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Invariantes de singularidades em característica positiva
(Universidade Federal de São Carlos, 2020-03-30)
This dissertation mainly follows the works of \cite{Gr2} and \cite{Gr5}.
Considering $\mathbb{K}$ a field, algebraically closed with positive characteristic, we presented invariants of singularities in $\mathbb{K}[[\u ...
Teoria dos operadores integrais singulares
(Universidade Federal de São Carlos, 2020-04-28)
We present in this work some of the main results regarding the continuity in Lp and the definition almost everywhere of operators known as Singular Integrals, as well as some classic examples and applications. We have ...
Fluxo de curvatura média e self-shrinkers
(Universidade Federal de São Carlos, 2020-06-12)
Mean curvature flow is a geometric flow that rises when evolving a hipersurface in the direction of its normal vector field with velocity at each point equal to the mean curvature at the very same point. As it is an evolution ...
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 a metrizabilidade do espaço de R-lugares de um corpo de funções F com trdeg_R=1
(Universidade Federal de São Carlos, 2020-02-28)
The main purpose of this work is to study the metrizability of the space of R-places of a function field, with transcendence degree 1 over a real closed field. Specifically, we are going to present a necessary and sufficient ...
Atratores pullback para uma equação de difusão não autônoma com retardo
(Universidade Federal de São Carlos, 2020-03-12)
Our goal in this work is to study a nonautonomous parabolic differential equation. We are going to show some results about existence of pullback attractors for this type of problem and for the equation without the delay.
Symmetric and non-symmetric Jack Functions
(Universidade Federal de São Carlos, 2020-05-29)
The goal of this dissertation is to present the theory of Jack functions from the standpoint of algebraic combinatorics. The presentation of symmetric functions is largely centred on the first chapter of MacDonald's ...
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, ...
Dinâmica topológica do operador deslocamento com pesos
(Universidade Federal de São Carlos, 2020-04-20)
In the present work, we will do a study of linear dynamics of operators, focusing mainly on
the concepts of topological transitivity, hypercyclicity and chaoticity. At rst, we will deal
with non-linear dynamical systems ...
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 ...