Elliot Tonkes

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Ant colony optimisation is a relatively new meta-heuristic search technique for solving optimisation problems. To date, much research has concentrated on solving standard benchmark problems such as the travelling salesman problem, quadratic assignment problem and the job sequencing problem. In this paper, we investigate the application of ant colony(More)
This note considers possible arrangements of the sectors of a generalised dartboard. The sum of the pth powers of the absolute differences of the numbers on adjacent sectors is introduced as a penalty cost function and a string reversal algorithm is used to determine all arrangements that maximise the penalty, for any p ≥ 1. The maximum value of the penalty(More)
Ω |∇u| N ) 1 N . The dual space is denoted W−1,N ′ , where N ′ is the Hölder conjugate of N , and has the associated norm ‖ · ‖∗. Denote strong convergence by “→”, weak convergence by “⇀” and convergence in the sense of measure (or distributions) as “⇀∗”. Unless otherwise denoted, integration is performed over the domain Ω. Specific constraints on e(x, u)(More)
In many parliamentary systems, election timing is an important decision made by governments in order to maximize their expected remaining life in power. Governments can also introduce policy or economic actions to enhance their popular standing and thus their chance of being re-elected. On the other hand, an oppositions’ natural objective is to gain power,(More)
We study a stochastic differential equation (SDE) describing a class of meanreverting diffusions on a bounded interval. The drift coefficient is not continuous near the boundaries. Nor does it satisfy either of the usual Lipschitz or linear growth conditions. We characterize the boundary behaviour, identifying two possibilities: entrance boundary and(More)
This paper considers bifurcation at the principal eigenvalue of a class of gradient operators which possess the Palais-Smale condition. The existence of the bifurcation branch and the asymptotic nature of the bifurcation is verified by using the compactness in the Palais Smale condition and the order of the nonlinearity in the operator. The main result is(More)