iosr-Jm   Volume-16 ~ Issue-1 ~ Jan – Feb 2020

Abstract: Taxation and foreign borrowing are major sources of revenue in Kenyan economy. The government uses revenues from these sources to finance its project such as construction of roads and railways (SGR ) and provision of services such as National Youth Service (NYS) to the youths and payment of wages to its employees and creating enabled environment for businesses among others. However, increased tax rates and foreign debt may pose a negative impact on the economic development of a state if the revenues from these sources are not put into fiscal uses.This study examines the impact of taxation as well as foreign borrowing on economic growth in Kenya. The study used a time series data for the period (1995-2018) to analyse and evaluate the impact. The study employed a multiple linear regression model with foreign borrowing and taxation as the independent variables and Gross Domestic Product...........

[1]. Amoating and Amoaku-Adu. (1996)"Economic growth,export and external debt casuality:the case of African countries."
[2]. Adam Smith. (1776 The Wealth of Nations)
[3]. Attiya Waris. (2012). A historical analysis of the kenyan taxation system
[4]. Baum et al. (2013)."debt and growth: new evidence for euro area."
[5]. Calvo. (1998).Balancce of payment crisis in emerging markets:Large capital inflowand sovereign government.

Abstract: Finite difference method is one of several powerful numerical techniques for obtaining an approximate solution for partial differential equations. It has been provenas an efficient technique to solve initial and boundary value problems for linear and nonlinear partial differential equations for any dimension. Here we implement such numerical technique to obtain the numerical solution for the Helmholtz equation and the biharmonic equation with one spatial variable and time-independent. At first, we formulate the finite difference method to the Helmholtz equation as an eigenvalue problem subject to the Neumann boundary conditions. Then we formulate such numerical techniques to the biharmonicequation as an eigenvalue problemsubject to different combinations.....

Keywords: Finite Difference Method, Helmholtz Equation, Modified Helmholtz Equation, Biharmonic Equation, Mixed boundary conditions, Neumann boundary conditions.

[1]. E. Zauderer, Partial Differential Equations of Applied Mathematics,3rd ed., John Wiley and Sons, Inc., Canada, 2006.
[2]. M. Morse and H. Feshback, Methods of Theoretical Physics, part I, McGraw-Hill Co., Inc, Tokyo, 1953.
[3]. G.Evans, J.Blackledge and P. Yardley. Analytic Methods for Partial Differential Equations, Springer undergraduate mathematics series, Springer-Verlage, London, 1999.
[4]. A. Iserles. A first Course in the Numerical Analysis of Differential Equations.Cambridge University Press, 1996.
[5]. F. B. Hildebrand, Introduction to Numerical analysis, McGraw-Hill Co., New York, 1974.

Abstract: The linear and the quadratic transformationsof the hypergeometric function are proven very useful in making various transformations and carryingout the analytic continuation of hypergeometric function into any part of the complex z-plane cut along the real axis from the point z= +1 to the point z= +∞. Here we shall represent the associated Legendre functions (or spherical functions) of the first kindin terms of the hypergeometric function to gain their analytic continuation into any part of the complex z-plane. Furthermore, the hypergeometric representation enables us to develop the theory of spherical functions by implementing the general theory of the hypergeometric function. Obtaining the hypergeometric representation of such functions by means of linear and quadratic transformations is more general and less complicated than the Euler's integral representation which is restricted to certain constraints to the values of the parameters of the hypergeometric function that are essential to make use of the integral definition of the Beta function.

Key Words: Hypergeometric function,hypergeometric series, associated Legendre functions of the first kind,spherical functions, linear and quadratic transformationsof the hypergeometric function.

[1]. AbramowitzM andStegun A.Handbook of mathematical functions. (Ninth edition)New York: Dover Publications Inc.,1968.
[2]. Andrews GEAskey RRoy R.Special functions. Cambridge Univ. Press,1999.
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Abstract: The triangle group Δ (3,4,k).............

Keywords: Conjugacy classes, Linear-fractional transformations, Parameterization and Non-degenerate homomorphismr coding scheme

[1]. Anna Torstensson, Coset diagrams in the study of finitely presented groups with an application to quotients of the modular group, J. Commut. Algebra, 2, 4(2010), 501−514.
[2]. M. Ashiq, T. Imran, M.A. Zaighum, Actions of Δ(3,n,k) on projective line, Transactions of A. Razmadze Mathematical Institute, 172(2018), 1−6.
[3]. M. Ashiq, T. Imran, M.A. Zaighum, Defining relations of a group Γ=G3,4(2,Z) and its action on real quadratic field, Bulletin of Iranian Mathematical Society (BIMS), 43(6)(2017), 1811−1820.
[4]. M. Ashiq, Q. Mushtaq and T. Maqsood, Parameterization of actions of a subgroup of the modular group, Quasigroups and Related System, 20(2012), 21-28.
[5]. M. Ashiq and Q. Mushtaq, Coset diagrams for a homomorphic image of Δ(3,3,k),Acta Mathematica Scientia,28B(2)(2008),363-370.

Abstract: Background: Lassa fever disease is a fatal zoonotic hemorrhagic disease caused by Lassa virus and endemic in West African countries. The aim of this paper is the application of mathematical modeling and analyses in controlling the spread of this disease. Materials and Methods: In this paper, a mathematical model which represents the transmission and control processes of Lassa fever disease among human and vector hosts is developed. The model is developed as a coupled system of 7 ordinary differential equations using the compartmental disease modeling approach. Three control strategies are incorporated into the model and the model analyzed for the existence of a positively invariant region within which its solutions are uniformly bounded. The model equations are solved numerically using the MATLAB ode45 method and simulations.......

