RESUMO O problema tratado é o desacoplamento de um sistema MIMO, com o número de entradas igual ao de saídas, bem como o controle ótimo desse sistema após o seu desacoplamento. Numa primeira etapa define-se uma estrutura de compensador para o sistema MIMO, que permite tornar cada saída dependente de uma única entrada. Para o sistema desacoplado propõe-se a aplicação de uma lei de controle por realimentação de saídas, onde a matriz de ganho de realimentação é determinada via otimização de um índice de desempenho definido como uma função de custo quadrática. O método de controle é baseado em LQR, através do qual adapta-se uma formulação LMI. MIMO saídas definese define se entrada propõese propõe quadrática LQR adaptase adapta LMI

ABSTRACT The problem addressed is the decoupling of a MIMO system, with the number of inputs equal to the number of outputs, as well as the optimal control of this system after its decoupling. The first step is to define a compensator structure for the MIMO system, which makes each output dependent on a single input. For the decoupled system, a feedback control law is proposed, where the feedback gain matrix is determined by optimizing a performance index defined as a quadratic cost function. The control method is based on LQR, through which an LMI formulation is adapted. outputs input proposed function LQR adapted

RESUMO Este trabalho apresenta resultados sobre grafos com pesos nos vértices associdos às aplicações estáveis entre duas superfícies fechadas, generalizando resultados obtidos para casos particulares de aplicações entre superfícies fechadas. fechadas

ABSTRACT In this work we present results on graphs with weights associated with stable mappings between two closed surfaces, extending the results already obtained to particular cases of maps between closed surfaces. surfaces

ABSTRACT Aedes aegypti is the main vector of multiple diseases, such as dengue, yellow fever, Zika, and chikungunya. Diseases associated with mosquitoes have been growing in recent years, with more than one-third of the world population at risk. Control techniques have been studied to prevent the spread of the Aedes aegypti, such that new formula and how to use adulticides and larvicides, among others. This paper proposes a novel approach in the field of partial differential equations and optimization. We consider a two-dimensional diffusion-reaction model that describes the interaction between aquatic and adult female stages spreading across a domain with parameters dependent on rainfall and temperature. We also formulate a mono-objective and multiobjective optimization problem to minimize the Aedes aegypti populations and the control, considering the application of adulticides and larvicides, using actual data from the city of Lavras/Brazil. The operator splitting technique is used to solve the diffusion-reaction system, coupling finite difference and the fourth-order Runge-Kutta method and optimal solutions were searched by using the Real-Biased Genetic Algorithm and Non-dominated Sorting Genetic Algorithm -II. Numerical results show significant reduction of the Aedes aegypti population. diseases dengue fever Zika chikungunya years onethird one third risk larvicides others twodimensional two dimensional diffusionreaction diffusion reaction temperature monoobjective mono objective control LavrasBrazil Lavras Brazil Lavras/Brazil system fourthorder fourth order RungeKutta Runge Kutta RealBiased Real Biased Nondominated Non dominated II. II -II

ABSTRACT An analytical solution for the interaction of cylindrical inhomogeneities in a complex potential was obtained using the analytical element method. This method utilizes expansions in the Laurent and Taylor series for the outer and inner parts, respectively, of each cylindrical inhomogeneity. The availability of individual solutions allowed the application of the superposition principle to obtain the solution of the flow problem in terms of discharge potential. This representation, however, required an iterative method for determining the coefficients of the series expansions, which used the minimum value for the absolute differences between successive iterations and a maximum number of iterations as a stop criterion. The implementation of the algorithm was performed in Python language v 3.6.7 and the numerical results after analysis of the convergence are presented in graphs containing the set of inhomogeneities used and their influence on the behavior of flow lines and potentials. These, through the precision and detail obtained, showed the ability of the MEA to characterize flow and identify preferred channels, evidencing its applicability to real situations.

