C.Q.D. - Revista Eletrônica Paulista de Matemática
type: channel
description: A C.Q.D. – Revista Eletrônica Paulista de Matemática, ISSN 2316-9664, é periódico acadêmico publicado em versão eletrônica pelo Departamento de Matemática, da Faculdade de Ciências, da Universidade Estadual Paulista “Julio de Mesquita Filho” – Unesp/Bauru. Direcionada à comunidade científica, a revista foi criada em 2012 e tem como objetivo incentivar a investigação e o estudo da Matemática. Para tanto, recebe e analisa artigos submetidos por professores e alunos, e publica eletronicamente aqueles que apresentam suficientes méritos científicos e editoriais. Trata-se de uma revista diferenciada por ser totalmente virtual, de acesso gratuito e de ampla abrangência, incluindo os temas de Matemática Pura, de Matemática Aplicada e de Educação Matemática.
publisher: Unesp
language: en
publication name: C.Q.D. - Revista Eletrônica Paulista de Matemática
issn: 2316-9664
items: Menor ímpar abundante
items: Analytic Conjugacy Between Reversible and Hamiltonian Systems in the Plane
items: Provando o Compêndio de Hoggatt das Identidades de Fibonacci e Lucas
items: Explorando teoremas clássicos de Geometria com visualização em Python/Manim e aplicações em problemas olímpicos
items: A numerical application of dengue models in the presence of Wolbachia and vaccination in Thailand.
items: A Primer on Mathematical Epidemiology
items: Refuting "Memórias de um matematiqueiro"
items: Quadratic Function: a specific case of the Parabola as a conic section
items: t-Dimensional Recurrence Relations of Square-Nonagonal Multifigured Numbers
items: The paths of the roots of the quadratic function - mold, model and style
items: Desenvolvimento de um modelo neural para estimar a massa de sólidos acumulada na filtração de água na irrigação localizada
items: Tauberian theorems for (N̄, p, q, w) summable triple sequences of fuzzy numbers
items: Fractional dynamics of a charged particle in an electromagnetic field
items: Incenter: five solved problems proposed for the International Mathematics Olympiad
items: A Study on the Jordan Canonical Form in vector spaces over finite fields
items: Aplicação de equações diferenciais em modelos presa-predador com fatores de inibição
items: Proportional fractional operators applied to the Logistic model
items: Algebraic estimation of apothems in regular polygons using linear regression and bootstrap optimization.
items: Study of Bacterial Growth Population Dynamics in Laboratory Using Interval Differential Equations
items: Characterization of Equilibrium Points and Stability Analysis of the SMIB Using the First and Second Lyapunov Methods
items: Towards an algebrization of a linear temporal logic
items: Interesting properties relating areas of two triangles
items: Topological structure of the phase portrait for linear vector fields in R3 and applications
items: The Pell sequence in the tricomplex ring
items: A characterization of adjunction in a many-valued modal system
items: Fuzzy model to check the susceptibility of young people in relation to fake news
items: Funções quadráticas na sala de aula: uma proposta de ensino através da modelagem matemática
items: Identification of fatty acids from açai in mistures subjected to crossflow microfiltration using Artificial Neural Networks
items: Oscillates in the area of ​​the square
items: Polinômios e números primos: explorando padrões através de cálculos computacionais e a Conjectura 41

Menor ímpar abundante
type: item
description: Este artigo apresenta a fórmula fundamental para a soma dos divisores positivos de um número inteiro e a aplica na classificação de números em perfeitos, abundantes ou deficientes. Deduzimos propriedades específicas sobre esses números que permitem a identificação do menor número abundante ímpar por meio de argumentos puramente teóricos, eliminando a necessidade de buscas computacionais exaustivas. Além disso, ao empregar um computador para classificar os primeiros 600.000 inteiros, fornecemos dados empíricos que destacam a raridade dos números abundantes ímpares e corroboram teoremas de densidade estabelecidos na literatura.
subject: Artigos de Pesquisa
  topic: section
subject: teoria elementar dos números; números perfeitos; números deficientes; números abundantes; soma dos divisores positivos.
  topic: keywords
creator: Isaque Damião Siqueira Costa
rights: Copyright (c) 2026 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2026-06-09
publication date: 2026-06-09
starting page: e27007
ending page: e27007
doi: 10.21167/cqdv27e27007

Analytic Conjugacy Between Reversible and Hamiltonian Systems in the Plane
type: item
description: We study the local structure of analytic planar vector fields that are reversible with respect to the linear involution \(R(u,v)=(u,-v)\). We show that every such reversible system with a nondegenerate equilibrium is locally analytically conjugate to a Hamiltonian vector field. We provide explicit Hamiltonian normal forms for the elliptic and hyperbolic cases, and we prove that the conjugacy can be chosen equivariantly with respect to the involution. We also discuss known obstructions to global equivalence and briefly comment on the situation in higher dimensions.
subject: Artigos de Pesquisa
  topic: section
subject: reversible systems; hamiltonian systems; normal forms; analytic conjugacy.
  topic: keywords
creator: Francisco José dos Santos Nascimento
rights: Copyright (c) 2026 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2026-07-08
publication date: 2026-07-08
starting page: e27009
ending page: e27009
doi: 10.21167/cqdv27e27009

