On fractional derivatives and primitives of periodic functions

In this paper we prove that the fractional derivative or the fractional primitive of a $T$-periodic function cannot be a $\tilde{T}$-periodic function, for any period $\tilde{T}$, with the exception of the zero function.Comment: 12 page

Linear partial divided-difference equation satisfied by multivariate orthogonal polynomials on quadratic lattices

In this paper, a fourth-order partial divided-difference equation on quadratic lattices with polynomial coefficients satisfied by bivariate Racah polynomials is presented. From this equation we obtain explicitly the matrix coefficients appearing in the three-term recurrence relations satisfied by any bivariate orthogonal polynomial solution of the equation. In particular, we provide explicit expressions for the matrices in the three-term recurrence relations satisfied by the bivariate Racah polynomials introduced by Tratnik. Moreover, we present the family of monic bivariate Racah polynomials defined from the three-term recurrence relations they satisfy, and we solve the connection problem between two different families of bivariate Racah polynomials. These results are then applied to other families of bivariate orthogonal polynomials, namely the bivariate Wilson, continuous dual Hahn and continuous Hahn, the latter two through limiting processes. The fourth-order partial divided-difference equations on quadratic lattices are shown to be of hypergeometric type in the sense that the divided-difference derivatives of solutions are themselves solution of the same type of divided-difference equations.Comment: 36 page

Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we are focused in the study of the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some new directions for a future research are formulated.Comment: Changed content; 34 pages, 41 reference

Virez, una experiencia de desarrollo multimedia interuniversitario

El artículo recoge las experiencias y reflexiones de profesores de cinco universidades españolas que durante el bienio 1993-94 trabajaron en el desarrollo de un CD-ROM con contenidos multimedia, orientado a la enseñanza. Tras presentar cómo surge la idea inicial, cada profesor describe como se integra en el proyecto, las actividades que realiza, los problemas encuentran y los resultados positivos han sacado del proyecto. También describen su experiencia las personas que tuvieron que cuidar la coordinación de todo este trabajo y quienes tuvieron que homogeneizar desarrollos dándoles consistencia en un producto final

The endogenous caspase-8 inhibitor c-FLIPL regulates ER morphology and crosstalk with mitochondria

Components of the death receptors-mediated pathways like caspase-8 have been identified in complexes at intracellular membranes to spatially restrict the processing of local targets. In this study, we report that the long isoform of the cellular FLICE-inhibitory protein (c-FLIPL), a well- known inhibitor of the extrinsic cell death initiator caspase-8, localizes at the endoplasmic reticulum (ER) and mitochondria-associated membranes (MAMs). ER morphology was disrupted and ER Ca2+-release as well as ER-mitochondria tethering were decreased in c-FLIP-/- mouse embryonic fibroblasts (MEFs). Mechanistically, c-FLIP ablation resulted in enhanced basal caspase-8 activation and in caspase-mediated processing of the ER-shaping protein reticulon-4 (RTN4) that was corrected by re-introduction of c-FLIPL and caspase inhibition, resulting in the recovery of a normal ER morphology and ER-mitochondria juxtaposition. Thus, the caspase-8 inhibitor c-FLIPL emerges as a component of the MAMs signaling platforms, where caspases appear to regulate ER morphology and ER-mitochondria crosstalk by impinging on ER-shaping proteins like the RTN4