Determinants of Financial Performance in Internet Service Providers in Kenya

Due to the increase in competition and increasing market liberalization, firms in the telecommunications industry are facing a threat to the profit sustainability. Furthermore, customers’ preferences are dangerously volatile and satisfaction of their diverse needs can prove arduous and the heightened customer awareness results in search for better alternative offerings in the market. As a result, customers may voluntarily switch from one vendor to the other. The study adopted a descriptive study design. The population was ISP firms in Kenya from which 10 large ISPs were selected. A total of 50 questionnaires were mailed to the managers of these firms. Primary data was collected through structured questionnaires. Data was analyzed using descriptive analysis and regression analysis. The study found that before customer make a decision to purchase or stay with a service provider, they considered service uptime, network coverage, and customer service. The regression results showed that product pricing, customer service, and service uptime had negative but insignificant effects on firm performance while parent shareholding and network coverage had positive effects on firm performance. The study concludes that the factors influencing customer staying in a provider were service uptime, customer service, and network coverage. The study also concludes that product pricing, customer service, parent shareholding, network coverage, and service uptime do not have a significant effect on firm performance. Thus the financial performance of ISPs in Kenya is not influenced by the churn factors.  The study recommends that Internet Service Providers in Kenya should ensure that they enhance the level of service uptime as this was a major factor that customers considered before making a decision to purchase an ISP product or to stay with the same ISP. The study also recommends that Internet Service Providers should have large network coverage and not just limit themselves to a small or specific area to cover. Third, the study recommends that Internet Service Providers should invest in a modern and efficient customer care service that can provide solutions to customers who have issues with their internet. This was an important purchase decision factor by customers. Keywords: Financial Performance, Internet Service Providers, Keny

Influence of Farm Characteristics on Financial Portfolio Diversification among Commercial Sugarcane Farmers in Bungoma and Kakamega Counties, Kenya

The main purpose of this study was to analyse the relationship between farm characteristics and financial portfolio diversification among sugarcane farmers in Bungoma and Kakamega Counties in Kenya. Descriptive correlation was used to describe and establish the relationships among the study variables. The target population for this study comprised of all sugarcane farmers around Kakamega and Bungoma Counties. Both primary and secondary data was used in this study and the positivistic approach to research guided data analysis will be used for the study. The study variables were measured using both the ordinal scale and summated scale (likert-type scale).The questionnaire was pre-tested on pilot respondents who were not be part of the study respondents but knowledgeable in the study aspects in order to ensure their validity and relevance. Cronbach’s alpha coefficient was used to measure the reliability of the scale. The relationship between return on investment of farm characteristics which was the dependent variable of the study and portfolio diversification was assessed using Pearson product moment correlation. The study found out that there was a positive correlation between contracting farmers secures farm funding and financial portfolio diversification which was statistically significant (r =.468, p<0.05). The regression results revealed that farm characteristics had overall significant positive relationship with the financial portfolio diversification among commercial sugarcane farmers in Kenya (β = 0.204, p-value = 0.012). The hypothesis criteria was that the null hypothesis H04 should be rejected if β ≠ 0 and p-value ≤ α otherwise fail to reject H04 if the p-value > α. From the above regression results, β ≠ 0 and p-value < 0.05, hence the study therefore rejected the null hypothesis since β ≠ 0 and p-value ≤ α and concludes that farm characteristics affected financial portfolio diversification among commercial sugarcane farmers in Kenya

Relationship between Financial Returns of Investable Capital and Financial Portfolio Diversification of Commercial Sugarcane Farmers in Kenya

The main purpose of this study was to establish the relationship between financial return on investable capital and financial portfolio diversification among sugarcane farmers in Bungoma and Kakamega Counties in Kenya. The study’s specific objective was to assess the relationship between financial returns of investable capital and financial portfolio diversification among commercial sugarcane farmers in Kenya. Descriptive correlation was then used to describe and establish the relationships among the study variables. The target population for this study comprised of all sugarcane farmers around Kakamega and Bungoma Counties. Both primary and secondary data will be used in this study and the positivistic approach to research guided data analysis will be used for the study. Primary data was collected through the use self- administered questionnaire. Secondary data on the other hand, was used to obtain information from already existing literature. The study variables were measured using both the ordinal scale and summated scale (likert-type scale).The questionnaire was pre-tested on pilot respondents who were not be part of the study respondents but knowledgeable in the study aspects in order to ensure their validity and relevance. Cronbach’s alpha coefficient was used to measure the reliability of the scale. The study focused on farmers of two counties: Bungoma and Kakamega. The regression results also showed that ROI of investable capital had explanatory power on financial portfolio diversification among commercial sugarcane farmers in that it accounted for 15.7 percent of its variability (R square = 0.157). The study results revealed that there was a statistically significant positive linear relationship between financial return on investment of investable capital and financial portfolio diversification among commercial sugarcane farmers (β= .238, p-value = 0.000). Based on these results, the study concludes that commercial sugarcane farmers in Kenya need to pay more attention on financial return on investment of investable capital because it has been found by this study to have a statistically significant and positive effect on commercial sugarcane farmers in Kenya. The study recommends that the commercial sugarcane farmers in Kenya should therefore strive to improve on their financial return on investable capital because it has been found to have a significant and positive effect on their financial portfolio diversification