RESUMO O efeito da interação do conjunto de inomogeneidades cilíndricas no potencial complexo em campo uniforme foi analisado por meio da solução proveniente do método de elementos analíticos. Esta, por sua vez, foi obtida por meio das expansões em Série de Laurent e Série de Taylor nas partes exterior e interior, respectivamente, de cada inomogeneidade cilíndrica. O formalismo do método de elementos analíticos, baseado no princípio da superposição, permitiu obter a solução do escoamento em termos de potencial de descarga. A determinação dos coeficientes complexos direcionou para a escolha de um método iterativo, o qual utilizou o valor mínimo para as diferenças absolutas entre iterações sucessivas e um número máximo de iterações como critério de parada. A respectiva implementação de todos os elementos do artigo foi realizada em linguagem Python v 3.6.7. Quanto à disposição das inomogeneidades, espaçamentos regulares e espaçamentos com posições e raios aleatórios são dois elementos considerados; quanto às condutividades quatro cenários são considerados em cada caso de disposição. Em todos os elementos, funções aleatórias foram utilizadas para caracterizar as condutividades do meio e de cada uma das inomogeneidades. Os resultados numéricos permitem avaliar a influência dos diversos cenários de condutividades, bem como a respectiva interação com os poços de bombeamento e injeção no caso de disposição aleatória. Além disso, a precisão e o nível de detalhamento que podem ser alcançados ilustram a capacidade do MEA para a caracterização do escoamento e identificação de canais preferenciais. Por fim, uma análise da convergência do algoritmo iterativo é apresentada para os cenários avaliados.

ABSTRACT In 2019, more than 90% of the world’s population was living in places where pollutant concentrations exceeded the air-quality guidelines. Anthropogenic activity has been the main cause of climate change in the last 20 years, especially in urban centres where industrial activities and motorized traffic mainly occur. This article presents a study of air pollutant dispersion by computational fluid dynamics modelling using OpenFOAM for urban street canyon simulations. The aim of this study was to investigate the influence of vegetation on natural ventilation, dispersion and CO2 mitigation. The behavior of pollutants was modeled by the Reynolds-averaged Navier-Stokes equations (RANS) and the k − ε fluid turbulence model. The results indicate that aerodynamic effects are more important at lower pollutant wind velocities, as they reduce turbulent dispersion and allow a higher reduction in the concentration of air pollutants. In addition, the direction of the wind, relative to the main axis of the street, had a significant impact on the results found. In general, in the presence of trees, perpendicular winds can lead to higher concentration of pollutants, while parallel winds allow improve air quality, considerably reducing those pollutant concentrations.

ABSTRACT During the first months of 2020 SARS-CoV-2 spread to all continents, virtually reaching all countries. In the subsequent months, new variants emerged in different regions of the world. A mathematical model based on the Covid-19 natural history encompassing the age-dependent fatality was applied to evaluate SARS-CoV-2 transmissibility and virulence. Transmissibility was assessed by calculating the basic reproduction number R 0 and virulence by counting the proportion of severe Covid-19 cases and deaths. The model parameters were adjusted against the data observed in the state of São Paulo, Brazil, considering two different levels of virulence. The severe Covid-19 cases and deaths were three times higher and R 0 was 25% lower when the more virulent SARS-CoV-2 variant was compared to the less virulent variant. However, under the high-virulence scenario the number of transmitting individuals is 25% lower, mainly due to the isolation of symptomatic individuals. The corollary that transmission increases in the low virulence scenario is also true. The estimated parameters, using data from São Paulo up to May 13, 2020, showed that the Covid-19 epidemic predicted with low virulence SARS-CoV-2 transmission matched the observed data just before the beginning of the relaxation, which occurred by mid-June 2020. The assessment of the interplay between transmissibility can be applied to explain in somehow the appearance of gamma and omicron variants of concern in São Paulo.

ABSTRACT In this work, inspired by Ramanujan’s fifth order Mock Theta function f 1( q ), we define a collection of functions and look at them as generating functions for partitions of some integer n containing at least m parts equal to each one of the numbers from 1 to its greatest part s , with no gaps. We set a two-line matrix representation for these partitions for any m ≥ 2 and collect the values of the sum of the entries in the second line of those matrices. These sums contain information about some parts of the partitions, which lead us to closed formulas for the number of partitions generated by our functions, and partition identities involving other simpler and well known partition functions.

