IME - Artigos publicados em periódicos

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

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A respeito da necessidade de revisão da história da matemática grega: 48 anos depois, por que continuamos a ensinar como antes?
(2025) Gonçalves, Bruno Felipe; Silva, Diamantino da; Clímaco, Humberto de Assis
In the present paper, we analyze the debate, held between 1975 and 1979, concerning the thesis that asserted the existence of analgebra expressed in geometric form inancient mathematical treatiesand the appropriateness of translating, in books on the history of mathematics, Greek results in algebraic terms. After demonstrating the importance of this debate for the comprehension of later transformations in the historiography of Greek mathematics, the insufficiency of the literature in Portuguese language regarding this subject and the serious consequences that arise from it – among which we mention the translation and publication in the Brazilian scenario of texts on the history of mathematicsoriginally published before the occurrence of the debate here presented and the subsequent teaching of concepts that were proved wrong decades ago –,we outlineto the Portuguese-speakingreader the content of the discussions heldby means of an exhaustive analysis of the first five papers published on this matter. We endbyexplaining our own conclusions and showing possible lines of research not yet explored, which can deepen the knowledge on this subject.
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.
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
This article addresses the role of Libras interpreters in mathematics teaching through a bibliographic review that investigates: "What do CAPES and BDTD research say between 2006 and 2023 about Libras interpreters in mathematics classes?" The objective is to map and analyze publications from these portals, adopting a qualitative approach and using Discourse Analysis to interpret the data collected using the descriptors "interpreter," "Libras," and "mathematics." The results reveal significant challenges faced by interpreters, including gaps in training and role definition. The lack of specific signs for complex mathematical concepts highlights the need for a more comprehensive vocabulary. Additionally, the partnership between teachers and interpreters needs to be strengthened to ensure effective content transmission. We conclude that it is essential to develop research and invest in the training of these professionals to ensure quality inclusive mathematics education.
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.
Formando professores de Matemática em projetos de extensão universitária
(2025-09) Rezende, Ana Clara Emanuele; Chaves, Marcos Henrique Alves; Cedro, Wellington Lima
This experience report aimed to understand how the extension activities developed by the group of undergraduate students in mathematics linked to the Tutorial Education Program of the Federal University of Goiás have influenced the academic and human development of future mathematics teachers. Four projects are analyzed: Basic Mathematics in Perspective, Mathematics in the Circus, Mathematics Club for Elementary and Mathematics Club for High School. Based on collective theoretical studies, the pre-service teachers seek, through the projects, to articulate school mathematics content with human activity. It is concluded that the projects corroborate the construction of a space conducive to the development of pedagogical skills and to overcoming the standards of teaching and learning mathematics. Thus, the study shows that university extension is important as a place for comprehensive education and social transformation.
O novo ensino médio: um eufemismo de reforma educacional e seus efeitos deletérios
(2025-12) Azevedo, Douglas Pereira; Cedro, Wellington Lima
This article is an excerpt from a doctoral thesis and aims to reflect on the impacts of neoliberal policy on Brazilian education, with emphasis on the implementation of the New High School (NEM). It is a theoretical work that analyzes, particularly, how this reform has influenced the school context and the subjective formation of students, based on the guidelines of the National Common Curricular Base (BNCC) and the pedagogy of competencies, which translate the interests of a business logic applied to public education. To support this analysis, official documents and theoretical contributions from experts are used, allowing a critical reading of the current educational scenario. It is argued that the NEM does not fully fulfill its function neither as a preparation for the labor market nor as a basis for entry into higher education. Instead of fostering critical and scientific training, it promotes a technical and utilitarian rationality, emptying the emancipatory role of education. The proposal meets privatist and minimalist interests, reinforcing an alienating model that compromises the quality of education offered to students in the public network.
Reformas no Ensino Médio: da pedagogia das competências à lógica empreendedora no mundo do trabalho
(2025-12) Azevedo, Douglas Pereira; Cedro, Wellington Lima
This article proposes a critical analysis of the presence of competency-based education and entrepreneurship in the educational reforms of high school in Brazil, identifying updates and continuities. It is a theoretical bibliographic work on studies of educational policy, understood as public policy, which,as such, is influenced by the social, political, and historical context in which it was implemented. Based on the critical analysis and discussion of official documents and authors who address the topic in question, it is possible to highlight and problematize the formative project of society presented. The conclusions reveal an unequal, fragmented, uncritical formation, guided by neoliberal logic aimed at the labor market, competitive and individualistic, distant from the needs of youth, whether for life in society, for the world of work, or for access to university.This profile reinforces social inequalities and the Brazilian educational duality, deepening the gaps between students from the outskirts and those from major urban centers, through the false freedom of choice and training.
