Abstract in English:

ABSTRACT To better understand the dynamics of air pollutants, several mathematical or computational models have been developed and employed. Among the pollutants of interest are those related to the cycle of formation of tropospheric ozone (O3), which involve nitrogen oxides NOx. In this process, there is a sequence of chemical reactions whose most elementary modeling can be described in terms of ordinary differential equations (ODEs), in which the concentrations (in µg/m3) of gases (O, NO, NO2, and O3) are functions of time. A novel study of the model is presented in terms of the qualitative theory of ordinary differential equations, for which the steady state of interest is non-hyperbolic. To study it, the Center Manifold Theorem was used to determine its stability. As for the results, our analytical calculations demonstrate the asymptotic local stability of the steady state, which was also numerically corroborated. Other than this new result of stability, the conclusion is that the simplified model of ozone kinetics with fixed kinetic parameters does not allow the behavior of sustained oscillatory solutions for the referred concentrations of pollutants, requiring other ingredients for this to be feasible.

Abstract in English:

ABSTRACT In this work, three implementation options for the ghost cell immersed boundary method are compared. These options are alternatives to a rather common implementation of the method that is susceptible to numerical instability in the calculation of the bilinear interpolation in some cases. The method is implemented for a second-order spatial discretization of the heat equation in a non-rectangular domain and the errors for each option are analyzed in terms of the order of accuracy and the way they are distributed in the domain. The best option, which was the only one to maintain the second order of convergence of the discretization, is to consider non-symmetric extrapolation with bilinear interpolation, instead of using inverse distance weighted interpolation with symmetric or non-symmetric extrapolation.

Abstract in English:

ABSTRACT Structural health monitoring (SHM) is a system that assesses the state of structures, whether aeronautical, civil or mechanical, and provides a prediction of their remaining life. This has arisen with the need for more economic viability in the monitoring of structures and in fault identification. Thus, this system was defined as a prophylactic, reliable and effective measure against structural failures. This work has as objective the theoretical basis and a bibliographical revision necessary for the execution of the acoustic impedance tube experiment, following the ISO10534-1(1996), as well as numerical simulations. The experimental data are compared with the numerical simulation of the acoustic pressure inside the impedance tube and the artificial immune system is used to characterize the experiment.

Abstract in Portuguese:

RESUMO O aumento das notificações por dengue contribui para a sobrecarga dos sistemas de saúde pública subtraindo recursos públicos que poderiam ser empregados no combate à pobreza e à melhoria da distribuição de renda da população. Embora a dengue seja uma doença veiculada por vetores, observa-se que populações residentes em áreas com diferentes padrões urbanísticos, econômicos e demográficos são impactadas diferenciadamente por essa arbovirose. Compreender como ocorreu nos últimos anos a evolução temporal da dengue pode proporcionar aos gestores em saúde um nível mais detalhado da dinâmica de propagação da dengue e dos seus vetores, visando auxiliar nas tomadas de decisões e subsidiar o controle local em áreas endêmicas. Para alcançar este objetivo propõe-se o ajuste de modelos para análise e previsão de séries temporais. O presente trabalho descreve um estudo realizado para os municípios de Guapimirim e Magé, localizados na região metropolitana do Rio de Janeiro. A modelagem de séries temporais foi fundamentada em modelos ARMAX, que possibilitam estimar a relação entre a incidência de dengue e as variáveis climáticas.

Abstract in English:

ABSTRACT The increase in notifications on the incidence of dengue testify to the overload of the public health systems and calls attention to the improper use of public resources that could be used to fight poverty and the consequent income inequality. Although dengue is a vector-borne disease, it has been observed that populations living in areas with different urban, economic and demographic patterns are impacted differently by this arbovirus. Understanding how the temporal evolution of dengue occurred in recent years can provide healthcare officials with a more detailed knowledge of the dynamics of the spread of dengue and its vectors, thus assisting the decision-making process and orienting local authorities in organizing controls in endemic areas. To achieve this objective, some time series models for analysis and forecasting were proposed and adjusted to the field data. This work describes a study carried out for the municipalities of Guapimirim and Magé, located in the metropolitan area of Rio de Janeiro. The modelling of the time series was based on ARMAX models, which allow to estimate the relationship between the incidence of dengue and climatic variables.