ABSTRACT Researchers from different areas of knowledge have used the Cox proportional-hazards model, due to its simplicity and easy interpretation when studying situations in which the response variable is the time until the occurrence of an event of interest. However, the traditional Cox proportional-hazards model is not suitable for modeling data sets that violate the assumption of proportionality of the risks (or failure rates) and the effects of covariates over time are not detected. The generalized time-dependent logistic (GTDL) model has been used as an alternative in the modeling of survival data, taking into account the assumption of non-proportionality of the risks. In the literature, we found a wide and relevant production in inferential procedures, but no contribution in diagnostic methods or techniques. In this paper, Cox-Snell, modified Cox-Snell, martingale, deviance, randomized quantiles, NMSP (normally-transformed modified survival probabilities) and NRSP (normally-transformed randomized survival probabilities) residuals are proposed to assess the suitability of the GTDL model to the data. A Monte Carlo simulation study is conducted in order to investigate the empirical distribution of these residuals. In summary, the obtained simulation results indicate the adequacy, for the GTDL model, of the randomized quantile and NRSP residuals, regardless of the proportion of censorship in the data. The GTDL library is built and made available in the R programming language. Finally, the methodology studied is applied to a set of real data, available in the literature, involving patients diagnosed with advanced-stage lung cancer. Codes for installing and using the GTDL library are shown in the Supplementary Material (https://github.com/carrascojalmar/GTDL-Material-Suplementar).

RESUMO Pesquisadores de diferentes áreas do conhecimento têm utilizado o modelo de riscos proporcionais de Cox devido à sua simplicidade e fácil interpretação ao estudar situações em que a variável resposta é o tempo até a ocorrência de um evento de interesse. No entanto, o modelo tradicional de Cox não é adequado para descrever conjuntos de dados que violam a suposição de proporcionalidade dos riscos (ou taxas de falha) e os efeitos das covariáveis ao longo do tempo não são detectados. O modelo logístico generalizado dependente do tempo (GTDL, do inglês generalized time-dependent logistic) tem sido utilizado como alternativa na modelagem de dados de sobrevivência, levando em consideração a suposição de não proporcionalidade dos riscos. Na literatura é encontrada uma ampla e relevante produção em procedimentos inferenciais, mas nenhuma contribuição em métodos ou técnicas de diagnóstico. Neste artigo, os resíduos de Cox-Snell, modificados de Cox-Snell, martingale, deviance, quantílicos aleatorizados, NMSP (do inglês normally-transformed modified survival probabilities) e NRSP (do inglês normally-transformed randomized survival probabilities) são propostos para avaliar a adequabilidade do modelo GTDL aos dados. Um estudo de simulação via Monte Carlo é conduzido com o proposito de investigar a distribuição empírica desses resíduos. Em suma, os resultados de simulação obtidos indicam a adequação, para o modelo GTDL, dos resíduos quantílicos aleatorizados e NRSP, independentemente da proporção de censura nos dados. A biblioteca GTDL é construída e disponibilizada na linguagem de programação R. Finalmente, a metodologia estudada é aplicada a um conjunto de dados reais, disponível na literatura, envolvendo pacientes diagnosticados com câncer de pulmão em estágio avançado. Os códigos de instalação e uso da biblioteca GTDL são exibidos no Material Suplementar (https://github.com/carrascojalmar/GTDL-Material-Suplementar).

ABSTRACT Segmentation is one of the inferential applications for detecting patterns in digital images, which has been widely used in the health area. Thresholding, a type of segmentation, consists of separating the gray groups of an image, through one or more thresholds applied to the histogram. Thus, we used the gray tone with the lowest Fuzzy Divergence found to apply the enhancement method, through membership values. This paper presents a method to assist physicians in interpreting lung radiography images, especially in the pandemic caused by COVID-19, when enhancing lung images. In addition, we consulted with a group of medical experts who saw an improvement in image quality, providing the perception of detail in the enhanced image compared to the original image.

ABSTRACT The presented article discusses the Stirling numbers of the first kind, which is a special case of the study of polynomials on various indeterminates over the integers ring and has relations between the coefficients and the respective roots of a given algebraic equation. The idea consists of an expansion of a class of polynomials on the indeterminates x, x 1 , x 2 ,··· , x n ∈ ℤ, defined by p n ( x ) = ∏ j = 1 n ( x - x j ), given a fixed positive integer n. The idea is even more special, because it comes from the Vieta’s formula of the study of homogeneous and symmetric polynomials, which consists of studying the polynomials in ��(x), where the coefficients are on the ring �� = ℤ(x 1 , x 2 , · · · , x n ), moreover the particular integer roots in Vieta’s formula, discussed here, are x 1 = 0, x 2 = −1,··· , x n = −(n − 1) making interesting algebraic identities whose combinatorial nature is evident and the coefficients of the powers of x in p n (x), in this case, can be the answer to various counting problems modeled after this generating function, more specifically, the sequence associated to p n (x) generates the Stirling numbers of the first kind.

