Dr. Vladislav V. Kravchenko

complex analysis, its generalizations (pseudoanalytic function theory and quaternionic analysis) and applications; ordinary and partial differential equations; models of mathematical physics; wave propagation in complex media.

Books

1. V. V. Kravchenko, M. V. Shapiro "Integral representations for spatial models of mathematical physics" Pitman Research Notes in Mathematics Series, v. 351, Addison Wesley Longman, 1996, 256 pp. ISBN 0582297419. ( In Google Books)

2. V. V. Kravchenko "Elementos del análisis moderno y teoría electromagnética" Editorial del Instituto Mexicano de Comunicaciones, Serie Técnica, Matemáticas Aplicadas, 1996, 149 pp.

3. V. V. Kravchenko "Applied quaternionic analysis" Heldermann-Verlag, Research and Exposition in Mathematics Series, v. 28, 2003, 136 pp. ISBN 3-88538-228-8.

4. V. V. Kravchenko "Applied pseudoanalytic function theory". Birkhäuser, Series: Frontiers in Mathematics, 2009 ISBN: 978-3-0346-0003-3.(In Google Books)

5. V. V. Kravchenko "Direct and inverse Sturm-Liouville problems: A method of solution". Birkhäuser, Series: Frontiers in Mathematics, 2020: ISBN 978-3-030-47848-3.

Books edited:

A. Karapetyants, V. Kravchenko, E. Liflyand (eds.), Modern Methods in Operator Theory and Harmonic Analysis, Springer Proceedings in Mathematics & Statistics v. 291, 2019. ISBN 978-3-030-26748-3.
V. V. Kravchenko, S. M. Sitnik (eds.), Transmutation Operators and Applications, Trends in Mathematics, Birkhäuser 2020, 686+xvii стр. ISBN 978-3-030-35913-3.

Member of Editorial Board of the journals:

Advances in Applied Clifford Algebras (Published by Springer);

Mathematical Methods in the Applied Sciences (Published by Wiley);

Journal of Fourier Analysis and Applications (Published by Springer);

Journal of Applied and Industrial Mathematics (Published by Springer);

Mathematical Problems in Engineering (Published by Hindawi) until 2015;

Journal of Complex Analysis (Published by Hindawi) until 2017;

ISRN Mathematical Analysis (Published by International Scholarly Research Network) until 2017;

Científica (The Mexican Journal of Electromechanical Engineering);

Revista Eureka

Guest Editor (together with R. Michael Porter) of the Special Issue "Complex-Analytic Methods" of the journal

Mathematical Methods in the Applied Sciences, v. 33, issue 4, 2010

Guest Editor (together with Sergii M. Torba) of the Special Issue "Wave Phenomena" of the journal

Mathematical Methods in the Applied Sciences, v. 38, issue 10, 2015

Guest Editor (together with Alexey N. Karapetyants and Elijah Liflyand) of the Special Issue "Operator Theory and Harmonic Analysis" of the journal

Mathematical Methods in the Applied Sciences, v. 43, issue 16, 2020

Recent publications (since 2003)

1. K.V. Khmelnytskaya, V. V. Kravchenko, V. S. Rabinovich Quaternionic fundamental solutions for electromagnetic scattering problems and application. Zeitschrift für Analysis und ihre Anwendungen, 2003, v. 22, No. 1, 147--166. (available from arxiv.org).

2. V. V. Kravchenko On Beltrami fields with nonconstant proportionality factor. Journal of Physics A, 2003, v. 36, No. 5, 1515-1522. (available from arxiv.org)

3. V. V. Kravchenko, H. Oviedo On a quaternionic reformulation of Maxwell's equations for chiral media and its applications. Zeitschrift für Analysis und ihre Anwendungen, 2003, v. 22, No. 3, 569 - 589.

4. V. G. Kravchenko, V. V. Kravchenko Quaternionic factorization of the Schrödinger operator and its applications to some first order systems of mathematical physics. Journal of Physics A, 2003, v. 36, No. 44, 11285-11297. (available from arxiv.org).

5. R. Castillo, V. V. Kravchenko General solution of the fermionic Casimir effect model. Bulletin de la Société des Sciences et des Lettres de Lódz, 2003, v. 53, Série: Recherches sur les déformations, No. 41, 115-123.

6. V. V. Kravchenko, M. Ramírez On a quaternionic reformulation of the Dirac equation and its relationship with Maxwell's system. Bulletin de la Société des Sciences et des Lettres de Lódz, 2003, v. 53, Série: Recherches sur les déformations, No. 41, 101-114.

7. S. M. Grudsky, K. V. Khmelnytskaya, V. V. Kravchenko On a quaternionic Maxwell equation for the time-dependent electromagnetic field in a chiral medium. Journal of Physics A, 2004, v. 37, 16, 4641-4647 (available from arxiv.org math-ph/0309062).

8. V. V. Kravchenko On force-free magnetic fields: quaternionic approach. Mathematical Methods in the Applied Sciences, 2005, v. 28, No. 4, 379-386.

