Browsing by Author "Pantazi, Chara"
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Analytic integrability of Bianchi Class A cosmological models with k=1
Ferragut Amengual, Antoni Manel; Llibre Saló, Jaume; Pantazi, Chara (2012)
Article
Restricted access  publisher's policyWe complete the study of the analytic integrability of the Class A of Bianchi cosmological models with k=1, characterizing the analytic first integrals of the Bianchi types V I0 and V III0. 
Centers of quasihomogeneous polynomial differential equations of degree three
Aziz, Waleed; Llibre Saló, Jaume; Pantazi, Chara (20140320)
Article
Restricted access  publisher's policyWe characterize the centers of the quasihomogeneous 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 (20210417)
Article
Open AccessThe 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
Open AccessIn 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
Open AccessWe 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
Open AccessIn 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 (20111101)
Research report
Open AccessIn 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 (20120714)
Article
Open AccessIn 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 (200910)
Article
Open AccessThe 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 nonintegrability of planar polynomial vector fields
Lázaro Ochoa, José Tomás; Pantazi, Chara; Acosta Humanez, Primitivo; Morales Ruiz, Juan José (20180226)
Article
Restricted access  publisher's policyWe 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, 202209)
Conference report
Open AccessEngiMath 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, 202209)
Conference report
Open AccessEngiMath 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 (202301)
Article
Open AccessAny 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(x1) . We classify the phase portraits of all quadratic polynomial differential ... 
Integrability and linearizability of a family of threedimensional quadratic systems
Pantazi, Chara; Amen, Azad; Aziz, Waleed (20210101)
Article
Open AccessWe consider a threedimensional 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, 20210101)
Article
Open AccessWe discuss criteria for the nonexistence, existence and computation of invariant algebraic surfaces for threedimensional 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 (20160201)
Article
Open AccessWe 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 (20111103)
Research report
Open AccessIn 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 (201312)
Article
Open AccessPolynomial vector fields which admit a prescribed Darboux integrat ing factor are quite wellunderstood 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 (20191005)
Article
Open AccessWe 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 PicardVessiot theory
Lázaro Ochoa, José Tomás; Morales Ruíz, Juan José; Acosta Humánez, Primitivo Belén; Pantazi, Chara (20120112)
Research report
Open AccessWe 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 ...