Renato Alvarez-Nodarse

Web page

Updated:

October 10, 2022

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Related sites

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• My book on "Maxima CAS" (PDF)
• My book on "q-polinomios"
• My book on "Linear Algebra"
• Los números de la covid-19
• Mis artículos de divulgación
• La Exposición: El legado de las Matemáticas   

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• Red Orthonet
• OPSpain

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Renato Álvarez-Nodarse's Publications

Google Scholar profile

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[Preprints]   [Papers]  [Edited Volumes]  [Contributions in Proceedings and books]  [Books]  [Others]  [Divulgación]  [Meetings]

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Preprints:



• Guillermo Gordillo-Núñez, Renato Alvarez-Nodarse, Niurka R. Quintero, The Schrödinger equation for the Rosen-Morse type potential revisited with applications. arXiv:2304.06730 [quant-ph] (2023)
• Renato Alvarez-Nodarse and Alberto Arenas-Gomez, On the q-algebra su(2) and its connection with the Quantum Theory of Angular Momentum: a survey. arXiv:2111.13751 [math.QA] (2022)

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To download some articles related with the COVID-19 pandemic (In Spanish) click here.

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Research papers:

[2022]  [2021]  [2020] 

[2019]  [2015]  [2014]  [2013]  [2012]  [2011]  [2010] 

[2009]  [2007]  [2006]  [2005]  [2004]  [2003]  [2002]

[2001]  [1999]  [1998]  [1997]  [1996]  [1995]  [1994]

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2022 

• P. Rabán, R. Álvarez-Nodarse, N.R. Quintero, Stability of solitary waves in nonlinear Klein-Gordon equations. Journal of Physics A: Mathematical and Theoretical, 55(46) (2022) 465201 (25pp). DOI: 10.1088/1751-8121/aca0d1
  
  
• R. Álvarez-Nodarse, K. Castillo, D. Mbouna, J. Petronilho, On discrete coherent pairs of measures. On discrete coherent pairs of measures, Journal of Difference Equations and Applications, 28 (2022) 853-868. DOI: 10.1080/10236198.2022.2097870
  
  
• Renato Alvarez-Nodarse y Fernando Carreño Navas, Modelando una epidemia. La Gaceta de la RSME. Volumen 25, número 3 (2022), 513-538. ISSN 1138-8927
  
  

  2021 

• R. Álvarez-Nodarse, F. J. Esteban, N.R. Quintero, Las matemáticas y la covid-19. La Gaceta de la RSME. Volumen 24, número 1 (2021), 91-109. ISSN 1138-8927
  
  
• R. Álvarez-Nodarse, N.R. Quintero, “Empaquetando” a los estudiantes en las aulas. Boletín de la Titulación de Matemáticas de la UAL Volumen XIV, número 3, 29 de abril de 2021, 12-14. ISSN 1988-5318
  
  

  2020 

• R. Álvarez-Nodarse, Ramanujan y las q-series. La Gaceta de la RSME. Volumen 23 número 2 (2020), 263-302. ISSN 1138-8927
  
  
• R. Álvarez-Nodarse, K. Castillo, D. Mbouna, and J. Petronilho, On classical orthogonal polynomials related to Hahn's operator. Integral Transforms and Special Functions 31, (2020) 487-505 (Published online: 17 Dec 2019). DOI: 10.1080/10652469.2019.1702981
  
  

  2019 

• N.R. Quintero, S. Shao, R. Alvarez-Nodarse, and F.G. Mertens, Driven Nonlinear Dirac Equation revisited: theory and simulations. Journal of Physics A: Mathematical and Theoretical (2019) 52(15) (2019) 155401 (17pp) (Published online 21 March 2019). DOI: 10.1088/1751-8121/ab0dd9
  
  
• L. D. Abreu, R. Alvarez-Nodarse, and J. L. Cardoso, Uniform convergence of Fourier-Bessel series on a q-linear grid. The Ramanujan Journal 49 (2019) 421-449 (Published online: 20 September 2018). DOI 10.1007/s11139-018-0070-3
  
  

