This thesis presents an in-depth investigation into the practical use of 3D for software visualisation. This work presents the first comprehensive user-centred study which examines the software engineering tasks users undertake currently, the issues that 3D addresses and a measure of benefit of the 3D solution compared to traditional approaches. This thesis also presents a mechanism for creating 3D software visualisations, a refined evaluation methodology and visualisation heuristics that together provide a valuable resource for further research into this area. The research results have been structured so they are directly applicable to industry and as such are already undergoing industrial adoption. This has been achieved through the following: Firstly the research augments current and accepted software visualisation approaches by basing the visual notation on the Unified Modelling Language (UML). This has enabled the current visual software engineering tasks to be studied and for representative user tasks to be captured and quantified. The 3D visualisations then complement the current working practices by solving

This thesis presents an in-depth investigation into the practical use of 3D for software visualisation. This work presents the first comprehensive user-centred study which examines the software engineering tasks users undertake currently, the issues that 3D addresses and a measure of benefit of the 3D solution compared to traditional approaches. This thesis also presents a mechanism for creating 3D software visualisations, a refined evaluation methodology and visualisation heuristics that together provide a valuable resource for further research into this area. The research results have been structured so they are directly applicable to industry and as such are already undergoing industrial adoption. This has been achieved through the following: Firstly the research augments current and accepted software visualisation approaches by basing the visual notation on the Unified Modelling Language (UML). This has enabled the current visual software engineering tasks to be studied and for representative user tasks to be captured and quantified. The 3D visualisations then complement the current working practices by solving

Petal diagrams of knots are projections of knots to the plane such that the diagram has exactly one crossing. Petal diagrams offer a convenient and combinatorial way of representing knots via their associated petal permutation. In this thesis we study the fundamental group and Seifert surfaces of knots in petal form. Using the Seifert-Van Kampen theorem, we give a group presentation of the fundamental group of the knot complement of a knot in petal form. We then discuss Seifert surfaces and use decomposition diagrams to represent the Seifert surfaces of knots in petal form. We finally give an algorithm to produce a set of decomposition diagrams for a spanning surface of a knot in petal form and prove that for incompressible surfaces such decomposition diagrams are unique up to perturbation moves.

Yes / This article presents the application of the Enhanced Sequence Diagram (ESD) for the analysis of the functionality of a system with shape-changing aspects in the context of its multiple operational modes, considering an active rear spoiler as a case study. The article provides new insights on the ESD support for model-based capture and articulation of functional requirements across multiple operation modes of the same system, with appropriate detail on attributes and metrics, and the alignment of these attributes and metrics in line with the concept of time through scope lines. The article also provides a comprehensive argument and discussion, exemplified based on the case study, for the support that the ESD provides for early systems functional and architecture analysis, within the context of a broader model-based Failure Mode Analysis methodology.

Specification plays a vital role in software engineering to facilitate the development of highly dependable software. The importance of specification in software development is to serve, amongst others, as a communication tool for stakeholders in the software project. The specification also adds to the understanding of operations, and describes the properties of a system. Various techniques may be used for specification work. Z is a formal specification language that is based on a strongly-typed fragment of Zermelo-Fraenkel set theory and first-order logic to provide for precise and unambiguous specifications. Z uses mathematical notation to build abstract data, which is necessary for a specification. The role of abstraction is to describe what the system does without prescribing how it should be done. Diagrams, on the other hand, have also been used in various areas, and in software engineering they could be used to add a visual component to software specifications. It is plausible that diagrams may also be used to reason in a semi-formal way about the properties of a specification. Many diagrammatic languages are based on contours and set theory. Examples of these languages are Euler-, Spider-, Venn- and Pierce diagrams. Euler diagrams form the foundation of most diagrams that are based on closed curves. Diagrams, on the other hand, have also been used in various areas, and in software engineering they could be used to add a visual component to software specifications. It is plausible that diagrams may also be used to reason in a semi-formal way about the properties of a specification. Many diagrammatic languages are based on contours and set theory. Examples of these languages are Euler-, Spider-, Venn- and Pierce diagrams. Euler diagrams form the foundation of most diagrams that are based on closed curves. The purpose of this research is to demonstrate the extent to which diagrams can be used to represent a Z specification. A case study is used to transform the specification modelled with Z language into a diagrammatic specification. Euler, spider, Venn and Pierce diagrams are combined for this purpose, to form one diagrammatic notation that is used to transform a Z specification / School of Computing / M. Sc. (Information Systems)

