Thesis (Ph.D.)--Baylor University, 2009. / Includes bibliographical references (p. 66-68).

The aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the so-called free mappings, a powerful tool for factorization of a wide class of abelian and non-abelian groups. By applying a certain group action on the blocks of a factorization, a number of combinatorial and computational problems were noted and studied. In particular, we analyze the case of the group Aut(Zn) acting on blocks of factorization of Zn. We present new theoretical facts that reveal the numerical structure of the stabilizer of a set in Zn, under the action of Aut(Zn). New algorithms for finding the stabilizer of a set and checking whether two sets belong to the same orbit are proposed. / by Vladimir Bozovic. / Thesis (Ph.D.)--Florida Atlantic University, 2008. / Includes bibliography. / Electronic reproduction. Boca Raton, FL : 2008 Mode of access: World Wide Web.

This dissertation contains results of the candidate's research on the generalized discrete logarithm problem (GDLP) and its applications to cryptology, in non-abelian groups. The projective special linear groups PSL(2; p), where p is a prime, represented by matrices over the eld of order p, are investigated as potential candidates for implementation of the GDLP. Our results show that the GDLP with respect to specic pairs of PSL(2; p) generators is weak. In such cases the groups PSL(2; p) are not good candidates for cryptographic applications which rely on the hardness of the GDLP. Results are presented on generalizing existing cryptographic primitives and protocols based on the hardness of the GDLP in non-abelian groups. A special instance of a cryptographic primitive dened over the groups SL(2; 2n), the Tillich-Zemor hash function, has been cryptanalyzed. In particular, an algorithm for constructing collisions of short length for any input parameter is presented. A series of mathematical results are developed to support the algorithm and to prove existence of short collisions. / by Ivana Iliâc. / Thesis (Ph.D.)--Florida Atlantic University, 2010. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web. FboU

Our research is focused on mapping binary sequences to permutation sequences. It is established that an upper bound on the sum of the Hamming distance for all mappings exists, and this sum is used as a criterion to ascertain how good previously known mappings are. We further make use of permutation trellis codes to investigate the performance of certain permutation mappings in a power-line communications system, where background noise, narrow band noise and wide band noise are present. A new multilevel construction is presented next that maps binary sequences to permutation sequences, creating new mappings for which the sum of Hamming distances are greater than previous known mappings. It also proved that for certain lengths of sequences, the new construction can attain our new upper bound on the sum of Hamming distances. We further extend the multilevel construction by showing how it can be applied to other mappings, such as permutations with repeating symbols and mappings with nonbinary inputs. We also show that a subset of the new construction yields permutation sequences that are able to correct insertion and deletion errors as well. Finally, we show that long binary sequences, formed by concatenating the columns of binary permutation matrices, are subsets of the Levenshtein insertion/deletion correcting codes. / Prof. H. C. Ferreira

Orientador: Paulo Roberto Gardel Kurka / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-16T16:41:02Z (GMT). No. of bitstreams: 1 DiazEspinosa_CarlosAndres_M.pdf: 5130242 bytes, checksum: 334f37aa82bbde2c9ddbfe192baa7c48 (MD5) Previous issue date: 2010 / Resumo: O presente trabalho descreve uma técnica de navegação autônoma, utilizando imagens estereoscópicas de câmeras para estimar o movimento de um robô em um ambiente desconhecido. Um método de correlação de pontos em imagens unidimensionais é desenvolvido para a identificação de pontos homólogos de duas imagens em uma cena. Utilizam-se métodos de segmentação de bordas ou contornos para extrair as principais características inerentes nas imagens. Constrói-se um mapa de profundidade dos pontos da imagem com maior similitude dentre os objetos visíveis no ambiente, utilizando um processo de triangulação. Finalmente a estimação do movimento bidimensional do robô é calculada aproveitando a relação epipolar entre dois ou mais pontos em pares de imagens. Experimentos realizados em ambientes virtuais e testes práticos verificam a viabilidade e robustez dos métodos em aplicações de navegação robótica / Abstract: The present work describes a technique for autonomous navigation using stereoscopic camera images to estimate the movement of a robot in an unknown environment. A onedimensional image point correlation method is developed for the identification of similar image points of a scene. Boundary or contour segments are used to extract the principal characteristics of the images. A depth map is built for the points with grater similarity, among the scene objects depicted, using a triangulation process. Finally, the bi-dimensional movement of a robot is estimated through epipolar relations between two or more correlated points in pairs of images. Virtual ambient and practical robot tests are preformed to evaluate the viability of employment and robustness of the proposed techniques / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica