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Item Open AccessA Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations.(Kabale University, 2021) Niringiye, RichardThere are several methods of solving a system of linear equations,. some of which are direct methods and others are iterative methods. In this work, .we study direct methods specifically Gaussian elimination and Cholesky decomposition and make a comparison between the two. It is found out that Gaussian elimination is an algorithm in linear algebra for solving a system of linear equations and can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix Whereas Cholesky decomposition is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions. Item EmbargoA Mathematical Model For The Dynamics of Polio.(Kabale University, 2021) Owobusingye, JohnanThere is a lack of treatment for poliomyelitis and it is only prevented through immunization with live oral polio vaccine (OPV) or/and inactivated polio vaccine (IPV). Poliomyelitis is a very contagious viral infection caused by poliovirus. Children are principally attacked. In this project, we assessed the impact of vaccination in the control of the spread of poliomyelitis via a deterministic SVElR (Susceptible-Vaccinated-Exposed-Infectious-Recovered) model of infectious disease transmission, where vaccinated individuals are also susceptible, although to a lesser degree. Using Lyapunov-Lasalle methods, we proved the global asymptotic stability of the dynamics of the disease whenever Ra < I. Numerical simulations, using poliomyelitis data from Kabale Regional Referral Hospital in Kabale district, have been conducted to approve analytic results and to show the importance of vaccination coverage in the control of disease spread. Item EmbargoA Mathematical Model For The Population Dynamics Of Disease Transmiting Vectors in Particular Female Anopheles Mosquitoes.(Kabale University, 2019) Turyamusiima, RichardIn this paper we present a mathematical model of population dynamics of female anopheles mosquitoes. The threshold dynamics of this model is determined and the stability of equilibrium points have been obtained using the jacobian matrix. The mosquito free equilibrium and endemic equilibrium have been determined by setting system of ordinary differential equations to zero. Basic reproduction has been determined using the next generation matrix management analyzed. Hence. we show that if the threshold dynamics quantities are less than unity, the mosquitos' population decreases to zero but if they are greater than unity, mosquitos' population persists. Item Open AccessA Platform For Solar Energy An Alternative Source For Kabale District at Kabale University.(Kabale University, 2021) Amanya, DevisThe energy received on Earth from the Sun is plentiful and renewable. Basically. the sun enabled life on our planet, and our life cannot be imagined without it. The sun is directly or indirectly at the origin for nearly all the energy resources on Earth, such as fossil fuels (coal. natural gas, and oil), hydro (global water circulation is due to the sun), wind, waves, biomass, etc. The sunlight was used as an energy resource already by ancient civilizations. Since I learned a lot of innovative technologies and advancements were performed in this field. The paper presents the main milestones of the developments performed in this important field of energy conversion. Even though the initial cost of setting up the solar panel system is considerably high because the solar cells are fragile and can easily break, there are cheaper options that have been proposed over time. This project discusses the design and construction of a prototype for a solar panel framework. Solar cells are used for sunlight detection. The solar panel is positioned where it can receive maximum light. Silicon solar cells produced an efficiency of 20% for the first time in 1985. Whereas there has been a steady increase in the efficiency of solar panels. the level is still not at its best. Most panels still operate at less than 40%. As a result, most people are forced to either purchase several panels to meet their energy demands or purchase single systems with large outputs. The solar panel framework was constructed by using solar cells from broken solar panels. In terms of cost, it is cheaper, less complex, and still achieves the required efficiency. Item Open AccessAnalysis of the Variation of Vitamin C Content in Different Varieties of Passion Fruits from Kabale Central Market(Kabale University, 2021) Ssenoga, ReganIn Uganda, there are three commercially grown passion fruits namely the small purple Grandilla, the Yellow variety and the Kawanda hybrid. Industries which process passion fruits for juice and people who consume these varieties on market do not consider nutrient content while making preferences on the variety to use. They make choices basing on the color of the outer cover of the fruit and availability. This study analyses and the compares the nutrient content of the three common varieties of passion fruits common in Kabale Central Market. Samples of each of the three varieties were obtained and juice from each representative sample of the varieties was obtained and collected. The concentration of Vitamin C was determined quantitatively by iodometric titration. The study found out that the Yellow variety had high levels of Vitamin C, followed by the Kawanda hybrid, and the small purple Grandilla had the lowest content. However when the juice of the small purple Grandilla was mixed with that of the other varieties higher concentrations of Vitamin C were observed, hence mixtures of juice from the varieties can provide generally high vitamin C contents. Item Open AccessApplication of Laplace Transform For Solving Population Growth and Decay Models.