Combinatorial generalizations and refinements of Euler's partition theorem

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. 9 December 2014.The aim of this research project is to survey and elaborate on various generalizations and re nements of Euler's celebrated distinct-odd partition theorem which asserts the equality of the numbers of partitions of a positive integer into distinct summands and into odd summands. Although the work is not originally my own, I give clarity where there is obscurity by bridging the gaps on the already existing work. I touch on combinatorial proofs, which are either bijective or involutive. In some cases I give both combinatorial and analytic proofs. The main source of this dissertation is [22, 5, 6, 8]. I start by rst summarizing some methods and techniques used in partition theory

Building positive Zimbabwean tourism festival, event and destination brand image and equity: a systematic literature review

This article aims to explore the concept of tourism festival and event destination branding and relate it to practices in Zimbabwean festivals and tourism events. The article is therefore based on the following objectives: to understand the concept of tourism festival, event and destination brand image in Zimbabwe; to explain its essence and importance in Zimbabwe; to explore the brand process by mainly looking at market analysis, brand development, brand positioning, brand personality, brand implementation, brand communication and brand tracking; to understand the necessary critical success factors; to explore the constructs of brand equity; and to analyse previous models and discussion in tourism festival and event destination brand equity. A systematic literature review was applied to gather relevant literature related to the study. The process involves a predetermined and comprehensive approach to searching, analysing and synthesising extant literature. Results showed that the image of country’s imagea and vital role in building a positive or negative perception towards a tourism destination image. However, it is essential to note that the image of a country might take a long time to restore itself, even going on for generations. The research study contributes to future research directions by unpacking existing research gaps and advancing knowledge relating to tourism festivals, events and destination brand image in Zimbabwe

Risk factors associated with a high incidence of sexually transmitted infections in Beitbridge, Zimbabwe

BACKGROUND: Sexually transmitted infections (STIs) are a major public health challenge, particularly in developing countries where the health infrastructure is often poor. Despite having a number of interventions in Beitbridge (such as the 24-h wellness centre), Zimbabwe, the incidence and prevalence of STIs is increasing. OBJECTIVES: This study, therefore, aims to assess the risk factors associated with the high incidence of STIs in urban Beitbridge. METHOD: A case-control study was conducted on 30 respondents who had suffered from STIs (selected from the registers at Beitbridge hospital and followed up) and 90 respondents who had not suffered from STIs (from the community) who resided in Beitbridge for at least 6 months and this excluded all those who were in transit. The factors contributing to the high incidence of STIs were identified using a pretested interviewer-administered semi-structured questionnaire in conjunction with a Likert scale to establish the attitudes and risk behaviours of the respondents on STIs. RESULTS: A significant association was observed between high STI incidences and the nature of occupation (odds ration [OR]: 3.8), area of residence (OR: 2.78), number of sexual partners (OR: 7.56), payment demanded for sex (OR 22), condom use (OR: 3.7), alcohol use (OR: 2.86), and suspicion that partners had other sexual companions (OR: 15.5). Furthermore, a larger proportion of controls were knowledgeable on STIs as compared to the cases who participated in the study. CONCLUSION: There is a need to develop awareness strategies that foster safe sexual practices, particularly among populations who do not choose abstinence or a single sexual partner lifestyle

Building positive Zimbabwean tourism festival, event and destination brand image and equity: a systematic literature review

AbstractThis article aims to explore the concept of tourism festival and event destination branding and relate it to practices in Zimbabwean festivals and tourism events. The article is therefore based on the following objectives: to understand the concept of tourism festival, event and destination brand image in Zimbabwe; to explain its essence and importance in Zimbabwe; to explore the brand process by mainly looking at market analysis, brand development, brand positioning, brand personality, brand implementation, brand communication and brand tracking; to understand the necessary critical success factors; to explore the constructs of brand equity; and to analyse previous models and discussion in tourism festival and event destination brand equity. A systematic literature review was applied to gather relevant literature related to the study. The process involves a predetermined and comprehensive approach to searching, analysing and synthesising extant literature. Results showed that the image of country’s imagea and vital role in building a positive or negative perception towards a tourism destination image. However, it is essential to note that the image of a country might take a long time to restore itself, even going on for generations. The research study contributes to future research directions by unpacking existing research gaps and advancing knowledge relating to tourism festivals, events and destination brand image in Zimbabwe

Effectiveness of peer to peer strategy in reducing accidents and injuries at a selected platinum mine in Zimbabwe

The selected mining company implemented the ''Peer to Peer'' strategy in 2008 to fast track achievement of zero tolerance to injuries and fatalities incidents at its workplace. Our study, therefore, sought to assess the effectiveness of this strategy in reducing accidents and injuries at this selected platinum mine in Zimbabwe. A mixed-method cross-sectional survey was conducted on 32-day shift employees using a semi-structured questionnaire with closed and open-ended questions. Furthermore, incident trend analysis was done on data obtained from the records from 2004 to 2017. Covert observations were then employed to triangulate findings from data collected using the questionnaire on practices. The tests Hotelling, Chi-square, time series plots, and Multiple Logistic Regressions were employed to compare the variables of interest before and after implementing the peer to peer strategy. There was a significant drop in the number of incidents after implementing the peer to peer strategy. There was no association between tested demographic characteristics and the level of employees' knowledge of the strategy. Employees were afraid to implement the strategy to their superiors fully. Findings pointed out that this strategy was effective despite being part of a cocktail of strategies. There was a vast decrease in the rate of occurrence of incidents after the implementation of this strategy. However, there is a need for engagement to address the subordinate management dynamics that was observed to be a threat in the comprehensive implementation of this strategy