This thesis is on quantum algorithms. It has three main themes: (1) quantum walk based search algorithms, (2) quantum rejection sampling, and (3) the Boolean function hidden shift problem. The first two parts deal with generic techniques for constructing quantum algorithms, and the last part is on quantum algorithms for a specific algebraic problem. In the first part of this thesis we show how certain types of random walk search algorithms can be transformed into quantum algorithms that search quadratically faster. More formally, given a random walk on a graph with an unknown set of marked vertices, we construct a quantum walk that finds a marked vertex in a number of steps that is quadratically smaller than the hitting time of the random walk. The main idea of our approach is to interpolate the random walk from one that does not stop when a marked vertex is found to one that stops. The quantum equivalent of this procedure drives the initial superposition over all vertices to a superposition over marked vertices. We present an adiabatic as well as a circuit version of our algorithm, and apply it to the spatial search problem on the 2D grid. In the second part we study a quantum version of the problem of resampling one probability distribution to another. More formally, given query access to a black box that produces a coherent superposition of unknown quantum states with given amplitudes, the problem is to prepare a coherent superposition of the same states with different specified amplitudes. Our main result is a tight characterization of the number of queries needed for this transformation. By utilizing the symmetries of the problem, we prove a lower bound using a hybrid argument and semidefinite programming. For the matching upper bound we construct a quantum algorithm that generalizes the rejection sampling method first formalized by von~Neumann in~1951. We describe quantum algorithms for the linear equations problem and quantum Metropolis sampling as applications of quantum rejection sampling. In the third part we consider a hidden shift problem for Boolean functions: given oracle access to f(x+s), where f(x) is a known Boolean function, determine the hidden shift s. We construct quantum algorithms for this problem using the "pretty good measurement" and quantum rejection sampling. Both algorithms use the Fourier transform and their complexity can be expressed in terms of the Fourier spectrum of f (in particular, in the second case it relates to "water-filling" of the spectrum). We also construct algorithms for variations of this problem where the task is to verify a given shift or extract only a single bit of information about it.

In this study a new tool was developed that made new approaches possible for the successful implementation of Demand Side Management (DSM) projects. The new approaches are incorporated into a generic tool that makes it possible for Energy Services Companies (ESCos) to undertake DSM projects that were previously not possible with currently available technology. Through these new approaches, maximum results can be obtained on a sustainable basis on the clear water pumping systems of South African mines. The author was responsible and participated in four different investigations and implementations of DSM projects. These were grouped into three case studies. Each of these studies required different new innovations. The innovations described in this thesis include the adaptation of the Real-time Energy Management System (REMS) that was developed and marketed by HVAC International, to mines with intricate pumping systems, mines without any instrumentation and control infrastructure, as well as to mines that make use of a Three Pipe Water Pumping System. The tool developed and applied in these projects was part of Eskom's DSM programme. In this programme, large electricity clients who wish to shift electrical load out of peak periods, are assisted by having the total costs of such projects funded by Eskom. The fact that the clients will most likely enjoy substantial electricity cost savings, (by not having to pay the high peak prices), is a major attraction of this programme. Nevertheless, the programme is not moving as fast as it should. The National Energy Regulator (NER) has set an annual target of 153 MW load to be shifted since 2003. By the end of 2005, the accumulated target load to be shifted will be 459 MW. However, Eskom has indicated that an accumulated total of only 181 MW load will have been shifted by the end of 2005. This means that the Eskom DSM programme has actually only achieved 39% of its target. The innovations described in this thesis will help ESCos to address this shortfall more effectively / Thesis (Ph.D. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2006

