Articles publicats (Matemàtica)
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Integrability conditions for Lotka–Volterra planar complex quintic systems
(Elsevier, 2010)In this paper we obtain necessary and sufficient integrability conditions at the origin for the Lotka–Volterra complex quintic systems which are linear systems perturbed by fifth degree homogeneous polynomials, i.e., we ... 
The center problem for a 2:3 resonant cubic Lotka–Volterra system
(Elsevier, 2013)In this paper we obtain conditions on the coefficients of a cubic Lotka–Volterra system of the form equation(1) x=x(2a20x2a11xya02y2), ẏ=y(3+b20x2+b11xy+b02y2), which fulfillment yields the existence in a ... 
Sexrelated differences in body condition and serum biochemical parameters in red deer (Cervus elaphus) naturally infected with Mycobacterium bovis
(Elsevier, 2013)Although Mycobacterium bovis infection is commonly reported in red deer (Cervus elaphus), potential differences in the effects of infection on male and female animals in terms of body condition and clinical biochemistry ... 
The threedimensional center problem for the zeroHopf singularity
(American Institute of Mathematical Sciences, 20160301)In this work we extend wellknown techniques for solving the Poincar\'eLyapunov nondegenerate analytic center problem in the plane to the 3dimensional center problem at the zeroHopf singularity. Thus we characterize the ... 
Cyclicity of a class of polynomial nilpotent center singularities
(American Institute of Mathematical Sciences, 20160401)In this work we extend techniques based on computational algebra for bounding the cyclicity of nondegenerate centers to nilpotent centers in a natural class of polynomial systems, those of the form $\dot x = y + P_{2m + ... 
Center problem for systems with two monomial nonlinearities
(American Institute of Mathematical Sciences, 2016)We study the center problem for planar systems with a linear center at the origin that in complex coordinates have a nonlinearity formed by the sum of two monomials. Our first result lists several centers inside this family. ... 
Integrability of LotkaVolterra planar complex cubic systems
(World Scientific, 2016)In this paper we study the LotkaVolterra complex cubic systems. We obtain necessary conditions of integrability for these systems with some restriction on the parameters. The sufficiency is proved for all conditions, ... 
Analytic integrability inside a family of degenerate centers
(Elsevier, 2016)In this paper we study the analytic integrability around the origin inside a family of degenerate centers or perturbations of them. For this family analytic integrability does not imply formal orbital equivalence to a ... 
Centers and isochronous centers for generalized quintic systems
(Elsevier, 2015)In this paper we classify the centers and the isochronous centers of certain polynomial differential systems in R2 of degree d≥5 odd that in complex notation are ż=(λ+i)z(zz̄)d−52(Az5+Bz4z̄+Cz3z̄2+Dz2z̄3+Ezz̄4+Fz̄5), ... 
Optimizing the enzymatic elimination of clogging of a microfiltration membrane by Parellada grape cake
(Wiley, 2016)Clogging of the filtration membranes is one of the main problems in the process of obtaining grape must for white wine; therefore, clogging must be reduced to the maximum. The aim of this work was to find the optimal values ... 
Centers for the Kukles homogeneous systems with odd degree
(London Mathematical Society, 2015)For the polynomial differential system x˙ = −y, y˙ = x+Qn(x; y), where Qn(x; y) is a homogeneous polynomial of degree n there are the following two conjectures done in 1999. (1) Is it true that the previous system for ... 
Integrability conditions of a resonant saddle perturbed with homogeneous quintic nonlinearities
(Springer, 2015)In this work we complete the integrability conditions (i.e. conditions for the existence of a local analytic first integral) for a family of a resonant saddle perturbed with homogeneous quintic nonlinearities studied in a ... 
Center conditions for nilpotent cubic systems using Cherkas method
(Elsevier, 2016)In this work we study the center problem of a cubic polynomial differential system with nilpotent linear part. The analysis is based on the application of the Cherkas method to the Takens normal form. The study needs many ... 
Center problem in the center manifold for quadratic differential systems in R^3
(Elsevier, 2016)Using tools of computer algebra based on the Gr\'{o}bner basis theory we derive conditions for the existence of a center on a local center manifold for fifteen sevenparameter families of quadratic systems on $\R^3$. To ... 
Reversible nilpotent centers with cubic homogeneous nonlinearities
(Elsevier, 2016)We provide 13 nontopological equivalent classes of global phase portraits in the Poincaré disk of reversible cubic homogeneous systems with a nilpotent center at origin, which complete the classification of the phase ... 
A sufficient condition in order that the real Jacobian conjecture in R^2 holds
(Elsevier, 2016)Let F=(f,g):R2→R2 be a polynomial map such that detDF(x,y) is different from zero for all (x,y)∈R2 and F(0,0)=(0,0). We prove that for the injectivity of F it is sufficient to assume that the higher homogeneous terms of ... 
ZeroHopf polynomial centers of thirdorder differential equations
(Springer Science+Business Media New York, 20161115)We study the 3dimensional center problem at the zeroHopf singularity in some families of polynomial vector fields arising from thirdorder polynomial differential equations. After proving some general properties we check ... 
Nonsmooth quadratic centers defined in two arbitrary sectors
(Elsevier, 20161125)In this paper we analyze the centerfocus problem of some families of piecewise planar quadratic vector fields on two zones of R2. The zones we consider are two unbounded sectors defined by an arbitrary angle α and a fixed ... 
Cyclicity of some symmetric nilpotent centers
(Elsevier, 2016)In this work we present techniques for bounding the cyclicity of a wide class of monodromic nilpotent singularities of symmetric polynomial planar vector fields. The starting point is identifying a broad family of nilpotent ... 
Inertial mass from Unruh temperatures
(World Scientific Publishing, 2016)It has been proposed that inertia can be explained as follows: when objects accelerate in one direction a Rindler horizon forms in the other direction, suppressing Unruh radiation on that side, and producing a net Unruh ...