We discuss several open problems related to analysis on fractals: estimates of the Green functions, the growth rates of the Markov factors with respect to the extension property of compact sets, asymptotics of orthogonal polynomials and the Parreau-Widom condition, Hausdorff measures and the Hausdorff dimension of the equilibrium measure on generalized Julia sets. 1 Background and notation 1.1 ...

Coherent lower previsions constitute a convex set that is closed and compact under the topology of point-wise convergence, and Maaß [2] has shown that any coherent lower prevision can be written as a ‘countably additive convex combination’ of the extreme points of this set. We show that when the possibility space has a finite number n of elements, these extreme points are either degenerate prec...

This paper is a contribution to the mathematical foundations of the theory of automata. We give a topological characterization of the transductions τ from a monoid M into a monoid N , such that if R is a recognizable subset of N , τ(R) is a recognizable subset of M . We impose two conditions on the monoids, which are fullfilled in all cases of practical interest: the monoids must be residually ...

This work is devoted to provide a way of representing $4D$ spherically symmetric and static compact stellar configurations into $5D$ space time, using the black string framework. We write four five dimensional line elements energy momentum tensor such that quantities are related by function $A(z)$, where $z$ represents extra dimension. Remarkably, one consequence our chosen form for element, fa...