http://ir.mu.ac.ke:8080/jspui/handle/123456789/3 2026-08-25T11:11:53Z http://ir.mu.ac.ke:8080/jspui/handle/123456789/10460 Title: Numerical ranges and Spetra of inner product type integral transfomers on Hilbert Spaces Authors: Ohuru, Priscah Moraa Abstract: The theory of linear operators in Hilbert spaces has seen substantial progress, particularly for integral operators of inner product-type, which are known to satisfy fundamental in equalities like Cauchy-Schwarz and Landau within unitarily invariant norm ideals. While these inequalities provide explicit formulas for operator norms, they do not inherently characterize or exclude the study of numerical range and spectrum- rather, they offer complementary information that bounds these spectral properties without fully describing them. This reveals a significant gap: explicit norm formulas exist but leave the numerical range, spectrum, and their relationship uncharacterized. This research addresses these gaps by systematically investigating the numerical range and spectrum of inner product type integral operators. Using operator-theoretic techniques including rank-one operators and tensor products, we construct the algebraic numerical range. Through spectral anal ysis employing abelian properties, commutators, and von Neumann algebra methods, we classify the spectrum into point, continuous, and residual components. Convexity arguments via the Toeplitz-Hausdorff theorem and norm inequalities establish bounds for the numerical range and ensure spectral inclusion. Our results demonstrate that the numerical range maintains essential classical properties, with the spectrum contained within its closure. The applications are substantial in quantum mechanics, providing a rigorous framework for characterizing quantum states and observables, with direct impli cations for evaluating system stability and dynamical behavior. We recommend future work develop more refined techniques- specifically, sharper spectral decomposition and numerical range characterization- to enable precise quantum dynamical predictions and extend these structures to open quantum systems. 2025-01-01T00:00:00Z http://ir.mu.ac.ke:8080/jspui/handle/123456789/10453 Title: Strategies of enhancement of public private partnership and performance of public Technical Vocational Education and Training institutions in South Rift Region, Kenya Authors: Jaafar Idd Faraj, Jaafar Idd Abstract: Technical Vocational Educational Training (TVET) sector remains a cornerstone for social-economy development and a driver for the attainment of the Sustainable Development Goals (SDGs). Therefore, promoting the performance of TVET institutions through their partnership with industry to form learning partnerships is inevitable. In spite of this, companies across sectors are struggling to find suitable candidates for job vacancies because the TVET courses offered at various training institutions often do not meet the requirements of the private sector. However, there are limited studies in the Kenyan context focusing on the impact of public private partnership practices on the performance of TVET institutions. In this regard the current study has been designed to investigate the impact of strategies of enhancement of public private partnership on performance of public Technical Vocational Education and Training Institutions in South Rift Region, Kenya. In this regard, the specific objectives of the study were to; find out the impact of partnership in infrastructure provision on performance of public Technical Vocational Education and Training Institutions , assess the impact of partnership in curriculum development on performance of public Technical Vocational Education and Training Institutions, analyse the impact of partnership in financing on performance of public Technical Vocational Education and Training Institutions, determine the impact of partnership in training on performance of public Technical Vocational Education and Training Institutions and assess the impact of partnership in staff development on performance of public Technical Vocational Education and Training Institutions in South Rift Region, Kenya. This study relied on resource-based view and stake holders’ theory. In a bid to effectively achieve this, the study adopted an Explanatory Sequential research design based on samples drawn from across the TVET institutions in South Rift Region which have public private partnership in their respective institutions. The target population was 470 trainers who included trainers of mechanical engineering departments, electrical engineering departments, building departments, management representative of TVET institutions in South rift region. Cluster, stratified random and sampling simple random technique was used. A sample size of 214 was drawn from a total population of 470 trainers. Data was collected by use of interview schedules and questionnaires from the respondents and analysed by use of both inferential statistics e.g., multiple regression, spearman’s correlation and descriptive statistics e.g., frequencies, standard deviation, means using SPSS version 25. From the findings, all the four predictors (Infrastructure, Curriculum development, Practical training and Staff development) jointly explained 72.4 per cent variation on Performance of public Technical Vocational Education and Training Institutions From the regression coefficient β values for Infrastructure (0.206), Curriculum development (0.268), Practical training (0.151) and Staff development (0.178) were positive. The positive β values indicate the direction of relationship between predictors and outcome. In the qualitative analysis of interviews, the findings showed that the public TVET institutions adopted private public partnership to ensure performance of public TVET institutions. The study therefore concludes that all the PPPs approaches under study positively and significantly affect performance of public TVET institutions. The study therefore recommends Therefore, there is need for strengthening private public partnership approaches to improve the performance of public TVET institutions. 