9. V. V. Kravchenko On the reduction of the multidimensional stationary Schrödinger equation to a first order equation and its relation to the pseudoanalytic function theory. Journal of Physics A: Mathematical and General, 2005, v. 38, No. 4, 851-868. (available from arxiv.org).

10. V. V. Kravchenko On a relation of pseudoanalytic function theory to the two-dimensional stationary Schrödinger equation and Taylor series in formal powers for its solutions. Journal of Physics A: Mathematical and General, 2005, v. 38, No. 18, 3947-3964. (available from arxiv.org).

11. V. V. Kravchenko On the relationship between p-analytic functions and the Schrödinger equation. Zeitschrift für Analysis und ihre Anwendungen, 2005, v. 24, No. 3, 487-496.

12. A. Castañeda and V. V. Kravchenko New applications of pseudoanalytic function theory to the Dirac equation. Journal of Physics A: Mathematical and General, 2005, v. 38, No. 42, 9207-9219. (available from arxiv.org).

13. V. V. Kravchenko On a factorization of second order elliptic operators and applications. Journal of Physics A: Mathematical and General, 2006, v. 39, No. 40, 12407-12425.

14. V. V. Kravchenko, H. Oviedo On explicitly solvable Vekua equations and explicit solution of the stationary Schrödinger equation and of the equation div(σgradu)=0. Complex Variables and Elliptic Equations, 2007, v. 52, Issue 5, pages 353 - 366.

15. V. V. Kravchenko On a transplant operator and explicit construction of Cauchy-type integral representations for p-analytic functions. Journal of Mathematical Analysis and Applications, 2008, v. 339, issue 2, 1103-1111.

16. V. V. Kravchenko, H. Oviedo On Beltrami fields with nonconstant proportionality factor on the plane. Reports on Mathematical Physics, 2008, v. 61, Issue 1, 29-38.

17. V. V. Kravchenko, D. Rochon, S. Tremblay On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory. J. of Phys. A 2008, v. 41, issue 6, 065205.

18. K V. Khmelnytskaya, V. V. Kravchenko On a complex differential Riccati equation. J. of Phys. A 2008, v. 41, issue 8, number 085205.

19. P. Cerejeiras, U. Kähler, V. V. Kravchenko On a factorization of the Schrödinger and Klein-Gordon operators. Mathematical Methods in the Applied Sciences, Volume 31 Issue 14, Pages 1722 - 1738.

20. V. V. Kravchenko A representation for solutions of the Sturm-Liouville equation. Complex Variables and Elliptic Equations, 2008, v. 53, No. 8, 775-789.

21. V. V. Kravchenko Recent developments in applied pseudoanalytic function theory. Beijing: Science Press "Some topics on value distribution and differentiability in complex and p-adic analysis", eds. A. Escassut, W. Tutschke and C. C. Yang, 267-300, 2008 (available from www.arxiv.org arXiv:math/0611400)

22. K. V. Khmelnytskaya, V. V. Kravchenko Biquaternions for analytic and numerical solution of equations of electromagnetic theory. Beijing: Science Press "Some topics on value distribution and differentiability in complex and p-adic analysis", eds. A. Escassut, W. Tutschke and C. C. Yang, 301-322, 2008, available from www.arxiv.org..

23. R. Castillo Pérez, K. V. Khmelnytskaya, V. V. Kravchenko, H. Oviedo Galdeano Efficient calculation of the reflectance and transmittance of finite inhomogeneous layers. Journal of Optics A: Pure and Applied Optics, 2009, v. 11, issue 6, 065707 (6pp).

24. V. V. Kravchenko, R. Reséndiz Vázquez Estimación del ancho de banda para comunicaciones satelitales tomando en cuenta la dispersión en la ionosfera. Científica: The Mexican Journal of Electromechanical Engineering, 2009, v. 13, No. 1, 9-16.

25. V. V. Kravchenko, R. Michael Porter Spectral parameter power series for Sturm-Liouville problems. Mathematical Methods in the Applied Sciences, 2010, v. 33, issue 4, 459-468, available from arXiv:0811.4488

26. K V. Khmelnytskaya, V. V. Kravchenko, H. Oviedo On the solution of the static Maxwell system in axially symmetric inhomogeneous media. Mathematical Methods in the Applied Sciences, 2010, v. 33, issue 4, 439-447, available from www.arxiv.org.

27. V. G. Kravchenko, V. V. Kravchenko, S. Tremblay Zakharov-Shabat system and hyperbolic pseudoanalytic function theory. Mathematical Methods in the Applied Sciences, 2010, v. 33, issue 4, 448-453, available from www.arxiv.org.

28. V. V. Kravchenko, S. Tremblay Explicit solutions of generalized Cauchy-Riemann systems using the transplant operator. Journal of Mathematical Analysis and Applications, 2010, v. 370, issue 1, 242-257, available from www.arxiv.org.

29. V. V. Kravchenko, H. Oviedo Time-dependent electromagnetic fields in chiral media. Journal of Physics A: Mathematical and Theoretical, 2010, v. 43, issue 45, # 455213 (9pp).

