Faculty of Science (ETDs)

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A study of the support effect of carbon dots-derived graphene-like sheets on the autoreduction of cobalt nanoparticles for Fischer–Tropsch synthesis
(2022) Mokoloko, Lerato Lydia
The aim of this study was to synthesize and characterize carbon dots (CDs) and to use them as a support material for cobalt (Co) based Fischer-Tropsch synthesis (FTS) reactions. The CDs were chosen for this study due to their small size (< 10 nm), easy surface functionalization and synthesis. The small size of the CDs was required for the study of inverse catalyst support effects. An inverse supported catalyst (in this case, the Co/CDs catalyst) refers to the dispersion of a support material that has a small size (d < 5 nm) onto the surface of a metal catalyst with a similar small size (d > 8 nm). The synthesis of this proposed catalyst was successful. FTS studies on the Co ‘supported’ CDs were attempted. Extremely poor FT activity was observed. Post analysis of the catalyst revealed that the CDs did not retain their quasi-spherical and small particle size morphology under the FTS reaction conditions (temperature 220 °C, 10 bar P; H2:CO ratio = 2:1). Instead, upon exposure to a heat treatment, the CDs were transformed into layered structures with a unique resemblance to graphene-based nanosheets (GNSs). This transformation impacted on the use of these catalysts in the FTS reaction. However, this result indicated an unusual transformation of the CDs into another carbon shape. In light of the fascinating transformation phenomenon, annealing studies were then conducted to investigate the effect of annealing temperatures on the CDs structural changes. The CDs (average d= ~ 2.5 nm) used in this study were obtained from the microwave-assisted carbonization of L-ascorbic acid and subjected to a heat treatment (i.e. annealing) at temperatures between 200 and 700 ℃ in a horizontal CVD apparatus under an inert nitrogen gas. It was observed that annealing transformed the CDs from 0-D qausi-spherical nanoparticles to 3- D multi-layered carbons (at 300-600 ℃) and finally 2-D layered materials (at 700 ℃). Furthermore, annealing at 700 ℃ yielded a 2-D single-layered material with comparable properties to traditionally reduced graphene oxide (rGO). A wide range of characterization techniques were used to gain an insight into the physicochemical properties of these novel CDs-derived allotropes as well as to rationalize their mechanism of formation. After evaluating the properties of these materials, it was clear that the surface oxygen functional groups, observed from XPS, 13C NMR and other studies, were responsible for the CDs to rGO transformation. It was proposed that the CDs are assembled to form rGO (and other CDs-rGO derivatives) by either the Ostwald ripening (in which the carbons agglomerated via a gas phase) or a solid phase reaction (involving reaction of CD edges). To further investigate the effect of annealing on the evolution of CDs to layered carbon structures, N-doped CDs (or NCDs) were also studied. The method used to make the pristine CDs was modified by incorporating urea as a nitrogen source to make the NCDs. Annealing the NCDs at temperatures between 200 and 700 ℃ also transformed the quasi-spherical NCDs (average d = ~ 4.1 nm) to multi-layered carbon sheets at temperature as low as 200 ℃. The CD transformation was also associated with the loss of surface functional groups, with % O and N contents of ca. 17 and 16 % (pristine NCDs) being reduced to ca. 8 and 7 % for NCDs annealed at 700 ℃. A similar mechanism for the formation of these N-doped layered carbon structures by annealing was also proposed here. For these samples, it was also observed that the N-bonds, especially the sp3 type nitrogen bonds found on the edges of the NCDs, also took part in the coalescence of the NCDs to give the layered materials. XPS data suggested that in the process, these sp3 type nitrogen bonds were transformed into sp2 pyrrolic-N, pyridinic-N and GraphiticN groups. The annealed CDs products were used to support Co (called Co3O4/T250, Co3O4/T400 and Co3O4/T700 where T is the temperature at which the CDs were annealed) for use in FT studies. Studies were conducted to evaluate the effect Co hydrogen reduction temperatures verses autoreduction temperature, catalyst thermal stability and performance in the FTS reaction at 220 °C (10 bar P; H2:CO ratio = 2:1). Upon investigation of the reduction behaviour of the Co/CDs derivative catalysts using in situ PXRD, it was found that these materials can successfully facilitate autoreduction of Co3O4 to Co face-centered-cubic (fcc) at temperatures > 400 ℃ by a reduction pathway similar to that observed using conventional H2 reduction conditions. As expected, the reduction under H2 took place at a lower activation temperature (> 250 ℃) than the autoreduction process. It was also noted that these novel carbon support derived from CDs gave reduced FTS performance compared to the unsupported Co, especially towards C5+ yields (< 30 % for all Co supported catalysts). These novel CDs-derived allotropes were found to have limited use as supports in Co-based FTS, due to Co agglomeration. These NCDs-derived allotropes (annealed at 200 ℃, 400 ℃ and 700 ℃) were incorporated as active layers in the fabrication of chemoresistive sensing device detection of volatile organic compounds (VOCs). These layered showed enhanced chemical vapour sensing properties, especially for methanol and ethanol detection at room temperature. Therefore, although there are great limitations for applications of these CDs-derived layered allotropes in FTS reaction, these materials show a much better potential for applications in facile and cost effective VOC sensors. Further studies on this will be conducted.
