Abstract in Portuguese:

RESUMO Estudamos neste artigo existência e unicidade de solução fraca global para a inequação variacional não linear degenerada K x , t u " + Δ 2 u + M u 2 - Δ u + u ' ≥ f u 0 = u 0 u ' 0 = u 1 u ⌊ Σ = ∂ u ∂ η ⌊ Σ = 0 em que K(x, t) é uma função definida em Q=Ω×]0,T[,K(x,t)≥0 para todo (x,t)∈Q, M uma função real contínua com propriedades específicas e f pertence a classe de funções L20,T;H01(Ω). Usaremos o Método de Faedo-Galerkin, operador monótono e Compacidade para provar a existência e a unicidade de soluções fracas.

Abstract in English:

ABSTRACT In this article, we study the existence and uniqueness of a global weak solution for the degenerate nonlinear variational inequality K x , t u " + Δ 2 u + M u 2 - Δ u + u ' ≥ f u 0 = u 0 u ' 0 = u 1 u ⌊ Σ = ∂ u ∂ η ⌊ Σ = 0 where K(x, t) is a function defined on Q=Ω×]0,T[,K(x,t)≥0 para todo (x,t)∈Q, M a continuous real function with specific properties and f belongs to the class of functions L20,T;H01(Ω). We will use the Faedo-Galerkin method, monotone operator and Compactness to prove the existence and uniqueness of weak solutions.

Abstract in English:

ABSTRACT In this work, we provide some sufficient conditions to study the global asymptotic stability of the endemic equilibrium for certain models in mathematical epidemiology with nonlinear incidence and removal functions. We also present numerical examples in order to illustrate our results.

Abstract in Portuguese:

RESUMO Este artigo tem por objetivo explorar soluções que representam relações de dependência entre grandezas geométricas, visando não só determinar associações não usuais entre a geometria e álgebra, como também desenvolver objetos de aprendizagem com Geometria Dinâmica. Neste contexto, analisam-se soluções que relacionam grandezas geométricas do triângulo e do semicírculo, estabelecendo relações entre as médias aritmética, geométrica, harmônica e quadrática, no intuito de compreender as características e propriedades trigonométricas, examinar polinômios e suas raízes, bem como abordar a geometria de forma computacional e dinâmica.

Abstract in English:

ABSTRACT This paper aims to explore solutions that represent dependency relationships between geometric quantities, aiming not only to determine unusual associations between geometry and algebra, but also to develop learning objects with Dynamic Geometry. In this context, solutions that relate geometric quantities of the triangle and the semicircle are analyzed, establishing relationships between the arithmetic, geometric, harmonic and quadratic means, with the aim of understanding the characteristics and trigonometric properties, examining polynomials and their roots, as well as addressing the geometry in a computational and dynamic way.

Abstract in Portuguese:

RESUMO Neste trabalho é proposto um modelo baseado na técnica de solução BVNS (Basic Variable Neighborhood Search) para solucionar o problema de restauração de sistemas de distribuição de energia elétrica, considerando no modelo a participação de clientes que fazem parte de um programa de resposta à demanda e que podem contribuir no processo de restauração permitindo que uma quantidade de suas cargas seja desligada pela concessionária. O modelo matemático consiste em minimizar o custo de energia não distribuída no sistema devido às seções não restauradas, somado aos custos de remuneração dos clientes que fazem parte do programa de resposta à demanda, sujeito às restrições técnicas, físicas e operacionais de redes de distribuição. Trata-se de um problema de programação não-linear inteira mista em que as propostas de soluções são obtidas através do algoritmo BVNS. A estrutura de vizinhança do algoritmo BVNS é baseada na técnica Representação Nó-profundidade. Nesse processo de restauração, realizado pelo algoritmo BVNS, para cada solução avaliada, caso alguma restrição seja violada, um Algoritmo Genético é processado para realizar cortes de cargas nas seções com clientes que fazem parte do programa de resposta à demanda. Para testar a eficiência do modelo proposto, apresentam-se resultados de testes em um sistema de distribuição de 53 seções.

Abstract in English:

ABSTRACT In this work, a model based on the BVNS (Basic Variable Neighborhood Search) solution technique is proposed to solve the problem of restoring electrical energy distribution systems, considering in the model the participation of customers who are part of a demand response program and that can contribute to the restoration process allowing a number of its loads to be disconnected by the utility. The mathematical model consists of minimizing the cost of energy not distributed in the system due to unrestored sections, added to the remuneration costs of customers who are part of the demand response program, subject to the technical, physical and operational restrictions of distribution networks. This is a mixed integer nonlinear programming problem in which solution proposals are obtained through the BVNS algorithm. The neighborhood structure of the BVNS algorithm is based on the Node-Depth Representation technique. In this restoration process, carried out by the BVNS algorithm, for each solution evaluated, if any restriction is violated, a Genetic Algorithm is processed to perform load cuts in the sections with customers who are part of the demand response program. To test the efficiency of the proposed model, test results on a 53-section distribution system are presented.