30. H. Campos, V. V. Kravchenko A finite-sum representation for solutions for the Jacobi operator. Journal of Difference Equations and Applications, 2011, v. 17, No. 4, 567–575, available from www.arxiv.org.

31. R. Castillo, V. V. Kravchenko and R. Reséndiz Solution of boundary value and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic formal powers. Mathematical Methods in the Applied Sciences, 2011, v. 34, issue 4, 455-468; available from www.arxiv.org.

32. V. V. Kravchenko, A. Meziani On the two dimensional stationary Schrödinger equation with a singular potential. Journal of Mathematical Analysis and Applications, 2011, v. 377, issue 1, 420-427.

33. V. V. Kravchenko On the completeness of systems of recursive integrals. Communications in Mathematical Analysis, Conf. 03 (2011), 172–176.

34. R. Castillo, V. V. Kravchenko, H. Oviedo, V. S. Rabinovich Dispersion equation and eigenvalues for quantum wells using spectral parameter power series. Journal of Mathematical Physics, 2011, v. 52, issue 4, # 043522 (10 pp.)

35. V. V. Kravchenko, R. Michael Porter Conformal Mapping of Right Circular Quadrilaterals. Complex Variables and Elliptic Equations. 2011, v. 56, issue 5, 399 - 415, available from www.arxiv.org.

36. V. V. Kravchenko, U. Velasco-García Dispersion equation and eigenvalues for the Zakharov-Shabat system using spectral parameter power series. Journal of Mathematical Physics, 2011, v. 52, issue 6, # 063517 (8 pp.)

37. V. V. Kravchenko, Marco P. Ramirez T. On Bers generating functions for first order systems of mathematical physics. Advances in Applied Clifford Algebras, 2011, v. 21, issue 3, 547-559, available from www.arxiv.org.

38. V. V. Kravchenko, S. Tremblay Spatial pseudoanalytic functions arising from the factorization of linear second order elliptic operators. Mathematical Methods in the Applied Sciences, 2011, v. 34, issue 16, 1999–2010, available from www.arxiv.org.

39. H. Campos, R. Castillo, V. V. Kravchenko Construction and application of Bergman-type reproducing kernels for boundary and eigenvalue problems in the plane. Complex Variables and Elliptic Equations, 2012, v. 57, Nos. 7–8, 787–824.

40. V. V. Kravchenko, S. Morelos, S. Tremblay Complete systems of recursive integrals and Taylor series for solutions of Sturm-Liouville equations. Mathematical Methods in the Applied Sciences, 2012, v. 35, issue 6, 704–715 available from arxiv.org.

41. H. Campos, V. V. Kravchenko, S. M. Torba Transmutations, L-bases and complete families of solutions of the stationary Schrödinger equation in the plane. Journal of Mathematical Analysis and Applications, 2012, v. 389, issue 2, 1222--1238, available from arxiv.org.

42. V. V. Kravchenko, S. M. Torba Transmutations for Darboux transformed operators with applications. Journal of Physics A: Mathematical and Theoretical, 2012, v. 45, issue 7, # 075201 (21 pp.), available from arxiv.org.

43. H. Campos, V. V. Kravchenko, L. M. Méndez Complete families of solutions for the Dirac equation: an application of bicomplex pseudoanalytic function theory and transmutation operators. Advances in Applied Clifford Algebras, 22, issue 3 (2012), 577–594, DOI: 10.1007/s00006-012-0349-1 available at arxiv.org.

44. K. V. Khmelnytskaya, V. V. Kravchenko, J. A. Baldenebro-Obeso Spectral parameter power series for fourth-order Sturm-Liouville problems. Applied Mathematics and Computation, 219 (2012) 3610–3624.

45. V. V. Kravchenko, S. M. Torba Transmutations and spectral parameter power series in eigenvalue problems. In: Operator Theory: Advances and Applications, 2013, v. 228 Operator Theory, Pseudo-Differential Equations, and Mathematical Physics, 209-238, Springer: Basel.

46. H. Campos, V. V. Kravchenko Fundamentals of bicomplex pseudoanalytic function theory: Cauchy integral formulas, negative formal powers and Schrödinger equations with complex coefficients. Complex Analysis and Operator Theory, 2013, Volume 7, Issue 2, pp 485-518, available from arxiv.org.

47. K. V. Khmelnytskaya, V. V. Kravchenko, S. M. Torba, S. Tremblay Wave polynomials, transmutations and Cauchy's problem for the Klein-Gordon equation. Journal of Mathematical Analysis and Applications, 399 (2013) 191–212, available at http://arxiv.org/abs/1208.5984

48. V. V. Kravchenko, H. Oviedo, V. S. Rabinovich Electromagnetic fields in dispersive chiral media generated by modulated nonuniformly moving sources. Russian Journal of Mathematical Physics, 2013, v. 20, No. 1, 39-55.

49. R. Castillo-Pérez, V. V. Kravchenko, S. M. Torba Spectral parameter power series for perturbed Bessel equations. Applied Mathematics and Computation, 2013, v. 220, issue 1, 676-694, available at arxiv.org.

