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Compactly-supported and relative integration in differential cohomology
(Universidade Federal de São Carlos, 2022-04-11)
In this work, we have constructed more general versions of differential integration maps
in differential cohomology theories. Among the obtained versions we can mention the
integration with compact supports, the integration ...
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. ...
Identidades polinomiais graduadas para a álgebra das matrizes triangulares superiores sobre um corpo finito
(Universidade Federal de São Carlos, 2021-12-14)
Let K be a field of characteristic p and let UTn = UTn(K) be the algebra of n x n upper triangular matrices over K with the usual product a . b of the elements a,b ∈ UTn. In this thesis we describe the set of all G-graded ...
Ações de Z2k com o conjunto de pontos fixos conexo e a propriedade CP
(Universidade Federal de São Carlos, 2021-10-27)
It is well known that if $\phi:G \times M^m \rightarrow M^m$ is a smooth action of a compact Lie group on a closed smooth manifold, then its fixed point set $F_{\phi} = \bigcup\limits_{i=0}^{n}F^{i}$ is a disjoint union ...
Differential cohomology on maps of pairs and relative-parallel product
(Universidade Federal de São Carlos, 2021-10-06)
In this thesis, we study three important topics. The first one provides an axiomatic framework to differential cohomology on maps of pairs of topological spaces, introducing the product between relative and parallel classes. ...
Extensões H-cleft distinguidas por H-identidades polinomiais
(Universidade Federal de São Carlos, 2022-05-27)
Our main object of study is the well-known question asking whether the set of polynomials identities distinguishes PI-algebras up to isomorphism. Let k be an algebraically closed field of characteristic 0 and H a non-semisimple ...
Applications of topological degree theory to generalized ODEs
(Universidade Federal de São Carlos, 2019-10-27)
In this work, we present original results concerning the theory of Generalized Ordinary Differential Equations (we write generalized ODEs for short) using tools from the Topological Degree theory. In particular, we proved ...
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 ...
Classificação de centros Hamiltonianos polinomiais biquadrados, e isocronicidade trivial versus formas canônicas para aplicações polinomiais no plano de Jacobiano unitário
(Universidade Federal de São Carlos, 2022-10-10)
This work, we classify a non- degenerate center at the origin of a planar Hamiltonian system associated to a function of the form $H(x,y)=A(x)+B(x)y^2 + C(x)y^4$, where $A$, $B$ and $C$ are polynomials. After seing a ...