IME - Artigos publicados em periódicos

URI Permanente para esta coleçãohttp://200.137.215.59//handle/ri/1341

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O papel do intérprete de Libras na educação matemática inclusiva: uma revisão bibliográfica
(2025) Silva , Sabrina Cosendey Dutra da; Alvarenga, Karly Barbosa; Priebe, Débora Danielle Alves Moraes
Registros de representação semiótica: uma análise da abordagem de limites em livros didáticos
(2025) Santos, Leniedson Guedes dos; Alvarenga, Karly Barbosa; Silva, Geci José Pereira da
Textbooks play a fundamental role as teaching instruments and their use as a research object makes it possible to understand learning difficulties, especially with regard to higher education. This article presents a bibliographic work, part of a doctoral research, of a qualitative nature with numerical support, which proposes to answer the question about how the textbooks Calculus with Analytical Geometry, by Louis Leithold and A Course in Calculus by Hamilton Luiz Guidorizzi, mobilize records of semiotic representation, to address the concept of limit. Thus, this research aims to investigate the way in which these Differential Calculus textbooks use semiotic representation registers to work on the concept of limit of functions of one variable. The methodology used consisted of identifying the types of representations of limits and functions that appear in the works, both in the text and in the exercises, as well as their transformations. For the treatment of the data, codification, categorization and construction of inventories and graphs were carried out, using Duval’s theory of semiotic representation registers to support the analyses. As a result, the predominance of algebraic language in the two analyzed books and the preference for conversions that depart from the algebraic record for the construction of graphs stand out.
Análise de um processo tradutório de Libras nas aulas de matemática à luz da teoria de Vygotsky
(2025) Silva, Sabrina Cosendey Dutra da; Alvarenga, Karly Barbosa; Priebe, Débora Danielle Alves Moraes
This article presents the results of a study with a Libras interpreter in math classes for a deaf person. The main objective is to detect and understand the challenges she has faced and how they can affect the interpretation of the content. The research is qualitative, of the case study type, using Textual Discourse Analysis in the light of Vygotsky's theory on mediation, higher mental functions and internalization, to examine the data obtained from an interview and the recordings of the interpreted lessons. The analysis pointed to three categories, and here we highlight in particular the analysis of the broadest: Interpreter's Work. The results indicated that interpreting into Libras in educational settings is a complex activity, due to: linguistic variation; lexicon limitations; the need for educational collaboration; among others. It was also observed that the translation process is permeated by subjectivity and requires a combination of linguistic, cognitive and cultural skills.
A matemática na formação dos nutricionistas percepções sobre o currículo
(2026) Priebe, Débora Danielle Alves Moraes; Alvarenga, Karly Barbosa
ABSTRACT: The domain of quantitative skills is vital for the daily practice of nutritionists, therefore, a familiarization with mathematics must be developed within its formative context. The objective of this study is to investigate the perceptions of nutritionists in practice and in undergraduation regarding the teaching of mathematics in the nutrition course, in terms of the disciplinary structure, the articulation between theory and practice and the training of professors. For this, 4 interviews were conducted with nutritionists at different stages of their careers, examined through Bardin's content analysis. The results revealed the strong presence of mathematics in most subjects, highlighting its relevance not made explicit by the curriculum text. The teaching of mathematics in the course is predominantly theoretical, abstract and little connected with nutritional practice. The lack of articulation between knowledge impairs students' perspective on the usefulness of mathematics and influences their motivation for learning. The insufficient pedagogical preparation of professors impacts the teaching of mathematics, leading to the adoption of approaches based on the transmission of contents, repetition and memorization. The area of undergraduation of professors who teach Mathematics is one of the factors that lead professors not to address the applicability of the subjects taught with the future profession. Mathematics professors need to consider the specificities and needs of the students' training area, understanding the language and contexts of nutrition, in order to teach mathematical topics relevant to this field.
