https://repositorio.ufba.br/handle/ufba/518 Sat, 02 May 2026 08:47:14 GMT 2026-05-02T08:47:14Z http://repositorio.ufba.br:80/retrieve/ddd784b7-f280-4ff4-a887-75ace44aa102/logo matematica.PNG https://repositorio.ufba.br/handle/ufba/518 https://repositorio.ufba.br/handle/ri/44401 Título: A teoria do transporte ótimo aplicada ao estudo de sistemas de funções iteradas Autor(es): Santos, Agábio Brasil dos Primeiro Orientador: Silva, Edgar Matias da Abstract: This work consists of a study of Iterated Function Systems that contract on average, using concepts and results from Optimal Transport Theory for this analysis. To support the discussion, it was necessary to revisit notions such as complete metric spaces, weak topology, as well as concepts from Measure Theory, Ergodic Theory, and Probability Theory. Within the latter, the notions of homogeneous Markov chains and the stationary measures associated with these chains are explored. Based on these preliminary concepts, optimal coupling is defined, demonstrating that, under certain conditions, the existence of such coupling is always guaranteed. The Wasserstein distance is also introduced, which plays an essential role in the subsequent results. Equipped with the tools of Optimal Transport Theory, this work investigates the stationary measures of Iterated Function Systems that contract on average, proving that, in this context, there is existence and uniqueness of a stationary measure, in addition to obtaining estimates for its moments of order q. Finally, the developed concepts are applied to the study of skew-products that have contractive fibers, showing that such systems admit a single "stationary measure'' with limited support. Editora / Evento / Instituição: Universidade Federal da Bahia Tipo: Dissertação Tue, 11 Nov 2025 00:00:00 GMT https://repositorio.ufba.br/handle/ri/44401 2025-11-11T00:00:00Z https://repositorio.ufba.br/handle/ri/44400 Título: Jogos educativos digitais com scratch: uma abordagem para o ensino de números inteiros no ensino fundamental Autor(es): Azevedo, Augusto Ferreira de Primeiro Orientador: Ferreira Junior, Perfilino Eugênio Abstract: The central objective of this research is to investigate the p otential of the Scratch digital platform in a lesson sequence with digital educational games aimed at teaching integers to 7th grade students in elementary school. Based on the principles of meaningful learning, educational games, computational thinking, a nd the guidelines of the Brazilian National Curriculum Base (BNCC), the proposal combines brief expository activities with digital games that explore the comparison of integers, absolute value, addition, subtraction (and its equivalence to the addition of the opposite), identification of Cartesian coordinates, and description of movements in the plane. The methodology adopted is based on the use of teaching sequences as a structuring strategy for the teaching and learning process of mathematics, in addition to exploratory research on the proposed theme. The study was developed in a public school class, in a context of technological infrastructure limitations, using as main data collection instruments: an initial diagnostic assessment, an exit assessment, and a feedback questionnaire. The Scratch applications were built by the teacher researcher based on diagnosed conceptual difficulties, functioning as "conceptual laboratories" to support the transition from concrete to abstract concepts, with a strong emphas is on visual representations and immediate feedback. The results indicated a significant increase in average correct answers, a consistent reduction in standard deviations, and greater homogenization of the class's performance, particularly in the more abs tract questions , where the greatest gains were observed. Participants with the lowest initial performance were the ones who improved the most, highlighting the inclusive nature of the teaching sequence. The feedback questionnaire revealed high acceptance o f the games, a perception that the applications helped to understand rules of signs and coordinate content, as well as increased motivation to study mathematics. As a final product, an educational resource is presented, consisting of a complete script of t he teaching sequence, guidelines for the replicating teacher, assessment instruments, and a detailed description of the conception of a model game in Scratch, which, although not applied to the class, serves as a reference for the creation and adaptation o f new games in different school contexts. Editora / Evento / Instituição: Universidade Federal da Bahia Tipo: Dissertação Wed, 07 Jan 2026 00:00:00 GMT https://repositorio.ufba.br/handle/ri/44400 2026-01-07T00:00:00Z https://repositorio.ufba.br/handle/ri/44277 Título: Operadores Dunford-Pettis em reticulados de Banach Autor(es): Antunes, Gleberson Gregorio da Silva Primeiro Orientador: Ribeiro, Joilson Oliveira Abstract: A Dunford–Pettis operator is a linear operator that maps weakly convergent sequences into norm-convergent sequences. This work investigates the properties of positive operators defined on Banach lattices, with an emphasis on domination results. Specifically, we analyze the behavior of operators S and T satisfying 0 ≤ S ≤ T, seeking to determine how the properties of the dominating operator T, such as compactness or being a Dunford–Pettis operator, influence the operator S and its powers. Editora / Evento / Instituição: UNIVERSIDADE FEDERAL DA BAHIA Tipo: Dissertação Tue, 24 Feb 2026 00:00:00 GMT https://repositorio.ufba.br/handle/ri/44277 2026-02-24T00:00:00Z https://repositorio.ufba.br/handle/ri/44276 Título: Testes não paramétricos em análise de sobrevivência no contexto de inferência causal Autor(es): Azevedo, Arthur Rios de Primeiro Orientador: Amorim, Leila Denise Alves Ferreira Abstract: Research aimed at estimating causal effects of interventions on time-to-event outcomes in observational studies faces challenges, notably when the goal is to compare groups in the presence of confounding. Propensity score–based methodologies are well established in the literature and provide a robust framework for causal inference in observational studies. Weighting procedures have already been employed in nonparametric methods, such as the Kaplan-Meier estimator, allowing the construction of pseudo-populations using propensity scores, which yield adjusted, unbiased estimates in the presence of confounding. However, their integration with nonparametric hypothesis tests in survival analysis is still limited to the Log-Rank test and remains an area in need of methodological developments. In this dissertation, a generalization of nonparametric tests adjusted by the inverse probability of treatment weighting is developed, with a focus on comparing survival functions under different hazard patterns. The proposed methodology is assessed through simulation studies that consider alternative hypotheses involving proportional hazards, early and late separation, and crossing survival curves, as well as different censoring and sample size scenarios. The results show substantial gains in test power when the separation pattern is aligned with the weighting scheme used, suggesting that tests adjusted with appropriate weights can outperform classical approaches in the detection of causal effects. Editora / Evento / Instituição: Universidade Federal da Bahia Tipo: Dissertação Thu, 18 Dec 2025 00:00:00 GMT https://repositorio.ufba.br/handle/ri/44276 2025-12-18T00:00:00Z