Sistema Regional de Información
en línea para Revistas Científicas de América Latina,
el Caribe, España y Portugal

Reseña de: Castelló-Cogollos, Rafael Camins d’incertesa i frustració. Les classes mitjanes valencianes (2004-2018) València: Institució Alfons el Magnànim, 2022.   Feito Alonso, Rafael Desigualdades de clase social en el siglo XXI València: Tirant lo Blanc, 2022

In this work, we consider the time-harmonic Maxwell’s equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface conditions between the subdomains. The advantage is that the interface condition can be updated without recomputing the Maxwell system at each step. The main part consists of a detailed description of the construction of the neural network for domain decomposition and the training process. To substantiate this proof of concept, we investigate a few subdomains in some numerical experiments with low frequencies. Therein the new approach is compared to a classical domain decomposition method. Moreover, we highlight current challenges of training and testing with different wave numbers and we provide information on the behaviour of the neural-network, such as convergence of the loss function, and different activation functions.

We revisit the celebrated Kohn-Vogelius penalty method and discuss how to use it for the unique continuation problem where data is given in the bulk of the domain. We then show that the primal-dual mixed finite element methods for the elliptic Cauchy problem introduced in [1] (E. Burman, M. Larson, L. Oksanen, Primal-dual mixed finite element methods for the elliptic Cauchy problem, SIAM J. Num. Anal., 56 (6), 2018) can be interpreted as a Kohn-Vogelius penalty method and modify it to allow for unique continuation using data in the bulk. We prove that the resulting linear system is invertible for all data. Then we show that by introducing a singularly perturbed Robin condition on the discrete level sufficient regularization is obtained so that error estimates can be shown using conditional stability. Finally we show how the method can be used for the identification of the diffusivity coefficient in a second order elliptic operator with partial data. Some numerical examples are presented showing the performance of the method for unique continuation and for impedance computed tomography with partial data.

The objective of the research is to estimate the transmission rate of an infection (β) in the SI epidemical model, using Bayesian statistical methods from observed data in Peru. After studying the SI mathematical model and Bayesian statistical inference metho’ds, a Bayesian estimator is proposed to estimate the transmisión rate of an infection in this model and a procedure is proposed to estimate this rate using Montecarlo simulation based on Markov chains - MCMC.

The duality theory of convex analysis is applied to the complete electrode model (CEM), which is a standard model in electrical impedance tomography (EIT). This results in a dual formulation of the CEM and a general error estimate. This new formulation of the CEM is written in terms of current fields and is shown to have a unique solution. Using this formulation, the general error estimate is proved, from which two a posteriori error estimates and a well known asymptotic result on CEM solutions are obtained. The first a posteriori error estimate assesses the accuracy of solutions to approximate problems, and the second one assesses the accuracy of approximate solutions. Numerical tests to apply this second estimate are performed, employing the finite element method to obtain approximate solutions.

A basic mathematical model in epidemiology is the SIR (Susceptible–Infected–Removed) model, which is commonly used to characterize and study the dynamics of the spread of some infectious diseases. In humans, the time scale of a disease can be short and not necessarily fatal, but in some animals (for example, insects) this same short time scale can make the disease fatal if we take into account their life expectancy. In this work, we will see how a positive feedback effect (decrease of the susceptible population at small densities) in a SIR model can cause a qualitative characterization of the dynamics defined by the original SIR model. Finally, we will also show with numerical simulations how a delay in the feedback effect causes very interesting qualitative changes of the system with epidemiological significance.

In this work, we simulate the dynamics of COVID-19 pandemic using a deterministic SIRD model and its stochastic SIRD model version. The model is used under a closed population of 32 625 984 from the peruvian country, where the coefficient of the transmission rate, the recovery rate, the dead rate and the initial condition are given for the data taken from the initial days reported by the first disease people in Peru.

We consider the adaptive finite element discretization of parameter estimation problems for nonlinear elliptic partial differential equations. The idea is to use a gradient method on the finite-dimensional parameter space for the minimization of the least-squares residual. Since the gradient involves solution of partial differential equations, it is not accesable, and is replaced by an approximation obtained by finite elements. This results into a perturbed gradient method. We use an (a posteriori) error estimator to control the accuracy of the gradient approximation and propose an algorithm, which links the estimator to the progress of the iteration. We show convergence of the algorithm under typical structural assumptions.

This research work presents the results of the external analysis of the problem of the management of the lower Moche river basin in the valley of the same name. These results are framed in the construction of a multicriteria objetive function, to determine a partition of the basin in particular study zones calleded cluster. The objetive function involves the main hydrogeological parameters and some external parameters such as coefficients that involve socio-political criteria and some too specific such as evapotranspiration of different types of plants cultivated in the valley on the underground aquifer.

We show the structure of the parameter space for a family of rational maps containing Blaschke products. Through numerical simulations using the orbit of a single critical point, we reveal the existence of infinitely many Mandelbrot-like sets along the unit circle, as well as eight-like structures in other regions of parameter space. We pose some open questions related to the parameter space of these functions.