Modern database systems use a query optimizer to identify the most efficient strategy, called "plan", to execute declarative SQL queries. Optimization is a mandatory exercise since the difference between the cost of best plan and a random choice could be in orders of magnitude. The role of query optimization is especially critical for the decision support queries featured in data warehousing and data mining applications. For a query on a given database and system configuration, the optimizer's plan choice is primarily a function of the selectivities of the base relations participating in the query. A pictorial enumeration of the execution plan choices of a database query optimizer over this relational selectivity space is called a "plan diagram". It has been shown recently that these diagrams are often remarkably complex and dense, with a large number of plans covering the space. An interesting research problem that immediately arises is whether complex plan diagrams can be reduced to a significantly smaller number of plans, without materially compromising the query processing quality. The motivation is that reduced plan diagrams provide several benefits, including quantifying the redundancy in the plan search space, enhancing the applicability of parametric query optimization, identifying error-resistant and least-expected-cost plans, and minimizing the overhead of multi-plan approaches. In this thesis, we investigate the plan diagram reduction issue from theoretical, statistical and empirical perspectives. Our analysis shows that optimal plan diagram reduction, w.r.t. minimizing the number of plans in the reduced diagram, is an NP-hard problem, and remains so even for a storage-constrained variation. We then present CostGreedy, a greedy reduction algorithm that has tight and optimal performance guarantees, and whose complexity scales linearly with the number of plans in the diagram. Next, we construct an extremely fast estimator, AmmEst, for identifying the location of the best tradeoff between the reduction in plan cardinality and the impact on query processing quality. Both CostGreedy and AmmEst have been incorporated in the publicly-available Picasso optimizer visualization tool. Through extensive experimentation with benchmark query templates on industrial-strength database optimizers, we demonstrate that with only a marginal increase in query processing costs, CostGreedy reduces even complex plan diagrams running to hundreds of plans to "anorexic" levels (small absolute number of plans). While these results are produced using a highly conservative upper-bounding of plan costs based on a cost monotonicity constraint, when the costing is done on "actuals" using remote plan costing, the reduction obtained is even greater - in fact, often resulting in a single plan in the reduced diagram. We also highlight how anorexic reduction provides enhanced resistance to selectivity estimate errors, a long-standing bane of good plan selection. In summary, this thesis demonstrates that complex plan diagrams can be efficiently converted to anorexic reduced diagrams, a result with useful implications for the design and use of next-generation database query optimizers.

An Euler diagram C = {c_1, c_2,..., c_n} is a collection of n simple closed curves (i.e., Jordan curves) that partition the plane into connected subsets, called regions, each of which is enclosed by a unique combination of curves. Typically, Euler diagrams are used to visualize the distribution of discrete characteristics across a sample population; in this case, each curve represents a characteristic and each region represents the sub-population possessing exactly the combination of containing curves' properties. Venn diagrams are a subclass of Euler diagrams in which there are 2^n regions representing all possible combinations of curves (e.g., two partially overlapping circles). In this dissertation, we study the Euler Diagram Generation Problem (EDGP), which involves constructing an Euler diagram with a prescribed set of regions. We describe a graph-theoretic model of an Euler diagram's structure and use this model to develop necessary-and-sufficient existence conditions. We also use the graph-theoretic model to prove that the EDGP is NP-complete. In addition, we study the related Area-Proportional Euler Diagram Generation Problem (w-EDGP), which involves constructing an Euler diagram with a prescribed set of regions, each of which has a prescribed area. We develop algorithms for constructing area-proportional Euler diagrams composed of up to three circles and rectangles, as well as diagrams with an unbounded number of curves and a region of common intersection. Finally, we present implementations of our algorithms that allow the dynamic manipulation and real-time construction of area-proportional Euler diagrams.

Industrial activities of mankind are feared to damage the environment irretrievably. Especially the release of huge amounts of harmful gases causes concern. In this regard the environmental pollution caused by the one billion motor vehicles on earth is particularly important. The platinum-group metals (PGM) are well known for their catalytic activity. They are used extensively for reducing the amounts of hydrocarbons, carbon monoxide and nitrogen oxides from the exhausts gas emitted by automobiles. In 2012 20% of platinum and 27% of palladium produced were used in the manufacture of catalytic converters. With the increasing use of PGM-containing autocatalysts, the reclaiming of PGMs from spent catalysts has become essential. Particularly attractive hydrometallurgical methods are those based on the use of halide ions e.g. sodium chloride, as complexing agent in conjunction with nitric acid as oxidant. The chemical reactions between mixtures of aluminium chloride and nitric acid have been studied, but the electrochemical reactions have received little attention. The research reported in this dissertation is aimed at providing data relating to the electrochemical behaviour of platinum in mixtures of aluminium chloride and nitric acid. The construction of Pourbaix diagrams of platinum in chloride environments confirmed that the stable chloro-complexes [PtCl4]2- and PtCl6]2-, as well as platinum oxides (PtO and PtO2) could play a role under the experimental conditions employed in this study. From the thermodynamic results it can be concluded that the systems deserving consideration favour high chloride concentrations and high temperatures. Notable anodic reactions found were the adsorption of chloride on the platinum surface and the gradual formation of [PtCl6]2-, followed by the formation of platinum oxides at 1.00 to 1.01 V. The results show that anodic currents diminished with lower chloride concentrations. A seemingly anomalous anodic behaviour at 35 °C and 45 °C could be explained in terms of a competition between platinum oxide formation and the formation of platinum chloro-complexes. Evidence for the following cathodic reduction reactions was found: hydrogen evolution, reduction of dissolved oxygen to hydrogen dioxide (-1.3 V SHE), nitrate ion reduction to nitrite ions (-0.01 V SHE), nitrite ion reduction to nitric oxide (-0.85 V SHE) and reduction of PtO and PtO2 to Pt (at -1.00 V and 1.01 V SHE, respectively). A brief study was undertaken in an attempt to relate the electrochemical results to the leaching of platinum from a virgin automotive exhaust catalyst. The recovery was low for mixtures with low chloride concentrations, which could be expected from the electrochemical polarisation curves obtained in electrolytes with different chloride concentrations. The maximum platinum recovery attained, was 60% at 45 °C in a mixture containing 0.6 M AlCl3 and 0.9 M HNO3. / MSc (Chemistry), North-West University, Potchefstroom Campus, 2014

