A dissertation submitted to the Faculty of Science, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 2015. / Invariant solutions for two-dimensional free and wall jets are derived by consid- ering the Lie point symmetry associated with the appropriate conserved vectors of Prandtl's boundary layer equations for the jets. For the two-dimensional jets we also consider the comparison, advantages and disadvantages between the standard method that uses a linear combination of all the Lie point symme- tries of Prandtl's boundary layer equations to generate the invariant solution with the new method explored in this paper which uses the Lie point sym- metry associated with a conserved vector to generate the invariant solution. Invariant solutions for two-dimensional classical and self-propelled wakes are also derived by considering the Lie point symmetry associated with the appro- priate conserved vectors of Prandtl's boundary layer equations for the wakes. We also consider and discuss the standard method that uses a linear combi- nation of all the Lie point symmetry of Prandtl's boundary layer equations to generate the invariant solutions for the classical and self-propelled wakes.

Purpose: The aim of this study was to establish clinically relevant guidelines for the selection of clasps for removable partial dentures (RPDs) by adapting RPD clasp arms of differing materials and diameter to a three-dimensional model based on the average curvature of premolars and molars. Method: Randomly selected discarded casts were collected that had intact first premolars and first molars. The normal clasp position for the buccal surfaces of these teeth was drawn on the cast and the teeth were then sectioned to this line, and scanned using a flatbed scanner. The average curvature and length for each group was determined using a graphics-drawing programme and a 3D model was printed using these data. Clasp materials were then be adapted to these models using the wrought wires: Leowire (Leone, Fiorentino, Italy) (stainless steel); Remanium Hard (Dentaurum, Pforzheim, Germany) (stellite alloy of chromium and cobalt); Noninium (Dentaurum, Pforzheim, Germany) (stainless steel, nickel free); and cast clasps cast in the stellite alloy Vitallium (Dentsply, Ontario, Canada). Two diameters of the wrought wire clasp groups were used (0.9mm and 1.0mm). Ten samples for each diameter and material were adapted to the 3D models as they would in a clinical case. Each clasp was then randomly deformed beyond its proportional limit in a tensile testing machine (Instron Corporation, High Wycombe, United Kingdom) and the forces exerted at that limit and at deflections of 0.25 mm, 0.5 mm, and 0.75 mm were measured, as these are the clinically encountered undercuts. Statistical analysis was carried out to determine if the forces exerted at these deflections were within the proportional limit of the clasp, but also significantly within the realistic limit (defined as two standard deviations from the proportional limit) to allow for variations in manufacture and application of the clasp arms. Results: The results confirmed the effect of material, length, and diameter on flexibility for the wrought wires. A table was produced with guidelines for those clasps which could be used safely within their realistic limits and therefore should provide longevity of service. The greatest force exerted on premolar clasp length arms was provided by Leowire at 0.25mm undercut (606g); although it was 2% greater than its realistic limit, this was considered sufficiently within the safety factor to iii recommend its clinical use. The greatest force exerted on molar clasp length arms was provided by Remanium Hard at a deflection of 0.5 mm (417g). Cast clasps for premolars should not be prescribed as they were all well above their realistic limits. Cast clasps should only be selected for molars if the clasp arm is longer than 14.5mm. At a deflection of 0.25 mm the cast arm exerted a force of 773g but whilst this was below its proportional limit, it was higher than its realistic limit. Conclusions: The results of this study provide valid guidelines for the clinical application of clasp arms in removable partial dentures. It is recommended that clinical studies be carried out to confirm the longevity of clasp arms based on these data. / MT2016

Demands on modern computing are becoming more intensive. Keeping up with these demands has increasing complexity. Moore's Law is in decline. Increasing the number of cores on a device has diminishing returns. Specialised architectures provide more efficient and higher performing processors. However, it is not always practical to include every architecture on every device. Running non-native tasks on architectures often results in a drop in performance. This research examines the benefits and limitations of Field Programmable Gate Arrays - Systems on Chip (FPGA-SoC) devices to provide flexible hardware accelerators for heterogeneous architectures. A number of topics are covered, including hardware acceleration of floating-point mathematical functions, dynamic reconfiguration and high-level synthesis. A number of case studies are presented. Dynamic reconfiguration is used to change the configuration of the FPGA at runtime, allowing the hardware accelerators to be changed depending on the current processor tasks. Changing accelerators at runtime has limitations, such as data perturbation. Context switching techniques are applied to the hardware to prevent loss of data and enable de-fragmentation of the FPGA. High level synthesis techniques are used in conjunction with the presented hardware accelerators to synthesise high-level languages into hardware descriptions with optimisations. Techniques for runtime synthesis of hardware accelerators are presented. These can be combined with dynamic reconfiguration to configure FPGAs with appropriate hardware accelerators from a high-level language at runtime. The research demonstrates that FPGA-SoC devices have the potential for providing reconfigurable accelerators for processors in heterogeneous architectures. Metrics show that the FPGA configurations can perform better than other commercial processors. It was demonstrated that it is possible to context switch hardware at runtime, meaning the most can be made of the FPGA-SoC at all times, even as situations change. However, there are many limitations that still need to be overcome, such as management of the implemented hardware, synthesis of new hardware at runtime, reconfiguration times, interfacing of hardware with software and the design of hardware accelerators.

