Codensity monads are ubiquitous, as are various different notions of compactness and finiteness. Two such examples of "compact" spaces are compact Hausdorff Spaces and Linearly Compact Vector Spaces. Compact Hausdorff Spaces are the algebras of the codensity monad induced by the inclusion of finite sets in the category of sets. Similarly linearly compact vector spaces are the algebras of the codensity monad induced by the inclusion of finite dimensional vector spaces in the category of vector spaces. So in these two examples the notions of finiteness, compactness and codensity are intertwined. In this thesis we generalise these results. To do this we generalise the notion of ultrafilter, and follow the intuition of the compact Hausdorff case. We give definitions of general notions of "finiteness" and "compactness" and show that the algebras for the codensity monad induced by the "finite" objects are exactly the "compact" objects.

Seja (X; t) um espaço topológico e seja F a família de todos os subconjuntos de X que satisfazem uma propriedade topológica dada P (invariante por homeomorfismos). Se acrescentarmos abertos novos à topologia e se F\' é a família de todos os subconjuntos do novo espaço que satisfazem a propriedade P, podemos ter que F ≠ F\'. Se isto sempre acontece, dizemos que o espaço (X; t) é maximal com respeito à família F. Neste trabalho estudaremos os espaços topológicos maximais com respeito a algumas famílias de subconjuntos: discretos, compactos, densos, conexos e das sequências convergentes. / Let (X; t) be a topological space and let F be the family of all subsets of X that satisfy a given topological property P (invariant under homeomorphisms). If we add new open sets to the topology and if F\' is the family of all subsets of the new space which satisfy the property P, we can have F ≠ F\'. If this is always the case, we say that (X; t) is maximal with respect to the family F. We show here some characterizations of maximal spaces with respect to the family of some of its subsets: compacts, dense, discrete and convergent sequences.

This thesis presents a simple method for the concurrent manipulation of linearly ordered data structures on hypercubes. The method is based on the existence of a pruned binomial search tree rooted at any arbitrary node of the binary hypercube. The tree spans any arbitrary sequence of n consecutive nodes containing the root, using a fan-out of at most [log₂ 𝑛] and a depth of [log₂ 𝑛] +1. Search trees spanning non-overlapping processor lists are formed using only local information, and can be used concurrently without contention problems. Thus, they can be used for performing broadcast and merge operations simultaneously on sets with non-uniform sizes. Extensions to generalized and faulty hypercubes and applications to image processing algorithms and for m-way search are discussed.

The development of communications technologies has led to an ever-increasing requirement for a wider bandwidth of microwave signal processing systems. To overcome the inherent electronic speed limitations, photonic techniques have been developed for the processing of ultra-broadband microwave signals. A dispersive delay line (DDL) is able to introduce different time delays to different spectral components, which are used to implement signal processing functions, such as time reversal, time delay, dispersion compensation, Fourier transformation and pulse compression. An electrical DDL is usually implemented based on a surface acoustic wave (SAW) device or a synthesized C-sections microwave transmission line, with a bandwidth limited to a few GHz. However, an optical DDL can have a much wider bandwidth up to several THz. Hence, an optical DDL can be used for the processing of an ultra-broadband microwave signal. In this thesis, we will focus on using a DDL based on a linearly chirped fiber Bragg grating (LCFBG) for the processing of broadband microwave signals. Several signal processing functions are investigated in this thesis. 1) A broadband and precise microwave time reversal system using an LCFBG-based DDL is investigated. By working in conjunction with a polarization beam splitter, a wideband microwave waveform modulated on an optical pulse can be temporally reversed after the optical pulse is reflected by the LCFBG for three times thanks to the opposite dispersion coefficient of the LCFBG when the optical pulse is reflected from the opposite ends. A theoretical bandwidth as large as 273 GHz can be achieved for the time reversal. 2) Based on the microwave time reversal using an LCFBG-based DDL, a microwave photonic matched filter is implemented for simultaneously generating and compressing an arbitrary microwave waveform. A temporal convolution system for the calculation of real time convolution of two wideband microwave signals is demonstrated for the first time. 3) The dispersion of an LCFBG is determined by its physical length. To have a large dispersion coefficient while maintaining a short physical length, we can use an optical recirculating loop incorporating an LCFBG. By allowing a microwave waveform to travel in the recirculating loop multiple times, the microwave waveform will be dispersed by the LCFBG multiple times, and the equivalent dispersion will be multiple times as large as that of a single LCFBG. Based on this concept, a time-stretch microwave sampling system with a record stretching factor of 32 is developed. Thanks to the ultra-large dispersion, the system can be used for single-shot sampling of a signal with a bandwidth up to a THz. The study in using the recirculating loop for the stretching of a microwave waveform with a large stretching factor is also performed. 4) Based on the dispersive loop with an extremely large dispersion, a photonic microwave arbitrary waveform generation system is demonstrated with an increased the time-bandwidth product (TBWP). The dispersive loop is also used to achieve tunable time delays by controlling the number of round trips for the implementation of a photonic true time delay beamforming system.