Provando o Compêndio de Hoggatt das Identidades de Fibonacci e Lucas
type: item
description: Este trabalho tem como objetivo apresentar demonstrações completas para as identidades envolvendo as sequências de Fibonacci e de Lucas listadas por Hoggatt no capítulo 10 de Fibonacci and Lucas Numbers. Nesse capítulo, o autor enuncia 47 identidades relacionadas aos números de Fibonacci e de Lucas, mas apenas as 12 primeiras são acompanhadas de prova, enquanto as demais aparecem sem justificativa. Motivado por essa lacuna, este estudo desenvolve e organiza demonstrações rigorosas para todas essas identidades, apresentando-as de maneira clara e sistemática. Trata-se de um trabalho elaborado no contexto de um projeto de Iniciação Científica, desenvolvido por estudantes sob orientação docente.
subject: Artigos de Pesquisa
  topic: section
subject: números de Fibonacci
  topic: keywords
subject: números de Lucas
  topic: keywords
subject: identidades
  topic: keywords
subject: sequências de recorrência
  topic: keywords
creator: Danilo Braga Lopes
creator: Arthur Martins
creator: Lucas Antonio Caritá
rights: Copyright (c) 2026 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2026-04-30
publication date: 2026-04-30
starting page: e27003
ending page: e27003
doi: 10.21167/cqdv27e27003

Explorando teoremas clássicos de Geometria com visualização em Python/Manim e aplicações em problemas olímpicos
type: item
description: Neste artigo, exploramos três resultados clássicos da geometria euclidiana: o Teorema de Viviani, o Ponto de Fermat e o Teorema de Napoleão. Para cada um, apresentamos demonstrações e discutimos suas aplicações na resolução de problemas de olimpíadas e competições de matemática. Como recurso visual, utilizamos figuras elaboradas em TikZ (\LaTeX) e animações desenvolvidas com a biblioteca Manim em Python, visando facilitar a compreensão dos teoremas e problemas abordados.
subject: Artigos de Pesquisa
  topic: section
subject: Python; Manim; Teorema de Viviani; Ponto de Fermat; Teorema de Napoleão; Problemas Olímpicos.
  topic: keywords
creator: Aldo Trajano Lourêdo
creator: Jefferson Barbosa de Lima
rights: Copyright (c) 2026 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2026-06-29
publication date: 2026-06-29
starting page: e27008
ending page: e27008
doi: 10.21167/cqdv27e27008

A numerical application of dengue models in the presence of Wolbachia and vaccination in Thailand.
type: item
description: Dengue virus is one of the leading causes of illness and death in the tropics. Currently, the main method to prevent transmission is vector control. Besides dengue, Zika, among others, is transmitted by mosquitoes, with Aedes aegypti as the main vector, although Aedes albopictus is also a possible carrier. In this work, we analyze several situations such as the vaccination campaign in Thailand starting in 2016, the presence of Wolbachia using a classic SEIR model, and the case of the release of infected females and the Wolbachia invasive model (WIM) using the Levenberg-Marquardt neural network backpropagation technique (NN-LM). Wolbachia, a bacterium present in 60% of insects, is generally not found in A. aegypti. For the numerical simulations, the Finite Difference method was used, which, despite its simplicity, proved efficient, with results comparable to those in the literature.
subject: Artigos de Pesquisa
  topic: section
subject: Dengue. Wolbachia. Finite Difference Method. Invasive Mode
  topic: keywords
creator: Luis Antonio da Silva Vasconcellos
creator: Flavio Alessandro Prado
rights: Copyright (c) 2026 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2026-05-04
publication date: 2026-05-04
starting page: e27004
ending page: e27004
doi: 10.21167/cqdv27e27004

A Primer on Mathematical Epidemiology
type: item
description: This text presents three models widely used in epidemiology: the SIS model, the SIR model, and a model for the transmission of toxoplasmosis in cats. The aim is to provide an initiation into the field of mathematical epidemiology by illustrating three common approaches in differential equations: explicit solution, qualitative analysis, and numerical experimentation. The methodology adopted was bibliographic research, which allowed us to present: the explicit solution of the SIS model, identifying conditions for disease persistence or extinction; a qualitative analysis of the SIR model, revealing the typical behavior of epidemic outbreaks; and some numerical experiments for the toxoplasmosis model, highlighting the influence of different parameters on the transmission dynamics. Given the importance of the subject and the level of detail in the exposition, we believe that this text offers a useful reading for students entering the field of epidemiology and/or the analysis of differential equations.
subject: Artigos de Pesquisa
  topic: section
subject: SIS model
  topic: keywords
subject: SIR model
  topic: keywords
subject: Toxoplasmosis
  topic: keywords
subject: Qualitative analysis
  topic: keywords
subject: Numerical experimentation
  topic: keywords
creator: Leonardo Maciel Mukdsse Misiara
creator: Pedro Roberto de Lima
rights: Copyright (c) 2026 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2026-06-09
publication date: 2026-06-09
starting page: e27006
ending page: e27006
doi: 10.21167/cqdv27e27006

