This study develops a method for analyzing jazz piano music, primarily focusing on the era 1935-1950. The method is based on axiomatic concepts of jazz harmony, such as the circle of fifths and root position harmonies. 7-10 motion between root and chordal seventh seems to be the driving force in jazz motion. The concept of tritone substitution leads to the idea of a harmonic level, i.e., a harmony's distance from the tonic. With this method in hand, various works of music are analyzed, illustrating that all harmonic motion can be labelled into one of three categories. The ultimate goal of this analytic method is to illustrate the fundamental harmonic line which serves as the harmonic framework from which the jazz composer builds.

This thesis treats Daniel Read's music analytically to establish style characteristics. Read's fuging tunes are examined for metric placement and structural occurrence of dissonance, and dissonance as text painting. Read's comments on dissonance are extracted from his tunebook introductions. A historical chapter includes the English origins of the fuging tune and its American heyday. The creative life of Daniel Read is discussed. This thesis contributes to knowledge of Read's role in the development of the New England Psalmody idiom. Specifically, this work illustrates the importance of understanding and analyzing Read's use of dissonance as a style determinant, showing that Read's dissonance treatment is an immediate and central characteristic of his compositional practice.

Dans cette thèse, on étudie les sous-groupes boréliens des groupes de Lie et leur dimension de Hausdorff. Si G est un groupe de Lie nilpotent connexe, on construit dans G des sous-groupes de dimension de Hausdorff arbitraire, tandis que si G est semisimple compact, on démontre que la dimension de Hausdorff d'un sous-groupe borélien strict de G ne peut pas être arbitrairement proche de celle de G. / Given a Lie group G, we investigate the possible Hausdorff dimensions for a measurable subgroup of G. If G is a connected nilpotent Lie group, we construct measurable subgroups of G having arbitrary Hausdorff dimension, whereas if G is compact semisimple, we show that a proper measurable subgroup of G cannot have Hausdorff dimension arbitrarily close to the dimension of G.

L'objectif général de cette thèse est d'analyser les processus de diffusion et les processus de réaction-diffusion dans plusieurs types de conditions non-idéales, et d'identifier dans quelle mesure ces conditions non idéales influencent la mobilité des particules et les réactions entre les molécules. Dans la première partie de la thèse, nous nous concentrons sur les effets de l'encombrement macromoléculaire sur la mobilité, ainsi élaborant une description des processus de diffusion dans des milieux densément peuplés. Tous les processus sont analysés à partir de la description microscopique du mouvement des agents individuels sous forme de marche aléatoire, tenant compte de l'espace occupé par les particules voisines. La deuxième partie de la thèse vise à caractériser le rôle de la géométrie de l'environnement et de la réactivité des corps qui y sont contenus sur la réaction entre des molécules sélectionnées. La théorie classique de Smoluchowski, formulée pour les réactions contrôlées par la diffusion dans un milieu dilué, est ainsi adaptée à des domaines arbitrairement décorés par des obstacles, dont certains réactifs, et l'équation stationnaire de diffusion est résolue avec des techniques d’analyse harmonique. Finalement, le calcul explicit de la constante de réaction et la dérivation des formules approximées sont utilisés pour étudier des applications biologiques et nano-technologiques. / The overall purpose of this thesis is to analyze diffusion processes and diffusion-reaction processes in different types of non-ideal conditions, and to identify to which extent these non-ideal conditions influence the mobility of particles and the rate of the reactions occurring between molecules. In the first part of the thesis we concentrate on the effects of macromolecular crowding on the mobility of the agents, providing therefore a description of various diffusion processes in densely populated media. All the processes are analyzed by modeling the dynamics of the single agents as microscopic stochastic processes that keep track of the macromolecular crowding. The second part of the thesis aims at characterizing the role of the environment’s geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) on the reaction between selected molecules. The Smoluchowski theory for diffusion influenced reactions is thus adapted to domains arbitrarily decorated with obstacles and reactive boundaries, and the stationary diffusion equation is explicitly solved through harmonic-based techniques. The explicit calculation of the reaction rate constant and the derivation of simple approximated formulas are used for investigating nano-technological applications and naturally occurring reactions.

