http://repositorio.ufc.br/handle/riufc/59 2026-08-16T11:21:28Z http://repositorio.ufc.br/handle/riufc/87470 Título: Critério de Kitai para operadores de composição. Autor(es): Pires, Victor Emanuel dos Santos Abstract: This work aims to study composition operators on the space of measurable functions, in which we will consider the characterization of hypercyclic and topological mixing composition operators obtained by Bayart, Darji, and Pires in 2018. We will show that hypercyclic and weak mixing composition operators coincide in this context. Furthermore, we provide a characterization for composition operators satisfying Kitai’s Criterion in invertible measurable systems and use this characterization to show that there exists a topological mixing composition operator that does not satisfy Kitai’s Criterion. Tipo: Dissertação 2026-01-01T00:00:00Z http://repositorio.ufc.br/handle/riufc/87292 Título: Fibrados universais e o teorema de Prill Autor(es): Brito, Matheus Miler Anunciação Abstract: The main result in this work is to show the theoretical development of the topology of fibre bundles, with focus on principal bundles, leading to the classification theorem for universal bundles and the caracterization theorem of universal bundles, for the purpose of justifying the details of Prill’s article (1967) in Complex Analytic Geometry, which states a regularity condition under which a complex cone becomes a linear subspace of the complex space. Tipo: Dissertação 2026-01-01T00:00:00Z http://repositorio.ufc.br/handle/riufc/86473 Título: Relação entre VC Dimension e menor testemunha Autor(es): Moura, Rafael Fernandes Abstract: The VC-dimension is an important combinatorial measure that, in a sense, indicates the complexity of a family of binary functions. It was originally defined in 1971 by Vapnik and Chervonenkis (VC) and gave rise to the so-called “Vapnik-Chervonenkis Theory”. It is of fundamental importance in Statistical Learning Theory, being used, for example, to predict probabilistic upper bounds for classification tests. Another important concept, now in Computational Learning Theory, is the “Teaching Dimension” (TD). It is related to the notion of “witnesses” for a family of binary functions. More precisely, if H is a set of binary functions with domain X, we say that S ⊆ X is a witness for a certain h ∈ H if it is possible to identify h (among the elements of H) from its restriction to S; that is, if no other function in H has the same restriction as h on S. Defining TDmin(H,h) as the size of the smallest witness for h, the Minimal Teaching Dimension of H, denoted by TDmin(H), is equal to the minimum value of TDmin(H,h) as h varies. The RTD (“Recursive Teaching Dimension”) conjecture relates the two above parameters, stating that the value of the Teaching Dimension of any family H, with finite domain, is less than or equal to the VC-dimension of H multiplied by an absolute constant. In this dissertation, we study the history and recent advances regarding this conjecture. Tipo: Dissertação 2026-01-01T00:00:00Z http://repositorio.ufc.br/handle/riufc/86255 Título: Lema de Hopf-Oleinik não homogêneo para operadores totalmente não lineares com termo hamiltoniano Autor(es): Silva, Antônio Valderlanio Ribeiro da Abstract: This work establishes a quantitative version of the inhomogeneous Hopf-Oleinik Lemma for supersolutions of fully nonlinear elliptic equations with Hamiltonian terms, and applies this result to obtain optimal regularity estimates for l-semiconvex supersolutions. Specifically, we analyze fully nonlinear equations of the form P_,Λ,W,`,< ( 2D, D, G) = 5 (G), where P_,Λ,W,`,< represents a class of Pucci-type extremal operators with gradient dependence and unbounded coefficients. Our results generalize classical estimates for fully nonlinear PDEs, highlighting the construction of barriers and the strong version of the Harnack inequality, as well as providing fundamental tools and ideas to deal with gradient-dependent structures under different growth regimes. It is worth noting that the Hopf-Oleinik Lemma established here remains valid even in the presence of unbounded nonlinearities, significantly strengthening previous results in this direction. Tipo: Tese 2025-01-01T00:00:00Z