Data

NameÁlvarez Nodarse, Renato
DepartmentAnálisis Matemático
Knowledge areaAnálisis Matemático
Professional categoryCatedrático de Universidad
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  • Items

    72

  • Visits

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  Publications

 

Final Degree Project
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El teorema de muestreo y sus aplicaciones

Álvarez Nodarse, Renato; García Fernández, José (2018-09-01)
En este trabajo nuestro objeto de estudio será la teoría de señales, el objetivo es llegar al teorema de muestreo de ...
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Uniform convergence of basic Fourier-Bessel series on a q-linear grid

Abreu, Luis Daniel; Álvarez Nodarse, Renato; Dos Santos Cardoso, José Luis (Springer, 2018-09-01)
We study Fourier-Bessel series on a q-linear grid, defined as expansions in complete q-orthogonal systems constructed with ...
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Functionals of harmonics functions

Quintero, Niurka R.; Cuesta Ruiz, José Antonio; Álvarez Nodarse, Renato (Multidisciplinary Digital Publishing Institute, 2018-01-01)
Let CsT, with T > 0, be the set of continuous, T-periodic functions f : R → Rs, and let Γ : CsT → R be a real functional on CsT.
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On q-polynomials and some of their applications

Álvarez Nodarse, Renato (2016-01-01)
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On linearly related sequences of difference derivatives of discrete orthogonal polynomials

Álvarez Nodarse, Renato; Soares Petronilho, José Carlos; Pinzón Cortés, Natalia Camila; Sevinik Adigüzel, Rezan (Elsevier, 2015-08-15)
Let ν be either ω ∈ C \ {0} or q ∈ C \ {0, 1}, and let Dν be the corresponding difference operator defined in the usual ...
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General approach for dealing with dynamical systems with spatiotemporal periodicities

Casado Pascual, Jesús; Cuesta, José A.; Quintero, Niurka R.; Álvarez Nodarse, Renato (American Physical Society, 2015-01-01)
Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected ...
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Paramagnetic colloidal ribbons in a precessing magnetic field

Álvarez Nodarse, Renato; Quintero, Niurka R.; Mertens, Franz G.; Casic, N.; Fischer, Thomas M. (American Physical Society, 2015-01-01)
We investigate the dynamics of a kink in a damped parametrically driven nonlinear Klein-Gordon equation.We show by using ...
PhD Thesis
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Orthogonal matrix polynomials and differential, difference and q-difference matrix operators

Durán Guardeño, Antonio José; Álvarez Nodarse, Renato; Martínez de los Ríos, Ana (2014-09-05)
In this thesis we present a series of result that are framed in the theory of Matrix Orthogonal Polynomials, a branch of ...
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On the limit of non-standard q-Racah polynomials

Álvarez Nodarse, Renato; Sevinik Adigüzel, Rezan (2014-03-15)
The aim of this article is to study the limit transitions from non-standard q-Racah polynomials to big q-Jacobi, dual ...
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Kink topology control by high-frequency external forces in nonlinear Klein-Gordon models

Álvarez Nodarse, Renato; Quintero, Niurka R.; Mertens, Franz G. (American Physical Society, 2014-01-01)
A method of averaging is applied to study the dynamics of a kink in the damped double sine-Gordon equation driven by both ...
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On the properties of special functions on the linear-type lattices

Álvarez Nodarse, Renato; Santos Cardoso, José Luis dos (Elsevier, 2013-09-01)
We present a general theory for studying the difference analogues of special functions of hypergeometric type on the ...
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On the generalized Askey-Wilson polynomials

Álvarez Nodarse, Renato; Sevinik Adigüzel, Rezan (Elsevier, 2013-06-01)
In this paper a generalization of Askey-Wilson polynomials is introduced. These polynomials are obtained from the Askey-Wilson ...
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Time-shift invariance determines the functional shape of the current in dissipative rocking ratchets

Cuesta, José Antonio; Quintero, Niurka R.; Álvarez Nodarse, Renato (2013-01-01)
Ratchets are devices that are able to rectify an otherwise oscillatory behavior by exploiting an asymmetry of the system. ...
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Comment on “Ratchet universality in the presence of thermal noise”

