. Thus, families of new solutions for the KdV equation, the mKdV equation, the sine-Gordon equation and the nonlinear Schrôdinger equation are obtained, avoiding the solution of some Riccati equations. Our results in the KdV case include those obtained recently by other investigators.
The wave resistance formula of J.H. Michell (1898) and Its significance to recent research in ship hydrodynamics
Authors: Tuck E. O.
Published: February 2009

John Henry Michell (1863–1940) published scientific papers only between 1890 and 1902, but included in his 23 papers from that short but productive period are some of the most important contributions ever made by an Australian mathematician. In this article I shall concentrate on the extraordinary 1898 paper “The wave resistance of a ship” Phil. Mag.(5) 45, 106–123. There are many reasons why this paper was an astounding achievement, but perhaps the most remarkable is that the resulting formula has not been improved upon to this day. In the computer age, many efforts have been made to do so, but with little success so far. The formula itself involves a triple integral of an integrand constructed from the offset data for the ship's hull, and even the task of evaluating this triple integral is not a trivial one on today's computers; another reason for admiration of Michell's own heroic hand-calculated numerical work in the 1890's. Lack of a routine algorithm for Michell's integral has inhibited its use by naval architects and ship hydrodynamic laboratories, and there has been a tendency for it to receive a bad press based on unfair comparisons, e.g. comparison of model experiments (themselves often suspect) with inaccurate computations or computations for the wrong hull, etc. The original integral is in fact quite reasonable as an engineering tool, and some new results confirming this are shown. Improvement beyond Michell is however needed in some important speed ranges, and indications are given of recent approaches that may be promising.
A functional differential equation arising in modelling of cell growth
Authors: Hall A. J. , Wake G. C.
Published: February 2009

A functional differential equation for the steady size distribution of a population is derived from the usual partial differential equation governing the size distribution, in the particular case where birth occurs by one individual of size x dividing into α new individuals of size x/α. This leads, in the case of constant growth and birth rate functions, to the functional differential equation y′(x) = −ay(x) + aαy(αx) together with the integral condition We first look at a number of properties that any solution of this equation and boundary condition must have, and then proceed to find the unique solution by the method of Laplace transforms. Results from number theory on the infinite product found in the solution are presented, and it is shown that y(x) tends to a normal distribution as α → 1+.
Correction of finite difference eigenvalues of periodic Sturm-Liouville problems
Authors: Andrew Alan L.
Published: February 2009

Computation of eigenvalues of regular Sturm-Liouville problems with periodic or semiperiodic boundary conditions is considered. A simple asymptotic correction technique of Paine, de Hoog and Anderssen is shown to reduce the error in the centred finite difference estimate of the kth eigenvalue obtained with uniform step length h from O(k4h2) to O(kh2). Possible extensions of the results are suggested and the relative advantages of the method are discussed.
Optimal control problems with elastic collisions
Authors: Murray J. M.
Published: February 2009

In this paper consider we optimal control problems with linear state constraints where the states can be discontinuous at the boundary. In fact the state vector models the cause the position and velocity of a particle where the collisions with the boundary that cause the discontinuities are elastic. Necessary conditions are derived by looking at limits of approximate problems that are unconstrained.
Sufficient optimality criteria and duality for variational problems with generalised invexity
Authors: Mond B. , Husain I.
Published: February 2009

A number of Kuhn-Tucker type sufficient optimality criteria for a class of variational problems under weaker invexity assumptions are presented. As an application of these optimality results, various Mond-Weir type duality results are proved under a variety of generalised invexity assumptions. These results generalise many well-known duality results of variational problems and also give a dynamic analogue of certain corresponding (static) results relating to duality with generalised invexity in mathematical programming.
Sensitivity bounds on a GI/M/n/n queueing system
Authors: Coyle Andrew
Published: February 2009

A method for determining the upper and lower bounds for performance measures for certain types of Generalised Semi-Markov Processes has been described in Taylor and Coyle [8]. A brief description of this method and its use in finding an upper bound for the time congestion of a GI/M/n/n queueing system will be given. This bound turns out to have a simple form which is quickly calculated and easy to use in practice.
A mathematical model and related problems of optimal management and design in a broadband integrated services network
Authors: Evans Suzanne P.
Published: February 2009