Benzannulation to porphyrin 2,3 positions has previously been accomplished using various methodologies in the past century, yet there remain limited methodologies to both annulate to the porphyrin periphery and add functional moieties that can then be derivatized for diverse applications. This dissertation describes the development of synthetic routes and characterization of a variety of linearly-annulated, functionalized, β,β'-π-extended porphyrins. There are five chapters in this dissertation, the first of which introduces synthesis and properties of porphyrins and π-extended porphyrins. Chapter 2 describes synthesis of pentacenequinone-fused and pentacene-fused poprhyrins with distinct and new optical absorbance properties. In chapter 3, synthesis and characterization of benzimidazole-fused porphyrins displaying external metal binding capability is described. The synthetic method developed in chapter 3 is extended in chapter 4 to synthesis of bisbenzimidazole-fused porphyrin dimers that show split Soret character, likely due to excitonic coupling between porphyrins of the dimer. Chapter 5 summarizes this dissertation and describes future directions that this dissertation provides foundation for.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18297号 / 工博第3889号 / 新制||工||1597(附属図書館) / 31155 / 京都大学大学院工学研究科高分子化学専攻 / (主査)教授 赤木 和夫, 教授 山子 茂, 教授 秋吉 一成 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 0048 / 新制・論文博士 / 博士(理学) / 乙第13217号 / 論理博第1562号 / 新制||理||1638(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 永江 知文, 教授 鶴 剛, 准教授 成木 恵 / 学位規則第4条第2項該当 / Doctor of Science / Kyoto University / DFAM

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O problema de minimização com restrições lineares e importante, não apenas pelo problema em si, que surge em várias áreas, mas também por ser utilizado como subproblema para resolver problemas mais gerais de programação não-linear. GENLIN e um método eficiente para minimização com restrições lineares para problemas de pequeno e médio porte. Para que seja possível a implementação de um método similar para grande porte, é necessário ter um método eficiente, também para grande porte, para projeção de pontos no conjunto de restrições lineares. O problema de projeção em um conjunto de restrições lineares pode ser escrito como um problema de programação quadrática convexa. Neste trabalho, estudamos e implementamos métodos esparsos para resolução de problemas de programação quadrática convexa apenas com restrições de caixa, em particular o clássico método Moré-Toraldo e o \"método\" NQC. O método Moré-Toraldo usa o método dos Gradientes Conjugados para explorar a face da região factível definida pela iteração atual, e o método do Gradiente Projetado para mudar de face. O \"método\" NQC usa o método do Gradiente Espectral Projetado para definir em que face trabalhar, e o método de Newton para calcular o minimizador da quadrática reduzida a esta face. Utilizamos os métodos esparsos Moré-Toraldo e NQC para resolver o problema de projeção de GENLIN e comparamos seus desempenhos / The linearly constrained minimization problem is important, not only for the problem itself, that arises in several areas, but because it is used as a subproblem in order to solve more general nonlinear programming problems. GENLIN is an efficient method for solving small and medium scaled linearly constrained minimization problems. To implement a similar method to solve large scale problems, it is necessary to have an efficient method to solve sparse projection problems onto linear constraints. The problem of projecting a point onto a set of linear constraints can be written as a convex quadratic programming problem. In this work, we study and implement sparse methods to solve box constrained convex quadratic programming problems, in particular the classical Moré-Toraldo method and the NQC \"method\". The Moré-Toraldo method uses the Conjugate Gradient method to explore the face of the feasible region defined by the current iterate, and the Projected Gradient method to move to a different face. The NQC \"method\" uses the Spectral Projected Gradient method to define the face in which it is going to work, and the Newton method to calculate the minimizer of the quadratic function reduced to this face. We used the sparse methods Moré-Toraldo and NQC to solve the projection problem of GENLIN and we compared their performances

A 50 MHz Frequency Modulated Continuous Wave (FMCW) radar system, developed at the University of Saskatchewan to provide improved spatial and temporal resolution measurements of auroral E-region plasma processes, introduces ambiguous spectral information, due to spectral ghosting, for scattering events in which multiple radar echoes are detected. This thesis identifies two Linearly Frequency Modulated (LFM) radar waveforms used by the FMCW system as the source of the ghosting. An analysis procedure designed to counteract the spectral ghosting problem is developed but is not an ideal solution, and therefore replacement of the LFM waveforms is recommended.<p> A detailed investigation of alternative radar waveforms using the Ambiguity Function and Ambiguity Diagram techniques is performed. A frequency coded continuous wave radar waveform based on a composite Costas sequence is proposed as a successor to the LFM waveforms. The composite Costas radar waveform will conserve the spatial and temporal resolutions extended by the LFM waveforms and preclude any spectral ghosting. Implementing the proposed radar waveform and avoiding receiver saturation issues with the mono-static FMCW radar system in which both the transmitting and receiving antenna arrays are simultaneously and continuously active and geographically co-located is also discussed.<p> In addition to this, two 50 MHz backscatter events are presented in this thesis to demonstrate the effectiveness of the FMCW system, notwithstanding the spectral ghosting complication. The first event from November 21, 2009 is identified as a Type 1 instability and the second from September 13, 2009 is identified as a Type 2 instability which lasted for ~ 16 minutes. Linear plasma fluid theory is used to provide a brief interpretation of both scattering events.