Geometria e topologia das superfícies através de recorte e colagem

Pós-graduação em Matemática Universitária - IGCE

Topological K-classification of finitely determined map germs

We consider smooth finitely C 0-K-determined map germs f: (ℝn, 0) → (ℝp, 0) and we look at the classification under C 0-K-equivalence. The main tool is the homotopy type of the link, which is obtained by intersecting the image of f with a small enough sphere centered at the origin. When f -1(0) = {0}, the link is a smooth map between spheres and f is C 0-K-equivalent to the cone of its link. When f -1(0) ≠ {0}, we consider a link diagram, which contains some extra information, but again f is C 0-K-equivalent to the generalized cone. As a consequence, we deduce some known results due to Nishimura (for n = p) or the first named author (for n < p). We also prove some new results of the same nature. © 2012 Springer Science+Business Media Dordrecht.

The use of classification methods for modeling the antioxidant activity of flavonoid compounds

A study using two classification methods (SDA and SIMCA) was carried out in this work with the aim of investigating the relationship between the structure of flavonoid compounds and their free-radical-scavenging ability. In this work, we report the use of chemometric methods (SDA and SIMCA) able to select the most relevant variables (steric, electronic, and topological) responsible for this ability. The results obtained with the SDA and SIMCA methods agree perfectly with our previous model, in which we used other chemometric methods (PCA, HCA and KNN) and are also corroborated with experimental results from the literature. This is a strong indication of how reliable the selection of variables is.