This paper describes a mathematical model for a broadband integrated services network offered traffic of many different types. Performance measures are introduced related to revenue generation and overall grade-of-service, providing criteria for the optimal management of resources. Simple asymptotic expressions are derived for quantities termed the “implied costs”, which measure the effect on performance of changes in parameters that are controllable by network management, or that are subject to variation. These implied costs may be used, both to implement optimal bandwidth allocation polices, and also to indicate which services may share a single facility without adversely affecting performance, and which might require a dedicated facility. Asymptotic results are also used to examine how to make efficient use of capacity that is shared between calls with fluctuating bit-rate requirements.
A net level performance analysis of stochastic Petri nets
Authors: Henderson W. , Lucic D. , Taylor P. G.
Published: February 2009

Stochastic Petri Nets are used extensively to find performance measures for communication protocols. This paper illustrates how equilibrium distributions for the markings of a wide class of nets can be found directly without the need to generate a large state space and then resort to equilibrium balance equations.
Fixed point models of loss networks
Authors: Kelly F. P.
Published: February 2009

In this paper we review a simple class of fixed point models for loss networks. We illustrate how these models can readily deal with heterogeneous call types and with simple dynamic routing strategies, and we outline some of the recent mathematical advances in the study of such models. We describe how fixed point models lead to a natural and tractable definition of the implied cost of carrying a call, and how this concept is related to issues of routing and capacity expansion in loss networks.
Monotone iterations for nonlinear obstacle problem
Authors: Korman Philip , Leung Anthony W. , Stojanovic Srdjan
Published: February 2009

The existence, uniqueness and regularity of solutions are proved for the obstacle problem with semilinear elliptic partial differential equations of second order. Computationally effective algorithms are provided and application made to steady state problem for the logistic population model with diffusion and an obstacle to growth.
Degenerate forms of Maxwell's equations
Authors: Carey A. L. , McNamara K.
Published: February 2009

This paper studies degenerate forms of Maxwell's equations which arise from approximations suggested by geophysical modelling problems. The approximations reduce Maxwell's equations to degenerate elliptic/parabolic ones. Here we consider the questions of existence, uniqueness and regularity of solutions for these equations and address the problem of showing that the solutions of the degenerate equations do approximate those of the genuine Maxwell equations.
The numerical solution of Hammerstein equations by a method based on polynomial collocation
Authors: Kumar Sunil
Published: February 2009

In recent papers we have considered the numerical solution of the Hammerstein equation

by a method which first applies the standard collocation procedure to an equivalent equation for z(t):= g(t, y(t)), and then obtains an approximation to y by use of the equation

In this paper we approximate z by a polynomial zn of degree ≤ n − 1, with coefficients determined by collocation at the zeros of the nth degree Chebyshev polynomial of the first kind. We then define the approximation to y to be

and establish that, under suitable conditions, , uniformly in t.
Nonlinear oscillations and buckling of anisotropic cylindrical shells under large initial stresses
Authors: Bera Rasajit Kumar
Published: February 2009

The large-amplitude oscillations and buckling of an anisotropic cylindrical shell subjected to the initial inplane biaxial normal stresses have been analysed. The concept of anisotropy used by Lekhnitsky has been introduced into the field equations for cylindrical shells of isotropic material deduced by Donnell. The method of Galerkin and the method of successive approximation have been used to obtain the desired approximate solution. The expression for the critical loads for the buckling of anisotropic cylindrical shells has been obtained during intermediate stages of analysis. Some relevant frequency response graphs of the obtained solution are also presented. The minimum critical loads for various classes of anisotropy have also been given at the end of the discussion, to exhibit the effects of large deflections and imperfections on elastic buckling.
Persistence and extinction in a predator-prey model consisting of nine prey genotypes
Authors: So Joseph W.-H.
Published: February 2009

A predator-prey model in which the prey population is subdivided into nine genotypes corresponding to a two-locus, two-allele problem is considered. Sufficient conditions are given which lead to extinction of all the prey allele types except one, as well as conditions which guarantee the persistence of all the allele types.
The isotropy mappings of Minkowski space-time generate the orthochronous poincaré group
Authors: Schutz John W.
Published: February 2009

