Artículos (Análisis Matemático)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10809

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A characterization of the classical orthogonal discrete and q-polynomials
(Elsevier, 2007-04-01) Alfaro García, Manuel; Álvarez Nodarse, Renato; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM262: Teoría de la Aproximación
In this paper we present a new characterization for the classical discrete and q-classical (discrete) polynomials (in the Hahn's sense).
A generalization of the classical Laguerre polynomials
(Springer, 1995) Álvarez Nodarse, Renato; Marcellán Español, Francisco; Universidad de Sevilla. Departamento de Análisis Matemático; Instituto de Cooperación Iberoamericana (ICI); Comisión Interministerial de Ciencia y Tecnología (CICYT). España
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 represent them as the hypergeometric function 3F3:
À la carte recurrence relations for continuous and discrete hypergeometric functions
(Sociedad Española de Matemática Aplicada, 2011-09) Álvarez Nodarse, Renato; Universidad de Sevilla. Departamento de Análisis Matemático; Dirección General de Enseñanza Superior. España; Junta de Andalucía
We show how, using the constructive approach for special functions introduced by Nikiforov and Uvarov, one can obtain recurrence relations for the hypergeometric-type functions not only for the continuous case but also for the discrete and q-linear cases, respectively. Some applications in Quantum Physics are discussed.
A q-analog of the Racah polynomials and the q-algebra SUq(2)
(Springer, 2006-01) Álvarez Nodarse, Renato; Smirnov, Yuri F.; Costas Santos, Roberto Santiago; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM262: Teoria de la Aproximacion
We study some q-analogues of the Racah polynomials and some of their applications in the theory of representation of quantum algebras.
A q-extension of the generalized Hermite polynomials with the continuous orthogonality property on R
(Academic Publications, 2004) Álvarez Nodarse, Renato; Atakishiyeva Kyazim Zade, Messouma; Atakishiyev Mektiyev, Natig; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM262: Teoría de la Aproximación
In this paper we study in detail a q-extension of the generalized Hermite polynomials of Szeg˝o. A continuous orthogonality property on R with respect to the positive weight function is established, a q-difference equation and a three-term recurrence relation are derived for this family of q-polynomials.
Asymptotic properties of generalized Laguerre orthogonal polynomials
(Elsevier, 2004-06) Álvarez Nodarse, Renato; Moreno Balcázar, Juan José; Universidad de Sevilla. Departamento de Análisis Matemático
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 introduced by Koekoek and Meijer in 1993 and extensively studied in the last years. We present some new asymptotic properties of these polynomials and also a limit relation between the zeros of these polynomials and the zeros of Bessel function Jα(x). The results are illustrated with numerical examples. Also, some general asymptotic formulas for generalizations of these polynomials are conjectured.
Comment on “Ratchet universality in the presence of thermal noise”
(2013) Quintero, Niurka R.; Álvarez Nodarse, Renato; Cuesta, José Antonio; Universidad de Sevilla. Departamento de Física Aplicada I; Universidad de Sevilla. Departamento de Análisis Matemático
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 periodic, symmetric potential. The authors claim that their simulations prove the existence of a universal waveform of the external force that optimally enhances directed transport, hence confirming the validity of a previous conjecture put forth by one of them in the limit of vanishing noise intensity. With minor corrections due to noise, the conjecture holds even in the presence of noise, according to the authors. On the basis of their results the authors claim that all previous theories, which predict a different optimal force waveform, are incorrect. In this Comment we provide sufficient numerical evidence showing that there is no such universal force waveform and that the evidence obtained by the authors otherwise is due to their particular choice of parameters. Our simulations also suggest that previous theories correctly predict the shape of the optimal waveform within their validity regime, namely, when the forcing is weak. On the contrary, the aforementioned conjecture does not hold.
Distribution of zeros of discrete and continuous polynomials from their recurrence relation
(Elsevier, 2002-05-25) Álvarez Nodarse, Renato; Sánchez Dehesa, Jesús; Universidad de Sevilla. Departamento de Análisis Matemático; Junta de Andalucía; Dirección General de Enseñanza Superior. España
The hypergeometric polynomials in a continous or a discrete variable, whose canonical forms are the so-called classical orthogonal polynomial systems, are ob jects which naturally appear in a broad range of physical and mathematical elds from quantum mechanics, the theory of vibrating strings and the theory of group representations to numerical analysis and the theory of Sturm-Liouville di erential and di erence equations. Often, they are encountered in the form of a three term recurrence relation (TTRR) which connects a polynomial of a given order with the polynomial of the contiguous orders. This relation can be directly found, in particular, by use of Lanczos-type methods, tight-binding models or the application of the conventional discretisation procedures to a given di erential operator. Here the distribution of zeros and its asymptotic limit, characterized by means of its moments around the origin, are found for the continuous classical (Hermite, Laguerre, Jacobi, Bessel) polynomials and for the discrete classical (Charlier, Meixner, Kravchuk, Hahn) polynomials by means of a general procedure which (i) only requires the three-term recurrence relation and (ii) avoids the often high-brow subleties of the potential theoretic considerations used in some recent approaches. The moments are given in an explicit manner which, at times, allows us to recognize the analytical form of the corresponding distribution.
