No description available.

No description available.

Random sampling is a technique which overcomes the alias problem in regular sampling. The randomization, however, destroys the symmetry property of the transform kernel of the discrete Fourier transform. Hence, when transforming a randomly sampled sequence to its frequency spectrum, the Fast Fourier transform cannot be applied and the computational complexity is N(^2). The objectives of this research project are (1) To devise sampling methods for random sampling such that computation may be reduced while the anti-alias property of random sampling is maintained : Two methods of inserting limited regularities into the randomized sampling grids are proposed. They are parallel additive random sampling and hybrid additive random sampling, both of which can save at least 75% of the multiplications required. The algorithms also lend themselves to the implementation by a multiprocessor system, which will further enhance the speed of the evaluation. (2) To study the auto-correlation sequence of a randomly sampled sequence as an alternative means to confirm its anti-alias property : The anti-alias property of the two proposed methods can be confirmed by using convolution in the frequency domain. However, the same conclusion is also reached by analysing in the spatial domain the auto-correlation of such sample sequences. A technique to evaluate the auto-correlation sequence of a randomly sampled sequence with a regular step size is proposed. The technique may also serve as an algorithm to convert a randomly sampled sequence to a regularly spaced sequence having a desired Nyquist frequency. (3) To provide a rapid spectral estimation using a coarse kernel : The approximate method proposed by Mason in 1980, which trades the accuracy for the speed of the computation, is introduced for making random sampling more attractive. (4) To suggest possible applications for random and pseudo-random sampling : To fully exploit its advantages, random sampling has been adopted in measurement Random sampling is a technique which overcomes the alias problem in regular sampling. The randomization, however, destroys the symmetry property of the transform kernel of the discrete Fourier transform. Hence, when transforming a randomly sampled sequence to its frequency spectrum, the Fast Fourier transform cannot be applied and the computational complexity is N"^. The objectives of this research project are (1) To devise sampling methods for random sampling such that computation may be reduced while the anti-alias property of random sampling is maintained : Two methods of inserting limited regularities into the randomized sampling grids are proposed. They are parallel additive random sampling and hybrid additive random sampling, both of which can save at least 75% , of the multiplications required. The algorithms also lend themselves to the implementation by a multiprocessor system, which will further enhance the speed of the evaluation. (2) To study the auto-correlation sequence of a randomly sampled sequence as an alternative means to confirm its anti-alias property : The anti-alias property of the two proposed methods can be confirmed by using convolution in the frequency domain. However, the same conclusion is also reached by analysing in the spatial domain the auto-correlation of such sample sequences. A technique to evaluate the auto-correlation sequence of a randomly sampled sequence with a regular step size is proposed. The technique may also serve as an algorithm to convert a randomly sampled sequence to a regularly spaced sequence having a desired Nyquist frequency. (3) To provide a rapid spectral estimation using a coarse kernel : The approximate method proposed by Mason in 1980, which trades the accuracy for the speed of the computation, is introduced for making random sampling more attractive. (4) To suggest possible applications for random and pseudo-random sampling : To fully exploit its advantages, random sampling has been adopted in measurement instruments where computing a spectrum is either minimal or not required. Such applications in instrumentation are easily found in the literature. In this thesis, two applications in digital signal processing are introduced. (5) To suggest an inverse transformation for random sampling so as to complete a two-way process and to broaden its scope of application. Apart from the above, a case study of realizing in a transputer network the prime factor algorithm with regular sampling is given in Chapter 2 and a rough estimation of the signal-to-noise ratio for a spectrum obtained from random sampling is found in Chapter 3. Although random sampling is alias-free, problems in computational complexity and noise prevent it from being adopted widely in engineering applications. In the conclusions, the criteria for adopting random sampling are put forward and the directions for its development are discussed.

No description available.

Este trabalho aplica metodologia de Wang (2003a, 2003b) para definir uma nova medida do produto de bancos brasileiros. Acredita-se que tal medida seja superior às comumente utilizadas na literatura por se tratar de uma variável de fluxo, incorporar os depósitos bancários de maneira teoricamente embasada e levar em consideração a exposição ao risco. Esta nova variável de produção é utilizada na estimação de fronteiras estocásticas de produção e custo para o setor bancário brasileiro, visando a mensurar sua eficiência técnica e econômica, assim como a magnitude de suas economias de escala. As fronteiras estimadas apresentam especificação dada pela forma funcional flexível de Fourier e incorporam variáveis determinantes da eficiência. Os resultados apontam para uma acentuada ineficiência do setor bancário, assim como para a ocorrência de retornos crescentes de escala. / This work applies the Wang (2003a, 2003b) methodology to define Brazilian banks\' output. It is believed that this new output measure is superior to the ones commonly used by the literature, since it treats output as a flow variable, provides a theoretical basis for defining the role of deposits and takes account of risk exposure in defining output. This new measure is applied to the estimation of stochastic production and cost frontiers for the Brazilian banking sector, aiming at measuring its technical and economic efficiency, and also the size of its scale economies. The frontiers follow a Fourier flexible functional form especification and incorporate efficiency determinants. The results point to the existence of high inneficiency in the banking industry, and also to the ocurrence of increasing returns to scale.

