On computing discriminants of subfields of ℚ (ζp r)

The conductor-discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal(ℚ(ζn)/ℚ), the discriminant of K can be obtained from H by computing the product of the conductors of all characters defined modulo n which are associated to K. By calculating these conductors explicitly, we derive a formula to compute the discriminant of any subfield of ℚ(ζpr), where p is an odd rime and r is a positive integer. © 2002 Elsevier Science USA.

Border detection in digital images: An approach by fuzzy numbers

The purpose of this paper is to introduce a new approach for edge detection in gray shaded images. The proposed approach is based on the fuzzy number theory. The idea is to deal with the uncertainties concerning the gray shades making up the image, and thus calculate the appropriateness of the pixels in relation to an homogeneous region around them. The pixels not belonging to the region are then classified as border pixels. The results have shown that the technique is simple, computationally efficient and with good results when compared with both the traditional border detectors and the fuzzy edge detectors. © 2007 IEEE.

Edge detection in digital images using fuzzy numbers

The purpose of this paper is to introduce a new approach for edge detection in grey shaded images. The proposed approach is based on the fuzzy number theory. The idea is to deal with the uncertainties concerning the grey shades making up the image and, thus, calculate the appropriateness of the pixels in relation to a homogeneous region around them. The pixels not belonging to the region are then classified as border pixels. The results have shown that the technique is simple, computationally efficient and with good results when compared with both the traditional border detectors and the fuzzy edge detectors. Copyright © 2009, Inderscience Publishers.

Two matrix-based lattice construction techniques

Let m and n be integers greater than 1. Given lattices A and B of dimensions m and n, respectively, a technique for constructing a lattice from them of dimension m+n-1 is introduced. Furthermore, if A and B possess bases satisfying certain conditions, then a second technique yields a lattice of dimension m+n-2. The relevant parameters of the new lattices are given in terms of the respective parameters of A,B, and a lattice C isometric to a sublattice of A and B. Denser sphere packings than previously known ones in dimensions 52, 68, 84, 248, 520, and 4098 are obtained. © 2012 Elsevier Inc. All rights reserved.

Reticulados modulares em espaços euclidianos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estudo da estabilidade a pequenas perturbações de sistemas elétricos multimáquinas com dispositivos FACTS do tipo SSSC e controladores suplementares (POD e PSS)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Sistemas dinâmicos finitos: Paciência Búlgara (Shift em partições e composições cíclicas)

Pós-graduação em Matemática - IBILCE

Discriminante de corpos de números

Pós-graduação em Matemática - IBILCE

Criptografia e curvas elípticas

Pós-graduação em Matemática Universitária - IGCE

Criptografia de chave pública, criptografia RSA

Pós-graduação em Matemática Universitária - IGCE

Um estudo sobre criptografia

Pós-graduação em Matemática Universitária - IGCE

Números primos e divisibilidade: estudo de propriedades

Pós-graduação em Matemática em Rede Nacional - IBILCE

Números transcedentes e de Liouville

Pós-graduação em Matemática em Rede Nacional - IBILCE

Corpos cujo condutor é potência de primo: caracterização e reticulados ideais associados

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Números primos: propriedades, aplicações e avanços

Pós-graduação em Matemática em Rede Nacional - IBILCE