Driven and damped double sine-Gordon equation: The influence of internal modes on the soliton ratchet mobility
(2009) Quintero, Niurka R.; Álvarez Nodarse, Renato; Mertens, Franz G.; Universidad de Sevilla. Departamento de Física Aplicada I; Universidad de Sevilla. Departamento de Análisis Matemático
This work studies the damped double sine-Gordon 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 in ratchet dynamics of kink is investigated within the framework of collective coordinate theories. It is found that the ratchet velocity of the kink, when an internal mode appears in this system, decreases contrary to what was expected. It is also shown that the kink exhibits a higher mobility in the double sine-Gordon without internal mode, but with a quasilocalized first phonon mode.
«Empaquetando» a los estudiantes en las aulas
(Universidad de Almería, 2021-04-29) Álvarez Nodarse, Renato; Quintero, Niurka R.; Universidad de Sevilla. Departamento de Análisis Matemático
La situación sanitaria que nos ha tocado vivir ha modificado radicalmente nuestra vida diaria, esencialmente en nuestra forma de relacionarnos. Extremar la higiene y mantener la «distancia social» son dos de las medidas fundamentales para detener la propagación del virus. En este artículo, los profesores de la Universidad de Sevilla Renato Álvarez Nodarse y Niurka Rodríguez Quintero nos presentan un modelo matemático que permite ubicar de forma óptima a los estudiantes en las aulas, de forma que se pueda mantener la distancia de seguridad recomendada por las autoridades sanitarias.
Factorization method for difference equations of hypergeometric type on nonuniform lattices
(IOP Publishing, 2001-06-29) Álvarez Nodarse, Renato; Costas Santos, Roberto Santiago; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM262: Teoria de la Aproximacion
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.
Factorization of the hypergeometric-type difference equation on the non-uniform lattices: dynamical algebra
(Institute of Physics, 2005-01-07) Álvarez Nodarse, Renato; Atakishiyev Mektiyev, Natig; Costas Santos, Roberto Santiago; Universidad de Sevilla. Departamento de Análisis Matemático
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 q-linear spectrum of the eigenvalues this directly leads to the dynamical symmetry algebra suq(1, 1), whose generators are explicitly constructed in terms of the difference operators, obtained in the process of factorization. Thus all models with the q-linear spectrum (some of them, but not all, previously considered in a number of publications) can be treated in a unified form.
Factorization of the hypergeometric-type difference equation on the uniform lattice
(2007) Atakishiyev Mektiyev, Natig; Álvarez Nodarse, Renato; Costas Santos, R.; Universidad de Sevilla. Departamento de Análisis Matemático
Jacobi-Sobolev-type orthogonal polynomials: second-order differential equation and zeros
(Elsevier, 1998-04-17) Arvesú Carballo, Jorge; Álvarez Nodarse, Renato; Marcellán Español, Francisco; Pan, Ke-Lin; Universidad de Sevilla. Departamento de Análisis Matemático; Dirección General de Enseñanza Superior. España; Universidad de Sevilla. FQM262: Teoria de la Aproximacion
We obtain an explicit expression for the Sobolev-type 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 − x)α(1 + x)β is the Jacobi weight function, α,β> − 1, A1,B1,A2,B2⩾0 and p, q ∈ P, the linear space of polynomials with real coefficients. The hypergeometric representation (6F5) and the second-order linear differential equation that such polynomials satisfy are also obtained. The asymptotic behaviour of such polynomials in [−1, 1] is studied. Furthermore, we obtain some estimates for the largest zero of Qn(x). Such a zero is located outside the interval [−1, 1]. We deduce his dependence of the masses. Finally, the WKB analysis for the distribution of zeros is presented.
