It is shown that, for any round-robin tournament, one can find a pairing of the teams and allocate home and away matches so that only one member of each pair plays at home in each round.

Solitary wave interaction is examined using an extended Benjamin-Bona-Mahony (eBBM) equation. This equation includes higher-order nonlinear and dispersive effects and is is asymptotically equivalent to the extended Korteweg-de Vries (eKdV) equation. The eBBM formulation is preferable to the eKdV equation for the numerical modelling of solitary wave collisions, due to the stability of its finite-difference scheme. In particular, it allows the interaction of steep waves to be modelled, which due to numerical instability, is not possible using the eKdV equation.

Numerical simulations of a number of solitary wave collisions of varying nonlinearity are performed for two special cases corresponding to surface water waves. The mass and energy of the dispersive wavetrain generated by the inelastic collision is tabulated and used to show that the change in solitary wave amplitude after interaction is of O(α4), verifying previously obtained theoretical predictions.

The paper is concerned with periodic solutions of the difference equation un + 1 = 2aun, where a and b are constants, with and b > 0. A new method is developed for dealing with this problem and, for period lengths up to 6, polynomial equations are given which allow the periodic solutions to be determined in a precise and practical manner. These equations apply whether the periodic solutions are stable or unstable and the elements of the cycle can be determined with an accuracy which is not affected by instability of the cycle.

A simple transformation puts the equation into the form , where A = a2 − a, and the detailed discussion is based on this simpler form. The discussion includes details such as the number of cyclic solutions for a given value of A, the pattern of the cycles and their stability. For practical purposes, it is enough to consider a restricted range of values of A, namely , although the equations obtained are valid for A > 2.

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.

We consider a nonlinear singular perturbation problem on a semi-infinite interval, that is a generalization of the well-known Lagerstrom model equation intended to model low Reynolds number flow. By applying a Green's function method and the contraction mapping principle, we are able to obtain existence, uniqueness and asymptoticity results for this problem.

It is shown that under some conditions a collection of continuous mappings gives rise to a set-valued dynamical system. Using this it is further shown that under some other conditions the system ẋ(t) ∈ F(x(t)) is equivalent to a set-valued dynamical system.

The characteristic function of a lognormal random variable is calculated in closed form as a rapidly convergent series of Hermite functions in a logarithmic variable. The series coefficients are Nielsen numbers, defined recursively in terms of Riemann zeta functions. Divergence problems are avoided by deriving a functional differential equation, solving the equation by a de Bruijn integral transform, expanding the resulting reciprocal Gamma function kernel in a series, and then invoking a convergent termwise integration. Applications of the results and methods to the distribution of a sum of independent, not necessarily identical lognormal variables are discussed. The result is that a sum of lognormals is distributed as a sum of products of lognormal distributions. The case of two lognormal variables is outlined in some detail.

By using the continuation theorem of coincidence degree theory, a sufficient condition is obtained for the existence of a positive periodic solution of a predator-prey diffusion system.

This work is devoted to numerical studies of nearly optimal controls of systems driven by singularly perturbed Markov chains. Our approach is based on the ideas of hierarchical controls applicable to many large-scale systems. A discrete-time linear quadratic control problem is examined. Its corresponding limit system is derived. The associated asymptotic properties and near optimality are demonstrated by numerical examples. Numerical experiments for a continuous-time hybrid linear quadratic regulator with Gaussian disturbances and a discrete-time Markov decision process are also presented. The numerical results have not only supported our theoretical findings but also provided insights for further applications.

In a previous paper the authors have shown that the classical barrier function has an O(r) rate of convergence unless the problem is degenerate when it reduces O(r½). In this paper a modified barrier function algorithm is suggested which does not suffer from this problem. It turns out to have superior scaling properties which make it preferable to the classical algorithm, even in the nondegenerate case, if extrapolation is to be used to accelerate convergence.

The problem of estimating the limit f∞ of a sequence fn converging as fn − f∞ = O(n−λ) as n → ∞, where λ > 0, is discussed. Using the generalization of the ε-algorithm proposed recently by Vanden Broeck and Schwartz, an acceleration scheme is developed. The method is illustrated on several test sequences and compared to other acceleration procedures.

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.

In this paper we introduce an impulsive control model of a rumour process. The spreaders are classified as subscriber spreaders, who receive an initial broadcast of a rumour and start spreading it, and nonsubscriber spreaders who change from being an ignorant to being a spreader after encountering a spreader. There are two consecutive broadcasts. The first starts the rumour process. The objective is to time the second broadcast so that the final proportion of ignorants is minimised. The second broadcast reactivates as spreaders either the subscriber stiflers (Scenario 1) or all individuals who have been spreaders (Scenario 2). It is shown that with either scenario the optimal time for the second broadcast is always when the proportion of spreaders drops to zero.

This paper studies the stability of large-scale impulsive delay differential systems and impulsive neutral systems. By developing some impulsive delay differential inequalities and a comparison principle, sufficient conditions are derived for the stability of both linear and nonlinear large-scale impulsive delay differential systems and impulsive neutral systems. Examples are given to illustrate the main results.

We consider the following model that describes the spread of n types of epidemics which are interdependent on each other:

Our aim is to establish criteria such that the above system has one or multiple constant-sign periodic solutions (u1, u2, …, un), that is, for each 1 ≤ i ≤ n, ui, is periodic and θiui ≥ 0 where θi, ε (1, −1) is fixed. Examples are also included to illustrate the results obtained.

Ronney and Sivashinsky [2] and Buckmaster and Lee [1] have proposed a certain non-autonomous first order ordinary differential equation as a simple model for an expanding spherical flame front in a zero-gravity environment. Here we supplement their preliminary numerical calculations with some analysis and further numerical work. The results show that the solutions either correspond to quenching, or to steady flame front propagation, or to rapid expansion of the flame front, depending on two control parameters. A crucial component of our analysis is the construction of a barrier orbit which divides the phase plane into two parts. The location of this barrier orbit then determines the fate of orbits in the phase plane.