E-commerce is an online transaction which normally takes place over the internet network and uses digital technology. These transactions include buying and selling of goods or services on the internet. Many e-commerce companies like Amazon, Netflix, booking.com and Jumia build their websites with recommender systems that that provide customers with personalized recommendations. These systems face challenges and limitations that reduce their performance, e.g. recommendations' overspecialization, cold start, and difficulties when items with unequal probability distribution appear MBA helps us identify items likely to be purchased together, and association rule mining finds correlations between items in a set of transactions. Association rule mining (ARM) identifies the association or relationship between a large set of data items and forms the base for market basket analysis. ARM has been used in different industries for example supermarkets, mail order, telemarketing, production, fraud detection of credit card and e-commerce.

For any linear operator T acting on a Hilbert space H, its Aluthge transform T˜ where T˜ = |T| 1 2U|T| 1 2 is another linear operator on H. It is known that T˜ preserves the spectral properties of T and more importantly that T has a non trivial closed invariant subspace if and only if T has. In this project Aluthge transforms of dierent classes of operators in Hilbert spaces were studied. In addition, generalized Aluthge transforms, as well as powers of Aluthge transformations were sort and looked at. Lastly, the numerical range of T was discussed but for some classes of operators.

Background Comorbidity of hypertension and diabetes leads to signicant risks of mortality and other non-communicable diseases (NCDs) such as heart attacks and strokes. Kenya, like many low and middle-income countries (LMICs), faces a rapid increase in NCDs burden. However, sub-national burden proles to inform health policy at the county level; the current health planning units are implausible due to small sample sizes from the existing NCDs data sources in Kenya. The main objective of this study was to determine the distribution of hypertension and diabetes disease prevalence at county units in Kenya using small area estimation methods. Methods Data from a nationally representative Kenya STEPwise survey for NCDs risk factors (STEPs-2015) was used. The survey collected health information (physical and biochemical measurements), risky behaviour and demographic indicators related to NCDs for 4,500 persons aged 18-69 years. Multivariate conditional autoregressive models that account for spatial autocorrelation and dependence between diseases (latent eects) were t to estimate the county-specic prevalence of hypertension and diabetes. Simple multivariate improper CAR, improper multivariate CAR, proper multivariate CAR and M-model latent eects were explored. A mixed-eects multinomial logistic regression model was t to identify the macro-risk factors of hypertension and diabetes in Kenya. Results The M-model was selected as the best t based on DIC. Substantial geographical variation in the prevalence of hypertension ranging from 9% in Wajir county and 54% in Nyeri county while diabetes ranged from 0.1% in Narok to 8.1% in Makueni were observed. Overall, 47% (22 counties) and 36% (17 counties) had hypertension and diabetes prevalence estimates above the national burden, 26.4% and 2.7% respectively. Notably, Mombasa, Kiambu, Embu and Nyeri had a substantial burden of both hypertension and diabetes. High cholesterol, central obesity, age, BMI, harmful alcohol intake and high sugar intake were signicantly associated with hypertension and diabetes. Conclusion The county-specic prevalence estimates provide the rst evaluation of hypertension and diabetes burden that policymakers can use to inform interventions aimed at prevention and treatment of NCDs in Kenya. Implementation of comprehensive screening programs and awareness building for NCDs control are crucial in reducing hypertension and diabetes burden in Kenya.

The purpose of this thesis is to model and forecast value-at-risk based on range-measuring rather than the commonly acknowledged volatility models that are based on closing prices. The use of close-to-close prices in modelling and forecasting value-at-risk might not capture important intra-day information about the price movement. As a result, crucial price movement information is lost and consequently the model becomes less ecient. This thesis recommends the inclusion or range-measuring, described as the dierence between the highest and lowest prices of an underlying stock within a time interval, a day, to compute Value-at-Risk. The project uses data of an NSE-listed and trading company, SASN, between November 2009 and November 2019 on which the predictability of range-based and close-to-close estimates was established. It was observed that the values obtained by range-based models were more accurate than when only the daily closing prices are used. The range-based models successfully capture dynamics of the volatility and achieves improve performance relative to the GARCH-type models. These ndings are fairly consistent and can be extended to applications like portfolio optimization.

Contract farming is becoming popular in most developing countries. Most African farmers operate relatively smaller farm sizes and are resource-poor, characterized by poor access to farm and financial inputs and operate in unreliable inputs and output markets. Extant literature shows that contract farming offers solutions to most of these constraints. However, not all smallholder farmers participate in contracts and those who do, often violate the contracts. Empirical research on effect of contract farming on smallholder livelihoods show inconclusive results; some studies have shown that contract farming improves farmers’ productivity and income, while others find it having a negative effect on income and productivity. This study therefore analyzed participation in contract farming and its effects on technical efficiency (TE) and smallholder farmers’ income in Bungoma and Busia counties in Western Kenya. The present study focused on chili and spider plants as the targeted vegetables due to their richness in vitamins and phytochemicals. Primary data was collected from 300 smallholder vegetable farmers in Bungoma and Busia counties. A Probit model was used to analyze the determinants of participation in contract farming while stochastic production frontier and metafrontier models were applied in analyzing TE and technology gaps. Endogenous treatment regression model was used to analyze the effect of participating in contract farming on farm income. Results revealed that, land size had a positive effect on participation in contract farming for both spider plant and pooled farmers. Contract farming had a positive effect on TE and technology gap ratios (TGRs) for both crops. Participation in contract farming had a positive effect on farm income for spider plant, chili and pooled vegetable farmers. The incentives and disincentives of contracting firms should be put into account when designing programmes and policies for promoting contract farming to ensure that there is a balance in benefits between the contracting and contracted parties

This case management study was conducted in Okiya village, Alwi, packwach district. This case management was carried out to help MR. Warom Peter who was experiencing mental illness created by continued fear for covid 19. This case was identified during the second phase of the COVID-19 lockdown .he was then put into a rehabilitation facility at Angal referral hospital in Nebbi district by the help of the senior medical offer because he had started acting aggressively to the entire family and the community I used the case management steps to help assess the needs of Mr. Warom Peter