http://hdl.handle.net/123456789/996 2026-04-09T23:38:35Z http://hdl.handle.net/123456789/1099 Extraction and Characterization of Natural Fiber from the Stem of Dombeya Buettneri Plant for Biodegradable Polymeric Composites Application Bichang’a, D. The global drive for a circular economy emphasizing sustainability in composite manufacturing processes has been the driving force for current ongoing research studies in natural fibers as sustainable substitutes for non-biodegradable synthetic fibers. The present study was carried out to characterize Dombeya buettneri fiber (DBF) extracted manually from the bark of the plant stem. Determination of physical and mechanical properties, quantitative chemical analysis, Fourier Transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), thermogravimetric analysis and scanning electron microscopy were used to characterize the extracted fiber. Fiber constituents and XRD results showed higher cellulose content (58.45%), crystallinity index (62.32%) and percent crystalline (72.63%). The fiber had a crystallite size of 2.16 nm as determined using the Debye-Scherrer’s equation while FTIR analysis confirmed the presence of various functional groups of lignin, hemicellulose and cellulose on the fiber structure. The results revealed that DBF fiber had a thermal resistance that is up to 229.57°C with a maximum thermal degradation temperature of 356.27°C. Based on the results of this research that are comparable with other studies on cellulosic fiber, DBF fiber has a great potential as an alternative reinforcement for the development of polymer-based bio-composites. 2023-12-01T00:00:00Z http://hdl.handle.net/123456789/1094 On the Generalization of the Number of Cyclic Codes Over the Prime Field GF(37) Ongili, P., Mude, L. H., & Ndung’u, K. J Research has explored the characterization of cyclic codes over GF(P), where P is prime for P ≤ 23. However, no study has characterized GF(37). Additionally, no study has generalized enumeration of the number of cyclic codes of the cyclotomic polynomials u n − 1 over GF(P). In particular, the generalization of the number of cyclic codes over GF(37) for u n − 1 is also lacking in research. This study focused on the monic irreducible polynomials of u n − 1 over the finite field GF(37) with the main objective of generalizing the enumeration of the number of distinct cyclic codes. The methodology involved determining the number ofirreducible monic polynomials of the cyclotomic polynomial u n − 1 over GF(37). These polynomials were found to correspond to the number of cyclotomic cosets of 37 mod n over GF(37). The study concluded that the number of cyclic codes over GF(37) can be generalized by NGF (37) = (37y + 1)Cxm ∀x, y, m ∈ Z +. The findings provide insights into abstract algebraic concepts in coding theory that can be used to generalize number of cyclic codes over a prime field GF(P) 2024-05-01T00:00:00Z http://hdl.handle.net/123456789/1012 Modelling Daily COVID-19 Cases in Kenya Using ARIMA Model Kamotho, C., Ngure, J., & Kinyua, M. Severe Acute Respiratory Syndrome is the primary cause of the current pandemic coronavirus disease (COVID-19). The first case was reported in Wuhan, China, on December 30th, 2019 with the first case on 13thMarch, 2020 in Kenya. This contagious disease has become a global issue because it has resulted in millions of deaths, economic disruption leading to loss of employment and economic instability. Researchers have fitted time series models but using a short data length and without a transition. There was therefore a need to model a longer data period of daily COVID-19 cases with a transition in Kenya using theAutoregressiveIntegrated Moving Average (ARIMA) model and forecast. Secondary data from the World Health Organization from 13thMarch, 2020 to 30thApril, 2023 was analyzed using R software. The data was found to be non-stationary using the Augmented Dickey Fuller test and regular differencing was done to make it stationary. The Box-Jenkins methodology was used to fit the model of the data and afterwards forecasting was done. The ARIMA (3,1,2) was selected as the best model since it had the least Akaike Information Criterion and Bayesian Information Criterion among the possible models. Model validation using test data was done by comparing the MAE, and RMSE of the model’s forecasts and it was the best amongst the possible models with MAE = 2.77 and RMSE =2.88. The model was fitted to the daily COVID-19 data and forecasting was then done for ninety days into the future 2023-09-01T00:00:00Z http://hdl.handle.net/123456789/1011 Modeling Cross SectionalData Using Fuzzy Regression Analysis: A Case Study of Value Price of Residential Properties in Ames Moturi, C; Musau, V; Muriungi, R Fuzzy regression analysis (FRA), also known as non-statistical regression analysis, is an approach used to establish relationship between an input and output variables that are fuzzy. Fuzzy regression analysis serves as an alternative method to classical regression analysis (CRA).The models used to model cross sectional data are statistical regression models which are based on linearity, normality and homoscedasticity assumptions. Howeverthese assumptions may not hold true leading to non normality, heteroscedasticity and non normality in the data. Thus, fuzzy regression analysis gives a solution to challenges that may arise when using statistical regression models. Because of the uncertainties that may arise in a given data, the model was based on cross sectional data for the price of residential properties sold in Ames Iowa. Since the price of residential properties fluctuates, the model was developed in three forms. Three fuzzy regression methods; possibilistic linear regression with least squares (PLRLS), possibilistic linear regression (PLR) and fuzzy least absolute residuals (FLAR) methods were used to fit the fuzzy linear regression model (FLRM).In this study lot area, total basement area square feet and garage area were selected as explanatory variables. The results show that by applying different fuzzy regression methods to model the data,fuzzy least squares methods yielded significant results for modelling the value of the residential properties. 2023-09-01T00:00:00Z