Minkowski space-time is specified with respect to a single coordinate frame by the set of timelike lines. Isotropy mappings are defined as automorphisms which leave the events of one timelike line invariant. We demonstrate the existence of two special types of isotropy mappings. The first type of isotropy mapping induce orthogonal transformations in position space. Mappings of the second type can be composed to generate Lorentz boosts. It is shown that isotropy mappings generate the orthochronous Poincaré group of motions. The set of isotropy mappings then maps the single assumed coordinate frame onto a set of coordinate frames related by transformations of the orthochronous Poincaré group.
A boundary-integral method applied to water coning in oil reservoirs
Authors: Lucas S. K. , Blake J. R. , Kucera A.
Published: February 2009

In oil reservoirs, the less-dense oil often lies over a layer of water. When pumping begins, the oil-water interface rises near the well, due to the suction pressures associated with the well. A boundary-integral formulation is used to predict the steady interface shape, when the oil well is approximated by a series of sources and sinks or a line sink, to simulate the actual geometry of the oil well. It is found that there is a critical pumping rate, above which the water enters the oil well. The critical interface shape is a cusp. Efforts to suppress the cone by using source/sink combinations are presented.
A pair of arbitrarily-oriented coplanar cracks in an anisotropic elastic slab
Authors: Ang W. T.
Published: February 2009

The problem of an anisotropic elastic slab containing two arbitrarily-oriented coplanar cracks in its interior is considered. Using a Fourier integral transform technique, we reduce the problem to a system of simultaneous finite-part singular integral equations which can be solved numerically. Once the integral equations are solved, relevant quantities such as the crack energy can be readily computed. Numerical results for specific examples are obtained.
Some integrals involving Legendre polynomials providing combinatorial identities
Authors: Klemm Anthony D. , Larsen Sigurd Y.
Published: February 2009

An integral involving a combination of Legendre polynomials, exponential and algebraic terms is solved using the generating function. Special cases of this result are compared with known expansions, and the previously known results are shown to be extendible to a particularly pleasing result as a limiting case. Comparisons provide some new combinatorial identities involving binomials. Finally, an effective numerical procedure is described which evaluates the integral to machine accuracy.
Poisson approximations for telecommunications networks
Authors: Brown T. C. , Pollett P. K.
Published: February 2009

In this paper, we review some techniques for studying traffic processes in telecommunications networks. The first of these allows one to identify Poisson traffic via the notion of “deterministic past-conditional arrival rate”. Our approach leads to a method by which one can assess the degree of deviation of traffic processes from Poisson processes. We explain how this can be used to delimit circumstances under which traffic is approximately Poissonian.
Sudden cardiac arrest and a problem in topology
Authors: Morris Sidney A. , Nyikos Peter J.
Published: February 2009

In the May 1983 issue of Scientific American, A.T. Winfree published an article which gave an explanation of sudden cardiac arrest in terms of topology. His topological argument was modified in his 1987 book called “When time breaks down”. In this paper we fill what appears to be a gap in Winfree's topological arguments.
Spectral factorisation and prediction of multivariate processes with time-dependent rational spectral density matrices
Authors: Spencer N. M. , Anh V. V.
Published: February 2009

This paper considers discrete multivariate processes with time-dependent rational spectral density matrices and gives a solution to the spectral factorisation problem. As a result, the corresponding state space representation for the process is obtained. The relationship between multivariate processes with time-dependent rational spectral density matrix functions and multivariate ARMA processes with time-dependent coefficients is discussed. Solutions for the prediction problem are given for the case when only finite data is available and the case when the whole history of the process is known.
A method for the study of fully developed parallel flow in straight ducts of arbitrary cross section
Authors: Mazumdar J. , Dubey R. N.
Published: February 2009

A method is presented for the study of fully developed parallel flow of Newtonian viscous fluid in uniform straight ducts of very general cross-section. The method is based upon the concept of contour lines of constant velocity in a typical cross section of the duct, and uses the function which describes the contour lines as an independent variable to derive the integral momentum equation. The resulting ordinary integro-differential equation is, in principle, much easier to solve than the original momentum equation in partial differential equation form. Several illustrative examples of practical interest are included to explain the method of solution. Some of these solutions are compared with available solutions in the literature. All details are explained by graphs and tables. The method has several interesting features. The study has relevance to biomedical engineering research for blood and urinary tract flow.
Ground motion on alluvial valleys under incident plane SH waves
Authors: Clements David L. , Larsson Ashley
Published: February 2009

