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Orientador: Carina Alves / Banca: Marta Cilene Gadotti / Banca: Cintya Wink de Oliveira Benedito / Resumo: Este trabalho aborda conceitos básicos de Álgebra Linear e suas aplicações no desenvolvimento da Teoria de Códigos Corretores de Erros. O uso desta ferramenta matemática simpli ca a geração e a decodi cação dos códigos lineares. Destacamos também a importância de se trabalhar com este tema na educação básica / Abstract: The present work addresses basic concepts of Linear Algebra and its applications in the development of the Theory of Error Correcting Codes. The use of this mathematical tool simpli es the generation and decoding of linear codes. This dissertation also highlights the importance of working with this subject in high school / Mestre

Bibliography: p. 199-224. / xviii, 224 p. : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis reviews models of the simple cell receptive field profile (RFP) and its variation over the simple cell population, and uses artifical neural networks to investigate the multi-dimensional signal processing role of the RFP in the formation of a cortical representation of the visual image. / Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, 1994?

by T.E. Djaferis and S.K. Mitter. / Bibliography: p. 33. / "February 1979." / Supported by ERDA under Grant ERDA-E(49-18)-2087 NASA Grant NGL-22-009-124 Defense Advanced Research Projects Agency, Office of Naval Research Contract no. N0014-75-C-0661 Work Order 2095

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI/Dissertation Abstracts International.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 53). Also available in electronic version. Access restricted to campus users.

published_or_final_version / Mathematics / Master / Master of Philosophy

Please refer to the thesis for the abstract. / Thesis (Ph.D.)-University of Natal, Durban, 1998.

The aim of this dissertation is to describe the conjugacy classes and some of the ordinary irreducible characters of the nite general linear group GL(n, q); together with character tables of some of its subgroups. We study the structure of GL(n, q) and some of its important subgroups such as SL(n, q); UT(n, q); SUT(n, q); Z(GL(n, q)); Z(SL(n, q)); GL(n, q)0 ; SL(n, q)0 ; the Weyl group W and parabolic subgroups P : In addition, we also discuss the groups PGL(n, q); PSL(n, q) and the a ne group A (n, q); which are related to GL(n, q): The character tables of GL(2; q); SL(2; q); SUT(2; q) and UT(2; q) are constructed in this dissertation and examples in each case for q = 3 and q = 4 are supplied. A complete description for the conjugacy classes of GL(n, q) is given, where the theories of irreducible polynomials and partitions of i 2 f1; 2; ; ng form the atoms from where each conjugacy class of GL(n, q) is constructed. We give a special attention to some elements of GL(n, q); known as regular semisimple, where we count the number and orders of these elements. As an example we compute the conjugacy classes of GL(3; q): Characters of GL(n, q) appear in two series namely, principal and discrete series characters. The process of the parabolic induction is used to construct a large number of irreducible characters of GL(n, q) from characters of GL(n, q) for m < n: We study some particular characters such as Steinberg characters and cuspidal characters (characters of the discrete series). The latter ones are of particular interest since they form the atoms from where each character of GL(n, q) is constructed. These characters are parameterized in terms of the Galois orbits of non-decomposable characters of F q n: The values of the cuspidal characters on classes of GL(n, q) will be computed. We describe and list the full character table of GL(n, q): There exists a duality between the irreducible characters and conjugacy classes of GL(n, q); that is to each irreducible character, one can associate a conjugacy class of GL(n, q): Some aspects of this duality will be mentioned. / Thesis (M.Sc. (School of Mathematical Sciences)) - University of KwaZulu-Natal, Pietermaritzburg, 2008.

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