  2015 

• R. Alvarez-Nodarse, N.R. Quintero, F.G. Mertens, N. Casic, and T. Fischer, Paramagnetic colloidal ribbons in a precessing magnetic field Phys. Rev. E 91 (2015) 032908. (DOI: http://dx.doi.org/10.1103/PhysRevE.91.032908)
  
  
• Jesús Casado-Pascual, José A. Cuesta, Niurka R. Quintero, Renato Alvarez-Nodarse General approach for dealing with dynamical systems with spatiotemporal periodicities Phys. Rev. E 91(2015) 022905, (DOI: http://dx.doi.org/10.1103/PhysRevE.91.022905)
  
  
• Renato Alvarez-Nodarse, Antonio J. Durán, Using D-operators to construct orthogonal polynomials satisfying higher order q-difference equations Journal of Mathematical Analysis and Applications, 424(1) 304–320 (2015), (DOI: http://dx.doi.org/10.1016/j.jmaa.2014.11.011)
  
  
• R. Alvarez-Nodarse, J. Petronilho, N. C. Pinzon-Cortes, R. Sevinik-Adıguzel, On linearly related sequences of difference derivatives of discrete orthogonal polynomials. Journal of Computational and Applied Mathematics. 284 (2015) 26-37. (DOI: http://dx.doi.org/10.1016/j.cam.2014.06.018)
  
  
  
  

  2014 

• R. Alvarez-Nodarse, N.R. Quintero, and F.G. Mertens. Kink topology control by high-frequency external forces in nonlinear Klein-Gordon models Phys. Rev. E 90(2014) 042916 (DOI: http://dx.doi.org/10.1103/PhysRevE.90.042916)
  
  
• R. Alvarez-Nodarse, R. Sevinik-Adıguzel. On the limits of non-standard q-Racah polynomials. J. Comput. Appl. Math. 259, Part B, (2014) 877–886 (DOI: http://dx.doi.org/10.1016/j.cam.2013.08.026)
  
  

  2013 

  
  
  
• José A. Cuesta, Niurka R. Quintero, Renato Alvarez-Nodarse. Time-shift invariance determines the functional shape of the current in rocking ratchets. Phys. Rev. X 3, (2013) 041014 [10 pages] (DOI: 10.1103/PhysRevX.3.041014) arXiv:1308.0491 [nlin.PS]
  
  
• N. Casic, N.R. Quintero, R. Alvarez-Nodarse, F.G. Mertens, L. Jibuti, W. Zimmermann, and T. Fischer. Propulsion efficiency of a dynamic self-assembled helical ribbon. Physical Review Letters 110 (2013) 168302. (DOI: 10.1103/PhysRevLett.110.168302)
  
  
• José A. Cuesta, Niurka R. Quintero, Renato Alvarez-Nodarse. Comment on "Ratchet universality in the presence of thermal noise" Phys. Rev. E 88 (2013) 066101 (DOI: http://link.aps.org/doi/10.1103/PhysRevE.88.066101)
  
  
• R. Alvarez-Nodarse, A. J. Durán, and A. M. de los Ríos. Orthogonal matrix polynomials satisfying second order difference equations. Journal of Approximation Theory 169 (2013) 40-55 (DOI: http://dx.doi.org/10.1016/j.jat.2013.02.003)
  
  
• R. Alvarez-Nodarse, R. Sevinik-Adıguzel. On the generalized Askey-Wilson Polynomials. Journal of Approximation Theory 170 (2013) 32-43. (DOI: 10.1016/j.jat.2012.03.001)
  
  
• R.Alvarez-Nodarse, J.L. Cardoso. On the Properties of Special Functions on the linear-type lattices. Journal of Mathematical Analysis and Applications 405 (2013) 271–285. (DOI: http://dx.doi.org/10.1016/j.jmaa.2013.03.058)
  
  

  2012 

  
  
  
• R. Alvarez-Nodarse, J. Petronilho, N.R. Quintero. Spectral properties of certain tridiagonal matrices. Linear Algebra and its Applications. 436 (2012) 682–698. (DOI: 10.1016/j.laa.2011.07.040)
  
