bluuebunny/crossref_metadata_2025_split huggingface dataset:
Boundary value controllability and observability problems for the wave and heat equation
Authors: Werner K.-D. 
Published: February 2009

AbstractIn this paper, we study controllability and observability problems for the wave and heat equation in a spherical region in Rn, where the control enters in the mixed boundary condition. In the main result, we show that all “finite energy” initial states (i.e. (ω0, ν0) ∈ H1(Ω) × L2 (Ω)) can be steered to zero at time T, using a control f ∈ L2 (∂Ω × [0, T]), provided T > 2. On this basis, we use the duality principle to investigate initial observability for the wave equation. Applying the Fourier transform technique, we obtain controllability and observability results for the heat equation.
Assessing regularised solutions
Authors: Lukas M. A. 
Published: February 2009

AbstractConsider the prototype ill-posed problem of a first kind integral equation ℛ with discrete noisy data di, = f(xi) + εi, i = 1, …, n. Let u0 be the true solution and unα a regularised solution with regularisation parameter α. Under certain assumptions, it is known that if α → 0 but not too quickly as n → ∞, then unα converges to u0. We examine the dependence of the optimal sequence of α and resulting optimal convergence rate on the smoothness of f or u0, the kernel K, the order of regularisation m and the error norm used. Some important implications are made, including the fact that m must be sufficiently high relative to the smoothness of u0 in order to ensure optimal convergence. An optimal filtering criterion is used to determine the order where is the maximum smoothness of u0. Two practical methods for estimating the optimal α, the unbiased risk estimate and generalised cross validation, are also discussed.
A flexible strategy for warring duopolists
Authors: Rickard John , Hathaway Neville 
Published: February 2009

AbstractThe behaviour of duopolists is considered within a framework that allows for flexibility of the adopted strategy against the rival. In a difficult external climate, a firm may concentrate on its own profit, whereas in a more favourable external climate, it may adopt a more aggressive attitude towards the rival. The strategy considered in this paper permits this flexible approach. The market functions are kept general to allow the widest interpretation of the results.
Groups defined on images in fluid diffusion
Authors: Bracken A. J. , Green H. S. , Bass L. 
Published: February 2009

AbstractA method based on the method of images is described for the solution of the linear equation modelling diffusion and elimination of substrate in a fluid flowing through a chemical reactor of finite length, when the influx of substrate is prescribed at the point of entry and Danckwerts' zero-gradient condition is imposed at the point of exit. The problem is shown to be transformable to an equivalent problem in heat conduction. Associated with the images appearing in the method of solution is a sequence of functions which form a vector space carrying a representation of the Lie group SO(2, 1) generated by three third-order differential operators. The functions are eigenfunctions of one of these operators, with integer-spaced eigenvalues, and they satisfy a third-order recurrence relation which simplifies their successive determination, and hence the determination of the Green's function for the problem, to any desired degree of approximation. Consequently, the method has considerable computational advantages over commonly used methods based on the use of Laplace and related transforms. Associated with these functions is a sequence of polynomials satisfying the same third-order differential equation and recurrence relation. The polynomials are shown to bear a simple relationship to Laguerre polynomials and to satisfy the ordinary diffusion equation, for which SO(2, 1) is therefore revealed as an invariance group. These diffusion polynomials are distinct from the well-known heat polynomials, but a relationship between them is derived. A generalised set of diffusion polynomials, based on the associated Laguerre polynomials, is also described, having similar properties.
A mathematical model for the process of gas exchange in lung capillaries usingnth order one-step kinetics of oxygen uptake by haemoglobin
Authors: Sharan Maithili , Singh M. P. , Singh Balbir 
Published: February 2009