Quintero, Niurka R.; Álvarez Nodarse, Renato; Cuesta, José Antonio (2013-01-01)
A recent paper [P. J. Martínez and R. Chacón, Phys. Rev. E 87, 062114 (2013)] presents numerical simulations on a system ...
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Propulsion efficiency of a dynamic self-assembled helical ribbon

Casic, Nebojsa; Quintero, Niurka R.; Álvarez Nodarse, Renato; Mertens, Franz G.; Jibuti, Levan; Zimmermann, Walter; Fischer, Thomas M. (2013-01-01)
We study the dynamic self-assembly and propulsion of a ribbon formed from paramagnetic colloids in a dynamic magnetic ...
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The q-Racah-Krall-type polynomials

Álvarez Nodarse, Renato; Sevinik Adigüzel, Rezan (Elsevier, 2012-08-01)
In this paper the Krall-type polynomials obtained via the addition of two mass points to the weight function of the standard ...
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Spectral properties of certain tridiagonal matrices

Álvarez Nodarse, Renato; Soares Petronilho, José Carlos; Quintero, Niurka R. (Elsevier, 2012-02-01)
We study spectral properties of irreducible tridiagonal k−Toeplitz matrices and certain matrices which arise as perturbations of them.
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El efecto ratchet en la partícula relativista

Álvarez Nodarse, Renato; Cuesta, José A.; Quintero, Niurka R. (2012-01-01)
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La corriente promedio en los ”rocking ratchets”

Quintero, Niurka R.; Álvarez Nodarse, Renato; Cuesta, José A. (2012-01-01)
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On the orthogonality of q-classical polynomials of the Hahn class

Taseli, Hasan; Álvarez Nodarse, Renato; Sevinik, Rezan (2012-01-01)
The central idea behind this review article is to discuss in a unified sense the orthogonality of all possible polynomial ...
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À la carte recurrence relations for continuous and discrete hypergeometric functions

Álvarez Nodarse, Renato (Sociedad Española de Matemática Aplicada, 2011-09-01)
We show how, using the constructive approach for special functions introduced by Nikiforov and Uvarov, one can obtain ...
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On the Krall-type polynomials on q-quadratic lattices

Álvarez Nodarse, Renato; Sevinik Adigüzel, Rezan (Elsevier, 2011-08-01)
In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear ...
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Ratchet effect on a relativistic particle driven by external forces

Quintero, Niurka R.; Álvarez Nodarse, Renato; Cuesta Ruiz, José Antonio (Institute of Physics, 2011-01-01)
We study the ratchet effect of a damped relativistic particle driven by both asymmetric temporal bi-harmonic and time-periodic ...
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Symmetries shape the current in ratchets induced by a biharmonic driving force

Álvarez Nodarse, Renato; Quintero, Niurka R.; Cuesta, José Antonio (2010-03-23)
Equations describing the evolution of particles, solitons, or localized structures, driven by a zero-average, periodic, ...
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Symmetries shape the current in ratchets induced by a biharmonic driving force [Rapid Comunication]

Quintero, Niurka R.; Cuesta, José A.; Álvarez Nodarse, Renato (American Physical Society, 2010-01-01)
Equations describing the evolution of particles, solitons, or localized structures, driven by a zero-average, periodic, ...
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Driven and damped double sine-Gordon equation: The influence of internal modes on the soliton ratchet mobility

Quintero, Niurka R.; Álvarez Nodarse, Renato; Mertens, Franz G. (2009-01-01)
This work studies the damped double sine-Gordon equation driven by a biharmonic force, where a parameter λ controls the ...
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Structural and recurrence relations for hypergeometric-type functions by Nikiforov-Uvarov method

Santos Cardoso, José Luis dos; Fernandes, Cibele M.; Álvarez Nodarse, Renato (Kent State University, 2009-01-01)
The functions of hypergeometric-type are the solutions y = yν(z) of the differential equation σ(z)y ′′ + τ(z)y ′ + λy = ...
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A characterization of the classical orthogonal discrete and q-polynomials

Alfaro García, Manuel; Álvarez Nodarse, Renato (Elsevier, 2007-04-01)
In this paper we present a new characterization for the classical discrete and q-classical (discrete) polynomials (in the Hahn's sense).
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Factorization of the hypergeometric-type difference equation on the uniform lattice

Atakishiyev Mektiyev, Natig; Álvarez Nodarse, Renato; Costas Santos, R. (2007-01-01)
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On characterizations of classical polynomials