  
• R. Alvarez-Nodarse, R. Sevinik-Adıguzel. The q-Racah-Krall-type polynomials. Applied Mathematics and Computation, 218(23) (2012) 11362–11369. (DOI: 10.1016/j.amc.2012.05.015)
  
  
• R. Alvarez Nodarse, R. Sevinik Adıgüzel, and H. Taseli. On the Orthogonality of q-Classical Polynomials of the Hahn Class SIGMA 8 (2012), 042, 30 pages. (DOI: 10.3842/SIGMA.2012.042). This is a slightly reduced version of the article: The orthogonality of q-classical polynomials of the Hahn class: A geometrical approach. arXiv:1107.2423v4 [math.CA]
  
  

  2011 

  
  
  
• N.R. Quintero, R. Alvarez-Nodarse, J.A. Cuesta. Ratchet effect on a relativistic particle driven by external forces. J. Phys. A: Math. Theor. 44 (2011) 425205. (DOI: 10.1088/1751-8113/44/42/425205)
  
  
• R. Alvarez-Nodarse and R. Sevinik Adıgüzel. On the Krall-type polynomials on q-quadratic lattices. Indagationes Mathematicae 21 (2011), pp. 181-203. (DOI: 10.1016/j.indag.2011.04.002)
  
  
• R. Alvarez-Nodarse. À la carte recurrence relations for continuous and discrete hypergeometric functions. SeMA Journal 55 (2011), 41-57 (antiguo Boletín de la Sociedad Española de Matemática Aplicada).
  
  

  2010 

• N.R. Quintero, J. Cuesta, and R. Alvarez-Nodarse, Symmetries shape the current in ratchets induced by a bi-harmonic force (see also the supplementary material) Physical Review E: Rapid Communications 81, 030102R1-4 (2010)
  
  

  2009 

• N.R. Quintero, R. Alvarez-Nodarse, and F. Mertens, Driven and damped Double sine-Gordon equation: the influence of internal modes in the soliton ratchet mobility. Physical Review E, 80 (2009) 016605 pp.1-8
  
  
• L. Cardoso, C. Fernandes and R. Alvarez-Nodarse, Structural properties of Hypergeometric-Type Functions by Nikiforov-Uvarov Method. ETNA 35 (2009) 17-39
  
  

  2007 

• M. Alfaro and R. Alvarez-Nodarse, A characterization of the classical orthogonal discrete and q-polynomials. J. Comput. Appl. Math. 201 (2007) 48-54
  
  
• R. Álvarez-Nodarse N. M. Atakishiyev, and R.S. Costas-Santos: Factorization of the hypergeometric-type difference equation on the uniform lattice. ETNA 27 (2007) 34-50
  
  
• R. Álvarez-Nodarse, Yu. F. Smirnov, Dual properties of orthogonal polynomials of discrete variable associated with quantum algebra Uq(su(2)). Journal of Russian Laser Research (2007) 28(21) (2007) 20-47
  
  

  2006 

• R. Alvarez-Nodarse: On characterizations of classical polynomials. J. Comput. Appl. Math. 196 (2006) 320-337
  
  
• R. Álvarez-Nodarse and R.S. Costas-Santos: Limit relations between q-Krall type orthogonal polynomials. J. Math. Anal. Appl. 322(1) (2006) 158-176. arXiv:1109.0485 [math.QA]. This is a revised version of the published paper. We have corrected a misprint in two basic formulas as well as in all the formulas that where derived from them. I would like to thanks Dr. R. Sevinik-Adıguzel for pointed out these misprints.
  
  
• R. Alvarez-Nodarse Modelos matemáticos en biología: un viaje de ida y vuelta. Bol. Soc. Esp. Mat. Apl. 35 (2006) 73-112
  [Estas son las notas ampliadas de la conferencia impartida en el curso de verano Modelos matemáticos en biología: un viaje de ida y vuelta que tuvo lugar el verano de 2005 en Baeza]
  
  
• R. Álvarez-Nodarse, Yu. F. Smirnov, and R. Costas-Santos: A q-analog of the Racah polynomials and the q-algebra SUq(2) Journal of Russian Laser Research, 27(1), (2006) 1-32. arXiv:0907.2029 [nlin.PS]
  
