A technique for decomposing the Optical Transfer Function (OTF) into a novel set of basis functions has been developed. The decomposition provides insight into the performance of optical systems containing both wavefront error and apodization, as well as the interactions between the various components of the pupil function. Previously, this technique has been applied to systems with circular pupils with both uniform illumination and Gaussian apodization. Here, systems with annular pupils are explored. In cases of annular pupil with simple defocus, analytic expressions for the OTF decomposition coefficients can be calculated. The annular case is not only applicable to optical systems with central obscurations, but the technique can be extended to systems with multiple ring structures. The ring structures can have constant area as is often found in zone plates and diffractive lenses or the rings can have arbitrary areas. Analytic expressions for the OTF decomposition coefficients again can be determined for ring structures with constant and quadratic phase variations. The OTF decomposition provides a general tool to analyze and compare a diverse set of optical systems.

Abstract The aim of this work was to study systematically the effects of composition and processing on austenite grain growth and static recrystallization (SRX) kinetics, austenite decomposition under controlled cooling as well as microstructures, mechanical properties and weldability of hot rolled low carbon bainitic (LCB) steels. The results showed that the coarsening of austenite grain structure is influenced by the chemical composition. Steels with Nb-Ti alloying exhibited fine and uniform austenite grain size up to 1125 °C, whereas higher temperatures led to formation of the bimodal grain structures. However, with Nb-Ti-B microalloying, the abnormal grain growth was already observed at 1050 °C. SRX rate at roughing temperatures, determined by the stress relaxation method, was found to be retarded markedly by Mo, Nb and B alloying. For the test conditions investigated, the decomposition of austenite started in the temperature range from 780 °C to below 550 °C. All alloying elements with the exception of Nb (0.04–0.10 wt-%) decreased the phase transformation temperatures and increased the hardness of dilatometric specimens. Detailed microstructural examinations enabled the identification of 4 different ferrite morphologies: polygonal ferrite, quasi-polygonal ferrite (QF), granular bainitic ferrite (GB) and bainitic ferrite (BF), generally as a mixed microstructure consisting of 2–3 types morphologies. Consistent with the microstructures detected in dilatometric experiments, the microstructures of rolled plates comprise various combinations of low C ferrite morphologies. These microstructure types provided the yield strengths from 500 MPa up to 850 MPa in hot rolled condition and from 500 MPa to 950 MPa in heat-treated condition (600 °C/1h). The yield strengths from 500 MPa to 570 MPa were mainly related to QF microstructures in as-rolled condition, while the steels with the yield strength from 570 to 700 MPa had GB-QF microstructures. Steels with the yield strengths above 700 MPa consisted of BF. The most effective alloying element regarding the strength properties is B. Also C, Mn, Cr, Mo and Ni have strong influences, but Nb in the range of 0.05–0.10 wt-% is ineffective. Strengthening with B and Mo was detrimental to toughness. Alloying with Ni and Mn is beneficial to good strength and toughness combination. Mn, Mo, Nb and B contents mainly dictate CGHAZ toughness.

