Ara es mostren els items 2-21 de 32

    • Centers of quasi-homogeneous polynomial differential equations of degree three 

      Aziz, Waleed; Llibre Saló, Jaume; Pantazi, Chara (2014-03-20)
      Article
      Accés restringit per política de l'editorial
      We characterize the centers of the quasi-homogeneous planar polynomial differential systems of degree three. Such systems do not admit isochronous centers. At most one limit cycle can bifurcate from the periodic orbits of ...
    • Change in gap perception within current practices in assessing students learning mathematics 

      Cellmer, Anna; Serrat Piè, Carles; Bruguera Padró, Maria Montserrat; Pantazi, Chara; Estela Carbonell, M. Rosa; Bocanet, Vlad I.; Brown, Ken; Uukkivi, Anne; Soares, Filomena; Feniser, Cristina; Serdean, Florina M.; Safiulina, Elena; Kelly, Gerald; Cymerman, Joanna; Kierkosz, Igor; Volodymyr, Sushch; Latõnina, Marina; Labanova, Oksana; Lopes, Ana Paula (2021-04-17)
      Article
      Accés obert
      The COVID pandemic has touched many aspects of everyone’s life. Education is one of the fields greatly affected by it, as students and teachers were forced to move online and quickly adapt to the online environment. ...
    • Counterexample to a conjecture on the algebraic limit cycles of polynomial vector fields 

      Llibre Saló, Jaume; Pantazi, Chara (2004)
      Article
      Accés obert
      In Geometriae Dedicata 79 (2000), 101{108, Rudolf Winkel conjectured: For a given algebraic curve f = 0 of degree m > 4 there is in general no polynomial vector ¯eld of degree less than 2m ¡ 1 leaving invariant f = 0 ...
    • Darboux integrability and dynamics of the Basener–Ross population model 

      Güngör, Faruk; Llibre Saló, Jaume; Pantazi, Chara (Circolo Matematico di Palermo, 2021)
      Article
      Accés obert
      We deal with the Basener and Ross model for the evolution of human population in Easter island. We study the Darboux integrability of this model and characterize all its global dynamics in the Poincaré disc, obtaining 15 ...
    • Darboux integrability and invariant algebraic curves for planar polynomial systems 

      Christopher, C.; Llibre Saló, Jaume; Pantazi, Chara; Zhang, Xiang (2004)
      Article
      Accés obert
      In this paper we study the normal forms of polynomial systems having a set of given generic invariant algebraic curves.
    • Darboux integrals for Schrödinger planar vector fields via Darboux transformations 

      Acosta Humánez, Primitivo Belén; Pantazi, Chara (2011-11-01)
      Report de recerca
      Accés obert
      In this paper we study the Darboux transformations of planar vector fields of Schrödinger type. Using the isogaloisian property of Darboux transformation we prove the “invariance” of the elements of the “Darboux Theory of ...
    • Darboux integrals for Schrödinger planar vector fields via Darboux transformations 

      Acosta Humánez, Primitivo Belén; Pantazi, Chara (2012-07-14)
      Article
      Accés obert
      In this paper we study the Darboux transformations of planar vector fields of Schr odinger type. Using the isogaloisian property of Darboux transformation we prove the \invariance" of the objects of the \Darboux theory ...
    • Darboux theory of integrability for a class of nonautonomous vector fields 

      Llibre Saló, Jaume; Pantazi, Chara (2009-10)
      Article
      Accés obert
      The goal of this paper is to extend the classical Darboux theory of integrability from autonomous polynomial vector fields to a class of nonautonomous vector fields. We also provide sufficient conditions for applying ...
    • Differential galois theory and non-integrability of planar polynomial vector fields 

      Lázaro Ochoa, José Tomás; Pantazi, Chara; Acosta Humanez, Primitivo; Morales Ruiz, Juan José (2018-02-26)
      Article
      Accés restringit per política de l'editorial
      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 ...
    • EngiMath online course. Effective feedback from UPC mathematics teachers 

