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

M.A. (African Studies) / The study deals with forms of address in isiZulu. Therefore, the various aspects of speech that play roles when addressing a person, the factors affecting forms of address in isiZulu and the effect of languages such as English, Afrikaans and other African languages on the forms of address in isiZulu are of interest. Research was conducted on forms of address in isiZulu in parts of Soweto and it was discovered that form of address are determined by different factors in a given situation and the influence of a variety of languages. The data was collected from: 1. Books on forms of address in other languages. 2. Recorded conversations and discussions. 3. Recorded television and radio programmes. In each chapter, sub-categories of addressing people, their use and factors determining them are highlighted.

Population fragmentation and subsequent isolation in different refugia during the glacial advances of the Pleistocene are believed to have had a significant impact on current levels of genetic and morphological diversity. Despite the importance of these glacial refugia for biodiversity, our understanding of their distribution on the northwestern coast of North America and their relative impact on populations remains limited. As the most isolated group of islands in the Pacific Northwest, Haida Gwaii has been the subject of intense study both from the perspective of its complex glacial history and endemic flora and fauna. The ubiquitous presence of glacial features on this archipelago points to extensive ice cover during the late Wisconsin (Fraser glaciation) and populations which could only have become established postglacially. However, the large assemblage of unique mammalian and avian fauna found on Haida Gwaii has led to suggestions that these divergent vertebrates actually evolved through long isolation by continuously inhabiting these islands or nearby regions throughout the last glacial maximum. To assess Haida Gwaii’s role as a glacial refugium and the relictual status of its endemic black bear (Ursus americanus), marten (Martes americana), short-tailed weasel (Mustela erminea), caribou (Rangifer tarandus) and Saw-whet Owl (Aegolius acadicus), a broad phylogeographic study using sequence comparisons of the mitochondrial gene cytochrome b was undertaken. Phylogeographic structure was observed in the black bear (n= 33), marten (n= 18) and short-tailed weasel (n= 32). Based on parsimony, maximum likelihood, and neighbour-joining analyses of 719 bp of cytochrome b, two geographically structured black bear lineages were unambiguously identified: 1) a continental lineage found in the Yukon, Alberta, Alaska, Montana and Pennsylvania (americanus) and mainland BC (americanus and cinnamomum) and 2) a coastal lineage found on Haida Gwaii (carlottae), Vancouver Island (vancouveri) and the Olympic Peninsula (altifrontalis). The two lineages were defined by 24 synapomorphies and an average sequence divergence of 3.6%. Average intralineage divergence was 0.1%. Similarly, two geographically structured lineages, continental and coastal, were also identified in marten using the same types of analyses on 3II bp of cytochrome b. The continental lineage included marten from mainland BC (caurina and abietinoides) and Newfoundland (atrata) whereas the coastal lineage included marten from Haida Gwaii (nesophila) and Vancouver Island (vancouverensis). The two lineages were defined by three synapomorphies and an average sequence divergence of 1.2%. Average intralineage divergence was 1%. Phylogeographic structure was also observed in the short-tailed weasel using 148 to 673 bp of cytochrome b. Three major lineages were identified and named according to their putative refugial source areas: Beringia, which included weasels from Japan (orientalis) and the Yukon (arctica), a continental or southern source, which encompassed weasels from mainland BC (richardsonii, invicta,fallenda), Manitoba (bangsi), and Ontario (cicognanii), and Haida Gwaii which included only those weasels from Haida Gwaii (haidarum). Short-tailed weasels from Vancouver Island (anguinae) and some areas along the coast demonstrated an affinity to both southern and Haida Gwaii weasels. Relative to the continental lineage, the coastal lineage was defined by 13 synapomorphies; the Beringian lineage was defined by 10 synapomorphies. Average sequence divergence was 2.5 % and 2.2% respectively. Divergence between the coastal weasels and Beringian weasels was 2.4%. There was little mtDNA diversity within the coastal lineage as the average intralineage divergence was 0.8%. Little or no phylogeographic structure was observed in the caribou and Saw-whet Owl. Of the 313 bp examined in two barren ground caribou (granti) and seven woodland caribou (four tarandus and three dawsoni), three tarandus and two dawsoni formed a lineage defined by one synapomorphy. The two barren ground, one tarandus, and one dawsoni were excluded from this lineage by one to three substitutions. Similarly, little phylogeographic structure was observed in the Saw-whet Owl. Analyses of a 241 bp of cytochrome b sequenced from this species indicated no genetic divergence between individuals as far apart as Haida Gwaii (brooksi) and Manitoba (acadicus). The maximum divergence observed between individuals was 0.4%. The phylogeographic patterns from these five species have two major implications with regard to the issue of glacial refugia and the relictual status of the Haida Gwaii endemics: 1) With the possible exception of haidarum, the suite of morphological features characterizing the endemics carlottae, nesophila, dawsoni and brooksi appear to have been derived postglacially. In fact close genetic affinity of these endemic subspecies with adjacent conspecifics suggest that population fragmentation caused by glaciers has had little effect on morphological differentiation and that adaptation to local ecological environments has played a more influential role in their evolution. 2) Emerging data of a mid-Pleistocene split of many vertebrate taxa and the geographic distribution of these various generic lineages, including the black bear, marten and short-tailed weasel in this region cumulatively suggests that a refugium existed on the continental shelf off the central coast of British Columbia and was possibly part of a larger (or series of refugia) refugium which extended further north and south along this coast. Given the broad assemblage of taxa which might have persisted here during the last glaciation, this refugium was probably ecologically productive and as such, was likely to have been an important alternate source area for the postglacial recolonizarion of northwestern North America. / Graduate