In computational fluid dynamics (CFD), there are two widely-used methods for computing the near-wall regions of turbulent flows: high Reynolds number (HRN) models and low Reynolds number (LRN) models. HRN models do not resolve the near-wall region, but instead use wall functions to compute the required parameters over the near-wall region. In contrast, LRN models resolve the flow right down to the wall. Simulations with HRN models can take an order of magnitude less time than with LRN models, however the accuracy of the solution is reduced and certain requirements on the mesh must be met if the wall function is to be valid. It is often difficult or impossible to satisfy these requirements in industrial computations. In this thesis the near-wall domain decomposition (NDD) method of Utyuzhnikov (2006) is developed and implemented into the industrial code, Code_Saturne, for the first time. With the NDD approach, the near-wall regions of a fluid flow are removed from the main computational mesh. Instead, the mesh extends down to an interface boundary, which is located a short distance from the wall, denoted y*. A simplified boundary layer equation is used to calculate boundary conditions at the interface. When implemented with a turbulence model which can resolve down to the wall, there is no lower limit on the value of y*. There is a Reynolds number-dependent upper limit on y*, as there is with HRN models. Thus for large y*, the model functions as a HRN model and as y*→ 0 the LRN solution is recovered. NDD is implemented for the k−ε and Spalart-Allmaras turbulence models and is tested on five test cases: a channel flow at two different Reynolds numbers, an annular flow, an impinging jet flow and the flow in an asymmetric diffuser. The method is tested as a HRN and LRN model and it is found that the method behaves competitively with the scalable wall function (SWF) on simpler flows, and performs better on the asymmetric diffuser flow, where the NDD solution correctly captures the recirculation region whereas the SWF does not. The method is then tested on a ribbed channel flow. Particular focus is given to investigating how much of the rib can be excluded from the main computational mesh. It is found that it is possible to remove 90% of the rib from the mesh with less than 2% error in the friction factor compared to the LRN solution. The thesis then focuses on the industrial case of the flow in an annulus where the inner wall, referred to as the pin, has a rib on its surface that protrudes into the annulus. Comparison is made between CFD calculations, experimental data and empirical correlations. It is found that the experimental friction factors are significantly larger than those found with CFD, and that the trend in the friction factor with Reynolds number found in the experiments is different. Simulations are performed to quantify the effect that a non-smooth surface finish on the pin and rib surface has on the flow. This models the situation that occurs in an advanced gas-cooled nuclear reactor, when a carbon deposit forms on the fuel pins. The relationship between the friction factor and surface finish is plotted. It is demonstrated that surface roughness left over by the manufacturing process in the experiments is not the source of the discrepancy between the experimental and CFD results.

Magister Commercii - MCom / South African labour relations are associated with a history of extensive discrimination and segregation, subject to various types of discrimination during the apartheid era, including employment discrimination. This study explores the effect of Affirmative Action on the reduction (if any) of employment discrimination since the advent of democracy. It investigates whether the extent of employment discrimination by race and gender has decreased, 20 years since the economic transition. The first part of the study gives an overview of the South African labour legislations, both discriminative legislations and statutes aimed at redressing the imbalances of the past. The empirical part of the paper employs a sample that represents the labour force (excluding informal sector workers, agricultural workers, domestic workers and self-employed) aged between 15 and 65 years. The methodology in this study firstly estimates probit models describing the labour force participation, employment and occupational attainment, followed by the Oaxaca-Blinder decomposition, using data from OHS 1997-1999, LFS 2000-2007, QLFS 2008-2014 and NIDS 2008-2012. The OHS/LFS/QLFS decomposition results show that the unexplained component of the White-Black employment probability gap does not reveal any strong downward trend overtime. Also, results on the occupational attainment gap indicate that there was an increasing occupational attainment probability gap between Whites and Blacks which was partially driven by an increase in the unexplained component. This implies that Affirmative Action was not successful in reducing racial discrimination in the South African labour market. Additionally, the unexplained component is most dominant in the male-female employment gap decomposition. This suggests employment discrimination against females is very serious. However, the male-female highly-skilled employment likelihood shows no clear trend over time. These results suggest that when it comes to employment discrimination against females, this may have taken place more seriously when it comes to the unskilled or semi-skilled occupations.

The LULU operators Ln and Un operate on neighbourhoods of size n. The Discrete Pulse Transform (DPT) of images is obtained via recursive peeling of so-called local maximum and minimum sets with the LULU operators as n increases from 1 to the maximum number of elements in the array. The DPT provides a new nonlinear decomposition of a multidimensional array. This thesis investigates the theoretical and practical soundness of the decomposition for image analysis. Properties for the theoretical justification of the DPT are provided as consistency of the decomposition (a pseudo-linear property), and its setting as a nonlinear scale-space, namely the LULU scalespace. A formal axiomatic theory for scale-space operators and scale-spaces is also presented. The practical soundness of the DPT is investigated in image sharpening, best approximation of an image, noise removal in signals and images, feature point detection with ideas to extending work to object tracking in videos, and image segmentation. LULU theory on multidimensional arrays and the DPT is now at a point where concrete signal, image and video analysis algorithms can be developed for a wide variety of applications. / Thesis (PhD)--University of Pretoria, 2013. / Mathematics and Applied Mathematics / unrestricted

The thermal decomposition of silver permanganate, pre-irradiated in BEPO and in a ⁶°C₀ Ϫ 'hot spot' has been investigated in the temperature range 100 - 125°C. The results are similar to those for irradiated KMn0₄ and the mechanism proposed for the latter is again suggested. The activation energy for the migration of point defects over the induction period is 1.03 ev. The decompositions of unirradiated and irradiated crystals differ in that the latter undergo physical disintegration over the acceleratory period. X-ray studies immediately prior to disintegration show strain and fragmentation in the irradiated crystal. An explanation involving the annealing of point defects at dislocation is advanced to explain the changes produced in the p/t plots with increased dosage, and fixed decomposition temperature. Summary, p. 94.

