On the ideals and semimodules of commutative semirings
- Authors: Olivier, Ruan
- Date: 2021-04
- Subjects: Gqeberha (South Africa) , Eastern Cape (South Africa) , South Africa
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10948/52782 , vital:44026
- Description: Semirings are a generalisation of rings where additive inverses need not exist. In this dissertation, we focus on results of commutative semirings with non-zero identity. Many results that we study are analogous to results from commutative rings with non-zero identity. Properties which are unique to semirings are also investigated, such as semirings where all elements are additively idempotent. The notion of ideals is examined in the context of a semiring. Specifically, prime ideals, maximal ideals, k-ideals and partitioning ideals of semirings are considered. Additionally, the module over a ring is generalised to a semimodule over a semiring. The emphasis is on prime subsemimodules and multiplication semimodules. Lastly, invertible ideals of semirings are examined. , Thesis (MSc) -- Faculty of Science, School of Computer Science, Mathematics, Physics and Statistics, 2021
- Full Text:
- Date Issued: 2021-04
- Authors: Olivier, Ruan
- Date: 2021-04
- Subjects: Gqeberha (South Africa) , Eastern Cape (South Africa) , South Africa
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10948/52782 , vital:44026
- Description: Semirings are a generalisation of rings where additive inverses need not exist. In this dissertation, we focus on results of commutative semirings with non-zero identity. Many results that we study are analogous to results from commutative rings with non-zero identity. Properties which are unique to semirings are also investigated, such as semirings where all elements are additively idempotent. The notion of ideals is examined in the context of a semiring. Specifically, prime ideals, maximal ideals, k-ideals and partitioning ideals of semirings are considered. Additionally, the module over a ring is generalised to a semimodule over a semiring. The emphasis is on prime subsemimodules and multiplication semimodules. Lastly, invertible ideals of semirings are examined. , Thesis (MSc) -- Faculty of Science, School of Computer Science, Mathematics, Physics and Statistics, 2021
- Full Text:
- Date Issued: 2021-04
Incidence of parasitic trematodes effects on the energetics and behaviour of Coryogalops sordidus (Family: Gobiidae) resident in microbialite pools, warm temperate South Africa
- Authors: Du Toit, Hendrik Daniël
- Date: 2021-04
- Subjects: Gqeberha (South Africa) , Eastern Cape (South Africa) , Gobiidae -- South Africa
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10948/52458 , vital:43666
- Description: Coryogalops sordidus(Epaulette goby), is a cryptobenthic species of the Family Gobiidae that iscommonly foundoccupying turbulent surf zones, calm rock pools, and sand and mud flats, where they are generally carnivorous predators. The distribution of C. sordidushas been recorded for Kenya, Tanzania, Mozambique, and South Africa. The species is also resident in the microbialite pools on the temperate south east coast of South Africa. Recent reports indicated these gobies to be covered in numerous dark lesions, possibly suggesting that the microbialite pools are a sub-optimal habitat. Preliminary analyses have indicated that the dark lesions are a result of encysted metacercaria of a digenetic trematode (fluke). There werehowever,no current recorded parasiticspecies occurring within microbialite pool nor any records of any parasitic species utilizingC. sordidus as a host in South Africa. Therefore, the aim of this study was to investigate parasite-host interactions and parasite presence in and around themicrobialite pool systems of Algoa Bay using C. sordidusas a study species. Coryogalops sordiduswas identified to be parasitised by digenetic trematode metacercaria of the Family Diplostomidae Poirier, 1886, localised primarily to the host musculature, fins, eyes, and integument with no settlement on any of the visceral organs. Furthermore, C. sordidus was found additionally parasitised by a green leech (Class: Hirundinea) of the Family Piscicolidae Johnston, 1865, localised exclusively to the ventral body surface, underneath the pelvic fin of the host. Further investigation into the life cycle of the trematode, suggested that the most probable final hosts wereherons,namely Ardea cinereaand Egretta garzetta garzetta, and intermediate host likely being the freshwater gastropod Assimineacf.capensis, present inthe upper microbialite pools. In both the microbialite and neighbouring rock pools trematode prevalence was found to oscillate in response to seasonal chemical and climatic conditions, whereas the secondary piscicolid leech parasite was influencedmoreby host presence than environmental conditions. Greater prevalence and intensity were measured in the microbialite pools suggesting that these systems likely contained a suit of favourable conditions that allowed for greater trematode loads to be maintained as compared to neighbouring rock pools. As parasites often have deleterious effects on their hosts, the response can manifest as an altered host behaviour or an increased energetic debt due to elevated immune response activity and the associated cost of tissue repair at sites of parasite aggregation.This study further investigatedifgobies (C. sordidus) infected with metacercarial cysts display higher metabolic ratesordifferent swimming behaviour compared to non-infected individuals. The results indicated that the metacercarial load carried by infected hosts had on average no significant impact on energetics, swimming ability, or swimming behaviour, concluding that the average metacercarial intensity present on the gobies is therefore below the threshold of an altered host response. , Thesis (MSc) -- Faculty of Science, School of Environmental Sciences, 2021
- Full Text:
- Date Issued: 2021-04
- Authors: Du Toit, Hendrik Daniël
- Date: 2021-04
- Subjects: Gqeberha (South Africa) , Eastern Cape (South Africa) , Gobiidae -- South Africa
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10948/52458 , vital:43666
