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This dissertation follows the history of functional ideas and their pedagogy, illuminates with many examples the implementation of my updated system of Functional Analysis, and discusses the pedagogical implications that this updated system implies. The main goal is to update a system of labeling to be as pedagogically friendly as possible, in order to assist students and teachers of harmony to more easily and enjoyably learn, teach, and engage with common-practice tonal harmonic practice. Example syllabi, assignments, classroom demonstrations, and long projects are also included, and each aspect of the labeling is carefully discussed as it is presented. By surveying the history of functional thinking in music theory, we find that desire to analyze for function is not a new idea, and has been a goal of many theorists and harmony teachers for centuries. However, the current methods for instructing in function still leave students confused or baffled, as they struggle to match functional concepts to labels that do not exemplify their analysis goals and methods that insist on starting from tiny detail instead of coming from a more complete musical perspective. The elaboration of each detail of my Functional Analysis system shows how each part of Functional Analysis has been designed to help make harmonic analysis quicker, easier, more intuitive, and more personalized. The greater pedagogical implications on a larger scale involving courses and curricula are also covered, informed by my experience both as a teacher of today’s standard system and from teaching Functional Analysis in the classroom.

Hung Ling Yan Lincoln. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 87-88). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Preliminary --- p.10 / Chapter 2.1 --- Background in geometry --- p.10 / Chapter 2.2 --- Background in harmonic maps --- p.12 / Chapter 3 --- Lie Point Transformations and Symmetries --- p.16 / Chapter 3.1 --- Definition of symmetries --- p.16 / Chapter 3.2 --- Determine the Lie point symmetries of partial differential equations --- p.25 / Chapter 3.2.1 --- Second order differential equations --- p.26 / Chapter 4 --- Similarity Variables --- p.30 / Chapter 4.1 --- "Similarity variables and group-invariant, solutions" --- p.30 / Chapter 4.2 --- Reduction of number of variables of the partial differential equations --- p.34 / Chapter 4.2.1 --- Determine the similarity variables --- p.34 / Chapter 4.2.2 --- Procedure to reduce the number of variables of a system of partial differential equations --- p.36 / Chapter 5 --- Group Invariant Harmonic Maps --- p.38 / Chapter 5.1 --- Determine the Lie point symmetries of the harmonic map equations --- p.39 / Chapter 5.2 --- Reduction of harmonic map equations to ordinary differ- ential equations --- p.54 / Chapter 5.3 --- Solving the harmonic map system which has been reduced to ordinary differential equations --- p.62 / Chapter 5.3.1 --- Case 1 of Theorem 5.2.1 --- p.62 / Chapter 5.3.2 --- Case 2 of Theorem 5.2.1 --- p.66 / Chapter 5.3.3 --- Case 3 of Theorem 5.2.1 --- p.75 / Bibliography --- p.87

Yung Po-lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 62-64). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The basics of doubling measures --- p.7 / Chapter 2.1 --- Existence of doubling measures --- p.7 / Chapter 2.2 --- More examples of doubling measures --- p.16 / Chapter 3 --- Doubling of self-similar measures --- p.20 / Chapter 3.1 --- Open set condition and doubling --- p.24 / Chapter 3.2 --- Examples of doubling with OSC --- p.31 / Chapter 3.3 --- Bernoulli convolution and golden ratio --- p.41 / Chapter 4 --- Applications of doubling measures --- p.48 / Chapter 4.1 --- Singular integral operators --- p.48 / Chapter 4.2 --- Poincare inequalities and local Sobolev embedding --- p.56 / Chapter 4.3 --- Remarks --- p.60 / Bibliography --- p.62

Thesis (Ph.D.)--Boston University / This study presents a descriptive outline of the principal harmonic devices employed by Darius Millhard, Arthur Honegger, Francis Poulenc, Georges Auric, Germaine, Tailleferre, and Louis Durey. The emphasis is upon the particular techniques peculiar to each composer. In addition, all the characteristic mechanisms pertaining to the composer's harmonic idiom, per se, are isolated - i.e. technical analyses include those pertinent factors surrounding the usage of harmony as well as elements intrinsically peculiar to harmonic structure alone. The attempt is then made to relate the devices of the harmonic idiom to the significant movements in music at the time Les Six were producing most prolifically as a group. The role played by polyharmony, for example, in the trend towards privitism and divionism; or the relation of polymodalit to the general movement towards superposition, which was characteristic of the arts in the first quarter of the twentieth century. [TRUNCATED]

Thesis (Ph.D.)--University of Missouri-Columbia, 2006. / 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 (February 28, 2007) Vita. Includes bibliographical references.

In this thesis a transformer fault diagnosis system using probabilistic neural network (PNN) is proposed and implemented. Many artificial neural networks (ANN) have been proposed to deal with the transformer fault diagnosis. However, when dissolved gas records change, adaptation capability becomes a problem in ANN applications. PNN analyzes the dissolved gas contents in the oil-immersed transformer to identify various fault types. Numerical gas ratios of oil and cellulose decomposition were used to create the training examples. Retraining can also be done by adding new examples without any iteration. With diagnostic gas records, computer simulations were conducted to show the effectiveness of the proposed system. The Internet based power transformer monitoring system was also proposed in this thesis . LabVIEW was used to develop the Man-Machine Interface (MMI), and DataSocket tool was used to share the information on Internet. Application of the harmonic load flow based on the Equivalent- Current Injection was used to solve harmonic problems. There are two sub-models including the fundamental and harmonic frequency models. The standard Fourier analysis was used to deal with the harmonic loads to get injection currents. A passive filter was also developed to improve harmonics to satisfy restriction standards of the Taiwan Power Company.

This thesis is to investigate the power quality problems for KMRT system and to derive the optimal strategy to mitigate the harmonic distortion. The mathematical models of dc network which includes the TSS, 3rd track and VVVF Converters will be derived. Based on the power system network configuration, the operation schedule and annual ridership of KMRT system, the ac/dc load flow analysis is executed to find the power demand and current harmonic components for each TSS and each BSS. The harmonic load flow analysis is then performed to solve the voltage harmonic distortion. The optimal planning of harmonic filters will be derived so that the proper locations and years for the harmonic filters to be committed can be determined. The active filters and high pass filters as well as the band pass filters are all considered in the study to achieve the best cost effective for harmonic filter investment. This thesis will also to analyze in the stray current for mass transit system the mathematical models of TSS rectification stations, 3rd rail, running rail, the insulation resistances between running rail, MRT structure and grounding are included in the computer simulation. The variation of stray current for the peak and off peak operation of KMRT system over each study year is derived. The sensitivity analysis of stray current with respect to the insulation level of running rail is executed . The nearby public pipes of the MRT network will be used for the analysis of cathode corrosion due to the stray current. Different strategies to mitigate the stray current are investigated.