https://repositorio.ufba.br/handle/ri/41737 Fri, 15 May 2026 07:23:15 GMT 2026-05-15T07:23:15Z https://repositorio.ufba.br/handle/ri/44457 Os grupos de tranças emolduradas e suas generalizações Leite, Ênio Carlos da Silva Uribe, Oscar Eduardo Ocampo 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. Universidade Federal da Bahia 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/43867 Variedades dualmente flat tóricas, famílias exponenciais e Grassmannianas afins. Figueirêdo, Danuzia Nascimento Molitor, Mathieu This work addresses two classification problems. First, we classify 1-dimensional connected dually flat manifolds M that are toric in the sense of (1), and show that the corresponding torifications are complex space forms. Special emphasis is put on the case where M is an exponential family defined over a finite set. The second problem addresses a classification question in statistical theory. Exponential families defined on a finite sample space Ω are determined by (n + 1)-uples of functions (C , F 1 , ..., F n ) defined on Ω. However, this representation in terms of functions is not unique, leading to the problem of classifying equivalent tuples of functions (C , F 1 , ..., F n ). This work presents a systematic Lie group theoretical approach to this classification problem. We explicitly describe the underlying symmetry group and, using a reduction by stages method, establish a one-to-one correspondence between the set of n-dimensional exponential families on Ω and the affine Grassmannian of a related function space. Universidade Federal da Bahia Tese Fri, 12 Dec 2025 00:00:00 GMT https://repositorio.ufba.br/handle/ri/43867 2025-12-12T00:00:00Z https://repositorio.ufba.br/handle/ri/43780 Sobre sistemas dissipativos com amortecimento do tipo derivada fracionária: dos semigrupos aos processos evolutivos. Jesus, Rafael Oliveira de Cunha, Carlos Alberto Raposo da This work addresses the analysis of three evolution problems with fractional derivative-type damping, investigating the existence, uniqueness, and asymptotic behavior of solutions. The first problem consists of a one-dimensional linear and autonomous model of a suspension bridge, whose deck is modeled by Timoshenko Beam Theory. The system incorporates fractional damping terms in each of its equations. For this model, the Theory of Semigroups of Bounded Linear Operators was applied to demonstrate the existence and uniqueness of global solution. The asymptotic analysis revealed that the energy decay of the system is not exponential but rather polynomial. The second problem addresses an abstract, nonlinear, autonomous N-dimensional model for a suspension bridge, governed by Kirchhoff plate theory for the deck and again subject to fractional damping. The proof of local solution existence was achieved using Classical Semigroup Theory. The demonstration that this solution is global (i.e., does not blow up in finite time) was carried out via energy estimates for the solution norms. The long-term behavior analysis was conducted using the Theory of Nonlinear Semigroups of continuous operators (dynamical systems), which established the existence of a compact global attractor that attracts all system trajectories. Finally, the third problem analyzes a nonlinear and non-autonomous wave equation model with an acoustic boundary condition, subject to a nonlinear internal damping and a fractional derivative-type damping on the boundary. The existence of a local solution was established by combining Semigroup Theory with Kato’s Cauchy-Duhamel (CD) Systems Theory. The proof that these solutions are global again followed from energy estimates. For the asymptotic study, the Theory of Evolutionary Processes, which generalizes the notion of semigroups to the non-autonomous context, was used. Through this theory, it was demonstrated that the solutions admit a time-dependent family of compact sets (a pullback attractor) that attracts the trajectories in the pullback sense, i.e., when solutions evolve from initial conditions taken at times increasingly remote in the past. Universidade Federal da Bahia Tese Wed, 17 Dec 2025 00:00:00 GMT https://repositorio.ufba.br/handle/ri/43780 2025-12-17T00:00:00Z https://repositorio.ufba.br/handle/ri/42080 On weak and strong large deviation principles for the empirical measure of random walks. Santana, Joedson de Jesus Erhard, Dirk This work is divided into two chapters. In the 竡rst chapter, we provide an introduction to the theory of large deviations and prove a weak Large Deviation Principle (LDP) for the empirical measure of the random walk with certain rates. To achieve this, we use the Parabolic Anderson Model (PAM) and the Gärtner-Ellis Theorem. In the second chapter we show that the empirical measure of certain continuous time random walks satis竡es a strong large deviation principle with respect to a topology introduced in [21] by Mukherjee and Varadhan. This topology is natural in models which exhibit an invariance with respect to spatial translations. Our result applies in particular to the case of simple random walk and complements the results obtained in [21] in which the large deviation principle has been established for the empirical measure of Brownian motion. Universidade Federal da Bahia Tese Fri, 21 Feb 2025 00:00:00 GMT https://repositorio.ufba.br/handle/ri/42080 2025-02-21T00:00:00Z