The Compact Implicit Integration Factor Scheme For the Solution of Allen-Cahn Equations

In this thesis we apply the compact implicit integration factor (cIIF) scheme towards solving the Allen-Cahn equations with zero-flux or periodic boundary conditions. The Allen-Cahn equation is a second-order nonlinear PDE which has been the focus of many applications spanning a wide range of fields, such as in material science where it was first introduced to model the phase separation of two metallic alloys, and in biology to study population dynamics, just to name a few. The compact implicit integration method works by first transforming the PDE into a system of ODEs by discretizing the spatial derivatives using the central differencing scheme. This yields a semi-discretized form which produces a nice compact representation to the original PDE. The resulting system is then integrated with respect to time, thereby treating the linear component of the PDE exactly. The nonlinear portion which represents the integrand is then approximated by a Lagrange interpolation polynomial of order r and then integrated exactly, with r = 0,1,2 in our study . Altogether, this a fully discrete scheme which is second-order accurate in space and (r + 1)-order accurate in time. Experiments are also performed to numerically demonstrate the stability and convergence properties of the proposed scheme

Variability in Proximate Analysis of Twelve Selected Elite Pigeonpea Genotypes Across Varied Agro-Ecological Zones in Kenya

Pigeonpea [Cajanus cajan (L.) Millsp.] is a legume crop majorly grown in semi-arid tropics as a warm-season perennial that is depended on by more than a billion people mainly in Asia and Africa as their main source of protein. The study was carried out to assess variation in nutritional quality and determine influence of environmental factors on nutritional composition among 12 elite pigeonpea genotypes through proximate analysis based on AOAC official methods. The field experiment was conducted in four varied agro-ecological zones (Kabete, Kerio Valley, UoE and Kiboko) in randomized complete block design (RCBD).The genotypes and environment varied significantly (P≤ 0.05) for all the parameters measured except for lipids. The mean proximate composition results of the 12 pigeonpea genotype seed samples across the four environments were; moisture (9.597), lipids (1.948), ash (3.89), protein (21.049) and Carbohydrates (63.51) g/100g. Kabete and Kerio Valley scored the highest level of proteins (22.02 & 21.99 g/100 g) respectively while university of Eldoret recorded the least (19.4 g/100 g). The identified potential genotypes with high protein and ash content can be utilized in breeding for better nutritional quality to enhance nutritional and food security. Keywords: Pigeonpea, malnutrition, food security, proximate analysis, agro-ecological zone

QTL mapping: a conceptual approach to improving cold tolerance at seedling stage in rice (Oryza sativa. L)

Much of what is known about the process of technological innovation in agriculture has yet to be captured in the discussions of abiotic stress plant tolerance as well as rice cold tolerance. The development of research and technological solutions to minimize risks of current abiotic stresses to the plant can lead to two possible outcomes: increase in agricultural productivity and assist the future of plant breeding work. Research efforts about the role of technological development, driven by abiotic stress constraints, are pivotal in making any assertion about the likely tolerance of plant to abiotic stress. Drawing upon the hypothesis of QTL mapping, this research investigates on detection of QTLs for cold tolerance at the seedling stage in rice (Oryza sativa. L), QTLs identified from a BC1F2 breeding population derived from the cross between Chomrongdhan, a donor parent tolerant with Vary botry a susceptible parent, that lead to increase rice productivity in Madagascar. Using a controlled environment and molecular work, out of total 500 BC1F2 segregating plants, 144 plants were used for genotyping based on of visual seedling stage cold tolerance symptom. A total of 4606 SNP markers evenly spread throughout the whole 12 rice genome was used for parental polymorphism survey. The 34% polymorphic markers were used for QTL mapping for cold tolerance at seedling stage. QTL analysis using inclusive composite interval mapping detected four QTLs on chromosome 2 and 10 with phenotypic variances (R2) of 11.11, 7.55, 12.8 and 8.8%, respectively. The position of QTL on chromosome 2 was flanked by 2262412 and 2237404, three other QTLs were detected on chromosome 10 conferred cold tolerances for seedling growth and leaf growth at 14day after recovery and appear to be a novel QTLs. Selected tolerant plant in this research should be useful for the farmers and the markers flanking those identified QTLs should be useful for molecular marker assisted breeding for cold tolerance for the breeder. Keywords: QTL mapping, cold tolerance, seedling, rice