(Kabale University, 2022) Natukunda, PamellahThis study is about the application of Laplace Transform for solving population growth and decay models. It is majorly concerned with the linearity property of the Laplace transform, How the Laplace transform is used in solving population growth and decay model, and How the Laplace transform is used in solving population growth and decay models demonstrated. Laplace can be used to convert complex differential equations to a simpler form having polynomials, convert derivatives into multiple domain variables, and then convert the polynomials back to the differential equation using the Inverse Laplace transform, telecommunication field to send signals to both sides of the medium. For example, when the signals are sent through the phone they are first converted into a time-varying wave and then superimposed on the medium and for many engineering tasks such as Electrical Circuit Analysis, Digital Signal Processing, and System Modelling. The given application shows the effectiveness of the Laplace transform for solving population growth and decay problems. The proposed scheme can be applied for compound interest and heat conduction problems. I encourage mathematicians to use the Laplace transform model in solving differential equations and population models since it is perfect and easy to solve. Item Open AccessApplication of Linear Programming in Profit Maximization (A Case Study of Crunches Fried Chicken at Miami Tours and Travel Hotel in Kabale District)(Kabale University, 2021) Tayebwa, OsbertThis project utilized the concept of the simplex method algorithm, an aspect of linear programming, to allocate raw materials to complete variables. The decision variables in the project work are the three different sizes of fried chicken (tomatoes, onions, and cooking oil) used in the production of fried chicken and the amount of raw materials required for each variable. It was observed that big fried chicken should be produced because it contributed objectively to the profit of the hotel. Item Open AccessApplication of Linear Programming in Profit Maximization: A Case Study of Crunches Fried Chicken at Miami Tours and Travel Hotel in Kabale District.(Kabale University, 2021) Tayebwa, OsbertThis project utilized the concept of simplex method algorithm; an aspect of linear programming to allocate raw materials to complete variables. The decision variables in the project work are the three different sizes of fried chicken on (tomatoes, onions and cooking oil) used in the production of fried chicken and amount of raw materials required for each variable. It was observed that big fried chicken should be produced because it contributed objectively to the profit of the hotel. V Item Open AccessApplication of Multiple Linear Regression Analysis on Academic Performance in Universities.(Kabale University, 2022) Nareeba, CrispusSome students can do well but do not apply themselves, while others with less ability will study extremely hard and get good grades. So, there is variability that shows up naturally. However, by looking at a large group of student's patterns, there should appear to be an estimate based on all of these different aspects of a student's past. The purpose of the study was to analyze the Application of multiple linear regression analysis on academic performance of students in Universities. Item Open AccessApplication of The Simplex Method in Crop Planning.(Kabale University, 2023) Masereka, JoelIn this study, the researcher intended to propose and investigate a model that describes how a farmer can allocate his land to three crops namely; maize, groundnuts, and beans, to maximize yields and consequently maximize profits, given that he has 20 acres of land and other resources amounting to 5,800,000 shillings to be spent on inputs, and 7,500,000 to be spent on labor. 'it further shows that, after applying the simplex method to the model, beans are more profitable compared to groundnuts and maize. Furthermore, we show that the farmer can make a maximum profit of 14,058,765 shillings if he plants 14.94 acres of land. This indicates that farming beans pay much better than farming groundnuts and maize. Item Open AccessAssessing The Impact of Tea Production on The Economic Development of Local Community: A Case Study of Kayonza Tea Factory in Kayonza Sub- County Kanungu District.(Kabale University, 2019) Tukwasibwe, JoabThis study assessed the impact of tea production on the economic development of the local community of Kayonza Sub County in Kammgu District, a case study of Kayonza grower's tea factory. The objectives of the study were to identify the factors that have favoured tea production, find out the contributions of tea production and investigate the challenges affecting tea production in Kayonza Sub County in Kanungu District. The study was carried out in Kanungu District where tea has been promoted as a strategic enterprise since 2004. Descriptive research design was used where the researcher used different data collection methods which included interviewing, questionnaire, and observation methods and a sample of 60 respondents was used for the study. The study findings show that the factors that have favoured tea production were land availability which is a major factor consisting 90% of the respondents, farm labour, relief, agro-input use and the growing promotion as a strategic agricultural enterprise, the contributions of tea production in Kayonza sub-county Kanungu District were a source of income which is the major contribution of tea production (97%), employment opportunities, foreign exchange earner for the county, contributing to food security, infrastructural development, and the challenges affecting tea production in Kayonza sub-county Kanungu District were pest and diseases which is the major challenge to tea production (90%) cost of production, lack of comprehensive policies, , poor road networks and infrastructures, poor agricultural technology, marketing and value¬addition constraints, climatic changes and seasonal effects and poor access to information. The government of Uganda under the Ministry of Agriculture initiated a strategy to support priority agricultural enterprises at the zone level and it is under this approach that tea production has been promoted over the years in Kanungu District. However, more actions should be taken to improve the quality and increase the quantity of tea produced through the supply of inputs by the government, adoption of new technologies and provision of more advisory services, improving the market both local and international, putting in place comprehensive policies such as large scale production as well as improving infrastructures for easy transportation of both green leaf tea and processed tea. Item Open AccessAssessing the Influence of High Population Growth Rate on Food Security in Nyamweru Subcounty Rubanda District.