Abstract in Portuguese:

RESUMO O objetivo deste trabalho é fornecer cenários possíveis da evolução da pandemia ocasionada pela COVID-19 a partir da aplicação de estratégias de controle ótimo. Uma vez que os dados sobre o coronavírus SARS-CoV-2 são repletos de incerteza ou mesmo falta de informação, a modelagem matemática intervalar é viável para o estudo de modelos epidemiológicos relacionados à COVID-19. Assim, foi proposto o modelo epidemiológico SI intervalar e o problema de controle ótimo intervalar correspondente. A solução do problema de controle ótimo intervalar ilustra cenários pessimistas e otimistas para a evolução da pandemia no Brasil. Dois critérios de tomada de decisão sob incerteza foram considerados e podem auxiliar os agentes de saúde pública. Ambos os critérios levam em consideração custos associados à tomada de decisão.

Abstract in English:

ABSTRACT The objective of this paper is to provide possible scenarios for the evolution of Coronavirus Disease-19 (COVID-19) from the application of optimal control strategies. Provided that data on the novel coronavirus (SARS-CoV-2) are fraught of uncertainty or even lack of information, interval mathematical models are feasible for the study of epidemiological models related to COVID-19. Thus, the interval SI epidemiological model and the corresponding interval optimal control problem were proposed. The solution of the interval optimal control problem illustrates pessimistic and optimistic scenarios for the evolution of the pandemic in Brazil. Two decision-making criterias under uncertainty have been considered and they can assist the decision making process by public health workers. Both criterias take into account costs associated with the decision-making.

Abstract in English:

ABSTRACT This paper proposes an integrated control model that enables the pesticide use according to the prey density and the insertion of the natural enemy, the predators, by fuzzy linear programming.The fall armyworm Spodoptera frugiperda (Lepidoptera: Noctuidae) is one of the main resistant pests of corn, which can cause damage to the productivity up to 34%. The control is strictly chemical.

Abstract in English:

ABSTRACT We apply the similarity method to the Korteweg-de Vries equation, where we obtain a new equation, in terms of similarity variable. We use the power series method, getting the similarity solution, which is exemplified graphically by particular cases.

Abstract in Portuguese:

RESUMO Uma versão analítica do método de ordenadas discretas (ADO) é usada para determinar uma solução precisa e consistente para o problema do Reverso de Temperatura em misturas binárias de gases rarefeitos. As equações cinéticas usadas são baseadas no modelo cinético McCormack. Apresenta-se o desenvolvimento completo de uma solução analítica na variável espacial, além de resultados numéricos para os valores críticos do calor latente para a inversão de sentido do gradiente de temperatura e do fluxo de calor de cada gás nas misturas Neônio-Argônio e Hélio-Xenônio. O algoritmo é considerado simples de ser elaborado e o código desenvolvido (em FORTRAN) requer em torno de um segundo para ser executado em um computador com processador Intel Core i3 - 2.30 GHz.

Abstract in English:

ABSTRACT An analytical version of the discrete ordinates method (ADO) is used to establish a concise and accurate solution for the Reverse Temperature Gradient problem in rarefied gas binary mixtures. The kinetic equations used are based in the McCormack kinetic model. It presents the complete development of an analytical solution in the spatial variable, in addition to numerical results for the critical values of latent heat for inversion from the direction of the temperature gradient and the heat flux of each gas in the mixtures Neon-Argon and Helium-Xenon. The algorithm is considered simple to elaborate and the code developed (in FORTRAN) requires around the one second to execute in a computer with Intel Core i3 - 2.30 GHz processor.

Abstract in English:

ABSTRACT Melanoma is considered one of the most aggressive types of cancer due to its high propensy for metastasis, which significantly reduces survival chances when detected late. Moreover, melanoma ex-hibits strong immunogenic characteristics, complicating its treatment, increasing the need to develop more effective techniques of therapy. In the field of oncology, mathematical modeling enables the analysis and distinction of the various mechanisms involved in tumor progression. This allows the analysis of numerous scenarios, which would be impractical experimentally. The main objective of this study is to develop a mathematical model that describes melanoma dynamics in the presence of Tumor-Associated Macrophages (TAM) and Chimeric Antigen Receptor (CAR) T-cell immunotherapy. The goal is to assess why this therapy often falls short in erradicating solid tumors like melanoma and to understand the role of TAM in this failure. This research encompasses stability analysis of the equilibrium points of the model, sensitivity analysis of its parameters, and the examination of numerical solutions. Our results showed that immunosuppression caused by TAM has a negative impact on the effectiveness of the dose and varying the cytotoxicity of CAR T-cells together with dose. Adjusting CAR T-cell cytotoxicity and treatment dosage may enhance tumor control, with the initial tumor burden playing a crucial role in treatment effectiveness.