AbstractA mathematical model is developed for the process of gas exchange in lung capillaries, taking into account the transport mechanisms of molecular diffusion and the facilitated diffusion of the species due to haemoglobin. We have assumed here equilibrium conditions which enable us to neglect advection effects. Thenth order one-step kinetics of oxygen uptake by haemoglobin, proposed by Sharan and Singh [8], have been incorporated. The solution of this coupled nonlinear facilitated diffusion-reaction problem together with the physiologically-relevant boundary conditions is obtained in the closed form.It is found that about 97.15% of total haemoglobin has combined with oxygen and 2.85% free pigment is left, which is present as carbaminohaemoglobin, met haemoglobin, carboxy haemoglobin etc. It is also shown that the percentage of free haemoglobin at a givenPO2andPCO2is independent of total haemoglobin content present in the blood.The well-known Hill's empirical relation is deduced from our solution. The results obtained from our model, based on physical formulation, are in good agreement with the documented data [6] and those computed from the Kelman [3] empirical relation.
Dominated strategies in searching for evolutionary stable strategies
Authors: Breen P. , Henderson W. 
Published: February 2009

AbstractThe paper asks and answers the question “When does dominance of a particular strategy play a role in the search for evolutionary stable strategies?” The answer is much less obvious than would appear at first glance.When there is strict dominance of a pure strategy, it is clear that the dominated strategy should never be employed in any conflict. However, when the dominance is not strict it is less obvious that the strategy should not be used. The research was originally intended to clear up this grey area in the theory of evolutionary stable strategies, but it has turned out to be of more than simply academic interest. The result can be used, with varying degrees of success, to simplify the search procedure for these evolutionary stable strategies when a reward matrix is given.
An application of the homotopy method to the generalised symmetric eigenvalue problem
Authors: Lin Wen-Wei , Lutzer Gerhard 
Published: February 2009

AbstractThe homotopy method is used to find all eigenpairs of a generalised symmetric eigenvalue problem Ax = λBx with positive definite B. The determination of n eigenpairs (x, λ) is reduced to curve tracing of n disjoint smooth curves in Rn × R × [0, 1]. The method might be attractive if A and B are sparse symmetric. In this paper it is shown that the method will work for almost all symmetric tridiagonal matrices A and B.
Some remarks on Pauli data in quantum mechanics
Authors: Friedman Charles. N. 
Published: February 2009

AbstractThe problem of determining a square integrable function from its modulus and that of its Fourier transform has been considered in an article by Corbett and Hurst ([1]). In this work we point out an error in one of the main results of the cited article concerning the Pauli uniqueness of real states, provide a proof of uniqueness for non-negative states, and present various related examples and discussion of the problem.
Duality between distant point and median of a tree network space
Authors: Kulshrestha D. K. 
Published: February 2009

AbstractA point on a tree network space is said to be a distant point if it maximises its minimum weighted distance from any of its vertices. The median minimises the sum of its weighted distances from the vertices. In this paper two constrained problems are discussed. The first problem is to maximise the minimum of the weighted distances from the vertices subject to an upper bound value of the sum of the weighted distances from the vertices, while the second problem is to minimise the sum of the weighted distances subject to a lower bound value of the minimum weighted distance to any of its vertices. It is shown that these two constrained problems are duals of each other in a well defined sense.
A computational method for combined optimal parameter selection and optimal control problems with general constraints
Authors: Teo K. L. , Goh C. J. 
Published: February 2009

AbstractIn this paper, we consider a class of combined optimal parameter selection and optimal control problems with general constraints. The first aim is to provide a unified approach to the numerical solution of this general class of optimisation problems by using the control parametrisation technique. This approach is supported by some convergence results. The second aim is to show that several different classes of optimal control problems can all be transformed into special cases of the problem considered in this paper. For illustration, four numerical examples are presented.
An analysis of the impact of T. M. Cherry's work on asymptotic expansions
Authors: Grimshaw R. 
Published: February 2009