Abstract in English:

ABSTRACT In this paper, we consider the following initial-boundary value problem ∂ t u = Δ u - g u . ∇ u + f u i n Q × 0 , T , σ ∂ t + ∂ v u = 0 o n ∂ Q × 0 , T , u x , 0 = u 0 x i n Q ¯ , where Q is a bounded domain in ℝN with smooth boundary ∂Q, ∆ is the Laplacian, ν is the exterior normal unit vector on ∂Q, u0∈C2Q¯. The dissipative parameter σ×∈C 1(∂Q×(0, ∞)) is a bounded function and u 0(x)>0, x∈Q¯. We perturbe the above problem and under some assumptions, we show that the solution of the perturbed form blows up in a finite time and we estimate its blow-up time. We also prove the continuity of the blow-up time with respect to the initial datum.

Abstract in Portuguese:

RESUMO A resolução do problema de análise de estabilidade de fases é fundamental no estudo do equilíbrio de fases, presente em vários processos da engenharia química onde é necessário prever o número de fases e calcular a composição das mesmas. Na prática, para determinar a estabilidade de uma mistura multicomponente, deve-se resolver um problema de otimização não linear restrita. Neste trabalho, estudamos a estabilidade de sistemas termodinâmicos multicomponentes. Para resolver o problema de otimização, empregamos a Inicialização Global Topográfica para selecionar bons pontos iniciais para um método de direções viáveis e pontos interiores, que foi empregado na busca local. Os resultados indicam que a presente metodologia é uma estratégia promissora para avaliar a estabilidade de misturas.

Abstract in English:

ABSTRACT Solving the problem of phase stability analysis is fundamental for the study of phase equilibrium in chemical engineering processes where it is necessary to predict the number of phases and calculate their compositions. In practice, to determine the stability of a multicomponent mixture, a constrained nonlinear optimization problem must be solved. In this work, we study the stability of the multicomponent thermodynamic systems. To solve the optimization problem, we employ the Topographical Global Initialization method to select good starting points for a feasible direction interior-point method, which was used in local search. The results indicate that the present methodology is a promising strategy for evaluating the stability of mixtures.

Abstract in English:

ABSTRACT This article presents a deterministic mathematical model for the transmission dynamics of Covid-19 from the reservoir to the people. The model system properties were analyzed, such as the feasibility of the solutions, positivity of the state variables, and stability of the model equilibria-both local and global equilibrium points. Also, the basic reproduction number, R 0, was computed along with its sensitivity to model parameters to identify the most persuading parameter, and the results proved that high values of the parameters associated with the rate of controlling the infection out of human life and back to the reservoir will drastically minimize the spread rate of Covid-19 among people. The local stability of disease-free equilibrium was determined through the trace and determinant of matrix method. The disease-free equilibrium will be asymptotically stable if the trJE0<0 and detJE0>0. The disease-free and endemic equilibria were found to be globally stable when the R 0 < 1 and R 0 > 1 respectively. The analysis of the numerical simulation for the model on various sets of parameters displayed that, there is a strong noteworthy effects on the virulent if the effort of controlling the inffection is at the rate not less than 50% to pull back the infection out of people to reservoir or vanishing.

Abstract in English:

ABSTRACT The main goal of this paper is to study the model of the sequences of (r, p, k)-generalized Jacobsthal numbers, by the approach based on the properties of its associated Jacobsthal fundamental Fibonacci system and its fundamental sequence. Some linear and combinatorial properties are established. Moreover, the related matrix formulation allows us to provide new identities, which are declined in combinatorial form. Especially, the linear Jacobsthal Cassini identity and its combinatorial formulation are furnished. Finally, illustrative special cases and examples are given.

