Thesis (Ph. D.)--Drexel University, 2007. / Includes abstract and vita. Includes bibliographical references (leaves [111]-116).

[From Introduction, p. 2] The first chapter of this thesis deals with an analysis of F2 critical frequency data first for SANAE and then for eleven other Antarctic and sub-Antarctic stations covering the period 1957 to 1969. This shows certain aspects of the F2 behaviour. Some of the results of this chapter have been reported in a paper by Gledhill and Williams. The two most important mechanisms thought to be responsible for the Antarctic f₀F2 behaviour are incoming corpuscular radiation and horizontal neutral winds. These two mechanisms together with two others (the temperature theory of Torr and Torr and the semi-annual variation of neutral atmospheric density) are discussed in detail in part 2 (Chapters 2 to 4) with a view to discovering which aspects of the f₀F2 behaviour over Antarctica can be explained by each theory. An attempt is made in Part 3 (Chapters 5 and 6) to explain the observed behaviour by solving the continuity equation of the ionosphere for high-latitude stations. Finally, besides the critical frequency, another parameter of importance in explaining the behaviour in the F2 region is the height at which the F2 maximum occurs. This quantity cannot be read directly from an ionogram and it is not an easy quantity to determine. In fact the way in which it is usually obtained is by "scaling" the ionogram in question and converting the virtual heights obtained into real heights. In Part 4 (Chapter 7 and 8) an outline is given of the two computer programs which were written to perform this conversion.

We investigate ionization and high harmonic generation (HHG) from the interaction of a mid infra-red laser pulse with a solid state system confined to nano-dimensions. The theory of strong field processes in solids is developed for confined quantum systems in general. Here it is applied to two-dimensional quantum wires with a driving field linearly polarised along the axis of the wires. Our findings indicate that that we are able to control the ionization and high-harmonic output by altering the width of the wire. Control of ionization leads to an increased damage threshold which has important implications for nano-engineering and realizing all solid state coherent XUV sources.

Ph.D. / Harmonic time series are often used to describe the periodic nature of a time series, for example the periodic nature of a variable star’s observed light curve. Statistical methods for determining the number of harmonic components to include in harmonic time series are limited. In this thesis a stepwise bootstrap procedure based on a F-type statistic is suggested. The performance of the stepwise procedure is compared to that of Schwartz’s Bayesian Criterion (SBC) and a procedure based on a statistic described by Siegel (1980). Harmonic series with correlated noise terms and irregularly spaced observations are also considered. Tests to detect changes in harmonic parameters are also derived in this thesis. A cumulative sum statistic to test for constant amplitude is derived. It is shown that testing for constant amplitude is equivalent to testing for constant slope in simple linear regression. We also derive a likelihood ratio statistic to test for constant amplitude. It is shown that the latter likelihood ratio statistic is asymptotically equivalent to the cumulative sum statistic. These statistics are compared to a quadratic form statistic used by Koen (2009). Likelihood ratio tests are also derived for detecting changes in the frequency or phase of harmonic time series. Graphical devices to aid in diagnostic checking are suggested.

Honey bees are some of the most important pollinators for agriculture in the world and are pivotal to the health of worldwide ecosystems. Like all insects, bees struggle with exposure to parasites, diseases, and other environmental factors that can negatively affect the overall health of the colony. Recently, a new unexplainable phenomenon called Colony Collapse Disorder (CCD) has been wreaking havoc on bee populations worldwide. As a result, a system capable of tracking bees is required to understand the different contributions of chemicals, parasites, etc. to CCD. This research seeks to show data supporting the development of systems for an X-band harmonic radar system. Overall, it was found the harmonic oscillator’s conversion and antenna efficiency were the most important design factors for determining detectability at increased ranges. Therefore, multiple harmonic oscillators were simulated and developed at a fundamental frequency of 5 GHz with these design factors in mind.

We investigate tiling properties of spectra of measures, i.e., sets Λ in R such that {e 2πiλx : λ ∈ Λ} forms an orthogonal basis in L 2 (µ), where µ is some finite Borel measure on R. Such measures include Lebesgue measure on bounded Borel subsets, finite atomic measures and some fractal Hausdorff measures. We show that various classes of such spectra of measures have translational tiling properties. This lead to some surprizing tiling properties for spectra of fractal measures, the existence of complementing sets and spectra for finite sets with the Coven-Meyerowitz property, the existence of complementing Hadamard pairs in the case of Hadamard pairs of size 2,3,4 or 5. In the context of the Fuglede conjecture, we prove that any spectral set is a tile, if the period of the spectrum is 2,3,4 or 5

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