School of Natural Science

DETERMINATION OF OPTICAL, ELECTRICAL, STRUCTURAL, AND MORPHOLOGICAL PROPERTIES OF MAPbI3 PEROVSKITE FILMS FOR PHOTOVOLTAIC APPLICATIONS

2025-11-01T00:00:00Z

DETERMINATION OF OPTICAL, ELECTRICAL, STRUCTURAL, AND MORPHOLOGICAL PROPERTIES OF MAPbI3 PEROVSKITE FILMS FOR PHOTOVOLTAIC APPLICATIONS ABOK, SILAS ODHIAMBO The study presents a combined analysis of optical, electrical, structural, and morphological properties of methylammonium lead iodide (MAPbI3) thin films as solar cells. Four MAPbI 3 samples were prepared and characterized via UV Vis spectroscopy, X-ray diffraction (XRD), scanning electron microscopy (SEM) and current-voltage (JV) measurements. Based on the optical analysis, it was established that an onset of absorption was sharp around 1.6 eV and that the coefficients of absorption (> 104 cm-1) verified the direct bandgap nature of MAPbI 3. Tauc plot extrapolation gave average optical bandgap values of 1.515 eV and this complies with most appropriate range of single-junction solar cells. The highest value of power conversion efficiency of 13.91 % was observed in the electrical characterization in a forward scan with moderate hysteretic losses that are ion migration and interfacial charge accumulation effects. It was established in the structural analysis that there was a prevalent (110) orientation as well as good crystallinity but larger values of FWHM at the higher Miller indices indicated localized lattice strain and smaller grain domain size. Morphological analysis yielded an average grain size of 196±36nm which were uniform and favorable to efficient charge transport and effective recombination. The large grain circularity and solidity also pointed to the excellent film quality that was attained by optimization of spin-coating thickness with a two step thermal annealing procedure. These results confirm the suitability of MAPbI3 regarding the usage of thin-film solar cells and elaborate on the significance of processing conditions towards the tailoring of film properties and thus the overall device performance. The study contributes to the body of knowledge regarding the determinants that contribute to enhancing efficiencies, as well as stability in perovskite-based Photovoltaics.

ON THE EXPONENTIAL AND APPROXIMATE POINT SPECTRUM OF A BOUNDED LINEAR OPERATOR IN A BANACH SPACE

2025-03-01T00:00:00Z

ON THE EXPONENTIAL AND APPROXIMATE POINT SPECTRUM OF A BOUNDED LINEAR OPERATOR IN A BANACH SPACE Kipruto, Maureen The exponential and spectrum of bounded linear operators have been investigated to a fair extend with regard to their characterization. Numerous studies have emphasized on the exponential stability of semigroups of linear operators in terms of its actions and the asymptotic behaviours. Similarly, Banach spaces have been studied and various f indings have been obtained. Due to the fundamental fact that operators on Banach spaces are bounded and linear, our main objective in this study was to investigate the exponential and approximate point spectrum of a bounded linear operator in Banach spaces. Specifically we have defined the operator exp(T) for a bounded linear operator T in a Banach space X and determined if exp(T) is invertible. We have shown that if S is a bounded linear operator in X and S commutes with T then exp(S +T) equals exp(T).exp(S) . If H is a Hilbert space and T is a bounded linear operator in H which is normal such that T commutes with a bounded linear operator S in H, then S commutes with the adjoint of T. We have shown that the converse of this statement holds. The spectrum of T can be expressed as the union of the approximate point spectrum of T and the compression spectrum of T. These two sets may overlap. For A a bounded linear operator in H, we have shown that the boundary of the spectrum of A is contained in the approximate point spectrum of A. Finally we have shown that if A and B are bounded linear operators in H which are similar, then A and B have the same spectrum, point spectrum, approximate point spectrum and compression spectrum. There exist some known results in spectral theory, for example the spectral mapping theorem which we have explored and demonstrated that the exponential and approximate point spectrum are independent of the Banach space. We have used the Fuglede’s Theorem to its converse. We have also exploited the properties of the spectrum and used the convergence norm to determine our result. The results we have obtained in this study will be of great importance to the study of the theory of analysis and spectral theory