Estimating Rice Yield under Changing Weather Conditions in Kenya Using CERES Rice Model

Effects of change in weather conditions on the yields of Basmati 370 and IR 2793-80-1 cultivated under System of Rice Intensification (SRI) in Mwea and Western Kenya irrigation schemes were assessed through sensitivity analysis using the Ceres rice model v 4.5 of the DSSAT modeling system. Genetic coefficients were determined using 2010 experimental data. The model was validated using rice growth and development data during the 2011 cropping season. Two SRI farmers were selected randomly from each irrigation scheme and their farms were used as research fields. Daily maximum and minimum temperatures and precipitation were collected from the weather station in each of the irrigation schemes while daily solar radiation was generated using weatherman in the DSSAT shell. The study revealed that increase in both maximum and minimum temperatures affects Basmati 370 and IR 2793-80-1 grain yield under SRI. Increase in atmospheric CO2 concentration led to an increase in grain yield for both Basmati and IR 2793-80-1 under SRI and increase in solar radiation also had an increasing impact on both Basmati 370 and IR 2793-80-1 grain yield. The results of the study therefore show that weather conditions in Kenya affect rice yield under SRI and should be taken into consideration to improve food security

Assessment of phenotypic and genetic variation against pod borer among a subset of elite pigeonpea (Cajanus cajan) genotypes in Kenya

Molecular marker information supported by quality morphological data facilitates the choice of suitable parents for applied breeding. The main aim of this study was to assess genetic diversity among 55 cultivated yield elite pigeonpea lines using 21 simple sequence repeat (SSR) markers that are well distributed across the genome. Among the 55 pigeonpea genotypes, 16 medium duration were selected and evaluated in the field for response to pod borer resistance in varied agro-ecological zones of Kenya during long rains of April-October cropping season Twenty one primer pairs detected 80 alleles with a mean of 3.9 alleles per locus and polymorphism information content (PIC) ranging from 0.09 to 0.75 averaging to 0.39 suggesting a low genetic diversity. However, marker CcM1820 revealed the highest number of alleles (9) with a PIC value of 0.75. The genotype response to pod borer attack was significant (P≤0.05) with three genotypes (ICEAPs 01541, 01154-2 and 00902) revealing tolerance to pod borer. The markers based on Neighbor Joining, grouped the 55 genotypes into three main clusters based on parentage selection. Most genotypes developed from ICEAP 00068 as the maternal parent were grouped in Cluster I while cluster II comprised of improved genotypes and cluster III comprised genotypes developed from ICPL 87091 as maternal parent. The resistant genotypes identified in the field experiment were grouped in cluster I except ICEAP 00902 which grouped in cluster II. Future studies should focus on broadening genetic base by including more landraces and wild relatives to maximize selection and improve breeding work

Effects of Relationship Marketing on Customer Loyalty: Evidence from Petrol Service Stations in Uasin-Gishu County Kenya

In order to maximize business profit and general performance of the business, it is critical to keep a customer with “ultimate loyalty”. For this reason, any organization must strive to keep loyal customers as long as possible. This is the reason behind the popularity of customer loyalty programs developed by marketing practitioners. Yet, despite efforts for attracting and retaining customers by many organizations, customer attrition exists for every organization. The main reason is that most organizations are still employing the traditional methods to attract and maintain customers with little emphasis if any on developing long lasting relationships with customers. The main objective of this study was to determine the effect of relationship marketing on customer loyalty in Uasin-Gishu County with a view of making recommendations towards effective utilization of relationship marketing strategies to retain and maintain customers.The study employed mainly explanatory survey design. Simple random and systematic sampling techniques were used to select a sample of 354 customers of petrol service stations within Uasin-Gishu County who participated in the survey. Factor analysis was used to validate the preconceived variables while correlation analysis and Multiple Regression were be utilized to test the hypotheses of this study. The findings of this study supported the hypotheses of the study using both correlation and regression analysis. For instance, the R of the independent variables (level of commitment, level of communication, level of trust, conflict handling capacity) on the dependent variable (level of customer loyalty) is 0.72; this showed that the level of customer loyalty was positively and highly affected by thelevel of trust, level of commitment, level of communication effectiveness and conflict handling capacity of the service providers. Consequently, the determinant of regression (R2) is 0.519; it shows that 51.9% of the variation in level of customer loyalty was explained by the four independent variables. The regression model achieved a satisfactory level of goodness of fit in predicting the variance of level of customer loyalty in relation to the four predictor variables mentioned above. These findings hold implications that firms wishing to retain and develop loyal customers should be trustworthy and committed to the service ethic, should communicate timely and accurately, and must resolve conflicts in a manner that will eliminate unnecessary loss and inconvenience to customers. Keywords: Customer Loyalty, Relationship Marketing, Trust, Commitment, Communication, Conflict Handling Capacit

Chemical Assessment and Antimicrobial Activity of Solvent Extracts from Kalanchoe densiflora

ABSTRACT Kalanchoe densiflora leaves were sequentially extracted using hexane, ethyl acetate, chloroform, acetone and methanol. The solvents were evaporated through rotor evaporation under vacuum to yield five extracts. The extracts were then subjected to chemical and photochemical analyses to identify the components present and their functional groups. In addition the extracts were tested for antimicrobial activities against eight micro-organisms; Bacillus subtilis, Candida albicans, Escherichia coli, Klebsiella pneumoniae, Salmonella typhi, Staphylococcus aureus, Proteus mirabilis and Pseudomonas aeruginosa. The extracts were found to posses' tannins, saponins, terpenoids, flavonoids and cardiac glycosides. It was also found that unsaturated bonds, carboxyl groups and aldehydes were present in the extracts. In addition, the extracts showed antimicrobial activity against Bacillus spp, E. coli and P. aeruginosa as indicated by presence of zones of inhibition. Acetonic and methanolic extracts were sensitive to P. aeruginosa, Bacillus spp. and S. aureus while hexane extract was highly sensitive to E.coli. K. densiflora extracts was found to have broad antimicrobial effect since it was active against gram positive and gram negative bacteria. Crude extracts from K. densiflora can be used in control of diseases such as; acute enteritis, pneumonias and opportunistic diseases amongst other diseases caused by these microorganisms

Evaluation of Genotype x Environment Interaction and Stability of Grain Yield and Related Yield Components in Pearl Millet (Pennisetum glaucum (L.) R.Br.)

Thirty six pearl millet genotypes were evaluated in randomized complete block design with two replications during 2011/2012 at two locations to study the magnitude of genotype by environment interaction for yield and yield related traits and identify the most stable high yielding genotypes. ANOVA of data at individual locations revealed significant differences among genotypes at Marigat and Koibatek for all yield components. Combined mean analysis of variance showed that the Genotype and location main effects and the genotype by environment interaction were highly significant (P≤0.01) for grain yield and other traits, indicating differential response of genotypes across testing locations and the need for stability analysis. Marigat was the most suitable environment and gave highest mean grain yield of 3620 kg/ha. The lowest yield 870 Kg/ha was recorded at Koibatek. Genotypes EUP 32, EUP 35, EUP 19 and EUP 10 produced high mean yield of 3530, 3080, 2690 and 2590 kg/ha respectively. The lowest grain 1290 kg/ha was obtained from genotype EUP 4.Based on the parameters of stability, three stable (widely adapted) and high yielding genotypes (EUP 34, EUP 18, and EUP 9) were identified. They also out-yield the standard open pollinated variety (OPV) check, Kat PM2. Genotypes EUP 32 was the highest yielding across all sites followed by EUP 35 and could be recommended for further multi-location evaluation in warmer environment and possible release for commercial production. The findings of this study showed that pearl millet hybrids have high potential for commercial production in Kenya than the OPVs. The ANOVA results showed that the effects of environments, genotypes and genotype x environment interaction (GE) were important in trait expression and performance of genotypes. In addition, it was observed that amount of rainfall received at both vegetative and post-anthesis phases and temperature had an effect on grain yield. The GGE biplot analysis characterised the environments in terms of stability and productivity, where Marigat was the best for grain yield; implying that environment-specific selection should be adopted. Genotypes EUP 34, EUP 18, and EUP 9 were the best performing since they out yielded the standard OPV check. These stable high yielding genotypes can be evaluated further in varied agro-ecologies and recommended for release as commercial hybrid varieties in ASALs of Kenya