On the effect of COVID-19 pandemic in the excess of human mortality. The case of Brazil and Spain

Excess of deaths is a technique used in epidemiology to assess the deaths caused by an unexpected event. For the present COVID-19 pandemic, we discuss the performance of some linear and nonlinear time series forecasting techniques widely used for modeling the actual pandemic and provide estimates for this metric from January 2020 to April 2021. We apply the results obtained to evaluate the evolution of the present pandemic in Brazil and Spain, which allows in particular to compare how well (or bad) these countries have managed the pandemic. For Brazil, our calculations refute the claim made by some officials that the present pandemic is "a little flu". Some studies suggest that the virus could be lying dormant across the world before been detected for the first time. In that regard, our results show that there is no evidence of deaths by the virus in 2019This work was supported in the form of funding in part by Ministerio de Ciencia e Innovacio´n of Spain (Grant No. PID2019-108079GB-C22/AEI/10.13039/501100011033)awarded to N

On an Energy-Dependent Quantum System with Solutions in Terms of a Class of Hypergeometric Para-Orthogonal Polynomials on the Unit Circle

We study an energy-dependent potential related to the Rosen–Morse potential. We give in closed-form the expression of a system of eigenfunctions of the Schrödinger operator in terms of a class of functions associated to a family of hypergeometric para-orthogonal polynomials on the unit circle. We also present modified relations of orthogonality and an asymptotic formula. Consequently, bound state solutions can be obtained for some values of the parameters that define the model. As a particular case, we obtain the symmetric trigonometric Rosen–Morse potential for which there exists an orthogonal basis of eigenstates in a Hilbert space. By comparing the existent solutions for the symmetric trigonometric Rosen–Morse potential, an identity involving Gegenbauer polynomials is obtained