  
• R. Alvarez-Nodarse, J. L. Cardoso, N.R. Quintero: On recurrence relations for radial wave functions for the N-th dimensional oscillators and hydrogenlike atoms: analytical and numerical study ETNA 24(2006) 7-23
  
  

  2005 

• R. Álvarez-Nodarse and J. L. Cardoso: Recurrence relations for discrete hypergeometric functions. J. Difference Equations. Appl. 11 (2005) 829-850
  
  
• R. Álvarez-Nodarse, J. Petronilho and N.R. Quintero. On some tridiagonal k-Toeplitz matrices: algebraic and analytical aspects. Applications. J. Comput. Appl. Math. 184 (2005) 518-537
  
  
• R. Álvarez-Nodarse N. M. Atakishiyev, and R.S. Costas-Santos: Factorization of the hypergeometric-type difference equation on the non-uniform lattices: dynamical algebra J. Phys. A: Math. Gen. 38 (2005) 153-174.
  
  
• R. Alvarez-Nodarse, M. Atakishiyeva, and N. M. Atakishiyev: On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on R Czechoslovak Journal of Physics, 55No. 11 (2005) 1315-1320.
  
  

  2004 

• R. Álvarez-Nodarse, J. Arvesú and F. Marcellán: On the Krall-type polynomials. J. Applied Math. 2004:5 (2004) 359-369.
  
  
• R. Álvarez-Nodarse and J.J. Moreno-Balcázar: Asymptotic properties of generalized Laguerre orthogonal polynomials. Indagationes Mathematicae 15(2) (2004) 151-165.
  
  
• R. Álvarez-Nodarse, J. Arvesú and F. Marcellán: Modifications of quasi-definite linear functionals via addition delta and derivatives of delta Dirac functions. Indagationes Mathematicae 15(1) (2004) 1-20
  
  
• R. Álvarez-Nodarse and J. Petronilho: On the Krall-type discrete polynomials. J. Math. Anal. Appl. 295(1) (2004) 55-69
  
  
• R. Álvarez-Nodarse, M. Atakishiyeva, and N. M. Atakishiyev: A q-extension of the generalized Hermite polynomials with the continuous orthogonality property on R. International J. Pure Appl. Math. 10(3) (2004) 335--347.

  2003 

• R. Álvarez-Nodarse: Some limit relations in the A₁ tableau of Dunkl-Cherednik operators. Indagationes Mathematicae 14(3,4) (2003) 293-308. (PDF file)
  
  
• R. Álvarez-Nodarse. Polinomios hipergemétricos y q-polinomios. Monografías del Seminario Matemático "García de Galdeano" Número 26. Prensas Universitarias de Zaragoza, Spain, 2003. ISBN 84-7733-637-7. 343 pages. Versión electrónica actualizada el 10 de noviembre de 2014.
  
  
• R. Álvarez-Nodarse, M. Atakishiyeva, and N. M. Atakishiyev: Mellin transforms for some families of q-polynomials J. Comput. Appl. Math 153 No.1-2, (2003) 9-18.
   
• J. L. Cardoso and R. Álvarez-Nodarse: Recurrence relations for radial wave functions for the N-th dimensional oscillators and hydrogenlike atoms J. Phys. A: Math. Gen. 36 (2003), 2055-2068.

  2002 

• R. Álvarez-Nodarse, M. Atakishiyeva, and N. M. Atakishiyev: On a q-extension of the Hermite polynomials H_n(x) with the continuous orthogonality property on R . Boletin de la Sociedad Mexicana de Matematicas 8 (2002), 221-232.
   
• R. Álvarez-Nodarse and J. S. Dehesa: Distribution of zeros of discrete and continuous polynomials from their recurrence relation. Appl. Math. and Comput. 128 (2002) 167-190.
   
