Articles publicats (Matemàtica)
Permanent URI for this collection
Browse
Recent Submissions
- ItemOpen AccessOn mixed radial Moore graphs of diameter 3(Elsevier, 2023-05-10) Ceresuela, Jesús M.; López Lorenzo, Ignacio; Chemisana Villegas, DanielRadial Moore graphs and digraphs are extremal graphs related to the Moore ones where the distance-preserving spanning tree is preserved for some vertices. This leads to classify them according to their proximity to being a Moore graph or digraph. In this paper we deal with mixed radial Moore graphs, where the mixed setting allows edges and arcs as different elements. An exhaustive computer search shows the top ranked graphs for an specific set of parameters. Moreover, we study the problem of their existence by providing two infinite families for different values of the degrees and diameter 3. One of these families turns out to be optimal.
- ItemOpen AccessAnalytically integrable system orbitally equivalent to a semi-quasihomogeneous system(Elsevier, 2023) Algaba, Antonio; García, Cristóbal; Reyes, Manuel; Giné, JaumeFor perturbations of integrable non-Hamiltonian quasi-homogeneous planar vector field whose origin is a non-degenerate singular point, orbital linearization and analytic integrability are equivalent. We show a class of analytically integrable vector fields whose origin is a degenerate singular point which is orbitally equivalent to a semi-quasi-homogeneous system, that is, it is not orbital equivalent to its lowest-degree quasi-homogeneous term.
- ItemOpen AccessGeneralized interacting Barrow Holographic Dark Energy: Cosmological predictions and thermodynamic considerations(Elsevier, 2023) Luciano, Giuseppe Gaetano; Giné, JaumeWe construct a generalized interacting model of Barrow Holographic Dark Energy (BHDE) with infrared cutoff being given by the Hubble horizon. We analyze the cosmological evolution of a flat Friedmann–Lemaître–Robertson–Walker Universe filled by pressureless dark matter, BHDE and radiation fluid. The interaction between the dark sectors of the cosmos is assumed of non-gravitational origin and satisfying both the second law of thermodynamics and Le Chatelier–Braun principle. We study the behavior of various model parameters, such as the BHDE density parameter, the equation of state parameter, the deceleration parameter, the jerk parameter and the square of sound speed. We also investigate cosmological perturbations in the linear regime on sub-horizon scales, studying the growth rate of matter fluctuations for clustering dark matter and a homogeneous dark energy component. We show that our model satisfactorily retraces the thermal history of the Universe and is consistent with current observations for certain values of model parameters, providing an eligible candidate to describe dark energy. We finally explore the thermodynamics of our framework, with special focus on the validity of the generalized second law.
- ItemOpen AccessThe Poincaré map of degenerate monodromic singularities with Puiseux inverse integrating factor(De Gruyter, 2023-04-01) García, I. A. (Isaac A.); Giné, JaumeWe consider analytic families of planar vector fields depending analytically on the parameters in Λ that guarantee the existence of a (may be degenerate and with characteristic directions) monodromic singularity. We characterize the structure of the asymptotic Dulac series of the Poincaré map associated to the singularity when the family possesses a Puiseux inverse integrating factor in terms of its multiplicity and index. This characterization is only valid in a restricted monodromic parameter space ∗ Λ\Λ associated to the nonexistence of local curves with zero angular speed. As a byproduct, we are able to study the center-focus problem (under the assumption of the existence of some Cauchy principal values) in very degenerated cases where no other tools are available. We illustrate the theory with several nontrivial examples.
- ItemOpen AccessGeneralized Heisenberg Uncertainty Principle due to the quantum gravitational effects in the Schwarzschild spacetime(Elsevier, 2023) Chemisana Villegas, Daniel; Giné, Jaume; Madrid, JaimeIn non-relativistic quantum mechanics, the Heisenberg Uncertainty Principle states a fundamental limit to the accuracy in the measurement of pairs of conjugate variables, such as position and momentum. Based on a semiclassical geometric approach, it has been recently proposed a generalization of the uncertainty principle under the relativistic case, which could be extended to General Relativity. This formalism was applied to the Schwarzschild and de Sitter spacetime, showing that the uncertainty relations obtained can be mapped into deformations of Generalized Heisenberg principles well-known in the literature and obtained from the different models of quantum gravity proposed. In the present study, the generalized Heisenberg Principle is derived from the commutator relation, and has been applied to the classical gravitational tests and the derived consequences are framed and analyzed.