Álvarez Nodarse, Renato (Elsevier, 2006-11-01)
It is well known that the classical families of Jacobi, Laguerre, Hermite, and Bessel polynomials are characterized as ...
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Special volume on orthogonal polynomials and mathematical physics

Álvarez Nodarse, Renato; Arvesú Carballo, Jorge; Marcellán Español, Francisco (Kent State University, 2006-01-01)
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A q-analog of the Racah polynomials and the q-algebra SUq(2)

Álvarez Nodarse, Renato; Smirnov, Yuri F.; Costas Santos, Roberto Santiago (Springer, 2006-01-01)
We study some q-analogues of the Racah polynomials and some of their applications in the theory of representation of quantum algebras.
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Modelos matemáticos en biología: un viaje de ida y vuelta

Álvarez Nodarse, Renato (Sociedad Española de Matemática Aplicada, 2006-01-01)
El objetivo de este trabajo es mostrar la provechosa interacción entre la Biología y la Matemática. Para ello veremos cómo, ...
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Limit relations between q-Krall type orthogonal polynomials

Álvarez Nodarse, Renato; Costas Santos, Roberto Santiago (Elsevier, 2006-01-01)
In this paper, we consider a natural extension of several results related to Krall-type polynomials introducing a modification ...
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On recurrence relations for radial wave functions for the N-th dimensional oscillators and hydrogenlike atoms: analytical and numerical study

Álvarez Nodarse, Renato; Cardoso, José Luis; Quintero, Niurka R. (2006-01-01)
Using a general procedure for finding recurrence relations for hypergeometric functions and polynomials introduced by ...
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On some tridiagonal k-Toeplitz matrices: algebraic and analytical aspects. Applications

Álvarez Nodarse, Renato; Soares Petronilho, José Carlos; Quintero, Niurka R. (Elsevier, 2005-12-15)
In this paper we use the analytic theory for 2 and 3-Toeplitz matrices to obtain the explicit expressions for the eigenvalues, ...
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On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on R

Álvarez Nodarse, Renato; Atakishiyeva Kyazim Zade, Messouma; Atakishiyev Mektiyev, Natig (Springer, 2005-11-01)
We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics, based on a q-extension of the classical ...
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Factorization of the hypergeometric-type difference equation on the non-uniform lattices: dynamical algebra

Álvarez Nodarse, Renato; Atakishiyev Mektiyev, Natig; Costas Santos, Roberto Santiago (Institute of Physics, 2005-01-07)
We argue that one can factorize the difference equation of hypergeometric type on the nonuniform lattices in general case. ...
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Recurrence relations for discrete hypergeometric functions

Álvarez Nodarse, Renato; Santos Cardoso, José Luis dos (Taylor & Francis, 2005-01-01)
We present a general procedure for finding linear recurrence relations for the solutions of the second order difference equation of hypergeometric type. Applications to wave functions of certain discrete system are also given.
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On the Krall-type discrete polynomials

Álvarez Nodarse, Renato; Soares Petronilho, José Carlos (Elsevier, 2004-07-01)
In this paper we present a unified theory for studying the so called Kralltype discrete orthogonal polynomials. In particular, ...
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Asymptotic properties of generalized Laguerre orthogonal polynomials

Álvarez Nodarse, Renato; Moreno Balcázar, Juan José (Elsevier, 2004-06-01)
In the present paper we deal with the polynomials L(α,M,N) n (x) orthogonal with respect to the Sobolev inner product (p, ...
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Modifications of quasi-definite linear functionals via addition of delta and derivatives of delta Dirac functions

Álvarez Nodarse, Renato; Arvesú Carballo, Jorge; Marcellán Español, Francisco (Elsevier, 2004-01-01)
We consider the general theory of the modifications of quasi-definite linear functionals by adding discrete measures. We ...
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On the Krall-type polynomials

Álvarez Nodarse, Renato; Arvesú Carballo, Jorge; Marcellán Español, Francisco (2004-01-01)
Using a general and simple algebraic approach, some results on Krall-type orthogonal polynomials and some of their extensions are obtained.
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A q-extension of the generalized Hermite polynomials with the continuous orthogonality property on R

