Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 2, 2009) Vita. Includes bibliographical references.

Thesis (doctoral)--Rheinischen Friedrich-Wilhelms-Universität, Bonn, 1980. / Includes bibliographical references (p. 252-258).

Thesis (Ph. D. in Mathematics)--Vanderbilt University, Aug. 2006. / Title from title screen. Includes bibliographical references.

No description available.

In recent years the field of real numbers expanded by a multiplicative subgroup has been studied extensively. In this thesis, the known results will be extended to expansions of the real field. I will consider the structure R consisting of the field of real numbers and an irrational power function. Using Schanuel conditions, I will give a first-order axiomatization of expansions of R by a dense multiplicative subgroup which is a subset of the real algebraic numbers. It will be shown that every definable set in such a structure is a boolean combination of existentially definable sets and that these structures have o-minimal open core. A proof will be given that the Schanuel conditions used in proving these statements hold for co-countably many real numbers. The results mentioned above will also be established for expansions of R by dense multiplicative subgroups which are closed under all power functions definable in R. In this case the results hold under the assumption that the Conjecture on intersection with tori is true. Finally, the structure consisting of R and the discrete multiplicative subgroup 2^{Z} will be analyzed. It will be shown that this structure is not model complete. Further I develop a connection between the theory of Diophantine approximation and this structure.

Orientador: Sergio Antonio Tozoni / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Cientifica / Made available in DSpace on 2018-08-18T00:43:47Z (GMT). No. of bitstreams: 1 Milare_GustavoHenrique_M.pdf: 1460238 bytes, checksum: e2c396949947fc2e7544f1c3b4a007fc (MD5) Previous issue date: 2011 / Resumo: As funções de Walsh formam um conjunto ortonormal completo de L2 [0; 1) que pode ser aplicado em diferentes situações tais como transmissão de dados, filtração, enriquecimento de imagem, análise de sinais e reconhecimento de padrão. Inicialmente estudamos alguns resultados básicos da Teoria dos Martingais, tais como a convergência de martingais, a Desigualdade de Doob e estimativas para a norma Lp da função quadrática associada a um martingal. Em seguida, estes resultados são usados no estudo da convergência das séries de Walsh em Lp e em um teorema de multiplicadores de séries de Walsh com a condição de Marcinkiewicz. Os resultados principais estudados nesta dissertação são estimativas de ordem de crescimento de entropia de operadores multiplicadores de séries de Walsh limitados de Lp em Lq / Abstract: The Walsh functions form a complete orthonormal set of functions of L2 [0; 1) which can be applied in different situations such as data transmission, filtering, image enhancement, signal analysis and patern recognition. Initially we study some basic results of the Theory of martingales, such as the convergence of martingales, Doob's inequality and estimatives for the Lp norm of the quadratic function associated to a martingale. Later, these results are used in the study of the convergence of the Walsh series in Lp and in a theorem of multipliers of Walsh series with Marcinkiewicz condition. The main results studied in this dissertation are estimatives of order of growth of entropy of limited multiplier operators of Walsh series from Lp to Lq / Mestrado / Analise / Mestre em Matemática

No description available.

This diploma thesis deals with a design modification of detection part of the laboratory instrument for measuring the topography of rough surfaces – laser goniometric scatterometer (SM II). Design modification is based on replacement of so far used detector instead for the detector of higher quality with better measurement parameters. The first part of the diploma thesis contains theoretical basics, which are necessary to understand the relationship between scalar diffraction theory and scattering measurements of monochromatic light. The emphasis is on the importance of choosing appropriate detection coordinates, which are affecting the aberrations of detected diffracted light. The practical part is dedicated to improving the sensitivity of the detection part of the scatterometer SM II that is used in The laboratory of coherence optics at IFE FME BUT. This part justifies the choice of the detector which predetermines both the use of optical elements and the overall design of the detection part as the goniometer.

Die vorliegende Arbeit ist der Untersuchung von Operatorfolgen gewidmet, die typischerweise bei der Anwendung von Approximationsverfahren auf stetige lineare Operatoren entstehen. Dabei stehen die Stabilität der Folgen sowie das asymptotische Verhalten gewisser Charakteristika wie Normen, Konditionszahlen, Fredholmeigenschaften und Pseudospektren im Mittelpunkt. Das Hauptaugenmerk liegt auf der Entwicklung der Theorie für Operatoren auf Banachräumen. Hierbei bildet ein dafür geeigneter Konvergenzbegriff, die sogenannte P-starke Konvergenz, den Ausgangspunkt, welcher das Studium der gewünschten Eigenschaften in einer erstaunlichen Allgemeinheit gestattet. Die erzielten Resultate kommen, neben einer Reihe weiterer Anwendungen, insbesondere für das Projektionsverfahren für banddominierte Operatoren zum Einsatz.