We consider a competition–diffusion system and study its singular limit as the interspecific competition rate tend to infinity. We prove the convergence to a Stefan problem with zero latent heat.

In this paper we consider the problem of hedging options in the presence of cost in trading the underlying asset. This work is an asymptotic analysis of a stochastic control problem, as in Hodges & Neuberger and Davis, Panas & Zariphopoulou;. We derive a simple expression for the ‘hedging bandwidth’ around the Black–Scholes delta; this is the region in which it is optimal not to rehedge. The effect of the costs on the value of the option, and on the width of this hedging band is of a significantly greater order of magnitude than the costs themselves. When costs are proportional to volume traded, rehedging should be done to the edge of this band; when there are fixed costs present, trading should be done to an optimal point in the interior of the no-transaction region.

Uniqueness and solvability theorems are proved for the two-dimensional Neumann–Kelvin problem in the case when a body is totally submerged in a subcritical stream of finite depth fluid. A version of source method is developed to find a solution. The Green's identity coupling the solution with a solution of the problem with opposite stream direction is used to prove that the solution is unique.

New modulation equations for hexagonal patterns in reaction–diffusion systems are derived for parameter régimes corresponding to the onset of patterns. These systems include additional nonlinearities which are not present in Rayleigh–Bénard convection or Swift–Hohenberg type models. The dynamics of hexagonal and roll patterns are studied using a combination of analytical and computational approaches which exploit the hexagonal structure of the modulation equations. The investigation demonstrates instabilities and new phenomena not found in other systems, and is applied to patterns of flame fronts in a certain model of burner stabilized flames.

We present a simple and rigorous mathematical model and efficient numerical algorithm for the three-dimensional thermal stress analysis of composite structures used in high-temperature catalytic combustors. Numerical experiments are carried out for three types of cell geometries. A homogenization algorithm is implemented, and asymptotic formulae are derived for the effective elastic moduli of the periodic structures.

Volume 9 (1998), pp. 485–506

One of the author's names was misprinted in this article. EPIFIANO G. VIRGA should read EPIFANIO G. VIRGA.

In addition, on page 502, line 9, the argument leading to evaluate g(∞) := limb→+∞g(b) is not conclusive. The passage

‘On the other hand, if it were g(∞)>0, taking the limit as b→+∞ in (9.9), we would get A=πh2, which by (3.11) is violated by all admissible values of A, but the limiting one. Thus we conclude that g(∞)=0.’

should be changed as follows:

‘On the other hand, taking the limit as b→+∞ in (9.9), we would get A=πh2, by which (3.11) is violated by all admissible values of A, but the limiting one. Thus we conclude that, in the limit as b→+∞, the equilibrium configuration must be singular whenever A>πh2, and so g(∞)=0 because, otherwise, by (9.7) there would be asymptotic regular configurations, as soon as h/2kc(τ0+w) is sufficiently small.’

On page 502, line −7, ‘below’ should be replaced with ‘above’ and ‘regular’ with ‘singular’.

We apologise for the errors in the above paper and hope that no inconvenience has been caused to readers.

Volume 9 (1998), pp. 245–259

The last sentence of §3.2 should read as follows:

For n=4, the splitting yields six such linear PDEs from the coefficients of the terms involving Y(6), Y(4), Y(5), Y(5), Y(4)3, Y(4)2 and Y(4).

In the first paragraph of §6, the penultimate sentence should read as follows:

For an nth-order scalar ODE the determining equations are a linear system of PDEs consisting of the adjoint of the determining equation for symmetries of the nth-order ODE and additional equations when n[ges ]2.

We apologise for the errors in the above paper and hope that no inconvenience has been caused to readers.