Refuting "Memórias de um matematiqueiro"
type: item
description: One day, in a discussion on the Discord app, one of the members of the discussion attached a link to an interview with Professor Carlos Pereira de Novaes, from UEFS, in which he claims to have developed a new algebra, which he calls ''pseudo-real algebra'', in which complex numbers do not exist. Still in the preface of the book where he presents his ideas, Professor de Novaes questions the limit $\lim\limits_{x\to\infty}\left(1+\frac{1}{x}\right)^x$, stating that its value should be 1, and not $e=2.71828...$. In this article I propose to answer his question and explain the reason for the discrepancy between the numerical results presented in the calculation of the expression for large values ​​of $x$ and the theoretical value $e$.
subject: Artigos de Pesquisa
  topic: section
subject: Euler's number
  topic: keywords
subject: Limit
  topic: keywords
subject: Floating-point arithmetic
  topic: keywords
creator: Allan Kenedy Santos Silva
rights: Copyright (c) 2026 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2026-04-23
publication date: 2026-04-23
starting page: e27002
ending page: e27002
doi: 10.21167/cqdv27e27002

Quadratic Function: a specific case of the Parabola as a conic section
type: item
description: This article presents a constructivist approach for the graph of the quadratic function and its properties, suitable for students in their first contact with the subject. Different from traditional approaches, a sequence inspired by Analytic Geometry is proposed, starting from the analysis of the function $g(x)=ax^2$ and using horizontal and vertical translations to construct the canonical form geometrically, motivating its algebraic deduction. The formalization that the graph of the quadratic function is a parabola was done in a simple way; to solidify the concept, two activities were proposed in \textit{GeoGebra}, the first for visualizing the geometric definition and the second with the objective to verify, in a specific case, that the function graph coincides with the geometric locus (parabola). The main objective was the conceptual enrichment for the student, contemplating from intuition to rigorous formalization, focusing on clarifying and justifying the properties of the quadratic function graph, contributing to more meaningful learning.
subject: Artigos de Pesquisa
  topic: section
subject: Quadratic Function; Parabola; Symmetry; GeoGebra; Mathematics Teaching.
  topic: keywords
creator: Sérgio Antônio Costa de Sousa
creator: Keidna Cristiane Oliveira Souza
creator: Élis Gardel da Costa Mesquita
rights: Copyright (c) 2026 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2026-05-12
publication date: 2026-05-12
starting page: e27005
ending page: e27005
doi: 10.21167/cqdv27e27005

t-Dimensional Recurrence Relations of Square-Nonagonal Multifigured Numbers
type: item
description: This article investigates square-nonagonal multifigurative numbers, a class of figurative numbers that belongs simultaneously to both square and nonagonal figurative numbers. Initially, the recurrence formula, the generating function, and the expression of the general term of the sequence are presented. Next, the process of complexification through the introduction of imaginary units is studied, which allows generalizations to higher dimensions. The two-dimensional, three-dimensional, and finally, t-dimensional relations are discussed, highlighting how such extensions expand the structural properties of these numbers and open perspectives for the study of other multifigurative number sequences.
subject: Artigos de Pesquisa
  topic: section
subject: Square-nonagonal multifigure numbers. Recurrent relations. Complexification of numerical sequences
  topic: keywords
creator: Francisco Hedyleno Coelho Bezerra
creator: Francisco Regis Vieira Alves
creator: Eudes Antonio Costa
creator: Paula Maria Machado Cruz Catarino
rights: Copyright (c) 2026 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2026-04-23
publication date: 2026-04-23
starting page: e27001
ending page: e27001
doi: 10.21167/cqdv27e27001

The paths of the roots of the quadratic function - mold, model and style
type: item
description: By fixing two real coefficients and varying the remaining real coefficient of the quadratic function, the model of the paths described by the two roots of the function in the complex plane is obtained (Yamaoka (2023)). A style is a set of models that are related to each other and share the same mold -structure- (except the style 4 originating from 𝑓𝑎 (𝑧) = 𝑎𝑧^2, 𝑎 ∈ R∗, consisting of a single model). We determine the number of connected components of the path of each root per model. We determine the connected components of each mold. We give examples of the molds. We discuss the continuity and differentiability of the two roots: they are continuous in their domains and the simple roots are infinitely differentiable (with the exception of the infinitely differentiable zero double root of 𝑓𝑎 (𝑧) = 𝑎𝑧^2, 𝑎 ∈ R∗, the other double roots that appear in the text are not differentiable). The theoretical foundation that supports the results obtained here belongs to Classical Analysis.
subject: Artigos de Pesquisa
  topic: section
subject: raízes da função quadrática
  topic: keywords
subject: caminhos
  topic: keywords
subject: molde
  topic: keywords
subject: modelo
  topic: keywords
subject: estilo
  topic: keywords
creator: Luís Cláudio Yamaoka
rights: Copyright (c) 2026 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2026-01-17
publication date: 2026-01-17
starting page: e26014
ending page: e26014
doi: 10.21167/cqdv26e26014