A symmetry perspective of third-order polynomial evolution equations
(University of the Witwatersrand, Johannesburg, 2024) Gwaxa, Bongumusa; Jamal, Sameerah
In this thesis, we analyse the full class of ten Fujimoto-Watanabe equations. In particular, these are highly nonlinear third-order and two fifth-order equations. With the aid of computer algebra software such as Mathematica, we calculate symmetries for these equations and we construct their commutator tables. The one dimensional system of optimal subalgebras is obtained via adjoint operators. Finally, we reduce these higher-order partial differential equations into ordinary differential equations, derive their solutions via a power series solution method and show how convergence may be tested. Lastly, we determine some conservation laws
Analysis of some convergence results for inertial variational inequalities problem and its application
(University of the Witwatersrand, Johannesburg, 2023) Kunene, Thembinkosi Eezy
Some core aspects of nonlinear analysis, which is a major branch of mathematics, are the optimization problems, fixed point theory and its applications. These concepts, that is, optimization theory, fixed point theory and its applications are widely applied in several fields of science such as networking, inventory control, engineering, economics, policy modelling, transportation and mathematical sciences to mention but a few. Due to its relevance to different fields, the theory of optimization and fixed point has been a popular field of research for a long time. Given its expansive nature, researchers continue to make new discoveries and advancements, contributing to its enduring significance across various disciplines. The goal of this dissertation is to explore some convergence iterative methods for approximating optimization problems. We propose a new modified projection and contraction algorithm for approximating solutions of a variational inequality problem involving a quasi-monotone and Lipschitz continuous mapping in real Hilbert spaces. We incorporate the technique of two-step inertial into a single projection and contraction method and prove a weak convergence theorem for the proposed algorithm. The weak convergence theorem proved requires neither the prior knowledge of the Lipschitz constant nor the weak sequential continuity of the associated mapping. Under additional strong pseudomonotonicity, the R-linear convergence rate of the two-step inertial algorithm is presented. Finally, some numerical examples are given to illustrate the effectiveness and competitiveness of the proposed algorithm in comparison with some existing algorithms in the literature
Comparing the effectiveness of LSTM, ARIMA, and GRU algorithms for forecasting customer charging behavior in the electric mobility industry in Europe
(University of the Witwatersrand, Johannesburg, 2023) Pelwan, Robyne Chimere
Forecasting, a powerful technique for unveiling potential future events, relies on historical data and methodological approaches to provide valuable insights. This dissertation delves into the domain of electric mobility, investigating the effectiveness of three distinct algorithms—Long Short-term Memory (LSTM), Autoregressive Integrated Moving Average (ARIMA), and Gated Recurrent Unit (GRU)—for predicting customer charging behavior. Specifically, it focuses on forecasting the number of charges over a 7-day period using time-series data from European electric mobility customers. In this study, we scrutinize the interplay between algorithmic performance and the intricacies of the dataset. Root mean squared error (RMSE) serves as a metric for gauging predictive accuracy. The findings highlight the supremacy of the ARIMA model in single-variable analysis, surpassing the predictive capabilities of both LSTM and GRU models. Even when additional features are introduced to enhance LSTM and GRU predictions, the superiority of ARIMA remains pronounced. Notably, this research underscores that ARIMA is particularly well-suited for time series data of this nature due to its tailored design. It contributes valuable insights for both researchers and practitioners in the electric mobility industry, aiding in the strategic selection of forecasting methodologies.
Determination of U and Th Radioisotopes in environmental samples by ICP-QMS
(University of the Witwatersrand, Johannesburg, 2023-07) Rikhotso, Xikhongelo Valentia; Sehata, James; Chimuka, Luke
Not Available
Estimating skills in discrete pursuit-evasion games
(University of the Witwatersrand, Johannesburg, 2023) Gomes, Byron John; Rosman, Benjamin
Game Theory is a well-established field in mathematics, economics, and computer science, with a rich history of studying n-person, zero-sum games. Researchers have utilized the best computational power of their time to create computational players that are able to beat the best human players at complex two-player, zero-sum games such as Chess and Go. In the field of Reinforcement Learning and Robotics, these types of games are considered useful environments to conduct experiments about agent behavior and learning. In this research report we explore a subset of discrete skill-dependent pursuit-evasion games upon which we build a framework to estimate player skills. In this game environment a player’s skill determines the actions available to them in each state and the transition dynamics resulting from the chosen action. The game offers a simplified depresentation of more complex games which often have vast state and action spaces, making it difficult to model and analyze player behavior. In this game environment we find that players with incorrect assumptions about an opponent’s skill perform sub-optimally at winning games. Given that knowledge of an opponent’s skill impacts on player performance, we demonstrate that players can use Bayesian inference to estimate their opponent’s skill, based on the action outcomes of an opponent. We also demonstrate that skill estimation is a valuable exercise for players to undertake and show that the performance of players that estimate their opponent’s skill converges to the performance of players given perfect knowledge of their opponent’s skill. This research contributes to our understanding of Bayesian skill estimation in skill-dependent pursuit-evasion games which may be useful in the fields of Multi-agent Reinforcement Learning and Robotics.
