https://repositorio.ufba.br/handle/ufba/518 2026-05-17T06:23:58Z 2026-05-17T06:23:58Z Leite, Ênio Carlos da Silva https://repositorio.ufba.br/handle/ri/44457 2026-05-06T19:07:14Z 2025-12-02T00:00:00Z

Título: Os grupos de tranças emolduradas e suas generalizações Autor(es): Leite, Ênio Carlos da Silva Primeiro Orientador: Uribe, Oscar Eduardo Ocampo Abstract: Let n ≥ 2 and let Bn denote the Artin braid group, also known as the braid group of the disk. We denote by FBn the framed braid group. In this thesis, we study framed braid groups and their generalizations. Initially, we develop a structural analysis of the group FBn , investigating several algebraic properties. In particular, we determine its center, lower central series, commutator subgroup, as well as certain Coxeter-type quotients and associated congruence subgroups. Next, we extend our study to the context of surfaces, considering the framed braid groups FBn(M) , where M may be an orientable or non-orientable surface, possibly with a finite number of punctures. Subsequently, we introduce and analyze two generalizations of the framed braid group: the framed virtual braid group FVBn and the framed singular braid group FSGn. For both cases, we present descriptions by generators and relations, and investigate structural properties analogous to those of FBn. Finally, we construct an invariant for singular knots, based on the virtual Temperley–Lieb algebra and the Markov trace, thus establishing a connection between the algebraic theory of braids and the theory of singular knots. Editora / Evento / Instituição: Universidade Federal da Bahia Tipo: Tese

2025-12-02T00:00:00Z Soares, Camila Braz https://repositorio.ufba.br/handle/ri/44456 2026-05-06T18:28:34Z 2025-12-15T00:00:00Z

Título: Aplicação de processos autorregressivos sazonais com valores inteiros (SINAR(1)) em dados de qualidade do ar: uma abordagem robusta Autor(es): Soares, Camila Braz Primeiro Orientador: Reisen, Valdério Anselmo Abstract: This paper investigates robust inference for the Seasonal Integer-Valued Autoregressive model (SINAR(1)), addressing the limitations of the classical Conditional Maximum Likelihood (CML) estimator under data contamination. We apply an alternative estimation approach based on Huber M-regression. Monte Carlo simulations evaluate the robustness efficiency trade-off under clean and contaminated scenarios. The robust model is more stable under contaminated scenarios, with a modest loss of efficiency under ideal conditions. An empirical application to seasonal Air Quality Index data derived from NASA’s MERRA-2 satellite reanalysis illustrates the proposed methodology, with coherent forecasting results indicating superior performance of the robust estimator. These findings highlight that robust M-regression provides a reliable alternative to likelihood-based estimation when data quality cannot be guaranteed. Editora / Evento / Instituição: Universidade Federal da Bahia Tipo: Dissertação

2025-12-15T00:00:00Z Santos, Agábio Brasil dos https://repositorio.ufba.br/handle/ri/44401 2026-04-20T22:28:48Z 2025-11-11T00:00:00Z

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

2025-11-11T00:00:00Z Azevedo, Augusto Ferreira de https://repositorio.ufba.br/handle/ri/44400 2026-04-20T21:07:08Z 2026-01-07T00:00:00Z

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

2026-01-07T00:00:00Z