Desenvolvimento de um modelo neural para estimar a massa de sólidos acumulada na filtração de água na irrigação localizada
type: item
description: Water conservation is a matter of great importance and, for this reason, new techniques are constantly being developed to minimize this challenge. In Brazil, localized irrigation techniques have been widely adopted to maximize water use efficiency. However, the effectiveness of this technique is compromised by the clogging of the water emitters orifices by solid particles of organic and inorganic matter that accumulate in the filters themselves. That's why, Artificial Neural Networks were employed to estimate this mass of solids accumulated in filtration, aiming for the best conditions for it to be as low as possible, thereby minimally affecting the water flow rate. Using an experimental database available in the literature, a neural model was implemented using the Levenberg-Marquardt learning algorithm, proving to be extremely effective in this case, with an average percentage relative error of 0.29\% in predicting values of mass of solids accumulated.
subject: Edição Especial ERMAC 2024
  topic: section
subject: Redes neurais artificiais
  topic: keywords
subject: Irrigação
  topic: keywords
subject: Massa de sólidos
  topic: keywords
creator: Mayumi Laura Daniel Kamachi
creator: Érica Regina Filletti
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-11-20
publication date: 2025-11-20
starting page: e25008
ending page: e25008
doi: 10.21167/cqdv25e25008

Tauberian theorems for (N̄, p, q, w) summable triple sequences of fuzzy numbers
type: item
description: In this paper, we introduce the notion of weighted mean method (N̄, p, q, w) of triple sequences of fuzzy numbers and and show necessary and sufficient Tauberian conditions under which convergence in Pringsheim's sense of a triple sequence of fuzzy numbers follows from its $ (\bar{N},p,q,w) $ summability. These conditions are weaker than the weighted analogues of Landau's conditions and Schmidt's slow oscillation condition in some senses for three-dimensional case.
subject: Artigos de Pesquisa
  topic: section
subject: Triple sequence of fuzzy numbers
  topic: keywords
subject: Weighted mean method
  topic: keywords
subject: Tauberian theorems and conditions
  topic: keywords
creator: Carlos Bernal Granados
creator: Ajoy Kanti Das
creator: Suman Das
rights: Copyright (c) 2026 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2026-01-15
publication date: 2026-01-15
starting page: e26013
ending page: e26013
doi: 10.21167/cqdv26e26013

Fractional dynamics of a charged particle in an electromagnetic field
type: item
description: In this work, we analyze the modeling of physical phenomena using fractional-order differential equations, specifically focusing on the force exerted on a charged particle in an electromagnetic field. The methodological approach involves replacing integer-order derivatives with fractional-order derivatives, in the Caputo sense, in the differential equations that describe the movement of a charged particle in an electromagnetic field. This allows for a more detailed and efficient description. The results demonstrate that modeling with the Caputo fractional derivative provides a more refined solution, including the presence of damping. It is concluded that the use of fractional calculus offers significant advantages over traditional calculus, particularly in its ability to more accurately capture the system's memory and incorporate factors initially neglected in classical modeling.
subject: Artigos de Pesquisa
  topic: section
subject: Fractional Differential Equations
  topic: keywords
subject: Caputo fractional derivative
  topic: keywords
subject: Fractional Calculus and Applications
  topic: keywords
subject: Lorentz Force
  topic: keywords
creator: Thiago Massolini Marchesin
creator: Rubens de Figueiredo Camargo
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-09-30
publication date: 2025-09-30
starting page: e26012
ending page: e26012
doi: 10.21167/cqdv26e26012

Incenter: five solved problems proposed for the International Mathematics Olympiad
type: item
description: Among the centers of triangles, incenter, the meeting point of the bisectors, is one of the best known due to its wide use in various fields of Mathematics and Physics. Five problems proposed for the International Mathematics Olympiad are discussed in detail. The proofs involved in the solutions are complemented by the availability of the respective links to the interactive figures using GeoGebra. It is expected that the article can be appreciated both by students preparing for the final stages of national or international competitions and by teachers interested in Olympic challenges.
subject: Artigos de Pesquisa
  topic: section
subject: Incentro
  topic: keywords
subject: Ensino Medio
  topic: keywords
subject: GeoGebra
  topic: keywords
subject: Olimp´ıada Internacional de Matematica
  topic: keywords
creator: Juan López Linares
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-09-24
publication date: 2025-09-24
starting page: e26011
ending page: e26011
doi: 10.21167/cqdv26e26011

