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Merge trees decoradas e TDA
(Universidade Federal de São Carlos, 2023-08-10)
In this document, first we will introduce Persistance Homology and Category Theory basic concepts. Afterwards, we will develop the Merge Tree Theory which will be useful to keep track of connected components evolution of ...
Algumas aplicações de p-pontos
(Universidade Federal de São Carlos, 2023-08-24)
In this work we analyze the concept of \(p\)-points in \(\omega\) and its relation with forcing, in particular Sacks forcing and side-by-side Sacks forcing. With this we verify that the existence of \(p\)-points with ...
On the classification of two dimensional flows
(Universidade Federal de São Carlos, 2023-08-02)
Lawrence Markus, a well-known mathematician, published, in 1954, a strong result about classification of planar vector fields. Afterwards, Dean Arnold Neumann generalized such work for continuous flows, and the result ...
Teorema da esfera suave via fluxo de Ricci
(Universidade Federal de São Carlos, 2023-08-04)
The goal of this dissertation is the theoretical development of the Ricci flow, a differential equation over a family of Riemannian metrics on an arbitrary differentiable manifold, and its use in the proof of the so-called ...
Campos de Yang-Mills fracamente estáveis na esfera de dimensão quatro
(Universidade Federal de São Carlos, 2023-05-03)
In this work we made a quick study on some basic results related to Groups and Lie Algebras,
action of Groups and Fiber Bundles with the objective of defining connections in Principal Bundles
and, later, in Associated ...