• R. Álvarez-Nodarse, J. Arvesú and F. Marcellán: On modifications of the Jacobi linear functional: Algebraic properties and zeros. Acta Applicandae Mathematicae 71 (2002) 127-158

  2001 

• G. Carballo, R. Álvarez-Nodarse and J. S. Dehesa: Chebyshev polynomials in a speech recognition model. Appl. Math. Letters 14 (5) (2001) pp. 581-585 (this is a extended version with more details)
   
• R. Álvarez-Nodarse and F. Marcellán: On the Favard Theorem and its extensions. J. Comput. Appl. Math 127 (2001) 231-254
   
• R. Álvarez-Nodarse, J. Arvesú and R. Yáñez: On the connection and linearization problem for discrete hypergeometric q-polynomials. J. Math. Anal. and Appl. 257 (2001) 52-78.
   
• R. Álvarez-Nodarse and R.S. Costas-Santos: On the factorization of the difference equation of hypergeometric-type in nonuniform lattices. J. Phys. A: Math. Gen 34 (No.17) (2001), 5551-5569.
   
• R. Álvarez-Nodarse: Polinomios ortogonales: historia y aplicaciones. Bol. Soc. Esp. Mat. Apl. 18 (2001), 19-45.
   
• J. C. Medem, R. Álvarez-Nodarse and F. Marcellán: On the q-polynomials: A distributional study. J. Comput. Appl. Math 135 (2001) 157-196.
   
• R. Álvarez-Nodarse and J. C. Medem: The q-classical polynomials and the q-Askey and Nikiforov-Uvarov Tableaus J. Comput. Appl. Math 135 (2001) 197-223.

  1999 

• R. Álvarez-Nodarse, N. R. Quintero and A. Ronveaux On the linearization problems involving Pochhammer symbols and their q-analogues. J. Comput. Appl. Math. 107 (1999) 133-146.
   
• R. Álvarez-Nodarse and J. Arvesú: On the q-polynomials on the exponential lattice x(s)= c ₁ q^s + c ₃ .Integral Trans. and Special Funct. 8 (1999) 299-324

  1998 

• R. Álvarez-Nodarse and F. Marcellán:On the modification of classical orthogonal polynomials: The symmetric case. Approx. Theory and its Applications 14(1) (1998) 8-28.
   
• R. Álvarez-Nodarse, J. Arvesú, F. Marcellán and K. Pan: Jacobi-Sobolev-Type Orthogonal Polynomials: Second Order Differential Equation and Zeros. J. Comput. Appl. Math. 90 (1998) 137-158
   
• R. Álvarez-Nodarse, F. Marcellán and J. Petronilho: WKB Approximations and Krall-type orthogonal polynomials. Acta Aplicandae Mathematicae 54 (1998) 27-58
   
• R. Álvarez-Nodarse, J. Arvesú K. H. Kwon and F. Marcellán: Some Extension of the Bessel Type Orthogonal Polynomials. Integral Trans. and Special Funct. 7 (1998) 191-214
   
• R. Álvarez-Nodarse: Second order difference equations for certain families of "discrete" polynomials. J. Comput. Appl. Math. 99 (1998) 135-156.

  1997 

• R. Álvarez-Nodarse, R.J. Yáñez and J.S. Dehesa: Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials. J. Comput. and Appl. Math. 89 (1997) 171-197.
   
• R. Álvarez-Nodarse, E.Buendía and J.S. Dehesa The distribution of zeros of general q-polynomials. J. Phys. A: Math. and Gen. 30 (1997) 6743-6768.
   
• R. Álvarez-Nodarse and F. Marcellán: The limit relations between generalized orthogonal polynomials.(revised version October 1996) Indagationes Mathematicae N.S. 8 (1997), 295-316.

  1996 

• R. Álvarez-Nodarse and F. Marcellán: A generalization of the classical Laguerre polynomials: Asymptotic Properties and Zeros. Applicable Analysis 62 , (1996), 349-366.
   
• R. Álvarez-Nodarse and A. Ronveaux: Recurrence relation for connection coefficients between q-orthogonal polynomials of discrete variables in the non-uniform lattice X(s) = q^2s. (revised version October 1996) J. Phys. A: Math. and Gen. 29 (22), (1996), 7165-7175.
   
• R. Álvarez-Nodarse and Yu.F. Smirnov: q-Dual Hahn polynomials on the non-uniform lattice x(s) = [s]_q [s+1]_q and the q-algebras q-SU(1,1) and q-SU(2). (revised version October 1996) J. Phys. A: Math. and Gen. 29(7), (1996), 1435-1451.