50. V. Barrera-Figueroa, V. V. Kravchenko, V. S. Rabinovich Spectral parameter power series analysis of isotropic planarly layered waveguides. Applicable Analysis, 2014, v. 93, No. 4, 729–755.

51. V. V. Kravchenko, S. M. Torba Modified spectral parameter power series representations for solutions of Sturm-Liouville equations and their applications. Applied Mathematics and Computation, 2014, v. 238, issue 1, 82-105, available at arXiv:1401.1877.

52. V. Barrera-Figueroa, H. Blancarte, V. V. Kravchenko The phase retrieval problem: a spectral parameter power series approach. Journal of Engineering Mathematics, 2014, v. 85, Issue 1, pp 179-209.

53. V. V. Kravchenko, S. M. Torba Analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems. Journal of Computational and Applied Mathematics, 2015, v. 275, 1-26, available at arxiv.org.

54. V. V. Kravchenko, S. M. Torba Construction of transmutation operators and hyperbolic pseudoanalytic functions. Complex Analysis and Operator Theory, 2015, v. 9, Issue 2, pp 379-429, available at arxiv.org.

55. K. V. Khmelnytskaya, V. V. Kravchenko, H. C. Rosu Eigenvalue problems, spectral parameter power series, and modern applications. Mathematical Methods in the Applied Sciences, 2015, v. 38, Issue 10, pp. 1945–1969, available at arxiv.org.

56. V. V. Kravchenko, S. M. Torba, U. Velasco-García Spectral parameter power series for Sturm-Liouville equations with a potential polynomially dependent on the spectral parameter and Zakharov-Shabat systems. Journal of Mathematical Physics, 56, 073508 (2015), available at arXiv:1401.1520.

57. R. Castillo-Pérez, V. V. Kravchenko, S. M. Torba Analysis of graded-index optical fibers by the spectral parameter power series method. Journal of Optics, 2015, v. 17, Issue 2 , # 025607, available at arXiv:1408.4147.

58. V. V. Kravchenko, S. M. Torba, S. Morelos Liouville transformation, analytic approximation of transmutation operators and solution of spectral problems. Applied Mathematics and Computation, v. 273 (2016), 321–336, available at arXiv.

59. K. V. Khmelnytskaya, V. V. Kravchenko, S. M. Torba Modulated electromagnetic fields in inhomogeneous media, hyperbolic pseudoanalytic functions and transmutations. Journal of Mathematical Physics, 57, 051503 (2016), available at arXiv:1410.4873.

60. V. V. Kravchenko, S. M. Torba Analytic approximation of transmutation operators and related systems of functions. Boletín de la Sociedad Matemática Mexicana, 22 (2016) 389–429, available at arXiv.

61. V. V. Kravchenko, L. J. Navarro, S. M. Torba Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions. Applied Mathematics and Computation, v. 314 No. 1 (2017), 173-192, available at arXiv.

62. V. V. Kravchenko, J. A. Otero, S. M. Torba, Analytic approximation of solutions of parabolic partial differential equations with variable coefficients. Advances in Mathematical Physics (2017) v. 2017, Article ID 2947275, 5 pages, doi:10.1155/2017/2947275.

63. V. V. Kravchenko, S. M. Torba Asymptotics with respect to the spectral parameter and Neumann series of Bessel functions for solutions of the one-dimensional Schrödinger equation. Journal of Mathematical Physics 58, issue 12, 122107 (2017).

64. V. V. Kravchenko, S. M. Torba, R. Castillo-Pérez A Neumann series of Bessel functions representation for solutions of perturbed Bessel equations. Applicable Analysis, 2018, v. 97, issue 5, 677-704. http://dx.doi.org/10.1080/00036811.2017.1284313

65. V. V. Kravchenko Construction of a transmutation for the one-dimensional Schrödinger operator and a representation for solutions. Applied Mathematics and Computation, 2018, v. 328, 75-81.

66. V. V. Kravchenko, S. M. Torba A Neumann series of Bessel functions representation for solutions of Sturm-Liouville equations. Calcolo, (2018) 55: 11. https://doi.org/10.1007/s10092-018-0254-7.

67. V. V. Kravchenko, E. L. Shishkina, S. M. Torba On a series representation for integral kernels of transmutation operators for perturbed Bessel equations. Mathematical Notes 2018, v. 104 (3-4), 530-544. https://doi.org/10.1134/S0001434618090201., available at arXiv.

68. V. V. Kravchenko, S. M. Torba, J. Yu. Santana-Bejarano Generalized wave polynomials and transmutations related to perturbed Bessel equations. Mathematical Methods in the Applied Sciences, v. 42 (2019), no. 15, 5008–5028, available at arXiv.

69. I. V. Kravchenko, V. V. Kravchenko, S. M. Torba Solution of parabolic free boundary problems using transmuted heat polynomials. Mathematical Methods in the Applied Sciences v. 42 (2019), no. 15, 5094–5105.

70. I. V. Kravchenko, V. V. Kravchenko, S. M. Torba, J. C. Dias Pricing double barrier options on homogeneous diffusions: a Neumann series of Bessel functions representation. International Journal of Theoretical and Applied Finance v. 22 (2019) no. 6, # 1950030, 24 pp, available at arXiv.

