Extremiana José Ignacio

Universidad de La Rioja (Spain) | UNIRIOJA · Mathematics and Computation

In a similar way that the Appell sequences of polynomials can be extended to the Dunkl context, where the ordinary derivative is replaced by Dunkl operator on the real line, and the exponential function is replaced by the so-called Dunkl kernel, one can expect that the discrete Appell sequences can be extended to the Dunkl context. In this extensio...

The aim of this paper is to study, from a topological and geometrical point of view, the iteration map obtained by the application of iterative methods (Newton or relaxed Newton’s method) to a polynomial equation. In fact, we present a collection of algorithms that avoid the problem of overflows caused by denominators close to zero and the problem...

The goal of this paper is to present a new project "A Julia Implementation for the Iteration of Univariate Rational Functions" which allows us to iterate a rational function on the Riemann sphere by using its geometry and complex structure. We have developed and implemented in Julia language a collection of algorithms for the iteration of a rationa...

In memory of Sibe Mardešić, our friend. Sibe Mardešić has enriched algebraic topology developing shape and strong shape theories with important constructions and theorems. This paper relates computational topology to shape theory. We have developed some algorithms and implementations that under some conditions give a shape resolution of some Julia...

When a semi-flow is induced by a d-fold branched covering \( f:M \rightarrow M \) defined on a Riemannian manifold M, the associated Julia set J(f) is a compact invariant subset of M and, therefore, there exists an induced restriction \( f | _ {J (f)} :J (f) \rightarrow J (f) \). In order to construct an inverse system of regular sub-complexes whos...

RESUMEN Este trabajo contiene algunos comentarios sobre las principales líneas de in-vestigación y algunos avances que el Grupo de investigación de Topología de la Universidad de La Rioja ha realizado durante los comienzos del siglo XXI. Se destacan las principales aportaciones teóricas y también algunas aplicaciones prác-ticas. Palabras clave: Teo...

Las soluciones de ecuaciones diferenciales autónomas tienen la estructura de un flujo continuo aunque no es así para el caso de funciones continuas no Lipchizianas, ya que algunas veces se obtienen resultados de existencia pero no de unicidad. Sin embargo, cuando sólo se obtiene unicidad para valores positivos de la variable tiempo las soluciones a...

The notion of closure finite complexes with weak topology introduced by J.H.C. Whitehead determines an adequate category for the study of homotopy theory. Nevertheless a noncompact space which can be described as a $CW$-complex always needs an infinite number of cells. In the present paper we develop a new notion that we call proper $CW$-complex wh...

We have developed Postnikov sections for Brown–Grossman homotopy groups and for Steenrod homotopy groups in the category of exterior spaces, which is an extension of the proper category. The homotopy fibre of a fibration in the factorization associated with Brown–Grossman groups is an Eilenberg–Mac Lane exterior space for this type of groups and it...

La belleza, una noción difícil de precisar, relacionada con la armonía, bondad, simplicidad y orden, está presente en todas las culturas a lo largo del tiempo y puede constatarse que de alguna manera hay un sentido universal de lo que es bello. El objetivo de crear algo bello, que en cierto modo representaría un reflejo de la perfección divina, apa...

POLIEDROS JOSÉJOS´JOSÉ IGNACIO EXTREMIANA ALDANA, LUIS JAVIER HERN´ANDEZHERN´ HERN´ANDEZ PARICIO Y MAR´IAMAR´MAR´IA TERESA RIVAS RODR´IGUEZRODR´RODR´IGUEZ Gracias, Chicho, te queremos Abstract. In this paper we have tried to explore the presence of polyhedra in some areas of the human activity. Taking as started point a reflection about the platoni...

For m n > 0, a map f between pointed spaces is said to be a weak [n, m]-equivalence if f induces isomorphisms of the homotopy groups π k for n k m. Associated with this notion we give two different closed model category structures to the category of pointed spaces. Both structures have the same class of weak equivalences but different classes of fi...

For each integer n>0, we give a distinct closed model category structure to the category of pointed spaces, Top * such that the corresponding localized category Ho(Top * n ) is equivalent to the standard homotopy category of (n-1)-connected CW-complexes. The structure of closed model category given by D. Quillen to Top * [Ann. Math., II. Ser. 90, 2...

The notion of closure finite complexes with weak topology introduced by J. H. C. Whitehead determines an adequate category for the study of homotopy theory. Nevertheless a noncompact space which can be described as a CW-complex always needs an infinite number of cells. In the present paper we develop a new notion that we call proper CW-complex whic...