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The object of this dissertation is to record and analyze the foreign policy of the Sultanate of Oman from the early twentieth century until 2004. It challenges the central assumption of the contemporary scholarship on the subject that Muscat's modern foreign policy begins in 1970. It is often presumed that the pre-1970 era does not merit a thorough investigation to understand Muscat's modus operandi today. This study argues that for a comprehensive understanding of Muscat's foreign policy since 1970, the frontier of the historical analysis of Oman's regional and international involvement should be pushed back to the 1930's, when the young Sultan Said assumed power over the country divided by the "Treaty" or the "Agreement" of Sib. Indeed, the thrust of this research lies at once in repudiating the conventional wisdom regarding both the persona of Sultan Said and the customary political/historical narrative of Said's reign. The critical analysis of this period is utilized to rebut the pervasive and largely inaccurate historical narrative of the events prior to 1970, to recount an original interpretation of the period, and to use the narrative as a preamble for subsequent foreign policy directions and initiatives. Furthermore, this dissertation covers the gaps in the literature resulting from the absence of any materials that either record or analyze Muscat's foreign policy from 1996 until 2004. In addition, his study provides new information and a fresh analysis of the international relations of the region, including great power rivalry, especially the competition between the United States and Great Britain, and the attitudes of major regional actors, such as Iran, Saudi Arabia, and Iraq. The use of a thorough historical inquiry is vital to support the central claim of this dissertation; therefore, a large section of this dissertation is based almost exclusively on archival materials collected from the British Public Records Office, the University of Oxford and the Library of Congress. This project represents the most comprehensive use of archival materials on the subject matter to date.

Objectives: This study used three lasers (red, green and blue) with a spectrophotometer to compare the light propagation [Absorption (A), Transmittance (T), Attenuation (K) and Scattering Anisotropy Coefficient (g)] in dental tissues and nano filled resin based composite using three incremental build-up techniques: one shade (Body), two shades (Enamel and Dentin), and three shades (Enamel, Transparent and Dentin). Methods: Twenty un-erupted recently extracted human 3rd molars (shade: B1) were used to obtain 40 tooth slabs (1.5 mm thickness x 4 mm length). The samples were randomized and equally distributed into four experimental groups: Positive Control (Dental Tissues – enamel, dentino- enamel-junction and dentin), Technique 1 (T1 = 1 shade, B1B), Technique 2 (T2 = 2 shades, A2Dentin/B1Enamel), and Technique 3 (T3 = 3 shades, A2Dentin/Transparent/B1Enamel). One calibrated operator performed all procedures and tests. Cavity preparation was standardized using a #58 carbide bur. Using the spectrophotometer, each specimen was irradiated by the three LASERs. A Voltmeter recorded the light output signal and from this raw data the following optical constants were calculated: absorption (A), transmittance (T), attenuation coefficient (K) and Scattering Anisotropy Coefficient (g). The data were analyzed using One-way ANOVA, followed by the post-hoc Tukey's test. All tests utilized a significance level of 0.05. Results: Regarding absorption and transmittance, dental tissues were significantly different compared to the three build-up techniques for all lasers. Regarding the attenuation coefficient, dental tissues were not significantly different for T2 and T3 for the blue and red lasers, however they were significantly different for the green laser. There was no significant difference among the three lasers for T2 and T3. Conclusion: Within the limitations of this study, none of the build-up techniques used was able to reproduce the dental tissues optical properties and Technique 2 (2 shades) and Technique 3 (3 shades) resulted in a similar pattern of light propagation.

The design profession is responding to the complex systems represented by architecture and planning by increasingly incorporating the power of computer technology into the design process. This represents a paradigm shift, and requires that designers rise to the challenge of both embracing modern technologies to perform increasingly sophisticated tasks without compromising their objective to create meaningful and environmentally sensitive architecture. This dissertation investigated computer-based fractal tools applied within a traditional architectural charette towards a design process with the potential to address the complex issues architects and planners face today. We developed and presented an algorithm that draws heavily from fractal mathematics and fractal theory. Fractals offer a quantitative and qualitative relation between nature, the built environment and computational mechanics and in this dissertation serve as a bridge between these realms. We investigated how qualitative/quantitative fractal tools may inform an architectural design process both in terms of generative formal solutions as well as a metric for assessing the complexity of designs and historic architecture. The primary research objective was to develop a compelling cybernetic design process and apply it to a real-world and multi-faceted case study project within a formal architectural critique. Jurors were provided a platform for evaluating design work and weighing in as practicing professional architects. Jurors' comments were documented and discussed and presented as part of the dissertation. Our intention was to open up the discussion and document the effectiveness or ineffectiveness of the process we presented. First we discussed the history of generative and algorithmic design and fractals in architecture. We begin with examples in ancient Hindu temple architecture as well as Middle Eastern architecture and Gothic as well as Art Nouveau. We end this section with a discussion of fractals in the contemporary architecture of Frank Lloyd Wright and the Organic school. Next we developed a cybernetic design process incorporating a computer-based tool termed DBVgen within a closed loop designer/algorithm back and forth. The tool we developed incorporated a genetic algorithm that used fractal dimension as the primary fitness criterion. We applied our design process with mixed results as discussed by the jurors whose feedback was chunked into ten categories and assessed along with the author/designer's feedback. Generally we found that compelling designs tended to have a higher FD, whereas, the converse was not true that higher FD consistently led to more compelling designs. Finally, we further developed fractal theory towards an appropriate consideration of the significance of fractals in architecture. We articulated a nuanced definition of fractals in architecture as: designs having multi-scale and multi-functional representations of some unifying organizing principle as the result of an iterative process. We then wrapped this new understanding of fractals in architecture to precedent relevant to the case study project. We present and discuss fractals in the work of Frank Lloyd Wright as well as Dean Bryant Vollendorf. We expand on how a theory of fractals used in architecture may continue to be developed and applied as a critical tool in analyzing historic and contemporary architecture as well as a creative framework for designing new architectural solutions to better address the complex world we live in.

Tropical polynomials are similar to classical polynomials, however addition and multiplication are replaced with tropical addition (minimums) and tropical multiplication (addition). Within this new construction, polynomials become piecewise linear curves with interesting behavior. All tropical polynomials are piecewise linear curves, and each linear component uniquely corresponds to a particular monomial. In addition, certain monomial in the tropical polynomial can be trivial due to the fact that tropical addition is the minimum operator. Therefore, it makes sense to consider a graph of connectivity of the monomials for any given tropical polynomial. We investigate tropical polynomials where all coefficients are chosen from a standard normal distribution, and ask what the distribution will be for the graphs of connectivity amongst the monomials. We present a rudimentary algorithm for analytically determining the probability and show a Monte Carlo based confirmation for our results. In addition, we will give a variety of different theorems comparing relative likelihoods of different types of tropical polynomials.

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