iosr-Jm   Volume-17 ~ Issue-5 ~ Sep. – Oct. 2021

Abstract:Background: Assignment problem is of great importance in mathematics and is also discuss in real physical world. In this paper we attempt to bring in a new effective method for solving assignment problem with algorithm and solution steps. We experiment a numerical example by using this method and enumerate by existing two methods. Moreover we assimilate the optimal solutions among this new method and two existing methods. The new proposed method is a systematic process, easy to apply for solving assignment problem. Result: The optimum solution of proposed method is same as the optimum solutions of existing method which is 41. Conclusion: New proposed method is different from two existing methods and is also effective for solving assignment problem.

Keywords: Assignment problem, Hungarian assignment method (HA-method), Matrix one's assignment method (MOA-method), Proposed method, Optimization

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Abstract: In this study we develop a mathematical model which describes the dynamics of prey- predator interaction with scavenger. We develop the model based on Holling type II functional response. We solved the equilibrium points and their existence. The positivity and of the solution of the model are also determined. Conditions for local and global stability analysis are studied both analytically and numerically. The study also addresses the effect of extinction of a population and mechanism that three species coexist. As a result the mechanism that three species become coexist if there is large number of prey population compute with small number of predator and average number of scavenger population. The scavenger species also has a great role in stabilizing as well as for coexistence of three species. Numerical simulations are carried out to illustrate the analytical findings. Finally the biological implication of analytical and numerical are discussed critically

Keywords: Prey-Predator, Scavenger, Lyapunov function, Local stability, Global stability

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[5]. K. Fujii. Complexity-stability relationship of two-prey{one-predator species system model: local and global stability. J. Theor. Biol (2005). (2004).

Abstract: The aim of this paper is to give and discuss stronger form of nano continuity called nano contra continuity using nano g.....

Keywords: Nano topology , Nano g**......

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[4]. M. Lellis Thivagar and Carnel Richard, "Weak forms of nano continuity", IISTE, 3(2013) No 7.
[5]. M. Lellis Thivagar and V. Sutha Devi, "On multigranular nano topology", South East Asian Bulletin of Mathematics, Springer – Verlag (2015).
[6]. M. Lellis Thivagar and V. Sutha Devi, "Computing Technique for Recruitment process via Nano Topology", Sohag J. Math 3(2016) Nol, 39 - 45..

Abstract: The Adomian decomposition method (ADM) is one of the powerful methods used to solve nonlinear differential equations which includes application to MHD boundary layer flow over a flat plate. In this study, we have shown the ability of the method to solve the governing equations of the MHD boundary layer flow problem. The effects of physical parameters such as magnetic field and Prandtl number embedded in the flow are presented and discussed. The results obtained are compared with existing work.

Keywords: Adomian decomposition method (ADM), magnetohydrodynamics, boundary layer

[1]. Ali, A. H. & Al-Saif, A. S. J. (2008)"Adomian Decomposition Method for Solving Models of Nonlinear Ordinary Differential Equations" Barash Journal of Science (A), 26 (1):1-11
[2]. Agom, E. U. &Badmus, A. M. (2015). "Application of Adomian Decomposition Method in Solving Second Order Nonlinear Ordinary Differential Equations" International Journal of Engineering Science Invention, 4 (11):60-65
[3]. Alhaddad, S. M. (2017). "Adomian Decomposition Method for Solving the Nonlinear Heat Equation" Int. Journal of Engineering Research and Application, 7 (7):97-100
[4]. Bhattacharyya, K. &Layek, G. C. (2012). "Similarity Solution of MHD Boundary Layer Flow with Diffusion and Chemical Reaction over a Porous Flat Plate with Suction/Blowing"Meccanica, 47:1043-1048
[5]. Chaudhary, S. & Kumar, P. (2015). "Unsteady MHD Boundary Layer Flow Near the Stagnation Point Towards a Shrinking Surface" Journal of Applied Mathematics and Physics, (3): 921-930.

Abstract: Malaria and Typhoid fever co-infection is the most endemic disease and a major public health problem in many tropical developing countries. Both diseases share similar transmission factor and often have the similar symptom. Because of the high prevalence of malaria and typhoid fever in these developing countries, co-infections are common. In addition to true co-infection of malaria and typhoid fever, the major challenges on managing controlling these diseases are false diagnoses due to similar signs and symptoms and false positive results in testing methods. In this study, we have formulated a mathematical model based on a system of non-linear first order ordinary differential equations to study the dynamics of the co-infection dynamics of plasmodium falciparum and typhoid.....

Keywords: Typhoid Fever, Malaria, Plasmodium Falciparum, Co-Infection, Reproduction Number, Sensitivity Analysis.

[1]. Bakary, T., Boureima, S. and Sado, T., 2018. A mathematical model of malaria transmission in a periodic environment. Journal of biological dynamics, 12(1), pp.400-432.
[2]. Djidjou-Demasse, R., Abiodun, G.J., Adeola, A.M. and Botai, J., 2018. A malaria transmission model with seasonal mosquito life-history traits. bioRxiv, p.377184.
[3]. Igwe M, Lynn M, Attahiru A, Seth GL, Maryam G, Florence S and Abdullfattah NS (2017).Prevalence of Malaria and Typhoid Co-Infections among Patients who Attended State Specialist Hospital Gombe from May to August 2015 for Malaria and Widal Tests. Greener Journal of Epidemiology and Public Health, 5(5): 037-043.
[4]. Kargbo, M.S., Massaquoi, L.D., Samura, S.K., Meng, X. and Zou, F., 2014. The relative prevalence of typhoid and malaria in febrile patients in Freetown, Sierra Leone. Open Journal of preventive medicine, 4(05), p.338.
[5]. Kgosimore, M.O.A.T.L.H.O.D.I. and Kelatlhegile, G.R., 2016. Mathematical analysis of typhoid infection with treatment. J. Math. Sci.Adv. Appl, 40, pp.75-91..

Abstract: The landau's problems could be addressed quickly and easily using a prime derivation formula as well as other new discoveries in mathematics which we shall know through the body of this article for the advancement of mathematics. These problems are related through these new mathematical concepts which we shall use to attack these problems.

Keywords: Goldbach's conjecture, Legendre's conjecture, Twin-prime conjecture, Near-square primes, Tor primes, Henry-Euchere primes.

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