Álvarez Nodarse, Renato; Atakishiyeva Kyazim Zade, Messouma; Atakishiyev Mektiyev, Natig (Academic Publications, 2004-01-01)
In this paper we study in detail a q-extension of the generalized Hermite polynomials of Szeg˝o. A continuous orthogonality ...
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Some limit relations in the A1 tableau of Dunkl-Cherednik operators

Álvarez Nodarse, Renato (Elsevier, 2003-12-15)
In this paper we study some limit relations involving some q-special functions related with the A1 (root system) tableau ...
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Mellin transforms for some families of q-polynomials

Álvarez Nodarse, Renato; Atakishiyeva Kyazim Zade, Messouma; Atakishiyev Mektiyev, Natig (Elsevier, 2003-04-01)
By using Ramanujan's q-extension of the Euler integral representation for the gamma function, we derive the Mellin integral ...
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On a q-extension of the Hermite polynomials Hn(x) with the continuous orthogonality property on R1

Álvarez Nodarse, Renato; Atakishiyeva Kyazim Zade, Messouma; Atakishiyev Mektiyev, Natig (Sociedad Matemática Mexicana / Springer, 2002-10-01)
We study a polynomial sequence of q-extensions of the classical Hermite polynomials Hn(x), which satisfi es continuous ...
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Distribution of zeros of discrete and continuous polynomials from their recurrence relation

Álvarez Nodarse, Renato; Sánchez Dehesa, Jesús (Elsevier, 2002-05-25)
The hypergeometric polynomials in a continous or a discrete variable, whose canonical forms are the so-called classical ...
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On a modification of the Jacobi linear functional asymptotic properties and zeros of the corresponding orthogonal polynomials

Arvesú Carballo, Jorge; Marcellán Español, Francisco; Álvarez Nodarse, Renato (Springer, 2002-04-01)
The paper deals with orthogonal polynomials in the case where the orthogonality condition is related to semiclassical ...
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q-Classical polynomials and the q-Askey and Nikiforov-Uvarov tableaus

Álvarez Nodarse, Renato; Medem Roesicke, Juan Carlos (Elsevier, 2001-10-15)
In this paper we continue the study of the q-classical (discrete) polynomials (in the Hahn's sense) started in Medem et ...
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On the q-polynomials: a distributional study

Medem Roesicke, Juan Carlos; Álvarez Nodarse, Renato; Marcellán Español, Francisco (Elsevier, 2001-10-15)
In this paper we present a uni1ed distributional study of the classical discrete q-polynomials (in the Hahn’s sense). From ...
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Factorization method for difference equations of hypergeometric type on nonuniform lattices

Álvarez Nodarse, Renato; Costas Santos, Roberto Santiago (IOP Publishing, 2001-06-29)
We study the factorization of the hypergeometric-type 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.
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On the connection and linearization problem for discrete hypergeometric q-polynomials

Álvarez Nodarse, Renato; Arvesú Carballo, Jorge; Yáñez García, Rafael José (Elsevier, 2001-05-01)
In the present paper, starting from the second-order difference hypergeometric equation on the non-uniform lattice x(s) ...
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On the "Favard theorem" and its extensions

Marcellán Español, Francisco; Álvarez Nodarse, Renato (Elsevier, 2001-01-15)
In this paper we present a survey on the "Favard theorem" and its extensions.
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Polinomios ortogonales: historia y aplicaciones

Álvarez Nodarse, Renato (Sociedad Española de Matemática Aplicada, 2001-01-01)
Chapter of Book
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Los q-polinomios hipergeométricos

Español González, Luis; Varona Malumbres, Juan Luis; Álvarez Nodarse, Renato (Universidad de La Rioja, 2001-01-01)
It is well known that the q-polynomials of hypergeometric type are the polynomial solutions of a certain second order ...
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On the linearization problem involving Pochhammer symbols and their q-analogues

Álvarez Nodarse, Renato; Quintero, Niurka R.; Rouveaux, André (Elsevier, 1999-07-15)
In this paper we present a simple recurrent algorithm for solving the linearization problem involving some families of q-polynomials in the exponential lattice x(s)=c1qs+c3. Some simple examples are worked out in detail.
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On the q-polynomials on the exponential lattice x(s)= c 1 qs + c 3

Álvarez Nodarse, Renato; Arvesú Carballo, Jorge (Taylor & Francis, 1999-01-01)
The main goal of this paper is to continue the study of the q-polynomials on non-uniform lattices by using the approach ...
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Second order difference equations for certain families of discrete polynomials

