Francisco Marcellán, nuevo presidente de la Real Sociedad Matemática Española (RSME)

La Real Sociedad Matemática Española (RSME) es una sociedad científica fundada en 1911 y entre sus objetivos cabe resaltar: La promoción y estímulo de la investigación matemática (la Francisco Marcellán, nuevo presidente de la Real Sociedad Matemática Española (RSME)

Criterios de garantía de calidad en educación superior: praxis europea.

In this contribution we overview the European trends in the framework of the quality assurance for the European higher education system. We emphasize the conclusions of the Bergen meeting held in May 2005. There, the Ministers of Education of the European countries involved in the Bologna Process agreed with the document “Standards and Guidelines for the Quality Assurance in the European Area of Higher Education” presented by the European Association for Quality Assurance (ENQA). We conclude with a description of the role and the challenges of ANECA in this context.En esta contribución se reflejan las tendencias europeas en garantía de calidad para los sistemas de educación superior en la perspectiva de un marco supranacional como es el denominado Espacio Europeo de Educación Superior. Se hace un especial énfasis en los acuerdos adoptados por los ministros de Educación en la reciente cumbre celebrada en Bergen (mayo 2005), se describen las líneas generales del documento de la European Association for Quality Assurance (ENQA) sobre criterios y directrices para la garantía de la calidad y se concluye con una descripción del papel y los retos de ANECA en este contexto

A generalization of the classical Laguerre polynomials

We consider a modi cation of the gamma distribution by adding a discrete measure supported in the point x = 0. For large n we analyze the existence of orthogonal polynomials with respect to such a distribution. Finally we represent them as the hypergeometric function 3F3:Instituto de Cooperación IberoamericanaComisión Interministerial de Ciencia y Tecnologí

Christoffel transforms and Hermitian linear functionals

8 pages, no figures.-- MSC2000 codes: Primary 42C05; Secondary 15A23.MR#: MR2192525 (2006h:42044)Zbl#: Zbl 1121.42017In this contribution we are focused on some spectral transformations of Hermitian linear functionals. They are the analogues of the Christoffel transform for linear functionals, i. e. for Jacobi matrices which has been deeply studied in the past. We consider Hermitian linear functionals associated with a probability measure supported on the unit circle. In such a case we compare the Hessenberg matrices associated with such a probability measure and its Christoffel transform. In this way, almost unitary matrices appear. We obtain the deviation to the unit matrix both for principal submatrices and the complete matrices respectively.The work of the first author (F. Marcellán) was supported by Dirección General de Investigación, Ministerio de Educación y Ciencia of Spain, under grant BFM 2003-06335-C03-02, and INTAS Research Network NeCCA INTAS 03-51-6637. The work of the second author (J. Hernández) was supported by Fundación Universidad Carlos III de Madrid.Publicad

The modification of classical Hahn polynomials of a discrete variable

We consider a modi cation of moment functionals for the Hahn classical polynomials of a discrete variable by adding two mass points at the ends of the interval, i.e., in x = 0 and x = N 1. We obtain the resulting orthogonal polynomials and identify them as hypergeometric functions. The corresponding three term recurrence relation and tridiagonal matrices are also studied.Instituto de Cooperación IberoamericanaComisión Interministerial de Ciencia y Tecnologí

Orthogonal polynomials and quadratic transformations

33 pages, no figures.-- MSC1991 code: Primary 42C05.MR#: MR1680116 (2000b:42021)Zbl#: Zbl 0936.42012Starting from a sequence $\{P_n\}_{n\geq 0}$ of monic polynomials orthogonal with respect to a linear functional ${\bf u}$, we find a linear functional ${\bf v}$ such that $\{Q_n\}_{\geq 0}$, with either $Q_{2n}(x)=P_n(T(x))$ or $Q_{2n+1}(x)=(x-a)\,P_n(T(x))$ where $T$ is a monic quadratic polynomial and a\in\C, is a sequence of monic orthogonal polynomials with respect to ${\bf v}$. In particular, we discuss the case when ${\bf u}$ and ${\bf v}$ are both positive definite linear functionals. Thus, we obtain a solution for an inverse problem which is a converse, for quadratic mappings, of one analyzed in [11].This paper was finished with financial support of a Grant from Junta Nacional de Investigação Científica e Tecnológica (JNITC) - BD976 - and Centro de Matemática da Universidade de Coimbra (CMUC) of Portugal. The work of the first author was supported by the Dirección General de Enseñanza Superior (DGES) of Spain - PB96-0120-C03-01.Publicad

Verblunsky parameters and linear spectral transformations

18 pages, no figures.-- MSC2000 codes: 42C05.In this paper we analyze the behavior of Verblunsky parameters for hermitian linear functionals deduced from canonical linear spectral transformations of a quasi-definite hermitian linear functional. Some illustrative examples are studied.The work of the first author has been supported by a grant of Universidad Autónoma de Tamaulipas. The work of the second author has been supported by Dirección General de Investigación, Ministerio de Educación y Ciencia of Spain, grant MTM06-13000-C03-02. Both authors have been supported by project CCG07-UC3M/ESP-3339 with the financial support of Comunidad de Madrid-Universidad Carlos III de Madrid.Publicad

Characterization of the Dᵂ-Laguerre-Hahn functionals

29 pages, no figures.-- MSC2000 codes: 33C45, 39A10.MR#: MR1914598 (2003e:33021)Zbl#: Zbl 1021.33007We give some characterization theorems for the DᵂLaguerre-Hahn linear functionals and we extend the concept of the class of the usual Laguerre-Hahn functionals to the Dᵂ-Laguerre-Hahn functionals, recovering the classic results when ᵂ tends to zero. Moreover, we show that some transformations carried out on the Dᵂ-Laguerre-Hahn linear functionals lead to new Dᵂ-Laguerre-Hahn linear functionals. Finally, we analyze the class of the resulting functionals and we give some applications relative to the first associated Charlier, Meixner, Krawtchouk and Hahn orthogonal polynomials.The work of the second author (FM) was supported by Ministerio de Ciencia y Tecnología (Dirección General de Investigación) of Spain under grant BFM 2000-0206-C04-01 and the INTAS project INTAS 2000-272.Publicad

On an inverse problem for a linear combination of orthogonal polynomials

This paper deals with the analysis of the orthogonality of a monic polynomial sequence defined as a linear combination of a sequence of monic orthogonal polynomials withwhere for . Moreover, we obtain the relation between the corresponding linear functionals as well as an explicit expression for the sequence of monic orthogonal polynomials . We obtain the connection between the Jacobi matrices associated with and , respectively, by using an LU factorization. Some special cases of the above type relation are analysed.The work of the first author (FM) has been supported by Ministerio de Economía y Competitividad of Spain, grant MTM 2012 36732 C03 01. This paper was completed during a stay of the second author (SV) in the Department of Mathematics of Universidad Carlos III de Madrid in the spring semester of the academic year 2012 2013. He acknowledges the kind reception there