Thesis (Ph. D.)--York University, 1998. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 73-77). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004 & res_dat=xri:pqdiss & rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation & rft_dat=xri:pqdiss:NQ39271.

Thesis (Ph.D.)--University of Wyoming, 2007. / Title from PDF title page (viewed on June 17, 2009). Includes bibliographical references (p. 91-97).

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 65-68). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 65-68). Also available on the Internet.

Thesis (Ph.D)--Physics, Georgia Institute of Technology, 2010. / Committee Chair: Rick Trebino; Committee Member: Ahmet Erbil; Committee Member: John Buck; Committee Member: Stephen Ralph; Committee Member: Zhigang Jiang. Part of the SMARTech Electronic Thesis and Dissertation Collection.

We prove several theorems in the intersection of harmonic analysis, combinatorics, probability and number theory. In the second section we use combinatorial methods to construct various sets with pathological combinatorial properties. In particular, we answer a question of P. Erdos and V. Sos regarding unions of Sidon sets. In the third section we use incidence bounds and bilinear methods to prove several new endpoint restriction estimates for the Paraboloid over finite fields. In the fourth and fifth sections we study a variational maximal operators associated to orthonormal systems. Here we use probabilistic techniques to construct well-behaved rearrangements and base changes. In the sixth section we apply our variational estimates to a problem in sieve theory. In the seventh section, motivated by applications to sieve theory, we disprove a maximal inequality related to multiplicative characters. / text

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Electron dynamics in atoms and molecules occurs on a time-scale of attoseconds (10⁻¹⁸s). With the availability of strong field (∼ 10¹²- 10¹³ W cm⁻²) femtosecond (10⁻¹⁵s) laser pulses with electric fields that can reach and exceed the Coulomb field strength experienced by an electron in the ground state of an atom, it is now possible to generate even shorter pulses with durations on the order of attoseconds by the process of high-harmonic generation (HHG). In this dissertation, experiments to study electron dynamics on attosecond time-scales in a helium atom using attosecond pulses generated by HHG will be described. We use extreme-ultraviolet (XUV) attosecond pulse trains and strong femtosecond near-infrared (IR) laser pulses to excite and ionize helium atoms. We first discuss an experimental technique that allows us to quantify and reduce the detrimental effects of Gouy phase slip on attosecond XUV-IR experiments. We then discuss our experiments to study the dynamic behavior of electronic states in a strong field modified helium atom where we use attosecond pulses to explore the strong-field modified atomic landscape. Using the Floquet theory to interpret our experimental observations we measure the variation in quantum phase of interferences between different fourier components of Floquet states as the IR intensity is varied and as different ionization channels dominate, in real-time. Next, we briefly discuss quantum interferences between photo-electrons ionized from XUV excited states in helium using an IR field which is polarized orthogonal to the XUV polarization. We observe variation in angular distribution of photo-electrons as a function of XUV-IR time-delay. We then discuss a new technique to measure the time-of-birth of attosecond pulses using XUV+IR photo-ionization in helium as a measurement probe. Finally, experiments to study the evolution of XUV excited wave-packets in helium on a time-scale of 100's of femtoseconds with attosecond resolution will be described.

In response to energy crisis and power quality concerns, three different methodologies to integrate the concept of active filtering into the alternators are proposed. Wind energy, due to its free availability and its clean and renewable character, ranks as the most promising renewable energy resource that could play a key role in solving the worldwide energy crisis. An Integrated Doubly-fed Electric Alternator/Active filter (IDEA) for wind energy conversion systems is proposed. The proposed IDEA is capable of simultaneous capturing maximum power of wind energy and improving power quality, which are achieved by canceling the most significant and troublesome harmonics of the utility grid and power factor correction and reactive power compensation in the grid. The back-to-back current regulated power converters are employed to excite the rotor of IDEA. The control strategy of rotor-side power converter is based on position sensoreless field oriented control method with higher power density. Analysis and experimental results are presented to demonstrate the effectiveness of the proposed IDEA. In next step, an integrated synchronous machine/active filter is discussed. The proposed technology is essentially a rotating synchronous machine with suitable modification to its field excitation circuit to allow dc and ac excitations. It is shown that by controlling the ac excitation, the 5th and 7th harmonics currents of the utility are compensated. The proposed method is cost effective because it can be applied to existing standby generators in commercial and industrial plants with minimal modification to the excitation circuits. To boost the gain of harmonic compensatory, an advanced electric machine is proposed. An Asymmetric Airgap Concentrated Winding Synchronous Machine (AACWSM) with ac and dc excitation was designed and employed. It is shown that the AACWSM with its unique design, in addition to power generation capability, could be used to compensate the most dominant current harmonics of the utility. The proposed AACWSM can compensate for the 5th and 7th harmonics currents in the grid by controlling the ac field excitation. In addition, the 11th and 13th harmonics currents are also significantly reduced. This system can be used at medium and low voltages for generation or motoring mode of operation.

Nonlinear microscopy has become an indispensable tool in the study of biological systems. It includes many nonlinear contrast mechanisms, each sensitive to different biological structures. However, interpretation of the images generated in nonlinear microscopy is a complex matter due to factors such as the structural complexity of the sample, phase relationships between the excitation beam and the detected signal and the nonlinear interactions in the focal volume of the microscope. This thesis contains a new theoretical and numerical framework that describes the focusing of an excitation beam in a nonlinear microscope, the nonlinear optical interactions with the material in the focal volume, and the resulting nonlinear optical signal in the far field. The framework is the first to include reflection and refraction of the excitation beam and nonlinear signals by an arbitrary number of interfaces in the focal volume, which is especially significant for the interpretation of third harmonic generation (THG). It also uses the chirp-z transform to speed up calculations by orders of magnitude compared to numerical integration techniques. The framework is used to investigate second harmonic generation (SHG) by collagen. Focusing effects alter polarization-dependent SHG measurements of collagen properties compared to the plane wave approximation, and this is verified experimentally. Furthermore, a technique of imaging the far field SHG radiation from collagen fibres is proposed, which can be used to extract the orientation of collagen fibres unambiguously. The framework is then applied to analyze the influence of interfaces on THG. Reflection effects at interfaces significantly affect THG, which leads to the development of a new super-resolution THG imaging technique based on backward-propagating THG. This super-resolution technique is experimentally demonstrated by imaging surface profiles with tens of nanometers resolution, which is the first time that such resolution is obtained in coherent nonlinear microscopy. Therefore, this imaging technique shows promise to become an important tool in high-resolution imaging of (biological) samples. The theoretical and numerical framework provides a foundation for future research on the origin of nonlinear microscopy signals. The new imaging techniques based on this framework have great potential in quantifying fibrillar structures and interfaces in biological samples.