A Study on the Jordan Canonical Form in vector spaces over finite fields
type: item
description: In this work, we will present the construction of the theorem that substantiates the existence of the Jordan Canonical Form for a given linear transformation on a vector space over and algebraically closed field using the fact that, if 𝑇 is a linear transformation in a vector space 𝑉 over a field K and 𝜆 is an eigenvalue of 𝑇, then the restriction of 𝑇 − 𝜆𝑖 to ker(𝑇 − 𝜆𝐼𝑑)𝑗 (where 𝑗 is the smallest integer such that ker(𝑇 − 𝜆𝐼𝑑)𝑗 = ker(𝑇 − 𝜆𝐼𝑑)𝑗+1) is nilpotent, which allows us to find a set of vectors 𝛽={𝑣, (𝑇 − 𝜆𝐼𝑑)(𝑣), . . . , (𝑇 − 𝜆𝐼𝑑)𝑚−1(𝑣)} such that the restriction of 𝑇 − 𝜆𝐼 to the set generated by 𝛽 can be represented by a matrix of the type 𝐽𝑚(0), therefore, the restriction of 𝑇 to [𝛽] can be represented by 𝐽𝑚(𝜆𝑖). Following that, we will use Field Theory to extend such construction in order to allow it to be used in vector spaces over finite fields, since if 𝑝(𝑥) is an irreducible polynomial over a field K, then K[𝑥]\⟨𝑝(𝑥)⟩ is a field where 𝑝(𝑥) has roots.
subject: Artigos de Iniciação Científica
  topic: section
subject: Linear Algebra
  topic: keywords
subject: Finite fields
  topic: keywords
subject: Canonical forms
  topic: keywords
creator: Isadora Vanzella Picinini
creator: Jahina Fagundes de Assis Hattori
creator: Wilian Francisco de Araújo
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-08-21
publication date: 2025-08-21
starting page: e26008
ending page: e26008
doi: 10.21167/cqdv26e26008

Aplicação de equações diferenciais em modelos presa-predador com fatores de inibição
type: item
description: Os modelos de interação do tipo presa-predador são comumente utilizados desde o controle biológico de pragas até mesmo na captura e emissão de carbono. Um modelo amplamente difundido é o de Lotka-Volterra (1926), sendo simples e validado. No entanto, esse modelo carece de correções que reproduzam melhor a realidade. Diante disso, foi realizada a análise qualitativa dos problemas presa-predador com fatores de inibição, utilizando as equações de Verhulst e Gompertz, juntamente com a análise numérica das aproximações para tais modelos com o software MATLAB. A análise qualitativa utilizou do estudo dos pontos de equilíbrio dos sistemas localmente lineares, da estabilidade dos sistemas lineares associados e dos sinais das derivadas, construindo trajetórias no plano de fase. Na análise numérica foram aproximadas trajetórias no plano de fase com a implementação do algoritmo de Runge-Kutta de 4a ordem. Todas as informações obtidas qualitativamente foram confirmadas por meio das aproximacões numéricas.
subject: Artigos de Pesquisa
  topic: section
subject: presa-predador
  topic: keywords
subject: inibição
  topic: keywords
subject: Análise qualitativa.
  topic: keywords
subject: análise numérica
  topic: keywords
creator: João Pedro Oliveira Pereira
creator: Ricardo de Sá Teles
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-08-04
publication date: 2025-08-04
starting page: e26006
ending page: e26006
doi: 10.21167/cqdv26e26006

Proportional fractional operators applied to the Logistic model
type: item
description: Com o objetivo de tentar descrever um fenômeno mais próximo da realidade, a Modelagem Matemática se apresenta como uma ferramenta essencial para a compreensão de fenômenos de diversas naturezas. Em uma mesma perspectiva, com o avanço do cálculo de ordem fracionária, diversos trabalhos foram publicados e esta Modelagem Matemática, se mostrou muito promissora. Desta forma, amparados por esta nova ótica e aliados a esta teoria generalizada de modelos de crescimento, este trabalho tem como objetivo estudar operadores fracionários proporcionais, para a avaliação das soluções analíticas e numéricas do modelo Logístico.
subject: Artigos de Pesquisa
  topic: section
subject: Calculo Fracionário
  topic: keywords
subject: EDOs de ordem fracionária
  topic: keywords
subject: Modelos de crescimento
  topic: keywords
creator: Gustavo Helias Vaz da Silva
creator: Erasmo
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-09-19
publication date: 2025-09-19
starting page: e26010
ending page: e26010
doi: 10.21167/cqdv26e26010

Algebraic estimation of apothems in regular polygons using linear regression and bootstrap optimization.
type: item
description: Estimating the apothem of regular polygons may be required in academical and real-life situations such as for calculating the area of regular polygons and the volume of prisms and pyramids. The calculus of apothem requires the use and knowledge of the tangent function. In the present article we describe an algebraic approximation procedure for estimation of the apothem of any regular polygon given only the length of one side and the number of sides. An initial approximation was obtained based on nearly linear correlation between the product of polygon sides number and length with the squared root of the sum of the squared apothem and squared hypotenuse of one of the inner right-angled triangles of the polygon. In a second step the bootstrap method was to use to obtain the coefficients of a second-degree polynomial. The resulting equation predicts the apothem with a minimum accuracy of 0.9997. In polygons of 3, 4, 6 and with more than 25 sides the accuracy was higher than 0.9999.
subject: Artigos de Pesquisa
  topic: section
subject: Apotema
  topic: keywords
subject: Polygon
  topic: keywords
subject: Polygon area
  topic: keywords
creator: Sergio Roberto Peres Line
creator: Walter Gonçales Martin
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-09-04
publication date: 2025-09-04
starting page: e26009
ending page: e26009
doi: 10.21167/cqdv26e26009

