Resumo em Português:
RESUMO Em indústrias de manufatura, um dos processos de produção consiste em cortar grandes objetos em peças menores. Em pesquisa operacional, o estudo desse processo é conhecido como o problema de corte de estoque (PCE) e, devido à sua dificuldade de resolução, métodos heurísticos vêm sendo desenvolvidos pelos pesquisadores da área. Neste trabalho, propomos utilizar técnicas de análise de decisão multicritério (MCDA) a fim de resolver o PCE de forma eficiente em termos de GAP e tempo computacional. Nossa estratégia consiste em selecionar previamente os melhores padrões de corte com técnicas MCDA e resolver o problema apenas com esses padrões selecionados. Os testes computacionais mostraram que a solução obtida com essa estratégia apresenta um GAP entre 0,25% e 4,25% quando comparada com a solução ótima, dando indícios da qualidade da abordagem proposta.Resumo em Inglês:
ABSTRACT In manufacturing industries, one of the production processes consists of cutting large objects into smaller pieces. In operational research, this process’s study is known as the cutting stock problem (CSP). Due to its difficulty in resolution, heuristics have been developed by researchers in the area. In this work, we propose to use multicriteria decision analysis (MCDA) techniques to solve the CSP in a reasonable computational time and aiming to obtain solutions very close to the optimum. Our strategy consists of selecting the best cutting patterns using MCDA techniques and solving the problem only with these chosen patterns. The computational tests showed that the solution obtained with this strategy presents a GAP between 0.25% and 4.25% compared to the optimal solution, giving indications that the proposal is promising.Resumo em Inglês:
ABSTRACT This work aims to study the transversal motion of a car’s chassis, modeled by a beam and supported at its ends by two sets of spring-damper elements. A finite differences method is utilized along with Robin boundary conditions to solve the mathematical modeling. The constants of the boundary conditions are modeled by a fuzzy parameter obtained through a Fuzzy Rule-Based System (FRBS) acting on the different vibrations of the model, depending on the number of spirals and time of use of the spring. The contributions of this study is based on considering the spring’s elastic constant as a relevant instrument acting in the system, due to the fact that analytic formula to perform these calculations, does not consider the time of use. Indeed, the vehicle’s mechanical components might have their properties altered due to the fatigue process, for example. The impacts of the car dynamics’s property evolution might induce undesirable passenger’s discomfort up to the vehicle performance loss. The results showed that the time of use of the spring influences the vehicle’s displacement due to the loss of stiffness, thus affecting its stability.Resumo em Inglês:
ABSTRACT Through algebraic number theory and Construction A we extend an algebraic procedure which generates nested complex lattice codes from the polynomial ring F2x/xn-1, where F2=0,1, by using ideals from the generalized polynomial ring F2x,12ℤ0x122n-1 through the ring of integers 𝒪𝕃 of the cyclotomic field L=ℚζ2s, where ζ2s is a 2s -th root of the unit, with s > 2.Resumo em Inglês:
ABSTRACT In this article, we intend to investigate the Leonardo sequence presenting the hybrid Leonardo quaternions. To explore Hybrid Quaternions of Leonardo, the priori, sequence of Leonardo, quaternions and hybrid numbers were presented. Soon after, its recurrence, characteristic equation, its relation with the Fibonacci quaternions, generating function, Binet’s formula, as well as its extension to non-positive integer indices were developed. Finally, identities involving Leonardo’s hybrid quaternions are presented.Resumo em Inglês:
ABSTRACT The characteristic method of lines is the most used numerical method applied to the water hammer problem. It transforms a system of partial differential equations involving the independent variables time and space in two ordinary differential equations along the characteristics curves and then solve it numerically. This approach, although showing great stability and quick execution time, creates ∆x-∆t dependency to properly model the phenomenon. In this article we test a different approach, using the method of lines in the usual form, without characteristics curves and then applying strong stability preserving Runge-Kutta Methods aiming to get stability with greater ∆t.Resumo em Inglês:
ABSTRACT In this work we focus on the numerical solution of a higher order bidirectional nonlinear model of Boussinesq type involving a nonlocal operator. Based on a von Neumann stability analysis for the linearized problem, an efficient and stable scheme for the nonlinear system is proposed. Our method is based on a numerical scheme known from the literature that solves satisfactorily a lower order linear system. Additionally, approximate periodic travelling wave solutions profiles for the higher order nonlinear system are presented. Such approximate travelling wave solutions are obtained from a solitary wave family of solutions for the Intermediate Long Wave (ILW) equation and the regularized Intermediate Long Wave (rILW) equation.Resumo em Inglês:
ABSTRACT A mathematical model was developed to describe the dynamics of the primary infection of dengue virus in infants who were born to a mother immune to some serotype of the dengue virus. The model is given by a system of nonlinear ordinary differential equations with time-dependent variables for the number of dengue virus antibodies of the infant transferred from their immune, uninfected, and infected monocytes and dengue virus. The mathematical analysis was carried out where the conditions for the existence of the disease-free equilibrium and the endemic equilibrium were established. The numerical simulations were performed considering different scenarios for a basic reproductive number, R 0, illustrating the global convergence of the numerical results for the equilibrium points. The results are in agreement with our derived global stability analysis. It can be concluded that dengue hemorrhagic fever in infants could occur in the peaks observed for the infected monocytes and dengue virus.Resumo em Português:
RESUMO As equações diferenciais governam inúmeros fenômenos físicos presentes em diversos campos de conhecimento da física-matemática. Uma vez que os modelos são compreendidos pela teoria de campo escalar, possibilitam a descrição de uma gama de aplicações práticas da engenharia, transitando de problemas na área da acústica, térmica, mecânica dos sólidos e fluidos, eletromagnetismo, dentre outras. Neste cenário, o vigente artigo concentra-se em apresentar o módulo específico do programa computacional, desenvolvido em Matlab, denominado NASEN, destinado à solução da equação de campo escalar por meio do método dos elementos finitos (MEF). Para tanto, a discretização espacial é realizada com base nos procedimentos matemáticos do método de Galerkin e a discretização temporal é realizado com base no método de integração de Newmark e o método-θ. Estuda-se problemas de diferentes naturezas, como problemas parabólicos não lineares, hiperbólicos e de autovalor. A metodologia empregada para solução dos problemas não lineares tem como base as estratégias incrementais e iterativas de Newton-Raphson. A avaliação de desempenho do programa computacional é realizada com as soluções analíticas, numéricas ou experimentais disponíveis na literatura. Em síntese, os resultados obtidos mostram-se satisfatórios, indicando que o código computacional é capaz de prever adequadamente os comportamentos físicos dos problemas propostos.Resumo em Inglês:
ABSTRACT Differential equations govern innumerable physical phenomena present in different fields of knowledge of physics-mathematical. Once the models are understood by the scalar field theory, they enable the description of a range of practical engineering applications, moving through problems in the area of ??acoustics, thermal, solids and fluids mechanics, electromagnetism, among others. In this scenario, the current article focuses on presenting the specific module of the computer program, developed in Matlab, called NASEN, aimed at solving the scalar field equation using the finite element method (FEM). Therefore, the spatial discretization is performed based on the mathematical procedures of the Galerkin method and the temporal discretization is performed based on the Newmark integration method and the A-method. Problems of different nature are studied, such as nonlinear parabolic, hyperbolic and eigenvalue problems. The methodology used to solve nonlinear problems is based on the incremental and iterative strategies of Newton-Raphson. The performance evaluation of the computer program is carried out with the analytical, numerical or experimental solutions available in the literature. In summary, the results obtained are satisfactory, indicating that the computational code is capable of adequately predicting the physical behavior of the proposed problems.Resumo em Inglês:
ABSTRACT In this contribution we analyze a discretized SIR (Susceptible, Infectious, and Removed) compartmental model, to investigate the role of individual interactions in the spread of diseases. The compartments S i,j , I i , j and Ri,j (i,j,=1,2,...,n) are spatially distributed in a two-dimensional n×n network. We assume that the dynamics follow the well-known SIR-like iteration within the population in each (i, j) site. Moreover, the dynamics are enriched by considering a multi-population interaction following a Gaussian spatial distribution. Therefore, the mobility of individuals between distinct networks is measured from the width α of the Gaussian distribution. The interaction of individuals between distinct sites, responsible for the contagion between different populations, is assumed to occur in a time interval smaller than a fixed interval h so that, the total population in each site (i, j), given by Ni,j=Si,j+Ii,j+Ri,j, remained constant (for example, individual leaves his home site (i, j) to work at a neighboring site and returns to his home in a time interval less than h). We numerically explore some scenarios of population interaction, based on distinct choices of width α, that include a hypothetically rapidly closedness and reopening of the economy. The results found show interesting dynamics in the infected population due to the interaction parameter α(t) between the populations. Finally, the model can be applied to evaluate the spread of diseases such as COVID-19 enabling decision making in different contexts.Resumo em Português:
RESUMO Neste artigo é realizada a estimativa de parâmetros e solução de um problema de transferência de calor, onde os resultados numéricos são comparados com dados experimentais obtidos na literatura. O modelo matemático é resolvido numericamente utilizando o Método das Diferenças Finitas (MDF) com formulação implícita. Já a estimativa dos parâmetros é feita utilizando os métodos de otimização estocástica Luus-Jaakola (LJ) e Algoritmo de Colisão de Partículas (do inglês, Particle Collision Algorithm PCA), bem como modificações propostas nos referidos métodos. Os resultados obtidos foram satisfatórios tendo as modificações apresentado uma redução do número de avaliações da função objetivo (NAF) necessários para encontrar os parâmetros de interesse, bem como possibilitou um bom ajuste entre as temperaturas obtidas experimentalmente e resultados numéricos, motivando novas aplicações em problemas de mesma natureza.Resumo em Inglês:
ABSTRACT In this article, the estimation of parameters and the solution of a heat transfer problem is performed, where the numerical results are compared with experimental data obtained in the literature. The mathematical model is solved numerically using the Finite Difference Method (MDF) with implicit formulation. The parameters are estimated using the Luus-Jaakola (LJ) and Particle Collision Algorithm (PCA) stochastic optimization methods, as well as proposed modifications to the referred methods. The results obtained were satisfactory and the modifications presented a reduction in the number of objective function evaluations (NAF) necessary to find the parameters of interest, as well as allowing a good adjustment between the temperatures obtained experimentally and numerical results, motivating new applications in problems of same nature.Resumo em Inglês:
ABSTRACT The FIFA Men’s World Cup (FWC) is the most important football (soccer) competition, attracting worldwide attention. A popular practice among football fans in Brazil is to organize contests in which each participant informs guesses on the final score of each match. The participants are then ranked according to some scoring rule. Inspired by these contests, we created a website to hold an online contest, in which participants were asked for their probabilities on the outcomes of upcoming matches of the FWC. After each round of the tournament, the ranking of all participants based on a proper scoring rule was published. In this article we estimate, by means of simulations, the ability of the best forecasters of our contest, considering that their good performances could be due to randomness. We also study the performance of some methods to aggregate individual forecasts, in order to study if some sort of wisdom of crowds (WOC) phenomenon was verified in the contest.Resumo em Inglês:
ABSTRACT Colorectal cancer morphogenesis begins at the cellular level from cell mutations in the intestinal epithelium cavities called crypts. These mutations lead to a pressure difference in the epithelium crypt walls, which can cause deformation and generate visible abnormalities in the epithelium. The geometrical modeling of these crypts and the mathematical modeling of the biomechanical process that leads to deformations can be simulated by using a Finite Element Method. The method solves numerically the system of partial differential equations (PDEs) that governs this phenomenon and permits to estimate the deformations of the crypt walls. In this work we simulate the crypt deformation when the cell mutations appear in several regions of the crypt epithelium.