71. V. V. Kravchenko, R. M. Porter, S. M. Torba Spectral parameter power series for arbitrary order linear differential equations. Mathematical Methods in the Applied Sciences v. 42 (2019), no. 15, 4902–4908 , DOI: 10.1002/mma.4769.

72. V. V. Kravchenko On a method for solving the inverse scattering problem on the line. Mathematical Methods in the Applied Sciences v. 42 (2019), no. 4, 1321–1327.

73. K. V. Khmelnytskaya, V. V. Kravchenko, S. M. Torba A representation of the transmutation kernels for the Schrödinger operator in terms of eigenfunctions and applications. Applied Mathematics and Computation, v. 353 (2019), 274–281.

74. V. V. Kravchenko On a method for solving the inverse Sturm-Liouville problem. Journal of Inverse and Ill-Posed Problems v. 27 (2019), no. 3, 401–407.

75. B. B. Delgado, V. V. Kravchenko A right inverse operator for curl+λ and applications. Advances in Applied Clifford Algebras v. 29 (2019), no. 3, Art. 40, 15 pp.

76. F. A. Gómez, V. V. Kravchenko On transmutation operators and Neumann series of Bessel functions representations for solutions of linear higher order differential equations. In: A. Karapetyants, V. Kravchenko, E. Liflyand (eds.), Modern Methods in Operator Theory and Harmonic Analysis, Springer Proceedings in Mathematics & Statistics 291, 2019, 371-385. ISBN 978-3-030-26748-3.

77. R. Castillo-Pérez, V. V. Kravchenko, S. M. Torba A method for computation of scattering amplitudes and Green functions of whole axis problems. Mathematical Methods in the Applied Sciences v. 42 (2019), no. 15, 5106–5117.

78. B. B. Delgado, K. V. Khmelnytskaya, V. V. Kravchenko The transmutation operator method for efficient solution of the inverse Sturm‐Liouville problem on a half‐line. Mathematical Methods in the Applied Sciences. v. 42 (2019) 7359–7366.

79. K. V. Khmelnytskaya, V. V. Kravchenko, S. M. Torba Time-dependent one-dimensional electromagnetic wave propagation in inhomogeneous media: exact solution in terms of transmutations and Neumann series of Bessel functions. Lobachevskii Journal of Mathematics, v. 41, issue 5, 2020, 785-796.

80. A. N. Karapetyants, K. V. Khmelnytskaya, V. V. Kravchenko, A practical method for solving the inverse quantum scattering problem on a half line. Journal of Physics: Conference Series, 1540 (2020), 012007, 7pp.

81. V. V. Kravchenko, S. M. Sitnik Some recent developments in the transmutation operator approach. In: V. V. Kravchenko, S. M. Sitnik (eds.), Transmutation Operators and Applications, Trends in Mathematics, Birkhäuser, 2020, pp. 3-9.

82. B. B. Delgado, K. V. Khmelnytskaya, V. V. Kravchenko A representation for Jost solutions and an efficient method for solving the spectral problem on the half line. Mathematical Methods in the Applied Sciences v. 43 (2020) 9304–9319.

83. V. V. Kravchenko, V. A. Vicente-Benítez Transmutation operators and complete systems of solutionsfor the radial Schrödinger equation. Mathematical Methods in the Applied Sciences v. 43 (2020) 9455–9486.

84. H. M. Campos, V. V. Kravchenko The Bergman kernel for the Vekua equation. Mathematical Methods in the Applied Sciences v. 43 (2020) 9448–9454.

85. V. V. Kravchenko, E. L. Shishkina, S. M. Torba A transmutation operator method for solving the inverse quantum scattering problem. Inverse Problems, v. 36 (2020) 125007 (23pp)

86. V. V. Kravchenko, S. M. Torba A direct method for solving inverse Sturm-Liouville problems. Inverse Problems v. 37, 2021, # 015015 (32 pp).

87. V. V. Kravchenko, S. M. Torba Transmutation operators and a new representation for solutions of perturbed Bessel equations. Mathematical Methods in the Applied Sciences v. 44 (2021) 6344–6375.

88. V. V. Kravchenko, P. E. Moreira, R. M. Porter Complete systems of Beltrami fields using complex quaternions and transmutation theory. Advances in Applied Clifford Algebras v. 31 issue 3 (2021) #31.

89. V. V. Kravchenko, S. M. Torba A practical method for recovering Sturm-Liouville problems from the Weyl function. Inverse Problems 2021, 37(6), 065011 https://doi.org/10.1088/1361-6420/abff06

90. V. V. Kravchenko, E.L. Shishkina, S.M. Torba (2021) A Neumann Series of Bessel Functions Representation for Solutions of the Radial Dirac System. In: Karapetyants A.N., Kravchenko V.V., Liflyand E., Malonek H.R. (eds) Operator Theory and Harmonic Analysis. OTHA 2020. Springer Proceedings in Mathematics & Statistics, vol 357. Springer, Cham. https://doi.org/10.1007/978-3-030-77493-6_18

91. V. V. Kravchenko, V. A. Vicente-Benítez Runge property and approximation by complete systems of solutions for strongly elliptic equations, Complex Variables and Elliptic Equations, DOI: 10.1080/17476933.2021.1955870

Tesis de Doctorado dirigidas: (PhD students)

1. Hector Oviedo Galdeano Nuevas representaciones para el campo electromagnético en medios quirales en base al análisis cuaterniónico. IPN, 8.06.2004.

