We have collected definitions and basic results for the (centered ball) density in metric space with respect to an arbitrary Hausdorff function. We have kept the definitions general: we do not assumeâ€¦ (More)

A Borel (or even analytic) subring of R either has Hausdorff dimension 0 or is all of R. Extensions of the method of proof yield (among other things) that any analytic subring of C having positiveâ€¦ (More)

We prove that the multifractal decomposition behaves as expected for a family of sets K known as digraph recursive fractals, using measures ^ of Markov type. For each value of a parameter a between aâ€¦ (More)

Suppose a graph-directed iterated function system consists of maps fe with upper estimates of the form d ( fe(x),fe(y) ) â‰¤ red(x,y). Then the fractal dimension of the attractor Kv of the IFS isâ€¦ (More)

From the simplest point of view, transseries are a new kind of expansion for real-valued functions. But transseries constitute much more than thatâ€”they have a very rich (algebraic, combinatorial,â€¦ (More)

Additional remarks and questions for transseries. In particular: properties of composition for transseries; the recursive nature of the construction of R x ; modes of convergence for transseries.â€¦ (More)

We investigate compositional iteration of fractional order for transseries. For any large positive transseries T of exponentiality 0, there is a family T [s] indexed by real numbers s correspondingâ€¦ (More)

We describe a puzzle consisting of a set of cards that are to be assembled into a picture of the `Dubuc Foresta fractal. This `deconstructiona also aids the more serious purpose of computing theâ€¦ (More)

Suppose a graph-directed iterated function system consists of maps fe with upper estimates of the form d ( fe(x), fe(y) ) â‰¤ red(x, y). Then the fractal dimension of the attractor Kv of the IFS isâ€¦ (More)

It is well-known that there is an intimate connection between the Radon-Nikodym property and martingale convergence in a Banach space. This connection can be "localized" to a closed bounded convexâ€¦ (More)