https://repositorio.ufba.br/handle/ri/41738 Sun, 17 May 2026 05:10:21 GMT 2026-05-17T05:10:21Z 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/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/41722 Functional CLT and Berry-Esseen estimates for non-homogeneous random walks. Pimenta, Eduardo Sampaio Franco, Tertuliano Franco Santos In this thesis, we establish a Trotter-Kato type theorem. More precisely, we charac- terize the convergence in distribution of Feller processes by examining the convergence of their generators. The main contribution here is to obtain quantitative rate estimates in the vague topology for fixed times. As an important application, a central functional limit theorem is derived for random walks on the positive half-line, which converges to Brownian motions on the positive half-line with boundary conditions, as well as random walks on the line converging to the Snapping Out Brownian motion. Universidade Federal da Bahia Tese Fri, 14 Mar 2025 00:00:00 GMT https://repositorio.ufba.br/handle/ri/41722 2025-03-14T00:00:00Z https://repositorio.ufba.br/handle/ri/40919 Pontes suspenas modeladas através de vigas de Timoshenko-Ehrenfest. Araújo, Leandro Correia Cunha, Carlos Alberto Raposo da This work deals with the global existence of a solution and the asymptotic behavior for three suspension bridge models: fully damped with friction, partially damped with friction and fully damped with Kelvin-Voigt type viscoelasticity. For both models, semigroup theory is applied to prove the global existence of the solution and to analyze the asymptotic behavior. In the first model mentioned above, we obtain analyticity for the associated semigroup, a property that implies the exponential decay of the solution. For the second we obtain exponential decay, if the condition k/ρ1= b/ρ2 is valid and otherwise the polynomial decay is valid. Finally, for the last model, we obtain exponential decay. Universidade Federal da Bahia Tese Sun, 15 Dec 2024 00:00:00 GMT https://repositorio.ufba.br/handle/ri/40919 2024-12-15T00:00:00Z