2. Raúl Castillo Pérez Extendibilidad de los campos electromagnéticos y espinoriales y aplicaciones. IPN, 16.03.2005.

3. Kira Khmelnytskaya Gerasimova Solución analítica y numérica de problemas con valores en la frontera para el campo electromagnético en medios quirales. IPN, 6.12.2005.

4. Marco Pedro Ramírez Tachiquin Estudios de sistemas de primer órden de la teoría de campos en medios no homogéneos. IPN, 6.12.2005.

5. Antonio Castañeda Solís Métodos pseudoanalíticos aplicados a modelos de la teoría de campos. IPN, 29.06.2006.

6. Rabindranath Reséndiz Vázquez Nuevos resultados en el estudio de campos en medios estratificados. IPN, 17.08.2012.

7. Hugo Miguel Fernandes Campos Funciones pseudoanlíticas bicomplejas y aplicaciones en métodos constructivos de solución de problemas con valores en la frontera. CINVESTAV del IPN, 25.09.2012.

8. Víctor Barrera Figueroa Spectral parameter power series for elliptic problems with sources. CINVESTAV del IPN, 28.06.2013.

9. Ulises Velasco García Series de potencias del parámetro espectral para haces polinomiales de operadores de Sturm-Liouville, sistemas de Zakharov-Shabat y aplicaciones. CINVESTAV del IPN, 24.09.2015 (dirección conjunta con S. M. Torba).

10. Jessica Yuniver Santana Bejarano Operadores de transmutación para la ecuación de Bessel perturbada y aproximación analítica de sus soluciones. CINVESTAV del IPN, 30.08.2016.

11. Josafath Alfredo Otero Jiménez Solución de problemas con valores de frontera para ecuaciones diferenciales parciales parabólicas con coeficientes variables usando operadores de transmutación. CINVESTAV del IPN, 12.02.2018 (dirección conjunta con S. M. Torba).

12. Nelson Jades Gutierrez Jimenez Propiedades y aplicaciones de operadores de transmutación para sistemas de Dirac unidimensionales. Matemáticas, Cinvestav (dirección conjunta con S. M. Torba). 8.11.2018.

13. Flor Alba Gómez Gómez Representaciones en series de Neumann de funciones de Bessel para soluciones de ecuaciones diferenciales lineales. Matemáticas, Cinvestav, 1.11.2019.

Tesis de Maestría dirigidas: (Master degree students)

1.Fernando Luis Ramos Alarcón Barroso "Resolución numérica de problemas de difracción electromagnética en tres dimensiones usando el método de soluciones fundamentales." ESIME-Zacatenco del IPN, 15.03.1999.

2.Antonio Castañeda Solis "Soluciones fundamentales cuaterniónicas para las ecuaciones de Maxwell y sus aplicaciones en la solución numérica de problemas con valores de frontera." ESIME-Zacatenco del IPN, 23.08.2000.

3.Benjamin David Williams "Una generalización cuaterniónica de la ecuación de Riccati." ESFM del IPN, 16.03.2001.

4.Raúl Castillo Pérez "Aplicación del análisis cuaterniónico a los problemas de frontera para las ecuaciones de Maxwell en los dominios no acotados". ESIME-Zacatenco del IPN, 18.04.2001.

5.Marco Pedro Ramírez Tachiquin "Nuevas soluciones de las ecuaciones de Maxwell para medios no homogéneos empleando el análisis cuaterniónico". ESIME-Zacatenco del IPN, 10.08.2001.

6.Hector Oviedo Galdeano "Aplicación del análisis cuaterniónico en el aprendizaje de la teoría de campos electromagnéticos". ESIME-Zacatenco del IPN, 17.10.2001.

7.Ricardo Oscar Magos Pérez "Cálculo de modos guíados en las guías de onda dieléctricas planas de índice de refracción gradual". ESIME-Zacatenco del IPN, 16.12.2002.

8.Bouchaib El Hatifi El Hamdani "Análisis asintótico de fibras ópticas del índice gradual". ESIME-Zacatenco del IPN, 29.05.2003

9.Ricardo de Anda "Principio de absorción límite para las ecuaciones de Maxwell en medios homogéneos". ESIME-Zacatenco del IPN, 10.12.2004

10.Rabindranath Reséndiz Vázquez "Estimación del ancho de banda para comunicaciones satelitales utilizando la teoría de propagación en medios con dispersión." ESIME-Zacatenco del IPN, 14.12.2004

11.Eric Gómez Gómez "Una herramienta para la estimación de la atenuación de las ondas de radio por la ionosfera." ESIME-Zacatenco del IPN, 25.08.2006

