Thesis (MSc)--University of Stellenbosch, 2006. / ENGLISH ABSTRACT: We are studying a possible implementation of an appropriate framework for a proper non- Hermitian quantum theory. We present the case where for a non-Hermitian Hamiltonian with real eigenvalues, we define a new inner product on the Hilbert space with respect to which the non-Hermitian Hamiltonian is Quasi-Hermitian. The Quasi-hermiticity of the Hamiltonian introduces the bi-orthogonality between the left-hand eigenstates and the right-hand eigenstates, in which case the metric becomes a basis transformation. We use the non-Hermitian quadratic Hamiltonian to show that such a metric is not unique but can be uniquely defined by requiring to hermitize all elements of one of the irreducible sets defined on the set of all observables. We compare the constructed metric with specific known examples in the literature in which cases a unique choice is made. / AFRIKAANSE OPSOMMING: Ons ondersoek die implementering van n gepaste raamwerk virn nie-Hermitiese kwantumteorie. Ons beskoun nie-Hermitiese Hamilton-operator met reele eiewaardes en definieer in gepaste binneproduk ten opsigtewaarvan die operator kwasi-Hermitiese is. Die kwasi- Hermities aard van die Hamilton operator lei dan tot n stel bi-ortogonale toestande. Ons konstrueer n basistransformasie wat die linker en regter eietoestande van hierdie stel koppel. Hierdie transformasie word dan gebruik omn nuwe binneproduk op die Hilbert-ruimte te definieer. Die oorspronklike nie-HermitieseHamilton-operator is danHermitiesmet betrekking tot hierdie nuwe binneproduk. Ons gebruik die nie-Hermitiese kwadratieseHamilton-operator omte toon dat hierdie metriek nie uniek is nie, maar wel uniek bepaal kan word deur verder te vereis dat dit al die elemente van n onherleibare versameling operatoreHermitiseer. Ons vergelyk hierdie konstruksiemet die bekende voorbeelde in die literatuur en toon dat diemetriek in beide gevalle uniek bepaal kan word.

Quantum theory is a probabilistic theory, where certain variables are hidden or non-accessible. It results in lack of representation of systems under study. However, I deduce system's representation in probabilistic manner, introducing probability of existence w, and quantize it exploiting Schrödinger's quantization rule. The formalism enriches probabilistic quantum theory, and enables system's representation in probabilistic manner.

Local government, as government at grassroot, has, probably undergone transformation more than any institution in post-1994 South Africa. State-of the- art legislation have been passed that have restructured municipalities, and, especially, in the areas of performance and conduct of councillors and officials. Prominent in the areas of transformation are the roles of the Executive Mayor, which are no longer ceremonial as well as the radical changes which have been legislated in municipal financial management. This study was undertaken to determine the challenges that confront the Executive Mayor in financial management in selected local municipalities in the Free State. The hypothesis was formulated that “despite the state-of-the art legislation to regulate municipal finance, Executive Mayors in municipalities face the challenge of poor service delivery as a result of noncompliance to financial statutes due to human resource incapacity”. To test the hypothesis, use was made by empirical research that comprised questionnaires completed by sample of managers and officials in the selected local municipalities of Mafube, Metsimaholo, Moqhaka and Ngwathe.The findings, amongst others, were that: • Human capital in the 4 selected local municipalities are in their prime age. 69 present of managers are in the aged between 30 years to 50 years; • 57 present of the managers responded that they have adequate qualifications and training to pursue the challenges in municipal finance; • All 4 municipalities normally get their budgets approved as required by compliance. • The hypothesis was consequently, invalidated. The study ends with recommendations to help improve standards and quality of financial management practice in the 4 municipalities. / MA (Industrial Psychology), North-West University, Vaal Triangle Campus, 2014

Purpose: This study aims to (1) describe and analyse the local ground operator’s role in the network of the Botswana tourism industry, (2) to investigate what factors characterize and influence their relationships with foreign tour operators, as well as (3) to provide implications for improving these relations. Methodology: This study has been conducted as a case study, where the empirical data was collected during a two months field trip to Botswana. A qualitative research method, and a deductive approach has been used. Five semi-structured interviews were conducted with ground operators to get their perspective of their own situation, and one with a person representing a governmental organisation. Most data was collected through the interviews, but participating observation also served as a source of information. The validity and reliability of the study has been enhanced by defining core concepts, interviewing several respondents, using an interview guide and recording most of the interviews. Results: Local ground operators play are crucial role in the network of Botswana’s tourism industry, as they are engaged in a high number of business relationships, are bringing the services at the destination together, and are connecting them to the tourists. They play a role as both customers and suppliers. Their relationship to tour operators abroad consists of a lot of resource ties, activity links as well as some actor bonds. Trust is found to be a very essential part of the relationship, and they perceive themselves as being dependent on the tour operators. Culture is not identified as a major influencing factor. As for managerial recommendations, a better communication in expectations and an increased adaptation of products and processes, to create customer dependence, are among the results advised.

We investigate properties of Koszmider spaces. We show that if K and L are compact Hausdor spaces with no isolated points, K is Koszmider and C(K) is isomorphic to C(L), then K and L are homeomorphic and, in particular, L is also Koszmider. We also analyse topological properties of Koszmider spaces and show that a connected Koszmider space is strongly rigid. In addition to Koszmider spaces, we introduce the notion of weakly Koszmider spaces. Having established an alternative characterisation thereof, we show that, while it is evident that every Koszmider space is weakly Koszmider, the reverse implication does not hold. We also prove that if C(K) and C(L) are isomorphic and K is weakly Koszmider, then so is L. However, if K is Koszmider, there always exists a non-Koszmider space L such that C(K) and C(L) are isomorphic. In the second part of the thesis we present two separable Koszmider spaces the construction of which does not use any set-theoretical assumptions except for the usual (ZFC) axioms. The first space is zero-dimensional, being the Stone space of a Boolean algebra. The second construction results in a separable connected Koszmider space.