Abstract in English:

ABSTRACT This study investigates numerically the interaction between a Gaussian pulse and variable topography using the linear Euler equations. The impact of topography variation on the amplitude and behavior of the wave pulse is examined through numerical simulations and statistical analysis. On one hand, we show that for slowly varying topographies, the incoming pulse almost retains its shape, and little energy is transferred to the small reflected waves. On the other hand, we demonstrate that for rapidly varying topographies, the shape of the pulse is destroyed, which is different from previous studies.

Abstract in Portuguese:

RESUMO O formalismo de células acopladas é um jeito sistemático de representar e estudar equações diferenciais acopladas não-lineares usando grafos direcionados. Verificamos que apenas digrafos acoplados bidirecionalmente podem representar sistemas hamiltonianos. Apresentamos resultados recentes em redes de sistemas hamiltonianos acoplados linearizados com uma discussão do teorema de Hopf hamiltoniano neste contexto. Mostramos que o autoespaço numa bifurcação de codimensão um de um equilíbrio síncrono de uma rede regular hamiltoniana pode ser expresso em termos dos autoespaços da matriz de adjacência do digrafo associado. Exibimos uma versão do teorema do centro de Lyapunov para esse tipo de rede.

Abstract in English:

ABSTRACT The coupled cell formalism is a systematic way of representing and studying nonlinear coupled differential equations using directed graphs. We observed that only bidirectionally coupled digraphs can represent Hamiltonian systems. We present recent results in networks of linearized coupled Hamiltonian systems with a discussion of the Hamiltonian Hopf theorem in this context. We show that the eigenspace in a bifurcation of codimension one of a synchronous equilibrium of a regular Hamiltonian network can be expressed in terms of the eigenspaces of the adjacency matrix of the associated digraph. We display a version of the Lyapunov center theorem for this type of network.

Abstract in Portuguese:

RESUMO Os métodos para otimização restrita desenvolvidos a partir da análise matemática clássica, são geralmente algoritmos numéricos muito eficientes. Entretanto, tais métodos dependem fortemente da localização dos pontos iniciais. Neste trabalho, utilizamos a Inicialização Global Topográfica para gerar bons pontos iniciais para o método de busca local utilizado na resolução de problemas restritos de minimização global. Para realizar as tarefas de busca local, usamos o Algoritmo de Direções Viáveis e Pontos Interiores (FDIPA). Em seguida, utilizamos oito problemas descritos na literatura para avaliar a eficácia da metodologia apresentada. Os resultados indicaram que a presente abordagem é uma estratégia eficiente para encontrar as soluções globais de problemas de otimização com restrições mistas.

Abstract in English:

ABSTRACT The constrained optimization methods, developed from the classical mathematical analysis, are generally very efficient numerical algorithms. However, such methods strongly depend on the location of the starting points. In this work we use the Topographical Initialization heuristic to generate adequate starting points for the local search method in order to solve global optimization problems with equality and inequality constraints. To perform the local search, we used the Feasible Direction Interior Point Algorithm (FDIPA). We performed computational experiments using 8 problems in order to test the method performance. The results show that the present methodology is feasible and efficient for the global minimization of functions subject to restrictions of equality and inequality.

Abstract in English:

ABSTRACT Wildfires pose a significant threat to natural ecosystems, human lives, and properties worldwide. Developing effective prevention and control strategies is crucial for minimizing the risk of catastrophic wildfire events. In this context, computational modelling has emerged as a valuable tool for simulating and analyzing wildfire behavior, which can aid in identifying potential areas for intervention and prevention measures. This article presents a cellular automata model for simulating forest fires in Sete Cidades National Park, Brazil. The model takes into account the wind direction and speed, vegetation type, and probability of burning in a two-dimensional lattice representing the forest area of interest. The simulation output is analyzed to determine the extent of the damage caused by the fire and to identify critical parameters for wildfire propagation. The results highlight the importance of considering wind direction and speed when developing prevention and control strategies for wildfires. By providing insights into the behavior of wildfires, computational modeling can support decision-making processes and facilitate the development of effective policies to manage the risk of wildfires.

