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Aplicações singulares via grupos de reflexões
(Universidade Federal de São Carlos, 2020-04-24)
Our objective with this essay is to describe a way to build germs of applications A-finite f:(\C^{n},0) \rightarrow (\C^{p},0) for p=2n and p=2n-1. In the case p<2n-1, we conclude that there is no germ of reflection ...
Graduações e identidades polinomiais graduadas para a álgebra de matrizes triangulares superiores
(Universidade Federal de São Carlos, 2020-12-03)
Let F be a field and let G be a group. Denote by UTn(F) the algebra of n × n upper triangular matrices over F.
The mathematicians Valenti and Zaicev described all G-gradings on UTn(F), and the mathematicians Di Vincenzo, ...
Espectro do Laplaciano de Dirichlet-Neumann em faixas estreitas
(Universidade Federal de São Carlos, 2020-08-11)
Let $\Omega_\varepsilon$ be a thin strip in $\mathbb{R}^2$ and $-\Delta_{DN}^{\Omega_\varepsilon}$ the Dirichlet-Neumann Laplacian in $\Omega_\varepsilon$. In this work, we study the spectral problem of $-\Delta_{DN}^{\O ...
Sobre fibrados e poliedros de dimensão finita
(Universidade Federal de São Carlos, 2021-02-01)
The objective of this work is to establish the existence of universal bundles and to relate this existence to finite dimension polyhedra. As a consequence, we present examples of universal bundles for the case of classic groups.
Teoremas ergódicos para sistemas multívocos e aleatórios com aplicações a semifluxos generalizados
(Universidade Federal de São Carlos, 2021-02-05)
This work focuses on four major themes: semiflows; generalized semiflows; invariant measure for set-valued maps; and random dynamical systems.
The study of semiflows aims to understand the asymptotic behavior of solutions ...
Um princípio de tangência e aplicações
(Universidade Federal de São Carlos, 2021-12-17)
We present tools, such as a maximum principle for elliptic functions and properties of a-hyperbolic polynomials, to study a tangency principle between two hypersurfaces with r-mean curvatures of a Riemannian manifold, which ...
Categoria de Lusternik-Schnirelmann e aplicações
(Universidade Federal de São Carlos, 2022-02-14)
The Lusternik-Schnirelmann category associates a positive integer to each topological space. This number is an important invariant in algebraic topology, critical point theory and symplectic geometry. In this dissertation ...
Um estudo de valorizações transcendentes e algébricas via polinômios-chaves e pares minimais
(Universidade Federal de São Carlos, 2022-02-24)
The main goal of this work is to study transcendental valuations and algebraic valuations. To achieve this, we use some of the main objects in Valuation Theory, such as key polynomials, truncations and minimal pairs. These ...
Laplaciano de Dirichlet em faixas com cantos
(Universidade Federal de São Carlos, 2022-02-24)
Let $\Omega_\theta$ be an unbounded V-shaped set of the plane $\mathbb{R}^2$ , that is, a strip with a corner, and consider $ - \Delta^{D}_{\Omega_\theta}$ the Dirichlet Laplacian in $ \Omega_\theta$. In this work, we will ...
Operadores de Calderón-Zygmund e o Teorema T(1)
(Universidade Federal de São Carlos, 2021-05-26)
The purpose of this work is to present, in a detailed way, one of the main topics of Harmonic Analysis: the singular integral operators or, in its general form, the Calderón-Zygmund operators. We did here, for the most ...