The scattering and diffraction of harmonicSHwaves by an arbitrarily shaped alluvial valley in a layered material is considered. The problem is solved in terms of boundary integral equations which yield a numerical solution.
Local transformations between some nonlinear diffusion equations
Authors: King J. R.
Published: February 2009

We derive local transformations mapping radially symmetric nonlinear diffusion equations with power law or exponential diffusivities into themselves or into other equations of a similar form. Both discrete and continuous transformations are considered. For the cases in which a continuous transformation exists, many additional forms of group-invariant solution may be constructed; some of these solutions may be written in closed form. Related invariance properties of some multidimensional diffusion equations are also exploited.
Critical initial conditions for spatially-distributed thermal explosions
Authors: Lacey A. A. , Wake G. C.
Published: February 2009

The problem of finding critical initial data which separate conditions leading to blow-up from those which give solutions tending to the (stable) minimal solution is considered. New criteria for blow-up and global existence are found; these are equivalent to obtaining upper and lower bounds respectively for the set of critical initial data.
Exact nonlinear solution for constant-rate expression from material of finite thickness
Authors: Broadbridge P. , Banksa P. J.
Published: February 2009

We present new exact solutions for the flow of liquid during constant-rate expression from a finite thickness of liquid-saturated porous material with nonlinear properties. By varying a single nonlinearity parameter and a dimensionless expression rate, we systematically investigate the effect of nonlinearity and of an impermeable barrier (e.g. a piston). We illustrate the water profile shape and the water ratio deficit at the expression surface (e.g. a filter membrane) as a function of time.
Interaction of buoyant plumes in open-channel flow
Authors: Wicks P. J.
Published: February 2009

In this paper, a model for lateral dispersion in open-channel flow is studied involving a diffusion equation which has a nonlinear term describing the effect of buoyancy. The model is used to investigate the interaction of two buoyant pollutant plumes. An approximate analytic technique involving Hermite polynomials is applied to the resulting PDEs to reduce them to a system of ODEs for the centroids and widths of the two plumes. The ODEs are then solved numerically. A rich variety of behaviour occurs depending on the relative positions, widths and strengths of the initial discharges. It is found that for two plumes of equal strength and width discharged side-by-side, the plumes move apart and the rate of spreading is inhibited by their interaction, whereas when one plume is initially much wider than the other, both plumes tend to drift to the side of the narrower plume. Finally, the PDEs are solved numerically for two sets of initial conditions and a comparison is made with the ODE solutions. Agreement is found to be good.
Cooling of an infinite slab in a two-fluid medium
Authors: Bera R. K. , Chakrabarti A.
Published: February 2009

A mixed boundary-valued problem associated with the diffusion equation, that involves the physical problem of cooling of an infinite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speed. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming one layer of the fluid to be of finite extent and the other of infinite extent. The main problem is solved through a three-part Wiener-Hopf problem of a special type, and the numerical results under certain special circumstances are obtained and presented in the form of a table.
Normal forms for elements of o(p, q) and Hamiltonians with integrals linear in momenta
Authors: Thompson Gerard
Published: February 2009

We solve the problem of finding a simultaneous matrix normal form for an element of the Lie algebra o(p, q) and the underlying indefinite inner product. The results are used to determine several classes of classical Hamiltonian dynamical systems which possess a first integral linear in the momentum variables.
Duality without constraint qualification for multiobjective programming
Authors: Egudo R. R. , Weir T. , Mond B.
Published: February 2009

Extending earlier duality results for multiobjective programs, this paper defines dual problems for convex and generalised convex multiobjective programs without requiring a constraint qualification. The duals provide multiobjective extensions of the classical duals of Wolfe and Schechter and some of the more recent duals of Mond and Weir.
Braess's paradox and power-law nonlinearities in networks
Authors: Calvert Bruce , Keady Grant
Published: February 2009