Well-posed problem for a combustion model in a multilayer porous medium
(2025) Batista, Marcos Roberto; Cunha, Alysson Tobias Ribeiro da; Mota, Jesus Carlos da; Santos, Ronaldo Antonio dos
Combustion occurring in porous media has various practical applications, such as in in-situ combustion processes in oil reservoirs, the combustion of biogas in sanitary landfills, and many others. A porous medium where combustion takes place can consist of layers with different physical properties. This study demonstrates that the initial value problem for a combustion model in a multi-layer porous medium has a unique solution, which is continuous with respect to the initial data and parameters in . In summary, it establishes that the initial value problem is well-posed in . The model is governed by a one-dimensional reaction–diffusion–convection nonlinear system, where the unknowns are the temperatures in the layers. Previous studies have addressed the same problem in . However, in this study, we solve the problem in a less restrictive space, namely . The proof employs a novel approach to combustion problems in porous media, utilizing an evolution operator defined from the theory of semigroups in Hilbert space and Kato’s theory for a well-posed associated initial value problem. Finally, we give numerical simulations of the nonlinear problem, where we observe that the characteristics of the solution profiles we find are in accordance with what is physically expected.
A relevância do professor na suspeita de autismo em crianças
(2026) Gomes, Guilherme Santos; Alarcão, Sunamita Souza Silva de
Autism Spectrum Disorder (ASD) is a neurodevelopmental condition characterized by difficulties in social communication and by restricted and repetitive patterns of behavior. Early identification is fundamental to ensuring appropriate interventions capable of significantly improving the child's development and quality of life. In this context, educators in Early Childhood Education and the first years of Elementary School play a central role in detecting initial signs, since it is in the school environment that the child spends most of their time in social interactions and structured activities. This article discusses the importance of teacher observation, the role of the school in building the process of suspicion and referral, and the challenges faced by education professionals. It concludes that continuous training and articulation with multidisciplinary teams are essential for an effective and responsible inclusion process.
Reverse divisors and magic numbers
(2025) Costa, Eudes Antonio da; Santos, Ronaldo Antonio dos
The study examines the relationship between Ball’s magic numbers and reverse divisors. These numbers are the source of beautiful and curious properties. Activities related to numbers can be a fun way to motivate mathematics students, while also enabling surprising analysis and connections.
Solving the interval eigenvalue problem via optimization and constraint interval theory
(2026) Mizukoshi, Marina Tuyako; Salles Neto, Luiz Leduino de; Lodwick, Weldon Alexander
This study develops the theory and numerical methods for solving the interval eigenvalue problem by optimizing the Constraint Interval Representation (CIR) of the problem that improves the computed results with respect to the accuracy compared to previous methods. The CIR is able to represent how the elements in the matrix are connected. Short example problems demonstrate the accuracy of the theory to find boundaries for interval eigenvalues and their associated matrices. While the real interval eigenvalue problem is a subset of the complex interval eigenvalue case, we develop each case separately. Indications of how to go from interval methods to the fuzzy eigenvalue problem are mentioned but not developed. Issues of complexity are discussed in terms of the complexity of the optimization methods that are used.
Proportional log survival model for discrete time-to-event data
(2025) Franque, Tiago Chandiona Ernesto; Cardial, Marcílio Ramos Pereira; Nakano, Eduardo Yoshio
The aim of this work is to propose a proportional log survival model (PLSM) as a discrete alternative to the proportional hazards (PH) model. This paper presents the formulation of PLSM as well as the procedures for verifying its assumption. The parameters of the PLSM are inferred using the maximum likelihood method, and a simulation study was carried out to investigate the usual asymptotic properties of the estimators. The PLSM was illustrated using data on the survival time of leukemia patients, and it was shown to be a viable alternative for modeling discrete survival data in the presence of covariates.
Reverse divisors are Ball numbers
(2025) Costa, Eudes Antonio da; Santos, Ronaldo Antonio dos
This study investigates the relationships between Ball magic numbers and reverse divi-sors. Specifically, we extend the set of numbers that are simultaneously reverse divisorsand Ball magic numbers. Webster and Williams [16] classify reverse divisors into threetypes: basic of the first and second types, and non-basic ones. The basic of the firsttype basics are numbers that begin with 10 and end with 89, with all intermediate digitsbeing 9, for example, 1099989. The basic of the second type is double that of a firsttype basic, such as 2199978. Non-basic reverse divisors are obtained by concatenat-ing magic reverse divisors. Costa and Santos [6] proved that a first type basic reversedivisor is a Ball’s magic number. This work demonstrated that a non-basic reverse di-visor, obtained by concatenating first-type basic reverse divisors, is also a Ball’s magicnumber.
A mixture model for survival data with both latent and non-latent cure fraction
(2025) Nakano, Eduardo Yoshio; Almeida, Frederico Machado; Cardial, Marcílio Ramos Pereira
One of the most popular cure rate models in the literature is the Berkson and Gage mixture model. A characteristic of this model is that it considers the cure to be a latent event. However, there are situations in which the cure is well known, and this information must be considered in the analysis. In this context, this paper proposes a mixture model that accommodates both latent and non-latent cure fractions. More specifically, the proposal is to extend the Berkson and Gage mixture model to include the knowledge of the cure. A simulation study was conducted to investigate the asymptotic properties of maximum likelihood estimators. Finally, the proposed model is illustrated through an application to credit risk modeling.