Influence of Return on Investment of Debt Financing on Financial Portfolio Diversification among Commercial Sugarcane Farmers in Kenya

The study’s specific objective was to evaluate the relationship between financial returns of debt financing and financial portfolio diversification among commercial sugarcane farmers in Kenya. Descriptive correlation was then used to describe and establish the relationships among the study variables. The target population for this study comprised of all sugarcane farmers in Kakamega and Bungoma Counties. The study variables were measured using both the ordinal scale and summated scale (likert-type scale).The questionnaire was pre-tested on pilot respondents who were not be part of the study respondents but knowledgeable in the study aspects in order to ensure their validity and relevance. Cronbach’s alpha coefficient was used to measure the reliability of the scale. The study focused on farmers of two counties: Bungoma and Kakamega. The regression results reveal statistically significant positive linear relationship between return on investment of debt financing and financial portfolio diversification (β = 0.789, p-value = 0.002). At the individual level, all the indicators of return on investment of debt financing had positive and significant effect on financial portfolio diversification as follows: Profits from Debt financing had positively influenced on financial portfolio diversification (β = 0.789 and p-value = 0.002) while Security flexibility of debt financing also positively affected financial portfolio diversification (β = 0.117, p-value = 0.003). The results also showed that financial return on investment of debt financing had moderately high explanatory power on financial portfolio diversification among commercial sugarcane farmers in Kenya in that it accounted for 62.3 percent of its variability therefore commercial sugarcane farmers in Kenya need to take into account financial return on investment of debt financing measures such as profits from farm outputs are sufficient enough to support my individual needs even as they diversify their portfolios

Accelerated Dirichlet-Robin Alternating Algorithm for Solving the Cauchy Problem for an Elliptic Equation using Krylov Subspaces

In this thesis, we study the Cauchy problem for an elliptic equation. We use Dirichlet-Robin iterations for solving the Cauchy problem. This allows us to include in our consideration elliptic equations with variable coefficient as well as Helmholtz type equations. The algorithm consists of solving mixed boundary value problems, which include the Dirichlet and Robin boundary conditions. Convergence is achieved by choice of parameters in the Robin conditions. We have also reformulated the Cauchy problem for the Helmholtz equation as an operator equation. We investigate the conditions under which this operator equation is well-defined. Furthermore, we have also discussed possible extensions to the case where the Helmholtz operator is replaced by non-symmetric differential operators by using similar operator equations and model problems which are used for symmetric differential operators. We have observed that the Dirichlet - Robin iterations are equivalent to the classical Landweber iterations. Having formulated the problem in terms of an operator equation is an advantage since it lets us to implement more sophisticated iterative methods based on Krylov subspaces. In particular, we consider the Conjugate gradient method (CG) and the Generalized minimal residual method (GMRES). The numerical results shows that all the methods work well.Funding agencies: ISP and the Eastern African UniversitiesMathematics Programme (EAUMP)</p

Regularization methods for solving Cauchy problems for elliptic and degenerate elliptic equations