We study flows in physical networks with a potential function defined over the nodes and a flow defined over the arcs. The networks have the further property that the flow on an arc a is a given increasing function of the difference in potential between its initial and terminal node. An example is the equilibrium flow in water-supply pipe networks where the potential is the head and the Hazen-Williams rule gives the flow as a numerical factor ka times the head difference to a power s > 0 (and s ≅ 0.54). In the pipe-network problem with Hazen-Williams nonlinearities, having the same s > 0 on each arc, given the consumptions and supplies, the power usage is a decreasing function of the conductivity factors ka. There is also a converse to this. Approximately stated, it is: if every relationship between flow and head difference is not a power law, with the same s on each arc, given at least 6 pipes, one can arrange (lengths of) them so that Braess's paradox occurs, i.e. one can increase the conductivity of an individual pipe yet require more power to maintain the same consumptions.
A finite element method for a diffusion equation with constrained energy and nonlinear boundary conditions
Authors: Pani Amiya K.
Published: February 2009

A finite element Galerkin method for a diffusion equation with constrained energy and nonlinear boundary condition is analysed and optimal error estimates in L2 and L∞-norms are derived. These results improve upon previously derived estimates by Cannon et al. [4].
Bow flows with smooth separation in water of finite depth
Authors: Hocking G. C.
Published: February 2009

The bow flow generated by a wide flat-bottomed ship moving in water of finite depth is examined. Solutions obtained using an integral equation technique are presented for a range of different depths and for a range of angles of the front of the bow. The solution for the limiting case of infinite Froude number is obtained as an integral, and numerical solutions are found for the nonlinear problem in which the Froude number is finite. Solutions with smooth separation are shown to exist for all values of Froude number greater than unity, for any bow slope.
Computer-controlled variable-structure systems
Authors: Yu Xinghuo , Potts Renfrey B.
Published: February 2009

A theory is developed for the computer control of variable-structure systems, using periodic zero-order-hold sampling. A simple two-dimensional system is first analysed, and necessary and sufficient conditions for the occurrence of pseudo-sliding modes are discussed. The method is then applied to a discrete model of a cylindrical robot. The theoretical results are illustrated by computer simulations.
Controllability of neutral Volterra integrodifferential systems
Authors: Balachandran K.
Published: February 2009

Sufficent conditions for controllability of nonlinear neutral Volterra integrodifferential systems are established. Controllability of an infinite-delay neutral Volterra system is also considered.
An extremal problem concerning finite dimensional subspaces of C[a, b] pertinent in signal theory
Authors: Halpern P. H. , Mohapatra R. N. , O'Hara P. J. , Rodriguez R. S.
Published: February 2009

Increase in dimensionality of the signal space for a fixed bandwidth leads to exponential growth in the number of different signals which must be encoded. In this paper we determine the best subspace of orthogonal functions which can be used to minimise the worst ratio of peak power to RMS power. A mathematical formulation of this problem has been made and it has been found that the Fourier basis satisfies the required constraints of optimality in terms of form factor (peak/RMS ratio).
Boundary conditions for approximate differential equations
Authors: Roberts A. J.
Published: February 2009

A large number of mathematical models are expressed as differential equations. Such models are often derived through a slowly-varying approximation under the assumption that the domain of interest is arbitrarily large; however, typical solutions and the physical problem of interest possess finite domains. The issue is: what are the correct boundary conditions to be used at the edge of the domain for such model equations? Centre manifold theory [24] and its generalisations may be used to derive these sorts of approximations, and higher-order refinements, in an appealing and systematic fashion. Furthermore, the centre manifold approach permits the derivation of appropriate initial conditions and forcing for the models [25, 7]. Here I show how to derive asymptotically-correct boundary conditions for models which are based on the slowly-varying approximation. The dominant terms in the boundary conditions typically agree with those obtained through physical arguments. However, refined models of higher order require subtle corrections to the previously-deduced boundary conditions, and also require the provision of additional boundary conditions to form a complete model.
The transition through resonance of a nonlinear non-autonomous system
Authors: Chapman P. B.
Published: February 2009

An approximate nonlinear perturbation analysis for the re-entry roll resonance model is given. The results are used to identify the dynamic processes involved, as characterised by terms in the model equations, and to suggest a prudent management rule for this and similar transiently-resonant systems.
A new form of Jensen's inequality and its application to statistical experiments
Authors: Nonnenmacher D. J. F. , Zagst R.
Published: February 2009

Jensen's inequality for the expectation of a convex function of a random variable is proved for a wide class of convex functions defined on a space of probability measures. The result is applied to statistical experiments using the concept of Blackwell-sufficiency. In particular, we show a monotonicity result for the expected information of Poisson-experiments. As an application to economics we consider the introduction of new production technologies.
Fast diffusion with loss at infinity
Authors: Philip J. R.
Published: February 2009