A apneia é um Distúrbio Respiratório do Sono com grande incidência, estimando-se que esteja presente em 13% dos homens e 6% das mulheres nos Estados Unidos. Correlacionados com a apoeia, estão a obesidade, a diabete mellitus e, principalmente, algumas doenças cardíacas. No Brasil ainda há poucas pesquisas, possivelmente pelo difícil acesso e pelo alto custo das Polissonografias. Neste trabalho são analisados alguns sinais de Polissonografia, como o Eletrocardiograma, a Saturação do Oxigênio no Sangue, o Flu.xo Respiratório e o Esforço Respiratório. Mostramos como a Transformada Wavelet Discreta e as Redes Nemais constituem ferramentas matemáticas computacionais que possibilitam a extração de características e a classificação, servindo de suporte ao diagnóstico utilizado at ualmente. / Apnea is a highly incident Sleep-Disordered Breathing, which a icts roughly 13% of men and 6% of the women in the USA. It is also found a few correlations with other diseases, like obesity, diabetes mellitus and, especially, certain cardiac diseases. In Brazil, there are few studies, possibly due to the di cult access and the cost of Polysomnography. In this study, we analyzed some signals of Polysomnography, as the electrocardiogram, the oxygen saturation, the respiratory ow and respiratory e ort. We show how the Discrete Wavelet Transform and Neural Network may be applied as computational mathematical tools that enable feature extraction and classi cation, serving to support the diagnosis currently used.

Neste trabalho foram estudados catalisadores heterogêneos para a reação de transesterificação e esterificação avaliando sua atividade catalítica. Sólidos impregnados em sílica e óxidos de hidrotalcita contendo cargas de Ba, Ca e Nb foram obtidos pelas técnicas de impregnação úmida e coprecipitação, respectivamente. NaOH e ureia foram utilizados como agente precipitantes na coprecipitação. A caracterização dos mesmos foi realizada através das técnicas tradicionais para o estado sólido, como Espectroscopia no Ultravioleta-visível (UV-vis), Espectroscopia por Infravermelho com Transformada de Fourier (IV), Difração de Raios-X (DRX) e Microscopia Eletrônica de Varredura (MEV). O requerimento de um cuidado especial na remoção de sódio em sólidos coprecipitados com NaOH foi observado. Os materiais contendo 25 e 35 % de BaO sobre a SiO2 apresentaram atividade para a reação de transesterificação, atingindo 93,5 e 87,0 % de conversão, respectivamente. No entanto, a presença de nitratos na análise de IV pode indicar uma tendência à lixiviação de espécies de Bário. O material obtido como Ca4MgAl apresentou conversão de 97,9 % em biodiesel, porém, há uma significativa contribuição da catálise homogênea, cerca de 22 %. / In this work we were studied heterogeneous catalysts for the reaction of transesterification and esterification evaluating its catalytic activity. Solid impregnated silica and hydrotalcite oxides containing loads of Ba, Ca and Nb were obtained by wet impregnation and coprecipitation techniques, respectively. NaOH and urea was used as precipitating agent in the coprecipitation. The characterization of these was carried out using traditional techniques to solid, such as Spectroscopy Ultraviolet-visible (UV-vis) Spectroscopy Infrared Fourier Transform (IV), X-Ray Diffraction (XRD) and Scanning Electron Microscopy (SEM). An application for a special care in sodium removal on solid co-precipitated with NaOH was observed. Materials containing 25 and 35 % BaO on SiO2 showed activity for the transesterification reaction, reaching 93,5 and 87,0 % conversion, respectively. However, the presence of nitrates in the IV analysis may indicate a tendency to leaching of barium species. The material obtained as Ca4MgAl showed 97,9 % conversion into biodiesel, however, there is a significant contribution of homogeneous catalysis, about 22 %.

