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A method due to É. Cartan was used to algebraically classify the possible four-dimensional manifolds that allow a (2, 2)-signature metric with a transitive group action which acts by isometries. These manifolds are classified according to the Lie algebra of the group action. There are six possibilities: four non-parameterized Lie algebras, one discretely parameterized family, and one family parameterized by R.

When modelling pollutants in the atmosphere, it is nearly impossible to get perfect results as the chemical and mechanical processes that govern pollutant concentrations are complex. Results are dependent on the quality of the meteorological input as well as the emissions inventory used to run the model. Also, models cannot currently take every process into consideration. Therefore, the model may get results that are close to, or show the general trend of the observed values, but are not perfect. However, due to the lack of observation stations, the resolution of the observational data is poor. Furthermore, the chemistry over large bodies of water is different from land chemistry, and in North America, there are no stations located over the great lakes or the ocean. Consequently, the observed values cannot accurately cover these regions. Therefore, we have combined model output and observational data when studying ozone concentrations in north eastern North America. We did this by correcting model output at observational sites with local data. We then interpolated those corrections across the model grid, using a Kriging procedure, to produce results that have the resolution of model results with the local accuracy of the observed values. Results showed that the corrected model output is much improved over either model results or observed values alone. This improvement was observed both for sites that were used in the correction process as well as sites that were omitted from the correction process.

Marfan Syndrome leads to the weakening of the thoracic aorta and ultimate rupture causing death of the patient. Current monitoring method involves measuring the diameter of the aorta near the heart. Our approach is to develop a new technology that will provide clinicians the ability to evaluate the size, shape and motion of the entire thoracic aorta using four-dimensional cardiac MRI. This project alters the existing research algorithms to provides an integrated application for processing the images and provides novel measurements about the aorta from a data set of 32 normal subjects and 38 patients with serial scans.

When modelling pollutants in the atmosphere, it is nearly impossible to get perfect results as the chemical and mechanical processes that govern pollutant concentrations are complex. Results are dependent on the quality of the meteorological input as well as the emissions inventory used to run the model. Also, models cannot currently take every process into consideration. Therefore, the model may get results that are close to, or show the general trend of the observed values, but are not perfect. However, due to the lack of observation stations, the resolution of the observational data is poor. Furthermore, the chemistry over large bodies of water is different from land chemistry, and in North America, there are no stations located over the great lakes or the ocean. Consequently, the observed values cannot accurately cover these regions. Therefore, we have combined model output and observational data when studying ozone concentrations in north eastern North America. We did this by correcting model output at observational sites with local data. We then interpolated those corrections across the model grid, using a Kriging procedure, to produce results that have the resolution of model results with the local accuracy of the observed values. Results showed that the corrected model output is much improved over either model results or observed values alone. This improvement was observed both for sites that were used in the correction process as well as sites that were omitted from the correction process.

In this thesis, we study exotic smooth structures on 4-manifolds with finite fundamental groups. For an arbitrary finite group G, we construct an infinite family of smooth 4-manifolds with fundamental group G, which are all homeomorphic but mutually non-diffeomorphic, using the small symplectic manifold with arbitrary fundamental group constructed by S. Baldridge and P. Kirk, together with the methods of A. Akhmedov, R.&amp / #221 / . Baykur and D. Park for constructing infinite families of exotic simply connected 4-manifolds. In the final chapter, pairs of small exotic 4-manifolds with a cyclic fundamental group of any odd order are constructed.

The aim of this thesis is to explain the change in the debate about police accountability in Britain that took place in the 1980s. In seeking such an explanation in the reinvention of police accountability over this period, a four dimensional analysis of accountability is presented. This is used to examine, in turn, the history of police governance in London, the debates about police accountability that took place in the 1980s, and the implications of the growing influence of community policing that culminated in the introduction by the Metropolitan Police of a new style of ‘sector policing’. A series of questions about whether and how police accountability was reinvented in the 1980s are posed, and the implications of the reconceptualisation that took place are assessed in their historical and theoretical contexts. Use is also made of empirical data drawn from a study of the implementation of sector policing on an inner city police area in North London. It is argued that far-reaching changes took place in the conceptualisation of police accountability during the 1980s on all four of the dimensions identified, and that this reinvention of the relationship between police and people made policing in London neither more democratic nor more consensual.