  1995 

• R. Álvarez-Nodarse, A.G. García and F. Marcellán: On the properties for modifications of classical orthogonal polynomials of discrete variables. (revised version October 1996) J. Comput. and Appl. Math. 65, (1995), 3-18.
   
• R. Álvarez-Nodarse and F. Marcellán: The modification of classical Hahn polynomials of a discrete variable.(revised version October 1996) Integral Trans. and Special Funct. 3(4), (1995), 243-262.
   
• R. Álvarez-Nodarse and F. Marcellán: Difference equation for modifications of Meixner polynomials. J. Math. Anal. and Appl. 194(3),(1995), 250-258.
   
• R. Álvarez-Nodarse and F. Marcellán: A generalization of the classical Laguerre polynomials. (revised version October 1996) Rend. Circ. Mat. Palermo. Serie II, 44, (1995), 315-329.

  1994 

• R.N. Álvarez, D. Bonatsos and Yu.F. Smirnov: q-Deformed vibron model for diatomic molecules. Physical Review A. 50 (1994) 1088-1095.

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Edited Volumes:

1. Special Volume of the Electronic Transactions on Numerical Analysis (ETNA) Orthogonal Polynomials and Mathematical Physics. ETNA 24, 2006 R. Álvarez-Nodarse, J. Arvesú, and F. Marcellán (Invited Eds.). Proceedings of the IWOP04
    
2. Special Volume of the Electronic Transactions on Numerical Analysis (ETNA) on Orthogonal Polynomials in Approximation Theory. ETNA 19, 2005 R. Álvarez-Nodarse, J. Arvesú, and F. Marcellán (Invited Eds.). Proceedings of the IWOP02
    
3. Laredo Lecture Notes (Lecture notes of the 1st SIAG Summer School on Orthogonal Polynomials and Special Functions, Laredo, Spain, July 24-29 2000). Nova Science Publisher (2004). R. Álvarez-Nodarse, F. Marcellán and W. Van Assche (Eds.). 2004 ISBN: 1-59454-09-8.
    
4. Special Volume of the Electronic Transactions on Numerical Analysis (ETNA) on Orthogonal Polynomials: Numerical and Symbolic Algorithms. ETNA 9, 1999 R. Álvarez-Nodarse and F. Marcellán (Invited Eds.). Proceedings of the IWOP98
    
5. Proceedings of the International Workshop on Orthogonal Polynomials on Mathematical Physics. M. Alfaro, R. Álvarez-Nodarse, G. López Lagomasino, and F. Marcellán Eds. Servicio de Publicaciones de la Universidad Carlos III de Madrid. Leganés, Madrid (1997). This monography is free avaliable from this site.

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Contributions to Proceedings and books

1. R. Álvarez-Nodarse. Los q-polinomios hipergeométricos . In: Margarita Matemática. En honor de José Javier Guadalupe ``Chicho''. L. Español y J.L. Varona Eds. Servicio de Publicaciones, Universidad de La Rioja, Logroño, Spain, 2001, pp 85-96.
    
2. R. Álvarez-Nodarse y Antonio J. Duran: Polinomios ortogonales. In: Actas del Encuentro de Matemáticos Andaluces. Universidad de Sevilla E. Briales Morales, A. Carriazo Rubio, T. Chacón, P. Real Jurado y A. Romero Jiménez Eds. Universidad de Sevilla, Secretariado de Publicaciones, (2001), pp. 25-42.
    
3. R. Álvarez-Nodarse, F. Marcellán and J. Petronilho: On Some Polynomial Mappings for Measures. Applications. . (1996) In: Proceedings of the International Workshop on Orthogonal Polynomials on Mathematical Physics. M. Alfaro, R. Álvarez-Nodarse, G. López Lagomasino, and F. Marcellán Eds. Leganés, Madrid (1997), 1-22. MA/UC3M/29/1996
    
4. R. Álvarez-Nodarse and Yu. F. Smirnov: The dual Hahn q-Polynomials in the lattice x(s) = [s]_q [s+1]_q and the q-algebras q-SU(1,1) and q-SU(2).(revised version October 1996) . In: Proceedings of Fourth Wigner Symposium N.Atakishiev, T.H.Seligman and K.B.Wolf Eds. World Scientific, Singapore, (1996), 429-434.
    