Fabrication of polyaniline/indium oxide /onion-like carbon ternary nanocomposite for room tempera ture gas sensing applications
(University of the Witwatersrand, Johannesburg, 2022-08) Mathe, Boipelo Nicholette; Linganiso, E.C; Tetana, Z; Moma, J
Monitoring and documenting chemical stimuli or environmental fluctuations is vital to daily health care and environmental monitoring. This objective can be accomplished through the development of high-performance sensors able to detect toxic gases such as ammonia, volatile organic compounds (VOCs) and many more. The modification of carbon nano-onions with metal oxides/conducting polymer could enhance sensing performances at room temperature. This research focuses on the development of a flexible room temperature gas sensor for ammonia sensing with a sensing layer composed of indium oxide (In2O3)/onion-like carbons (OLCs)/ polyaniline (PANI). The current sensors were tested at a 40-45 percentage humidity. Polyaniline was produced utilizing the rapid polymerization technique with aniline and ammonium persulfate as precursors. Carbon nano-onions were obtained by the flame pyrolysis process with candle wax as the carbon source. The present study compared two microwave-assisted solution-phase methods for the synthesis of indium oxides. The first methods produced indium hydroxide (In(OH)3) followed by its conversion to In2O3 through annealing at 400 oC, and the second used a one-step method where ethanol was used as a solvent instead of water. Different reaction times were used to determine the effect of microwave power on the indium oxide formed through a solution-phase method, and several characterizations techniques were performed to characterize the products, including transmission electron microscopy, X-ray diffraction, Fourier transform infrared spectroscopy, Raman spectroscopy, scanning electron microscopy, Brunauer-Emmett-Teller, X-ray photoelectron spectroscopy and Ultraviolet-visible spectroscopy. The ternary In2O3/PANI/OLCs nanocomposite was fabricated using physical mixing by adding varying amounts of In2O3 to fixed quantities of PANI and OLCs. Using gold-plated interdigitated electrodes (IDEs) embedded on a printed circuit board (PCB) substrate, inexpensive and room temperature functional sensors based on plain PANI, OLCs, OLCs/PANI, and OLCs/PANI/In2O3 were developed. The sensors based on ternary composites outperformed of sensors based on pure PANI, OLCs, and PANI/OLCs, due synergic effect of PANI, OLCs and In2O3 when combined. The sensor with the highest response among the sensors with the ternary nanocomposite as the sensing layer, was chosen for further evaluations of recovery time, reaction time, repeatability, and selectivity. The sensor containing (4.6 mg) B-In2O3/PANI/OLCs was particularly responsive to ammonia in comparison to other analytes (hexane, isopropanol, acetone), with the response and recovery durations of 2.2 minutes and 4.3 minutes, respectively, spanning a concentration range of 25 ppm to 125 ppm. Current results showed that In2O3 materials can be successfully applied in room temperature gas sensing application and further enhance the sensing response to levels that cannot be obtained when using PANI or OLC individually.
Fast oxide ion conductors for solid oxide fuel cells: average and local structure – property correlations in solid solutions of bi2o3
(University of the Witwatersrand, Johannesburg, 2023) Masina,Sikhumbuzo Mfanawemphi; Billing, David Gordon
In this thesis, substituted Bi2O3 systems were fabricated and characterized. W, Dy, Erand Nb were used as substituents in a goal to stabilise the highly conductive δ-Bi2O3like phases (hence forth referred to as the δ-phases) to ambient temperatures. Changes in both the average and local structures of the substituted Bi2O3 systems were correlated with the physical property conductivity. In the first part of the thesis, powder X-ray diffraction and Raman spectroscopy were used to show that WO3 on its own did not stabilise the δ-phase at ambient temperatures. The true equilibrium phase in the Bi2O3- WO3 system was a mixture of two tetragonal phases 7Bi2O3·2WO3 and 7Bi2O3·WO3. The co-doping strategy was used to fabricate the Bi2O3-Dy2O3-WO3 system (DWSB, where D =Dy, SB = stabilised Bi2O3). The δ-phase was stabilised with a minimum of 15 mol% total substituent concentration. Powder X-ray diffraction indicated that the δ- phases obtained in this system were metastable and degraded after isothermal annealing at ~ 500 °C for 100 hours. Addition of Er to the DWSB system to create the novel system Bi2O3-Dy2O3-Er2O3-WO3 (DEWSB, where E=Er) was found to significantly improve the stability of the δ-phase when annealed at virtually identical conditions as DWSB. The rest of the thesis is focused on the effect of each substituent cation on phase stability, local structure and the ageing phenomenon–the decrease in ionic conductivity upon isothermal annealing without any observable changes in average structure under powder X-ray diffraction. X-ray pair distribution function, X-ray absorption spectroscopy and photoluminescence were used to probe the local structure around the host Bi cations and some of the substituent cations (Dy, Er, W). The results indicated that some of the Bi cations are displaced away from the 4a site of the defect fluorite structure (Fm-3m) and that at the local level, the Bi cations assume an arrangement similar to that found in the monoclinic α-Bi2O3 phase. Dy and Er were also found to prefer local environments similar to those in their parent oxides. The resemblance increased as the material aged and might explain why the conductivity decreases upon ageing