Study of Bacterial Growth Population Dynamics in Laboratory Using Interval Differential Equations
type: item
description: This work focused on studying the population dynamics of Escherichia coli growth in a laboratory setting using Interval Differential Equations (IDEs). Specifically, the Malthus and Verhulst models were considered to describe population growth dynamics, using parameters collected from laboratory experiments. These parameters, as reported in the article, have an interval-valued characteristic. Supported by analytical and numerical methods—Euler and fourth-order Runge-Kutta, modified for the interval theory context—interval numerical solutions were produced to study these models. The work demonstrated that IDEs, particularly the Verhulst model, faithfully represent biological data due to the intrinsic uncertainties of the system.
subject: Artigos de Pesquisa
  topic: section
subject: Interval Differential Equations
  topic: keywords
subject: Malthus Model
  topic: keywords
subject: Verhulst Model
  topic: keywords
subject: Escherichia coli
  topic: keywords
subject: Euler Method
  topic: keywords
subject: Runge-Kutta Method
  topic: keywords
creator: Vitor Eduardo Girotto Barelli
creator: Vinícius Francisco Wasques
creator: Juliana Helena Costa Smetana
creator: Ana Luiza Poletto Loss
creator: Gabriel Viégas Ribeiro
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-07-16
publication date: 2025-07-16
starting page: e26003
ending page: e26003
doi: 10.21167/cqdv26e26003

Characterization of Equilibrium Points and Stability Analysis of the SMIB Using the First and Second Lyapunov Methods
type: item
description: Stability analysis in dynamic systems plays a crucial role in ensuring the safe and reliable operation of power systems. This work aims to investigate the characteristics of equilibrium points and conduct a stability analysis in a Single Machine Infinite Bus (SMIB) power system. To achieve this, a detailed approach to nonlinear dynamic systems analysis will be considered to describe the behavior of the aforementioned power system, focusing on rotor angle stability analysis under large disturbances, exploring the First and Second Lyapunov Methods, as well as LaSalle's Invariance Principle. The simulations will be conducted using an algorithm implemented in the MATLAB environment, which will enable spectral analysis of the SMIB to investigate its stability conditions.
subject: Edição Especial ERMAC 2024
  topic: section
subject: Stability
  topic: keywords
subject: Power systems
  topic: keywords
subject: Equilibrium points
  topic: keywords
creator: Nathalia Massambani
creator: André Christóvão Pio Martins
creator: Antonio Roberto Balbo
creator: Edilaine Martins Soler
creator: Leonardo Nepomuceno
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-07-25
publication date: 2025-07-25
starting page: e25006
ending page: e25006
doi: 10.21167/cqdv25e25006

Towards an algebrization of a linear temporal logic
type: item
description: The subject of this paper is the Propositional Neighbourhood Logic (PNL), a case of linear temporal logic and an extension of Classical Propositional Logic that results from the inclusion of modal operators that deal with certain temporal aspects. In this context, the validity of a proposition is strictly related to some temporal interval. We highlight some formal aspects of this logic and its formalization in some deductive systems (or proof systems), which naturally reflect the formal aspects of time. We aim to investigate algebraic models for Propositional Neighbourhood Logic. However, in this work, we focus exclusively on presenting the Soundness result, one of the necessary steps towards obtaining an adequate (sound and complete) model, between the axiomatic system of PNL and the planned algebraic model.
subject: Edição Especial ERMAC 2024
  topic: section
subject: Logic
  topic: keywords
subject: Algebraic Logic
  topic: keywords
subject: Temporal Logic
  topic: keywords
subject: Neighbourhood Logic
  topic: keywords
creator: Romulo Albano de Freitas
creator: Hércules de Araujo Feitosa
creator: Luiz Henrique da Cruz Silvestrini
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-07-25
publication date: 2025-07-25
starting page: e25007
ending page: e25007
doi: 10.21167/cqdv25e25007

Interesting properties relating areas of two triangles
type: item
description: This article explores an interesting geometric relationship between the areas of two triangles, in which each vertex of the smaller triangle is located on distinct sides of the larger triangle. We present and demonstrate three unusual properties, using practical examples with notable points, such as the barycenter, incenter, circumcenter, orthocenter and Gergonne point. The results obtained open paths for future geometric investigations, highlighting classical and modern concepts, such as Euler's theorem applied to pedal triangles, which relates the area of ​​triangles to orthogonal projections of a point on the sides of a triangle.
subject: Artigos de Pesquisa
  topic: section
subject: Orthic triangle
  topic: keywords
subject: Remarkable points
  topic: keywords
subject: Median
  topic: keywords
subject: Barycenter
  topic: keywords
subject: Bisector
  topic: keywords
creator: Luis Antonio Ponce Alonso
creator: Francisco Nery de Souza Campos
creator: Edmundo Capelas de Oliveira
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-07-25
publication date: 2025-07-25
starting page: e26004
ending page: e26004
doi: 10.21167/cqdv26e26004