5. R. N. Alvarez, D. Bonatsos, and Yu.F. Smirnov: q-Deformed vibron model for diatomic molecules. In: Perspectives for the interacting boson model}. Proceedings of Padova conference. On the occasion of its 20th anniversary R.F. Casten, A. Vitturi, A.B. Balantekin, B.R. Barrett, J. N. Ginocchio, G. Maino and T. Otsuka (Eds.) World Scientific, (1994), 575-589.

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Books:

• R. Álvarez-Nodarse. Polinomios hipergemétricos y q-polinomios. Monografías del Seminario Matemático "García de Galdeano" Número 26. Prensas Universitarias de Zaragoza, Spain, 2003. ISBN 84-7733-637-7. 343 pages. Versión electrónica actualizada el 10 de noviembre de 2014.
  
  
• J. Arvesú, R. Álvarez-Nodarse y F. Marcellán ``Álgebra Lineal y aplicaciones'' Editorial Síntesis, ISBN 84-7738-702-8. (for more information see the book Home Page.
  
  
• R. Álvarez-Nodarse. Introducción a Maxima CAS con aplicaciones a la resolución de ecuaciones diferenciales ordinarias (updated at December 1st, 2017). This is a concise introductory course to the Computer Algebra System Maxima. The wxMaxima source files for each chapter are avaliable from HERE.
  
  
• R. Álvarez-Nodarse. Breve introducción a la mecánica cuántica (updated at December 1st, 2017). This is the full text on some courses given at the Universidad de Zaragoza, Universidade de Coimbra and also at the FISMAT2015 in Sevilla in the Summer of 2015. It includes and introduction to the Quantum Mechanics on Hilbert Spaces, the classical orthogonal polynomials as well as two methods for solving the Schrödinger equation: the Nikiforov-Uvarov method and the Factorization method of E. Schrödinger.

Others:

The following four items are included in the more recent book Polinomios hipergemétricos y q-polinomios. Monografías del Seminario Matemático "García de Galdeano" Número 26. Prensas Universitarias de Zaragoza, Spain, 2003. ISBN 84-7733-637-7. 343 pages. Click HERE to access to the electronic version (updated on November 10th, 2014).

• R. Álvarez-Nodarse. Las funciones especiales y la física matemática. (out of date see the aforesaid book)
  This is the full text of a course given in Sevilla and Granada Universities for a very general audience and PhD students. There some historical remarks on classical polynomials, the theory of classical orthogonal polynomials (continue and discrete case) and some of their applications in Physics and Group theory
  
  
• R. Álvarez-Nodarse. Propiedades espectrales de los polinomios ortogonales.(out of date see the aforesaid book)
  This is the full text of a seminar given at Departamento de Matemáticas of the Universidad de Zaragoza (Seminario Rubio de Francia , June 5, 1998). This is a survey where it is considered the global properties of zeros of orthogonal polynomials. Special emphasis is given to the information obtained from the three-term recurrence relation. Examples of classical polynomials as well as q-polynomials are included. Any suggestion, remarks etc will be welcome.
  
  
• R. Álvarez-Nodarse. Linearization and connection problems for discrete hypergeometric polynomials.(out of date see the aforesaid book)
  This is the full text of a series of seminars on the Linearization and connection problems for discrete hypergeometric polynomials given in Coimbra and in the IV INTAS workshop at Leuven.
  
  
• R. Álvarez-Nodarse. q-Polinomios y q-álgebras. (out of date see the aforesaid book)
  This a little survey on the connection of q-polynomials from the point of view of the Nikiforov-Uvarov approach and q-algebras.

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Some articles on science popularization

Here you can find the links to my articles on popular science. The links are to the Spanis original version of the works, but almost all of then have been transilated to English.