(Kabale University, 2019) Twinamasiko, DerrickThis study assessed the influence of the high population growth rate on food security in the Nyamweru Sub-County Rubanda district. The objectives of the study were to examine the role of population growth rate towards food security, to examine challenges affecting population growth rate on food security, and to find out ways of how a high population growth rate promotes food insecurity in Nyamweru sub-county Rubanda district. A cross-sectional survey design was used. Self-administered questionnaires and interviews were used in data collection and data was analyzed using Excel, a computer software to generate descriptive statistics such as frequencies and percentages, and data was presented in tables and text. From the study findings, the role of the population growth rate towards food security in the Nyamweru sub-county Rubanda district promotes food production. encourages saving and investments, high population growth puts greater pressure on health and improves its quality, leads to a rapid increase in school-age population that calls for more investment in education, high population growth leads to an efficiency of developing countries and their political system and high population puts pressure on urban physical infrastructures leading to development, the study results also on challenges affecting population growth rate on food security in Nyamweru sub county Rubanda district, were inadequate capital for investment, shortage of enough land. poor infrastructure development, climatic changes, over-utilization of land, and political instability the study results also on how a high population growth rate promotes food security in the Nyanweru sub-county Rubanda district the findings were through the development of drought-resistant crops, investment in rural infrastructure, irrigation, improved storage facilities and investment in sustainable technologies. The study recommends that family planning programs should be designed to provide information, services, and modern means of fertility control to those who are interested, the study recommended that the government should use several methods to control high population growth such as one or two children per family policy, girl child education through giving them scholarships and the researcher recommended that there should be sensitization of people through mass media about the dangers of high population so that people can reduce on early marriages. Item Open AccessAn Assessment of the Impacts of Inadequate Housing on the Health of Urban Dwellers: A Case Study of Bweyale Town Council of Kiryandongo District(Kabale University, 2014) Malaki, WanjalaIn this study, the researcher assess the impact of inadequate housing on the health of urban dwellers: a case study of Bweyale town council. The researcher discusses the causes of inadequate housing impact of inadequate housing on the health of the people and finally proposes measures to overcome the problem. Findings showed that poverty, poor waste management high price of land, water stress, high price of building materials, poor location were the drivers of poor housing. Furthermore the researcher assessed the impacts of poor housing on health and came up with respiratory diseases, waterborne disease, allergies, home accidents, hearing disorders and mental disorders among others. The researcher also came up with measures to overcome inadequate housing such as provision of housing finance, proper physical planning, real estate development, lowering the cost of building materials pollution control and provision of tenure security. To arrive at these results the researcher employed several strategies such as personal interviews with key respondents; questionnaire were filled by selected respondents review of secondary information by different scholars. The result from the field were analyzed using frequency tables, pie charts, bar graphs and Microsoft word. The researcher finally concludes by giving recommendations to better the state of housing in Bweyale town council such as : control of design and construction of new dwellings; adequate damp proofing; provision to maintain controlled ventilation; effective protection against noise penetration ; mandatory installation smoke and carbon monoxide detectors; public education and awareness by public health agencies through provision of information regarding ways of making homes healthier and safer and help with effort to eliminate hazardous wastes and toxins from homes. Item Open AccessCauses and Effects of Land Degradation in Karangazi Sector, Nyagatare District Rwanda.(Kabale University, 2014) Fred, MujyambereThe study aimed at investigating the causes and effects of land degradation in Karangazi sector, Nyagatare District Rwanda. The objectives of the study were: to establish the causes of land degradation, to find out effects of land degradation and to find out possible ways to mitigate land degradation in Karangazi sector, Nyagatare District. The study utilized the questionnaire and interview guide in data collection. The study found out that bush burning, deforestation, over grazing and use of pesticides were the major causes of land degradation in Karangazi sector. The effects of land degradation were famine, soil fertility reduction, reduction in plant species, floods, diseases, low produce and migration due to landslides and destruction of roads and houses. Growing of cover crops, a forestation programmes, water harvesting, community participation and sensitization were the major ways to reduce land degradation in Karangazi sector. Item Open AccessThe Climate Change Impact on Agriculture Productivity in Karama Sector, Nyagatare District, Rwanda.