Research

You can check my profiles in some academic databases.

orcid.org/0000-0002-9508-1549
Scopus ID/7102884719
researchgate.net/profile/Jose_Vallejo6
Google Scholar/Jose A Vallejo
arXiv/vallejo_j_2
publons.com/a/1390549/ (Researcher-ID/A-9793-2008)

I serve as an editor for the Electronic Journal of Mathematics and Technology (eJMT), which is a free (that is, there are no publication charges), international refereed journal hosted by Radford University. As the name states, the journal covers applications of technology (CAS, ICT and the like) to mathematical teaching and research. Submission guidelines here.

I am also a member of the editorial board of the free electronic journal Sahuarus, this one hosted by the University of Sonora and aimed to university students and teachers interested in mathematics, both in education and in research.

Here is a complete list of the papers I have (co)authored. Those items marked with a ○ symbol are written in collaboration with a student.

• Symplectic scalar curvature on supermanifolds (with R. Hernández-Amador and Yu. Vorobiev). Download preprint (2020).
• Automated solving of constant-coefficients second-order linear PDEs using Fourier analysis (with E. Roque). Download preprint (2020).
• Closed stable orbits in a strongly coupled resonant Wilberforce pendulum (with M. Avendaño-Camacho and A. Torres-Manotas). To appear in Journal of Vibration and Control (2021). Download preprint.
• A radical approach to the role of computational thinking in teaching Mathematics. J. Phys.: Conf. Ser. 1581 (2020) 012071. Download the published paper.
• Using Oshima splines to produce accurate numerical results and high quality graphical output (with S. Takato). Mathematics in Computer Science 14 1 (2020) 399-413. Download preprint.
• Acausal quantum theory for non-Archimedean scalar fields (with M. L. Mendoza-Martínez and W. A. Zúñiga-Galindo). Reviews in Mathematical Phyics 31 04 (2019) 1950011. Download preprint.
• Synchronization of dynamical systems: an approach using a Computer Algebra System (with G. Dávila and A. Morante). Electronic Journal of Mathematics and Technology 13 1 (2019) 1-24. Download preprint.
• Hamiltonian dynamical systems: symbolical, numerical and graphical study (with S. Takato). Mathematics in Computer Science 13 1-2 (2019) 281-295 . Download preprint.
• Robust Optimal Design of Quantum Electronic Devices (with O. Morales and F. Periago). Mathematical Problems in Engineering (2018) Article ID 3095257. Download paper.
• Number theory and cryptography in your smartphone (with R. Ipiña). Electronic Journal of Mathematics and Technology 12 1 (2018) 230-246. Download preprint here. Available at the journal's homepage.
• Virtual beams and the Klein paradox for the Klein-Gordon equation (with A. Molgado and O. Morales). Revista Mexicana de Física E 64 1 (2018) 1-6. Download the paper here.
• A perturbation theory approach to the stability of the Pais-Uhlenbeck oscillator (with M. Avendaño-Camacho and Yu. Vorobiev). Journal of Mathematical Physics 58 (2017) 093501. Download the preprint here.
• Interfacing Free Computer Algebra Systems and C with KeTCindy (with S. Takato). In 'Computer Algebra Systems in Teaching and Research', Siedlce University of Natural Sciences and Humanities Volume 6 (2017) 172--185. Download preprint here.
• G-invariant deformations of almost-coupling Poisson structures (with Yu. Vorobiev). Symmetry, Integrability and Geometry: Methods and Applications SIGMA 13 (2017) 022, 13 pages. Download the paper here.
• Collaborative use of KeTCindy and free Computer Algebra Systems (with S. Takato, A. McAndrew and M. Kaneko). Mathematics in Computer Science 11 3-4 (2017) 503-514. Download preprint here.
• Supermanifolds, symplectic geometry and curvature (with R. Hernández-Amador and J. Monterde). Download the preprint here. Chapter 12 in 'Geometry, Algebra and Applications: From Mechanics to Cryptography'. Springer Proceedings in Mathematics and Statistics, vol. 161 (2016).
• Computer-aided strategies to shorten the gap between high school and university math courses (with A. Morante). Proceedings of the XX Asian Technology Conference in Mathematics. Held in Leshan (China). December, 2015. Available at the Conference webpage.
• Lie algebroids generated by cohomology operators (with D. García Beltrán and Yu. Vorobjev). Journal of Geometric Mechanics 7 3 (2015) 295-315. Download preprint.
• Invariant Poisson realizations and the averaging of Dirac structures (with Yu. Vorobiev). Symmetry, Integrability and Geometry: Methods and Applications SIGMA 10 (2014) 096, 20 pages. Download pdf.
• Quillen superconnections and connections on supermanifolds (with J. V. Beltrán and J. Monterde). Journal of Geometry and Physics 86 (2014) 180-193. Download pdf.
• A simple global representation for second-order normal forms of Hamiltonian systems relative to periodic flows (with M. Avendaño-Camacho and Yu. Vorobjev). Journal of Physics A: Mathematical and Theoretical 46 (2013) 395201. Download pdf.
• Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems (with M. Avendaño-Camacho and Yu. Vorobjev). Journal of Mathematical Physics 54 (2013) 082704. Download pdf.
• Chaotic Dynamics with Maxima (with A. Morante). Electronic Journal of Mathematics and Technology 7 Special Issue June (2013). Download pdf. This paper is free-access (through a free subscription), you can also download it from the journal's page.
• The Principle of Stationary Action in the Calculus of Variations (with E. López-Cerdà and A. Molgado). Communications in Mathematics 20 2 (2012) 89-116. Download pdf. This paper is free-access, you can also download it from the journal's page.
• Implementing the RSA cryptosystem with Maxima CAS (with J. Monterde). Electronic Journal of Mathematics and Technology 6 1 (2012) 1-20. Download pdf. This paper is free-access (through a free subscription), you can also download it from the journal's page.
• On Lie algebroids and Poisson algebras (with D. García Beltrán and Yu. Vorobjev). Symmetry, Integrability and Geometry: Methods and Applications SIGMA 8 (2012) 006, 14 pages. Download pdf. This paper is free-access, you can also download it from the journal's page.
• Symplectic connections and Fedosov's quantization on supermanifolds. Journal of Physics: Conference Series 343 (2012) 012124. Download pdf. This paper is free-access, you can also download it from the journal's page.
• Modelling the landing of a plane in a calculus lab (with A. Morante). International Journal of Mathematical Education in Science and Technology (2011). 13 pages, doi:10.1080/0020739X.2011.633626. Download pdf.
• An approach to omni-Loday algebroids using quasi-derivations (with D. García Beltrán). Journal of Generalized Lie Theory and Applications Vol. 5 (2011), Article ID G100801, doi:10.4303/jglta/G100801. Download pdf.
• Software libre para el estudio de sistemas dinámicos (with A. Morante). La Gaceta de la Real Sociedad Matemática Española, Vol. 14 1 (2011) 111–132. Download pdf.
• Introducción a la supersimetría. Matemàtiques 5 1 (2010) 3-57. Download pdf.
• The Meaning of Time and Covariant Superderivatives in Supermechanics (with G. Salgado). Advances in Mathematical Physics, vol. 2009, Article ID 987524, 21 pages, 2009. doi:10.1155/2009/987524. Download pdf. This paper is free-access, you can also download it from the journal's page.
• Critical points of functionals defined on Fréchet manifolds. Journal of Nonlinear Mathematical Physics 16 4 (2009) 443-454. Download pdf.
• Harmonic superfunctions and supersymmetric sigma models (with J. Muñoz-Masqué). International Journal of Geometric Methods in Modern Physics 6 5 (2009) 839-849. Download pdf.
• Harmonicity in supermanifolds and sigma models (with J. Muñoz-Masqué). Proceedings of the American Institute of Physics. Geometry and Physics Vol. 1130 (2009) 171-175. Copyright 2009 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. Download pdf.
• The structure of Fedosov supermanifolds (with J. Monterde and J. Muñoz-Masqué). Journal of Geometry and Physics 59 (2009) 540-553. Download pdf.
• The Poincaré-Cartan form in Superfield Theory (with J. Monterde and J. Muñoz-Masqué). International Journal of Geometric Methods in Modern Physics 3 4 (2006) 775-822. Download pdf.
• Composition operators on weighted spaces of holomorphic functions on JB*-triples (with M. Mackey and P. Sevilla-Peris). Letters in Mathematical Physics 76 1 (2006) 19-26. Download pdf.
• Calculus of variations and field theory on graded fiber bundles (with J. Monterde and J. Muñoz-Masqué). Proc. of the XIV Fall Workshop on Geometry and Physics. Publ. de la RSME Vol. 10 (2006) 218-224. Download pdf.
• Generating operators of the Krasil'shchik-Schouten bracket. Letters in Mathematical Physics 68 (2004) 1, 1-17. Download pdf.
• The symplectic structure of Euler-Lagrange superequations and Batalin-Vilkoviski formalism (with J. Monterde): Journal of Physics A: Mathematical and Theoretical 36 18 (2003) 4993-5009. Download pdf.
• Geometric Structures on Supermanifolds. Applications to Physics: Publicacions de la Universitat de València, València (2003), ISBN: 84-370-5722-1.
• The modular class of even symplectic manifolds (with J. Monterde): (Russian) Teoret. Mat. Fiz. 132 (2002) 1, 50-59; translation in Theoretical and Mathematical Physics 132 1 (2002) 934-941. Download pdf.
• Poisson brackets of even symplectic forms on the algebra of differential forms (with J. Monterde): Annals of Global Analysis and Geometry 22 3 (2002) 267-289. Download pdf.
• Nambu-Poisson manifolds and associated n-ary Lie algebroids: Journal of Physics A: Mathematical and Theoretical 34 13 (2001) 2867-2881. Download pdf and Corrigendum: J. Phys. A. 34 (2001) 45, 9753.

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