PhD Theses/ Dissertations

STOCHASTICMODELLINGOFPREDATOR-PREYDYNAMICSINA THREE-PATCHECOSYSTEMWITHOPTIMALHARVESTING

2026-04-16T13:16:40Z

STOCHASTICMODELLINGOFPREDATOR-PREYDYNAMICSINA THREE-PATCHECOSYSTEMWITHOPTIMALHARVESTING Mayabi, Lucian Talu Predator-prey interactions play a pivotal role in shaping ecological dynamics, and understand ing these interactions is critical for sustainable resource management and effective conservation. Existing literature predominantly focused on deterministic models incorporating optimum har vesting policy involving two ecosystems or less. Moreover, while stochastic models had been employed to account for randomness and uncertainty in ecological interactions, these studies were often limited to single-patch ecosystems. The stochastic dynamics of predator prey models involving more than two ecosystems had been given little attention in literature yet they are crit ical in conservation and resource management. Therefore, this research developed a stochastic predator-prey model with optimum harvesting for three patches namely “cages” which are within a lake, containing a predator-prey system involving large Nile perch as predators and smaller fish as prey. The dynamics of the prey population could transfer from one cage to the other. The study aims to investigate how randomness and harvesting controls affect population stability and sus tainability. Stability analysis of the deterministic part was carried out in order to study the long term behaviour of solutions around equilibrium points. Stability analysis of the stochastic model was done using stochastic Lyapunov function method assessing its impact on the system dynam ics. Numerical analysis was done to explain the analytic approach. From the results, when ei < 1 (ei is the predator’s efficiency in converting prey into a new predator), the lyapunov function, V(t), stays bounded indicating stochastic stability, and when ei > 1, V(t) grows without bound indicating that the system is unstable. An optimal control problem was formulated to derive harvesting functions that maximize resource utility while maintaining a sustainable ecosystem employing the Pontryagin’s Maximum Principle. From Numerical simulation, prey populations remained viable when the harvesting rates were maintained below ν1 = 0.02, ν2 = 0.02, and ν3 =0.02, and noise intensities were controlled at σ = 0.10, and σ = 0.90. The findings high light the impact of human activities, particularly harvesting, on ecosystem balance. They also contribute to conservation biology, fisheries management, and mathematical ecology, providing insights for sustainable resource management and effective conservation strategies.

THE STRUCTURES OF MATRICES AND INDICES OF ZERO DIVISOR GRAPHS OF 3,4-RADICAL ZERO COMPLETELY PRIMARY FINITE RINGS

2026-04-16T13:14:33Z

THE STRUCTURES OF MATRICES AND INDICES OF ZERO DIVISOR GRAPHS OF 3,4-RADICAL ZERO COMPLETELY PRIMARY FINITE RINGS Ndago, Frank Omondi A zero divisor graph of the ring R is a graph whose vertices are entirely from the set of zero divisors of the ring and two vertices of the graph are adjacent if and only if their product is zero. The study of zero divisor graphs is important for it provides a better way of relating graph geometry to matrix conformations and formulation of encryption algorithms in coding therefore fundamental in interpretation of patterns, maps and networks in computer programs and modelling. Reasonable research has been done concerning zero divisor graphs of commutative rings with identity 1 ̸ = 0, however the generalization of the structures of the matrices of zero divisor graphs is still not extensive in the existing literature. Much of the recent works on zero divisor graphs of finite commutative rings have been restricted to the algebraic properties of the graphs such as colouring, girth, spectral radii and classification in terms of their completeness up to isomorphism. This has left the characterization of finite commutative rings via the structures of the matrices and indices of their graphs fairly untouched. In particular, matrices and indices of the zero divisor graph Γ(R) of finite commutative rings of 3-radical zero and 4-radical zero have not been characterized. This research has determined and investigated the properties of the matrices and indices of Γ(R) of finite rings R with unique maximal ideal J(R) such that J(R)3 = (0) and J(R)2 ̸ = (0); J(R)4 = (0) and J(R)3 ̸ = (0). It has also established the singularity and the relationship that exist between the eigenvalue multiplicities in the spectrum to the nullity of the graphs. We have validated the construction of these classes of rings using idealization procedure and the zero divisor graphs drawn from the isolated zero divisors using the Tikz Software. The matrices have been formulated from the graphs using standard definitions and the Mathematica software applied in investigating some of their algebraic properties. The results of this study can find an application to networking such as Google PageRank algorithms, developing more improved codes for better graph interpretation in operation systems. It will also advance the ring classification problem by revealing the interplay between ring theory, graph theory and linear algebra therefore contributing fundamentally to the literature of advanced algebra

THE EFFICACY OF MORAL EDUCATION IN ADDRESSING GENDER-BASED VIOLENCE IN PUBLIC SECONDARY SCHOOLS IN VIHIGA COUNTY, KENYA: A PHENOMENOLOGICAL APPROACH