Kink topology control by high-frequency external forces in nonlinear Klein-Gordon models
(American Physical Society, 2014) Álvarez Nodarse, Renato; Quintero, Niurka R.; Mertens, Franz G.; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. Departamento de Física Aplicada I
A method of averaging is applied to study the dynamics of a kink in the damped double sine-Gordon equation driven by both external (nonparametric) and parametric periodic forces at high frequencies. This theoretical approach leads to the study of a double sine-Gordon equation with an effective potential and an effective additive force. Direct numerical simulations show how the appearance of two connected π kinks and of an individual π kink can be controlled via the frequency. An anomalous negative mobility phenomenon is also predicted by theory and confirmed by simulations of the original equation.
Limit relations between q-Krall type orthogonal polynomials
(Elsevier, 2006) Álvarez Nodarse, Renato; Costas Santos, Roberto Santiago; Universidad de Sevilla. Departamento de Análisis Matemático; Ministerio de Educación y Ciencia (MEC). España; Junta de Andalucía
In this paper, we consider a natural extension of several results related to Krall-type polynomials introducing a modification of a q-classical linear functional via the addition of one or two mass points. The limit relations between the q-Krall type modification of big q-Jacobi, little q-Jacobi, big q-Laguerre, and other families of the q-Hahn tableau are established.
Mellin transforms for some families of q-polynomials
(Elsevier, 2003-04-01) Álvarez Nodarse, Renato; Atakishiyeva Kyazim Zade, Messouma; Atakishiyev Mektiyev, Natig; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM262: Teoria de la Aproximacion
By using Ramanujan's q-extension of the Euler integral representation for the gamma function, we derive the Mellin integral transforms for the families of the discrete q-Hermite II, the Al-Salam–Carlitz II, the big q-Laguerre, the big q-Legendre, the big q-Jacobi and the q-Hahn polynomials.
Modelos matemáticos en biología: un viaje de ida y vuelta
(Sociedad Española de Matemática Aplicada, 2006) Álvarez Nodarse, Renato; Universidad de Sevilla. Departamento de Análisis Matemático; Ministerio de Educación y Ciencia (MEC). España; Junta de Andalucía
El objetivo de este trabajo es mostrar la provechosa interacción entre la Biología y la Matemática. Para ello veremos cómo, por una parte, la Matemática es una herramienta sumamente interesante para entender distintos fenómenos biológicos como la dinámica del ADN, el crecimiento de tumores, dinámica de poblaciones, etc., y estos, a su vez, son una fuente de problemas matemáticos difíciles.
Modifications of quasi-definite linear functionals via addition of delta and derivatives of delta Dirac functions
(Elsevier, 2004) Álvarez Nodarse, Renato; Arvesú Carballo, Jorge; Marcellán Español, Francisco; Universidad de Sevilla. Departamento de Análisis Matemático
We consider the general theory of the modifications of quasi-definite linear functionals by adding discrete measures. We analyze the existence of the corresponding orthogonal polynomial sequences with respect to such linear functionals. The three-term recurrence relation, lowering and raising operators as well as the second order linear differential equation that the sequences of monic orthogonal polynomials satisfy when the linear functional is semiclassical are also established. A relevant example is considered in details.
Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials
(Elsevier, 1998-03-09) Álvarez Nodarse, Renato; Yáñez García, Rafael José; Sánchez Dehesa, Jesús; Universidad de Sevilla. Departamento de Análisis Matemático; Dirección General de Enseñanza Superior. España; Junta de Andalucía; Universidad de Sevilla. FQM262: Teoria de la Aproximacion
Starting from the second-order difference hypergeometric equation satisfied by the set of discrete orthogonal polynomials ∗pn∗, we find the analytical expressions of the expansion coefficients of any polynomial rm(x) and of the product rm(x)qj(x) in series of the set ∗pn∗. These coefficients are given in terms of the polynomial coefficients of the second-order difference equations satisfied by the involved discrete hypergeometric polynomials. Here qj(x) denotes an arbitrary discrete hypergeometric polynomial of degree j. The particular cases in which ∗rm∗ corresponds to the non-orthogonal families ∗xm∗, the rising factorials or Pochhammer polynomials ∗(x)m∗ and the falling factorial or Stirling polynomials ∗x[m]∗ are considered in detail. The connection problem between discrete hypergeometric polynomials, which here corresponds to the product case with m = 0, is also studied and its complete solution for all the classical discrete orthogonal hypergeometric (CDOH) polynomials is given. Also, the inversion problems of CDOH polynomials associated to the three aforementioned nonorthogonal families are solved.

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Examinando Artículos (Análisis Matemático) por Autor "Álvarez Nodarse, Renato"