Eskom is currently facing an energy crisis due to the limited operational electricity generating capacity in South Africa. The historically low electricity price, the rapid growth in economy and the energy intensive nature of South African industries are the most common reasons for the peak supply problem. Various supply and demand technologies have been identified to address this energy crisis. Due to the lengthy process of building new peaking load power stations, Eskom has initiated the Demand-side Management (DSM) programme as a solution to the short-term supply problem. The National Energy Regulator (NER) has set targets to Eskom DSM to reduce the evening peak demand by 153 MW per annum and 4 255 MW over a 20-year planning horizon. Due to the energy intensive nature of the mining industry, it has been targeted for DSM savings. To date there have been a number of DSM projects implemented on the clear-water pumping systems of various mines, with a large potential for DSM savings identified on future projects still unrealised. The generation benefit of DSM load-shifting projects is twofold; firstly Eskom's evening load capacity increases due to the reduction in demand during these periods and secondly, the mine receives electricity cost savings due to load management practices. Because Eskom DSM is dependent on the client consumer to accept and roll-out the DSM programme, client satisfaction is of paramount importance. Due to the fact that load-shifting efforts require from the mine to change their normal operating schedules, there is uncertainty on the impact and knock-on effects of DSM projects on a mine. Therefore, the purpose of this study is to investigate and thereafter quantify the overall impact of DSM load-shifting on the clear-water pumping system of South African mines. A generic model was developed by performing case studies on existing DSM projects. This model was then applied to future DSM projects to validate the findings made throughout the research study. The case studies performed on existing DSM projects, as well as the results obtained when modelling the overall impact of DSM on future mines, proofs that DSM definitely benefits a mine. The total annual cost saving on the four future DSM projects is predicted to be in the order of R 7.64 million instead of the R 4.27 million when considering only the electricity cost savings to the mine. / Thesis (M.Ing. (Electrical Engineering))--North-West University, Potchefstroom Campus, 2007.

South Africa's national power utility, Eskom, initiated a Demand Side Management (DSM) drive to help alleviate the electricity supply shortage experienced in South Africa. The focus of this study is on a load-shifting intervention applied in the mining environment. Load shifting is an appealing way of reducing peak demand. The mining sector is one of the largest consumers of electricity in South Africa. The application of DSM in this sector has the potential of yielding significant electrical load shifting. Firstly, this helps Eskom because they are struggling to keep up their supply. Secondly, the mines also benefit because electrical load is shifted to less expensive off-peak times. Electricity cost as a percentage of the total cost of mining output is bound to increase considerably the next few years. An investigation was conducted into the potential ofperforming load shifting on complex underground rock winders the mining sector. This involved a thorough study on existing load-shifting applications on rock winder systems. Simulations were performed on rock winder systems in their different configurations at deep-level gold mines. The simulation results indicated that there was potential for the application ofload shifting. Tau Tona was selected as a case study. This decision was based on simulations to establish which of the initially identified mines would be the best candidate for load shifting. Tau Tona has a complex underground rock winder system. Multiple rock winders feeding each other are used in a cascaded configuration. A potential load shifting target of 3' MW in the evening peak period was determined by means of simulation. The rock winder system was sequentially automated. An average evening peak demand load shift of 1 MW (or 4,2 MWh) was achieved. This translates to an average annual cost saving of R 240 000. If the load-shifting target of 3 MW could be obtained, the annual cost savings would increase by 30% to R 343 000. A study was also conducted on the feasibility of implementing maximum demand monitoring and control. Rock winders could be used in future to prevent the mines from exceeding their maximum demand. This is because rock winders consume very large amounts of electricity and can be stopped and restarted very quickly. Huge financial obligations can be prevented by making sure that the mines do not exceed their negotiated maximum demand. The necessary - and costly infrastructure to do this could not be procured during this study. / Thesis (M.Ing. (Electrical Engineering))--North-West University, Potchefstroom Campus, 2010.