Although the overall levels of harmonics in modern power supply systems are in most of the practical cases still below the prescribed tolerance limits and thresholds (e.g. these stipulated in [IEC 61000-3-2 and 61000-3-12]), the sources of harmonics are constantly increasing in numbers and are expected to increase even more in the future. Some of the examples of modern non-linear power electronic (PE) devices that are expected to be employed on a much wider scale in LV networks in the future include: light-emitting diode (LED) lamps, switched-mode power supplies (SMPS'), electric vehicle battery chargers (EVBCs) and photovoltaic inverters (PVIs), which are all analysed in this thesis. The thesis first reviews the conventional harmonic analysis methods, investigating their applicability to modern PE devices. After that, the two most widely used forms of harmonic models, i.e. component-based models (CBMs) and frequency-domain models (FDMs), are applied for modelling of the four abovementioned types of modern PE devices and their models are fully validated by measurements. The thesis next investigates the impact of supply voltage conditions and operating modes (e.g. low vs high operating powers) on the device characteristics and performance, using both measurements and developed CBMs and FDMs. The obtained results confirm that both supply conditions and operating modes have an impact on the characteristics of most of the considered PE devices, which is taken into account in the developed models and demonstrated on a number of case studies. As the next contribution, the thesis proposes new indices for the evaluation of current waveform distortions, allowing for a separate analysis of contributions of low and high frequency harmonics and interharmonics to the total waveform distortion of PE devices. As the modern PE devices are normally based on high-frequency switching converters or inverters, the impact of circuit topologies and control algorithms on their harmonic emission characteristics and performance is also investigated. Special attention is given to the operation of PE devices at low powers, when there is a significant increase of current waveform distortion, a substantial decrease of efficiency and power factors and when input ac current might lose its periodicity with the supply voltage frequency. This is analysed in detail for SMPS', resulting in the proposal of a new methodology ("operating cycle based method") for evaluating overall performance of PE devices across the entire range of operating powers. Finally, a novel and simple hybrid harmonic modelling technique, allowing for the use of both time-domain and frequency-domain models in the same simulation environment, is proposed and illustrated on the selected case studies. This is accompanied with a frequency-domain aggregation approach, which is applied in the thesis to investigate the impact of increasing numbers of different types of modern PE devices on the LV network. The implementation of the developed hybrid harmonic modelling approach and frequency-domain aggregation technique is demonstrated on the example of a typical (UK) urban generic LV distribution network and used for the analysis of different deployment levels of EVs and PVIs. The presented harmonic modelling framework for individual PE devices and, particularly, for their aggregate models, fills the gap in the existing literature on harmonic modelling and characterisation of modern PE devices, which is important for the correct evaluation of their harmonic interactions and analysis of the impact of their large-scale deployment on the overall network performance.

The presence of information and communication technologies in the field of energy is increasing every day. Smart grid subject which aims to increase the percentage of energy generation through renewable resources and to make consumers to be involved in grid actively, is gaining importance day by day. In order to provide an effcient and reliable operation of smart grid network, it is necessary to collect relevant parameters from network components via communication infrastructure and to evaluate collected information. Also, with the inclusion of distributed energy sources in the power lines, collection of relevant data becomes important in order to ensure the quality of power. In the scope of this study, to measure current parameters, two DSP based electronic circuits and necessary embedded software have been developed. Data acquisition card is a fixed device which is to be installed to a point on the power line to gather current value samples. By means of being fed through magnetic induction from the line, this part of the system could stay on-line permanently and this allows taking measurements on demand. Sampling of line current is performed through principle of magnetic induction from the line on current sensing instrument which is connected to data-acquisition part. Also by utilization of clamp-on instruments, cutting of energy lines is not needed. Samples received by control card over radio frequency or infrared communication, are evaluated with the help of Discrete Fourier Transform (DFT). Control card can show information about Root mean square (RMS) value and harmonic components of line current and total harmonics distortion (THD) on graphic LCD. Present state of the system was tested in LV and MV environments and shown to be used on distribution lines. The system presented in this study is open to improvements and suggestions to make the system to be able to work on high voltage lines are made.