Projeto Político-Pedagógico e relação entre mundos: a experiência das escolas indígenas Javaé
(2026) Ferreira, Mariângela Barbosa; Moraes, Moema Gomes
RESUMENEl Proyecto Político-Pedagógico (PPP) constituye un instrumento central de la acción educativa, al expresar concepciones de escuela, currículo y formación. En las escuelas indígenas de la etnia Javaé, sinembargo, este documento necesita superar su función burocrática y configurarse como un espacio de traducción cultural y mediación entre saberes. Este artículo problematiza la distancia entre los modelos de PPP elaborados por los organismos estatales y lasrealidades socioculturales de los pueblos indígenas, con énfasis en el pueblo Javaé, ubicado en la Isla del Bananal, en el estado de Tocantins, Brasil. La investigación, de carácter cualitativo y documental, analiza los PPP de cuatro escuelas indígenas, confrontando sus directrices con los principios de la educación intercultural y bilingüe previstos en la legislación educativa brasileña (Constitución Federal de 1988, Ley de Directrices y Bases de la Educación Nacional de 1996 y Referencial Curricular Nacional para las Escuelas Indígenas de 1999). El estudio se fundamenta en la pedagogía intercultural (Ducasse, 2015; Baniwa, 2006), en las reflexiones sobre alteridad y experiencia (Benjamin, 2012; Larrosa, 2002) y en el concepto de capital cultural (Bourdieu, 1998), con el propósito de comprender cómo el PPP puede ser apropiado por la comunidad como ejercicio de autonomía. Los resultados indican que, aunque aún influidos por estructuras normativas externas, los documentos analizados presentan iniciativas de participación comunitaria y valorización de la lengua Iny rybè y de las prácticas tradicionales Javaé, evidenciando procesos de resignificación del PPP. Se concluye que, cuando se construye de forma dialógica, el PPP puede constituirse como un territorio de enunciación intercultural y fortalecer la diversidad cultural en la educación escolar indígena.
Ações mentais matemáticas mobilizadas por estudantes no estudo de Limite de uma função
(2026) Peixoto, Emanuel Gomes; Alvarenga, Karly Barbosa
This article discusses and presents the possible mathematical mental actions mobilized by students in the Differential and Integral Calculus discipline when studying the concept of the limit of a function. The main theoretical framework adopted is the Theoretical Model of Mathematical Mental Actions, which articulates premises from Advanced Mathematical Thinking and Cognitive Neurosciences. This model encompasses a set of 49 mental actions, making it possible to identify cognitive processes that, although often subliminal, are fundamental for understanding, manipulating, and solving mathematical problems.Of a qualitative nature, the study is characterized as exploratory and descriptive. Data were collected from students in the Mathematics Degree program at the Federal University of Goiás, with 34 responses analyzed, three of which were selected for discussion. The results indicate that the participants mobilized several mathematical mental actions but were limited by the lack of conscious interaction between these actions or by a lack of the necessary depth.In general, the mental actions of Classifying, Connecting previous experiences (met-before), Interpreting, and Representing proved to be recurrent. One student activated a formal and algebraic path, mastering the action of formalizing through the epsilon-delta definition. In contrast, the other two resorted to visual and graphical approaches, mobilizing the actions of "graphing" and visualizing, but facing difficulties in articulating intuitive understanding with mathematical formalization. It is concluded that the intentional and integrated stimulation of multiple mental actions, encouraging the transition between algebraic and visual registers, can enhance conceptual understanding and assist in mitigating the high rates of failure and dropout in the Differential and Integral Calculus.
Approximate proximal methods for variational inequalities on Hadamard manifolds
(2025) Bento, Glaydston de Carvalho; Ferreira, Orizon Pereira; Papa Quiroz, Erik Alex
In this paper, we present an approximate proximal point method for addressing the variational inequality problem on Hadamard manifolds, and we analyse its convergence properties. The proposed algorithm exhibits inexactness in two aspects. Firstly, each proximal subproblem is approximated by utilizing the enlargement of the vector field under consideration, and subsequently, the next iteration is obtained by solving this subproblem while allowing for a suitable error tolerance. As an illustrative application, we develop an approximate proximal point method for nonlinear optimization problems on Hadamard manifolds.