Abstract in English:

ABSTRACT The numerical solution to the Poisson Problem is widely known and studied in various fields of science for its vast applications. However, most applications consider the case in two dimensions, with fewer studies addressing the problem in dimension three or higher. Most literature texts present a twodimensional case implementation using an approach that makes it difficult to extend to higher dimensions. Our work aims to propose a generalization of the numerical solution to the Poisson problem that can be implemented for any dimension. The strategy used considers an index function that enumerates the mesh points so that, using this index, the implementation is easily extended to any dimension. In addition to the numerical solution extension, we developed the mathematical foundation for the consistency and stability of the solution in arbitrary dimension. The preliminary results consider the implementation in Python and experiments that demonstrate the feasibility of the proposed methodology.

Abstract in English:

ABSTRACT In this paper, we consider a certain third-order linear recurrence and then give generating matrices for the sums of positively and negatively subscripted terms of this recurrence. Further, we use matrix methods and derive explicit formulas for these sums.

Abstract in English:

ABSTRACT Throughout human history, epidemics have been a constant presence. Understanding their dynamics is essential to predict scenarios and make substantiated decisions. Mathematical models are powerful tools to describe an epidemic behavior. Among the most used, the compartmental ones stand out, dividing the population into classes with well-defined characteristics. One of the most known is the SIR model, based on a set of differential equations describing the rates of change of three categories over time. These equations consider parameters such as the disease transmission rate and the recovery rate, which both change over time. However, typically models use constant parameters and can not describe the behavior of a disease over long periods. In this work, it is proposed a method to estimate the parameters of a SIR model with a time-varying transmission rate, based on an optimization problem that minimizes the sum of the squares of the errors between the model and historical data. Additionally, based on the infection rates determined by the algorithm, the model’s ability to predict disease activity in future scenarios was also investigated. Epidemic data released by the government of the State of Rio Grande do Sul in Brazil was used to evaluate the models. The models showed a very good forecasting ability, resulting in errors for predicting the total number of accumulated infected persons of 0.13% for 7 days ahead and 0.6% for 14 days ahead.

Abstract in Portuguese:

RESUMO O cenário pandêmico causado pelo coronavírus SARS-CoV-2 fez aumentar o interesse e a divulgação de modelos matemáticos capazes de projetar a evolução do número de casos (e mortes) devido à COVID-19, em países, estados e cidades. Em muitos artigos, o número acumulado de casos é modelado por um modelo de crescimento não-linear, tais como os modelos exponencial, logístico e de Gompertz. Motivados por este fato, neste artigo, apresentamos uma revisão detalhada sobre estes três modelos de crescimento. Iniciamos com a obtenção da expressão matemática do modelo exponencial utilizando um exemplo simples de divisão celular. A partir do modelo exponencial, apresentamos em detalhes o desenvolvimento matemático para obtenção das expressões dos modelos logístico e de Gompertz, e como obter as coordenadas do ponto de inflexão deste dois modelos. Apresentada a revisão, ilustramos o uso destes três modelos na modelagem do número acumulado de mortes por COVID-19 registradas no estado de São Paulo no período de 17/03/2020 a 30/04/2021. Nesta modelagem, apresentamos um critério para o ajuste de um modelo por partes haja vista que os valores registrados apresentam um comportamento heterogêneo ao longo do tempo.

Abstract in English:

ABSTRACT The pandemic scenario caused by the SARS-CoV-2 coronavirus has increased the interest and divulgation of mathematical models capable of projecting the evolution of the number of cases (and/or deaths) due to COVID-19, in countries, states and/or cities. In many articles, the cumulative number of cases is modeled by a non-linear growth model, such as the exponential, logistic or Gompertz model. Motivated by this fact, in this article, we present a detailed review of these three growth models. We begin by obtaining the mathematical expression of the exponential model using a simple example of cell division. Based on the exponential model, we present in detail the mathematical development to obtain the expressions of the logistic and Gompertz models and how to obtain the coordinates of the inflection point of these two models. We also illustrate the use of these three growth models in the modeling of the cumulative number of deaths from COVID-19 recorded in the state of São Paulo in the period from 03/17/2020 to 04/30/2021. In this modeling, we present a criterion for adjusting a piecewise model since the recorded values showed heterogeneous behaviour over time.