Abstract in English:

ABSTRACT This work deals with solving continuous-time nonlinear complementarity problems defined on two types of nonempty closed convex cones: a polyhedral cone (positive octant) and a second-order cone. Theoretical results that establish a relationship between such problems and the variational inequalities problem are presented. We show that global minimizers of an unconstrained continuous-time programming problem are solutions to the continuous-time nonlinear complementarity problem. Moreover, a relation is set up so that a stationary point of an unconstrained continuous-time programming problem, in which the objective function involves the Fischer-Burmeister function, is a solution for the continuous-time complementarity problem. To guarantee the validity of the K.K.T. conditions for some auxiliary continuous-time problems which appear during the theoretical development, we use the linear independence constraint qualification. These constraint qualification are posed in the continuous-time context and appeared in the literature recently. In order to exemplify the developed theory, some simple examples are presented throughout the text.

Abstract in Portuguese:

RESUMO O presente trabalho lança um olhar matemático sobre uma obra de arte de um dos pioneiros do concretismo brasileiro, Lothar Charoux (1912-1987). Trata-se de um desenho a nanquim de 1958, sem título, de marcante apelo geométrico. A partir do traço do artista, definimos um jogo de curvas parametrizadas diferenciáveis, batizadas “espirais ocultas de Charoux”, e estudamos sua curvatura. Pretende-se que a descrição matemática da obra, com o emprego das ferramentas da geometria diferencial, possa enriquecer a fortuna crítica do artista. Para tanto, são estabelecidos pontos de contato entre a matemática presente na obra analisada e as impressões que Charoux deixou entre críticos, jornalistas culturais e historiadores da arte.

Abstract in English:

ABSTRACT This study takes a mathematical look at a work of art by one of the pioneers of Brazilian concretism, Lothar Charoux (1912-1987). We examined a drawing with a striking geometric appeal dating back to 1958. Based on its patterns, we defined a set of differentiable parameterized curves, referred to as “hidden Charoux spirals”, and studied their curvature. We intend that the mathematical description of this artwork, using the tools of differential geometry, can enrich the artist’s critical fortune. To this end, we confronted the mathematical description of the drawing with the impressions Charoux left among critics, cultural journalists, and art historians.

Abstract in English:

ABSTRACT This paper proposes a family of line-search methods to deal with weighted orthogonal procrustes problems. In particular, the proposed family uses a search direction based on a convex combination between the Euclidean gradient and the Riemannian gradient of the cost function. The non-monotone line-search of Zhang and Hager, and an adaptive Barzilai-Borwein step-size are the chosen tools, in order to speed up the convergence of the new family of methods. One of the extremes of that convex combination is reduced to well-known spectral projected gradient method, while the another one can be interpreted as a Riemannian steepest descent method. To preserve feasibility of all the iterates, we use a projection operator based on the singular value decomposition, which can be computed efficiently via the spectral decomposition of an appropriate matrix. In addition, we prove that the entire uncountable collection of search directions satisfies a descent condition. Some numerical experiments are provided in order to demonstrate the effectiveness of the new approach.

Abstract in English:

ABSTRACT We present two slightly different constructions of a SIR model in which both the time taken to remove the individual from the infectious compartment and the infectivity have a memory according to Mittag-Leffler distributions. The second construction clearly points out where the proposed generalizations are acting, starting from the classic SIR model. Using integrodifferential techniques, we state and demonstrate novel analytically results on positivity, monotonicity in limiting case, and equilibrium points. The results are also verified numerically.

Abstract in English:

ABSTRACT We investigate the problem of determining time dependent parameters for discrete-time epidemiological compartmental models such as the Susceptible-Infected-Recovered (SIR). We show how to determine parameters based on minimal error type iterative schemes. Such methods involve the computation of the adjoint of the derivative operator of a nonlinear function. This is a nontrivial task that we accomplish by carefully crafting auxiliary problems. To show the efficiency of the method, we consider examples involving real COVID-19 data.

Abstract in English:

ABSTRACT Punishment is probably the most frequently used mechanism to increase cooperation in Public Goods Games (PGG); however, it is expensive. To address this problem, this paper introduces an optimal control problem that uses fractional punishment to promote cooperation. We present a series of computational experiments illustrating the effects of single and combined terms of the optimization cost function. In the findings, the optimal controller outperforms the use of constant fractional punishment and gives an insight into the period and size of the penalization to be implemented with respect to the defection in the game.

