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Browsing by Author "Álvarez Nodarse, Renato"
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A characterization of the classical orthogonal discrete and qpolynomials [Article]
Alfaro García, Manuel; Álvarez Nodarse, Renato (Elsevier, 20070401)In this paper we present a new characterization for the classical discrete and qclassical (discrete) polynomials (in the Hahn's sense).

A generalization of the classical Laguerre polynomials [Article]
Álvarez Nodarse, Renato; Marcellán Español, Francisco (Springer, 1995)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 ...

A qanalog of the Racah polynomials and the qalgebra SUq(2) [Article]
Álvarez Nodarse, Renato; Smirnov, Yuri F.; Costas Santos, Roberto Santiago (Springer, 200601)We study some qanalogues of the Racah polynomials and some of their applications in the theory of representation of quantum algebras.

A qextension of the generalized Hermite polynomials with the continuous orthogonality property on R [Article]
Álvarez Nodarse, Renato; Atakishiyeva Kyazim Zade, Messouma; Atakishiyev Mektiyev, Natig (Academic Publications, 2004)In this paper we study in detail a qextension of the generalized Hermite polynomials of Szeg˝o. A continuous orthogonality property on R with respect to the positive weight function is established, a qdifference equation ...

Asymptotic properties of generalized Laguerre orthogonal polynomials [Article]
Álvarez Nodarse, Renato; Moreno Balcázar, Juan José (Elsevier, 200406)In the present paper we deal with the polynomials L(α,M,N) n (x) orthogonal with respect to the Sobolev inner product (p, q) = 1 Γ(α+1) Z ∞ 0 p(x)q(x) x α e −x dx + M p(0)q(0) + N p 0 (0)q 0 (0), N,M ≥ 0, α > −1, firstly ...

À la carte recurrence relations for continuous and discrete hypergeometric functions [Article]
Álvarez Nodarse, Renato (Sociedad Española de Matemática Aplicada, 201109)We show how, using the constructive approach for special functions introduced by Nikiforov and Uvarov, one can obtain recurrence relations for the hypergeometrictype functions not only for the continuous case but also ...

Comment on “Ratchet universality in the presence of thermal noise” [Article]
Quintero, Niurka R.; Álvarez Nodarse, Renato; Cuesta, José Antonio (2013)A recent paper [P. J. Martínez and R. Chacón, Phys. Rev. E 87, 062114 (2013)] presents numerical simulations on a system exhibiting directed ratchet transport of a driven overdamped Brownian particle subjected to a spatially ...

La corriente promedio en los ”rocking ratchets” [Presentation]
Quintero, Niurka R.; Álvarez Nodarse, Renato; Cuesta, José A. (2012) 
Distribution of zeros of discrete and continuous polynomials from their recurrence relation [Article]
Álvarez Nodarse, Renato; Sánchez Dehesa, Jesús (Elsevier, 20020525)The hypergeometric polynomials in a continous or a discrete variable, whose canonical forms are the socalled classical orthogonal polynomial systems, are ob jects which naturally appear in a broad range of physical and ...

Driven and damped double sineGordon equation: The influence of internal modes on the soliton ratchet mobility [Article]
Quintero, Niurka R.; Álvarez Nodarse, Renato; Mertens, Franz G. (2009)This work studies the damped double sineGordon equation driven by a biharmonic force, where a parameter λ controls the existence and the frequency of an internal mode. The role of internal oscillations of the kink width ...

El efecto ratchet en la partícula relativista [Presentation]
Álvarez Nodarse, Renato; Cuesta, José A.; Quintero, Niurka R. (2012) 
Factorization method for difference equations of hypergeometric type on nonuniform lattices [Article]
Álvarez Nodarse, Renato; Costas Santos, Roberto Santiago (IOP Publishing, 20010629)We study the factorization of the hypergeometrictype difference equation of Nikiforov and Uvarov on nonuniform lattices. An explicit form of the raising and lowering operators is derived and some relevant examples are given.

Factorization of the hypergeometrictype difference equation on the nonuniform lattices: dynamical algebra [Article]
Álvarez Nodarse, Renato; Atakishiyev Mektiyev, Natig; Costas Santos, Roberto Santiago (Institute of Physics, 20050107)We argue that one can factorize the difference equation of hypergeometric type on the nonuniform lattices in general case. It is shown that in the most cases of qlinear spectrum of the eigenvalues this directly leads to ...

Factorization of the hypergeometrictype difference equation on the uniform lattice [Article]
Atakishiyev Mektiyev, Natig; Álvarez Nodarse, Renato; Costas Santos, R. (2007) 
Functionals of harmonics functions [Presentation]
Quintero, Niurka R.; Cuesta Ruiz, José Antonio; Álvarez Nodarse, Renato (Multidisciplinary Digital Publishing Institute, 201801)Let CsT, with T > 0, be the set of continuous, Tperiodic functions f : R → Rs, and let Γ : CsT → R be a real functional on CsT.

General approach for dealing with dynamical systems with spatiotemporal periodicities [Article]
Casado Pascual, Jesús; Cuesta, José A.; Quintero, Niurka R.; Álvarez Nodarse, Renato (American Physical Society, 2015)Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected in the properties of these systems through a dependence on the parameters of their periodic terms. ...

JacobiSobolevtype orthogonal polynomials: secondorder differential equation and zeros [Article]
Arvesú Carballo, Jorge; Álvarez Nodarse, Renato; Marcellán Español, Francisco; Pan, KeLin (Elsevier, 19980417)We obtain an explicit expression for the Sobolevtype orthogonal polynomials {Qn} associated with the inner product 〈p,q〉=∫−11 p(x)q(x)p(x)dx + A1p(1)q(1) + B1p(−1)q(−1) + A2p′(1)q′(1) + B2p′(−1)q′(−1), where p(x) = (1 − ...

Kink topology control by highfrequency external forces in nonlinear KleinGordon models [Article]
Álvarez Nodarse, Renato; Quintero, Niurka R.; Mertens, Franz G. (American Physical Society, 2014)A method of averaging is applied to study the dynamics of a kink in the damped double sineGordon equation driven by both external (nonparametric) and parametric periodic forces at high frequencies. This theoretical approach ...

Limit relations between qKrall type orthogonal polynomials [Article]
Álvarez Nodarse, Renato; Costas Santos, Roberto Santiago (Elsevier, 2006)In this paper, we consider a natural extension of several results related to Kralltype polynomials introducing a modification of a qclassical linear functional via the addition of one or two mass points. The limit relations ...

Mellin transforms for some families of qpolynomials [Article]
Álvarez Nodarse, Renato; Atakishiyeva Kyazim Zade, Messouma; Atakishiyev Mektiyev, Natig (Elsevier, 20030401)By using Ramanujan's qextension of the Euler integral representation for the gamma function, we derive the Mellin integral transforms for the families of the discrete qHermite II, the AlSalam–Carlitz II, the big qLaguerre, ...