Subsampled cubic regularization method for finite-sum minimization
(2025) Gonçalves, Max Leandro Nobre
This paper proposes and analyses a subsampled Cubic Regularization Method (CRM) for solving finite-sum optimization problems. The new method uses random subsampling techniques to approximate the functions, gradients and Hessians in order to reduce the overall computational cost of the CRM. Under suitable hypotheses, first- and second-order iteration-complexity bounds and global convergence analyses are presented. We also discuss the local convergence properties of the method. Numerical experiments are presented to illustrate the performance of the proposed scheme.
An inexact proximal point method with quasi-distance for quasiconvex multiobjective optimization problems on Riemannian manifolds
(2025) Upadhyay, Balendu Bhooshan; Poddar, Subham; Ferreira, Orizon Pereira; Jen-Chih, Yao
In this paper, we investigate a class of unconstrained multiobjective optimization problems in the framework of Riemannian manifolds (abbreviated as, MOP-RM), where the components of the objective function are assumed to be locally Lipschitz and quasiconvex. By employing the powerful tool of Mordukhovich limiting subdifferential, we introduce an inexact proximal point algorithm with quasi-distance (abbreviated as, IPPMQ-RM), to solve MOP-RM. Moreover, we establish the well-definedness of the sequence generated by the IPPMQ-RM algorithm. Based on two different versions of error criteria, we introduce two variants of IPPMQ-RM, namely, IPPMQ-RM1 and IPPMQ-RM2. We deduce that the cluster points of the sequences generated by the IPPMQ-RM1 and IPPMQ-RM2 algorithms are Pareto-Mordukhovich critical points of MOP-RM. Further, we derive that if the components of the objective function of MOP-RM are geodesic convex, then these cluster points become Pareto efficient solutions of MOP-RM. We establish the finite termination of the IPPMQ-RM1 and IPPMQ-RM2 algorithms. By employing MATLAB R2023b, a non-trivial numerical example has been furnished to illustrate the effectiveness of the proposed algorithms, namely, IPPMQ-RM1 and IPPMQ-RM2. Moreover, to demonstrate that the sequence generated by the IPPMQ-RM algorithm converges faster than the algorithms existing in the literature, we furnish several non-trivial numerical examples in the framework of well-known Riemannian manifolds.
Quasilinear elliptic problems via nonlinear rayleigh quotient
(2025) Carvalho, Marcos Leandro Mendes; Gasiński, Leszek; Santos Júnior, João Rodrigues dos; Silva, Edcarlos Domingos da
It is established existence and multiplicity of solution for the following class of quasilinear elliptic problems:{−ΔΦu = 𝜆a(x)|u|q−2u + |u|p−2u, x ∈ Ω,u = 0, x ∈ 𝜕Ω,where Ω ⊂ ℝN, N ≥ 2, is a smooth bounded domain, 1 < q < 𝓁 ≤ m < p < 𝓁∗ and Φ : ℝ → ℝ is suitable N-function.The main feature here is to show whether the Nehari method can be applied to ﬁnd the largest positive number 𝜆∗ > 0in such a way that our main problem admits at least two distinct solutions for each 𝜆 ∈ (0, 𝜆∗ ). Furthermore, using someﬁne estimates and some extra assumptions on Φ, we prove the existence of at least two positive solutions for 𝜆 = 𝜆∗and 𝜆 ∈ (𝜆∗, 𝜆) where 𝜆 > 𝜆∗
Conformally invariant skew curves for the total skew curvature on surfaces of R3
(2025) Narvaez Plaza, Luis Felipe; Garcia, Ronaldo Alves
In differential geometry, curvature-based functionals, such as the total Gaussian curvature, the Willmore energy, and the total geodesic torsion, play a central role in both theoretical investigations and practical applications. In this paper, we study geometric properties of the extremal curves for the next functional where ds is the arc element on S and are the principal curvatures. First, we establish that a necessary and sufficient condition for a surface to be a Dupin cyclide is that its lines of curvature and the extremal curves of functional intersect at a constant angle. Secondly, we demonstrate that the extremal curves of the functional are invariant under inversion. Finally, we show that the determination of functional extremal curves of for any cone, general cylinder, and surfaces of revolution can be reduced to quadratures.
