Bounded distortion homeomorphisms on ultrametric spaces

It is well-known that quasi-isometries between R-trees induce power quasi-symmetric homeomorphisms between their ultrametric end spaces. This paper investigates power quasi-symmetric homeomorphisms between bounded, complete, uniformly perfect, ultrametric spaces (i.e., those ultrametric spaces arising up to similarity as the end spaces of bushy trees). A bounded distortion property is found that characterizes power quasi-symmetric homeomorphisms between such ultrametric spaces that are also pseudo-doubling. Moreover, examples are given showing the extent to which the power quasi-symmetry of homeomorphisms is not captured by the quasiconformal and bi-H\"older conditions for this class of ultrametric spaces.Comment: 20 pages, 1 figure. To appear in Ann. Acad. Sci. Fenn. Mat

Complementary Riordan arrays

Abstract Recently, the concept of the complementary array of a Riordan array (or recursive matrix) has been introduced. Here we generalize the concept and distinguish between dual and complementary arrays. We show a number of properties of these arrays, how they are computed and their relation with inversion. Finally, we use them to find explicit formulas for the elements of many recursive matrices

El problema de la intersección de ANR’s de Borsuk y métricas en el hiperespacio del cubo de Hilbert

En este artículo relacionamos dos problemas abiertos en Homotopía y Teoría de la Forma planteados por Borsuk. Demostramos que la respuesta a, al menos,uno de ellos es negativa, y obtenemos algunas consecuencias

Spaces of discrete shape and c-refinable maps that induce shape equivalences

Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEDGICYTpu

Commutators and commutator subgroups of the Riordan group

We calculate the derived series of the Riordan group. To do that, we study a nested sequence of its subgroups, herein denoted by Gk. By means of this sequence, we first obtain the n-th commutator subgroup of the Associated subgroup. This fact allows us to get some related results about certain groups of formal power series and to complete the proof of our main goal, Theorem 1 in this paper