Mestrado em Matemática
URI Permanente para esta coleção
Nível: Mestrado Acadêmico
Ano de início: 2006
Conceito atual na CAPES: 3
Ato normativo: Homologado pelo CNE ( Port. MEC 609, de 14/03/2019, DOU 18/03/2019)
Periodicidade de seleção: Anual
Área(s) de concentração: Matemática
Url do curso: https://matematica.ufes.br/pt-br/pos-graduacao/PPGMAT/detalhes-do-curso?id=1401
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- ItemEspaços de convergência e aplicações(Universidade Federal do Espírito Santo, 2025-03-25) Perim, João Marcos Falcão; Mezabarba, Renan Maneli; https://orcid.org/0000-0001-9780-1872; http://lattes.cnpq.br/6964574819360293; https://orcid.org/0009-0006-7857-8533; http://lattes.cnpq.br/6946053374331749; Pereiro, Carolina de Miranda e; https://orcid.org/0009-0006-0831-6546; http://lattes.cnpq.br/1868229075781437; Botós, Hugo Cattarucci; https://orcid.org/0000-0003-0627-358X; http://lattes.cnpq.br/3180578353518979This dissertation investigates the theory of convergence spaces as an alter native approach to studying topological and analytical properties. In contrast to the classical approach based on neighborhoods and open sets, convergence spaces use filters and nets to define limits, offering a more flexible structure compatible with Functional Analysis and Algebraic Topology. The work pre sents a review of General Topology, exploring the transition from filters to nets, and discusses relevant applications, including the Arzel`a-Ascoli theorem and the construction of the fundamental group for limit spaces. In doing so, it aims to consolidate the importance of convergence spaces as a theoretical and practical tool for various areas of Mathematics
- ItemSemifluxos generalizados impulsivos(Universidade Federal do Espírito Santo, 2024-08-26) Modesto, Karine Ramos; https://orcid.org/0009-0005-9448-3748; http://lattes.cnpq.br/4359368936721064; Souto, Ginnara Mexia; https://orcid.org/0000-0001-8675-6199; http://lattes.cnpq.br/2095148182435653; Demuner, Daniela Paula; https://orcid.org/0009-0009-8807-3784; http://lattes.cnpq.br/6010222845541176; Bonotto, Everaldo de Mello; http://lattes.cnpq.br/2183693074268993This dissertation is an explanatory and self-contained text focused on the study of impulsive semidynamic systems when there is no guarantee of uniqueness of solutions, where we present the definition of impulsive generalized semiflow. The dissertation focuses on the study of global attractors and is mainly based on the article [6], where the Condition (T) is presented that guarantees the invariance of the global attractor and the continuity of the impact time function. Results from the article [7] are also included. Sufficient conditions are compared to guarantee the invariance of the global attractor, and examples that motivate the study of this topic are discussed.
- ItemSobre a geometria Lipschitz de polinômios quase-homogeneos(Universidade Federal do Espírito Santo, 2024-10-21) Aquino Neto, Gabriel da Macena de; Câmara, Leonardo Meireles; https://orcid.org/0000-0002-4637-8573; http://lattes.cnpq.br/9240898305551070; https://orcid.org/0009-0002-3889-6044; http://lattes.cnpq.br/0868237399371299; Silva, Thiago Filipe da; https://orcid.org/0000-0002-3152-0987; http://lattes.cnpq.br/5049713215002090; Fernandes, Alexandre César Gurgel ; https://orcid.org/0000-0001-7846-0312; http://lattes.cnpq.br/8791056897839415In this work, we will show how to determine, in a general context, whether two real quasi-homogeneous polynomials in two variables with weights ϖ = (p,q) are R-semialgebraically Lipschitz equivalent. Initially, we characterize the Lipschitz equivalence of real polynomial functions of one variable by comparing the values and also the multiplicities of the polynomial functions at their critical points. Sub sequently, under general conditions, we will reduce the problem of R-semialgebraic Lipschitz equivalence of quasi-homogeneous polynomials in two variables to the pro blem of Lipschitz equivalence of real polynomial functions of one variable. As an application of the theory developed throughout this dissertation, we will analyze the properties, in the context of R-semialgebraic Lipschitz equivalence, of a specific fa mily of quasi-homogeneous polynomials considered in [9, Henry and Parusinski], to show that the bi-Lipschitz equivalence of germs of analytic functions (R2,0) → (R,0) admits continuous moduli. Consequently, the R-semialgebraic Lipschitz equivalence of real quasi-homogeneous polynomials in two variables also admits continuous mo duli. Finally, we explore the possibility of simplifying the classification space of quasi-homogeneous polynomials.
- ItemPerfil do cutoff do processo de exclusão no grafo completo(Universidade Federal do Espírito Santo, 2024-04-15) Oliveira, Éric Santana; Jara Valenzuela, Milton David; https://orcid.org/; http://lattes.cnpq.br/7496571533341165; Silva, Fábio Júlio da ; https://orcid.org/0000-0003-2405-7696; http://lattes.cnpq.br/8745134398831488; https://orcid.org/; http://lattes.cnpq.br/4639522148187770; Bessam, Diogo Manuel Fernandes ; https://orcid.org/; http://lattes.cnpq.br/2356936612360198; Hernandez Romero, Freddy Rolando ; https://orcid.org/0000-0001-5410-3062; http://lattes.cnpq.br/2961243559975382This dissertation delves into the study of Markov chains, evolutionary processes characterized by “memory loss”, widely applied in diverse fields such as biology, statistics, and finance. The convergence of these chains to a stationary distribution is analyzed using the “total variation distance”. The times of 𝜀-mixing are introduced, representing the time required for convergence. The concept of coupling between Markov chains is presented, demonstrating its utility in de termining bounds for mixing times. The phenomenon of cutoff, an abrupt decrease in total variation distance, is explored, providing a detailed understanding of convergence. The ulti mate goal is to calculate the cutoff profile for the simple exclusion processes on complete graphs. Chapters cover the construction of chains, technical concepts, couplings, and mixing times, cul minating in the analysis of the cutoff phenomenon and its specific application to the exclusion process in the complete graph
- ItemA Transformada de Fourier para o Laplaciano Generalizado(Universidade Federal do Espírito Santo, 2024-03-05) Ramos Junior, Jomar Ferreira; Valentim, Fábio Júlio da Silva; https://orcid.org/0000-0003-2405-7696; http://lattes.cnpq.br/8745134398831488; https://orcid.org/0009-0006-1032-5169; http://lattes.cnpq.br/1800635453022041; Aranda, José Miguel Mendoza; https://orcid.org/; http://lattes.cnpq.br/8615067875072268; Silva, Jean Carlos da; https://orcid.org/; http://lattes.cnpq.br/9490078990099931This academic dissertation aims primarily to contribute to the enhancement of understanding of the Fourier Theory applied to the generalized Laplacian. The proposed methodology involves the construction of an orthonormal basis of eigenfunctions for the operator, based on the appropriate choice of Green’s functions. The central problem consists of finding the solution u(x) that satisfies certain boundary conditions for the equation Lu = f, using a series representation of the eigenfunctions of the operator L. The dissertation addresses fundamental aspects such as the definition of the domain of the generalized Laplacian, the analysis of Green’s functions and their applications in solving partial differential equations, as well as transformations for the generalized Laplacian. The interest in consolidating the Fourier Theory for the generalized Laplacian aims to provide a deeper understanding of the properties of this operator and its relation to Fourier Theory, establishing a foundation for future research, including more complex cases such as the differential operator in reverse order. This work represents a significant contribution to the understanding of the theory of the generalized Laplacian and its connections with Fourier Theory.