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The JOOUST Repository aims to store, preserve, disseminate, and provide access to scientific and intellectual outputs, ensuring the preservation of the University’s intellectual memory.
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Item type: Item , Access status: Open Access , Effects of Problem-Solving Approach to Teaching and Learning of Mathematics on Students with Different Achievement Abilities in Kenyan Secondary Schools(Global Scientific Journals (GSJ), 2024-10) Mulwa, Emily Mali; Odindo, Fred; Kevogo, NebertDespite mathematics being one of the core subjects in Kenya’s secondary school curriculum, many students have continued to perform dismally in the subject in Kenya Certificate of Secondary Education (KCSE) with the overall national mean score remaining below 30%. This study aimed at exploring whether there were any significant differences in mathematics’ mean achievement scores of the High Achievers (HAs) and Low Achievers (LAs) between the experimental and control groups. It was anchored on the social constructivism learning theory. The study employed a quasi-experimental non-equivalent control group post-test only design. The study population was 2162 form two learners from 26 schools. A purposive sampling technique was used to sample 14 schools that were at the same level in syllabus coverage and had two streams. Simple random sampling was employed to get the study sample of eight schools with 774 form two learners. Data collection instruments were Baseline Mathematics Achievement Test (BMAT) and Post Mathematics Achievement Test (PMAT). The study data was analyzed using both descriptive and inferential statistics where the means, standard deviations and independent samples t-test to test significant differences in means at an alpha value of 0.05 were used with the help of the Statistical Package for Social Sciences (SPSS) version 29. In this study, findings indicated that there was a significant difference between the mean mathematics achievement scores of HAs and LAs taught through PSA as compared to those taught by conventional methods. This good performance was perhaps due to leaner active involvement, peer interactions, self-directed learning and increased confidence among the learners. This enhanced better understanding of the mathematics concepts which finally translated to improved performance. It was recommended that teachers of mathematics should be encouraged to use PSA so as to improve the performance of learners in mathematics especially LAs who are usually believed to lower the school performance mean scores.Item type: Item , Access status: Open Access , Influences of Knowledge Management Processes on Employee Performance in Food Manufacturing Firms in Kenya(EdinBurg Peer Reviewed Journals and BooksPublishers, 2025-03-08) Onjolo SamuelThis research aimed to assess the influences of knowledge management processes on employee performance in food manufacturing firms in Kenya; and decomposed processes into three constructs of knowledge creation, sharing and application. The study adopted post-positivism philosophy and used explanatory research design with stratified proportionate sampling technique. A sample of 384 respondents from a target population of about 12,643 employees from 60 food manufacturing firms was obtained using Fisher’s (1991) formula. A 5-point Likert scale questionnaire was used to collect primary data -quantitative and qualitative, which underwent descriptive and inferential analyses. The study findings revealed that knowledge management processes had a positive and significant relationship with employee performance as tcal=15.184>tcrit=1.96 at p=0.000. Thus, null hypothesis that knowledge management processes have no significant influence on employee performance was rejected; with regression outcome of β=0.676, p=0.000 indicating that a unit enhancement in knowledge management processes results in employee performance enhancement by similar units in the same direction. The study concluded that knowledge management processes influence employee performance. Industry management should ensure continuous needs assessment on knowledge management processes, for continued suitability to support knowledge management system and facilitate employee performance.Item type: Item , Access status: Open Access , On Certain Integral Operator Inequalities in Normed Spaces(ICSRS, 2025-11-10) Wafula, Anthony; Okelo, Benard; Kangogo, WillyA lot of researches have been carried out on inner product type integral transformers (IPTIT) with regard to various aspects including spectra, numerical ranges and operator inequalities. Consider M and N to be weakly µ-measurable operator valued (OV) functions such that M, N : Ω → B(X) for any Q ∈ B(H). If M and N are integrable with respect to Gel’fand axiom, then we obtain a linear transformation arising from the inner product space as Q 7→ R Ω MtQNt∂(t). There exists an open problem regarding IPTIT while studying inequalities for IPTIT with spectra limited to the unit disc in complex domains. It has been pointed out that the inequalities, and in particular Cauchy-Schwarz (CS) and CauchyBuniakowski-Schwarz (CBS) inequalities, can only be attained for these IPTIT if only one of the operator M or N is normal. Therefore, in this note we solve this problem by obtaining CBS-inequalities for IPTIT in Banach spaces.Item type: Item , Access status: Open Access , Determining Equations for a Wave Equation Arising Due to Collapse of Shafts in Power Transmission System(Asian Journal of Mathematics and Computer Research, 2025-05-10) Nyangwe G. O.; Omolo O.; Aminer T. J. O.The study of wave propagation in mechanical systems plays a crucial role in understanding the dynamic behavior of components under stress or failure. One such scenario is the collapse of shafts in power transmission systems, where the sudden failure of structural components can trigger wave-like disturbances that propagate through the system, potentially causing further damage and system-wide disruptions. The ability to predict and analyze these wave phenomena is essential for ensuring the stability, safety, and efficiency of power transmission networks. In this paper, we study a fourth-order nonlinear wave equation which arises due to collapse of shafts in power transmission systems. Lie symmetry analysis is used to derive the corresponding determining equations that describe the symmetries of the system, which can then be used to reduce the problem to lower-order equations, find exact solutions, or gain insights into the underlying dynamics. By applying Lie group analysis, we systematically prolonged the corresponding infinitesimal generator and applied the symmetry condition to the given wave equation to yield the required determining equations. These equations enable a pathway to exact solutions and system simplification. The work reinforces the value of symmetry-based methods in understanding the dynamic behavior of mechanical systems under collapse-induced wave propagation.Item type: Item , Access status: Open Access , Estimation of Radii of Regions of Starlikeness and Spirallikeness for Analytic Mappings(CSRS Publication, 2026-01-25) Nyawalo, Mofat; Aminer, Titus; Okelo, BenardMany researchers in complex analysis have invested time particularly in investigating geometric properties like starlikeness and spirallikeness of analytic mappings on the unit disk. Finding the exact lengths of the radii in the starlike and or spirallike regions for these functions is very difficult since these shapes are not regular. This therefore requires that an estimation of the radii of these regions be carried out. This research seeks to estimate the radii within which analytic mappings in the unit disk remain starlike or spirallike. This note derives sharp radii estimates and constructs extremal functions achieving these estimates. The methodology involved using techniques of differential subordination, coefficient estimates, distortion theorems, and subordination principles. Moreover, algorithm development techniques were used as well as numerical methods to come up with pictorial representation of starlikeness and spirallikeness regions. Advancement of theoretical development of geometric function theory and also in providing sharp radii bounds useful in modeling involving conformal maps which enhances applications in engineering, fluid dynamics, and signal theory requires the results generated in this work.