DM - GAMA - Comunicaciones en Congresos y otros eventos

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Generalized mixed type Bernoulli-Gegenbauer and Lagrange-based hypergeometric Bernoulli polynomials
(2023-02-28) Quintana, Yamilet
The aim of this talk is to present a brief report about two new families of special polynomials generated via the generating function method. We will explore some of the algebraic and analytic properties for these families, including, a matrix-inversion formula for each one of them. Part of this talk is based on joint work with Azhar Iqbal and Waseem A. Khan, Prince Mohammad Bin Fahd University, and Sahar Albosaily, University of Ha'il.
Group Actions and Monotone Metric Tensors: The Qubit Case
(Springer, 2021-07-21) Ciaglia, Florio Maria; di Nocera, F.
In recent works, a link between group actions and information metrics on the space of faithful quantum states has been highlighted in particular cases. In this contribution, we give a complete discussion of this instance for the particular case of the qubit.
From classical trajectories to quantum commutation relations
(Springer, 2018-03-05) Ciaglia, Florio Maria; Marmo, Giuseppe; Schiavone, Luca
In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian description because of the Noether theorem and because they are the starting point for the quantization. As a matter of fact many ambiguities arise in each step of such a reconstruction which must be solved by the ingenuity of the theoretician. In the present work we describe geometric structures emerging in Lagrangian, Hamiltonian and Quantum description of a dynamical system underlining how many of them are not really fixed only by the trajectories observed by the experimentalist.
On linearly related sequences of difference derivatives of discrete orthogonal polynomials
(Elsevier, 2015-08-15) Álvarez-Nodarse, Renato; Petronilho, José; Pinzón-Cortés, Natalia Camila; Sevinik-Adıgüzel, Rezan
Let ν be either ω∈C∖{0} or q∈C∖{0,1} , and let Dν be the corresponding difference operator defined in the usual way either by Dωp(x)=p(x+ω)−p(x)ω or Dqp(x)=p(qx)−p(x)(q−1)x . Let U and V be two moment regular linear functionals and let {Pn(x)}n≥0 and {Qn(x)}n≥0 be their corresponding orthogonal polynomial sequences (OPS). We discuss an inverse problem in the theory of discrete orthogonal polynomials involving the two OPS {Pn(x)}n≥0 and {Qn(x)}n≥0 assuming that their difference derivatives Dν of higher orders m and k (resp.) are connected by a linear algebraic structure relation such as ∑Mi=0ai,nDmνPn+m−i(x)=∑Ni=0bi,nDkνQn+k−i(x),n≥0, Turn MathJax off where M,N,m,k∈N∪{0} , aM,n≠0 for n≥M , bN,n≠0 for n≥N , and ai,n=bi,n=0 for i>n . Under certain conditions, we prove that U and V are related by a rational factor (in the ν− distributional sense). Moreover, when m≠k then both U and V are Dν -semiclassical functionals. This leads us to the concept of (M,N) - Dν -coherent pair of order (m,k) extending to the discrete case several previous works. As an application we consider the OPS with respect to the following Sobolev-type inner product ⟨p(x),r(x)⟩λ,ν=⟨U,p(x)r(x)⟩+λ⟨V,(Dmνp)(x)(Dmνr)(x)⟩,λ>0, Turn MathJax off assuming that U and V (which, eventually, may be represented by discrete measures supported either on a uniform lattice if ν=ω , or on a q -lattice if ν=q ) constitute a (M,N) - Dν -coherent pair of order m (that is, an (M,N) - Dν -coherent pair of order (m,0) ), m∈N being fixed.
Zeros of Orthogonal Polynomials Generated by the Geronimus Perturbation of Measures
(Springer, 2014) Branquinho, Amílcar; Huertas Cejudo, Edmundo José; Rafaeli, Fernando R
This paper deals with monic orthogonal polynomial sequences (MOPS in short) generated by a Geronimus canonical spectral transformation of a positive Borel measure μ, i.e., (x−c) −1dμ(x)+Nδ(x−c), for some free parameter N ∈ IR+ and shift c. We analyze the behavior of the corresponding MOPS. In particular, we obtain such a behavior when the mass N tends to infinity as well as we characterize the precise values of N such the smallest (respectively, the largest) zero of these MOPS is located outside the support of the original measure μ. When μ is semi-classical, we obtain the ladder operators and the second order linear differential equation satisfied by the Geronimus perturbed MOPS, and we also give an electrostatic interpretation of the zero distribution in terms of a logarithmic potential interaction under the action of an external field. We analyze such an equilibrium problem when the mass point of the perturbation c is located outside the support of μ.
Edge detection based on Krawtchouk polynomials
(Elsevier, 2015-08-15) Rivero Castillo, Daniel; Pijeira Cabrera, Héctor Esteban; Assunçao, Pedro
Discrete orthogonal polynomials are useful tools in digital image processing to extract visual object contours in different application contexts. This paper proposes an alternative method that extends beyond classic first-order differential operators, by using the properties of Krawtchouk orthogonal polynomials to achieve a first order differential operator. Therefore, smoothing of the image with a 2-D Gaussian filter is not necessary to regularize the ill-posed nature of differentiation. Experimentally, we provide simulation results which show that the proposed method achieves good performance in comparison with commonly used algorithms.
On the convergence of type I Hermite-Padé approximants for rational perturbations of a Nikishin system
(Elsevier, 2014-01-20) López Lagomasino, Guillermo; Medina Peralta, Sergio
We study the convergence of type I Hermite-Padé approximation for a class of meromorphic functions obtained by adding a vector of rational functions with real coefficients to a Nikishin system of functions.
