Includes bibliographical references (p. 38-40).

published_or_final_version / Mathematics / Master / Master of Philosophy

Element abundance trends with overall metallicity contain vital clues to the formation and evolution of the Galaxy. Abundances may be used to elucidate nucleosynthesis mechanisms and to ascertain rates of Galactic enrichment. To obtain accurate abundances, several crucial inputs such as high-quality spectroscopic observations, rigorous calculations of line transfer, and precise atomic data (e.g. transition probabilities) are necessary. The current work endeavors to improve abundance values for key elements with a four-fold approach: accumulation of hundreds of high-resolution stellar spectra in order to commence a systematic and thorough Manganese abundance derivation in cluster and halo field stars; re-determination of the neutral chromium oscillator strengths and application of this data to stellar abundance analyses; modification of a radiative line transfer code in order to yield accurate abundances from evolved stars; and semi-empirical derivation of transition probabilities to allow for the utilization of spectral features in the red visible and infrared wavelength ranges for abundance determinations. The first comprehensive investigation of manganese in globular clusters is done in this work. A subsolar Mn abundance trend for both halo globular cluster and field stars is found. The analysis shows that for the metallicity range -0.7>(Fe/H)>-2.7 stars of 19 globular clusters have a a mean relative abundance of <(Mn/Fe)>= -0.37±0.01 (σ=0.10), a value in agreement with that of the field stars: <(Mn/Fe)>= -0.36± 0.01 (σ=0.08). Remarkably, the <(Mn/Fe)> ratio remains constant in both stellar populations over a 2 orders of magnitude span in metallicity. Next, the present study employed branching fraction measurements from Fourier transform spectra in conjunction with published radiative lifetimes to determine transition probabilities for 263 lines of neutral chromium. These laboratory values are used to derive a new photospheric abundance for the Sun: log [element of](Cr I)⊙= 5.64±0.01 (σ=0:07). In addition, oscillator strengths for singly-ionized chromium recently reported by the FERRUM Project are employed to determine: log [element of](Cr II)⊙ = 5.77±0.03 (σ= 0.13). No indications of departures from LTE are found in the neutral chromium abundances. The current work then takes advantage of the fact that transition metals exhibit relatively pure LS coupling and employs standard formulae to yield semi-empirical oscillator strengths. These data were then compared to experimental gf values in order to assess accuracy. Finally, this study undertakes a new abundance investigation of the RGB and RHB stars of the M15 globular cluster. A detailed examination of the both the metallicity and n capture elements is performed. This work appears to confirm that star-to-star abundance variations do occur among the M15 giants (which was initially observed by Sneden et al. 1997, 2000). / text

In both physical and social sciences, we usually use controlled differential equation to model various continuous evolving system; describing how a response y relates to another process x called control. For regular controls x, the unique existence of the response y is guaranteed while it would never be the case for non-smooth controls via the classical approach. Besides, uniform closeness of controls may not imply closeness of their corresponding responses. Theory of rough paths provides a solution to both concerns. Since the creation of rough path theory, it enjoys a fruitful development and finds wide applications in stochastic analysis. In particular, rough path theory provides an effective method to study irregularity of curves and its geometric consequences in relation to integration of differential forms. In the chapter 2, we demonstrate the power of rough path theory in classical complex analysis by showing the rough path nature of the boundaries of a class of Holder's domains; as an immediate application, we extend the classical Gauss-Green's theorem. Until recently, there has been only limited research on applications of theory of rough paths to high dimensional geometry. It is clear to us that many geometric objects, in some senses appearing as solids, are actually comprised of filaments. In the chapter 3, two basic results in the theory of rough paths which will motivate later development of my thesis has been included. In the chapters 4 and 5, we identify a sensible way to do geometric calculus via those filaments (more precisely, space-filling rough paths) in dimension 3. In a recent joint work of Hambly and Lyons, they have shown that every rectifiable path can be completely characterized, up to tree-like deformation, by an algebraic object called the signature, tensor of all iterated integrals, of the path. It is clear that all tree-like deformation of the path would not change its topological features. For instance, the number of times a planar loop of finite length winds around a point (not lying on the path) is unaltered if one deforms the path in tree-like ways. Therefore, it should be plausible to extract this topological information out from the signature of the loop since the signature is a complete algebraic invariant. In the chapter 6, we express the winding number of a nice loop (respectively linking number of a pair of nice loops) as a linear functional of the signature of the loop (respectively signatures of the pair of loops).

published_or_final_version / Applied Statistics / Master / Master of Social Sciences

published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

No description available.

Infant and child mortality rates are one of the health indicators in a given community or country. It is the fourth millennium development goal that by 2015, all the united nations member countries are expected to have reduced their infant and child mortality rates by two-thirds. Uganda is one of those countries in sub-Saharan Africa with high infant and child mortality rates and therefore has the need to find out the factors strongly associated to these high rates in order to provide alternative or maintain the existing interventions. The Uganda Demographic Health Survey (UDHS) funded by USAID, UNFPA, UNICEF, Irish Aid and the United kingdom government provides a data set which is rich in information. This information has attracted many researchers and some of it can be used to help Uganda monitor her infant and child mortality rates to achieve the fourth millennium goal. Survival analysis techniques and frailty modelling is a well developed statistical tool in analysing time to event data. These methods were adopted in this thesis to examine factors affecting under-five child mortality in Uganda using the UDHS data for 2011 using R and STATA software. Results obtained by fitting the Cox-proportional hazard model and frailty models and drawing inference using both the Frequentists and Bayesian approach showed that, Demographic factors (sex of the household head, sex of the child and number of births in the past one year) are strongly associated with high under-five child mortality rates. Heterogeneity or unobserved covariates were found to be signifcant at household but insignifcant at community level. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.

Atmospheric particles play a crucial role in climate, visibility, air pollution, and human health. Reactions between gas-phase molecules and particles (heterogeneous reactions) affect not only the particle composition and morphology, but also the composition of the atmosphere. This thesis investigates the heterogeneous chemistry of organic mixtures and inorganic solutions coated with organic monolayers as proxies for atmospheric particles. The first topic of interest was the reaction between N₂0₅ and aqueous inorganic solutions coated with organic monolayers. The goal of this work was to better understand how organic monolayers on aqueous particles affect the mass transport and kinetics of N₂0₅ uptake by aqueous aerosols, and consequently what effectthe monolayer can have on predicted concentrations of N₂0₅ in the atmosphere. To investigate heterogeneous reactions of inorganic solutions coated with an organic monolayer a new rectangular channel flow reactor was developed. This newly developed flow reactor was described in detail and validated. Subsequently, the new flow reactor was used to study the reactive uptake of N₂0₅ on sulfuric acid solutions in the presence of a variety of 1- and 2-component monolayers with varying functional groups, solubilities, chain lengths, surface pressures, and molecular surface areas. Reactive uptake of N₂0₅ on aqueous sulfuric acid solutions was found to correlate most strongly with the molecular surface area or packing density of the monolayer. These results provide a good foundation for determining the influence of monolayers on heterogeneous reactions in the atmosphere, and highlight the need for characterization of monolayer surface properties of organic monolayers present on atmospheric particles. The second topic of interest was reactions between 0₃ and proxies for meat cooking aerosols with the goal to better understand the effect of the phase and microstructure of the mixtures on the lifetime of oleic acid (OA) in atmospheric particles. The reactive uptake of 0₃ was approximately 1 order of magnitude slower on binarysolid-liquid mixtures and multicomponent mixtures that closely represent compositions of meat-cooking aerosols compared to the liquid solutions. Lifetimes up to 75 min were obtained for these mixtures.

No description available.