Topological structure of the phase portrait for linear vector fields in R3 and applications
type: item
description: This paper presents an analysis of the sign of the real part of the roots of a polynomial of degree 3 as a function of its coefficients. The problem is treated mainly from an analytical point of view, knowing that from an algebraic point of view the problem has already been treated in the literature without significant advances. As an application of the results obtained, we will fully characterize the dynamics and topological structure of the phase portrait for linear fields in R3. In addition, we present applications in the local qualitative study of equilibrium points for vector fields in R3 defined with one or more parameters.
subject: Artigos de Pesquisa
  topic: section
subject: Tridimensional linear vector fields
  topic: keywords
subject: Roots of cubic polynomials
  topic: keywords
subject: Local dynamics near to equilibrium points
  topic: keywords
subject: Bifurcation diagram
  topic: keywords
creator: Luan Lima da Silva
creator: Durval José Tonon
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-08-05
publication date: 2025-08-05
starting page: e26007
ending page: e26007
doi: 10.21167/cqdv26e26007

The Pell sequence in the tricomplex ring
type: item
description: In this study we investigate a Pell-type sequence, perpetrated by a second-order linear recurrence which specifies the Horadam sequence. Here, we present, study and analyze results concerning this new class of Pell sequences.
subject: Artigos de Pesquisa
  topic: section
subject: Pell Sequence
  topic: keywords
subject: Tricomplex Pell Sequence
  topic: keywords
subject: Tagiuri-Vajda's Identity
  topic: keywords
subject: Partial Sums
  topic: keywords
creator: Eudes Antonio Costa
creator: Francival Santos Monteiro
creator: Vitor Manoel Alves de Souza
creator: Douglas Catulio dos Santos
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-07-30
publication date: 2025-07-30
starting page: e26005
ending page: e26005
doi: 10.21167/cqdv26e26005

A characterization of adjunction in a many-valued modal system
type: item
description: Galois connections are pairs of functions, defined over ordered sets, that preserve some particular aspects. They are studied in the context of algebraic structures. As a logic topic, we take the four-valued logic PM4N that contemplates, at least, two modal operators for the notions of necessary and possible. In this paper, we develop a particular four-valued implication for PM4N, which constitutes a Galois pair with the two modal operators. Then, we show some properties of the logic just considering the correlates algebraic developments.
subject: Edição Especial ERMAC 2024
  topic: section
subject: Galois connection
  topic: keywords
subject: Many-valued logic
  topic: keywords
subject: Modal logic
  topic: keywords
subject: Algebraic logic
  topic: keywords
creator: Hércules de Araujo Feitosa
creator: Romulo Albano de Freitas
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-07-08
publication date: 2025-07-08
starting page: e25005
ending page: e25005
doi: 10.21167/cqdv25e25005

Fuzzy model to check the susceptibility of young people in relation to fake news
type: item
description: Known as fake news, the various forms of misinformation have become a major vulnerability in today's world. They can influence, shape or distort our perception of what is real. In this work, we present a Fuzzy Rule-Based System (FRBS) with the objective of establishing an appropriate modeling that allows inferring how susceptible, in terms of believing and/or sharing; a person may be when faced with fake news. To do this, we use data collected from online forms from participants in one of the Project modules titled “Artificial Intelligence: from Logic to Humanities” supported by CNPq. The data was used to feed a fuzzy model that allows inferring the participants' degree of susceptibility to misinformation. The results showed that in a sample of 42 project participants, only 9.5% had a high degree of contamination by “fake news”. The internal validity of the model was established by comparing the results obtained through the FRBS with a manual analysis of the data by the expert.
subject: Artigos de Pesquisa
  topic: section
subject: Lógica Fuzzy
  topic: keywords
subject: Fake news
  topic: keywords
subject: Sistema baseado em regras fuzzy
  topic: keywords
subject: Notícias falsas
  topic: keywords
creator: Aline Tiemi Terasawa
creator: Luiz Henrique da Cruz Silvestrini
creator: Ana Claudia de Jesus Golzio
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-07-08
publication date: 2025-07-08
starting page: e26002
ending page: e26002
doi: 10.21167/cqdv26e26002

