http://hdl.handle.net/10150/129652 Sun, 19 May 2013 01:24:23 GMT 2013-05-19T01:24:23Z http://arizona.openrepository.com:80/arizona/retrieve/313666/Dissertations.jpg http://hdl.handle.net/10150/129652 http://hdl.handle.net/10150/290700 Title: The c-function for affine Kac-Moody algebras Author: Dang, Son Xuan, 1964- Abstract: In this paper, we will first study the Harish-Chandra transform and the c-function for finite type Kac-Moody groups. The Harish-Chandra transform is essentially the Gelfand transform on L¹( K\G/K). From our point of view, the c-function arises as the Fourier transform of the diagonal distribution for Haar measures of K. A brief account of Kac-Moody algebras, especially affine Kac-Moody algebras, is also presented. Then we use a formula of Harish-Chandra for the c-function for finite type Kac-Moody groups to discuss the definition of the c-function for affine Kac-Moody algebras, especially the twisted affine Kac-Moody algebras. It turns out the c-function for an affine Kac-Moody algebra can be written as a product of trigonometric functions over the positive roots of the corresponding finite type Kac-Moody algebra. This finite type Kac-Moody algebra is the Lie algebra of a finite type Kac-Moody group G. Then the c-function can be thought as the Fourier transform of the diagonal distribution for a Haar type measure of G. For the affine Kac-Moody algebra of type A⁽¹⁾₁ , G is SL(2, C) and the measure is (trace(g* g))⁻³. This leads to the question of whether (trace( g* g))⁻ᵐ on SL(n, C) is that measure for the affine Kac-Moody algebra of type A⁽¹⁾(n-1). In the last part, for any positive integer l, the Harish-Chandra transform of (trace(g* g) ⁻⁽⁽ⁿ⁽ⁿ⁻¹⁾⁾/²⁾⁻¹ on SL(n, C) is calculated to check if the Fourier transform of the diagonal distribution for (trace(g* g) ⁻⁽⁽ⁿ⁽ⁿ⁻¹⁾⁾/²⁾⁻¹ is the c-function for the affine Kac-Moody algebra of type A⁽¹⁾(n-1). Mon, 01 Jan 1996 00:00:00 GMT http://hdl.handle.net/10150/290700 1996-01-01T00:00:00Z http://hdl.handle.net/10150/290699 Title: Dynamic neuronal ensembles: A new paradigm for learning Author: Vahie, Sankait, 1968- Abstract: This document presents a new paradigm for learning, based on an abstraction of the mechanisms found in biological neural networks. Biologically motivated neurons, referred to as Dynamic Neurons are connected together in a knowledge-bearing topology to create Dynamic Neuronal Ensembles. The neurons are developed by first identifying key mechanisms and analyzing their computational significance. These mechanisms are then incorporated into the implementation of the dynamic neurons that make up the dynamic neuronal ensemble. While almost all these mechanisms have been studied and incorporated into the development of models of biological neurons in isolation or as subgroups, a single model incorporating these mechanisms in their computationally abstract form has not been implemented and analyzed. The motivation for this research is two-fold. Firstly, to provide biologists with a modular, flexible tool, incorporating current state-of-the-art modeling and simulation capabilities for use in hypothesis testing, development and analysis. Conversely, to provide engineers with a new paradigm for the development of adaptable, evolutionary systems capable of learning in a dynamic environment. Preliminary results of an implementation of the DNE models in DEVS are presented. A biological model of the Snail Aplysia and an application of its behavioral functionality for engineering are also demonstrated. Mon, 01 Jan 1996 00:00:00 GMT http://hdl.handle.net/10150/290699 1996-01-01T00:00:00Z http://hdl.handle.net/10150/290698 Title: A three-dimensional mechanistic ozone transport model: Applications to midlatitude trends and 11-year variability Author: McCormack, John Patrick Abstract: Thirteen years of satellite-based total ozone measurements, extending from January 1979 through December 1991, are analyzed with a multiple regression statistical model to isolate the components of interannual variability associated with (1) linear trends and (2) the 11-year variation in solar ultraviolet irradiance. Lower stratospheric temperature and geopotential height data obtained from satellite- and ground-based sources are analyzed in