Abstract in Portuguese:

RESUMO Para avaliar a energia depositada em órgãos e tecidos radiossensíveis do corpo humano é preciso desenvolver modelos computacionais de exposição (MCEs). A fonte nos MCEs corresponde a um algoritmo destinado a produzir o estado inicial da simulação. Usando técnicas Monte Carlo (MC) implementadas em robustos códigos disponíveis na comunidade científica, são simuladas as histórias das partículas, de interação em interação, até que suas energias estejam abaixo de um limiar de corte ou elas saiam do fantoma, que representa o corpo na simulação. Este trabalho apresenta um novo MCE chamado MSUPREE, onde a fonte implementada gera amostras de elétrons oriundos do decaimento do radionuclídeo ítrio 90 (Y-90), usado em radioembolização, um tratamento de tumores hepáticos. O estado inicial de um elétron é definido, principalmente, pela posição de largada, direção de deslocamento e energia inicial. No MSUPREE os sorteios das posições iniciais ocorrem em uma esfera dentro do fígado com centro e raio definidos nos arquivos de entrada do MCE. A partir disso, os elétrons se deslocam no espaço com ângulos polares e azimutais uniformemente sorteados nos seus domínios com energia inicial sorteada na tabela do espectro do Y-90 contida em um arquivo de entrada específico para o MSUPREE. A execução do MSUPREE produziu dados dosimétricos que permitem não apenas concluir que o acoplamento fantoma + fonte + código MC está correto, mas também que os autores, e pesquisadores do tema, dispõem de um novo MCE para dosimetria interna que pode ser aperfeiçoado para outras distribuições espaciais e energéticas de emissores beta.

Abstract in English:

ABSTRACT To evaluate the energy deposited in radiosensitive organs and tissues of the human body, it is necessary to develop exposure computational models (ECMs). The source in ECMs corresponds to an algorithm intended to produce the initial state of the simulation. Using Monte Carlo (MC) techniques implemented in robust codes available in the scientific community, the histories of particles are simulated, from interaction to interaction, until their energies are below a cutoff threshold, or they leave the phantom. This work presents a new ECM called MSUPREE, where the implemented source generates electron samples originating from the decay of the radionuclide yttrium 90 (Y-90), used in radioembolization, a treatment for liver tumors. The initial state of an electron is defined mainly by its starting position, direction of movement and initial energy. In MSUPREE, the initial positions are drawn on a sphere inside the liver with center and radius defined in the ECM input files. From this, the electrons move in space with polar and azimuthal angles uniformly drawn in their domains with initial energy drawn from the Y-90 spectrum table contained in a specific input file for MSUPREE. The execution of MSUPREE produced dosimetric data that allow us to conclude not only that the phantom + source + MC code coupling is correct, but also that the authors, and researchers on the subject, have a new ECM for internal dosimetry that can be improved for other spatial and energetic distributions of beta emitters.

Abstract in English:

ABSTRACT This work involves the study and development of epidemiological models described through systems of evolutionary and nonlinear ordinary differential equations. Additionally, it includes case studies related to the dynamics of COVID-19. The proposed original models examine the impact of contingency measures and vaccination strategies on the social dynamics of infectious diseases. Finally, a comparative discussion is presented, analyzing the results of the proposed models and their computational simulations against real data collected in Brazil.