12.María Rosalía Tenorio González "Un nuevo método numérico para la solución de problemas electromagnéticos en medios no homogéneos." ESIME-Zacatenco del IPN, 02.03.2007

13.Adriana Alvarado Cervantes "Compensación de fase en medios con el índice de refracción negativa y sus aplicaciones." ESIME-Zacatenco del IPN, 11.12.2007

14. Salvador Cruz Bohórquez "Factorización de la ecuación de Schrödinger no estacionaria, análisis y soluciones." Departamento de Matemáticas, CINVESTAV del IPN, 25.08.2010

15. Ulises Velasco García "El problema de los eigenvalores para el sistema de Zakharov-Shabat utilizando series de potencias para el parámetro espectral." Departamento de Matemáticas, CINVESTAV del IPN, 25.08.2010

16. Azucena Del Carmen Cedillo Díaz "Análisis para el cálculo de la reflectancia y transmitancia en un medio estratificado no homogéneo con punto de retorno." Maestría en Tecnología Avanzada, Unidad Profesional Interdisciplinaria en Ingeniería y Tecnología Avanzadas (UPIITA) del IPN, 28.06.2012

17. Víctor Alfonso Vicente Benítez "Teoría espectral de grafos cuánticos." Departamento de Matemáticas, CINVESTAV del IPN, 9.07.2018

Tesis de licenciatura dirigidas:

1. Saydeth Lili Ledesma Molinero "Estudio sobre los operadores de transmutación y sus aplicaciones." Licenciatura en Matemáticas Aplicadas, Facultad de Ingeniería, Universidad Autónoma de Querétaro, 7.08.2015

2. Víctor Alfonso Vicente Benítez "Representación SPPS para las soluciones de la ecuación de Bessel perturbada." Licenciatura en Matemáticas Aplicadas, Universidad del Istmo, Campus Tehuantepec, Oaxaca, 23.09.2016

Awards

1. Prize of the National Polytechnic Institute of Mexico for the best Research in1998 and 2005

(Premio a la Investigación en 1998 y en 2005, otorgado por el Instituto Politécnico Nacional.)

2. Prize of the National Polytechnic Institute of Mexico to the Scientific Advisor of the best Postgraduate Thesis in 2001 and 2004

(Premio al Director de la Mejor Tesis de Posgrado en 2001 y en 2004, otorgado por el Instituto Politécnico Nacional)

3. ISAAC Award 2001 (Premio otorgado por la International Society for Analysis, Applications and Computation) en 2001. http://mathisaac.org/Award.html

4. Reconocimiento por la dirección de la mejor Tesis Nacional de Licenciatura en Matemáticas Aplicadas (Premio MIXBAAL) otorgado por El Comité Organizador del 2do Encuentro Nacional de Matemáticas Aplicadas, 2016.

Plenary and Invited Lectures

1.International Workshop "Functional-analytic and complex methods, their interactions, and applications to partial differential equations", Graz, Austria, febrero de 2001 con la ponencia plenaria: Applied quaternionic analysis.

2.Summer School "Applied Mathematics", Atenas, Grecia, junio 2003 con una serie de pláticas: Applied Quaternionic Analysis.

3.The 7th International Conference on Clifford Algebras and their Applications, Toulouse, Francia, Mayo 19-29, 2005, con la plática plenaria de una hora: Factorization of the multidimensional Schrödinger operator and its applications.

4.Minitaller "Física Matemática: Simetrías", Zacatecas, México, 1-2 de diciembre de 2005 con la ponencia invitada de una hora: Factorización del operador de Schrödinger, sistemas completos de soluciones exactas y otras aplicaciones.

5.Preconference School "Function Theories in Higher Dimensions", Tampere, Finlandia, 8-10 de junio, 2006, con la plática plenaria de una hora Waves in complex media: hypercomplex approach.

6.International Conference: Function Theories in Higher Dimensions, Finlandia, Tampere , junio 12-16, 2006, con la plática plenaria de una hora: Bicomplex pseudoanalytic function theory, its applications and generalization.

7.International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2006), Hersonissos, Creta, Grecia, septiembre 15-19, 2006 con la plática plenaria de una hora Complex and hypercomplex factorization of elliptic operators and applications.

8.International Conference on Applied Analysis (ICAA 2007), Querétaro, Mexico, mayo 2-6, 2007 con la plática invitada On a transplant operator and explicit construction of Cauchy-type integral representations for a class of generalized analytic functions.

9.XL Congreso Nacional de la Sociedad Matemática Mexicana, Monterrey 14-19 de octubre de 2007 con la ponencia invitada de una hora: Funciones pseudoanalíticas y nuevos métodos de solución de ecuaciones de la física matemática.

10.Encuentro Nacional Actualidad de las Matemáticas Aplicadas (AMA 2008), Querétaro 6-8 de octubre de 2008 con la ponencia invitada de una hora:

Números complejos, más complejos y sus aplicaciones.

11. XLI Congreso Nacional de la Sociedad Matemática Mexicana, Valle de Bravo 20-24 de octubre de 2008 con la ponencia invitada: Una nueva representación para las soluciones de ecuaciones de Sturm-Liouville y sus aplicaciones.

