Articles publicats (Matemàtica)

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    Open Access
    Privacy-Preserving Electricity Trading for Connected Microgrids
    (MDPI, 2024) Alàs Cercós, Oriol; Sebé Feixas, Francesc
    The electricity market is evolving from the traditional unidirectional model into a bidirectional one in which households also generate and sell energy. This new scenario requires technology able to manage the available energy and guarantee that all the participants pay or are paid appropriately. Unfortunately, fine-grained monitoring of energy production and consumption makes it possible to infer sensitive information about confidential aspects of people’s private life. In this paper, we propose a system designed for privacy-preserving electricity trading in a connected microgrid. The system guarantees that at the end of a billing period, the distribution system operator can compute the quantity to be charged or paid to each household while being unable to trace its consumption details.
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    Open Access
    The linear term of the Poincaré map at singularities of planar vector fields
    (Elsevier, 2024-03-07) García, I. A. (Isaac A.); Giné, Jaume
    The aim of this work is to give conditions on the parameters of a family of analytic planar vector fields with a fixed Newton diagram and a monodromic singularity in order to guarantee that the coefficient (generalized first Lyapunov constant) of the linear part of the Poincaré map has an explicit formula that depends only on the Newton diagram. As far as we know, all the monodromic classes appearing in the literature satisfy that formula.
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    Open Access
    The blow-up method applied to monodromic singularities
    (Bolyai Institute, 2024) Fercec, Brigita; Giné, Jaume
    The blow-up method proves its effectiveness to characterize the integrability of the resonant saddles giving the necessary conditions to have formal integrability and the sufficiency doing the resolution of the associated recurrence differential equation using induction. In this work we apply the blow-up method to monodromic singularities in order to solve the center-focus problem. The case of nondegenerate monodromic singularities is straightforward since any real nondegenerate monodromy singularity can be embedded into a complex system with a resonant saddle. Here we apply the method to nilpotent and degenerate monodromic singularities solving the center problem when the center conditions are algebraic
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    Open Access
    The Horizons in Circular Accelerated Motions and Its Consequences
    (MDPI, 2023) Giné, Jaume
    In this work, we study the existence of horizons in circular accelerated motions and its consequences. One particular case is the existence of two horizons in any uniform circular motion. The radiation of the Poincaré invariant vacuum is related to the spontaneous breakdown of the conformal symmetry in Quantum Field Theory The main consequence of the existence of these horizons is the Unruh radiation coming from such horizons. This consequence allows us to study the possible experimental detection of the Unruh radiation in such motions. The radiation of the Poincaré invariant vacuum is related to the spontaneous breakdown of the conformal symmetry in Quantum Field Theory. This radiation is associated with an effective temperature that can be detected using an Unruh–DeWitt detector. In fact, this effective temperature at the relativistic limit depends linearly with respect to the proper acceleration. However, in general, this dependence is not linear, contrary of what happens in the classical Unruh effect. In the relativistic limit and high density case, the uniform circular motion becomes a rotating black hole. This allows for future studies of pre-black hole configurations.
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    Open Access
    On the spectra and spectral radii of token graphs
    (Springer, 2024-01-06) Reyes, Mònica Andrea; Dalfó, Cristina; Fiol Mora, Miguel Ángel
    Let G be a graph on n vertices. The k-token graph (or symmetric k-th power) of G, denoted by Fk(G), has as vertices the (n/k) k-subsets of vertices from G, and two vertices are adjacent when their symmetric difference is a pair of adjacent vertices in G. In particular, Fk(Kn) is the Johnson graph J(n, k), which is a distance-regular graph used in coding theory. In this paper, we present some results concerning the (adjacency and Laplacian) spectrum of Fk(G) in terms of the spectrum of G. For instance, when G is walk-regular, an exact value for the spectral radius (or maximum eigenvalue) of Fk(G) is obtained. When G is distance-regular, other eigenvalues of its 2-token graph are derived using the theory of equitable partitions. A generalization of Aldous’ spectral gap conjecture (which is now a theorem) is proposed.