Since the start of the COVID-19 pandemic in December 2019, much research has been done to develop the spatial-temporal methods to track it and to predict the spread of the virus. In this thesis, a COVID-19 dataset containing the number of biweekly infected cases registered in Ontario since the start of the pandemic to the end of June 2021 is analysed using Bayesian Spatial-temporal models and Area-to-area (Area-to-point) Poisson Kriging models. With the Bayesian models, spatial-temporal effects on infected risk will be checked and ATP Poisson Kriging models will show how the virus spreads over the space and the spatial clustering feature. According to these models, a Shinyapp website https://mujingrui.shinyapps.io/covid19 is developed to present the results.

Spatial interpolation techniques play an important role in hydrology as many point observations need to be interpolated to create continuous surfaces. Despite the availability of several tools and methods for interpolating data, <a>not all of them work consistently for hydrologic applications</a><a>. One of the techniques, Laplace Equation, which is used in hydrology for creating flownets, has rarely been used for interpolating hydrology data</a>. The objective of this study is to examine the efficiency of Laplace formulation (LF) in interpolating hydrologic data and compare it wih other widely used methods such as the inverse distance weighting (IDW), natural neighbor, and kriging. Comparison is performed quantitatively for using root mean square error (RMSE), visually for creating reasonable surfaces and computationally for ease of operation and speed. Data related to surface elevation, river bathymetry, precipitation, temperature, and soil moisture data are used for different areas in the United States. RMSE results show that LF performs better than IDW and is comparable to other methods for accuracy. LF is easy to use as it requires fewer input parameters compared to IDW and Kriging. Computationally, LF is comparable to other methods in terms of speed when the datasets are not large. Overall, LF offers an robust alternative to existing methods for interpolating various hydrology data. Further work is required to improve its computational efficiency with large data size and find out the effects of different cell size.

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The study of defects in semiconductors has been on-going for over 50 years. During this time, researchers have been studying the origins and identity of process induced defects, a task which has proved to be very demanding. While defects in silicon, the most widely used semiconductor, have been widely studied, there is more literature on n-type silicon than on p-type silicon. Compared to n-type silicon, p-type silicon is challenging to work with when it comes to making good Schottky diodes. A good rectifying device is essential for the performing of electrical characterisation techniques such as deep-level transient spectroscopy. In spite of this challenge p-silicon cannot be ignored. Many of the electronic devices are a combination of both n- and p-silicon therefore the need to understand the electronic properties of both materials. In this thesis, defects introduced in p-Si by electron beam deposition (EBD) were investigated. In order to understand these defects better, defects introduced by conditions of electron beam deposition (EBD) without metal deposition, were investigated. This process will be referred to as electron beam exposure (EBE). Finally, the defects were compared to defects induced by alpha-particle irradiation. EBD defects, introduced during electron beam deposition (EBD) of titanium (Ti) contacts on p-Si were investigated. The Schottky contacts were annealed within a temperature range of 200–400 oC. Current-voltage (I-V) measurements were conducted to monitor the change in electrical characteristics with every annealing step. Deep-level transient spectroscopy (DLTS) and Laplace-DLTS techniques were employed to identify the defects introduced after EBD and isochronal annealing of the Ti Schottky contacts. DLTS revealed that the main defects introduced during metallisation were hole traps with activation energy of 0.05 eV, 0.23 eV and 0.38 eV. Depth profiles of these defects showed that the formed close to the interface within a depth of 0.4 μm. Defects induced by EBE were studied by exposing samples for 50 minutes after which nickel (Ni) Schottky contacts were fabricated using resistive deposition. Only one defect with an activation energy of 0.55 eV was observed. This activation energy is similar to that of the I-defect. DLTS depth profiling revealed that the defect could be detected up to a depth of 0.8μm below the junction, which is significantly deeper than EBD defects. Defects induced when p-Si was irradiated by alpha particles from a 5.4 MeV americium (Am) 241 foil radioactive source with a fluence rate of 7×106 cm−2 s−1 at room temperature were investigated. After exposure at a fluence of 5.1×1010 cm−2, hole traps with the following activation energies were observed: 0.10 eV, identified as a tri-vacancy related defect, 0.33 eV, the interstitial carbon (Ci), 0.52 eV, a B-related defect and 0.16 eV. Low temperature irradiation experiments were also carried out using alpha- particles with the same fluence rate. Measurements were taken between 35 K and 120 K. The defect levels were at 0.10 eV, 0.14 eV and 0.18 eV. These levels were attributed to the boron-substitutional vacancy complex, the mono-vacancy and a vacancy-related defect, respectively. We conclude that EBD and EBE induced more complex defects than those induced by alpha-particle irradiation. / Thesis (PhD)--University of Pretoria, 2019. / Physics / PhD / Unrestricted

Nowadays, financial derivatives play an increasingly important role in the global financial system, and options are popular structural financial derivatives, which attract much attention from academia and the industry. China Financial Futures Exchange (CFFEX) initiated the CSI 1000 index future and CSI 1000 index option in the Chinese market on July 22, 2022, which indicates a trend of acceleration in financial innovations in China’s financial market. This dissertation focuses on the volatility models in option pricing and modern numerical procedures that approximate option prices. In this dissertation, different stochastic volatility models, for example, the Black–Scholes model and the Heston stochastic volatility model, are introduced and applied to price in not only European options but also exotic options, which possess complicated payoff structures. Moreover, a comprehensive empirical analysis is conducted to demonstrate these option pricing algorithms based on the recent data of CSI 1000 index options in the Chinese market. / Business Administration/Finance

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A parallel domain decomposition Laplace transform Boundary Element Method, BEM, algorithm for the solution of large-scale transient heat conduction problems will be developed. This is accomplished by building on previous work by the author and including several new additions (most note-worthy is the extension to 3-D) aimed at extending the scope and improving the efficiency of this technique for large-scale problems. A Laplace transform method is utilized to avoid time marching and a Proper Orthogonal Decomposition, POD, interpolation scheme is used to improve the efficiency of the numerical Laplace inversion process. A detailed analysis of the Stehfest Transform (numerical Laplace inversion) is performed to help optimize the procedure for heat transfer problems. A domain decomposition process is described in detail and is used to significantly reduce the size of any single problem for the BEM, which greatly reduces the storage and computational burden of the BEM. The procedure is readily implemented in parallel and renders the BEM applicable to large-scale transient conduction problems on even modest computational platforms. A major benefit of the Laplace space approach described herein, is that it readily allows adaptation and integration of traditional BEM codes, as the resulting governing equations are time independent. This work includes the adaptation of two such traditional BEM codes for steady-state heat conduction, in both two and three dimensions. Verification and validation example problems are presented which show the accuracy and efficiency of the techniques. Additionally, comparisons to commercial Finite Volume Method results are shown to further prove the effectiveness.