- Description: Coryogalops sordidus(Epaulette goby), is a cryptobenthic species of the Family Gobiidae that iscommonly foundoccupying turbulent surf zones, calm rock pools, and sand and mud flats, where they are generally carnivorous predators. The distribution of C. sordidushas been recorded for Kenya, Tanzania, Mozambique, and South Africa. The species is also resident in the microbialite pools on the temperate south east coast of South Africa. Recent reports indicated these gobies to be covered in numerous dark lesions, possibly suggesting that the microbialite pools are a sub-optimal habitat. Preliminary analyses have indicated that the dark lesions are a result of encysted metacercaria of a digenetic trematode (fluke). There werehowever,no current recorded parasiticspecies occurring within microbialite pool nor any records of any parasitic species utilizingC. sordidus as a host in South Africa. Therefore, the aim of this study was to investigate parasite-host interactions and parasite presence in and around themicrobialite pool systems of Algoa Bay using C. sordidusas a study species. Coryogalops sordiduswas identified to be parasitised by digenetic trematode metacercaria of the Family Diplostomidae Poirier, 1886, localised primarily to the host musculature, fins, eyes, and integument with no settlement on any of the visceral organs. Furthermore, C. sordidus was found additionally parasitised by a green leech (Class: Hirundinea) of the Family Piscicolidae Johnston, 1865, localised exclusively to the ventral body surface, underneath the pelvic fin of the host. Further investigation into the life cycle of the trematode, suggested that the most probable final hosts wereherons,namely Ardea cinereaand Egretta garzetta garzetta, and intermediate host likely being the freshwater gastropod Assimineacf.capensis, present inthe upper microbialite pools. In both the microbialite and neighbouring rock pools trematode prevalence was found to oscillate in response to seasonal chemical and climatic conditions, whereas the secondary piscicolid leech parasite was influencedmoreby host presence than environmental conditions. Greater prevalence and intensity were measured in the microbialite pools suggesting that these systems likely contained a suit of favourable conditions that allowed for greater trematode loads to be maintained as compared to neighbouring rock pools. As parasites often have deleterious effects on their hosts, the response can manifest as an altered host behaviour or an increased energetic debt due to elevated immune response activity and the associated cost of tissue repair at sites of parasite aggregation.This study further investigatedifgobies (C. sordidus) infected with metacercarial cysts display higher metabolic ratesordifferent swimming behaviour compared to non-infected individuals. The results indicated that the metacercarial load carried by infected hosts had on average no significant impact on energetics, swimming ability, or swimming behaviour, concluding that the average metacercarial intensity present on the gobies is therefore below the threshold of an altered host response. , Thesis (MSc) -- Faculty of Science, School of Environmental Sciences, 2021
- Full Text:
- Date Issued: 2021-04
Bayesian tolerance intervals and their application to ballistic grouping consistency in competitive shooting
- Authors: Gardiner, Marcell
- Date: 2021-04
- Subjects: Gqeberha (South Africa) , Eastern Cape (South Africa) , Bayesian statistical decision theory -- South Africa
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10948/52456 , vital:43662
- Description: Competitive shooting has become immensely popular since the first modern Games held in 1896. Competitive shooting remains the fastest growing segment in the firearm industry, catering to individuals of all ages. Elite shooters are capable of reaching extreme levels of precision and accuracy, despite many factors existing that affect performance in Olympic shooting. One such factor is speed variability, which is dependent on the mass of the bullet, how constant is the lead being used, and, how constant the gunpowder is. The study focusses on the Bayesian simulation method proposed by Wolfinger (1998) for determining three kinds of tolerance intervals when applied to competitive shooting data, particularly examining speed variability. These tolerance intervals included the (𝛼𝛼,𝛿𝛿) tolerance interval (where 𝛼𝛼 is the content and 𝛿𝛿 is the confidence), the 𝛼𝛼 - expectation tolerance interval (where 𝛼𝛼 is the expected coverage of the interval) and the fixed-in advance tolerance interval in which the interval is held fixed and the proportion of process measurements it contains, is estimated. Speed measurements of individual shots fired were measured with either an Oeler 35P or Magneto Speed V3 chronograph and the data was fitted to a one-way random effects model. , Thesis (MSc) -- Faculty of Science, School of Computer Science, Mathematics, Physics and Statistics, 2021
- Full Text:
- Date Issued: 2021-04
- Authors: Gardiner, Marcell
- Date: 2021-04
- Subjects: Gqeberha (South Africa) , Eastern Cape (South Africa) , Bayesian statistical decision theory -- South Africa
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10948/52456 , vital:43662
- Description: Competitive shooting has become immensely popular since the first modern Games held in 1896. Competitive shooting remains the fastest growing segment in the firearm industry, catering to individuals of all ages. Elite shooters are capable of reaching extreme levels of precision and accuracy, despite many factors existing that affect performance in Olympic shooting. One such factor is speed variability, which is dependent on the mass of the bullet, how constant is the lead being used, and, how constant the gunpowder is. The study focusses on the Bayesian simulation method proposed by Wolfinger (1998) for determining three kinds of tolerance intervals when applied to competitive shooting data, particularly examining speed variability. These tolerance intervals included the (𝛼𝛼,𝛿𝛿) tolerance interval (where 𝛼𝛼 is the content and 𝛿𝛿 is the confidence), the 𝛼𝛼 - expectation tolerance interval (where 𝛼𝛼 is the expected coverage of the interval) and the fixed-in advance tolerance interval in which the interval is held fixed and the proportion of process measurements it contains, is estimated. Speed measurements of individual shots fired were measured with either an Oeler 35P or Magneto Speed V3 chronograph and the data was fitted to a one-way random effects model. , Thesis (MSc) -- Faculty of Science, School of Computer Science, Mathematics, Physics and Statistics, 2021
- Full Text:
- Date Issued: 2021-04
- «
- ‹
- 1
- ›
- »