• Algebraic and qualitative remarks about the family yy′ = (αxm+k–1 + βxm–k–1)y + γx2m–2k–1 

      Rodríguez-Contreras, Jorge; Acosta-Humánez, Primitivo B.; Reyes-Linero, Alberto (De Gruyter, 2019)
      The aim of this paper is the analysis, from algebraic point of view and singularities studies, of the 5-parametric family of differential equations yy′=(αxm+k−1+βxm−k−1)y+γx2m−2k−1,y′=dydx where a, b, c ∈ ℂ, m, k ∈ ℤ ...
    • Differential Galois theory and non-integrability of planar polynomial vector fields 

      Acosta-Humánez, Primitivo B.; Lázaro, J. Tomás; Morales-Ruiz, Juan J.; Pantazi, Chara (Elsevier, 2018-06)
      We study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular ...
    • Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials 

      Rodríguez Contreras, Contreras; Reyes Linero, Alberto; Campo Donado, Maria; Acosta-Humánez, Primitivo B. (Southwest Jiaotong University, 2020-08)
      In the present work, our goal is to establish a study of some families of quadratic polynomial vector fields connected to orthogonal polynomials that relate, via two different points of view, the qualitative and the algebraic ...
    • Integrability of stochastic birth-death processes via differential galois theory 

      Acosta-Humánez, Primitivo B.; Capitán, José A.; Morales-Ruiz, Juan J. (EDP Sciences, 2020)
      Stochastic birth-death processes are described as continuous-time Markov processes in models of population dynamics. A system of in nite, coupled ordinary diferential equations (the so- called master equation) describes ...
    • Isomonodromy for the Degenerate Fifth Painlev e Equation 

      Acosta-Humánez, Primitivo B.; Van Der Put, Marius; Top, Jaap (Eusko Jaurlaritza Gobierno Vasco, 2017-05-09)
      This is a sequel to papers by the last two authors making the Riemann{Hilbert correspondence and isomonodromy explicit. For the degenerate fifth Painlev e equation, the moduli spaces for connections and for monodromy are ...
    • A model of anaerobic digestion for biogas production using abel equations 

      Acosta-Humánez, Primitivo B.; Machado Higuera, Maximiliano; Sinitsyn, Alexander V. (Pushpa Publishing House, 2017)
      Mathematical models for biogas production are studied due to their importance in the use of control and optimization of renewable resources and clean energy. In this paper, we combine two algebraic methods to obtain ...
    • Pasting and reversing approach to matrix theory 

      Acosta-Humánez, Primitivo B.; Chuquen, Adriana L. (Pushpa Publishing House, 2016)
      The aim of this paper is to study some aspects of matrix theory through pasting and reversing using linear mappings. We obtain new properties and new sets in matrix theory. In particular, we introduce new linear mappings: ...