We study the equation

Here s is not necessarily integral; m is initially unrestricted. Material-conserving instantaneous source solutions of A are reviewed as an entrée to material-losing solutions. Simple physical arguments show that solutions for a finite slug losing material at infinity at a finite nonzero rate can exist only for the following m-ranges: 0 < s < 2, −2s−1 < m ≤ −1; s > 2, −1 < m < −2s−1. The result for s = 1 was known previously. The case s = 2, m = −1, needs further investigation. Three different similarity schemes all lead to the same ordinary differential equation. For 0 < s < 2, parameter γ (0 < γ < ∞) in that equation discriminates between the three classes of solution: class 1 gives the concentration scale decreasing as a negative power of (1 + t/T); 2 gives exponential decrease; and 3 gives decrease as a positive power of (1 − t/T), the solution vanishing at t = T < ∞. Solutions for s = 1, are presented graphically. The variation of concentration and flux profiles with increasing γ is physically explicable in terms of increasing flux at infinity. An indefinitely large number of exact solutions are found for s = 1,γ = 1. These demonstrate the systematic variation of solution properties as m decreases from −1 toward −2 at fixed γ.
A nonmonotone inexact Newton algorithm for nonlinear systems of equations
Authors: Xiao Yi , Chu Eric King-Wah
Published: February 2009

In this paper, an inexact Newton's method for nonlinear systems of equations is proposed. The method applies nonmonotone techniques and Newton's as well as inexact Newton's methods can be viewed as special cases of this new method. The method converges globally and quadratically. Some numerical experiments are reported for both standard test problems and an application in the computation of Hopf bifurcation points.
The Hadamard product of two Brownian matrices: Analytic inverse and determinant
Authors: Valvi F. N.
Published: February 2009

The explicit inverse and determinant of a class of matrices is given. The class is the Hadamard product of two already known classes. Its elements are defined by 3n − 1 parameters, analytical expressions of which compose the Hessenberg form inverse. These expressions enable a recursive formula to be obtained, which gives the inverse in O(n2) multiplications/divisions and O(n) additions/subtractions.
On Gerchberg's method for the Fourier inverse problem
Authors: Connolly T. J. , Landman K. A. , White L. R.
Published: February 2009

If a finite segment of a spectrum is known, the determination of the finite object function in image space (or the full spectrum in frequency space) is a fundamental problem in image analysis. Gerchberg's method, which solves this problem, can be formulated as a fixed point iteration. This and other related algorithms are shown to be equivalent to a steepest descent method applied to the minimization of an appropriate functional for the Fourier Inversion Problem. Optimal steepest descent and conjugate gradient methods are derived. Numerical results from the application of these techniques are presented. The regularization of the problem and control of noise growth in the iteration are also discussed.
General iterative methods for nonlinear boundary value problems
Authors: Shridharan Radha , Agarwal Ravi P.
Published: February 2009

In this paper we shall develop existence-uniqueness as well as constructive theory for the solutions of systems of nonlinear boundary value problems when only approximations of the fundamental matrix of the associated homogeneous linear differential systems are known. To make the analysis widely applicable, all the results are proved component-wise. An illustration which dwells upon the sharpness as well as the importance of the obtained results is also presented.
Asymptotic behaviour of the spectrum of a direct feedback control system
Authors: Guo Bao Zhu
Published: February 2009

This paper establishes an estimate for the asymptotic behaviour of the spectrum of a direct strain feedback (DSF) control system. The results show that the system operator corresponding to the closed loop system cannot have an analytic extension and that the decay rate for the system energy is not proportional to the feedback constant.
Geomatric ergodicity and quasi-stationarity in discrete-time birth-death processes
Authors: van Doorn Erik A. , Schrijner Pauline
Published: February 2009

We study two aspects of discrete-time birth-death processes, the common feature of which is the central role played by the decay parameter of the process. First, conditions for geometric ergodicity and bounds for the decay parameter are obtained. Then the existence and structure of quasi-stationary distributions are discussed. The analyses are based on the spectral representation for the n-step transition probabilities of a birth-death process developed by Karlin and McGregor.
Using fractal geometry for solving divide-and-conquer recurrences
Authors: Dube Simant
Published: February 2009