12. AppliedMath 4, 4to Congreso Internacional en Matemáticas Aplicadas, México D.F., 29-31 de octubre, 2008 con la plática magistral

Recent developments in complex-analytic methods for solving equations of mathematical physics.

13. I Reunión conjunta Sociedad Matemática Mexicana y Real Sociedad Matemática Española, Oaxaca, 22-24 de julio de 2009 con la plática invitada

Resolviendo ecuaciones lineales de la física matemática con el uso de la teoría de funciones pseudoanalíticas.

14. Encuentro Nacional Actualidad de las Matemáticas Aplicadas (AMA 2009), Querétaro 21-23 de octubre de 2009 con la ponencia invitada de una hora:

Variable Compleja y la Física.

15. International Conference Waves in Science and Engineering (WIS&E 2009), Mexico City, 26-30 de octubre de 2009 con la plática plenaria

Spectral parameter power series for Sturm-Liouville problems and their applications in analysis and physics.

16. International Workshop "Analysis, Mathematical Physics and Applications", Ixtapa, Mexico, 1-5 of March, 2010 con la plática plenaria Solution of boundary value and spectral problems using new results from pseudoanalytic function theory.

17. 12th Annual Workshop on "Applications and Generalizations of Complex Analysis", Aveiro, Portugal, 22 of May, 2010 con la plática invitada

Factorization of second-order partial differential operators, pseudoanalytic functions and applications.

18. 18^th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (18^thICFIDCAA), Macau, China, 13-17 of August, 2010 con la plática invitada: Solving boundary and eigenvalue problems for operators with variable coefficients using pseudoanalytic functions.

19. 13th International Conference on Mathematical Methods in Electromagnetic Theory (MMET2010), Kiev, Ukraine, 6-8 of September, 2010 con la plática plenaria: Construction and use of reproducing kernels for boundary and eigenvalue problems in the plane using pseudoanalytic function theory.

20. Taller Internacional sobre aspectos modernos del Análisis Complejo e Hipercomplejo, Mexico DF, Mexico, 11-15 de Octubre 2010 con la plática invitada: Factorization of second-order partial differential operators, pseudoanalytic functions and applications.

21. Encuentro Nacional Actualidad de las Matemáticas Aplicadas (AMA 2010), Querétaro 20-22 de noviembre de 2010 con la ponencia invitada de una hora:

Ondas y Ecuaciones Diferenciales.

22. International Conference Waves in Science and Engineering (WIS&E 2011), Mexico City, 7-11 de noviembre de 2011 con la plática plenaria: Inhomogeneous media, spectral parameter power series and transmutation operators.

23. 45 Congreso Nacional de la Sociedad Matemática Mexicana, Querétaro 28 de octubre - 2 de noviembre, 2012 con la ponencia invitada: Nuevos resultados en la solución de problemas espectrales para ecuaciones diferenciales.

24. 9na Gran Semana Nacional de Matemáticas, Puebla 23-27 de septiembre, 2013 con la ponencia plenaria: Problemas espectrales en física e ingeniería: nuevos métodos de solución desde Querétaro.

25. International Conference Waves in Science and Engineering (WIS&E 2013), Huatulco, 4-8 de noviembre de 2013 con la plática plenaria: Transmutation operators and highly accurate solution of spectral problems.

26. International Workshop "Analysis, Mathematical Physics and Applications", Ixtapa, Mexico, 24-28 of February, 2014 con la plática plenaria: Elliptic equations with complex coefficients in 2D, bicomplex pseudoanalytic functions and Cauchy's integral formulas.

27. 16th Annual Workshop on Applications and Generalizations of Complex Analysis, Aveiro, Portugal, March 21-22, 2014 con la plática plenaria: Cauchy integral formulas for bicomplex pseudoanalytic functions and Schrödinger equations with complex coefficients.

28. Octavo Encuentro Internacional sobre la Enseñanza del Cálculo, México D.F., 17-18 de septiembre, 2015 con la plática plenaria: Las currículas y los maestros del siglo XXI.

29. International Workshop WIENER-HOPF METHOD, TOEPLITZ OPERATORS, AND THEIR APPLICATIONS, November 03-07, 2015, Boca del Rio, Veracruz, Mexico,

con la ponencia invitada: Representation of solutions to the Sturm-Liouville equation in terms of Neumann series of Bessel functions.

30. 6th International Conference “Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis”, April 24-29, 2016, Rostov del Don, Rusia, con la plática plenaria: Transmutations and Neumann series of Bessel functions in solution of Sturm-Liouville equations.

31. 8th St. Petersburg Conference in Spectral Theory dedicated to the memory of M.Sh.Birman 2016, June 3-6, 2016, St. Petersburg, con la plática invitada: Construction of transmutations and applications to spectral problems.

32. 7th International Conference “Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis”, April 24-28, 2017, Rostov del Don, Rusia, con la plática plenaria: Construction of transmutations and their applications.

Some videos of talks:

https://www.youtube.com/watch?v=ew0A9GtJ2fQ

http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=23640

http://wlkt.ustc.edu.cn/video/detail_5372_24835.htm