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    Influences of Knowledge Management Processes on Employee Performance in Food Manufacturing Firms in Kenya
    (EdinBurg Peer Reviewed Journals and BooksPublishers, 2025-03-08) Onjolo Samuel
    This 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.
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    On Certain Integral Operator Inequalities in Normed Spaces
    (ICSRS, 2025-11-10) Wafula, Anthony; Okelo, Benard; Kangogo, Willy
    A 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.
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    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.
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    Estimation of Radii of Regions of Starlikeness and Spirallikeness for Analytic Mappings
    (CSRS Publication, 2026-01-25) Nyawalo, Mofat; Aminer, Titus; Okelo, Benard
    Many 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.
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    Computational Modeling of Vibronic Transitions and Stokes Shift in Poly(3-hexylthiophene) Aggregates: Insights into Molecular Ordering and Optical Behavior
    (Research Square, 2026-01-26) Agumba, John Onyango; Barasa, Godfrey Okumu
    Conjugated polymers such as poly(3-hexylthiophene) (P3HT) exhibit optical and electronic properties that depend strongly on molecular ordering and aggregation. This study employed Gaussian-based simulations to model the absorption and emission spectra of P3HT under varying temperature (25-125°C), crystallization time (1-8 h), concentration (0.5-2.5 a.u.), and solvent conditions. In solution, P3HT showed a broad π-π* band at 455 nm with a weak 495 nm shoulder, while aggregates exhibited sharp vibronic peaks at 520 nm, 560 nm, and 610 nm. Increasing temperature and concentration produced red-shifts, spectral narrowing, and higher 0-2/0-1 ratios, signifying enhanced π-π stacking and molecular order. Poor-solvent systems yielded stronger aggregation with 0-2/0-1 ratios of 1.2-1.3 compared to 0.8-0.9 in good solvents. Calculated Stokes shifts of 0.35 eV (solution) and 0.477 eV (aggregate) confirm exciton relaxation and interchain coupling, providing quantitative insight into P3HT’s structure-property relationships for organic optoelectronic design.