Digitized by Kansas Correctional Industries

This thesis consists of two unrelated parts. In the first part of this thesis, we give explicit expressions for the Fourier coefficients of Eisenstein series E∗(z, s, χ) twisted by modular symbols ⟨γ, f⟩ in the case where the level of f is prime and equal to the conductor of the Dirichlet character χ. We obtain these expressions by computing the spectral decomposition of an automorphic function closely related to E∗(z, s, χ). We then give applications of these expressions. In particular, we evaluate sums such as Σχ(γ)⟨γ, f⟩, where the sum is over γ ∈ Γ∞\Γ0(N) with c^2 + d^2 < X, with c and d being the lower-left and lower-right entries of γ respectively. This parallels past work of Goldfeld, Petridis, and Risager, and we observe that these sums exhibit different amounts of cancellation than what one might expect. In the second part of this thesis, given an elliptic curve E and a point P in E(R), we investigate the distribution of the points nP as n varies over the integers, giving bounds on the x and y coordinates of nP and determining the natural density of integers n for which nP lies in an arbitrary open subset of {R}^2. Our proofs rely on a connection to classical topics in the theory of Diophantine approximation.

本論文給出了在鏡像對稱中對非拉格朗日A-膜的Fourier型的變換。 / SYZ構想斷言，鏡像對稱應該來自於一種在卡拉比-丘流形上逐纖維的Fourier-Mukai變換。在半平坦卡拉比-丘流形上的拉格朗日A-膜的情形下，這已經被實現。然而， Kapustin和Orlov指出，對於一些特殊的卡拉比-丘流形， A-膜範疇應該加上某些額外的物件。他們稱這些額外的物件為餘迷向A-膜。在半平坦卡拉比-丘流形的情況下，我們需要加入一些在每個纖維上是楊-米爾斯的A-膜以及B-膜。 / 我們首先推廣Nahm變換到環面上的楊-米爾斯叢。這也可以看作一種Fourier型的變換。然後我們在半平坦卡拉比-丘流形上實施逐纖維的這種Nahm變換。我們在一些半平坦卡拉比丘流形上構造了一些新的B-膜的例子。這些B-膜限制到每一個纖維環面上都是環面上的楊-米爾斯叢。並且我們驗證了在這種逐纖維的變換下，他們恰好就是Kapustin和Orlov所提出的餘迷向A 膜。 / This thesis gives the construction of Fourier type transformations in mirror symmetry for non-Lagrangian A-branes. / The SYZ proposal asserts that mirror symmetry should come from a fiberwise Fourier-Mukai transformation along torus fibrations on Calabi-Yau manifolds. This can be realized explicitly for Lagrangian A-branes in semi-flat case. However, Kapustin and Orlov pointed out that for certain Calabi-Yau manifolds some extra objects called coisotropic A-branes should be added into the category of A-branes. In semi-flat cases, we need to include A-and B-branes which are Yang-Mills along fibers. / We first generalize the Nahm transformation to Yang-Mills line bundles over tori which can also be regarded as a Fourier type transformation. Then we carry out a family version of this transformation for semi-flat Calabi-Yau manifolds. More precisely, we construct a new class of B-branes in semi-flat Calabi-Yau manifolds which are Yang-Mills line bundles when restricted to each fiber torus. And we show that this fiberwise transformation of these B-branes produce the coisotropic A-branes predicted by Kapustin and Orlov. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Zhang, Yi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 61-62). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Fourier-Mukai Transformation --- p.10 / Chapter 2.1 --- A torus case --- p.10 / Chapter 2.1.1 --- Moduli space of flat U(1) bundles over T --- p.11 / Chapter 2.1.2 --- Poincare line bundle P --- p.12 / Chapter 2.1.3 --- Definition of the Fourier-Mukai Transformation for a torus --- p.13 / Chapter 2.1.4 --- Some concrete computations --- p.14 / Chapter 2.2 --- Semi-flat Calabi-Yau case --- p.15 / Chapter 2.2.1 --- Semi-flat Calabi-Yau manifolds and semi-flat branes --- p.15 / Chapter 2.2.2 --- Fourier-Mukai transformation for semi-flat branes --- p.18 / Chapter 3 --- Coisotropic A-branes --- p.23 / Chapter 3.1 --- Why Lagrangian branes are not enough? --- p.23 / Chapter 3.2 --- An example --- p.27 / Chapter 4 --- Nahm transformation --- p.29 / Chapter 4.1 --- Spinor bundle and the Dirac operator --- p.30 / Chapter 4.1.1 --- Clifford algebra and spin group --- p.30 / Chapter 4.1.2 --- Spinor bundle --- p.33 / Chapter 4.1.3 --- Dirac operator --- p.36 / Chapter 4.2 --- Nahm transformation for a torus (T, g) --- p.38 / Chapter 4.3 --- Fourier-Mukai transformation for coisotropic A-branes --- p.53