Stability and bifurcation analysis of a Holling-Tanner model with discontinuous harvesting action
(2025) Cristiano, Rony
This work addresses the study of dynamics and bifurcations in a prey–predator model, known in the literature as the Holling–Tanner model, subject to a harvesting action of predators that is activated when the prey population is less than a certain threshold, and stopped otherwise. Such a model is represented by a piecewise smooth system with a switching boundary given by a straight line that is defined by the threshold established for the prey population. Under certain conditions on the system parameters, a pseudo-focus point appears at the switching boundary. Based on the Poincaré map defined in a neighborhood of the pseudo-focus, explicit conditions are given on the system parameters that determine its local stability, the occurrence of Hopf-like bifurcations and the emergence of crossing limit cycles. In addition to Hopf-like bifurcations, other local and global bifurcations such as the classical Hopf bifurcation, the Boundary Equilibrium bifurcations, the Saddle–Node bifurcation of periodic orbits and the Grazing bifurcation are also identified. A complete description of the existence and stability of equilibria and periodic orbits is provided based on the obtained two-parameter bifurcation set, from which the coexistence of four periodic orbits in the phase portrait of the system under study is proved.
On projection mappings and the gradient projection method on hyperbolic space forms
(2025) Bergmann, Ronny; Ferreira, Orizon Pereira; Németh, Sándor Zoltán; Jian-Kang, Zhu
This paper presents several new properties of the intrinsic -projection into -hyperbolically convex sets of -hyperbolic space forms, along with closed-form formulas for the intrinsic -projection into specific -hyperbolically convex sets. It also discusses the relationship between the intrinsic -projection, the Euclidean orthogonal projection and the Lorentz projection. These properties lay the groundwork for analyzing the gradient projection method and hold importance in their own right. Additionally, new properties of the gradient projection method to solve constrained optimization problems in -hyperbolic space forms are established, considering both constant and backtracking step sizes in the analysis. It is shown that every accumulation point of the sequence generated by the method for both step sizes is a stationary point for the given problem. Additionally, an iteration complexity bound is provided that upper bounds the number of iterations needed to achieve a suitable measure of stationarity for both step sizes. Finally, the properties of the constrained Fermat–Weber problem are explored, demonstrating that the sequence generated by the gradient projection method converges to its unique solution. Numerical experiments on solving the Fermat–Weber problem are presented, illustrating the theoretical findings and demonstrating the effectiveness of the proposed methods.
Predicting leishmaniasis outbreaks in Brazil using machine learning models based on disease surveillance and meteorological data
(2025) Donizette, André Cintas; Rocco, Cleber Damião; Queiroz, Thiago Alves de
Leishmaniasis poses a significant global health concern due to the absence of vaccines for humans and high infection rates in some countries. It is classified as a neglected tropical disease. In 2022, roughly 85% of global visceral leishmaniasis cases were reported in seven countries: Brazil, Ethiopia, India, Kenya, Somalia, South Sudan, and Sudan. Despite Brazil’s advanced medical capabilities compared to other affected regions, certain areas still witness a significant number of cases, prompting increased attention from researchers and raising concerns within the healthcare system. This study explores the application of artificial intelligence algorithms, particularly machine learning (ML) models to predict leishmaniasis outbreaks in selected Brazilian cities based on accumulated cases from 2007 to 2022, leveraging available meteorological data to enhance model accuracy. Our investigation concentrated on the following cities in Brazil: Fortaleza/CE, Teresina/PI, and São Luís/MA were chosen for the study of visceral leishmaniasis, whereas Manaus/AM, Rio Branco/AC, and Macapá/AP were selected for the study of tegumentary leishmaniasis, encompassing both cutaneous and mucocutaneous forms. Several Artificial Neural Network (ANN) architectures were evaluated, including a Simple Feedforward Neural Network (SFNN), a Deep Feedforward Neural Network (DFNN), and a Long Short-Term Memory (LSTM) recurrent neural network. Additionally, the Support Vector Machine (SVM), specifically the Support Vector Regression (SVR), was tested. Various metrics were used to identify the most effective models, in which the Root Mean Squared Error (RMSE) was the primary one. The results highlight the significance of meteorological data as a crucial factor in ML models for predicting leishmaniasis outbreaks, while also emphasizing the importance of fine-tuning these models to achieve greater accuracy. Finally, data and the pseudo-code of the models are accessible through an open repository to encourage further studies in this area.
