In the numerical solution of the two point "boundary value problem, [ equation omitted ] (1) the usual method is to approximate the problem by a finite difference analogue of the form [ equation omitted ] (2) with k = 2, and the truncation error T.E. = O(h⁴) or O(h⁶), where h is the step-size. Varga (1962) has obtained error bounds for the former when the problem (1) is linear and of class M . In this thesis, more accurate finite difference methods are considered. These can be obtained in essentially two different ways, either by increasing the value k in difference equations (2), or by introducing higher order derivatives. Several methods of both types have been derived. Also, it is shown how the initial value problem y' = ϕ(x,y) can be formulated as a two point boundary value problem and solved using the latter approach. Error bounds have been derived for all of these methods for linear problems of class M . In particular, more accurate bounds have been derived than those obtained by Varga (1962) and Aziz and Hubbard (1964). Some error estimates are suggested for the case where [ equation omitted ], but these are not accurate bounds, especially when [ equation omitted ] not a constant. In the case of non-linear differential equations, sufficient conditions are derived for the convergence of the solution of the system of equations (2) by a generalized Newton's method. Some numerical results are included and the observed errors compared with theoretical error bounds. / Science, Faculty of / Mathematics, Department of / Graduate

This thesis investigates the viability of two boundary element methods for solving steady state problems, the continuous least squares method and the Galerkin minimization technique. In conventional boundary element methods, the singularities of the fundamental solution involved are usually located at fixed points on the boundary of the problem's domain or on an auxiliary boundary. This leads to some difficulties: when the singularities are located on the problem domain's boundary, it is not easy to evaluate the solution for points on or near that boundary whereas if the singularities are placed on an auxiliary boundary, this auxiliary boundary would have to be carefully chosen. Hence the methods studied here allow the singularities, initially located at some auxiliary boundary, to move until the best positions are found. These positions are determined by attempting to minimize the error via the least squares or the Galerkin technique. This results in a highly accurate, adaptive, but nonlinear method. We study various methods for solving systems of nonlinear equations resulting from the Galerkin technique. A hybrid method has been implemented, which involves the objective function from the least squares method while the gradient is due to the Galerkin method. Numerical examples involving Laplace's equation in two dimensions are presented and results using the discrete least squares method, the continuous least squares method and the Galerkin method are compared and discussed. The continuous least squares method appears to give the best results for the sample problems tried. / Science, Faculty of / Computer Science, Department of / Graduate

A one-dimensional, single phase Stefan Problem is considered. This problem is shown to have a unique solution which depends continuously on the boundary data. In addition two algorithms are formulated for its approximate numerical solution. The first algorithm (the Similarity Algorithm), which is based on Similarity, is shown to converge with order of convergence between one half and one. Moreover, numerical examples illustrating various aspects of this algorithm are presented. In particular, modifications to the algorithm which are suggested by the proof of convergence are shown to improve the numerical results significantly. Furthermore, a brief comparison is made between the algorithm and a well-known difference scheme. The second algorithm (a Collocation Scheme) results from an attempt to reduce the problem to a set of ordinary differential equations. It is observed that this set of ordinary differential equations is stiff. Moreover, numerical examples indicate that this is a high order scheme capable of achieving very accurate approximations. It is observed that the apparent stiffness of the system of ordinary differential equations renders this second algorithm relatively inefficient. / Science, Faculty of / Statistics, Department of / Graduate

The purpose of the study was to establish relationships pertaining to the use of practices involving the prevention or correction of discipline problems between academic and industrial arts teachers.

