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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 ...
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 ...
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 ...
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 ...
Boa postura analítica e Gevrey da “boa” equação de Boussinesq
(Universidade Federal de São Carlos, 2021-03-11)
In both the line and the circle, we shall to prove that the Cauchy problem for the ``good'' Boussinesq equation is locally well-posed in a class of Gevrey functions, which includes a class of analytic functions that can ...
Involuções fixando somas conexas de espaços projetivos e melhorias para o Five Halves Theorem quando Fix(T ) = F n ∪ F j
(Universidade Federal de São Carlos, 2022-12-06)
Let M m be a closed and smooth m-dimensional manifold, and T : M m → M m a smooth involution,
that is, a period 2 diffeomorphism defined on M m . It is well known the fact that the fixed point set
of T , F = {x ∈ M m |T ...
Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos
(Universidade Federal de São Carlos, 2022-08-24)
We started this work by reviewing an application of periodic quantum graph theory to model monolayer hexagonal materials with δ_a and δ_b parameters associated with the different types of atoms located in their vertices. ...
On the existence of free actions of the groups Z_2, S^1 and S^3 on some finitistic spaces and cohomology of orbit spaces
(Universidade Federal de São Carlos, 2021-12-16)
Let G be a compact Lie group and X be a finitistic space. If G acts continuously on X, we can construct the fibration
X \hookrightarrow X_{G} \arrow & B_{G}, (1)
called Borel fibration, where G\hookrightarrow ...
Identidades e polinômios centrais com involução para a álgebra de Grassmann e álgebra das matrizes triangulares de ordem 3
(Universidade Federal de São Carlos, 2020-11-30)
Let F be an infinite field of characteristic different from 2. In this thesis we will study the polynomial identities and central polynomials with involution for two important classes of algebras. More precisely, we describe ...