Some consequences of restarting stochastic search algorithms are studied. It is shown under reasonable conditions that restarting when certain patterns occur yields probabilities that the goal state… (More)

We provide some conditions as to when K(X) = K(Y) for two locally compact spaces X and Y (where K(X) is the lattice of all Hausdorr compactiications of X). More speciically, we prove that K(X) = K(Y)… (More)

In this paper, we generalize the zeta function for a fractal string (as in [18]) in several directions. We first modify the zeta function to be associated with a sequence of covers instead of the… (More)

This paper considers the problem of extending the notion of an IFS with probabilities from the case of nitely many maps in the IFS to the case of innnitely many maps. We prove that under an average… (More)

We use the idea of a scalarization of a cone metric to prove that the topology generated by any cone metric is equivalent to a topology generated by a related metric. We then analyze the case of an… (More)

Overcompression is the process of post-processing compressed images to gain either further size reduction or improved quality. This is made possible by the fact that the set of all “reasonable”… (More)

A Cantor set is a nonempty, compact, totally disconnected, perfect subset of IR. Now, the set being totally disconnected means that it is scattered about like a “dust”. If you shine light on a clump… (More)

We consider a variational optimization problem involving multifunctions and we prove a stability result with respect to the Monge-Kantorovich metric. We then show an application to variational… (More)

We estimate the Hausdorff measure and dimension of Cantor sets in terms of a sequence given by the lengths of the bounded complementary intervals. The results provide the relation between the decay… (More)

In this short survey, we review the current status of fractal-based techniques and their application to the solution of inverse problems for ordinary and partial differential equations. This involves… (More)