AbstractDuring the late 1940s, T. M. Cherry published a series of research papers on uniform asymptotic formulae for transition points in ordinary differential equations. This work, together with his research into transonic gas flows, for which it was a necessary precursor, is probably his best known and most widely quoted piece of research. An analysis is made of the impact of Cherry's work on subsequent developments in this field, both in comparison to the work of others and with respect to Cherry's work on other topics.
Mathematical research at the Aeronautical Research Laboratories 1939–1960
Authors: Hurley D. G. 
Published: February 2009

AbstractThe Aeronautical Research Laboratories were established in Australia in 1939 as the CSIR Division of Aeronautics. Mathematicians were amongst the first staff employed, and their number reached a peak in the mid 1950s. They were an able group: in their subsequent careers 12 became Professors, 5 obtained higher doctorates, 6 became Fellows of the Australian Academy of Science and 6 Fellows of the Royal Society. They published over 100 papers, and these are discussed here under 11 separate headings.The length of discussion given here to the various areas of research is not uniform. I have emphasised those with which I am familiar and those that interest me personally. Nevertheless, I believe the present paper provides an accurate picture of the mathematical research that was carried out at ARL during the period under review, and makes it clear that mathematicians at ARL made substantial contributions to many areas of theoretical aeronautics.
On generalised toroidal-poloidal solutions of vector field equations
Authors: Ivers D. J. 
Published: February 2009

AbstractThe orthogonal coordinate systems ξi(i = 1, 2, 3) are determined, in which the gneralised toroidal and poloidal fields, defined respectively by T{T} = ∇ × {T∇ξ1} and S{S} = ∇ × T{S}, have the following three properties:GP1 Decoupling of the vector Helmholtz equation: There exist linear differential operators L1 and L2 such that Hu = 0, where H is the vector Helmholtz operator [see equation (1)] and u = T{T} + S {S}, if and only if L1T = 0 and L2S = 0.GP2 OrthogonalityGP3 Closure: ∇ × S{S} is a T field.Two choices of T and S fields are considered: type I fields with potentials T and S, which may depend on ξ1, ξ2 and ξ3, and type II fields with ξ1-independent potentials. It is shown that properties GP1–GP3 only hold for type I fields in spherical and cylindrical coordinate systems, and for type II fields in azimuthal and cylindrical coordinate systems with axisymmetric and two-dimensional potentials, respectively. Analogues of GP1 for the vector wave and diffusion equations, and the Navier equation of linear elasticity, are also only true in the same four cases. Generalisations of type I and II T and S fields to arbitrary coordinate systems are indicated.
On the existence and sensitivity analysis of optimal catital accumulation paths in continuous time, infinite horizon models
Authors: Flytzanis E. , Papageorgiou Nikolaos S. 
Published: February 2009

AbstractIn this paper we consider an infinite horizon, continuous time model of economic growth. We prove two theorems; one on the existence of optimal paths of capital accumulation and the other on the dependence of the set of optimal paths on the initial capital stock (sensitivity analysis). In the existence result the underlying technology set is nonconvex and only its “investment’ slices are convex. The proof is direct, without any use of necessary conditions. In the sensitivity analysis, the technology set is convex and so we have that the value function is concave. Then having that, we show that the set of optimal paths is an upper semicaontinuous multifunction of the initial capital stock.
Normal shock reflection-transmission in rubber-like elastic material
Authors: Kosinski S. , Duszczyk B. 
Published: February 2009

AbstractA finite transverse shock wave propagates through an unbounded medium consisting of two joined incompressible elastic half-spaces of different material properties, in the direction normal to the plane interface. A semi-inverse method is used to examine the reflection-transmission of this wave at the interface. It is found that, depending on the material properties, the reflected wave is either a simple wave or a shock; the transmitted wave is always a shock.
Appropriate initial conditions for asymptotic descriptions of the long term evolution of dynamical systems
Authors: Roberts A. J. 
Published: February 2009