Abstract in English:

ABSTRACT The increasing use of new technologies and the internet underscores the need to ensure users’ privacy and security while browsing the web. To achieve this, encryption schemes rely on sharing keys among parties involved in message exchange. The concept of homomorphism, crucial in both mathematics and cryptography, provides a solution by enabling computations on encrypted data without the need for decryption. Furthermore, the RSA and ElGamal algorithms exemplify how homomorphism is applied in practice, each with its specific methods for maintaining data security and privacy during cryptographic processing.

Abstract in Portuguese:

RESUMO Em decorrência do crescente desenvolvimento tecnológico e das consequentes aplicações industriais, técnicas de controle de alto desempenho e Aprendizado por Reforço estão sendo desenvolvidas, não só para solucionar novos problemas de controle, mas também para melhorar o desempenho de controladores já implementados em sistemas do mundo real. As abordagens de Aprendizado por Reforço e do Regulador Linear Quadrático Discreto são conectadas pelos métodos de Programação Dinâmica Adaptativa. Esta união é orientada para o projeto de controladores ótimos em sistemas multivariáveis. Implementa-se para o caso do Regulador Linear Quadrático Discreto, os algoritmos de resolução de Aprendizado por Reforço online, Política de Iteração e Valor de Iteração. O método proposto para sintonia de controladores Regulador Linear Quadrático Discreto fornece diretrizes para construção de heurísticas que serão aplicadas na seleção das matrizes de ponderação com recompensa instantânea. Investiga-se o desempenho das heurísticas associadas com a sintonia de controladores lineares discretos e aspectos de convergência que estão relacionados com as variações QR no algoritmo Ação Dependente. O algoritmo e a sintonia são avaliados pela capacidade em estabelecer a política de controle ótimo que mapeia o plano-Z em um sistema dinâmico multivariável de terceira ordem.

Abstract in English:

ABSTRACT As a result of increasing technological development and the resulting industrial applications, high-performance control techniques and Reinforcement Learning are being developed, not only to solve new control problems, but to improve the performance of controllers already implemented in real-world systems. The Reinforcement Learning and Discrete Linear Quadratic Regulator approaches are connected by Adaptive Dynamic Programming methods. This union is oriented towards the design of optimal controllers in multivariable systems. For the case of the Discrete Linear Quadratic Regulator, the online Reinforcement Learning, Iteration Policy and Iteration Value resolution algorithms are implemented. The proposed method for tuning Discrete Linear Quadratic Regulator controllers provides guidelines for constructing heuristics that will be applied in the selection of weighting matrices with instantaneous reward. The performance of heuristics associated with the tuning of discrete linear controllers and aspects of convergence that are related to variations are investigated. QR in the Dependent Action algorithm. The algorithm and tuning are evaluated by the ability to establish the optimal control policy that chart the Z-plane into a third-order multivariable dynamic system.

Abstract in English:

ABSTRACT Ridge and Lasso regressions are types of linear regression, a machine learning tool for dealing with data. Based on multiobjective optimization theory, we transform Ridge and Lasso regression into bi-objective optimization problems. The Pareto fronts of the resulting problems provide a range of regression models from which the best one can be selected. We employ the NFDA-Nonsmooth Feasible Directions Algorithm devised for solving convex optimization problems to construct the Pareto fronts of Ridge and Lasso when regarded as bi-objective problems.

Abstract in English:

ABSTRACT The dynamics of information propagating among populations that interact might have an enormous impact on public opinion, particularly when such information is false, known as fake news. In this contribution, we propose and analyze the fake news dissemination that occurs when two distinct sub-populations (not necessarily homogeneous) share information, using a reinterpretation of a compartmental model for disease dissemination. We show the model’s well-posedness. Furthermore, we utilize the model solution property to derive an estimation that allows one to estimate the impact of the influence of one population on the other in the fake news dissemination. The theoretical results are complemented with numerically simulated scenarios for the dynamics of fake news spreading among populations, with the model parameters associated with some human development and influence indices among countries. The results obtained show that the speed of diffusion of fake news among populations is largely impacted by the gap between the human development indices of each population and the influence of one population on another. It is also shown that a small percentage of control over information shared by the population leads to a large decrease in the amount and velocity of fake news diffusion.

Abstract in English:

ABSTRACT A new calculation of Green’s function for Poisson’s equation in plane polar coordinates is presented. The method consists in first calculating the solution to the simpler problem, but with the same Green’s function, that is obtained with the homogenization of the boundary conditions and then inferring Green’s function by comparing this calculated solution with Green’s solution formula. Depending on how the solution to the simplified problem is calculated, Green’s function may result as an integral or an infinite series, but it is finally presented in a closed form, because it is possible to calculate the integral or the sum of this series.