Funções quadráticas na sala de aula: uma proposta de ensino através da modelagem matemática
type: item
description: We propose a didactic approach to teaching quadratic functions through mathematical modeling. The proposal is based on a problem that requires determining one side of a rectangle as a function of the height of a trapezoid formed within a triangle, under the condition that the areas of the regions formed are equal. Additionally, the triangle and the rectangle must have the same total areas and heights. We explored this problem situation through an experiment involving the transfer of liquids by gravity between triangular and rectangular reservoirs, allowing students to manipulate, investigate, and validate mathematical concepts. The use of tools such as spreadsheets and GeoGebra simulations provided a dynamic learning environment, enhancing the understanding of the properties of quadratic functions. The proposal was implemented with a first-year high school class, followed by an analysis of the results obtained.
subject: Edição Especial ERMAC 2024
  topic: section
subject: Ensino
  topic: keywords
subject: Modelagem matem´atica e aplicações
  topic: keywords
subject: Ensino de funções quadráticas
  topic: keywords
creator: Wladimir Seixas
creator: Cleber Aparecido de Almeida
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-07-07
publication date: 2025-07-07
starting page: e25004
ending page: e25004
doi: 10.21167/cqdv25e25004

Identification of fatty acids from açai in mistures subjected to crossflow microfiltration using Artificial Neural Networks
type: item
description: This article proposes the use of Artificial Neural Networks as an alternative tool to classify mixtures of fatty acids from açai subjected to crossflow microfiltration. The neural networks were trained with the Levenberg-Marquardt and Bayesian Regularization supervised learning algorithms, using the software MATLAB and datasets from literature, related to pressure, flow speed, time and transmembrane flow rate. The evaluation criteria were consists on analyzing the confusion matriz, the error histogram and the performance graphics. The neural network that used the Bayesian Regularization had 99,1\% accuracy for the mixtures with water/oleic acid and water/palmitic acid and also 96,5\% accuracy when a third class was added to the datasets, containing water and both the fatty acids, showing the validity of the tool.
subject: Edição Especial ERMAC 2024
  topic: section
subject: Redes neurais artificiais
  topic: keywords
subject: Ácidos graxos
  topic: keywords
subject: Açaí
  topic: keywords
subject: Microfiltração tangencial
  topic: keywords
creator: Matheus Nonis Passerini
creator: Érica Regina Filletti
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-09-08
publication date: 2025-09-08
starting page: e25003
ending page: e25003
doi: 10.21167/cqdv25e25003

Oscillates in the area of ​​the square
type: item
description: In this article we examine how to approximately infer the area of ​​the region in the $xy$ plane bounded by the graph of the function $x\in[0,1]\mapsto 1+\frac{1}{n}sin(x\sqrt{n}) $, $n\in\mathbb{N}$, and along the $x$ and $y$ axes, and along the line $x=1$ using elements from Elementary Mathematics (covered in Basic Education). We also show how this analysis can be considered for the approximate calculation of areas of flat figures obtained by varying the sides of polygons via trigonometric functions; To this end, we define the notion of functions with good oscillatory behavior. We obtain formulas using geometric concepts from plane geometry aimed at activities at the Basic Education level. We use the graphic packages \LaTeX\ 'animate', 'tikz', 'tkz-euclide' and 'pgfplots' to produce figures and animations.
subject: Artigos de Pesquisa
  topic: section
subject: Animate
  topic: keywords
subject: Área
  topic: keywords
subject: Oscilação
  topic: keywords
subject: Quadrado
  topic: keywords
subject: Tikz
  topic: keywords
creator: Flank David Morais Bezerra
creator: Leonardo Pires
rights: Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2025-07-08
publication date: 2025-07-08
starting page: e26001
ending page: e26001
doi: 10.21167/cqdv26e26001

Polinômios e números primos: explorando padrões através de cálculos computacionais e a Conjectura 41
type: item
description: Hardy e Littlewood, ao longo de suas notáveis carreiras, propuseram várias conjecturas matemáticas. Em particular, a Conjectura F de Hardy-Littlewood, formulada em 1922, sugere que certas funções quadráticas geram infinitos números primos e estabelece uma relação assintótica para a função de contagem de números primos. Este trabalho apresenta um polinômio de segundo grau, v41(x)=x2+81x+412, derivado do n-quadrado Zeta, que representa uma aplicação específica da Conjectura F. Propomos, portanto, uma abordagem alternativa para a demonstração da Conjectura F através da Conjectura 41. "A Conjectura 41 postula que ``A função de contagem de primos-41, gerada pelo polinômio v41(x), é assintoticamente igual a x/(Alnx + B)". Adicionalmente, constatamos que, se a Conjectura 41 for verdadeira, o polinômio em questão gerará infinitos números primos.
subject: Artigos de Pesquisa
  topic: section
subject: Números primos
  topic: keywords
subject: n-quadrado Zeta
  topic: keywords
subject: Polinômio v41(x)
  topic: keywords
subject: Conjetura F
  topic: keywords
subject: Conjetura 41
  topic: keywords
creator: Jorge Andrés Julca Avila
creator: Éder Luis Tostes
creator: Gabriel Silva de Andrade
rights: Copyright (c) 2024 C.Q.D. - Revista Eletrônica Paulista de Matemática https://creativecommons.org/licenses/by/4.0
date: 2024-12-17
publication date: 2024-12-17
starting page: e24012
ending page: e24012
doi: 10.21167/cqdv24e24012