In this thesis, we study Cauchy problems for the elliptic and degenerate elliptic equations. These problems are ill-posed. We split the boundary of the domain into two parts. On one of them, say Γ0, we have available Cauchy data and on remaining part Γ1 we introduce unknown Robin data. To construct the operator equation which replaces our Cauchy problem we use two boundary value problems (BVP). The first one is the mixed BVP with Robin condition on Γ1 and with Dirichlet condition on Γ0 and the second BVP with Dirichlet Data on Γ1 and with Robin data on Γ0. The well–posedness of these problems is achieved by an appropriate choice of parameters in Robin boundary conditions. The first Dirichlet–Robin BVP is used to construct the operator equation replacing the Cauchy problem and the second Robin–Dirichlet problem for adjoint operator. Using these problems we can apply various regularization methods for stable reconstruction of the solution. In Paper I, the Cauchy problem for the elliptic equation with variable coefficients, which includes Helmholtz type equations, is analyzed. A proof showing that the Dirichlet–Robin alternating algorithm is convergent is given, provided that the parameters in the Robin conditions are chosen appropriately. Numerical experiments that shows the behaviour of the algorithm are given. In particular, we show how the speed of convergence depends on the choice of Robin parameters.  In Paper II, the Cauchy problem for the Helmholtz equation, for moderate wave numbers k2, is considered. The Cauchy problem is reformulated as an operator equation and iterative method based on Krylov subspaces are implemented. The aim is to achieve faster convergence in comparison to the Alternating algorithm from the previous paper. Methods such as the Landweber iteration, the Conjugate gradient method and the generalized minimal residual method are considered. We also discuss how the algorithms can be adapted to also cover the case of non–symmetric differential operators.  In Paper III, we look at a steady state heat conduction problem in a thin plate. The plate connects two cylindrical containers and fix their relative positions. A two dimensional mathematical model of heat conduction in the plate is derived. Since the plate has sharp edges on the sides we obtained a degenerate elliptic equation. We seek to find the temperature on the interior cylinder by using data on the exterior cylinder. We reformulate the Cauchy problem as an operator equation, with a compact operator. The operator equation is solved using the Landweber method and the convergence is investigated.  In Paper IV, the Cauchy problem for a more general degenerate elliptic equation is considered. We stabilize the computations using Tikhonov regularization. The normal equation, in the Tikhonov algorithm, is solved using the Conjugate gradient method. The regularization parameter is picked using either the L–curve or the Discrepancy principle.  In all papers, numerical examples are given where we solve the various boundary value problems using a finite difference scheme. The results show that the suggested methods work quite well. I denna avhandling studerar vi Cauchy-problem för elliptiska och degenererade elliptiska ekvationer. Dessa problem är illa ställda. Vi delar upp randen till området i två delar. På en av dem, säg Γ0, har vi Cauchy–data tillgängligt, och på den återstående delen, Γ1 introducerar vi okända Robin-villkor. För att konstruera operatorekvationen som ersätter vårt Cauchy-problem använder vi två randvärdesproblem (BVP). Det första problemet är ett BVP med Robin–villkor på Γ1 och Dirichlet–villkor på Γ0. Det andra problemet är ett BVP med Dirichlet–data på Γ1 och med Robin–data på Γ0. Dessa problem är välställda om parametrar i Robinvillkoren väljs lämpligt. Det första Dirichlet–Robin problemet används för att konstruera operatorekvationen som ersätter Cauchy problemet, och det andra Robin–Dirichlet-problemet används för att definiera den adjungerande operatorn. Vi kan sedan tillämpa olika regulariseringsmetoder och återskapa lösningen till problemet på ett stabilt sätt. I Artikel I analyseras Cauchy-problemet för den elliptiska ekvationen med variabla koefficienter, vilket inkluderar ekvationer av Helmholtz-typ. Ett bevis som visar att den Dirichlet–Robin alternerande algoritmen är konvergent ges, förutsatt att parametrarna i Robin–villkoren väljs på lämpligt sätt. Numeriska experiment som illustrerar algoritmens beteende ges. I synnerhet visar vi hur konvergen-shastigheten beror på valet av Robin-parametrar. I Artikel II behandlas Cauchy–problemet för Helmholtz ekvation, för medelstora vågtal k2. Cauchy–problemet omformuleras som en operatorekvation och iterativa metoder, baserade på Krylov rum, implementeras. Syftet är att uppnå snabbare konvergens jämfört med den ursprungliga alternerande algoritmen som studerades i den föregående artikeln. Vi diskuterar också hur algoritmerna kan anpassas till fallet med icke-symmetriska differentialoperatorer. I Artikel III tittar vi på ett stationärt värmeledningsproblem i en tunn platta. Plattan sammanbinder två cylindriska behållare och fixerar deras relativa position. En tvådimensionell matematisk modell av värmeledning i plattan härleds. Eftersom plattan har vassa kanter på sidorna får vi en degenererad elliptisk ekvation. Vi försöker hitta temperaturen på den inre cylindern genom att använda data på den yttre cylindern. Vi omformulerar Cauchy–problemet som en operatorekvation, med en kompakt operator. Operatorekvationen löses med Landwebers metod och konvergensen undersöks. I Artikel IV behandlas Cauchy problemet för en mer allmän degenererad elliptisk ekvation. Vi stabiliserar beräkningarna med hjälp av Tikhonov–regularisering, där normal ekvationen löses med Konjugerade gradientmetoden. Reguleringsparametern väljs med antingen L–kurva eller Diskrepansprincipen. I alla artiklar ges numeriska exempel där vi löser de olika randvärdesproblemen med hjälp av finita differenser. Resultaten visar att de föreslagna metoderna fungerar ganska bra.

Solving stationary inverse heat conduction in a thin plate

We consider a steady state heat conduction problem in a thin plate. In the application, it is used to connect two cylindrical containers and fix their relative positions. At the same time it serves to measure the temperature on the inner cylinder. We derive a two dimensional mathematical model, and use it to approximate the heat conduction in the thin plate. Since the plate has sharp edges on the sides the resulting problem is described by a degenerate elliptic equation. To find the temperature in the interior part from the exterior measurements, we formulate the problem as a Cauchy problem for stationary heat equation. We also reformulate the Cauchy problem as an operator equation, with a compact operator, and apply the Landweber iteration method to solve the equation. The case of the degenerate elliptic equation has not been previously studied in this context. For numerical computation, we consider the case where noisy data is present and analyse the convergence

Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations

The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers k2, in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of k2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters