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**public sources and our publisher partners.**What do we mean by "Fractal-Based Analysis".- Basic IFS.- IFS on Spaces of Functions.- IFS, Multifunctions, and Measure-Valued Functions. -IFS on Spaces of Measures.-The Chaos Game.-Inverse Problems… Expand

Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems.… Expand

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 Hausdorff compactifications of X). More specifically, we prove that K(X) C… Expand

In this paper, we generalize the zeta function for a fractal string (as in Lapidus and Frankenhuijsen 2006 Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal… Expand

Two "pathological" properties of Minkowski content are that countable sets can have positive content (unlike Hausdorff measures) and the property of a set being Minkowski measurable is quite rare. In… Expand

The Monge–Kantorovich distance gives a metric between probability distributions on a metric space $${\mathbb X}$$X and the MK distance is tied to the underlying metric on $${\mathbb X}$$X. The MK… Expand

It is well known that the action of a “Fractal Transform” or (Local) Iterated Function System with Grey Level Maps (IFSM) on a function f(x) induces a very simple mapping on its expansion… Expand

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… Expand

Let fwi; pig be a contractive IFS with probabilities. We provide a simple proof that for almost every address sequence and for all x the limit limn 1=n P in f ? w n w n?1 w 1 (x) exists and is equal… Expand

Previously, the use of non-separable wavelets in image processing has been hindered by the lack of a fast algorithm to perform a non-separable wavelet transform. We present two such algorithms in… Expand