⚛   General Science

• Galileo y las Matemáticas del Universo
• Einstein, Wigner y el misterio de las Matemáticas
• Y las matemáticas se hicieron experimentales
• 1+1=2 o las matemáticas y las verdades absolutas
• Un ejemplo sencillo de modelización matemática: El crecimiento de poblaciones
• ¿Pero esto es Física o Matemáticas?
• Y las matemáticas comenzaron a vivir una peculiar vida propia
• El triunfo de la Razón: El Programa de Newton
• La segunda nubecilla de Lord Kelvin
• La segunda nubecilla de Lord Kelvin: el desenlace
• Einstein y los quanta de luz
• Y las ondas se convirtieron en partículas
• Bose, el cometa indio que brilló “solo” una vez
• El gran velo se levanta: ¿y si todo no son más que ondas?
• Las matemáticas y la estructura atómica I
• Las matemáticas y la estructura atómica II: un danés en la corte del Rey Arturo.
• Poniendo un poco de orden: La mecánica ondulatoria de Schrödinger
• Poniendo un poco de orden II: La mecánica matricial de Heisenberg
• Poniendo un poco de orden III: Heisenberg vs Schrödinger
• ¿Dios juega a los dados?
• Dios sí juega a los dados (II)
• Determinismo o indeterminismo, esa es la cuestión
• “Si 2+2 diera 3” por La Renga
• Dirac y la mecánica cuántica relativista
• Condorcet y la felicidad de los “negros”
• Beber tanto como se quiera y más (por A.F. Nikiforov)
• Y las matemáticas comenzaron a vivir una peculiar vida propia (II)
• De matemáticas y volcanes. Entrada en colaboración con Luis Javier Álvarez
• De la universalidad de las matemáticas
• Más allá de las funciones elementales
• Legendre, Abel, Jacobi y las funciones elípticas

😷 On the COVID-19 pandemic

• ¿Cuánto puede durar el coronavirus fuera de nuestro organismo? Entrada en colaboración con Francisco J. Esteban.
• ¿Hasta dónde llega un virus al estornudar? Entrada en colaboración con Francisco J. Esteban y Niurka R. Quintero.
• ¿Cómo nos infecta un virus? Entrada en colaboración con Francisco J. Esteban.
• ¿Cómo nos infecta un virus? II Entrada en colaboración con Francisco J. Esteban y Niurka R. Quintero.
• «Empaquetando» a los alumnos en las aulas. Entrada en colaboración con Niurka R. Quintero.
• La apertura de los colegios en tiempos de pandemia: el caso de Andalucía. Entrada en colaboración con Niurka R. Quintero.
• ¿Cómo entender el dato del número de contagios publicado diariamente?
• ¿Durante cuánto tiempo estamos seguros en una habitación cerrada?
• ¿Cuán rápido crecen los contagios en la tercera ola de la covid-19?
• Más sobre la velocidad de contagios de la covid-19
• Modelando una epidemia I: Confinamientos. Entrada en colaboración con Fernando Carreño Navas.
• Modelando una epidemia II: efecto del comportamiento de la población. Entrada en colaboración con Fernando Carreño Navas.
• Modelando una epidemia III: Efectos de la vacunación. Entrada en colaboración con Fernando Carreño Navas.

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Web pages of some meetings which I have co-organized

• IV Escuela Orthonet (Logroño, March 2020, Cancelled)
• III Escuela Orthonet (Bilbao, 19-23/11/2018)
• I Escuela Orthonet (Sevilla, 14-18/11/2016)
• FISMAT2015 (Sevilla, 29/06/2015-10/07/2015)
• EARCO 2015 (Carmona, 21/05/2015-23/05/2015)
• OPSFA 2011 (Leganés, 29/08/2011-02/08/2011)
• Stochgame (Carmona 12-14/02/2009)
• IWOPA08 (2008)
• OPIP07 (2007)
• Special Functions, Information Theory and Mathematical Physics (2007)
• Ratchets07 (2007)      
• Minicurso sobre el ADN (2006)
• Modelos matemáticos en Biología: un viaje de ida y vuelta (2005)
• IWOP'04 (2004)
• IWOP'02 (2002)
• IWOP'98 (1998)
• IWOP'96 (1996)

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