A relationship between the fractal geometry and the analysis of recursive (divide-and-conquer) algorithms is investigated. It is shown that the dynamic structure of a recursive algorithm which might call other algorithms in a mutually recursive fashion can be geometrically captured as a fractal (self-similar) image. This fractal image is defined as the attractor of a mutually recursive function system. It then turns out that the Hausdorff-Besicovich dimension D of such an image is precisely the exponent in the time complexity of the algorithm being modelled. That is, if the Hausdorff D-dimensional measure of the image is finite then it serves as the constant of proportionality and the time complexity is of the form Θ(nD), else it implies that the time complexity is of the form Θ(nD logpn), where p is an easily determined constant.
Derivatives of addition theorems for Legendre functions
Authors: Winch D.E. , Roberts P.H.
Published: February 2009

Differentiation of the well-known addition theorem for Legendre polynomials produces results for sums over order m of products of various derivatives of associated Legendre functions. The same method is applied to the corresponding addition theorems for vector and tensor spherical harmonics. Results are also given for Chebyshev polynomials of the second kind, corresponding to ‘spin-weighted’ associated Legendre functions, as used in studies of distributions of rotations.
The EM response due to a plane sheet of arbitrary shape and conductivity profile
Authors: Hurley D. G. , Siew P. F.
Published: February 2009

The eddy currents induced in a thin sheet of variable conductivity by a sinusoidally varying primary magnetic field are investigated in the low frequency limit when the depth of penetration of the primary field is much greater than the thickness of the sheet. The problem is formulated in terms of a set of integro-differential equations. The method of solution is applicable to bodies with arbitrary planar shape and the result is particularly useful in inverse problems involving bodies with conductivity inhomogeneities.
On the acoustic scattering amplitude for a multi-layered Scatterer
Authors: Athanasiadis Christodoulos
Published: February 2009

We consider the boundary-value problems corresponding to the scattering of a time-harmonic acoustic plane wave by a multi-layered obstacle with a sound-soft, hard or penetrable core. Firstly, we construct in closed forms the normalized scattering amplitudes and prove the classical reciprocity and scattering theorems for these problems. These results are then used to study the spectrum of the scattering amplitude operator. The scattering cross-section is expressed in terms of the forward value of the corresponding normalized scattering amplitude. Finally, we develop a more general theory for scattering relations.
Optimal consumption/portfolio choice with borrowing rate higher than deposit rate
Authors: Xu Wensheng , Chen Shuping
Published: February 2009

In this paper, optimal consumption and investment decisions are studied for an investor who has available a bank account and a stock whose price is a log normal diffusion. The bank pays at an interest rate r(t) for any deposit, and vice takes at a larger rate r′(t) for any loan. Optimal strategies are obtained via Hamilton-Jacobi-Bellman (HJB) equation which is derived from dynamic programming principle. For the specific HARA case, we get the optimal consumption and optimal investment explicitly, which coincides with the classical one under the condition r′(t) ≡ r(t)
On the integrability and exact solutions of the nonlinear diffusion equation with a nonlinear source
Authors: Vijayakumar K.
Published: February 2009

The generalized diffusion equation with a nonlinear source term which encompasses the Fisher, Newell-Whitehead and Fitzhugh-Nagumo equations as particular forms and appears in a wide variety of physical and engineering applications has been analysed for its generalized symmetries (isovectors) via the isovector approach. This yields a new and exact solution to the generalized diffusion equation. Further applications of group theoretic techniques on the travelling wave reductions of the Fisher, Newell-Whitehead and Fitzhugh-Nagumo equations result in integrability conditions and Lie vector fields for these equations. The Lie group of transformations obtained from the exponential vector fields reduces these equations in generalized form to a standard second-order differential equation of nonlinear type, which for particular cases become the Weierstrass and Jacobi elliptic equations. A particular solution to the generalized case yields the exact solutions that have been obtained through different techniques. The group-theoretic integrability relations of the Fisher and Newell-Whitehead equations have been cross-checked through Painlevé analysis, which yields a new solution to the Fisher equation in a complex-valued function form.
The effect of surface tension in porous wave maker problems
Authors: Chakrabarti A. , Sahoo T.
Published: February 2009

Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.