Industrial activities of mankind are feared to damage the environment irretrievably. Especially the release of huge amounts of harmful gases causes concern. In this regard the environmental pollution caused by the one billion motor vehicles on earth is particularly important. The platinum-group metals (PGM) are well known for their catalytic activity. They are used extensively for reducing the amounts of hydrocarbons, carbon monoxide and nitrogen oxides from the exhausts gas emitted by automobiles. In 2012 20% of platinum and 27% of palladium produced were used in the manufacture of catalytic converters. With the increasing use of PGM-containing autocatalysts, the reclaiming of PGMs from spent catalysts has become essential. Particularly attractive hydrometallurgical methods are those based on the use of halide ions e.g. sodium chloride, as complexing agent in conjunction with nitric acid as oxidant. The chemical reactions between mixtures of aluminium chloride and nitric acid have been studied, but the electrochemical reactions have received little attention. The research reported in this dissertation is aimed at providing data relating to the electrochemical behaviour of platinum in mixtures of aluminium chloride and nitric acid. The construction of Pourbaix diagrams of platinum in chloride environments confirmed that the stable chloro-complexes [PtCl4]2- and PtCl6]2-, as well as platinum oxides (PtO and PtO2) could play a role under the experimental conditions employed in this study. From the thermodynamic results it can be concluded that the systems deserving consideration favour high chloride concentrations and high temperatures. Notable anodic reactions found were the adsorption of chloride on the platinum surface and the gradual formation of [PtCl6]2-, followed by the formation of platinum oxides at 1.00 to 1.01 V. The results show that anodic currents diminished with lower chloride concentrations. A seemingly anomalous anodic behaviour at 35 °C and 45 °C could be explained in terms of a competition between platinum oxide formation and the formation of platinum chloro-complexes. Evidence for the following cathodic reduction reactions was found: hydrogen evolution, reduction of dissolved oxygen to hydrogen dioxide (-1.3 V SHE), nitrate ion reduction to nitrite ions (-0.01 V SHE), nitrite ion reduction to nitric oxide (-0.85 V SHE) and reduction of PtO and PtO2 to Pt (at -1.00 V and 1.01 V SHE, respectively). A brief study was undertaken in an attempt to relate the electrochemical results to the leaching of platinum from a virgin automotive exhaust catalyst. The recovery was low for mixtures with low chloride concentrations, which could be expected from the electrochemical polarisation curves obtained in electrolytes with different chloride concentrations. The maximum platinum recovery attained, was 60% at 45 °C in a mixture containing 0.6 M AlCl3 and 0.9 M HNO3. / MSc (Chemistry), North-West University, Potchefstroom Campus, 2014

According to Plato, we live in a substitute world. The things we see around us are shadows of reality, imperfect imitations of perfect originals. Beyond the world of the senses, there is another, changeless world, more real and more beautiful than our own. But how can we get at this world, or attain knowledge of it, when our senses are unreliable and the perfect philosophical method remains out of reach? In the Divided Line passage of the Republic, Plato is clear that mathematics has a role to play, but the debate about the exact nature of that role remains unresolved. My reading of the Divided Line might provide the answer. I propose that the ‘mathematical’ passages of the Meno and Phaedo contain evidence that we can use to construct the method by which Plato means us to ascend to knowledge of the Forms. In this dissertation, I shall set out my reading of Plato’s Divided Line, and show how Plato’s use of mathematics in the Meno and Phaedo supports this view. The mathematical method, adapted to philosophy, is a central part of the Line’s ‘way up’ to the definitions of Forms that pure philosophy requires. I shall argue that this method is not, as some scholars think, the geometric method of analysis and synthesis, but apagōgē, or reduction. On this reading, mathematics is pivotal on our journey into the world of the Forms.