Research

My research papers:

  • (with P.L. Clavería) The  volume of an isocanted cube is a determinant, Linear Multilinear Algebra, (03 July 2024) DOI: 10.1080/03081087.2024.2368240.
  • (with B. Bakhadly and A. Guterman) Normal Tropical (0,-1)-Matrices and Their Orthogonal  Sets, Journal of Mathematical Sciences, vol 269, n. 5, February 2023,  pp 614–631, DOI 10.1007/S10958-023-06305-4,  Translated from Fundamentalnaya i Prikladnaya Matematika, vol 24, n. 1, pp 5–30, 2022.
  • (with B. Bakhadly and A. Guterman) Orthogonality for (0,-1) tropical normal matrices, Spec. Matrices, 2020, vol 8, pp 40–60, https://doi.org/10.1515/spma-20220-0006.
  • (with P.L. Clavería) Volume of Alcoved Polyhedra and Mahler Conjecture, ISSAC’18, : 2018, New York, NY, USA, ACM, New York,  USA, 8 pages, https://doi.org/10.1145/3208976.3208990.
  • (with P.L. Clavería) Isocanted Alcoved Polytopes, Appl. Math. 2020 v.65, n.6, 703-726, ISSN 0862-7940
  •  Quasi-Euclidean classification of alcoved convex polyhedra, (2019) Linear Multilinear Algebra, DOI: 10.1080/03081087.2019.1572065
  • (with J. Linde) Matrices commuting with a given normal tropical matrix, Linear Algebra Appl. 2015, vol 482, pp 101–121, http://dx.doi.org/10.1016/j.laa.2015.04.032
  • Distances on the tropical line determined by two points
    Kybernetika (Prague) 50 (2014), no. 3, 408–435, MR3245538.
  • Kybernetika (Prague) 49 (2013), no. 6, 897–910. MR3182647.
  • (with A. Jiménez) Six combinatorial clases of maximal convex tropical polyhedra, (2012) arXiv: 1205.4162.
  • Tropical maps on the plane, Linear Algebra Appl. 2011,
  • (with Elisa Lorenzo García) An algorithm to describe the solution set of  any tropical linear system A \odot x=B \odot x , Linear Algebra Appl. (2010)
  • (with M. Ansola) A note on tropical triangles in the plane, Acta Math. Sin. (Engl. Ser.), vol 25 (2009) , n.11, pp 1775–1786.
  • (with M. Ansola) Tropical conics for the layman, (2009) Contemporary Mathematics, vol 495, pp 87–101
  • Real plane algebraic curves, Exp0. Math. (2002), vol 20, pp 291–314.
  • (with M. Coste)  Atypical values at infinity of a polynomial function on the real plane: an erratum, and an algorithmic criterion, J. Pure Appl. Algebra 162 (2001) no.1, 23-35, MR 1844807
  • A complex version of the Baer-Krull theorems,
    Comm. Algebra 28 (2000), no. 8, 3727–3737, MR1767584 .
  • The complex spectrum of a ring, Contemp. Math., 253
    American Mathematical Society, Providence, RI, 2000, 235–249.
    ISBN: 0-8218-0804-4, MR1747588.
  • Specializations and a local homeomorphism theorem for real Riemann surfaces of rings,
    Pacific J. Math. 176 (1996), no. 2, 427–442, MR1435000.
  • (with J. Ferrera Cuesta) The asymptotic values of a polynomial function on the real plane, J. Pure Appl. Algebra 106 (1996), no. 3, 263–273, MR1375824 –
  • (with J. Ferrera Cuesta)  Level curves of open polynomial functions on the real plane,  Comm. Algebra 22 (1994), no. 14, 5973–5981. MR1298760, https://doi.org/10.1080/00927879408825172.
  • The compatible valuation rings of the coordinate ring of the real plane
    Contemp. Math., 155
    American Mathematical Society, Providence, RI, 1994, 231–242.
    ISBN: 0-8218-5154-3, MR1260710 , DOI: 10.1090/conm/155/01382

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