The COVID-19 pandemic has forced policy makers to decree urgent confinements to stop a rapid and massive contagion. However, after that stage, societies are being forced to find an equilibrium between the need to reduce contagion rates and the need to reopen their economies. The experience hitherto lived has provided data on the evolution of the pandemic, in particular the population dynamics as a result of the public health measures enacted. This allows the formulation of forecasting mathematical models to anticipate the consequences of political decisions. Here we propose a model to do so and apply it to the case of Portugal. With a mathematical deterministic model, described by a system of ordinary differential equations, we fit the real evolution of COVID-19 in this country. After identification of the population readiness to follow social restrictions, by analyzing the social media, we incorporate this effect in a version of the model that allow us to check different scenarios. This is realized by considering a Monte Carlo discrete version of the previous model coupled via a complex network. Then, we apply optimal control theory to maximize the number of people returning to “normal life” and minimizing the number of active infected individuals with minimal economical costs while warranting a low level of hospitalizations. This work allows testing various scenarios of pandemic management (closure of sectors of the economy, partial/total compliance with protection measures by citizens, number of beds in intensive care units, etc.), ensuring the responsiveness of the health system, thus being a public health decision support tool.

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The use of a non-commutative algebra in hypercomplex function theory requires a large variety of different representations of polynomials suitably adapted to the solution of different concrete problems. Naturally arises the question of their relationships and the advantages or disadvantages of different types of polynomials. In this sense, the present paper investigates the intrinsic relationship between two different types of monogenic Appell polynomials. Several authors payed attention to the construction of complete sets of monogenic Appell polynomials, orthogonal with respect to a certain inner product, and used them advantageously for the study of problems in 3D-elasticity and other problems. Our goal is to show that, as consequence of the binomial nature of those generalized Appell polynomials, their inner structure is determined by interesting combinatorial relations in which the central binomial coefficients play a special role. As a byproduct of own interest, a Riordan-Sofo type binomial identity is also proved. Information

The classical Joukowski transformation plays an important role in different applications of conformal mappings, in particular in the study of flows around the so-called Joukowski airfoils. In the 1980s H. Haruki and M. Barran studied generalized Joukowski transformations of higher order in the complex plane from the view point of functional equations. The aim of our contribution is to study the analogue of those generalized Joukowski transformations in Euclidean spaces of arbitrary higher dimension by methods of hypercomplex analysis. They reveal new insights in the use of generalized holomorphic functions as tools for quasi-conformal mappings. The computational experiences focus on 3D-mappings of order 2 and their properties and visualizations for different geometric configurations, but our approach is not restricted neither with respect to the dimension nor to the order.

In the recent past, the problem of constructing bases for spaces of monogenic polynomials, in the framework of Clifford Analysis, has been considered by several authors, using different methods. In this talk we consider bases of 3D monogenic polynomials isomorphic to the complex powers, which are particularly easy to handle, from the computational point of view. Explicit constructions of such polynomial bases are performed and a numerical cost comparison with the well known Fueter polynomial basis is carried out.

The fact that generalized Appell sequences of monogenic polynomials in the setting of hypercomplex function theory also satisfy a corresponding binomial type theorem allows to obtain their explicit structure. Recently it has been obtained a complete characterization in the case of paravector valued homogeneous polynomials of three real variables. The aim of this contribution is the study of paravector valued homogeneous polynomials of four real variables, where new types of generalized Appell sequences could be detected.

It is evident, that the properties of monogenic polynomials in (n + 1)−real variables significantly depend on the generators e 1 , e 2 ,. .. , e n of the underlying 2 n-dimensional Clifford algebra Cℓ 0,n over R and their interactions under multiplication. The case of n = 3 is studied through the consideration of Pascal's tetrahedron with hypercomplex entries as special case of the general Pascal simplex for arbitrary n, which represents a useful geometric arrangement of all possible products. The different layers L k of Pascal's tetrahedron (or pyramid) are built by ordered symmetric products contained in the trinomial expansion of (e 1 + e 2 + e 3) k , k = 0, 1,. .. .

Resumo Objetivo refletir sobre os cuidados de enfermagem aos pacientes em hemodiálise no contexto da pandemia de COVID-19. Método trata-se de um estudo reflexivo, realizado mediante análise de documentos oficiais dos órgãos de saúde, artigos científicos e outras fontes conceituadas. Está organizado nos seguintes eixos: Pandemia de COVID-19; Insuficiência Renal Crônica e o tratamento hemodialítico; e Cuidados de enfermagem aos pacientes em tratamento hemodialítico no contexto da COVID-19. Resultado as ações de educação em saúde, educação continuada e a supervisão em enfermagem ganharam destaque no contexto da pandemia. Elas garantiram as orientações necessárias aos pacientes e familiares e à equipe de enfermagem, para prevenção e controle da COVID-19. Consequentemente, contribuíram para a proteção da saúde dos pacientes com insuficiência renal crônica, que já apresentavam sua saúde comprometida e não poderiam deixar de realizar a hemodiálise. Considerações finais e implicações para a prática no contexto da pandemia da COVID-19, os profissionais de enfermagem precisam redobrar a atenção na assistência prestada aos pacientes em tratamento hemodialítico, além de adaptarem-se às novas orientações. Espera-se que esta reflexão contribua para que os cuidados de enfermagem sejam os mais seguros possíveis, tanto para pacientes e familiares quanto para os profissionais de enfermagem.