Night shift or non-standard work continues to grow throughout the economy (Beers, 2000). Women's roles in society are changing as they find themselves having to join the work force due to economic need. South African women most of whom are mothers are no exception in this regard. Many of these mothers are obliged to do night shift work. Sectors like manufacturing and public-oriented industries often use shift work to ensure efficient continuous operation and uninterrupted response to the needs of society. This article aims to explore the role that night shift work plays in the relationships between mothers and their adolescent children; whether the mutual perceptions of night shift working mothers and their adolescent children regarding their relationships differ from those of non-shift working mothers and their adolescent children; and whether there is a difference between the night shift working group and the non-shift working group with regard to the perceptions of their relationships. Lastly, the article aims to determine the reliability of the measuring instrument that was used in this study, namely the Parent-Adolescent-Relationship-Questionnaire (PARQ). Available literature shows that shift work has a negative impact on health, for example stress-related illnesses due to lack of sleep (Akerstedt, 1998, 2003; Fletcher & Dawson, 1997, 2001; Presser, 2005). Family life is also affected and relationship difficulties have been reported (Chang, Wang, & Liu, 1993; Holland, 2004; Grosswald, 2003, 2004; Presser, 1995, 2000, 2003, 2005), while shift work is seen as a threat to family cohesion. Adolescence is a critical developmental stage and mothers have an important role to enhance healthy adolescent development in terms of issues like self-identity and autonomy. The mother's unusual working hours can have a negative impact on the mother-adolescent relationship. A cross-sectional design was used in this study. There were two groups: 35 night shift working mothers and their adolescent children, and 35 non-shift working mothers and their adolescent children. Participants were requested to complete a PARQ questionnaire. Data was analysed by means of SAS and SPSS programmes. Descriptive statistic methods such as central tendency, mean and median, variability, range and standard deviation, skewness and kurtosis were used to explore data. Independent and dependent t-tests were used to determine differences between the mean scores of the night shift working and non-shift working mothers and their adolescent children. The effect size was used to provide an objective measure of a practical effect. The findings indicate that PARQ is a reliable measure for this study as it showed good internal consistency. The skewness and kurtosis indicate acceptable normality. Adolescent children of non-shift working mothers perceive communication with their mothers as more efficient than adolescent children of night shift working mothers, and there is an indication of a significant practical effect. Adolescent children of non-shift working mothers have a more positive perception of the Mothers' Problem Solving than adolescent children of night shift working mothers, with indications of a significant practical effect between the two groups. There is no statistically significant difference between and no significant practical effect in any of the variables concerning the two groups of mothers, as reflected in Table 4. However, Table 5 shows a difference between the perceptions of the two groups of adolescents. There is a statistically significant difference between Cohesion for non-shift working mothers and for their adolescent children, with an indication of a significant practical effect. Tables 5 and 6 show a statistically significant difference between Conventionalisation of the two groups, with an indication of a significant practical effect. Both night shift working and non-shift working mothers have a more positive perception of Conventionalisation than their adolescent children. Findings also indicate a statistically significant difference in Global Distress between night shift working mothers and their adolescent children, with an indication of a significant practical effect. Night shift working mothers experience higher levels of Global Distress than their adolescent children. For both groups -night shift working mothers and their adolescent children; and non-shift working mothers and their adolescent children there is a statistically significant difference between the mothers' and the adolescents' perception of Ruination. This study has several limitations and it is recommended that future studies use a larger sample size and include longitudinal studies. Future research should also explore the construct of the night shift working mother's parenting style and their coping strategies. Father-adolescent relationships should also be a research focus. In some families in both groups, the study created a platform for dialogue between adolescents and their mothers. / Thesis (M.A. (Clinical Psychology))--North-West University, Potchefstroom Campus, 2010.