Keywords: Lassa Fever, Mathematical Model, Numerical Simulation, Sensitivity Analyses, Stability Analyses

[1]. Adewale, S., Olopade, I., Ajao, S., Adeniran, G., and Oyedemi, O. (2016). Mathematicalanalysis of lassa fever model with isolation. Asian Journal of Natural & Applied Sciences,5(3), pp 47-57.
[2]. Afolabi, A. and Sobowale, A. (2017). A mathematical model for the control of lassa fever. Transaction of the Nigerian association of mathematical physics, 5(September and November, 2017), pp 279-284.
[3]. Akinade, M. O., Afolabi, A. S., and Kimathi, M. E. (2019). Mathematical modeling and stability analyses of lassa fever disease with the introduction of the carrier compartment. Journal ofMathematical Theory and Modeling, 9(6), pp 45-62.
[4]. Akinpelu, F. O. and Akinwande, R. (2008). Mathematical model for lassa fever and sensitivity analysis. Journal of Scientifi and Engineering Research, 5(6), pp 1-9.
[5]. Bawa, M., Abdulrahman, S., Jimoh, O., and Adabara, N. (2013). Stability analysis of the Disease-free equilibrium state for lassa fever disease. Journal of Science, Technology, Mathematics and Education (JOSTMED), 9(2), pp 115-123.

Abstract: The 0/1 knapsack problem is an example of the combinatorial optimization problem which is to maximize the value of the objects in the knapsack without passing its capacity, with the aim of obtaining the best solution among other solutions. Knapsacks problems appear in practical-world decision-making processes in a wide variety of fields. There are various ways to solve the knapsack problem. In this work, dynamic programming and branch and bound were presented to solve the knapsack problem, along with the analysis of its efficiency, effectiveness, accuracy, and time execution. The data were analysed with the help of a programming language MATLAB and general purpose mixed integer programming solver CPLEX was used for the analysis. The dynamic programming suffers the best execution of time. The two methods dynamic programming and branch and bound has the same optimal solution in term of accuracy which means they are both effective for the selection of items without exceeding its capacity. In other word, our best solution values match the optimal values obtained by the CPLEX mixed integer solver, except the fact that the time required for the dynamic problem is faster than that of the CPLEX mixed integer solver

Keywords: Knapsack; CPLEX; Dynamic Programming; Optimization

[1]. Akçay, Y., Li, H., & Xu, S. H. (2007). Greedy algorithm for the general multidimensional knapsack problem. Annals of Operations Research, 150(1), 17-29.
[2]. Babaioff, M., Immorlica, N., Kempe, D., & Kleinberg, R. (2007). A knapsack secretary problem with applications. Approximation, randomization, and combinatorial optimization. Algorithms and techniques, 16-28.
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[5]. Da Silva, C. G., Clímaco, J., & Figueira, J. R. (2008). Core problems in bi-criteria {0, 1}-knapsack problems. Computers & Operations Research, 35(7), 2292-2306.

Abstract: Performance evaluation of lecturers at a university becomes very important because it is the basis for performance-based remuneration and rewards, as well as improving services to student satisfaction. Lecturers are required to be professional to be able to provide a good understanding and motivation to learn to students in accordance with their functions in higher education. Student motivation is influenced by several factors. The main factor that really affects is the lecturer, because in the teaching and learning process of students who are dealing directly with the lecturer. This, of course, greatly affects the level of student satisfaction with lecturer performance. So, this study tries to find the relationship between student satisfaction variables and lecturer performance. The purpose of this study is to examine and analyze pedagogical competence factors, professional competence......

Keywords: Student Satisfaction, Lecturer Performance, Competence

[1]. Savitri, Citra. 2016. "Analisis Kinerja Dosen Mengajar terhadap Kepuasan Mahasiswa Program Studi Manajemen Semester 2 Tahun Ajaran 2015-2016". Jurnal Manajemen & Bisnis Kreatif ISSN 2528-0597, Volume 1, Nomor 2.
[2]. Trisnaningsih, S. 2011. "Faktor – Faktor yang Mempengaruhi Kinerja Dosen Akuntansi". Jurnal Akuntansi & Auditing, Volume 8 Nomor 1, November.
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Abstract: In the present work a study of the dynamics of a drug in a human organism is analyzed the possibility if its elimination, for a patient that temporarily for the consumption as for the one that continues the use of the drug; the most commonly used drugs in Brazil are indicated, as well as their main effects. A model that simulates this kinetics is presented; two critical cases are dealt with, reducing the system to simpler forms; a qualitative study of the system of equations presented is made and conclusions are drawn regarding the future patient situation.

Key Words: Drug, model, organ, patient

[1]. Aguilar B, Libório A, Sánchez S, Ribeiro Z, Lacort M, Ferreira R., Ruiz A. I. "Mathematical Modeling of an Ingerable Drug"
IOSR Journal of Mathematics Volume 15, Issue 3 Ser. I (May – June 2019), PP 75-80.
[2]. Behrens, D. A., Caulkins, J. P., Tragler, G., Haunschmied, J. L., &Feichtinger, G. . A dynamic model of drug initiation:
implications for treatment and drug control. Mathematical Biosciences, 159 (1), 1-20. 1999.