Metabolic Engineering of Streptomyces
(University of the Witwatersrand, Johannesburg, 2023-09) Nosarka, Zainab; Moodley, Sanchia; Rumbold, Karl
The Streptomyces genus demonstrates remarkable potential as a source and host for the production and discovery of industrially relevant secondary metabolites. The genus natively produces approximately 75% of antibiotics and several other compounds encoded by biosynthetic gene clusters (BCGs). However, most BCGs are poorly expressed or dormant under laboratory conditions and thus require metabolic engineering. Several technologies have been developed for this purpose but the pCRISPomyces-2 plasmid system, which employs Cas9 engineering, exhibits the most promising efficacy. This dissertation outlined foundational research to determine the capacity to introduce pCRISPomyces-2 plasmids into Streptomyces albulus BCRC11814 that produces high quantities of ɛ-poly-L-lysine, an antimicrobial and anti-phage compound. In addition, the strain has several other industrially relevant BCGs that have not been studied but possess engineering potential. To achieve the outlined aim, pCRISPomyces-2 plasmids were Sanger sequenced to ensure structural integrity and related functionality. A ClustalW alignment referenced against the plasmid’s nucleotide sequence verified a sequence identity > 98%. Subsequently, an intergeneric conjugation system was established by transforming pCRISPomyces-2 plasmids into Escherichia coli donor cells with an average transformation efficiency (TE) of 1.49 × 105 cfu/µg. Attempts to optimise TE were hindered by the plasmids’ large size and inherent Cas9 toxicity. Thereafter, the transformed donor cells were conjugated with S. albulus BCRC11814 and a comparative model strain Streptomyces coelicolor A3(2). Successful exconjugants were only obtained with S. coelicolor A3(2). The absence of conjugal mating with S. albulus BCRC11814, despite optimisation attempts, was hypothesised to result from the presence of a methyl-specific restriction modification system. This was confirmed by comparative electro-transformation with methylated and non-methylated DNA that demonstrated specificity to dam and dcm methylated DNA. Furthermore, spontaneous resistance to the selectable marker apramycin was confirmed in both Streptomyces strains. Additional efforts are required to effectively introduce pCRISPomyces-2 plasmids into S. albulus BCRC11814.
Modification of boron nitride nanostructures induced by medium energy ion irradiation
(University of the Witwatersrand, Johannesburg, 2023-08) Lisema, Lehlohonolo Innocent; Madhuku, Morgan; Derry, Trevor
This research focused on using Chemical Vapour Deposition (CVD) to synthesize boron nitride nanostructures, particularly nanotubes, and selectively introducing defects into them through ion implantation. Boron ion implantations were carried out at ambient temperature at 150 keV energy and fluences 1x1014 and 5x1014 ions/cm2. The synthesized samples were analyzed using scanning electron microscopy (SEM), Raman spectroscopy, and Grazing incidence X-ray diffraction (GIXRD). Ion implantation was found to introduce defects into the surface of the samples, resulting in increased stress levels and a higher local density that favoured more crystallized nanostructures. SEM images showed clear evidence of BN nanostructures and boron nitride nanotubes (BNNTs), with the latter appearing as long, thin structures with diameters ranging from ⁓30-90nm. After ion implantation, the Raman spectra of samples implanted with ion fluence 5×1014 ions/cm2 at 1000oC, show an amorphous h-BN peak, and a narrower, intense E2g vibrational mode of h-BN is observed around 1366 cm-1 for samples synthesized at 1100oC and 1200oC. Raman analysis did not show any E2g mode of vibration of h-BN for all samples at implanted with ion fluence 1×1014 ions/cm2. The samples synthesized at 900 ºC had no active 1366 cm-1 Raman peak present. Grazing incidence X-ray diffraction (GIXRD) spectra revealed a prominent peak between 54 and 56 ° 2θ, corresponding to the (004) h-BN reflection, which was used to determine the average a and c lattice parameters 0.249 ± 0.0002 nm and 0.662 ± 0.001 nm, respectively, yielding an interplanar distance of 0.166 ± 0.0001 nm representing the stacking direction of the BN layers. The majority of the samples had broad peaks, indicative of a nanocrystalline material. The only exception was the sample grown at 1200 °C, which was found to have a Scherrer crystallite size >100 nm. In contrast, the rest of the samples had an average size of 3.5 ± 0.3nm. The average crystalline domain size values confirmed that after ion implantation, the phonon lifetime would be longer due to a large domain size, indicating that the BN nanostructures were more crystallized. The fluence of 5x1014 ions/cm2 showed to be the optimal growth condition for BNNTs. Overall, BNNTs and BN nanostructures were effectively synthesized at 900°C, 1000°C, 1100°C, and 1200°C CVD temperatures, and insights into the influence of ion implantation on the composition as well as properties of BN nanostructures are presented. The most noteworthy finding of the experiment was the substantial increase in the size of the Raman derived crystallite domains in the 1100°C and 1200°C samples following ion implantation with boron ions at a fluence of 5x1014 ions/cm2.