MPH / Department of Public Health / Abstract Lecturers are important agents in the provision of tertiary education at Technical Vocational Education and Training Colleges, however their effectiveness is highly compromised by health related factors. Lecturers can be exposed to variety of hazards in the workplace owing to chemicals, biological agents, physical factors, adverse ergonomic conditions, allergens and a complex network of safety risks. This conditions can led to the development of certain health related factors that can intern impose negative effects on lecturers job performance. The aim of the study was to determine the health-related factors affecting lecturers’ job performance at Vhembe Technical Vocational Education and Training College. A quantitative approach in the form of a survey, using a descriptive research design, was used in this study. Data was collected from permanent lecturers at Vhembe Technical Vocational Education and Training College. Total sampling was used due to the number of lecturers which is already low. A total of 250 respondents were used to collect data, with edge ranges from 26 to 60 years. A structured questionnaire was used to collect data regarding demographic characteristics, physical health problems, emotional problems, mental health problems and chronic diseases. The Statistical Package for Social Sciences version 25.0 was used to analyse the data. Validity and reliability was ensured. The researcher also observed the primary ethical principles upon which standards of ethical conduct in research was based. The results of this study indicate that health related factors affect lecturers’ job performance. About 85% of the respondents indicated that they are absent from work due to work related problems. More than 50% of the respondents revealed that lecturers consult doctors several times within a year due to health related problems, are affected by emotional problems, mental health problems, physical health problems as well as chronic diseases. It is recommended that Management should address the issue of absenteeism comprehensively. An institution of higher learning should have a clinic which is fully supplied with medicines including health professionals such as registered Nurses. Management should employ registered counsellors and registered Psychometrics. Management should put in place health-promoting conditions within the campuses. Giving lecturers reasonable amount of work load would be useful. Management should develop a plan to monitor and evaluate the working environment. Lecturers should organise their work and prioritise activities to avoid rush production. / NRF

Thesis (M.A.)--Boston University / Procedures to reshape the cornea to correct refractive errors have been a longstanding and fast-evolving area of interest for centuries. As recent advances in excimer laser technology allow keratorefractive treatments to deliver precise treatments with fewer associated risks and complications, the popularity of modern refractive procedures continues to grow at unprecedented rates. For this reason, it is imperative to continue correlating patient characteristics to outcomes so that refractive surgeons can more accurately foresee the results of the selected procedure. This study examined the outcomes of refractive surgeries at a full-scope ophthalmology clinic from January 2011 to November 2011. The main objectives of th is study were to determine the differences between the outcomes of LASIK vs. LASEK, Custom vs. Traditional treatment plans, myopic vs. hyperopic patients and MMC exposure vs. no MMC exposure (LASEK only). More importantly, the data was scrutinized to determine whether or not any of these treatments and/or patient characteristics correlated with poor visual outcomes or the need for an enhancement. Of the 590 myopic eyes treated with Custom LASIK, 90.85% (n=536 eyes) had UDVA of 20/20 or better, 96.10% (n=567 eyes) had UDVA of 20/25 or better and 99.32% (n=586 eyes) had UDVA of 20/40 or better. Of the 170 myopic eyes treated with Custom LASEK, 70.59% (n=120 eyes) had a UDVA of 20/20 or better, 82.94% (n=141 eyes) had a UDVA of 20/25 or better and 96.47% (n=164 eyes) had a UDVA of 20/40 or better. Of the 45 hyperopic eyes that were treated with Traditional LASIK, 44.44% (n=20 eyes) had postoperative UDVA of 20/20 or better, 62.22% (n=28 eyes) had postoperative UDVA of 20/25 or better and 82.22% (n=37 eyes) had postoperative UDVA of 20/40 or better. Of the 536 eyes receiving LASIK, 91.42% (n=490 eyes) had an UDVA of 20/20 or better, 96.46% (n=517 eyes) had an UDVA of 20/25 or better and 99.44% (n=533 eyes) had an UDVA of 20/40 or better. Of the 146 low or moderately myopic eyes receiving Custom LASEK, 74.65% (n=106 eyes) had an UDVA of 20/20 or better, 86.62% (n=123 eyes) had an UDVA of 20/25 or better and 96.48% (n=137 eyes) had an UDVA of 20/40 or better. Of the 54 highly myopic eyes treated with Custom LASIK, 85.19% (n=46 eyes) had an UDVA of 20/20 or better, 92.59% (n=50 eyes) had an UDVA of 20/25 or better, and 98.15% (n=53 eyes) had an UDVA of 20/40 or better. Of the 28 highly myopic eyes treated with Custom LASEK, 53.57% (n=15 eyes) had an UDVA of 20/20 or better, 64.29% (n=18 eyes) had an UDVA of 20/25 or better, and 96.43% (n=27 eyes) had an UDVA of 20/40 or better. An analysis of these data yields significantly greater percentages of myopic (low, moderate and high) eyes achieving 20/20 or better after treatment by Custom LASIK versus Custom LASEK. The data suggested no correlations between poor visual outcomes and/or the need for an enhancement treatment and intraoperative complications, magnitude of ametropia, pupil size, age, treatment type, and treatment plan. All of the LASEK patients who underwent an enhancement treatment were exposed to MMC during their original procedure. Hyperopic patients displayed significantly reduced visual outcomes than comparable myopic treatments. Future studies should investigate similar preoperative characteristics and attempt to correlate them to results to improve predictability and, thus, visual outcomes.