2025-01-01T00:00:00Z http://ir.mu.ac.ke:8080/jspui/handle/123456789/10402 Title: Situational analysis of clinical learning environment for the undergraduate nursing students at selected health facilities in Central and Eastern Kenya Authors: Jemesunde, Millicent Kapigen Abstract: Background: Clinical learning environment has an impact on the learning outcomes and performance. Nursing students, nurse educators, nurse preceptors and administrators play a major role in clinical learning. However, the extent to which these roles are effectively performed depends on the quality of clinical learning environment and the level of support provided. Learning opportunities change, therefore, should be identified. Challenges can hinder skill acquisition, reduce confidence, and compromise students’ readiness for independent practice. Identification of strategies can strengthen clinical learning. However, gaps persist in many settings. A situational analysis of the clinical learning environment can help in establish the state of clinical learning environment. Objectives: To assess the role of stakeholders, explore opportunities, explore challenges and evaluate strategies used to improve clinical learning in selected health facilities in Central and Eastern Kenya. Methods: The study used mixed methods cross-sectional study design with empiricism and grounded theory approach. No hypothesis was used, the study sought to answer research questions in line with the objectives. Taro Yamane formula was used to get a sample size of 235 students and 153 nurse preceptors. A census was used for the 23 nurse educators and 7 administrators from selected universities and hospitals. Stratified random sampling was used for students according to the year of study as well as nurses according to the wards. Proportionate random sampling was used to select participants from each stratum. A semi-structure questionnaire and key informant interview guide were used to collect data. SPSS Version 26 was employed to analyze quantitative data. Qualitative data collected were put in broad categories of themes and analyzed in frequencies. Results: The findings showed that majority of students, preceptors, and educators were aware of their roles in the clinical learning environment, while the majority of the administrators said: “I appoint the clinical coordinators and approve placement of students in the clinical rotations.” Likert Score means for nursing students, nurse preceptors and nurse educators for the opportunities available in the clinical learning environment indicators were 3.8±0.3, 3.9±0.5 and 3.8±0.3 respectively indicating that the respondents’ opinions oscillated between neutral and agree. The majority of the administrators said, “... the goals of clinical learning are in line with the Nursing Council of Kenya and that means we have no problem with the regulatory body as far as clinical learning is concerned.” The means for the challenges in clinical learning environment indicators were 2.9±0.4, 2.9±0.7 and 2.9±0.5 respectively indicating that the respondents’ opinion oscillated between neutral and disagree. According to administrators, space is a challenge as one said, “... the clinical sites are not adequate in number and also too small in size to accommodate all the nursing students from the universities.” 36 (20.8%) of the students said that the learning resource centres should be located within the hospitals, 71 (50%) of nurse preceptors said clinical instructors should be proactive in supervising students. On the other hand, 6 (26.1%) of the nurse educators said the number of trained mentors should be increased to supervise students closely. Majority of administrators said, “... proper means of communication between students and supervisors would minimize frustrations and misunderstandings that can hinder smooth learning during clinical rotations.” Conclusion: This study concludes that all stakeholders are aware of their key roles on clinical learning environment. The clinical learning experience of nursing students is significantly influenced by opportunities and challenges identified in clinical learning environment. The most crucial strategy is the need to improve collaboration between universities and hospitals to ensure proper planning of students’ placement in clinical learning environment. Recommendations: The study recommends that stakeholders be encouraged to understand one’s own role within the clinical learning environment. Learning opportunities should be supported and evaluated periodically. Challenges are addressed by adequate preparation of stakeholders. Collaboration between stakeholders is important. 2026-01-01T00:00:00Z http://ir.mu.ac.ke:8080/jspui/handle/123456789/10322 Title: Ergonomic redesign of sewing workstation for garments manufacturing: a case study of Rivatex East Africa Limited, Eldoret, Kenya Authors: Abdalla, Esmaeel E. A. Abstract: Worldwide, the design of a workstation in many garment industries is usually done with minimal consideration of anthropometric data. This may cause hazards and reduce work efficiency as a result of sitting for long periods of time in uncomfortable positions. Ergonomically redesigned workstations are known to reduce Musculoskeletal Disorders (MSDs) and improve the motivation of the garment workers in the workstation environment. The main objective of this study was to redesign an ergonomic sewing workstations for garment manufacturing using selected anthropometric data collected at Rivatex East Africa Limited (REAL), Eldoret, Kenya. The specific objectives were: to assess work-related risks and hazards for garments making workers at sewing workstations; to determine the relevant anthropometric dimensions from garments-making workers for a sewing workstation; to redesign a sewing workstation for garments-making workers; to simulate the redesigned sewing workstation; to optimize the redesigned workstation for garments-making workers at sewing operations; and to fabricate the redesigned sewing workstation. Rapid Entire Body Analysis (REBA) method was used to assess the ergonomic risk of the existing workstation. The sample size of 100 was determined. Eleven anthropometric measurements were taken from workers using ISO 7250-1:2017 and compared using one-way analysis of variance (ANOVA). Using the anthropometric data, a redesigned sewing workstation model was proposed. The model was analyzed using Computer Aided Three-Dimensional Interactive Application (CATIA V5) software based on Rapid Upper Limb Analysis (RULA). The model was simulated using SolidWorks 2024 software based on Finite Element Analysis (FEA). Aluminum alloy 1060 was selected for FEA. The FEA criteria included: stress, displacement, strain and Factor of Safety (FOS). The model was optimised using design study. The model was then fabricated in accordance with the necessary manufacturing process. ANOVA tests results failed to reject the null hypothesis in the data sets (P > 0.05), thus, there was no significant difference between the anthropometric data. The recommended dimensions for workstations are redesigned, significantly reducing the mismatches between workstation dimensions to the relevant body dimensions. Analysis results of the workers' posture for the existing sewing workstation had a final REBA score of 5, implying existence of medium ergonomic risk, hence, changes were necessary. The proposed sewing workstation had a final RULA score of 1, meaning that the ergonomic risk is negligible. The FEA results showed that the maximum stress was 7.175E-01 MPa and did not exceed the yield strength; the maximum deformation was 0.03209 mm, which was below the assigned safety level; the maximum strain was 6.258E-06 and within the range for the material; and the minimum FOS distribution was 3 implying that the model was within the safety range limits. The optimisation results showed that the optimal dimension of the model was 416.5 mm for seat height, 457 mm for seat depth and 472.8 mm for seat width; the optimal stress of the model was 2.662E+01 MPa; and the optimal mass of the model was 19865.24 g. In conclusion, the dimensions of the redesigned sewing workstation was recommended. The proposed redesigned workstation should be suitable for all garment workers in Kenya. 2026-01-01T00:00:00Z