On polarity-based semantics for non-distributive modal logics
(University of the Witwatersrand, Johannesburg, 2023) Clingman, R.; Conradie, Willem
This masters study builds upon recent research in polarity-based semantics for non-distributive modal logics (NDMLs). Current formulations of polarity-based semantics for NDML impose compatibility requirements on additional relations of polarity-based frames, hindering applicability of the semantics, as arbitrary frames need not be compatible. In this study we develop a polarity-based semantics for NDML with modalites that are, in general, neither normal nor distributive and without the imposition of compatibility requirements. We provide a sound and complete axiomatization of this logic. The second half of the thesis focuses on a special class of enriched polarities, those who are in a sense liftings of Kripke frames. The compatibility of these liftings combined with the intuitive nature of the underlying Kripke frames makes for a useful case study in which to explore p-morphisms between enriched polarities, and enriched polarity-based models, from a relational perspective.
Overlapping multidomain paired quasilinearization methods for solving boundary layer flow problems
(University of the Witwatersrand, Johannesburg, 2024) Nefale, Mpho Mendy; Otegbeye, Olumuyiwa; Oloniiju, Shina Daniel
There is a constant and continuous need to refine current numerical approaches used to solve non-linear differential equations, which are employed to model real- world problems that often do not have analytical solutions. Spectral-based techniques have proven to be one of the most efficient numerical techniques for finding solutions of differential equations. Numerous spectral-based linearization techniques have been developed, such as the spectral relaxation (SRM), the spectral local linearization (SLLM), the spectral quasilinearization (SQLM), and the paired quasilinearization (PQLM) methods, among others. Previous research suggests that the PQLM is an efficient approach for solving complex non-linear systems of ordinary (ODEs) and partial differential equations (PDEs). However, it has been observed that this method requires further enhancement when utilized for problems described over a large domain, be it temporal or spatial. This research aims to address this limitation by proposing a modified version of the PQLM called the overlapping multi-domain paired quasilinearization method (OMD-PQLM), that enhances the accuracy and convergence speed of the original approach. The new approach entails solving a system by a technique that involves decoupling the system into pairs of equations and partitioning the large domain into smaller overlapping sub-domains. A comparison between the OMD-PQLM and the PQLM is conducted by solving systems of ODEs and PDEs. The proposed numerical approach is evaluated based on the norms of the residual and convergence errors, computational time, and the influence of the number of grid points and sub-domains on the convergence speed of the iterative scheme and the accuracy of the solutions. The findings demonstrate that the OMD-PQLM remarkably improves the accuracy of the solution compared to the PQLM, suggesting that partitioning the problem domain into overlapping multiple-domains optimizes the performance of the PQLM.
Parageobacillus thermoglucosidasius and the water-gas shift reaction: Investigating the influences of gas composition and H2- uptake hydrogenases
(University of the Witwatersrand, Johannesburg, 2024) Mol, Michael; Maayer, De
H2 gas is an increasingly important commercial reagent in a range of industries, including as a potential fuel and energy carrier. Production of H2 gas is carried out almost exclusively reliant on fossil fuel reformation through a relatively limited set of environmentally harmful processes. Pressing environmental concerns and the shift in climate policies towards greater incorporation of cleaner H2 gas production strategies and the implementation of H2 as a more sustainable and environmentally friendly alternative energy vector have necessitated development of renewable and cleaner H2 production processes. Chapter one discusses available literature on the present applications, predominant production processes and emerging alternative production strategies of H2 gas, with particular focus on the applicability and mechanism of biological H2 gas production by the thermophile, Parageobacillus thermoglucosidasius, via the water-gas shift reaction. The application of P. thermoglucosidasius to produce H2 gas is presently in its formative laboratory-scale stage of development. Although progress has been made at a fundamental level, various aspects of P. thermoglucosidasius H2 gas metabolism, remain uncharacterised or poorly understood. In Chapter two, the potential influences of two putative H2-uptake hydrogenases, encoded on the genome of a P. thermoglucosidasius strain previously identified to conduct the hydrogenogenic biological water-gas shift reaction was explored through knock- out mutagenesis. Furthermore, in Chapter three, to establish the practical implementation of pertinent and inexpensive gas feedstocks for the water-gas shift reaction, we explored the influences of various industrial mimetic gas feedstock compositions on the H2 gas evolution-, metabolic- and growth-profiles of P. thermoglucosidasius. Considering the highly variable compositions of industrial off-gases, which may contain oxygen and the highly sensitive nature of this system to oxygen, we further explored the impacts of varied volumetric and temporal oxygen perturbations on the system. Aside from hydrogen production, P. thermoglucosidasius and closely related thermophilic taxa from the genera Parageobacillus and Saccharococcus represent appealing targets for various other biotechnological developments. In Chapter four, we performed a comprehensive comparative genomic and phylogenomic analysis to further explore the biotechnological potential of Parageobacillus and Saccharococcus spp. for a range of whole cell applications as well as a source of industrially relevant thermostable enzymes
Resolvability of groups
(University of the Witwatersrand, Johannesburg, 2020) Ndhlalane, Mororiseng
A topological group is called resolvable if it can be partitioned into two dense subsets. A group is absolutely resolvable if it can be partitioned into two subsets dense in any nondescript group topology. The aim of this dissertation is to give a unified exposition of some major results about resolvability of groups. In particular, we show that; 1. Every countable nondescript topological group not containing an open Boolean subgroup is resolvable, 2. Every infinite Abelian group not containing an infinite Boolean subgroup is absolutely resolvable.
