Articles publicats (Matemàtica)
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- ItemOpen AccessComputation and validation of the Expected Value of Power of Two Terminal Series–Parallel PV arrays(Elsevier, 2024) Ceresuela, Jesús M.; Chemisana Villegas, Daniel; López Lorenzo, IgnacioPV arrays are susceptible to various types of failures such as partial shading that can negatively affect their performance and efficiency. Studying the impact of these circumstances in the performance of the PV array is key for the development of more efficient PV systems. In this study, the definition of the expected value of power (EVP) that a PV array can produce under a random failure scenario is revised and improved. An algorithm to compute EVP that minimizes the number of simulations is developed and tested in three different PV arrays. Results show a 96.6% reduction on average of the number of simulations needed to compute the EVP for PV arrays made up of 9 modules. The model is validated through an experiment that reproduces the random fault scenario and determines the mean power produced by the PV arrays. For all three experiments, the computed EVP fits the experimental data with 𝑅2 > 0.995.
- ItemOpen AccessToken graphs of cayley graphs as lifts(International Linear Algebra Society, 2024-05) Dalfó, Cristina; Fiol Mora, Miguel Ángel; Pavlíková, Sona; Siran, JozefThis paper describes a general method for representing k-token graphs of Cayley graphs as lifts of voltage graphs. This allows us to construct line graphs of circulant graphs and Johnson graphs as lift graphs on cyclic groups. As an application of the method, we derive the spectra of the considered token graphs. The method can also be applied to dealing with other matrices, such as the Laplacian or the signless Laplacian, and to construct token digraphs of Cayley digraphs.
- ItemOpen AccessA Polynomial System of Degree Four with an Invariant Square Containing At Least Five Limit Cycles(Springer, 2024) Grau Montaña, Maite; Szántó, IvánWe consider a class of polynomial systems of degree four with four real invariant straight lines that form a square, called this an invariant square, and also that contains in its interior at least five small amplitude limit cycles for a certain choice of the parameters. Moreover, we will obtain the necessary and sufficient conditions for the critical point inside the square to be a center.
- ItemOpen AccessCenter Conditions for Nilpotent Singularities in the Plane Using Invariant Solutions(Springer, 2024) Giné, JaumeRecalling that at any regular point we always have a unique particular solution curve passing through it. In this work it is constructed such particular solution curve not passing through the nilpotent singularity but as close as we want to the singularity. By product the existence of such particular curve allows to use it to determine necessary conditions to have a center for nilpotent singularities in the plane. Several involve methods to solve the center problem are known all based in the existence of a change of variables and a scaling transformation of time bringing any differential system with a nilpotent center into a time-reversible system. Here we present a new algebraic method based on the existence of such particular solution curve not passing through the singular point and the involution associated to the nilpotent system with a center. The algebraic method needs the computation of this particular curve up to certain order, which can be done with the help of an algebraic manipulator. Finally a new algebraic method is derived computing the vanishing of a unique function which really gives a scalar method for computing the necessary conditions.
- ItemOpen AccessSummary characteristics for multivariate function-valued spatial point process attributes(Wiley, 2024) Eckardt, Matthias; Comas Rodríguez, Carles; Mateu, JorgePrompted by modern technologies in data acquisition, the statistical analysis of spatially distributed function-valued quantities has attracted a lot of attention in recent years. In particular, combinations of functional variables and spatial point processes yield a highly challenging instance of such modern spatial data applications. Indeed, the analysis of spatial random point configurations, where the point attributes themselves are functions rather than scalar-valued quantities, is just in its infancy, and extensions to function-valued quantities still remain limited. In this view, we extend current existing first- and second-order summary characteristics for real-valued point attributes to the case where, in addition to every spatial point location, a set of distinct function-valued quantities are available. Providing a flexible treatment of more complex point process scenarios, we build a framework to consider points with multivariate function-valued marks, and develop sets of different cross-function (cross-type and also multi-function cross-type) versions of summary characteristics that allow for the analysis of highly demanding modern spatial point process scenarios. We consider estimators of the theoretical tools and analyse their behaviour through a simulation study and two real data applications.
