2008-2009 Academic Year:

Friday, July 3, 2009.
Venue: Seminar of Applied Mathematics, University of Almería
Session: 17.00: Dr. Andras Kroo (Alfred Rényi Institute of Mathematics, Hungarian Academy of Sciences)
Title: On the exact Markov inequality for k-monotone polynomials in uniform and L1-norms.
Abstract: click here. 

Friday, March 27, 2009.
Venue: Room A-23, Fac. Science, Granada University
Session: 17.00: Dr. Miguel Ángel Fortes Escalona (Granada University)
Title: Minimum Energy Surfaces. Applications.
Abstract (in Spanish): click here.

Session 18.00: Dr. Andrei Martínez-Finkelshtein (University of Almería)
Title: Asymptotics of Heine-Stieltjes polynomials and related issues
Abstract: We investigate the asymptotic zero distribution of Heine-Stieltjes 
polynomials - polynomial solutions of a second order differential equations with complex 
polynomial coefficients. In the case when all zeros of the leading coefficients are all real, 
zeros of the Heine-Stieltjes polynomials were interpreted by Stieltjes as discrete distributions 
minimizing an energy functional. In a general complex situation one deals instead with a critical 
point of the energy. We introduce the notion of discrete and continuous critical measures 
(saddle points of the weighted logarithmic energy on the plane), and prove that a weak-* 
limit of a sequence of discrete critical measures is a continuous critical measure. Thus, 
the limit zero distributions of the Heine-Stieltjes polynomials are given by continuous 
critical measures. We give a detailed description of such measures, showing their connections 
with quadratic differentials. In doing that, we obtain some results on the global structure 
of rational quadratic differentials on the Riemann sphere that have an independent interest. 
This is a joint work with E. A. Rakhmanov.
 

Friday, December 5, 2008.
Venue: Seminar of Applied Math, University of Almería. 
Session: 11.00 am. Dr. Domingo Barrera  (Universidad de Granada).
Title: "Some recent contributions to the theory of quasi-interpolation"
Abstract: The approximation of functions and empirical data is one of the most frequent problems
arising in practice, and for that purpose multiple techniques have been developed. Among them, those based on splines play a 
central role. Frequently data or function is interpolated, making it necessary to solve as system of linear (or nonlinear) euqtions.
The quasi-interpolating splines provide approximants without solving any system, being their coefficients determined directly 
from the available information.

Recently new results concerning the construction of discrete quasi-interpolant and integrals of small sup norm have 
been obtained. In the case of one variable or for a box spline of two variables explicit solutions have been found 
for the corresponding problems of B-splines of low degree. This problem has an independent interest since a small sup
norm helps to control the error propagation of the approximate data. Nevertheless, in order to obtain quasi-interpolants
of the mentioned type (and also of differential quasi-interpolants) with small constants in the error estimates for 
sufficiently regular functions a specific methodology has been considered, in which certain splines independent of the
linear form involved play an important role. In the usual cases in practice (cases C^1 and C^2) really small constants
are obtained.

The most recent line of research deals with the construction of non-standard quasi-interpolants, starting from a discrete
quasi-interpolant with certain algebraic precision. The new technique allows to increase the precision building for that
appropriate differential quasi-interpolants. This technique will be used in the future in different problems, both uniform
and non-uniform.
 

Session: 12.00. Dr. Alejandro Zarzo  (ETSII, Universidad Politécnica de Madrid).
Title: "Something new on Hypergeometric-Type Functions?"
Abstract: Hypergeometric-type functions are well known mathematical objects
widely studied in the literature. In spite in this fact, it is the 
aim of this talk to modestly claim that something new can be said
by making an attempt towards a (let's say) "unified approach" of
Hypergeometric-Type Functions, and so of the close connected
Special functions of Mathematical Physics, including the varying
case, giving rise to some algorithms and symbolic programs to
manage them. We hope to put in clear along the talk what we
understand by "unified approach" and the interest of considering
the aforementioned varying case. Such a task will be tackle with
the help of examples related with zero distribution and zero
asymptotics of special functions and also by dealing with some
very general algebraic properties of them.

Friday, November 21, 2008.
Venue: Room A-5, Faculty of Sciences, University of Granada. 
Session: 11.00 am. Dr. Herbert Stahl  (Technische Fachhochschule Berlin, Germany).
Title: "Calculating Rational Best Approximants on (-∞, 0]"
Abstract: We shall present an algorithm for the calculation of rational best approximants to real functions 
on a real interval. The development of this algorithm was motivated by the need to calculate rational best approximants 
on (-∞,0] to perturbations of the exponential function or to functions of a similar type. We
shall open our talk by several examples from this area.
Then the basic structure of the algorithm will be explained (it shares many aspects with the Remez algorithm), 
and as far as time allows, we will have a closer look on some of its key elements.

Session: 12.00. Dr. Cleonice Fátima Bracciali  (UNESP - Universidade Estadual Paulista, Brasil).
Title: "Determination of certain Quadrature Rules on the Unit Circle and the Frequency Analysis Problem"
Abstract: click here.

Wednesday, October 29, 2008.
Venue: Seminar of Applied Math, University of Almería. 
Session: 10.30 am. Maxim Yattselev  (INRIA, Sophia-Antipolis, France).
Title: "On Convergence of AAK Approximants for Cauchy Transforms with Polar Singularities"
Abstract: In this talk we consider AAK approximants for Cauchy transforms of complex measures 
perturbed by a rational function. Results are combined into two groups depending on 
the assumptions on the measure. In the first setting measures may vanish on a significant 
portion of the convex hull of its support but only convergence in capacity is obtained. 
In the second setting measures are much more smooth but strong asymptotics for the error 
of approximation is derived.

Monday, October 6, 2008.
Venue: Seminar of Applied Math, University of Almería. 
Session: 11.00pm. Reinaldo Rodríguez-Ramos  (Universidad de La Habana, Cuba).
Title: "Method of asymptotic homogeneization and some of its applications"
Abstract: Currently it is of great importance to obtain new materials due to the 
increasing use of the so called composite materials in industry. The technological development poses the problem
of mathematical modelling and analysis of these materials. The method of asymptotic homogeneization is one of the
tools used to forecast the physical properties of materials containing heterogeneities. We illustrate this method
with the case of piezoelectric composite materials and discuss several further applications.