Global well-posedness for a quasilinear combustion model in multilayer porous media
(2026) Batista, Marcos Roberto; Cunha, Alysson Tobias Ribeiro da; Mota, Jesus Carlos da; Santos, Ronaldo Antonio dos
We investigate a class of nonlinear reaction-diffusion-convection systems modeling combustion fronts in multilayer porous media. The model describes the coupled dynamics of temperature and fuel concentration, departing from previous approaches that assumed prescribed fuel profiles to simplify the analysis. By integrating the fuel concentration equations, we derive a non-autonomous quasilinear evolution problem formulated purely in terms of the temperature vector. To address the analytical difficulties arising from the absence of a linear part in the differential operator, we introduce a higher-order regularization strategy that ensures control over second derivatives in Sobolev spaces. Using Banach’s fixed-point theorem and detailed Sobolev estimates, we establish global-in-time existence, uniqueness, and continuous dependence on both initial data and model parameters. By removing the assumption of prescribed fuel profiles and regularizing the fully nonlinear system, this work provides the first global well-posedness result for a quasilinear combustion model in multilayer porous media, with numerical simulations confirming the theoretical predictions and capturing physically consistent front propagation.
Minimal surfaces in non-Minkowskian Randers spaces
(2025) Solórzano Chávez, Newton Mayer; Souza, Marcelo Almeida de
In this paper, we investigate minimal hypersurfaces in ℝ𝑛 with respect to the Busemann—Hausdorff measure in a class of Finsler 𝑛-spaces (ℝ𝑛,˜𝐹𝑏 =˜𝛼 +˜𝛽), called Randers spaces, where ˜𝛼 is the Euclidean metric and ˜𝛽 =𝑏(𝑥)𝑑𝑦𝑛 is a controlled one-form. We emphasize the fact that 𝐹 is non-Minkowskian, since 𝑏 =𝑏(𝑥) is a non-constant function of 𝑥, which is allowed here. We particularly examine graphs defined on the 𝑥𝑦-plane that are invariant under one-dimensional isometry groups of (ℝ3,˜𝐹𝑏). By reducing the minimal graph equation to an ordinary differential equation (ODE), we obtain a new class of explicit examples of minimal surfaces in Finsler geometry.
A discrete Weibull proportional odds survival model
(2025) Cardial, Marcílio Ramos Pereira; Cobre, Juliana; Nakano, Eduardo Yoshio
The purpose of this paper is to present the development of the Proportional Odds Model for discrete time-to-event data in a survival analysis context. In this work, inferences about the model parameters considering the discrete Weibull as baseline distribution are presented, obtaining the point and interval estimates of the model parameters. In addition, procedures for checking the proportional odds assumption were proposed. Simulation studies were performed to evaluate the asymptotic properties of the estimators. The proposed model is illustrated using a dataset on the survival time of patients with Leukemia.
Curves with prescribed curvature and associated surfaces
(2025) Vasquez Corro, Armando Mauro; Ferro, Marcelo Lopes
In this work, we study surfaces with a canonical principal direction (CPD surfaces) under the simultaneousprescription of two extrinsic geometric invariants: one principal curvature and the support function. Basedon these prescriptions, we reformulate thefirst and second fundamental forms, which enables us to constructexplicit examples of such surfaces. Finally, we show that when the curvature of the profile curve is constant,that is, when one of the principal curvatures is constant, the corresponding CPD surface is a tubularsurface.
Geometry of a navigation problem: the λ−Funk Finsler metrics
(2025) Solórzano Chávez, Newton Mayer; Martínez León, Víctor Arturo; Rodrigues Filho, Alexandre Henrique; Souza, Marcelo Almeida de
We investigate the travel time in a navigation problem from a geometric perspective, with respect to a new class of Finsler metrics. We present the λ−Funk Finsler Metrics. The setting involves an open disk centered at the origin, representing a circular lake perturbed by a symmetric wind flow proportional to the distance from the origin with proportionality factor λ. The Randers metric, which is an important Finsler metric, derived from this physical problem, generalizes the well-known Euclidean metric (λ = 0) on the Cartesian plane and the Funk metric on the unit disk (λ = 1). We obtain the formula for distance, or travel time, from point to point, and the circumference equations. In addition, we obtain the distance formulas from point to line and vice versa.
The defective beta-gompertz distribution for cure rate regression models
(2025) Tojeiro, Cynthia Arantes Vieira; Tomazella, Vera Lucia Damasceno; Jerez Lillo, Nixon Andrés; Ramos, Pedro Luiz
This paper introduces a novel approach to cure fraction modeling, also known as long-term survival modeling, by focusing on scenarios where a portion of observations is not susceptible to the event of interest. We propose a new defective distribution model based on the Beta distribution, specifically utilizing the defective Gompertz distribution as a foundation, while accounting for censored data and covariates. We demonstrate that the resulting Beta-Gompertz distribution also exhibits defective characteristics, making it particularly suitable for modeling data with cure fractions. To perform inference on the parameters, maximum likelihood estimation is employed, and its asymptotic properties are examined through simulation studies. The proposed methodology is illustrated using a real-world dataset related to the survival time of patients with triple-negative breast cancer from the A.C. Camargo Cancer Center Hospital, located in São Paulo, Brazil.

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