Serious games have the potential to add value to the teaching and learning environment but are currently not used to its full potential in the Computer Science class. Many reasons why serious games are not used are debated in the literature and a particular problem identified from the literature is that educators find it difficult to select appropriate serious games for use in the classroom environment. The research philosophy adopted for this study included the Critical Social Theory paradigm and action research as the research method. The five phases of the action research process, namely diagnosing, action planning, action taking, evaluating and specifying learning were used to provide educators with a useful model to help with the selection of serious games for the Computer Science class. During the diagnosing phase, the problem for this study was identified and a questionnaire was used to determine educators‘ perceptions of serious games that confirmed the problem identified during the literature survey. During the action planning phase the evaluation of three serious game selection models, namely the four-dimensional framework, the RETAIN model and the Magic Bullet model were planned. Participants were provided with a checklist in the form of tables so that they could familiarise themselves with the models. During the action taking phase participants evaluated the four-dimensional framework, the RETAIN model and the Magic Bullet model using the checklists and examples provided to them. During the evaluation phase the three different models were evaluated by the participants and a questionnaire was used to gather data. The data were analysed and results were reported. A major problem was identified and it was decided to initiate a second cycle of the action research process. This time participants were provided with serious games and in a joint effort of the participants the problem was addressed. During the second cycle the problems identified in the first cycle was resolved. Finally this study is concluded with a reflection on all the research questions identified, a report on the findings, recommendations and a discussion of the limitations of the research project. / MSc (Computer Science)--North-West University, Vaal Triangle Campus, 2015

Serious games have the potential to add value to the teaching and learning environment but are currently not used to its full potential in the Computer Science class. Many reasons why serious games are not used are debated in the literature and a particular problem identified from the literature is that educators find it difficult to select appropriate serious games for use in the classroom environment. The research philosophy adopted for this study included the Critical Social Theory paradigm and action research as the research method. The five phases of the action research process, namely diagnosing, action planning, action taking, evaluating and specifying learning were used to provide educators with a useful model to help with the selection of serious games for the Computer Science class. During the diagnosing phase, the problem for this study was identified and a questionnaire was used to determine educators‘ perceptions of serious games that confirmed the problem identified during the literature survey. During the action planning phase the evaluation of three serious game selection models, namely the four-dimensional framework, the RETAIN model and the Magic Bullet model were planned. Participants were provided with a checklist in the form of tables so that they could familiarise themselves with the models. During the action taking phase participants evaluated the four-dimensional framework, the RETAIN model and the Magic Bullet model using the checklists and examples provided to them. During the evaluation phase the three different models were evaluated by the participants and a questionnaire was used to gather data. The data were analysed and results were reported. A major problem was identified and it was decided to initiate a second cycle of the action research process. This time participants were provided with serious games and in a joint effort of the participants the problem was addressed. During the second cycle the problems identified in the first cycle was resolved. Finally this study is concluded with a reflection on all the research questions identified, a report on the findings, recommendations and a discussion of the limitations of the research project. / MSc (Computer Science)--North-West University, Vaal Triangle Campus, 2015

Computer animation has been limited almost exclusively to 2D and 3D. The tools for 3D computer animation have been largely in place for decades and are well-understood. Existing tools for visualizing 4D geometry include minimal animation features. Few tools have been designed specifically for animation of higher-dimensional objects, phenomena, or spaces. None have been designed to be familiar to 3D animators. A general-purpose 4D animation system can be expected to facilitate more widespread understanding of 4D geometry and space, can become the basis for creating unique 3D visual effects, and may offer new insight into 3D animation concepts. We have developed a software package that facilitates general-purpose animation in four spatial dimensions. Standard features from popular 3D animation software have been included and adapted, where appropriate. Many adaptations are trivial; some have required novel solutions. Several features that are possible only in four or more dimensions have been included. The graphical user interface has been designed to be familiar to experienced 3D animators. Keyframe animation is provided by using a set of curves that defines movement in each dimension or rotation plane. An interactive viewport offers multiple visualization methods including slicing and projection. The viewport allows for both manipulation of 4D objects and navigation through virtual 4D space.