The work consists of two parts. In the first part which is concerned with random walks, we construct the conditional versions of a multidimensional random walk given that it does not leave the Weyl chambers of type C and of type D, respectively, in terms of a Doob h-transform. Furthermore, we prove functional limit theorems for the rescaled random walks. This is an extension of recent work by Eichelsbacher and Koenig who studied the analogous conditioning for the Weyl chamber of type A. Our proof follows recent work by Denisov and Wachtel who used martingale properties and a strong approximation of random walks by Brownian motion. Therefore, we are able to keep minimal moment assumptions. Finally, we present an alternate function that is amenable to an h-transform in the Weyl chamber of type C. In the second part which is concerned with Brownian motion, we examine the non-exit probability of a multidimensional Brownian motion from a growing truncated Weyl chamber. Different regimes are identified according to the growth speed, ranging from polynomial decay over stretched-exponential to exponential decay. Furthermore we derive associated large deviation principles for the empirical measure of the properly rescaled and transformed Brownian motion as the dimension grows to infinity. Our main tool is an explicit eigenvalue expansion for the transition probabilities before exiting the truncated Weyl chamber.

The spider mite occurrence, on soybean (Glycine max (L.) Merril), is sporadic and associated whit dry periods. Recently, in continuous years, was reported mite outbreaks in soybean, in some sites of Rio Grande do Sul State. In this context two research was conducted, one in summer crop 2004/05 and other in 2005/06. The first was carried for study the mite occurrence and geographic distribution, on soybean, from some place of Rio Grande do Sul State. The second was conducted for study the effect of the two soybean cultivars and of some weed management systems on mite density and study their population dynamic on soybean. In summer crop 2004/05 was carried some mite samplings in soybean field at State. The mite species found, all beloung to the Tetranychidae family, are Mononychellus planki (McGregor), Tetranychus desertorum Banks, T. gigas Pritchard & Baker, T. ludeni Zacher and T. urticae Koch. Most of this species are well distributed in the diferents sampling regions of this study. From the results was made a species distribution map and a taxonomic key. In summer crop 2005/06, in Santa Maria, RS, 11 treatments was study. Its was constitute in two soybean cultivars, one transgenic glyphosato-tolerant and other non-transgenic, every one whit five weed management systems: (1) without management; (2) hand management; (3) herbicide bentazone + sethoxydim; (4) bentazone only; (5) sethoxydim only. The 11th treatment was the herbicide glyphosate sprayed on the transgenic soybean. The mite species found in this study are M. planki and T. gigas. The weed management systems is more determinant, on the spider mite population on soybean, than the soybean cultivar. The mite population presenteded inverse correlation whit weed infestation and weed density. The climatic fators determined the mite population flutuation and the population peak occured in the initial period of soybean pods development. / A ocorrência de ácaros-praga em soja (Glycine max (L.) Merril) é esporádica e está, comumente, associada à períodos de estiagem. Recentemente, em safras seguidas, foram observados ataques severos de ácaros à soja em algumas regiões do estado do Rio Grande do Sul. Neste contexto foram realizados dois experimentos, um na safra agrícola 2004/05 e outro em 2005/06. O primeiro teve objetivo de estudar a ocorrência e a distribuição geográfica de ácaros fitófagos, associados à soja, em municípios de seis regiões produtoras do estado do Rio Grande do Sul. O segundo objetivou avaliar o efeito de duas cultivares de soja e de diferentes sistemas de manejo de plantas daninhas sobre a densidade populacional de ácaros em soja e estudar a dinâmica populacional destes ácaros na cultura. Em 2004/05 foram realizadas amostragens de ácaros em lavouras de soja no Estado. As espécies de ácaros encontradas são Mononychellus planki (McGregor), Tetranychus desertorum Banks, T. gigas Pritchard & Baker, T. ludeni Zacher e T. urticae Koch, todos são tetraniquídeos. A maior parte destas espécies estiveram bem distribuídas nas diferentes regiões amostradas neste levantamento. Com base nestes resultados foi elaborado um mapa com a distribuição das espécies e uma chave de identificação. Em 2005/06 foram estudados, em Santa Maria, RS, 11 tratamentos. Estes consistiram em duas cultivares de soja, uma transgênica glifosato-tolerante e a outra não-transgênica, cada uma sob cinco sistemas de manejo de plantas daninhas: (1) sem controle; (2) arranquio manual; (3) manejo tradicional com os herbicidas bentazona e setoxidim; (4) apenas com bentazona; (5) apenas com setoxidim. E adicionalmente um tratamento com o herbicida glifosato sobre a cultivar de soja transgênica. Os ácaros-praga ocorrentes foram M. planki e T. gigas. A densidade populacional destes ácaros em soja foi mais afetada pelos sistemas de manejo de plantas daninhas do que pela cultivar, e esteve inversamente correlacionada com a quantidade e diversidade de plantas daninhas. A flutuação populacional destes ácaros foi influenciada por fatores climáticos e o pico populacional ocorreu na fase de início da formação de legumes da soja.

The work consists of two parts. In the first part which is concerned with random walks, we construct the conditional versions of a multidimensional random walk given that it does not leave the Weyl chambers of type C and of type D, respectively, in terms of a Doob h-transform. Furthermore, we prove functional limit theorems for the rescaled random walks. This is an extension of recent work by Eichelsbacher and Koenig who studied the analogous conditioning for the Weyl chamber of type A. Our proof follows recent work by Denisov and Wachtel who used martingale properties and a strong approximation of random walks by Brownian motion. Therefore, we are able to keep minimal moment assumptions. Finally, we present an alternate function that is amenable to an h-transform in the Weyl chamber of type C. In the second part which is concerned with Brownian motion, we examine the non-exit probability of a multidimensional Brownian motion from a growing truncated Weyl chamber. Different regimes are identified according to the growth speed, ranging from polynomial decay over stretched-exponential to exponential decay. Furthermore we derive associated large deviation principles for the empirical measure of the properly rescaled and transformed Brownian motion as the dimension grows to infinity. Our main tool is an explicit eigenvalue expansion for the transition probabilities before exiting the truncated Weyl chamber.

Mr Justice Corbett made a substantial contribution to the South African tax law as he delivered several judgements during his long career on the bench. Starting from the lower ranks as a judge he became Chief Justice of South Africa. Precedents set by his judgements are considered important and indicative of the level of South African tax law. This dissertation observes his background, looks at the operations of the tax court in South Africa and examines whether his judgements were cited and applied in subsequent cases as accepted precedent. International case law is referred to, to compare his judgements with comparable international tax law. / Auditing / M. Comm. (Accounting)

Mr Justice Corbett made a substantial contribution to the South African tax law as he delivered several judgements during his long career on the bench. Starting from the lower ranks as a judge he became Chief Justice of South Africa. Precedents set by his judgements are considered important and indicative of the level of South African tax law. This dissertation observes his background, looks at the operations of the tax court in South Africa and examines whether his judgements were cited and applied in subsequent cases as accepted precedent. International case law is referred to, to compare his judgements with comparable international tax law. / Auditing / M. Comm. (Accounting)

Principles of “transforming leadership” have been widely promoted since the publication of James McGregor Burns’ book Leadership, especially among Christian leaders. The purpose of this study is to examine the ethical foundations of his model and Bernard Bass’ “transformational leadership”. Imprecise use of the terms “transforming”, “charismatic”, and “transformational” leads to an adoption of methods without adequate understanding of the underlying value system. This literature review compares and evaluates the source texts within a framework of world view, intention, character and menschenbild, as well as the Christian ethical mandates of Dietrich Bonhoeffer. Valuing the imago Dei in others has significant implications for a leader-follower relationship. Bonhoeffer’s mandates will help leaders reflect their position within their organisations and the wider society. Though the incentive for this research was leadership within the context of the Wycliffe Global Alliance, its findings will be relevant to Christian leadership in general, especially in intercultural contexts. / Philosophy & Systematic Theology / M. Th. (Theological Ethics with specialisation in Christian leadership in context)

Principles of “transforming leadership” have been widely promoted since the publication of James McGregor Burns’ book Leadership, especially among Christian leaders. The purpose of this study is to examine the ethical foundations of his model and Bernard Bass’ “transformational leadership”. Imprecise use of the terms “transforming”, “charismatic”, and “transformational” leads to an adoption of methods without adequate understanding of the underlying value system. This literature review compares and evaluates the source texts within a framework of world view, intention, character and menschenbild, as well as the Christian ethical mandates of Dietrich Bonhoeffer. Valuing the imago Dei in others has significant implications for a leader-follower relationship. Bonhoeffer’s mandates will help leaders reflect their position within their organisations and the wider society. Though the incentive for this research was leadership within the context of the Wycliffe Global Alliance, its findings will be relevant to Christian leadership in general, especially in intercultural contexts. / Philosophy and Systematic Theology / M. Th. (Theological Ethics with specialisation in Christian leadership in context)