published_or_final_version / Mathematics / Master / Master of Philosophy

PART I. A modified Hadamard transform has been developed and applied to the analysis of biologically active species using capillary electrophoresis. Hadamard transformations, a matrix based multiplexing technique, when coupled with a capillary electrophoresis instrument capable of rapid sample injection, provides a means to semi-continuously inject samples. The multiple injections separate, interpenetrate, and are detected as the summation of the multiple injections. Deconvolution of the multiplexed signal by multiplication with the inverse of the injection matrix yields a single injection electropherogram that exhibits improved S/N. In modified Hadamard transform capillary electrophoresis (mHTCE), an injection sequence of half the length as conventional HTCE (cHTCE) is utilized. Modifying the manner in which the raw data is manipulated before deconvolution facilitates the reduced injection sequence. When coupled with software, mHTCE can reduce the collection time for a Hadamard sequence by up to 48%. The substantial time reduction afforded by mHTCE is utilized to demonstrate the first time-resolved application of Hadamard transformations for the analysis of neurotransmitters. Additionally, mHTCE has been demonstrated as a means to improve the sensitivity for analysis of amino acids and proteins including gamma-aminobutyric acid, dopamine, and enhanced green fluorescent protein (EGFP) with picomolar detection limits.Part II. Two-photon excitation provides a means to activate chemical and physical processes with high spatial resolution and improved depth penetration compared to one-photon excitation. When combined with three-dimensional lithographic microfabrication (3DLM), these advantages provide a means to fabricate complex structures through radical and cationic two-photon induced polymerization (TPIP). A strategy for realizing high-fidelity microstructures is reported that considers the inherent structural limitations of acrylate monomers. Utilizing this strategy, a series of high-fidelity microstructures is reported for application in microfluidic devices, microelectromechanical systems (MEMS), and microoptical devices such as photonic bandgap (PBG) crystals. Improved periodicity is reported here for f.c.c. PBG crystals compared to earlier examples through addition of micromechanical supports that provide increased strength to the high-aspect ratio crystals. To extend TPIP to cationic polymerization, a series of two-photon activatable photoacid generators has been developed. The new PAGs exhibit one to two orders of magnitude lower polymerization threshold intensities than conventional ultraviolet-sensitive initiators.

Our main aim in this thesis is to produce new T-matrices from the set of existing T-matrices. In Theorem 4.3 a multiplication method is introduced to generate new T-matrices of order st, provided that there are some specially structured T-matrices of orders s and t. A class of properly amicable and double disjoint T-matrices are introduced. A number of properly amicable T-matrices are constructed which includes 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 18, 22. To keep the new matrices disjoint an extra condition is imposed on one set of T-matrices and named double disjoint T-matrices. It is shown that there are some T-matrices that are both double disjoint and properly amicable. Using these matrices an infinite family of new T-matrices are constructed. We then turn our attention to the application of T-matrices to construct orthogonal designs and complex Hadamard matrices. Using T-matrices some orthogonal designs constructed from 16 circulant matrices are constructed. It is known that having T-matrices of order t and orthogonal designs constructible from 16 circulant matrices lead to an infinite family of orthogonal designs. Using amicable T-matrices some complex Hadamard matrices are shown to exist. / iii, 49 leaves ; 29 cm

Thesis (M. Phil.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 35-36).

Techn. Hochsch., Diss., 2001--Aachen.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Engenharia Elétrica. / Made available in DSpace on 2012-10-22T12:58:31Z (GMT). No. of bitstreams: 1 234083.pdf: 4014648 bytes, checksum: ca9aba14dc03d197a335d5be935d9af1 (MD5) / Esta dissertação apresenta um estudo da aplicação da Transformada de Walsh-Hadamard (WHT) em diferentes sistemas OFDM. Os sistemas avaliados envolvem a transmissão sem fio entre uma antena transmissora e uma receptora (sistema SISO), e duas antenas transmissoras e uma receptora (sistema MISO Alamouti). A WHT espalha o sinal de informação antes de ser modulado no sistema OFDM. Conseqüentemente, os efeitos de desvanecimento provocados pelos canais correspondentes a cada subportadora OFDM também são espalhados, resultando em uma condição de desvanecimento médio destes canais. Isto leva a um aumento da robustez dos canais das subportadoras que mais sofreram com a transmissão puramente OFDM, mas degrada a condição de desvanecimento das mais robustas. Para verificar esta característica da WHT e o ganho de desempenho que ela possa impactar ao sistema OFDM, foram realizadas simulações com sistemas OFDM com e sem o uso da WHT. Assim, foi possível avaliar o desempenho desta técnica nos

Hadamard matrices are defined, and their basic properties outlined. A survey of historical and recent literature follows, in which a number of existence theorems are examined and given context. Finally, a new result for Hadamard matrices over $\Z_2$ is presented and given a graph-theoretic interpretation. / Master of Science

Neste trabalho estudaremos alguns resultados propostos por Benoit Kloe kner [Kl2] em sua tese de doutorado. Apresentamos prin ipalmente a prova da não-existência de compactificações diferenciáveis de Hadamard em espaços simétri os de tipo não- ompa to de posto k ≥ 2. / In this dissertation we will study some results proposed by Benoit Kloe kner [Kl2] in his do toral thesis. We mainly present the proof of non-existen e of diferentiable Hadamard compactific ations in symmetric spaces of non compact type of rank ≥ 2.

Neste trabalho estudaremos alguns resultados propostos por Benoit Kloe kner [Kl2] em sua tese de doutorado. Apresentamos prin ipalmente a prova da não-existência de compactificações diferenciáveis de Hadamard em espaços simétri os de tipo não- ompa to de posto k ≥ 2. / In this dissertation we will study some results proposed by Benoit Kloe kner [Kl2] in his do toral thesis. We mainly present the proof of non-existen e of diferentiable Hadamard compactific ations in symmetric spaces of non compact type of rank ≥ 2.

Neste trabalho estudaremos alguns resultados propostos por Benoit Kloe kner [Kl2] em sua tese de doutorado. Apresentamos prin ipalmente a prova da não-existência de compactificações diferenciáveis de Hadamard em espaços simétri os de tipo não- ompa to de posto k ≥ 2. / In this dissertation we will study some results proposed by Benoit Kloe kner [Kl2] in his do toral thesis. We mainly present the proof of non-existen e of diferentiable Hadamard compactific ations in symmetric spaces of non compact type of rank ≥ 2.