Problem: Many individuals with chronic illnesses such as stroke and ongoing activity limitations report self-perceived health related quality of life (HRQL) that is similar to that of healthy individuals. This phenomenon is termed response shift (RS). RS describes how people change: internal standards in assessing HRQL (recalibration), values (reprioritization), or how they define HRQL (reconceptualization), after an event such as stroke. Changes in HRQL post stroke may be inaccurate if RS is not taken into account. Increased knowledge of RS may affect the way in which HRQL measures are used, both clinically and in research. The overall objective was to assess RS in construct specific HRQL models post stroke: physical function, mental health, and participation. Methods: Data were analysed from the longitudinal study “Understanding Quality of Life Post-Stroke: A Study of Individuals and their Caregivers”. Six-hundred and seventy- eight persons with stroke at 1, 3, 6, and 12 months post stroke participated. Generic and stroke specific HRQL measures were collected. Descriptive analysis was completed with SAS, and identification of RS utilized structural equation modeling with LISREL. Results: Mean age of participants was 67 years (SD 14.8), and 45% were female. RS was identified in mental health using a framework which was developed for identifying RS statistically with multiple time points. RS was also identified in physical function where it had not been expected, possibly due to the self perceived nature of the response options. The effect size of change in physical function was affected by the presence of RS. The timing of RS in mental health and physical function was primarily around the 12 month time period, and predominantly recalibration RS. RS was also identified in participation. Conclusions: The framework that was developed was useful in identifying RS and incorporated important issues such as multiple testing and validation of the model. The presence of RS affects measurement of HRQL constructs post stroke; recalibration RS can be measured clinically with specific methods to account for RS. RS should also be measured in research studies to ensure accurate measurement of change. Future research should evaluate additional models in stroke and other populations.

Eskom is currently facing an energy crisis due to the limited operational electricity generating capacity in South Africa. The historically low electricity price, the rapid growth in economy and the energy intensive nature of South African industries are the most common reasons for the peak supply problem. Various supply and demand technologies have been identified to address this energy crisis. Due to the lengthy process of building new peaking load power stations, Eskom has initiated the Demand-side Management (DSM) programme as a solution to the short-term supply problem. The National Energy Regulator (NER) has set targets to Eskom DSM to reduce the evening peak demand by 153 MW per annum and 4 255 MW over a 20-year planning horizon. Due to the energy intensive nature of the mining industry, it has been targeted for DSM savings. To date there have been a number of DSM projects implemented on the clear-water pumping systems of various mines, with a large potential for DSM savings identified on future projects still unrealised. The generation benefit of DSM load-shifting projects is twofold; firstly Eskom's evening load capacity increases due to the reduction in demand during these periods and secondly, the mine receives electricity cost savings due to load management practices. Because Eskom DSM is dependent on the client consumer to accept and roll-out the DSM programme, client satisfaction is of paramount importance. Due to the fact that load-shifting efforts require from the mine to change their normal operating schedules, there is uncertainty on the impact and knock-on effects of DSM projects on a mine. Therefore, the purpose of this study is to investigate and thereafter quantify the overall impact of DSM load-shifting on the clear-water pumping system of South African mines. A generic model was developed by performing case studies on existing DSM projects. This model was then applied to future DSM projects to validate the findings made throughout the research study. The case studies performed on existing DSM projects, as well as the results obtained when modelling the overall impact of DSM on future mines, proofs that DSM definitely benefits a mine. The total annual cost saving on the four future DSM projects is predicted to be in the order of R 7.64 million instead of the R 4.27 million when considering only the electricity cost savings to the mine. / Thesis (M.Ing. (Electrical Engineering))--North-West University, Potchefstroom Campus, 2007.

South Africa's national power utility, Eskom, initiated a Demand Side Management (DSM) drive to help alleviate the electricity supply shortage experienced in South Africa. The focus of this study is on a load-shifting intervention applied in the mining environment. Load shifting is an appealing way of reducing peak demand. The mining sector is one of the largest consumers of electricity in South Africa. The application of DSM in this sector has the potential of yielding significant electrical load shifting. Firstly, this helps Eskom because they are struggling to keep up their supply. Secondly, the mines also benefit because electrical load is shifted to less expensive off-peak times. Electricity cost as a percentage of the total cost of mining output is bound to increase considerably the next few years. An investigation was conducted into the potential ofperforming load shifting on complex underground rock winders the mining sector. This involved a thorough study on existing load-shifting applications on rock winder systems. Simulations were performed on rock winder systems in their different configurations at deep-level gold mines. The simulation results indicated that there was potential for the application ofload shifting. Tau Tona was selected as a case study. This decision was based on simulations to establish which of the initially identified mines would be the best candidate for load shifting. Tau Tona has a complex underground rock winder system. Multiple rock winders feeding each other are used in a cascaded configuration. A potential load shifting target of 3' MW in the evening peak period was determined by means of simulation. The rock winder system was sequentially automated. An average evening peak demand load shift of 1 MW (or 4,2 MWh) was achieved. This translates to an average annual cost saving of R 240 000. If the load-shifting target of 3 MW could be obtained, the annual cost savings would increase by 30% to R 343 000. A study was also conducted on the feasibility of implementing maximum demand monitoring and control. Rock winders could be used in future to prevent the mines from exceeding their maximum demand. This is because rock winders consume very large amounts of electricity and can be stopped and restarted very quickly. Huge financial obligations can be prevented by making sure that the mines do not exceed their negotiated maximum demand. The necessary - and costly infrastructure to do this could not be procured during this study. / Thesis (M.Ing. (Electrical Engineering))--North-West University, Potchefstroom Campus, 2010.

Night shift or non-standard work continues to grow throughout the economy (Beers, 2000). Women's roles in society are changing as they find themselves having to join the work force due to economic need. South African women most of whom are mothers are no exception in this regard. Many of these mothers are obliged to do night shift work. Sectors like manufacturing and public-oriented industries often use shift work to ensure efficient continuous operation and uninterrupted response to the needs of society. This article aims to explore the role that night shift work plays in the relationships between mothers and their adolescent children; whether the mutual perceptions of night shift working mothers and their adolescent children regarding their relationships differ from those of non-shift working mothers and their adolescent children; and whether there is a difference between the night shift working group and the non-shift working group with regard to the perceptions of their relationships. Lastly, the article aims to determine the reliability of the measuring instrument that was used in this study, namely the Parent-Adolescent-Relationship-Questionnaire (PARQ). Available literature shows that shift work has a negative impact on health, for example stress-related illnesses due to lack of sleep (Akerstedt, 1998, 2003; Fletcher & Dawson, 1997, 2001; Presser, 2005). Family life is also affected and relationship difficulties have been reported (Chang, Wang, & Liu, 1993; Holland, 2004; Grosswald, 2003, 2004; Presser, 1995, 2000, 2003, 2005), while shift work is seen as a threat to family cohesion. Adolescence is a critical developmental stage and mothers have an important role to enhance healthy adolescent development in terms of issues like self-identity and autonomy. The mother's unusual working hours can have a negative impact on the mother-adolescent relationship. A cross-sectional design was used in this study. There were two groups: 35 night shift working mothers and their adolescent children, and 35 non-shift working mothers and their adolescent children. Participants were requested to complete a PARQ questionnaire. Data was analysed by means of SAS and SPSS programmes. Descriptive statistic methods such as central tendency, mean and median, variability, range and standard deviation, skewness and kurtosis were used to explore data. Independent and dependent t-tests were used to determine differences between the mean scores of the night shift working and non-shift working mothers and their adolescent children. The effect size was used to provide an objective measure of a practical effect. The findings indicate that PARQ is a reliable measure for this study as it showed good internal consistency. The skewness and kurtosis indicate acceptable