      Serrat Piè, Carles; Estela Carbonell, M. Rosa; Bruguera Padró, Maria Montserrat; Pantazi, Chara (Universitat Politècnica de Catalunya, 2022-09)
      Text en actes de congrés
      Accés obert
      EngiMath is a 3 ECTS online course in engineering mathematics, in seven different languages, and it is the main and practical output of the ERASMUS+ project entitled “Mathematics online learning model in engineering ...
    • EngiMath online course. Effective feedback from upc mathematics teachers (concept) 

      Serrat Piè, Carles; Estela Carbonell, M. Rosa; Bruguera Padró, Maria Montserrat; Pantazi, Chara (Universitat Politècnica de Catalunya, 2022-09)
      Text en actes de congrés
      Accés obert
      EngiMath is a 3 ECTS online course in engineering mathematics, in seven different languages, and it is the main and practical output of the ERASMUS+ project entitled “Mathematics online learning model in engineering ...
    • Global phase portraits of the quadratic systems having a singular and irreducible invariant curve of degree 3 

      Pantazi, Chara; Llibre Saló, Jaume (2023-01)
      Article
      Accés obert
      Any singular irreducible cubic curve (or simply, cubic) after an affine transformation can be written as either y2=x3 , or y2=x2(x+1) , or y2=x2(x-1) . We classify the phase portraits of all quadratic polynomial differential ...
    • Integrability and dynamics of a simplified class B laser system 

      Llibre Saló, Jaume; Pantazi, Chara (American Institute of Physics (AIP), 2023-10-12)
      Article
      Accés obert
      A simplified class B laser system is a family of differential polynomial systems of degree two depending on the parameters a and b. Its rich dynamics has already been observed in 1980s, see Arecchi et al. [Opt. Commun. 51, ...
    • Integrability and linearizability of a family of three-dimensional quadratic systems 

      Pantazi, Chara; Amen, Azad; Aziz, Waleed (2021-01-01)
      Article
      Accés obert
      We consider a three-dimensional vector field with quadratic nonlinearities and in general none of the axis plane is invariant. For our investigation, we are interesting in the case of (1:-2:1) – resonance at the origin. ...
    • Invariant algebraic surfaces of polynomial vector fields in dimension three 

      Kruff, Niclas; Llibre Saló, Jaume; Pantazi, Chara; Walcher, Sebastian (Springer, 2021-01-01)
      Article
      Accés obert
      We discuss criteria for the nonexistence, existence and computation of invariant algebraic surfaces for three-dimensional complex polynomial vector fields, thus transferring a classical problem of Poincaré from dimension ...
    • Limit cycles bifurcating from a degenerate center 

      Llibre Saló, Jaume; Pantazi, Chara (2016-02-01)
      Article
      Accés obert
      We study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second order and perturbing inside the class of ...
    • Morphisms and inverse problems 

      Christopher, Colin; Llibre Saló, Jaume; Pantazi, Chara; Walcher, Sebastian (2011-11-03)
      Report de recerca
      Accés obert
      In order to investigate polynomial vector ¯elds admitting a prescribed Darboux integrating factor, we show that it is helpful to employ morphisms of the a±ne plane. In particular, such morphisms may be used to remove ...
    • Morphisms and inverse problems for Darboux integrating factors 

      Llibre Saló, Jaume; Pantazi, Chara; Walcher, Sebastian (2013-12)
      Article
      Accés obert
      Polynomial vector fields which admit a prescribed Darboux integrat- ing factor are quite well-understood when the geometry of the underlying curve is nondegenerate. In the general setting morphisms of the affine plane ...
    • On planar polynomial vector fields with elementary first integrals 

      Christopher, Colin; Pantazi, Chara; Llibre Saló, Jaume; Walcher, Sebastian (2019-10-05)
      Article
      Accés obert
      We show that under rather general conditions a polynomial differential system having an elementary first integral already must admit a Darboux first integral, and we explicitly characterize the vector fields in this class. ...
    • On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory 

      Lázaro Ochoa, José Tomás; Morales Ruíz, Juan José; Acosta Humánez, Primitivo Belén; Pantazi, Chara (2012-01-12)
      Report de recerca
      Accés obert
      We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results ...