Oscillatory integral operators have been of interest to both mathematicians and physicists ever since the emergence of the work Theorie Analytique de la Chaleur of Joseph Fourier in 1822, in which his chief concern was to give a mathematical account of the diffusion of heat. For example, oscillatory integrals naturally arise when one studies the behaviour at infinity of the Fourier transform of a Borel measure that is supported on a certain hypersurface. One reduces the study of such a problem to that of having to obtain estimates on oscillatory integrals. However, sub-level set operators have only come to the fore at the end of the 20th Century, where it has been discovered that the decay rates of the oscillatory integral I(lambda) above may be obtainable once the measure of the associated sub-level sets are known. This discovery has been fully developed in a paper of A. Carbery, M. Christ and J.Wright. A principal goal of this thesis is to explore certain uniformity issues arising in the study of sub-level set estimates.

>Magister Scientiae - MSc / Although the interior operators correspond to a special class of neighbourhood operators, the closure operators are not nicely related to the latter. We introduce and study the notion of topogenous orders on a category which provides a basis for categorical study of topology. We show that they are equivalent to the categorical neighbourhood operators and house the closure and interior operators. The natural notion of strict morphism with respect to a topogenous order is shown to capture the known ones in the settings of closure, interior and neighbourhood operators.

MPH, Occupational Hygiene, Faculty of Health Sciences, University of the Witwatersrand / Introduction Locomotive operators in the mining industry are exposed to high levels of noise and vibration. There is currently limited information indicating whole-body vibration exposure levels conducted over an 8-hour time weighted average (TWA) exposure period; most of the available data are based on instantaneous measurements. The 10-Ton New Era locomotive was specifically designed with the focus on areas such as ergonomics, safety, future automation, productivity and flexibility of use. The locomotive has a single cab and can be driven and controlled with maximum visibility in the direction of travel. Most mining houses are converting from the use of the 10 Ton Goodman battery operated locomotive to the 10Ton New Era locomotive, hence the focus of noise and vibration measurements on the latter. Objectives This research report documents a project to measure noise and whole-body vibration exposure levels of locomotive operators working in an underground platinum mine. The objectives of the study are: • to describe the eight hour time weighted average occupational noise exposure levels of locomotive operators operating the 10-Ton New Era locomotive in an underground platinum mine over 2008 and 2009; • to describe personal whole-body vibration exposure levels of locomotive operators operating the 10-Ton New Era locomotive in an underground platinum mine over 2008 and 2009; and 5 • to determine whether personal noise and whole-body vibration exposure levels of locomotive operators operating the 10-Ton New Era locomotive in an underground platinum mine over 2008 and 2009 comply with national and international standards. Methods Personal noise and whole-body vibration exposure measurements were obtained from 21 underground locomotive operators. Measurements were conducted in accordance with the procedures described in the SANS 10083 standard for personal noise dosimetry and the ISO 2631-1 standard for whole-body vibration. Determination of likely health risks for the operators were based on a comparison of the measured time-weighted noise exposure levels with the South African OEL and the ACGIH threshold limit value; whole-body vibration levels were compared with the HGCZ limits presented in Annex B of the ISO 2631-1 standard and the EU directive daily exposure limits. Results The measured noise and whole-body vibration levels taken over an 8-hour TWA exposure period were higher when compared to national and international standards. The mean LTWA levels for noise was 66.5 dB(A) with 12.5% of the measurements exceeding the South African OEL of 85dB(A). 45% of the wholebody vibration measurements fell within the HGCZ indicating that whole-body vibration exposure on locomotive operators presents a moderate probability for an adverse health outcome. Discussion and Conclusion Locomotive operators are exposed to potentially harmful levels of noise and whole-body vibration. The Mine Health and Safety Act requires an employer to assess the health and safety risks that hazards pose to their employees, and to take reasonably practicable steps towards eliminating or controlling those risks. Like any other risks at a workplace, noise and whole-body vibration needs to be 6 identified and controlled, and the approach to be taken is one of a risk management

A Thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg for the Degree of Doctor of Philosophy. Johannesburg, 1979

The purpose of the study was to evaluate hairdressers self monitoring. The frame of the questions were for instance to find out if hairdressers self monitoring were sufficient and the experience among operators and inspectors. Self monitoring by operators is a crucial part of Swedish environmental law. It is required that operators has control of every aspect of the business and complies with the environmental law. Self monitoring include routines that occurs in the daily operation. Non mandatory to report environmentally hazardous businesses are not required to have a documented self monitoring. Data were collected through inspection and interviews with nine operators and eleven inspectors. Results showed that hairdressers usually had adequate self monitoring. In 17 of 24 controlled businesses there were no discrepancies noticed. The operators were mostly positive towards supervision and self monitoring. The study showed that operators in non mandatory to report businesses had a slightly inaccurate depiction of the supervisory authority. Inspectors claim that discrepancies in self monitoring usually depend on lack of knowledge and limited economical resources. The inspectors suggested that the requirements of self monitoring should be made more evident.