Tableaux and Decision Procedures for Many-Valued Modal Logics
(University of the Witwatersrand, Johannesburg, 2024) Axelrod, Guy Ross
The aim of this dissertation is to present results expanding on the work done by Melvin Fitting in [22] and [24]. In [22], Fitting introduces a framework of many-valued modal logics, where modal formulas are interpreted via generalized Kripke models in which both the propositional valuation and the accessibility relation take on values from some Heyting algebra of truth values. For a fixed arbitrary finite Heyting algebra, H, [24] presents a signed semantic tableau system that is sound and complete with respect to all H-frames. We go on to consider the many-valued generalizations of frame properties such as reflexivity and transitivity (as presented in [39]) and give parameterized tableau systems which are sound and complete with respect to classes of H-frames satisfying such properties. Further, a prefixed tableau system is introduced, which allows us to define an intuitive decision procedure deciding the logics of the above- mentioned H-frame classes, as well as logics of H-frames satisfying generalized symmetry properties, which cannot be captured by Fitting’s unprefixed systems. Further, they allow us to derive finite frame properties. Such a decision procedure has been implemented, and is available on GitHub.
The nineteenth century Matabele settlements on the South African Highveld
(University of the Witwatersrand, Johannesburg, 2023) Van der Merwe, Renier Hendrik; Sadr , Karim; Fowler, Kent
The rise of the Zulu kingdom in KwaZulu-Natal, South Africa, has been a topic of historical research since the 1870s and coincided with increased conflict within the area. The development of the Matabele as a distinct cultural grouping was a gradual process that occurred for decades. Although, initially, only a small group of Khumalo (a northern Nguni clan that formed the elite of the Matabele), they soon started to incorporate the surrounding Sotho/Tswana communities. A clear understanding of their archaeological signatures is needed for Matabele sites to be identified on the landscape. No clear archaeological signature has yet been developed for the Matabele. Therefore, this project aims to describe the organisation of the Matabele military settlements and determine how they evolved during the migration from KwaZulu-Natal to southern Zimbabwe. A settlement organisational model was created that determined that the Matabele and Zulu had a similar settlement organisation, with important differences that allow for individual identification of each group’s settlement. Furthermore, the Matabele utilised perishable material in the construction of the settlement, with no mention of the use of stone found within the historical accounts. Consequently, a difference existed between settlements constructed by Matabele viewed as Nguni and those not regarded as Nguni. This Nguni-non-Nguni divide was also reflected in the presence or absence of the Nguni culture among the inhabitants. This model was then used to develop a Matabele settlement signature that could be used to locate these settlements on the landscape via the use of satellite and multispectral satellite images. A satellite images-based survey was then undertaken to find potential Matabele settlements between Zeerust and Millvale, with 667 potential sites being identified. With the identification of these sites, archaeological excavations can be conducted to develop a clearer understanding of the Matabele. As our knowledge of the Matabele improves, it will allow for a more detailed examination of the northern Nguni as a wider cultural grouping.
The relationship between dental complexity and mandibular shape: implications for dietary inference in stem mammals
(University of the Witwatersrand, Johannesburg, 2024) Harris, Wade; Choiniere, Jonah N.
