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Equisingularidades de funções definidas em ICIS e IDS
(Universidade Federal de São Carlos, 2020-03-10)
We study the equisingularity of a family of function germs $\{f_t\colon(X_t,0)\to (\mathbb{C},0)\}$, where $\{(X_t,0)\}$ is a family of $d$-dimensional isolated determinantal singularity. We define the $(d-1)$th polar ...
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 ...
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 ...
Extensões auto-adjuntas do operador de Schrödinger magnético em domínios com pouca regularidade
(Universidade Federal de São Carlos, 2020-02-20)
We find one parametrization of all self-adjoint extensions of the magnetic Schrödinger
operator, in a quasi-convex domain with compact boundary, and magnetic potentials
with low regularity. In this parametrization we use ...
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 ...
Espaços de Hardy radial
(Universidade Federal de São Carlos, 2020-02-06)
One presents in this work an atomic decomposition via radial atoms for distributions on subspace $\mathcal{H}^{p}_{rad}(\mathds{R}^{n})$ for $0 < p\leqslant 1$, of Hardy radial spaces $H_{rad}^{p}(\mathds{R}^{n}) \doteq ...
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.
Grafeno multicamadas através de grafos quânticos periódicos: cones de Dirac
(Universidade Federal de São Carlos, 2020-03-06)
We study the spectral characterization and Dirac cones, always through periodic quantum graphs, in three situations. Firstly, we model bidimensional honeycomb materials, for instance, Graphene and Boron Nitride. We consider ...