Submitted in partial fulfillment of the requirements for the degree MASTER OF EDUCATION in the Department of Educational Psychology and Special Needs Education of the Faculty of Education at the University of Zululand, 2008. / The aim of this study was to pursue an investigation into the impact reading disabilities have on the academic achievement of a primary school learner. From the literature study it became evident that learners with reading problems are faced with a lot of problems in primary schools. These problems are manifest in the form of prejudice stigmatization, humiliation and pressure as they often find the teaching and learning materials beyond their scope of comprehension. There is a need for educator support so that they can fine-tune their instruction to suit the level of the learners with reading problems and for educators to garner the support of parents who may be uninterested about what obtains at school. Learners with reading problems can be helped by educators whose learning activities are well planned and prepared and their presentation has to captivate the learner’s attention, interest and involvement. If learners with reading problems do not receive adequate support, they may exhibit the following:  Behavioural problems e.g. being disobedient to the educator.  Have a low frustration threshold.  Develop a negative self-esteem.  Set unrealistic goals for themselves.  Ultimately drop out of school.  Play truant  Shirk their school work.  Absent themselves from school. Nevertheless, educators need to create a stimulating atmosphere, to exploit reinforcement strategies and set good examples, such as:  Tangible motivators, for example, stars, edibles (nuts and fruits), cinema tickets, colouring books.  Activity orientated motivators such as helping the educator, free play, watching television, painting or drawing.  Social motivators, such as a smile, nod of head etc. In conclusion a summary was presented on the findings of the literature and empirical study and recommendations are made based on the nature of assistance required by the educators in order to help the learner with reading problems. The recommendations touched on remedial approaches and teaching activities that educators need to utilize to help the reading disabled learner. Further research should be conducted on barriers to learning that could emanate from inappropriate pedagogy, insufficient support for educators, inappropriate and unfair assessment procedures

Submitted in Partial Fulfillment of the Requirements for the Degree of PhD (Community Psychology) Faculty of Arts University of Zululand, 2008. / Research indicates that the prevalence of childhood depression is increasing, the onset of depression is occurring earlier in life, and that depression coexists with other mental health problems such as anxiety and disruptive behaviour disorders. Teachers are more responsive to behavioural manifestations such as hyperactivity, disruptive behaviour and aggression. They are less responsive to interpersonal difficulties and less disruptive behaviours such as withdrawal and social isolation. While they can correctly recognize that internalizing symptoms such as withdrawal and sadness are indicators of depression, they are unable to correctly recognize that externalizing behaviours such as disruptiveness and aggression can also be indicators of depression. Since many of these symptoms of depression manifest in the school, it is imperative that teachers are able to correctly identify the symptoms of depression. The correct management of the child prevents the depression from worsening and leading to disastrous consequences. The purpose of this study was to establish whether teachers were fully knowledgeable about the behavioural symptoms of depression. A former purpose was to determine the management strategies used at school, and to develop a guideline document for teachers. Survey methodology and interview techniques were used to collect data for the study. These methods provided quantitative and qualitative data. The participants comprised 56 primary school teachers from three randomly selected schools. Two questionnaires were specially designed to gather data for the study. The results of the study revealed that teachers were not fully knowledgeable about the behavioural symptoms of depression and that they lacked the depth of knowledge required to recognize the significance of the diagnostic criteria of depression "which manifest as behavioural symptoms in school. The results showed mat more than 57 % of participants felt that parents and home factors were responsible for depression. Results also indicated that the majority of participants were not able to recognize the multiplicity of factors that could cause and result in depression. In the perceived absence of psychological support from the Department of Education, participants indicated a need for guidelines for identification and management of symptoms of depression. There was overwhelming support for the implementation of a self-esteem programme at schools. At the conclusion of the study, a document which outlined recognition and management of the behavioural symptoms of depression, was developed by the researcher. As a result of the findings of the study, recommendations were made to teachers, the schools' management team, as well as to the Department of Education. Recommendations made to teachers included training the child in social skills and cognitive strategies, and maintaining contact with parents. One important recommendation to the schools' management was the timely referral of depressed children to mental health professionals. Recommendations made to the Department of Education included the facilitation of the formation of multidisciplinary teams which would comprise teachers, management staff, parents and school psychologists. These multidisciplinary teams would manage the successful implementation of programmes that will foster healthy social and emotional development of all children.

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