AbstractA centre manifold or invariant manifold description of the evolution of a dynamical system provides a simplified view of the long term evolution of the system. In this work, I describe a procedure to estimate the appropriate starting position on the manifold which best matches an initial condition off the manifold. I apply the procedure to three examples: a simple dynamical system, a five-equation model of quasi-geostrophic flow, and shear dispersion in a channel. The analysis is also relevant to determining how best to account, within the invariant manifold description, for a small forcing in the full system.
Criticality dependence on data and parameters for a problem in combustion theory, with temperature-dependent conductivity
Authors: Tam K. K. 
Published: February 2009

AbstractA problem in combustion theory with tenperature-dependent conductivity is considered. It is shown that information regarding criticality dependence on data and parameters can be obtained from a transformed equation in which the conductivity is constant, while the nonlinear source term is modified. Some previous work can then be used in such a study.
An evolutionary monotone follower problem in [0, 1]
Authors: Sun Min 
Published: February 2009

AbstractWe consider in this article an evolutionary monotone follower problem in [0,1]. State processes under consideration are controlled diffusion processes , solutions of dyx(t) = g(yx(t), t)dt + σu(yx(t), t) dwt + dυt with yx(0) = x ∈[0, 1], where the control processes υt are increasing, positive, and adapted. The cost functional is of integral type, with certain explicit cost of control action including the cost of jumps. We shall present some analytic results of the value function, mainly its characterisation, by standard dynamic programming arguments.
A conjugate direction implementation of the BFGS algorithm with automatic scaling
Authors: Coope Ian D. 
Published: February 2009

AbstractA new implementation of the BFGS algorithm for unconstrained optimisation is reported which utilises a conjugate factorisation of the approximating Hessian matrix. The implementation is especially useful when gradient information is estimated by finite difference formulae and it is well suited to machines which are able to exploit parallel processing.
On nonblocking multiconnection networks composed of digital switching matrices
Authors: Jajszczyk Andrzej 
Published: February 2009

AbstractIn the paper we study the conditions under which multiconnection networks are nonblocking. A multiconnection network deals with the connections of pairs {(T1, T2)} where T1 is a subset of the input terminals and T2 is a subset of the output terminals. We investigate networks composed of digital switching matrices. Such networks can be treated as a very general case encompassing many kinds of networks used in practice as well as studied theoretically.We present four routing strategies and then develop conditions under which multiconnection networks are nonblocking when each of these strategies is used. We also show that the obtained conditions reduce to known results for some values of network parameters.
Analytic error bounds for approximations of queueing networks with an application to alternate routing
Authors: Van Dijk Nico M. 
Published: February 2009

AbstractA general condition is provided from which an error bound can be concluded for approximations of queueing networks which are based on modifications of the transition and state space structure. This condition relies upon Markov reward theory and can be verified inductively in concrete situations. The results are illustrated by estimating the accuracy of a simple throughput bound for a closed queueing network with alternate routing and a large finite source input. An explicit error bound for this example is derived which is of order M—1, where M is the number of sources.
Slowly-varying bifurcation theory in dissipative systems
Authors: Denier J. P. , Grimshaw R. 
Published: February 2009

AbstractSystems of coupled nonlinear differential equations with an externally controlled slowly-varying bifurcation parameter are considered. Canonical equations governing the transition between bifurcated solutions are derived by making use of methods of “steady” bifurcation theory. It is found that, depending on the initial amplitudes, the solutions of the transition equations are either asymptotically equivalent to the bifurcated solutions or the solutions develop algebraic singularities at some positive finite time. These singularities correspond to a transition to a solution of a fully nonlinear problem.
Strong uniqueness in sequential linear programming
Authors: Osborne M. R. , Womersley R. S. 
Published: February 2009

AbstractIt is known that strong uniqueness can be used to prove second order convergence of the generalised Gauss-Newton algorithm. Formally this algorithm includes sequential linear programming as a special case. Here we show that the second order convergence result extends when the sequential linear programming algorithm is formulated appropriately. Also this discussion provides an example which shows that the assumption of Lipschitz continuity is necessary for the second order convergence result based on strong uniqueness.
Propagation of flame fronts
Authors: Smyth N. F. 
Published: February 2009

