This is an expository thesis on integral domains which are not unique factorization domains. We focus on restoring a type of unique factorization using prime ideals within quadratic integer rings. In particular, we examine which quadratic integer rings will admit such factorization.

Consider a region Ω in the plane and a point z0 in Ω. If a particle which travels randomly, by Brownian motion, is released from z0, then it will eventually cross the boundary of Ω somewhere. We define the harmonic measure distribution function, or h-function hΩ, in the following way. For each r > 0, let hΩ(r) be the probability that the point on the boundary where the particle first exits the region is at a distance at most r from z0. We would like to know, given a function f, whether there is some region Ω such that f is the h-function of that region. We investigate this question using convergence properties of domains and of h-functions. We show that any well behaved sequence of regions must have a convergent subsequence. This, together with previous results, implies that any function f that can be written as the limit of the h-functions hΩn of a sufficiently well behaved sequence{Ωn}ofregionsis the h-function of some region. We also make some progress towards finding sequences {Ωn} of regions whose h-functions converge to some predetermined function f, and which are sufficiently well behaved for our results to apply. Thus, we make some progress towards showing that certain functions f are in fact the h- function of some region.

The current waste management strategy for spent nuclear fuel (SNF) mandated by the U.S. Congress is the disposal of high-level waste (HLW) in a geological repository at Yucca Mountain. Ongoing efforts on closed-fuel cycle options and difficulties in opening and safeguarding such a repository have led to investigations of alternative waste management strategies. One potential strategy would make use of fuels containing transuranic (TRU) nuclides in nuclear reactors. This would prolong reactor operation on a single fuel loading and by doing so, would reduce current HLW stockpiles. The analysis has already shown that high-temperature gas-cooled reactors (HTGRs) and their Generation IV extensions, very-high-temperature reactors (VHTRs), have encouraging performance characteristics that will allow for prolonged operation with no intermediate refueling, as well as for transmutation of TRUs. The objective of this research was to show that TRU-fueled VHTRs have the possibility of prolonged operation on a single fuel loading while retaining their Generation IV safety features. In addition, this research evaluated performance characteristics, and identified operational domains of these systems, as well as the possibility of HLW reduction. A whole-core, 3-D model of a power size prismatic VHTR with a detailed temperature distribution was developed for calculations with the SCALE 5.1 code package. Results of extensive criticality and depletion calculations with multiple fuel loadings showed that VHTRs are capable and suitable for autonomous operation when loaded with TRU fuel.

Thesis--Université de Paris XI. / Includes bibliographical references.

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Dissertation (Ph.D.)--Auburn University, 2007. / Abstract. Vita. Includes bibliographic references (p.31).

Thesis (Ph. D.)--University of Florida, 1980. / Description based on print version record. Typescript. Vita. Includes bibliographical references (leaves 61-62).