Abstract in English:

ABSTRACT This article addresses the challenges of imbalanced classification in machine learning, where algorithms often incorrectly assume balanced class distributions. This issue is prevalent in real-world scenarios, leading to poor representation of minority classes in training data. To address this challenge, Cost-Sensitive Learning (CSL) techniques have been developed, focusing on minimizing the overall cost of misclassification rather than merely optimizing accuracy. These techniques are categorized into three types: Cost-Sensitive Algorithms, Resampling, and Hybrid approaches. This research presents a comprehensive case study on classifying lawsuit decisions into repetitive themes at São Paulo Court, Brazil, using cost-sensitive approaches on an imbalanced dataset. The study implements a rigorous evaluation framework including baseline models (dummy classifiers, Naive Bayes, standard algorithms), statistical significance testing, and cross-validation analysis. Results demonstrate that cost-sensitive XGBoost achieves optimal performance (98.76% balanced accuracy), while statistical analysis confirms significant improvements over baseline methods (p < 0.001). The goal is to automate lawsuit classification to improve judicial efficiency, reduce manual workload, and accelerate case resolution. The study validates the effectiveness of cost-sensitive techniques for handling imbalanced classification in legal text processing, providing a methodological framework for practical deployment in judicial systems.

Abstract in English:

ABSTRACT This paper presents a comparison of four predictive models for classification tasks: logistic regression, support vector machines (SVM), Gaussian process (GP) classification, and a model based on partial exchangeability. The models were evaluated using a dataset with 7 binary covariates, where 70% of the sample was used for training and the remaining 30% for testing. Predictive performance was assessed through three metrics: the area under the receiver operating characteristic curve (AUC), Brier score, and logarithmic score. Results show that, while the SVM model performed distinctly, the other three models exhibited similar performance, with logistic regression demonstrating the best overall results, though not by a large margin. Theoretical insights from de Finetti’s representation theorem for partially exchangeable data suggest that logistic regression can be seen as a specific case of a more general model, which captures the influence of covariates on the outcome probabilities. Furthermore, we explored the Bayesian counterpart of logistic regression, using a flat prior on the model coefficients, and found that its predictive performance was almost identical to the frequentist approach. Although logistic regression was the most effective model for this dataset, the paper discusses the advantages of more flexible models, like SVM and GP classification, which may be better suited for capturing complex nonlinear relationships in data. The results indicate that while logistic regression is a reliable, fast, and interpretable model, alternative models may outperform it in cases where complex interactions between covariates and the target variable exist. However, the results shown in Section 4 indicate that the dataset studied in this article most probably does not reveal complex nonlinear interactions between the covariates and the target variable.

Abstract in English:

ABSTRACT The efficacy of numerical methods like integral estimates via Gaussian quadrature formulas depends on the localization of the zeros of the associated family of orthogonal polynomials. Following the renewed interest in quadrature formulas on the unit circle and RII type polynomials, in this work we present properties satisfied by the zeros of the complementary Romanovski-Routh polynomials. Our results include extreme bounds, convexity, density, and the connection of such zeros with the zeros of classical orthogonal polynomials via asymptotic formulas.

Abstract in English:

ABSTRACT This work addresses a problem related to the packing of identical regular polyhedra in arbitrary Euclidean space. The problem aims to maximize the number of identical regular polyhedra that can be packed within a convex set, referred to as the domain. The problem is modeled as a nonlinear differentiable programming problem.

Abstract in English:

ABSTRACT This article investigates the numerical modeling and two-dimensional simulation of elec-troosmotic two-phase flows involving complex fluids in rectangular channels with no pressure differ-ence. We apply mainly the nonlinear Poisson-Boltzmann (PB) model for charge distribution coupled to the Navier-Stokes equations, constitutive equations for viscoelastic fluids, and the interface transport by Volume-of-Fluid with Piecewise-Linear Interface Construction. The numerical framework is implemented in the HiG-Flow system, which simulates incompressible flows in hierarchical cartesian meshes of arbitrary refinement represented by generalized trees with interpolations by a robust meshless moving least squares method. In two-phase systems, we analyze droplet deformation under both neutral and electroosmotic shear, exploring the impact of permittivity variations between matrix and droplet fluids. Our results suggest that the Korteweg-Helmholtz force may play a crucial role in interface deformation patterns, while viscoelastic-ity demonstrates itself capable of moderating surface tension effects and stabilizing deformations in uniform and non-uniform permittivity cases.