Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

by K. Tong and T. L. Johnson. / Bibliography: .71-72. / Research supported by the National Aeronautics and Space Administration NASA/Ames Grant NGL 22-009-124.

Bibliography: leaves 177-181. This thesis investigates determinants of factors associated with retention of injecting drug users on the South Australian methadone program over the decade 1981 to mid 1991. Truncated multivariate survival models are proposed for the analysis of data from the program, and the theory of graphical chain models applied to the data. A detailed analysis is presented which gives further insight into the nature of the relationships that exist amongst these data. This provides an application of graphical chain models to survival data.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (p. 99-100).

This thesis investigates stochastic optimal control problems with discrete delay and those with both discrete and exponential moving average delays, using the stochastic maximum principle, together with the methods of conjugate duality and dynamic programming. To obtain the stochastic maximum principle, we first extend the conjugate duality method presented in [2, 44] to study a stochastic convex (primal) problem with discrete delay. An expression for the corresponding dual problem, as well as the necessary and sufficient conditions for optimality of both problems, are derived. The novelty of our work is that, after reformulating a stochastic optimal control problem with delay as a particular convex problem, the conditions for optimality of convex problems lead to the stochastic maximum principle for the control problem. In particular, if the control problem involves both the types of delay and is jump-free, the stochastic maximum principle obtained in this thesis improves those obtained in [29, 30]. Adapting the technique used in [19, Chapter 3] to the stochastic context, we consider a class of stochastic optimal control problems with delay where the value functions are separable, i.e. can be expressed in terms of so-called auxiliary functions. The technique enables us to obtain second-order partial differential equations, satisfied by the auxiliary functions, which we shall call auxiliary HJB equations. Also, the corresponding verification theorem is obtained. If both the types of delay are involved, our auxiliary HJB equations generalize the HJB equations obtained in [22, 23] and our verification theorem improves the stochastic verification theorem there.

Master of Science / Department of Food, Nutrition, Dietetics and Health / Edgar Chambers IV / Sensory analysis techniques play a key role in the pet food industry to ensure the final product meets both the pets’ and pet owners’ demands and expectations. To date, the study of the pet owners’ perception towards pet foods is still an emerging field of study and a few number of publications have been released on the topic. In particular, little research has been conducted on exploring the pet owners’ perception regarding the appearance of pet foods. The objective of this work is to study the effect of the visual characteristics of dry dog food on the acceptability and perception by consumer segments of dog owners in the US and in Poland and to explore whether differences exist within countries and across the two countries. For this purpose, dog owners in both locations evaluated the appearance of thirty dry dog food samples with varying visual properties. The participants rated their degree of acceptability towards the appearance of the samples with four different attributes using 9-point hedonic scales. Also, the consumers were asked to associate each one of the samples with a list of positive and negative beliefs on a check-all-that-apply question. Cluster Analysis, ANOVA, and Correspondence Analysis were used to analyze the consumer feedback. The results demonstrate that the acceptability of the appearance of dry dog food is affected by the number of different kibbles present, color(s), shape(s), and size(s) in the product. Similarities were found both within countries and across countries and consumer segments. Consumers overall showed a preference for single-kibble samples of medium brown colors, medium kibble sizes, low-dimensional contrast kibbles and traditional kibble shapes. Furthermore, extra-small or extra-large sized kibble sizes and kibble shapes with a high-dimensional contrast were rejected by the consumers overall. In addition, differences across consumer segments within countries and across countries were identified from the results. The findings indicate that this topic have possibly been overlooked and opportunities for further research on this field are identified. Dry dog food manufacturers should take special consideration with the appearance of their products to enhance the acceptability by dog owners. The outcome of this work can help to drive dry dog food companies meet consumers’ needs and demands in a constantly changing pet food market, with benefits anticipated to the pet food industry and the wellbeing of dog owners.

Exponential asymptotics, which deals with the interpretation of divergent series, is a highly topical field in mathematics. Exponentially small quantities frequently arise in applications, and Poincar´e’s definition of an asymptotic expansion, unfortunately, fails to emphasise the importance of such small exponentials, as they are hidden behind the algebraic order terms. In this thesis, we introduce a new method of hyperasymptotic expansion by inspecting resultant remainders of series. We study the method from two different concepts. First, deriving the singularities and the late order terms, where we truncate expansions at the least value and observe if the remainder is exponentially small. Substitution of the truncated remainder into original differential equation generates an inhomogeneous differential equation for the remainders. We expand the remainder as an asymptotic power series, and then the truncation leads to a new remainder which is exponentially smaller whence the related error estimate gets smaller, so that the numerical precision increases. Systematically repeating this process of reexpansions of the truncated remainders derives the exponential improvement in the approximate solution of the expansions and minimises the ignored terms, i.e., error estimate. Second, in establishing the level one error, which is a function of level zero and level one truncation points, we study asymptotic behaviour in terms of the truncation points and allow them to vary. Writing the estimate as a function of the preceding level truncation point and varying the number of the terms decreases the error dramatically. We also discuss the Stokes lines originating from the singularities of the expansion(s) and the switching on and off behaviour of the subdominant exponentials across these lines. A key result of this thesis is that when the higher levels of the expansions are considered in terms of the truncation points of preceding stages, the error estimate is minimised. This is demonstrated via several differential equations provided in the thesis.

M.A. (Psychology) / Please refer to full text to view abstract

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Magister Scientiae - MSc / Bioactivity-guided fractionation was used to identify the most potent antioxidant and antimutagenic fractions contained in the methanol extract of unfermented rooibos (Aspalathus linearis), as well as the bioactive principles for the most potent antioxidant fractions. The aim of this thesis was to investigate whether the same flavonoids are responsible for both the potent antioxidant and antimutagenic properties of unfermented rooibos. / South Africa