Thesis--Copenhagen.

Thesis (Ph. D.)--University of Wisconsin. 1965. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

In this dissertation we obtain integral representations for positive linear functionals on commutative algebras with involution and semigroups with involution. We prove Bochner and Plancherel type theorems for representations of positive functionals and show that, under some conditions, the Bochner and Plancherel representations are equivalent. We also consider the extension of positive linear functionals on a Banach algebra into a space of pseudoquotients and give under conditions in which the space of pseudoquotients can be identified with all Radon measures on the structure space. In the final chapter we consider a system of integrated Cauchy functional equations on a semigroup, which generalizes a result of Ressel and offers a different approach to the proof.

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Typescript, etc. / Digitized by Kansas State University Libraries

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.)--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.