On small breathers of nonlinear Klein-Gordon equations via exponentially small homoclinic splitting
(2025) Gomide, Otávio Marçal Leandro; Guardia, Marcel; Martinez-Seara Alonso, Maria Teresa; Chongchun, Zeng
Inexact Newton methods for solving generalized equations on riemannian manifolds
(2025) Louzeiro, Maurício Silva; Silva, Gilson do Nascimento; Jinyun, Yuan; Daoping, Zhang
The convergence of inexact Newton methods is studied for solving generalized equations on Riemannian manifolds by using the metric regularity property, which is also explored. Under appropriate conditions and without any additional geometric assumptions, local convergence results with linear and quadratic rates, as well as a semi-local convergence result, are obtained for the proposed method. Finally, the theory is applied to the problem of finding a singularity for the sum of two vector fields. In particular, the KKT system for the constrained Riemannian center of mass on the sphere is explored numerically.
An adaptive cubic regularization inexact-Newton method on riemannian manifolds
(2025) Louzeiro, Maurício Silva; Silva, Gilson do Nascimento; Jinyun, Yuan; Daoping, Zhang
The convergence of inexact Newton methods is studied for solving generalized equations on Riemannian manifolds by using the metric regularity property, which is also explored. Under appropriate conditions and without any additional geometric assumptions, local convergence results with linear and quadratic rates, as well as a semi-local convergence result, are obtained for the proposed method. Finally, the theory is applied to the problem of finding a singularity for the sum of two vector fields. In particular, the KKT system for the constrained Riemannian center of mass on the sphere is explored numerically.
A proof of a conjecture of W. Hsiang on invariant cmc hypersurfaces with a singularity at the origin
(2025) Silva, Hilário Alencar da; Garcia, Ronaldo Alves; Silva Neto, Gregório Manoel da
In differential geometry, curvature-based functionals, such as the total Gaussian curvature, the Willmore energy, and the total geodesic torsion, play a central role in both theoretical investigations and practical applications. In this paper, we study geometric properties of the extremal curves for the next functional where ds is the arc element on S and are the principal curvatures. First, we establish that a necessary and sufficient condition for a surface to be a Dupin cyclide is that its lines of curvature and the extremal curves of functional intersect at a constant angle. Secondly, we demonstrate that the extremal curves of the functional are invariant under inversion. Finally, we show that the determination of functional extremal curves of for any cone, general cylinder, and surfaces of revolution can be reduced to quadratures.
Broyden quasi-Newton secant-type method for solving constrained mixed generalized equations
(2025) Silva Júnior, Paulo César da; Ferreira, Orizon Pereira; Silva, Gilson do Nascimento
This paper presents a novel variant of the Broyden quasi-Newton secant-type method aimed at solving constrained mixed generalized equations, which can include functions that are not necessarily differentiable. The proposed method integrates the classical secant approach with techniques inspired by the Conditional Gradient method to handle constraints effectively. We establish local convergence results by applying the contraction mapping principle. Specifically, under assumptions of Lipschitz continuity, a modified Broyden update for derivative approximation, and the metric regularity property, we show that the algorithm generates a well-defined sequence that converges locally at a Q-linear rate.
On generating properties of the weak commutativity of p-groups, p odd
(2025) Bastos Júnior, Raimundo de Araújo; Oliveira, Ricardo Nunes de; Gonçalves, Nathália Nogueira; Monetta, Carmine
In the present paper, we examine the generating properties of Sidki’s weak commutativity group. More precisely, if G and G φ are two isomorphic groups, the weak commutativity group χ(G) is the group generated by G and G φ subject to the relations[g, g φ ] = 1 for all g ∈ G. Here we provide bounds for the number of generators of some subgroups of χ(G) when G is a p-group of odd order and either G is powerful or D(G) is abelian.

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