iosr-Jm   Volume-14 ~ Issue-5 ~ Sep-Oct 2018

Abstract: There are many methods for solving a nonlinear algebraic equation. Here a recurrence iteration for-mula for two-roots finding is derived based on the quadratic expansion of Taylor series. The general formula of quadratic equation is obtained using the derived formula. A family of iteration functions is derived from the derived formula. This family includes the Newton,Patrik, Halley, and Schroder'smethods.All methods of the family are cubically convergent for a simple root(except Newton's which is quadratically convergent).A simple general formula is derived and proved to be one of the familyof Halley-like method..

Key Words: Simple roots, Nonlinear equations, Halley method, Taylor expansion

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[5]. Thoo, J. B. "Some derivatives of Newton's method." Problems, Resources, and Issues in Mathematics Undergraduate Studies 12.2 (2002): 165-180..

Abstract: In this study, certain independence and domination properties of generalized Fibonacci graphs are considered. Domination, upper domination, total domination, upper total domination, independent domination and connected domination numbers of generalized Fibonacci graphs are calculated. Several illustrative examples are given.

Keywords: Heston partial differential equation, Heston stochastic volatility model, Elzaki transform method, reckless interest rate.

[1]. M. Korenblit and V. E. Levit, Mincuts in generalized Fibonacci graphs of degree 3, Journal of Computational Methods in Sciences and Engineering, 11(5,6), 2011, 271–280.
[2]. M. Korenblit and V. E. Levit, The 𝑠𝑡-connectedness problem for a Fibonacci graph, WSEAS Transactions on Mathematics 1(2), 2002, 89–93.
[3]. H. Akyar and E. Akyar, Certain properties of generalized Fibonacci graphs, Suleyman Demirel University Journal of Natural and Applied Sciences, 22(2), 2018, 661–666.
[4]. H. Akyar, On the Cartesian product of generalized Fibonacci graphs, International Journal of Mathematics and its Applications, 6(2-A), 2018, 63–70.
[5]. S. El-Basil, Theory and computational applications of Fibonacci graphs, Journal of Mathematical Chemistry, 2(1), 1988, 1–29..

Abstract: In this paper, the mathematical and stability analyses of the SIR model of malaria with the inclusion of infected immigrants are analyzed. The model consists of SIR compartments for the human population and SI compartments for the mosquito population. Susceptible humans become infected if they are bitten by infected mosquitoes and then they move from susceptible class to the infected class. In the similar fashion humans from infected class will go to recovered class after getting recovered from the disease. A susceptible mosquito becomes infected after biting an infected person and remains infected till death. The reproduction number 𝑅0 of the model is calculated using the next generation matrix method. Local asymptotical stabilities of the steady states are discussed using the.........

Keywords: Infected immigrants, Reproduction number, Steady states, Local stability, Lyapunov function.

[1]. Gbenga J. Abiodun, P. Witbooi and Kazeem O. Okosun. Modelling the impact of climatic variables on malaria transmission. Hacettepe Journal of Mathematics and Statistics. Volume 47 (2) (2018), 219 – 235.
[2]. Bakary Traor´e et al. A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality. Journal of Applied Mathematics. Volume 2017, Article ID 6754097,https://doi.org/10.1155/2017/6754097, 1-15.
[3]. R. Ross. The prevention of malaria, London, John Murray, 1911.
[4]. A. George Maria Selvam, A. Jenifer Priya: Analysis of a Discrete SEIR Epidemic Model. International Journal of Emerging Technologies in Computational and Applied Science, 12(1-5), (2015) Pp. 73-76.
[5]. Abid Ali Lashari, Shaban Aly, Khalid Hattaf, Gul Zaman, Hyo Jung, and Xue-Zhi Li. Presentation of Malaria Epidemics Using Multiple Optimal Controls. Journal of Applied Mathematics. Volume 2012, Article ID 946504, 1-17 .doi:10.1155/2012/946504...

Abstract: This paper studies about the dynamics of three population species interactions in biological ecology. Here, an interaction among two mutualistic preys and one predator populations has been considered. The population interaction areas are classified into two: free area and refuge area. In free area only the second prey and predator population species exist and interact while in a refuge area only the first prey population species exists. In the refuge area the predator population species cannot enter and attack the prey species. However, in the refuge area the two preys can interact and help each other. Additionally, in this model proportional harvesting function and functional responses are considered among these population interactions. Based on the unique and positive equilibrium points, local and global stability can be determined analytically and numerically. Simulation results supporting the analytical part are considered.

Keywords: Mutualism, Functional response, Local stability, Global stability, Harvesting function, Boundedness and Positivity.

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