A Jacobi type Christoffel–Darboux formula for multiple orthogonal polynomials of mixed type
(Elsevier, 2016-07) Araznibarreta, Gerardo; Mañas, Manuel
An alternative expression for the Christoffel–Darboux formula for multiple orthogonal polynomials of mixed type is derived from the LU factorization of the moment matrix of a given measure and two sets of weights. We use the action of the generalized Jacobi matrix J, also responsible for the recurrence relations, on the linear forms and their duals to obtain the result.
Learning dynamics explains human behavior in Prisoner's Dilemma on networks
(The Royal Society, 2014-03-31) Cimini, Giulio; Sánchez, Angel
Cooperative behavior lies at the very basis of human societies, yet its evolutionary origin remains a key unsolved puzzle. Whereas reciprocity or conditional cooperation is one of the most prominent mechanisms proposed to explain the emergence of cooperation in social dilemmas, recent experimental findings on networked Prisoner's Dilemma games suggest that conditional cooperation also depends on the previous action of the player—namely on the 'mood' in which the player currently is. Roughly, a majority of people behave as conditional cooperators if they cooperated in the past, while they ignore the context and free-ride with high probability if they did not. However, the ultimate origin of this behavior represents a conundrum itself. Here we aim specifically at providing an evolutionary explanation of moody conditional cooperation. To this end, we perform an extensive analysis of different evolutionary dynamics for players' behavioral traits—ranging from standard processes used in game theory based on payoff comparison to others that include non-economic or social factors. Our results show that only a dynamic built upon reinforcement learning is able to give rise to evolutionarily stable moody conditional cooperation, and at the end to reproduce the human behaviors observed in the experiments.
Recent trends in orthogonal polynomials and their applications
(Sociedad Española de Matemática Aplicada (SEMA), 2001) Marcellán Español, Francisco José; Arvesú Carballo, Jorge
In this contribution we summarize some new directions in the theory of orthogonal polynomials. In particular, we emphasize three kinds of orthogonality conditions which have attracted the interest of researchers from the last decade to the present time. The connection with operator theory, potential theory and numerical analysis will be shown.
On the stability of recurrence relations for hypergeometric functions
(Wiley VCH, 2005) Deaño Cabrera, Alfredo; Segura, Javier
We consider the three term recurrence relations y_n+1 + a_n y_n + b_n y_n-1 = 0 satisfied simultaneously by confluent hypergeometric functions M(a+kn; c+mn; x) and U(a+kn; c+mn; x) (up to normalizations not depending on x). The parameters a, c, x are fixed and k,m = 0,±1. The existence of minimal solutions when n -> ∞ is a crucial piece of information when we intend to use a recurrence relation for computation. However, in some cases the behavior of the solutions for moderate values of n can be opposite to the asymptotic behaviour. We provide numerical examples of this phenomenon, already noted by W. Gautschi in the case (k,m) = (1,1), both for the recurrence relations and for the associated continued fractions.
Asymptotic behavior of orthogonal polynomials primitives
(Universidad de La Rioja, 2001) Fundora, Alfredo; Pijeira Cabrera, Héctor Esteban; Urbina, Wilfredo
We study the zero location and the asymptotic behavior of the primitives of the standard orthogonal polynomials with respect to a finite positive Borel measure concentrate on [−1,1].
Approximation theory for weighted Sobolev spaces on curves
(Universidad de La Rioja, 2001) Álvarez, Venancio; Pestana, Domingo; Rodríguez, José M.; Romera, Elena
In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete. We also prove the density of the polynomials in these spaces for non-closed compact curves and, finally, we find conditions under which the multiplication operator is bounded on the completion of polynomials. These results have applications to the study of zeroes and asymptotics of Sobolev orthogonal polynomials.
Laguerre polynomials in a relativistic quantum-statistical model
(Universidad Carlos III de Madrid, Departamento de Matemáticas, 1996) Arvesú Carballo, Jorge
The main aim of this work is to find analytical expressions for the eigenvalues and eigenfunctions corresponding to Dirac equation, for hot and dense matter. It is shown that the Laguerre polynomials depending on the effective charge are solutions for self-consistent fields. To determine the screening constant and affective charge we introduce and minimize a functional. These formulas are accurate for machine calculation of bound-bound, bound-free and free-free transitions, including large values of principal quantum numbers. Hence these expressions would be in accordance with quantum-statistical results based on more sophisticated calculations. Comparison with the solutions of the Schrödinger equation for different substancies are discussed.
Convergencia relativa de polinomios ortogonales variantes
(Universidad de La Rioja, 2001) Calle Ysern, Bernardo de la; López Lagomasino, Guillermo
We consider the relative asymptotic behaviour of orthogonal polynomials with respect to varying measures supported on the real line and the unit circle. The main feature of the results is the generality of the class of measures studied.
k-Coherence of measures with non-classical weights
(Universidad de La Rioja, 2001) Marcellán Español, Francisco José; Martínez-Finkelshtein, Andrei; Moreno Balcázar, Juan José
The concept of k-coherence of two positive measures μ1 and μ2 is useful in the study of the Sobolev orthogonal polynomials. If μ1 or μ2 are compactly supported on R then any 0-coherent pair or symmetrically 1-coherent pair (μ1, μ2) must contain a Jacobi measure (up to affine transformation). Here examples of k-coherent pairs (k ≥ 1) when neither μ1 nor μ2 are Jacobi are constructed.
Problemas abiertos en series de Fourier de Jacobi-Sobolev
(Universidad de La Rioja, 2001) Marcellán Español, Francisco José; Osilenker, Boris P.; Álvarez Rocha, Ignacio
In this paper we deal with several problems concerning estimates of polynomials orthogonal with respect to Sobolev inner products. These problems have been motivated by some previous work by J. J. Guadalupe et al. when the standard orthogonality using measures with mass points is considered in the study of Fourier expansions in terms of orthogonal polynomials.

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