RESUMO O presente artigo trata-se do polinômio de Stirling do primeiro tipo, que é um caso particular do estudo de polinômios em várias indeterminadas sobre o anel dos inteiros e existem relações entre os coeficientes e as respectivas ráızes de uma dada equação algébrica. A ideia consiste na expansão de uma classe de polinômios nas indeterminadas x, x 1 , x 2 ,··· , x n ∈ ℤ, definidos por p n ( x ) = ∏ j = 1 n ( x - x j ), fixado um inteiro n positivo. A ideia é mais particular ainda, pois provém das relações de Girard do estudo de polinômios homogêneos e simétricos que consiste em estudar polinômios em ��(x), cujos coeficientes estão no anel �� = ℤ(x 1 , x 2 , · · · , x n ) e além disso as raízes inteiras particulares nas relações de Girard, em questão, são x 1 = 0, x 2 = −1,··· , x n = −(n− 1) gerando interessantes identidades algébricas cuja natureza combinatória é evidente e o coeficiente das potências de x em p n (x), nesse caso, pode ser resposta de diversos problemas de contagem modelado por meio dessa função geradora, mais especificamente, a sequência associada a p n (x) geram os números de Stirling do primeiro tipo.

ABSTRACT In this work we introduce a methodology to determine an optimal vaccination strategy for the COVID-19 disease with limited vaccination capacity, considering the delays between vaccine doses in order to minimize the number of deaths. We start proposing a compartmental model in order to study the evolution of the pandemic before the existence of a vaccine, in the city of Tandil, province of Buenos Aires, Argentina. We calibrate the parameters involved according to official data. Based on that model, we design an age-structured optimal control problem to determine the best way of administrate the available vaccines, taking into account their characteristics and the vaccination capacity. Finally, we compare optimal solutions with other feasible strategies, considering or not strict isolation measures.

ABSTRACT Within metal constructions there are structures made up of parallel members called legs, connected to each other by diagonals. Some of these structures, with a triangular cross section, turn out to be the guyed masts used in the communications industry, but also columns and beams used in metal structures. In the present work, the equations that allow obtaining the equations of the elastic of a spatial lattice of triangular cross section are developed, in which the legs are joined together by zig-zag diagonals. To do this, we start from an energy proposal in which the differential equations of equilibrium and the boundary conditions of the proposed problem are determined. Finally, examples are presented where results are obtained with the equations developed, and they are compared with the results obtained from the application of the expressions given in CIRSOC 303 Recommendation (1996) and from finite element models.

ABSTRACT Over the past few years, there has been a steady increase in the use of aircraft vehicles, in particular unmanned aerial vehicles (UAV). UAV navigation is generally controlled by a human pilot. But the challenge for the scientific community is to carry out autonomous navigation. Some solutions have been proposed for the UAV autonomous navigation. Studies indicate as a solution to use data fusion and/or image processing navigation. Kalman Filter (KF) can be employed as a data fuser, but the KF has disadvantages. An alternative to the KF is based on artificial intelligence. Here, the KF is replaced by a self-configured neural network. This work investigates a way to select data for training the neural fuser, based on cross-validation techniques. The results are compared to the data fusion done by a KF.

ABSTRACT The characterization of inverses of symmetric tridiagonal and block tridiagonal matrices and the development of algorithms for finding the inverse of any general non-singular tridiagonal matrix are subjects that have been studied by many authors. The results of these research usually depend on the existence of the LU factorization of a non-sigular matrix A, such that A = LU . Besides, the conditions that ensure the nonsingularity of A and its LU factorization are not promptly obtained. Then, we are going to present in this work two extremely simple sufficient conditions for existence of the LU factorization of a Toeplitz symmetric tridiagonal matrix A. We take into consideration the roots of the modified Chebyshev polynomial, and we also present an analysis based on the parameters of the Crout’s method.

ABSTRACT The d-minimal path (d-MP) problem is to find all the system state vectors (SSV) under which d units of data can be transmitted from a source node to a destination node in a stochastic-flow network (SFN). This problem has been very attractive in the last decades as one can compute the exact amount of the network’s reliability through the d-MPs. Although several algorithms have been proposed in the literature to address the problem, the research continues because it is NP-hard. Since the number of d-MPs grows exponentially with the size of the network, the available algorithms in the literature are not so practical. Hence, we employ the vectorization techniques for proposing an improved algorithm to address the problem. We conduct many experimental results on the known benchmarks and two hundred randomly generated SFNs in the sense of performance profile introduced by Dolan and Moré. The experimental results show the vectorization algorithm to be considerably more efficient than the non-vectorization ones.