Convergence properties of simple genetic algorithms

The essential parameters determining the behaviour of genetic algorithms were investigated. Computer runs were made while systematically varying the parameter values. Results based on the progress curves obtained from these runs are presented along with results based on the variability of the population as the run progresses

Condensation cyclization reactions of electron deficient aromatics. 4: Tricyclic nitropropene nitronates from the reaction of phloroglucinol and cycloalkanones with sym-trinitrobenzene

Interesting similarities have been shown between the reactions of sym-trinitrobenzene with cycloalkanones, and with phloroglucinol. Previously unsuspected common intermediates have been shown to intervene. The structurally similar products in each case are tricyclic nitropropene nitronates. Protonation of these yields the corresponding nitronic acids in certain instances

A discrete time relativistic Toda lattice

Four integrable symplectic maps approximating two Hamiltonian flows from the relativistic Toda hierarchy are introduced. They are demostrated to belong to the same hierarchy and to examplify the general scheme for symplectic maps on groups equiped with quadratic Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flows are found for all the maps.Comment: 32 pages, LaTe

On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity

This paper develops necessary and sufficient conditions for the preservation of asymptotic convergence rates of deterministically and stochastically perturbed ordinary differential equations with regularly varying nonlinearity close to their equilibrium. Sharp conditions are also established which preserve the asymptotic behaviour of the derivative of the underlying unperturbed equation. Finally, necessary and sufficient conditions are established which enable finite difference approximations to the derivative in the stochastic equation to preserve the asymptotic behaviour of the derivative of the unperturbed equation, even though the solution of the stochastic equation is nowhere differentiable, almost surely