In this work the methods of mode decomposition and Fourier analysis of quantum fields on curved spacetimes previously available mainly for the scalar fields on Friedman-Robertson-Walker spacetimes are extended to arbitrary vector fields on general spatially homogeneous spacetimes. This is done by developing a rigorous unified framework which incorporates mode decomposition, harmonic analysis and Fourier analysis. Explicit constructions are performed for a variety of situations arising in homogeneous cosmology. A number of results concerning classical and quantum fields known for very restricted situations are generalized to cover almost all cosmological models.

The main bulk of electric power systems use a three¿phase configuration with an alternating current flow. Pursuing the optimal performance of these networks and avoiding possible technical problems, it is preferred balanced operating conditions, i.e., the currents of all phases have the same magnitude and form a direct sequence with a phase of 120º. However, if several single¿phase loads (such as high speed traction systems) are present in these systems, the operating condition turns unbalanced, provoking an asymmetric voltage supply. This undesirable working condition can be avoided by the use of two reactances connected with the single-phase load using a triangle configuration, in such a way that the total current consumption turns out to be balanced. This approach is commonly known as Steinmetz circuit or symmetrizing circuit. Due to the reactances of the symmetrizing circuit, the connection of the circuit in an electric network changes the system frequency response, appearing new resonances of several types and presenting impedance values too small or too large. Moreover, the quantity of nonlinear loads (i.e., loads with consume nonsinusoidal currents, such as arc furnaces, power electronics devices like high-speed rail systems...) is increasing nowadays. The harmonic current injection by these charges may interact with the resonances caused by the Steinmetz circuit, resulting in a large harmonic distortion in voltage. The aim of this doctoral thesis is to analyze the presence of several types of resonances in order to avoid this problem. It is used a simplified scheme of a network in which the single¿phase load and the symmetrized circuit are connected. This system also encloses nonlinear loads that generate harmonic currents. This set is analyzed from the viewpoint of nonlinear loads and of the network for parallel and series resonance frequencies location, respectively. By obtaining these resonant frequencies and knowing the harmonic injection of nonlinear loads, the trouble of voltage supply distortion can be anticipated and avoided.

Sampling theory is an active field of research that spans a variety of disciplines from communication engineering to pure mathematics. Sampling theory provides the crucial connection between continuous and discrete representations of information that enables one store continuous signals as discrete, digital data with minimal error. It is this connection that allows communication engineers to realize many of our modern digital technologies including cell phones and compact disc players. This thesis focuses on certain non-Fourier generalizations of sampling theory and their applications. In particular, non-Fourier analogues of bandlimited functions and extensions of sampling theory to functions on curved manifolds are studied. New results in bandlimited function theory, sampling theory on curved manifolds, and the theory of self-adjoint extensions of symmetric operators are presented. Besides being of mathematical interest in itself, the research contained in this thesis has applications to quantum physics on curved space and could potentially lead to more efficient information storage methods in communication engineering.

Sampling theory is an active field of research that spans a variety of disciplines from communication engineering to pure mathematics. Sampling theory provides the crucial connection between continuous and discrete representations of information that enables one store continuous signals as discrete, digital data with minimal error. It is this connection that allows communication engineers to realize many of our modern digital technologies including cell phones and compact disc players. This thesis focuses on certain non-Fourier generalizations of sampling theory and their applications. In particular, non-Fourier analogues of bandlimited functions and extensions of sampling theory to functions on curved manifolds are studied. New results in bandlimited function theory, sampling theory on curved manifolds, and the theory of self-adjoint extensions of symmetric operators are presented. Besides being of mathematical interest in itself, the research contained in this thesis has applications to quantum physics on curved space and could potentially lead to more efficient information storage methods in communication engineering.