Fractional velocity as a tool for the study of non-linear problems

Singular functions and, in general, H\"older functions represent conceptual models of nonlinear physical phenomena. The purpose of this survey is to demonstrate the applicability of fractional velocity as a tool to characterize Holder and in particular singular functions. Fractional velocities are defined as limit of the difference quotient of a fractional power and they generalize the local notion of a derivative. On the other hand, their properties contrast some of the usual properties of derivatives. One of the most peculiar properties of these operators is that the set of their non trivial values is disconnected. This can be used for example to model instantaneous interactions, for example Langevin dynamics. Examples are given by the De Rham and Neidinger's functions, represented by iterative function systems. Finally the conditions for equivalence with the Kolwankar-Gangal local fractional derivative are investigated.Comment: 21 pages; 2 figure

Bouncing Branes

Two classical scalar fields are minimally coupled to gravity in the Kachru-Shulz-Silverstein scenario with a rolling fifth radius. A Tolman wormhole solution is found for a R x S^3 brane with Lorentz metric and for a R x AdS_3 brane with positive definite metric.Comment: 6 pages, LaTe

On the quasi-component of pseudocompact abelian groups

In this paper, we describe the relationship between the quasi-component q(G) of a (perfectly) minimal pseudocompact abelian group G and the quasi-component q(\widetilde G) of its completion. Specifically, we characterize the pairs (C,A) of compact connected abelian groups C and subgroups A such that A \cong q(G) and C \cong q(\widetilde G). As a consequence, we show that for every positive integer n or n=\omega, there exist plenty of abelian pseudocompact perfectly minimal n-dimensional groups G such that the quasi-component of G is not dense in the quasi-component of the completion of G.Comment: minor revisio