Non-mammalian cynodonts exhibit some of the first major morphological innovations that contributed to the success of their descendent lineage, mammals. This includes features that are hypothesized to enable adaptation to a highly varied suite of diets such as specialized tooth crowns with complex occlusal surfaces and a jaw muscle configuration where two major muscles contribute to jaw closing. Surprisingly, inferences on cynodont diets so far have been based on qualitative evidence, and the quantification of these dietary adaptations could assist in testing these inferences. Here, I evaluate the relationships of mandibular shape, dental complexity and the combined data on body mass and relative mandible size, to known diets in living mammals, to assess the utility of these ecomorphological proxies for inferring the diets of extinct non-mammalian cynodonts. To assess relationships between diet and jaw shape, I collected 12 fixed landmarks (type 2) and four sliding landmarks (type 3) for six non- mammalian cynodonts, 51 marsupial mammals and 211 placental mammals. Dental complexity (OPCR) values were collected using the R package molaR, for a sample of 19 non-mammalian cynodonts, 47 marsupial mammals and 193 placental mammals. Procrustes-aligned shape coordinates, OPCR values, body mass estimates and relative mandible size data were then subjected to phylogenetic Procrustes ANOVA regressions and phylogenetic regressions. Neither mandible shape nor OPCR are strongly correlated to diet (carnivory, frugivory, granivory, herbivory, nectivory, invertivory), but the combination of these variables are a somewhat reliable predictor of diet, particularly mandible shape. Extinct non-mammalian cynodonts have mandible shapes that are comparable to those of mammals, however they occupy a narrow morphospace and their OPCR scores are generally much lower than those of mammals. Consequently, when these variables were entered into a predictive framework for diet, I observed limited inferential power since non-mammalian cynodonts do not strongly resemble mammals.
The reporting of the sustainability goals and the Sustainable Development Goals (SDGs) in the context of the private sector in South Africa
(University of the Witwatersrand, Johannesburg, 2022) Mosi, Tumelo
Sustainability challenges continue to mount and the fate of this planet lies in a precarious position. In response, the United Nations has introduced a global agreement known as the Sustainable Development Goals (SDGs). These are 17 goals underpinned by 169 targets for addressing social, economic and environmental issues on a global scale. The SDGs seek to do so by unlocking the potential that lies within the private sector and more. The aim of my research was to assess the sustainability goals disclosed by the top 25 Johannesburg Stock Exchange (JSE) listed companies against that of five other countries in 2017. Furthermore, I compared the environmental SDG disclosure of five companies from the metals and mining sector as well as the consumer products sector respectively, within the same period. The sample was selected from the original sample of the top 25 JSE listed companies. Comparisons were done by analysing sustainability/annual/integrated reports of the top 25 JSE listed companies. The results for the sample showed South Africa to be lagging behind the other countries with regards to disclosing sustainability goals in the corporate sustainability reporting for 2017. From 2017 to 2019, the number of reports addressing environmental SDGs from the selected sectors showed an increase. Furthermore, the study companies from the metal and mining sector performed better than those from the consumer products sector with regards to environmental SDG disclosure. However, the environmental SDG score of the study companies from the consumer products sector increased relatively more within the three years of assessment (2017-2019). Variation was also found between the study companies from the two sectors with regards to preference for specific environmental SDGs which included Responsible Consumption and Production (SDG 12), Climate Action (SDG 13), Life Below Water (SDG 14) and Life on Land (SDG 15). Moreover, the iii interviews conducted with the relevant participants revealed that SDG awareness has improved overtime, however internalisation of the SDGs remains the biggest challenge.
Trans-crustal and temporal perspectives of Palaeoproterozoic porphyry copper deposit formation (Haib deposit, Namibia)
(University of the Witwatersrand, Johannesburg, 2023) Jogee, Bibi Ayesha
Porphyryِcopperِdepositsِareِtheِworld’sِprimaryِsourceِofِcopperِwhichِisِanِessentialِcriticalِ metal in the green energy sector. These deposits are most often temporally found within the Phanerozoic Eon and occur principally at convergent plate boundaries. The Haib porphyry copper deposit is a rare example of a Palaeoproterozoic porphyry copper deposit. The Haib porphyry copper deposit is hosted by the rock types of the Richtersveld Subprovince. The Richtersveld Subprovince consists of an older volcano-sedimentary sequence, the Orange River Group (ORG), which was intruded by an extensive composite cogenetic suite of plutonic rocks, the Vioolsdrif Intrusive Suite (VIS). The Vioolsdrif Intrusive Suite is subdivided into several subunits, known as the Vuurdood Subsuite (mafic-ultramafic), Gaobis Diorite, Khoromus porphyry, Goodhouse Subsuite (Granodiorite) and the Ramansdrif Alkali Granite. These subsuites are variably composed of diorites, granodiorites, monzogranites, quartz- feldspar porphyry granodiorites and leucogranites as well as poorly-described clinopyroxenites and gabbros (named the Kokerboom Intrusion in this study). The age-range for the Richtersveld Subprovince is between approximately 1910 and 1865 Ma. The mineralization occurs as disseminations, blebs and veins in the feldspar porphyry andesites and quartz-feldspar porphyry granodiorites. The age of mineralization is bracketed at 1884ِ ±ِ 2ِMa. The Haib porphyry copper deposit is in