similarly, providing a comprehensive assessment of the interannual variability in the lower stratosphere over the 1979-1991 period. The results of the statistical analyses indicate coherent variations in ozone, temperature, and geopotential height at extratropical latitudes in NH winter which are related to both the trend and solar-cycle components; the amplitudes of these variations exhibit pronounced spatial dependences. A three-dimensional mechanistic ozone transport model is used to describe the spatial distribution of total ozone in NH winter using observed lower stratospheric temperature and geopotential height fields. Application of this model on a year-to-year basis demonstrates that a large percentage of the observed interannual variability in the spatial distribution of total ozone is directly associated with changes in the dynamical structure of the lower stratosphere. The influence of dynamical variability on zonal mean total ozone is also investigated using an empirical approach. From the results of the observational and modeling studies, it is concluded that changes in the dynamics of the lower stratosphere over the 1979-1991 period have contributed significantly to the observed total ozone trends in the Northern Hemisphere. In contrast, the observed variability in total ozone associated with the 11-year solar cycle could not be explained in terms of a systematic variation in the dynamical forcing of the lower stratosphere in-phase with the 11-year cycle. Mon, 01 Jan 1996 00:00:00 GMT http://hdl.handle.net/10150/290698 1996-01-01T00:00:00Z http://hdl.handle.net/10150/290697 Title: Photostability of laser dyes in sol-gel-derived hosts Author: Suratwala, Tayyab Ishaq, 1970- Abstract: Improving the photostability of laser dyes within sol-gel derived hosts has been the focus of this study. To accomplish this, synthetic routes were established to incorporate laser dyes within various sol-gel matrices, the mechanisms of dye photodegradation were determined, and molecular engineering techniques were employed to improve the photostability of the dye doped sol-gel hosts. Various Coumarin (silylated and unsilylated) and Pyrromethene laser dyes were incorporated within sol-gel derived hosts ranging from SiO₂ xerogel films to SiO₂:PDMS Polyceram monoliths which were optically transparent, crack-free, and polishable. Processing parameters, such as the water content and the pre-hydrolysis of the silylated Coumarin dyes, greatly affected the degree of dye bonding. The chemical stability of the Pyrromethene laser dye was also greatly affected by processing parameters, such as the acid/base content. Both the Coumarin and Pyrromethene dyes were found to degrade by photo-oxidation processes. Therefore, it was expected that the photostability would improve by incorporating the dye molecules within molecular cages within the solid hosts, thereby preventing interactions of the dye with photo-reactive impurities such as oxygen. The photostability was found to improve using the following molecular engineering methods: (1) by covalently bonding the dye to the host matrix, where the photostability improvement was attributed to the greater probability of obtaining dye caging with the silylated dye; (2) by removing porosity within the host through control of sol-gel processing and composition, where the photostability improvement was attributed to the elimination of highly photo-reactive dyes located in the pores of the host; (3) by incorporating additives such as bases and hindered amine antioxidants which slowed the steps of the photodegradation process. The fluorescence photostability (fluorescence output intensity as a function of pump pulses) of the dye doped films and monoliths showed a characteristic behavior in the fluorescence output, signified by a rapid initial decay (attributed to dyes located within pores of the matrix) and then a slower long-term decay (attributed to photostable dye molecules located within SiO₂ cages). A model, which applied a Gaussian distribution of the photostabilities of the dye molecules, quantitatively described the observed photostability behavior of the dye doped samples. Mon, 01 Jan 1996 00:00:00 GMT http://hdl.handle.net/10150/290697 1996-01-01T00:00:00Z