AbstractThe propagation of a flame front in a combusting gas is considered in the limit in which the width of the reaction-zone is small compared with some overall flow dimension. In this approximation, the front propagates along its normals at a speed dependent on the local curvature of the front and is governed by a nonlinear equivalent of the geometric optics equations. Some exact solutions of this equation are found and a numerical scheme is developed to solve the equation for more complicated geometries.
Nonlinear interaction of positive and negative energy modes in Hamiltonian systems
Authors: Denier J. P. , Grimshaw R. H. J. 
Published: February 2009

AbstractWe consider the nonlinear evolution of a Hamiltonian system as the system passes through a linear resonance (as the system parameters vary). Two cases are considered. In the first case the linearized problem (at resonance) possess a full complement of normal mode solutions. This case is presented in the context of the interaction between modes which may have oppositely signed energy. The second case considered has an additional degeneracy in that the linearized problem (at resonance) has a single normal mode solution.Both cases are analysed using normal form theory and in both cases the systems governing the transition through resonance are shown to be completely integrable in the classical sense. Possible bifurcations as the resonance is traversed are discussed. Conditions for the existence of algebraic singularities at some finite positive time are also presented.
Functional differential equations determining steady size distributions for populations of cells growing exponentially
Authors: Hall A. J. , Wake G. C. 
Published: February 2009

AbstractA population of cells growing and dividing often goes through a phase of exponential growth of numbers, during which the size distribution remains steady. In this paper we study the function differential equation governing this steady size distribution in the particular case where the individual cells themselves are growing exponentially in size. A series solution is obtained for the case where the probability of cell division is proportional to any positive power of the cell size, and a method for finding closed-form solutions for a more general class of cell division functions is developed.
An optimal strategy for the control of a train
Authors: Howlett Phil 
Published: February 2009

AbstractA train travels from one station to the next along a level track. The journey must be completed within a given time and it is desirable to minimise the energy required to drive the train. It has been shown with an appropriate formulation of the problem that an optimal strategy exists and that this strategy must satisfy a Pontryagin type criterion. In this paper the Pontryagin principle will be used to find the nature of the optimal strategy and this information will then be used to determine the precise optimal strategy.
On hearing the shape of an arbitrary doubly-connected region in R2
Authors: Zayed E. M. E. 
Published: February 2009

AbstractThe basic problem in this paper is that of determining the geometry of an arbitrary doubly-connected region in R2 together with an impedance condition on its inner boundary and another impedance condition on its outer boundary, from the complete knowledge of the eigenvalues for the two-dimensional Laplacian using the asymptotic expansion of the spectral function for small positive t.
Duality for fractional minimax programming problems
Authors: Yadav Shri Ram , Mukherjee R. N. 
Published: February 2009

AbstractDuality theory is discussed for fractional minimax programming problems. Two dual problems are proposed for the minimax fractional problem: minimize maxy∈Υf(x, y)/h(x, y), subject to g(x) ≤ 0. For each dual problem a duality theorm is established. Mainly these are generalisations of the results of Tanimoto [14] for minimax fractional programming problems. It is noteworthy here that these problems are intimately related to a class of nondifferentiable fractional programming problems.
A note on the flow induced by a line sink beneath a free surface
Authors: Hocking G. C. , Forbes L. K. 
Published: February 2009

AbstractThe problem of withdrawing water through a line sink from a region containing an homogeneous fluid beneath a free surface is considered. Assuming steady, irrotational flow of an ideal fluid, solutions with low Froude number containing a stagnation point on the free surface above the sink are sought using a series substitution method. The solutions are shown to exist for a value of the Froude number up to a critical value of about 1.4. No solutions of this type are found for Froude numbers greater than this value.