normality. Adolescent children of non-shift working mothers perceive communication with their mothers as more efficient than adolescent children of night shift working mothers, and there is an indication of a significant practical effect. Adolescent children of non-shift working mothers have a more positive perception of the Mothers' Problem Solving than adolescent children of night shift working mothers, with indications of a significant practical effect between the two groups. There is no statistically significant difference between and no significant practical effect in any of the variables concerning the two groups of mothers, as reflected in Table 4. However, Table 5 shows a difference between the perceptions of the two groups of adolescents. There is a statistically significant difference between Cohesion for non-shift working mothers and for their adolescent children, with an indication of a significant practical effect. Tables 5 and 6 show a statistically significant difference between Conventionalisation of the two groups, with an indication of a significant practical effect. Both night shift working and non-shift working mothers have a more positive perception of Conventionalisation than their adolescent children. Findings also indicate a statistically significant difference in Global Distress between night shift working mothers and their adolescent children, with an indication of a significant practical effect. Night shift working mothers experience higher levels of Global Distress than their adolescent children. For both groups -night shift working mothers and their adolescent children; and non-shift working mothers and their adolescent children there is a statistically significant difference between the mothers' and the adolescents' perception of Ruination. This study has several limitations and it is recommended that future studies use a larger sample size and include longitudinal studies. Future research should also explore the construct of the night shift working mother's parenting style and their coping strategies. Father-adolescent relationships should also be a research focus. In some families in both groups, the study created a platform for dialogue between adolescents and their mothers. / Thesis (M.A. (Clinical Psychology))--North-West University, Potchefstroom Campus, 2010.

This thesis presents a study of high-redshift obscured (type-2) quasars, selected at mid-infrared and radio wavelengths. This population had remained elusive, even to hard X-ray surveys, and in Chapter 2 I compare the selection of type-2 quasars in X-ray and mid-infrared surveys, as well as explaining the criteria I will use to search for these objects at z ~ 2, around the peak in the unobscured (type-1) quasar activity. Chapter 3, presents a sample of radio-intermediate type-2 quasars selected from the criteria de- scribed in Chapter 2. Optical spectroscopy shows indeed that at least half of the objects have the characteristic narrow emission lines, and lie around the expected redshift of z = 2. The other half of the objects are consistent with also being type-2 quasars at similar redshifts, although no emission lines are visible. In Chapter 4,1 discuss the possibility of two types of obscured quasars, some obscured by a dusty torus and some by a dusty host galaxy, to explain the lack of emission lines in half of the sample. I model the number of type-1 quasars expected to follow similar selection criteria and at the same redshifts as our type-2 quasars, and find that the obscured quasars outnumber the unobscured by a ~2-3:1 ratio. I conclude that most supermassive black hole growth is obscured by dust. When comparing this to predictions from unified schemes, I find that this result is only consistent with the schemes provided host-obscuration is indeed happening. The lower ratio of type-2 to type-1 quasars inferred from X-ray surveys (~1:1) suggests that some of the type-2 quasars in this sample might be Compton thick. Radio data taken at three frequencies, are presented in Chapter 5, to study the spectral properties and intrinsic luminosities of our sample. I show that some type-2 quasars have flat radio spectra, which is inconsistent with obscuration by the torus, but consistent with host-obscuration. Some gigahertz-peaked spectra, characteristic of young radio jets, are present, but the majority of the sources have very steep spectra. These steep spectral indices can be explained by active developed jets in which continuous injection of electrons is accompanied by inverse-Compton losses against the cosmic microwave background. In Chapter 6, I select a similar sample of type-2 quasars in a different field, where X-ray data are available. The selection criteria are kept identical, except for the radio flux density cut, which is lowered. This is expected to introduce significant numbers of starburst contaminants. To filter these out, and due to a lack of spectroscopy, I use a bayesian method to fit the spectral energy distributions, obtain photometric redshifts, and select between a quasar and a starburst model. I measure the X-ray properties for the resultant sample of type-2 quasars. The entire sample is found to be Compton-thick, and repeating the modelling of Chapter 4, I find that the population of Compton-thick quasars is at least comparable to the population of unobscured quasars, and probably larger.