This thesis studies several problems dealing with weighted inequalities and vector-valued operators. A weight is a nonnegative locally integrable function, and weighted inequalities refers to studying a given operator's continuity from one weighted Lebesgue space to another. The case where the underlying measure of both Lebesgue spaces is given by the same weight is known as a one weight inequality and the case where the weights are different is called a two weight inequality. These types of inequalities appear naturally in harmonic analysis from attempts to extend classical results to function spaces where the underlying measure is not necessarily Lebesgue measure. For most operators from harmonic analysis, Muckenhoupt weights represent the class of weights for which a one weight inequality holds. Chapters II and III study questions involving these weights. In particular, Chapter II focuses on determining the sharp dependence of a vector-valued singular integral operator's norm on a Muckenhoupt weight's characteristic; we determine that the vector-valued operator recovers the scalar dependence. Chapter III presents material from a joint work with M. Lacey. Specifically, in this chapter we estimate the weak-type norms of a simple class of vector-valued operators, but are unable to obtain a sharp result. The final two chapters consider two weight inequalities. Chapter IV characterizes the two weight inequality for a subset of the vector-valued operators considered in Chapter III. The final chapter presents examples to argue there is no relationship between the Hilbert transform and the Hardy-Littlewood maximal operator in the two weight setting; the material is taken from a joint work with M. Reguera.

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Numerous approaches have been proposed in order to resolve the problems of current harmonics in electrical distribution systems. The rapid development of power semiconductors along with the revolutionary advances on microprocessors consolidated the motor drives industry and with it a massive proliferation of non-linear loads. It was thought that these very same technological advances would trigger an explosive development of harmonic solutions based on power electronics. Moreover, the introduction of the instantaneous active and reactive power theory or the so-called p, q theory which simplifies and gives more robustness to the control strategies of active filters reinforced this idea. Three decades have passed since the first IGBT was introduced in early 1980s, and active harmonic solutions are not the first choice to solve harmonic pollution in electrical distribution systems, mainly due to the high cost and the perception of low reliability. Given this scenario, in this work two main approaches are explored. First, the combination of an asymmetric 18-pulse rectifier with a reduced KVA active harmonic filter to improve the performance under abnormal utility conditions. Second, an interleaved active harmonic filter using multiple inverters connected in parallel at the ac and dc size, which will allow for higher power ratings and power density increase. The performance issues of the asymmetric 18-pulse rectifier under unbalanced voltage and pre-existing harmonic components are analyzed, as well as the current distortion improvement, achieved when an active power filter is introduced. On the other hand, the high frequency harmonic cancellation when interleaved inverters are used, the circulation of zero-sequence current and the impact of interleaving on dc bus capacitor are analyzed. Finally, some methods to mitigate the low frequency circulating currents based on eliminating the zero-sequence component, and the introduction of common mode inductors to reduce the high frequency circulating current are studied. Without a doubt the search for new cost-effective topologies able to reach broader power levels and voltage ranges will continue emerging giving more alternatives to users. Moreover, extensive research on wide band gap devices such as Silicon Carbide (SiC) and Gallium Nitride (GaN), with which it is possible to reach higher voltage breakdown and at least an order-of-magnitude lower switching losses, makes the future more promising for active solutions.

Nowadays, ‘green’ communication is of great importance to save electric energy. In communication systems, power amplifiers (PAs) play an important role and consume large amount of power. As a consequence, the enhancement of amplifier efficiency is significantly important for saving energy.   This thesis describes a method to enhance the amplifier efficiency. The goal for this thesis is to find the matching impedances of harmonics for optimum efficiency performance of an amplifier. The idea is to control and change the load impedances at 2nd and 3rd harmonics for maximum efficiency performance of an amplifier at fundamental frequency and finally to build a matching network according to the matching impedances at harmonics.   The load pull technique is applied in this thesis to control the impedances with automatically controlled tuners. In this way, different impedances correspond to specific tuner positions. Then for different tuner positions, the corresponding load impedances of the harmonics are determined, the input, output as well as DC power of the amplifier are measured, and the corresponding efficiency is computed. Therefore, after appropriate efficiency sweep for specific tuner positions, the matching impedances with maximum efficiency performance can be found.   The efficiency of the amplifier with harmonic matching (the method implemented in this thesis) can be improved 2.13 percent which proves the feasibility of the method investigated in this thesis.

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Thesis (M.A.) in Mathematics--University of Maine, 2007. / Includes vita. Includes bibliographical references (leaves 57-59).

Univ., Diss.--Sendai, 1999.