<div>For decades nuclear fusion space propulsion has been studied but due to technological set backs for self-sustaining fusion, it has been repeatedly abandoned in favor of more near-term or present day solutions. While these present day solutions of chemical and electric propulsion have been able to accomplish their missions, as the human race looks to explore Mars, a near term solution utilizing nuclear fusion propulsion must be sought as the fusion powered thruster case currently does not meet the minimum 0.2 thrust-to-weight ratio requirement. The current work seeks to investigate the use of a ssion powered magnetic fusion thruster for a manned Mars mission with an emphasis on creating a very near-term propulsion system. This will be accomplished by utilizing present day readily available technology and adapting methods of nuclear electric and nuclear fusion propulsion to build this ssion assisted propulsion system. Near term solutions have been demonstrated utilizing both DT and D-He3 fuels for a ssion powered and ssion assisted Dense Plasma Focus fusion device capable of achieving thrust-to-weight ratios greater than 0.2 for V's of 20 km/s. The Dense Plasma Focus can achieve thrust-to-weight ratios of 0.34 and 0.4 for ssion assisted and ssion powered cases, respectively, however, the Gasdynamic Mirror device proved to be an infeasible design as a ssion powered thruster due to the increased weight of a ssion reactor.</div>

The essence of the interest rate modeling by using Heath-Jarrow-Morton framework is to find the drift condition of the instantaneous forward rate dynamics so that the entire term structure is arbitrage free. In this study, instantaneous forward interest rates are modeled using random fields and Markov Jump processes and the drift conditions of the forward rate dynamics are given. Moreover, the methodology presented in this study is extended to certain financial settings and instruments such as multi-country interest rate models, term structure of defaultable bond prices and forward measures. Also a general framework for bond prices via nuclear space valued semi-martingales is introduced.

In this dissertation we establish results concerning in locally convex spaces-valued measures and measurable functions. The results are explained in three parts: Firstly, we establish Liapounoff convexity-type results for locally convex space-valued measures defined on fields (of sets) or equivalently on Boolean Algebras. Liapounoff convexity-type theorems concern the compactness and convexity of the closure of the range of a vector measure. We specifically investigate such results for measures defined on fields and fields of sets with the interpolation property. We find that vector measures defined on fields with the interpolation property have properties very similar to the status quo, while similar results may not hold for vector measures defined on general fields. In the latter case we consider vector measures with properties stronger than non-atomicity, specifically, the strong continuity property. We investigate these properties and certain locally convex spaces for which some of the additivity conditions can be relaxed. In the second part of this dissertation, we firstly consider the existence of weak integrals in locally convex spaces specifically, locally convex spaces whose duals are barrelled spaces. Then, inspired by results of J. Diestel we investigate the "improved" properties of the composition of nuclear maps with a locally convex space-valued measures and functions and the properties of nuclear space-valued vector measures and functions. Amongst others we find that the measurability and integrability properties of locally convex space-valued measurable functions are improved with such a composition compared to the functions considered on their own. The third part of this dissertation involves the factorization of measurable functions. We first consider the factorization of Polish space-valued measurable functions along the lines of the famous "Doob-Dynkin's lemma", a result found in (scalar-valued) stochastic processes. This allows us to determine when, for two measurable functions, f and g it is possible to find a measurable function h, such that g= h ○ f. Similar results are established for various classes of measurable functions. We discover similar factorization results for certain multifunctions (set-valued functions) and operator-valued measurable functions. Another consequence is a factorization scheme for operators on L1(µ). / Thesis (PhD(Mathematics))--University of Pretoria, 2010. / Mathematics and Applied Mathematics / unrestricted