Wong Chun Wai Carto. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 78-80). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- The Probabilistic Approach --- p.9 / Chapter 2.1 --- Diffusion on the Sierpinski gasket --- p.9 / Chapter 2.2 --- A Laplacian from the diffusion process --- p.18 / Chapter 2.3 --- Other ramifications --- p.24 / Chapter 3 --- The Analytic Approach --- p.28 / Chapter 3.1 --- Discrete Laplacians on finite sets --- p.28 / Chapter 3.2 --- Laplacian from a compatible sequence --- p.33 / Chapter 3.3 --- Compatible sequence from a harmonic structures --- p.40 / Chapter 3.4 --- Existence theorem for harmonic structures --- p.50 / Chapter 4 --- On Two Related Classes of Symmetric Polytopes --- p.55 / Chapter 4.1 --- Symmetries and regular polytopes --- p.56 / Chapter 4.2 --- Classification of highly symmetric polytopes --- p.62 / Chapter 4.3 --- Classification of strongly symmetric polytopes --- p.66 / Bibliography --- p.78

Lee, Chak Shing. / "August 2011." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 60-62). / Abstracts in English and Chinese. / Chapter 1 --- Model Problems --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- The curl-curl operator --- p.2 / Chapter 1.3 --- The convection-diffusion equation --- p.6 / Chapter 2 --- Staggered DG method for the Curl-Curl operator --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- Discontinuous Galerkin discretization --- p.8 / Chapter 2.3 --- Stability for aligned fields --- p.14 / Chapter 2.4 --- Error estimates --- p.17 / Chapter 2.5 --- Numerical experiments --- p.21 / Chapter 2.6 --- Concluding Remarks --- p.32 / Chapter 3 --- Staggered DG method for the convection-diffusion equation --- p.33 / Chapter 3.1 --- Introduction --- p.33 / Chapter 3.2 --- Method description --- p.33 / Chapter 3.3 --- Preservation of physical structures --- p.38 / Chapter 3.4 --- Stability and convergence --- p.42 / Chapter 3.4.1 --- Static problem --- p.42 / Chapter 3.4.2 --- Time-dependent problem --- p.46 / Chapter 3.5 --- Fully discrete scheme --- p.49 / Chapter 3.6 --- Numerical examples --- p.55 / Chapter 3.6.1 --- The static problem --- p.55 / Chapter 3.6.2 --- Time dependent problem --- p.56 / Chapter 3.7 --- Concluding Remark --- p.59 / Bibliography --- p.60

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Tse, Wang Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 75-77). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- On bounded interval with n jumps in inhibitor diffusivity --- p.3 / Chapter 2.1 --- Introduction --- p.3 / Chapter 2.2 --- Preliminaries --- p.5 / Chapter 2.3 --- Review of previous results in the two segment case: interior spike and spike near the jump discontinuity of the diffusion coefficient --- p.7 / Chapter 2.4 --- The construction and analysis of spiky steady-state solutions --- p.9 / Chapter 2.5 --- Stability Analysis --- p.10 / Chapter 2.6 --- Spikes near the jump discontinuity xb of the inhibitor diffusivity --- p.11 / Chapter 2.7 --- Stability Analysis II: Small Eigenvalues of the Spike near the Jump --- p.16 / Chapter 2.8 --- Existence of interior spikes for N segments --- p.20 / Chapter 2.9 --- Existence of a spike near a jump for N segments --- p.24 / Chapter 2.10 --- Appendix: The Green´ةs function for three segments --- p.25 / Chapter 3 --- On a compact Riemann surface without boundary --- p.30 / Chapter 3.1 --- Introduction --- p.30 / Chapter 3.2 --- Some Preliminaries --- p.35 / Chapter 3.3 --- Existence --- p.43 / Chapter 3.4 --- Refinement of Approximate Solution --- p.50 / Chapter 3.5 --- Stability --- p.52 / Chapter 3.6 --- Appendix I: Expansion of the Laplace-Beltrami Operator --- p.67 / Chapter 3.7 --- Appendix II: Some Technical Calculations --- p.73

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Includes bibliographical references (leaves 158-163). Concerns the development of high-order finite-difference methods on a uniform rectangular grid for advection and diffuse problems with smooth variable coefficients. This technique has been successfully applied to variable-coefficient advection and diffusion problems. Demonstrates that the new schemes may readily be incorporated into multi-dimensional problems by using locally one-dimensional techniques, or that they may be used in process splitting algorithms to solve complicatef time-dependent partial differential equations.

Includes bibliographical references (leaves 158-163). / vi, 166 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Concerns the development of high-order finite-difference methods on a uniform rectangular grid for advection and diffuse problems with smooth variable coefficients. This technique has been successfully applied to variable-coefficient advection and diffusion problems. Demonstrates that the new schemes may readily be incorporated into multi-dimensional problems by using locally one-dimensional techniques, or that they may be used in process splitting algorithms to solve complicatef time-dependent partial differential equations. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 2001