MODELLING THE EFFECT OF COVID– 19 MORTALITY SHOCK ON FERTILITY RATE IN KENYA USING NEGATIVE BINOMIAL REGRESSION MODEL

2025-11-01T00:00:00Z

MODELLING THE EFFECT OF COVID– 19 MORTALITY SHOCK ON FERTILITY RATE IN KENYA USING NEGATIVE BINOMIAL REGRESSION MODEL Wakhu, Linus Omina Fertility is known as one of the three primary components that determine the struc ture, size, and composition of the population of any country, the other two being mortality and migration. Mortality has been shown to have some effects on fertil ity by various researchers. The world has experienced mortality shocks as a result of various deadly disasters that have previously occurred, from the influenza epi demics of 1918 to COVID-19 that was first reported in 2019. Various studies have been conducted by various researchers on the effects of mortality shocks on fertil ity but little documentation on effect of mortality shock as a result of COVID-19 on fertility is available. Some of the mortality shocks experienced were as a re sult of epidemics, natural calamities and violences i.e influenza epidemic, spanish f lu, famines, genocides, tsunamis, earthquakes, ebola and severe acute respiratory syndrome virus. More recently the world experienced COVID-19 epidemic which resulted into mortality shock. Few empirical studies have examined the impact of the COVID-19 mortality shock on fertility. This study addresses this gap by mod eling the effect of COVID-19–related mortality on fertility rates in Kenya using the Negative Binomial Regression model. The study used secondary data from KDHS. Parameters were etimated using maximum likelihood estimation (MLE), R- soft ware was used for analysis. Results of analysis based on both IRR and p-values revealed that the effect of COVID-19 mortality shock was significant on fertility rate. There was a slightly higher expected count value of 7.488 after COVID-19 compared to 7.146 Before COVID-19. The two values were statistically significant at α =0.05. Thedispersion parameters of 1.537 and 1.572 had a minimal difference, indicating that both models captured overdispersion similarly. The significance of this study is that it offers key insights into how mortality shocks like COVID-19 af fect fertility trends in Kenya, providing evidence to guide demographic projections, policy decisions, and further research on the links between health crises, reproduc tive behavior, and population dynamics. The study concluded that the COVID-19 mortality shock had a positive impact on fertility.

A STOCHASTIC MODEL FOR THE SPREAD OF HIV/AIDS IN A HETEROSEXUAL POPULATION

2025-11-01T00:00:00Z

A STOCHASTIC MODEL FOR THE SPREAD OF HIV/AIDS IN A HETEROSEXUAL POPULATION MATEKWA, GREGORY JOHN Population dynamics and fluctuations exert strong effects on infectious disease transmis sion dynamics of infections such as HIV/AIDS. Existing stochastic HIV/AIDS models predominantly focused on homosexual populations and high-risk groups, largely ne glecting the unique dynamics of heterosexual transmission. This oversight was partic ularly problematic given the distinct contact patterns that characterize heterosexual spread. In this study, a stochastic differential equation (SDE) model was derived to analyze HIV/AIDS transmission within a heterosexual population with incorporation of random perturbations to account for variability in the environment, migration, and other population uncertainties. The model partitions the population into suscepti ble S(t), infected I(t), and AIDS A(t) compartments, with transmission governed by frequency-dependent contact rates. We established the model’s mathematical well posedness through positivity and boundedness proofs, and derived both deterministic R0 and stochastic RS 0 reproduction numbers, demonstrating how environmental noise reduced transmission potential through the correction term − σ2 2 2(µ+δ) . Itˆo’s lemma was used to derive the mean and variance equations for each compartment. Stability analysis revealed that the disease-free equilibrium becomes locally asymptotically stable when RS 0 < 1, while an endemic equilibrium emerges when RS 0 > 1. Numerical simulations with noise intensities (σ1 = 0.1, σ2 = 0.15, σ3 = 0.1) showed significant fluctuations in disease prevalence, particularly in the infected compartment. The study further devel oped a discrete-time Markov chain framework to analyze transition probabilities under noise effects, providing a comprehensive stochastic perspective on HIV/AIDS transmis sion dynamics that more accurately reflected real-world epidemic behavior compared to deterministic approaches.