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

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Rheological characterization of pharmaceutical semisolids is of importance as it provides fundamental information required for the assessment of some of the final properties of a product such as viscosity, elasticity, quality and storage stability. The effect of formulation variables on product characteristics such as consistency and correlation of consumer evaluation of consistency can also be attained. (Ramachandran et al., 1999) This study focussed on using rheological techniques to fully characterize the properties of various semisolid formulations being developed or produced at a South African-based generic pharmaceutical company. Various tests were employed to characterize the semisolid dosage forms (creams and ointments), including continuous shear tests such as flow and viscosity curves and yield point measurements, oscillatory tests such as amplitude and frequency sweeps, as well as step and temperature ramp tests. A method to determine justifiable and meaningful viscosity specifications was developed, where excellent reproducibility of results were obtained when compared to the single-point viscosity determinations usually used. An evaluation as to whether rheology can be utilized as an assessment tool for product stability revealed varying results, with the oscillation-frequency sweep test displaying modest predictive capabilities. Observable differences in rheological character were found when evaluating ointment formulations exhibiting deviating quality characteristics. When analysing the effect of varying processing parameters, namely, cooling rate and mixing speed, during the manufacture of a cream, statistically significant rheological differences were obtained, while a thorough characterization of a scale-up procedure was also achieved upon analysis of various rheological properties.

In this thesis we prove the existence of vector-valued automorphic forms for an arbitrary Fuchsian group and an arbitrary finite dimensional complex representation of this group. For small enough values of the weight as well as for large enough values, we provide explicit formulas for the spaces of these vector-valued automorphic forms (holomorphic and cuspidal). To achieve these results, we realize vector-valued automorphic forms as global sections of a certain family of holomorphic vector bundles on a certain Riemann surface associated to the Fuchsian group. The dimension formulas are then provided by the Riemann-Roch theorem. In the cases of 1 and 2-dimensional representations, we give some applications to the theories of generalized automorphic forms and equivariant functions.

We study sums of squares formulae from the perspective of normed bilinear maps and their Hopf constructions. We begin with the geometric properties of quadratic forms between euclidean spheres. Let F: Sm → Sn be a quadratic form. For every point q in the image, the inverse image F⁻¹ (q) is the intersection of Sm with a linear subspace wq, whose dimension can be determined easily. In fact, for every k ≤ m+1 with nonempty Yk = {q ∈ Sn: dim Wq = k}, the restriction F⁻¹ (Yk) → Yk is a great (k-1) - sphere bundle. The quadratic form F is the Hopf construction of a normed bilinear map if and only if it admits a pair of "poles" ±p such that dim Wp + dim W₋p = m+1. In this case, the inverse images of points on a "meridian", save possibly the poles, are mutually isoclinic. Furthermore, the collection of all poles forms a great sphere of relatively low dimension. We also prove that the classical Hopf fibrations are the only nonconstant quadratic forms which are harmonic morphisms in the sense that the composite with every real valued harmonic function is again harmonic. Hidden in a quadratic form F: Sm → Sn are nonsingular bilinear maps Rk x Rm-k⁺¹ → Rn, one for each point in the image, all representing the homotopy class of F, which lies in Im J. Moreover, every hidden nonsingular bilinear map can be homotoped to a normed bilinear map. The existence of one sums of squares formula, therefore, anticipates others which cannot be obtained simply by setting some of the indeterminates to zero. These geometric and topological properties of quadratic forms are then used, together with homotopy theory results in the literature, to deduce that certain sums of squares formulae cannot exist, notably of types [12,12,20] and [16,16,24]. We also prove that there is no nonconstant quadratic form S²⁵ → S²³. Sums of squares formulae with integer coefficients are equivalent to "intercalate matrices of colors with appropriate signs". This combinatorial nature enables us to establish a stronger nonexistence result: no sums of squares formula of type [16,16, 28] can exist if only integer coefficients are permitted. We also classify integral [10,10,16] formulae, and show that they all represent ±2Ʋ∈ π [s over 3]. With the aid of the KO theory of real projective spaces, we determine, for given δ ≤ 5 and s, the greatest possible r for which there exists an [r,s,s+δ] formula. An explicit solution of the classical Hurwitz-Radon matrix equations is also recorded. / Science, Faculty of / Mathematics, Department of / Graduate

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The aim of this thesis is to provide an introduction to the study of elliptic curves and modular forms over general commutative rings or schemes. We will recall a few aspects of the classical theory of these objects (over the complex numbers) while placing emphasis on the geometric picture. Moreover, we will formulate the theory of elliptic curves in the modern language of algebraic geometry following the work of Katz and Mazur. In addition, we provide an application of p−adic modular forms to the theory of p−adic heights on elliptic curves.