close vicinity to clinopyroxene and amphibole-rich cumulates, which host novel sulphide mineralization, and present lines of evidence suggesting these are the deeper parts of the porphyry copper system. The mineralization is characterized into two main phases based on drill-core sample descriptions, petrographic observations, mineral liberation maps and isotopic analyses. Previous studies show that garnet and/or amphibole fractionation is related to the petrogenesis of porphyry copper deposits. The Haib porphyry copper deposit shows evidence for amphibole fractionation as opposed to garnet fractionation, which is supported by petrological and geochemical observations in this study. The Haib porphyry copper deposit also has limited ranges in δ65Cuِ andِ δ 56Fe signatures supporting exposure at deeper crustal levels of an arc system. Typical cumulates from deep crustal arc sections (arclogites) are coarse-grained, show cumulate textures and are composed of garnet-clinopyroxene-amphibole-iron-titanium oxides and in some cases plagioclase. The mafic-ultramafic cumulates such as the clinopyroxenites observed in the Kokerboom Intrusion, in close proximity to the Haib porphyry copper deposit, are coarse-grained, are composed of clinopyroxene-amphibole-iron-titanium oxides and consist of non-cotectic proportion of mineral phases. They also comprise a high modal abundance of pyroxene (>70 %) and show distinct cumulate textures. This study has demonstrated that the clinopyroxene and amphibole-rich cumulates which belong to the ultramafic end member of the Kokerboom Intrusion form part of the Vuurdood Subsuite. This conclusion was made through the analysis of lithological characteristics, mineral and alteration assemblages, major and trace element geochemistry and U-Pb age data. Various lines of evidence from this study indicate that the Haib porphyry copper deposit represents the deeper levels of the porphyry system. These lines of evidence include the lack of shallow alteration assemblages (propylitic and argillic alteration), the presence of early dark micaceous veins, the coarse-grained nature of the Vioolsdrif Intrusive Suite (clinopyroxenites, granodiorites, diorites, gabbros), which is indicative of slow cooling at mid-crustal batholith depths, and the presence of clinopyroxene and amphibole rich cumulates of the Kokerboom Intrusion. The clinopyroxenites are mafic, dense, and usually occur at mid- to lower-crustal levels. Geothermobarometry conducted on rocks of the Vioolsdrif Intrusive Suite yield anapproximate depth of crystallization between ~4-12 km which forms part of the mid-crustal levels of an arc system.
Transfer reactions to populate the pygmy dipole resonance in 96Mo
(University of the Witwatersrand, Johannesburg, 2023) Khumalo, Thuthukile Charmane; Pellegri, L.; Wiedeking, M.
The presence of a low-lying dipole strength in neutron-rich nuclei has been established and its location in the vicinity of the neutron threshold (Sn) has implications in nucleosynthesis and specifically in neutron-capture reaction rate calculations. Additionally, a correlation of this low-lying dipole strength with neutron-skin thickness has been discussed. Since its observation, there has been a great deal of work in an attempt to understand its nature, both theoretically and experimentally. Some of the characteristics of this low-lying dipole strength include isospin mixing, which allows the use of different experimental probes to study it. In addition, compared to the IVGDR, the degree to which the low-lying dipole states are collective is under scrutiny and remains an open question of interest. This study was aimed at addressing the question of collectivity of these dipole states and one-nucleon transfer reactions were the chosen probes as they have been shown to be powerful in probing the single-particle property of nuclei. In particular the (p,d) and (d,p) reactions have been instrumental in such measurements. To allow the investigation from both neutron addition and removal, the 96Mo nucleus is particularly attractive as it can be populated via both mechanisms, with the availability of stable targets as a bonus. In addition, the (d,p) has been successfully used recently used for PDR related measurements on 120Sn and 208Pb with results alluding to a strong single-particle contribution, hence conducting the investigation on 96Mo provides access to a different mass region. 97Mo(p,d)96Mo and 95Mo(d,p)96Mo transfer reactions were performed in normal kinematics using the MAGNEX magnetic spectrometer at INFN-LNS. The 25 MeV/u proton beam and 5 MeV/u deuteron beam from the Tandem accelerator interacted with the 97Mo and 95Mo targets, respectively. The MAGNEX spectrometer was utilised to analyse the scattered particles based on their momentum prior to being detected at the focal-plane. Excitation energy spectra were obtained and angular distributions were computed for the bound states and the higher excitation energy region of interest (above Ex = 4 MeV). These were fitted, using the MDA with DWBA calculations considering different single-particle configurations from a simplistic shell model. Comparing spectra from the two reactions, same excitation energy regions were populated. The results from the MDA of the (p,d) data, show a strong single-particle component in the Ex region that was analysed, with one particular configuration that excites 1− states dominating. The QPM was used for the theoretical interpretation and below 6 MeV, the configuration ((2d5 2 )+1 N(1g9 2 )−1) that populates 2+ states dominates but in the experimental data, this configuration was found to be suppressed as the momentum matching conditions were optimized for l=1 momentum transfer. When considering the QPM predictions involving only the sp configurations of momentum transfer of l=1, 2 and 3, an agreement with the data was found. Extraction of reliable angular distributions from the (d,p) was not possible thus future (d,pγ) experiments are envisaged

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