We establish a strong connection between buildings and Hecke algebras through the study of two algebras of averaging operators on buildings. To each locally finite regular building we associate a natural algebra B of chamber set averaging operators, and when the building is affine we also define an algebra A of vertex set averaging operators. In the affine case, it is shown how the building gives rise to a combinatorial and geometric description of the Macdonald spherical functions, and of the centers of affine Hecke algebras. The algebra homomorphisms from A into the complex numbers are studied, and some associated spherical harmonic analysis is conducted. This generalises known results concerning spherical functions on groups of p-adic type. As an application of this spherical harmonic analysis we prove a local limit theorem for radial random walks on affine buildings.

Based on a Ph.D. thesis in the Dept. of Electrical Engineering, 1965. / Bibliography: p. 67.

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Pulse-width modulation methods are widely used for the synthesis of ac voltages at the terminals of a voltage-sourced converter (VSC). Traditionally sinusoidal pulsewidth modulation (SPWM) has been used. A powerful alternative for this purpose is space-vector modulation (SVM), in which the converter is placed in a finite number of states in order to best approximate the reference voltage. This method offers better utilization of the dc bus voltage and provides several degrees of freedom for enhancement of the harmonic spectrum as well as switching losses. This thesis studies the SVM method for two- and three-level VSCs. A model for implementation of SVM in the electromagnetic transients simulation program PSCAD/EMTDC is developed. The model is able to generate firing pulses in linear as well as overmodulation range and is used to study the performance of different SVM strategies in terms of their harmonic spectra and associated converter and harmonic losses. The model is also used to demonstrate the suitability of the method for network applications. The thesis also employs genetic algorithms to find an optimized SVM sequence for improved harmonic performance. An objective function is defined that seeks to minimize the most significant harmonic components of the generated waveform, while keeping the other harmonic components within the acceptable range outlined in the available standards. The obtained sequence shows great improvement over the conventionally-used SVM sequence. / October 2007

This thesis develops the theory of operator algebras from the perspective of abstract harmonic analysis, and in particular, the theory of von Neumann algebras. Results from operator algebras are applied to the study of spaces of coefficient functions of unitary representations of locally compact groups, and in particular, the Fourier algebra of a locally compact group. The final result, which requires most of the material developed in earlier sections, is that the group von Neumann algebra of a locally compact group is in standard form.

This thesis develops the theory of operator algebras from the perspective of abstract harmonic analysis, and in particular, the theory of von Neumann algebras. Results from operator algebras are applied to the study of spaces of coefficient functions of unitary representations of locally compact groups, and in particular, the Fourier algebra of a locally compact group. The final result, which requires most of the material developed in earlier sections, is that the group von Neumann algebra of a locally compact group is in standard form.

¡@¡@The impacts of global warming and climate change were the important issue in the last few decades. The sea level rising was one of most discussion topics of physical impact which derived from global warming. In this study, about forty year¡¦s sea level records (from Harbor & Marine Technology Center) were used to analysis the long term water level trends at Keelung Harbor, Taichung Harbor and Kaohsiung Harbor in the western Taiwan. ¡@¡@We rearranged the records format, filtered out error data, and then sorted the data by the logged time. Three kinds of analysis method were applied to investigate the trend of water level change. The first one was harmonic analysis which was used to eliminate the effects of astronomical tide. The second method was spectrum analysis and it assisted to obtain the amplitudes and phases of tidal component. Finally, we used the moving average method to smooth data and discussed the tendency of water level change. ¡@¡@The result showed no evidence of sea level rising along the western coast of Taiwan. The average water level raised and declined evenly in the duration of forty years, and the general trends of water level varied near the zero level. The result also showed the variation of water level that affected by the measurement instruments was more over the physical effects.

In the design and plan of the coast engineering, long-term and continual tidal database represent the indispensable role. This paper collect the tidal database, their locations include the ocean around the Taiwan and the South China Sea. Use the artificial neural networks (ANN) to build model and find the relationship between neighbor tidal observation stations. There are many reasons to cause the tide phenomenon, include the tide generating force, season, coastal geography, geography of sea floor, resonance of gulf or estuary, change depth of sea, and so on, it will be determined by local environment. The tide analysis and prediction usually use the harmonic analysis method. This method need long-term and continual tidal record, and the theory depend on the tide generating force, it has limit about accuracy. The application of artificial neural networks is used in nonlinear science problems in general cases. The back propagation (BP) networks is the one model of the artificial neural networks, this paper use ANN-BP model to build the relationship from different tide observed stations, and verify the quality of model. From the result of verified models, the ANN-BP model can predict and supplement the tide record very well. The items of research include: ¡i1¡j the relationship between two neighbor tide observed stations. (one station input, one station output) ¡i2¡jthe relationship between three neighbor tide observed stations. (two station input, one station output) ¡i3¡j input several tide observed stations and output one station. ¡i4¡j the correlation of connected weight and threshold between different models. ¡i5¡j change the parameters of ANN-BP model and discus the affect of model¡¦s quality. ¡i6¡j application of truly case. From the result of this paper, in the design and plan of the coast engineering, the long-term tide observed record can be predict from the ANN-BP model and tide record of neighbor observed stations. When the tide record has miss or lost cause by machine or other reasons, the ANN-BP model can supplement the lost tide record well. This paper show the ANN-BP model can be apply to predict and supplement the tide record very well, and will be possible applied method.

This thesis addresses four topics in the area of applied harmonic analysis. First, we show that the affine densities of separable wavelet frames affect the frame properties. In particular, we describe a new relationship between the affine densities, frame bounds and weighted admissibility constants of the mother wavelets of pairs of separable wavelet frames. This result is also extended to wavelet frame sequences. Second, we consider affine pseudodifferential operators, generalizations of pseudodifferential operators that model wideband wireless communication channels. We find two classes of Banach spaces, characterized by wavelet and ridgelet transforms, so that inclusion of the kernel and symbol in appropriate spaces ensures the operator is Schatten p-class. Third, we examine the Schatten class properties of pseudodifferential operators. Using Gabor frame techniques, we show that if the kernel of a pseudodifferential operator lies in a particular mixed modulation space, then the operator is Schatten p-class. This result improves existing theorems and is sharp in the sense that larger mixed modulation spaces yield operators that are not Schatten class. The implications of this result for the Kohn-Nirenberg symbol of a pseudodifferential operator are also described. Lastly, Fourier integral operators are analyzed with Gabor frame techniques. We show that, given a certain smoothness in the phase function of a Fourier integral operator, the inclusion of the symbol in appropriate mixed modulation spaces is sufficient to guarantee that the operator is Schatten p-class.

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