Abstract. The simplest necessary conditions for an entire functionto be in the Laguerre-Pólya class are the Turán inequalities γ 2 k −γ k+1 γ k−1 ≥ 0. These are in fact necessary and sufficient conditions for the second degree generalized Jensen polynomials associated with ψ to be hyperbolic. The higher order Turán inequalities 4(are also necessary conditions for a function of the above form to belong to the Laguerre-Pólya class. In fact, these two sets of inequalities guarantee that the third degree generalized Jensen polynomials are hyperbolic.Pólya conjectured in 1927 and Csordas, Norfolk and Varga proved in 1986 that the Turán inequalities hold for the coefficients of the Riemann ξ-function. In this short paper, we prove that the higher order Turán inequalities also hold for the ξ-function, establishing the hyperbolicity of the associated generalized Jensen polynomials of degree three.

A stable and sustainable energy industry contributes indubitably to the business development, as well as to guarantee the quality of life of a population. However, the economic and social development of insular regions is very vulnerable, due to the high external energetic dependency. Therefore, it is necessary to change the current paradigm of those regions, to take advantage of their endogenous resources to generate electrical energy. The developed work analyses the potential renewable energies (wind and solar) present on the island of Brava, Cape Verde, and assesses its capacity to combine them with an energy storage system that can meet the energetic requirements of the island. The first step consists in the analysis and profiling of the data (energy consumption, solar radiation, wind speed) observed in the island for one year. Simultaneously, several types of storing technologies are analyzed to find the best fitting solution, given the characteristics of the electrical system of the island. The next step consists in the development of a mathematical model, based on LCOE calculus and on the renewable penetration level that determines the optimal mix of power to install of each technology. The results allow to conclude that, despite the inferior solar power generation when compared to the wind power, the most economical solution to the implementation of a 100% renewable system consists of an electricity production park primarily composed by solar powers.

Denote by P (α,β) n (x) and L α n (x) the classical Jacobi and Laguerre polynomials. In a recent paper Driver and Jordaan developed a method to obtain limits for zeros of orthogonal polynomials and applied it for the zeros of Jacobi and Laguerre polynomials. We show how to refine the method to obtain sharper limits for the same zeros. It turns out that the new limits obtained in this note are very precise.

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L’article analyse quelques poèmes et poètes brésiliens des décennies 1970, 1980 et 1990 dans le but de comprendre les différentes stratégies poétiques créées pendant cette période pour répondre aux défis spécifiques du régime d’historicité présentiste (Hartog) propre à l’expérience contemporaine. La relation entre poésie et histoire, l’énonciation poétique et ses contextes, se transforme. Le poème internalise, intensifie et mobilise la perception de perte de garantie discursive et la multiplicité des temps dans le temps, en mettant en action des variations et modulations entre différents contextes et temporalités, comme on le verra dans certains poèmes de Haroldo de Campos, Paulo Leminski, Nuno Ramos et autres.