2026-04-16T13:12:45Z

THE EFFICACY OF MORAL EDUCATION IN ADDRESSING GENDER-BASED VIOLENCE IN PUBLIC SECONDARY SCHOOLS IN VIHIGA COUNTY, KENYA: A PHENOMENOLOGICAL APPROACH Odero, Monicah Achieng’ Moral education had long been recognized as a cornerstone of character development, emphasizing respect, empathy, and justice. In the context of secondary education, moral education provides students with tools to navigate through ethical dilemmas and it foster respectful relationships. However, the persistence of gender-based violence (GBV) in schools underscored a gap in translating moral education into actionable change. Therefore, this study sought to investigate the efficacy of moral education in addressing gender-based violence in public secondary schools in Vihiga County, Kenya, using a phenomenological approach. Three main objectives guided the study: To examine lived experiences of teachers on the effectiveness of moral education in addressing GBV in public secondary schools in Vihiga County, Kenya, to investigate the lived experiences of teachers on the role of moral education in curbing GBV in secondary schools in Vihiga County, Kenya and to establish effective moral strategies in mitigating GBV in public secondary schools in Vihiga County, Kenya. The study was guided by Aristotelian theory of virtue ethics. Additionally, the study employed phenomenological hermeneutic and critical methods. Purposive sampling was used to recruit five guidance and counseling teachers from five public secondary schools in Vihiga County, Kenya. At the same time, unstructured interviews were employed to collect primary data. Data was analyzed thematically using Braun and Clarke's six steps. The study established that moral education is a crucial component in the development of students’ ethical beliefs and perceptions, especially regarding GBV. Secondly lived experience of teachers revealed that they understood that moral education could help in preventing GBV, but they encountered several barriers in its practice. Also, it was found that in order to improve the effectiveness of moral education in combating GBV, schools should incorporate more participatory teaching methods and engage with parents and communities more actively. The study recommended that, the Ministry of Education and other stakeholders should design training programs that will enable teachers to teach moral education and handle issues to do with GBV, the Kenya Institute of Curriculum Development (KICD) should ensure that moral education curriculum is well structured and should include issues to do with GBV and schools should involve parents and other members of the community in moral education programs to enhance ethical standards outside the classroom environment.

SYNCHROTRON-BASEDIN-SITUANDEX-SITUINVESTIGATIONOF PEROVSKITEFORPHOTOVOLTAICAPPLICATIONS

2026-04-16T13:10:27Z

SYNCHROTRON-BASEDIN-SITUANDEX-SITUINVESTIGATIONOF PEROVSKITEFORPHOTOVOLTAICAPPLICATIONS Shatsala, Elly Miller The advancement of perovskite-based optoelectronic devices hinges on overcoming their intrinsic instability challenges. Synchrotron-based techniques have been widely employed to characterize various materials, including the structural and interactive properties of perovskite crystals and their complexes, using ex situ, in situ, and operando approaches. Grazing Incidence Wide-Angle X-ray Scattering (GIWAXS) and Small Angle X-ray Scattering (GISAXS) studies have revealed inherent crystal peaks in perovskite films through both in situ and ex situ methods. This thesis investigates the crystallization dynamics, humidity resilience, and defect passivation strategies of triple cation (Cs₀.₀₅(FA₀.₈₃MA₀.₁₇)₀.₉₅Pb(I₀.₈₃Br₀.₁₇)₃) perovskite thin films, along with co passivation strategies applied to Cs₀.₁FA₀.₉PbI₃ using phenylethylammonium chloride (PEACl) and 2,8-Bis(diphenylphosphoryl)dibenzo[b,d]furan (PPF), aiming to enhance structural, optical, and electronic properties for efficient photovoltaic applications. A comprehensive experimental approach was adopted, combining solvent engineering, anti-solvent optimization, and co-passivation strategies. Film fabrication and degradation behaviors were characterized using synchrotron-based in situ and ex situ GIWAXS techniques, micro-X-ray diffraction (μ-XRD), photoluminescence (PL) spectroscopy, UV-Vis absorption spectroscopy, Atomic Force Microscopy (AFM), Scanning Electron Microscopy (SEM), and Energy Dispersive X-ray Spectroscopy (EDS) for detailed analysis. Results reveal that 5% cesium incorporation into triple cation perovskites yields superior crystal structures, minimizing δ-perovskite phase and PbI₂ formation while enhancing humidity resistance. Solvent treatments, particularly with ethyl acetate (EA) and chlorobenzene (CB), influenced grain size, surface morphology, and film smoothness. Co-passivation of Cs₀.₁FA₀.₉PbI₃ with PEACl and PPF slowed crystallization kinetics, regulated grain orientation, suppressed non-radiative recombination centers, and stabilized the thermodynamically favorable α-perovskite phase. GIWAXS data confirmed the evolution of highly oriented 2D/3D mixed-phase architectures with enhanced c-axis unit cell alignment. Surface and elemental analysis demonstrated uniform passivant distribution, stronger Pb–O bonding, and reduced ion migration pathways. Photo-physical studies showed narrowed PL peaks, bandgap tuning, and reduced trap densities. This work establishes a strategic framework for achieving high-quality, stable perovskite films, laying the foundation for fabricating full solar modules at MMUST Materials Research Laboratory. The outcomes also pave the way for future collaborations, contributing toward the commercialization of perovskite photovoltaics with power conversion efficiencies exceeding 40%. Additionally, ongoing work involving robot automation and Machine Learning for high-throughput experiments at the Advanced Light Source, along with the development of a new multimodal spin-coater design to eliminate overheating and mechanical wobbles, is expected to further enhance beamline studies for perovskite, polymer, and battery research.