(Kabale University, 2014) Odile, TwagiramariyaThe climate change may change the frequency and intensity of weather events which will likely challenge human and natural systems more than normal change. Agriculture is considered one of the most vulnerable systems to climate change. The main goal of this study was to investigate climate change impact on agriculture productivity in Karama sector, Nyagatare District, Eastern province in Rwanda. The study relied on the following objectives: to identify factors influencing climate change in Karama sector, to assess the impact of climate change on agricultural productivity in Karama sector and suggest strategies to mitigate climate change in Karama sector. The study was descriptive and employed both qualitative and quantitative approaches in data collection and analysis. The study utilized the questionnaire to collect quantitative data from 50 farmers in Karama sector and interviews to collect qualitative data from local leaders. The study found out that the main factors recognized by respondents to influence climate change in Karama sector were; deforestation, bush burning, increased emissions of greenhouse gases and orbital variations. The study revealed that, low agriculture productivity, scarcity of food, drying of agriculture plants, and reduction of crops and low production of livestock are the most impacts of climate change on agricultural productivity in Karama sector. Also the study showed that the most agricultural products affected by climate change in Karama sector are respectively maize, beans, bananas, pineapple, sorghum and coffee. Finally the study found out that the measures taken by farmers to reduce climate change in Karama sector are among others the control of bush burning, effective use of energy, effective use of land and effective forest harvesting. It also showed that mass ;sensitization , enhancing afforestation policy, energy conservation, control of atmosphere, improve acclimatization, increase biofuels and adoption of global warming actions are some of the most measures to be taken by the administration to reduce climate change in Rwanda. The effective strategies to mitigate climate change in Karama sector found by the study were the reduction of anthropogenic activities, reduction of burning fossils, regulation of agricultural activities and regulation of forestation. The reality captured by the study is that climate change may affect positively or negatively the agriculture productivity. Hence effective major to mitigate climate change may sustain agriculture. Item Open AccessComparison Between Newton's Interpolation and Lagrange Method with Runge Kutt a Method in Solving First Order Differential Equations.(Kabale University, 2019) Muligi, AmosThe main aim of the study was to make a comparison between a combination of Newton's interpolation and language method with Runge Kutta second order method. The study was guided by objectives like identifying a simpler method of solving first-order differential equations given a combination of Newton's interpolation and Lagrange and Runge-Kutta and identifying a method of solving first-order equations with increased accuracy given a combination of Newton's interpolation and Lagrange and Runge- Kutta. The method used to solve first-order differential equations were Newton's interpolation and Lagrange methods with Runge Kutta and Analytic method which gave the exact values of the solved first-order differential equations. The result showed that a combination of Newton's interpolation and Lagrange method gives a small absolute error and therefore efficient method for solving first-order differential equations. The numerical method used (Runge Kutta) is cumbersome and has a bigger percentage error. I therefore recommend the use of combined Newton's interpolation and Lagrange method to solve first Order Differential equations Item Open AccessComparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation.(Kabale University, 2022) Nzabonimpa, GodfreyThere are several methods of solving a system of linear equations. Some of which are direct methods and others are iterative methods. In this work, we study direct methods specifically Gaussian elimination and Cholesky decomposition and make a comparison between the two. It is found out that Gaussian elimination is an algorithm in linear algebra for solving a system of linear equations and can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix Whereas Cho!sky decomposition is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions. Item EmbargoComparison of Variation of Vitamin C Content with Ripening Stages in Fruit Extracts of Solanum Gilo, Solanum Anguivi And Solanum Aculeastrum.(Kabale University, 2022) Ayebare, HappinessInvestigation of change in the amount of vitamin C in S. aculeastrum, S. anguivi, and S. gila as a result of ripening time involved titration of aqueous extracts from green, yellow, and red fruits separately using potassium iodate. The results obtained showed the content of vitamin C in green fruits which varied as follows; aculeastrum: 0.0088M, S.anguivi: 0.0077M, and S. gila: 0.0061M. The yellow fruits had S. aculeastrum: 0.0073M, S. anguivi: 0.0062M, and S. gilo: 0.0046M, and red fruits had S. aculeastrum: 0.0058M, S. anguivi: 0.0047M, and S. glo: 0.0003M. The data revealed a decrease in the concentration of vitamin C in fruits that turned green from yellow to red. In dietary terms, these fruits should be consumed when green because in that form they contain the highest concentration of vitamin C. Item Open AccessComputer Aided Platform For Teaching Physical Geography: A Case Study Of Kigezi High School.(Kabale University, 2020) Tumukunde, PakarasioComputers have become an important tool for keeping databases, filing systems, and track records. It has made record-keeping much easier than it ever was. It has made data analysis extremely easy, and it can be done with a single click of the mouse unlike the traditional way of teaching which needs a lot of time to read books . While using CAI as an instructional way of teaching students are more interested in reading their lessons. The purpose of this was to develop a computer-aided platform for teaching Physical geography at Kigezi High School.