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Três resultados de sistemas dinâmicos em dimensões baixas
(Universidade Federal de São Carlos, 2020-12-18)
This work contains three independent results that can be framed within the research
area named low-dimensional dynamics. The first result is a lower bound for the maximal
number of inseparable leaves of non-singular ...
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 ...
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 ...
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.
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 ...
Grupos de tranças de superfícies finitamente perfuradas e grupos cristalográficos
(Universidade Federal de São Carlos, 2020-12-07)
The link between braid groups on surfaces and crystallographic groups has become such an interesting topic. In the last years some advances were found in the studies of this relation, specially in the case of Artin braid ...
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 ...
Identidades polinomiais para a álgebra de Jordan das matrizes triangulares superiores 2x2
(Universidade Federal de São Carlos, 2021-10-28)
Let K be a field (finite or infinite) of char(K) ≠ 2, and let UTn = UTn(K) be the n x n upper triangular matrix algebra over K. If · is the usual product on UTn, then with the new product a ○ b = (1/2)(a·b + b·a), UTn ...