Due to the fast development in 3D technology during recent decades, many approaches in 3D representation technologies have been proposed worldwide. In order to get an accurate information to render a 3D representation, more data need to be recorded compared to normal video sequence. In this case, how to find an efficient way to transmit the 3D representation data becomes an important part in the whole 3D representation technology. Recent years, many coding schemes based on the principle of encoding the depth have been proposed. Compared to the traditional multiview coding schemes, those new proposed schemes can achieve higher compression efficiency. Due to the development of depth capturing technology, the accuracy and quality of the reconstructed depth image also get improved. In this thesis we propose an efficient depth data compression scheme for 3D images. Our proposed depth data compression scheme is platelet based coding using Lagrangian optimization, quadtree decomposition and quadratic curve fitting. We study and improve the original platelet based coding scheme and achieve a compression improvement of 1-2 dB compared to the original platelet based scheme. The experimental results illustrate the improvement provided by our scheme. The quality of the reconstructed results of our proposed curve fitting based platelet coding scheme are better than that of the original scheme.

Stochastic delay differential equations naturally arise in models of complex natural phenomena, yet continue to resist efforts to find analytical solutions to them: general solutions are limited to linear systems with additive noise and a single delayed term. In this work we solve the case of distributed delays in linear systems with additive noise. Key to our solution is the development of a consistent interpretation for integrals over stochastic variables, obtained by means of a virtual discretization procedure. This procedure makes no assumption on the form of noise, and would likely be useful for a wider variety of cases than those we have considered. We show how it can be used to map the distributed delay equation to a known multivariate system, and obtain expressions for the system's time-dependent mean and autocovariance. These are in the form of series over the system's natural modes and completely define the solution. — An interpretation of the system as an amplitude process is explored. We show that for a wide range of realistic parameters, dynamics are dominated by only a few modes, implying that most of the observed behaviour of stochastic delayed equations is constrained to a low-dimensional subspace. — The expression for the autocovariance is given particular attention. A recurring problem for stochastic delay equations is the description of their temporal structure. We show that the series expression for the autocovariance does converge over a meaningful range of time lags, and therefore provides a means of describing this temporal structure.

Macromolecular structures, such as lignin and cellulose, are important components of soil organic carbon, the major terrestrial global carbon pool. The degradation of these macromolecules, including lignin and cellulose, in plant-derived soil organic matter, is important to the global carbon cycle. In grasslands, saprotrophic (decomposer) fungi are major decomposers of such organic material. Some of these compounds, such as lignin are relatively resistant to decay by the microbial community if compared with other compound classes such as cellulose. In this work we investigate the involvement of fungi in the decomposition of both lignin and cellulose and look to link the decomposition processes observed in the field to those observed in a laboratory-controlled environment. The key findings of this work are:- Field based experiments in both tropical and temperate environments indicated that lignin can be degraded completely, most likely by white-rot fungi, as shown by the shifts in the [Ac/Al]S, [Ac/Al]G and [S/G] relative lignin decomposition state proxies. The results confirm that even in a very low carbon environment, fungi are able to completely degrade lignin over time. However, lignin is degraded much faster in tropical environments. Culturing experiments showed that it was possible to isolate a number of fungi present on the degraded wheat straw collected in the field, especially soft-rot fungi. When used in microcosm experiments using a range of organic substrates, the relative lignin decomposition state proxies indicated that Absidia cylindrospora and Trichoderma koningii are not able to completely degrade lignin but preferentially degrade cellulose. Cellulose degradation rates are much higher than those of lignin in degraded field samples over time, confirming previous work.

In this study twelve types of top soil were collected under aseptic conditions. The cellulose-decomposing rates of these were compared in order to determine the relative rates in the cellulose-decomposing potential of the microorganisms involved. Furthermore, this investigation is designed to acquire pertinent information on the rate at which natural cellulose materials are returned to available plant food.