https://repositorio.ufba.br/handle/ufba/518 Sat, 16 May 2026 08:38:43 GMT 2026-05-16T08:38:43Z 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/44458 Título: Uma abordagem para o ensino de frações usando um kit manipulável Autor(es): Cerqueira, Ana Paula Costa Primeiro Orientador: Santos, Evandro Carlos Ferreira dos Abstract: The study of fractions begins in the initial years of Elementary School, deepening throughout the years until the end of Elementary School. According to data from PISA 2022, about 73% of students recorded low performance in Mathematics, against only 1% who achieved high performance. This low achievement is present in all content covered in Basic Education. Given this scenario, with the aim of creating a tool that could assist teachers in the process of teaching fractions in a more dynamic and interesting way, this dissertation, in conjunction with the educational product associated with it, uses the manipulable material entitled the “fraction kit” as an alternative for teaching fractions. The workshops using the aforementioned manipulable material were carried out with a 2nd-year high school class from the Santa Rita de C´assia State College in September 2024, aiming to contribute to the students’ understanding and the teaching work, resulting in a qualitative improvement in students’ understanding of the subject matter. Editora / Evento / Instituição: Universidade Federal da Bahia Tipo: Dissertação Wed, 28 Jan 2026 00:00:00 GMT https://repositorio.ufba.br/handle/ri/44458 2026-01-28T00:00:00Z https://repositorio.ufba.br/handle/ri/44457 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 Tue, 02 Dec 2025 00:00:00 GMT https://repositorio.ufba.br/handle/ri/44457 2025-12-02T00:00:00Z https://repositorio.ufba.br/handle/ri/44456 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 Mon, 15 Dec 2025 00:00:00 GMT https://repositorio.ufba.br/handle/ri/44456 2025-12-15T00:00:00Z 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