Álvarez Nodarse, Renato (Elsevier, 1998-11-16)
In this paper we will consider two algorithms which allow us to obtain second order linear di erence equations for certain ...
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WKB approximation and Krall-Type orthogonal polynomials

Álvarez Nodarse, Renato; Marcellán Español, Francisco; Soares Petronilho, José Carlos (Springer, 1998-10-01)
We give an uni ed approach to the Krall-type polynomials orthogonal with respect to a positive measure consisting of an ...
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Jacobi-Sobolev-type orthogonal polynomials: second-order differential equation and zeros

Arvesú Carballo, Jorge; Álvarez Nodarse, Renato; Marcellán Español, Francisco; Pan, Ke-Lin (Elsevier, 1998-04-17)
We obtain an explicit expression for the Sobolev-type orthogonal polynomials {Qn} associated with the inner product ...
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Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials

Álvarez Nodarse, Renato; Yáñez García, Rafael José; Sánchez Dehesa, Jesús (Elsevier, 1998-03-09)
Starting from the second-order difference hypergeometric equation satisfied by the set of discrete orthogonal polynomials ...
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On the modification of classical orthogonal polynomials: the symmetric case

Álvarez Nodarse, Renato; Marcellán Español, Francisco (Springer, 1998-03-01)
We consider the modifcations of the monic Hermite and Gegenbauer polynomials via the addition of one point mass at the ...
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Some extension of the Bessel-type orthogonal polynomials

Arvesú Carballo, Jorge; Álvarez Nodarse, Renato; Marcellán Español, Francisco; Kwon, Kil Hyun (Taylor & Francis, 1998-01-01)
We consider the perturbation of the classical Bessel moment functional by the addition of the linear functional M0 (x) + ...
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The distribution of zeros of general q-polynomials

Álvarez Nodarse, Renato; Buendía Ávila, Enrique; Sánchez-Dehesa Moreno-Cid, Jesús (Institute of Physics, 1997-10-07)
A general system of q-orthogonal polynomials is de ned by means of its three-term recurrence relation. This system encompasses ...
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The limit relations between generalized orthogonal polynomials

Álvarez Nodarse, Renato; Marcellán Español, Francisco (Elsevier, 1997-09-01)
We consider the different limit transitions for modifications of the classical polynomials obtained by the addition of one ...
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Recurrence relations for connection coefficients between q-orthogonal polynomials of discrete variables in the non-uniform lattice X(s) = q2s

Álvarez Nodarse, Renato; Ronveaux, André (Institute of Physics, 1996-11-21)
We obtain the structure relations for q-orthogonal polynomials in the exponential lattice q 2s and from that we construct ...
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The dual Hahn q-polynomials in the lattice x(s) = [s]q[s + 1] q and the q-Algebras SUq(2) and SUq(1; 1)

Álvarez Nodarse, Renato; Smirnov, Yuri F. (Institute of Physics, 1996-04-07)
The dual q-Hahn polynomials in the non uniform lattice x(s) = [s]q[s + 1]q are obtained. The main data for these polynomials ...
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On the properties for modifications of classical orthogonal polynomials of discrete variables

Álvarez Nodarse, Renato; García García, Antonio; Marcellán Español, Francisco (Elsevier, 1995-12-29)
We consider a modi cation of moment functionals for some classical polynomials of a discrete variable by adding a mass ...
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A generalization of the classical Laguerre polynomials

Álvarez Nodarse, Renato; Marcellán Español, Francisco (Springer, 1995-01-01)
We consider a modi cation of the gamma distribution by adding a discrete measure supported in the point x = 0. For large ...
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The modification of classical Hahn polynomials of a discrete variable

Álvarez Nodarse, Renato; Marcellán Español, Francisco (Taylor & Francis, 1995-01-01)
We consider a modi cation of moment functionals for the Hahn classical polynomials of a discrete variable by adding two ...
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q-Deformed Vibron model for diatomic molecules

Álvarez Nodarse, Renato; Bonatsos, Dennis; Smirnov, Yuri F. (American Physical Society, 1994-08-01)
A deformed version of the vibron model for diatomic molecules is constructed. Both the O(4) and U(3) dynamical symmetries ...