iosr-Jm   Volume-17 ~ Issue-1 ~ Jan. – Feb. 2021

Abstract: Vector identities are produced in non-customary way. The results are shown in different forms such as to stick on tips. The method adopted exhibits the new operators appearing with commutation brackets. Nabla with order of dot, cross and their combination appears to have new type of operators.

Keywords: vector identities, operator in commutation bracket, combination of dot, cross with nabla.

[1]. G Arfken, Mathematical Methods for Physicists AP, NY 2000
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[3]. R S Meghwal, Corresponding author, The idea of operators newly introduced*

Abstract: In a graph G = (V, E), a set S of vertices is said to be strong dominating set if for every v ∈ V − S, there exists a vertex u ∈ S such that uv∈E(G) and deg u >deg v. The subgraph induced by a strong dominating set is called strong dominating subgraph of G. The cardinality of a minimum strong dominating set is denoted by y3 set. For a given class D of connected graphs it is an interesting problem to characterize the class SD(D) of graphs G such that each connected induced subgraph of G contains a strong dominating subgraph belonging to D. In this paper we determine SD(D) where D = {P1, P2, P3}, D = {{Kn/n >1} ∪ P3} and D = {connected graphs on atmost four vertices}.

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Abstract: Management should be effective and efficient in resource for various activate to regularly meet the eventual objectives. Delivering goods the lowest cost has become such an environment amidst fire completion that minimizing transpiration cost has become a challenge for companies. This study sheds light on linear programming and spreadsheet applications that promote transportation at the least cost. In this study, we have only analyzed how we can minimize the minimum transportation cost of the polymer, which given additional benefit to the companies.

Keyword: Transportation cost, linear programming, balance sheet

[1]. Operation Research principles and practice by Don T. Phillips and James S. Solberg (WILEY STUDEN EDITION 2010)
[2]. Operation Research BY Er. Prem Kumar Gupta and Dr. D. S. Hira (S. Chand & Company Pvt. Ltd. 2016)
[3]. Operation Research by Dr. H. K. Pathak (Siksha Sahitya Prakashan, Meerut 2013)
[4]. Operation Research by S. D. Sharma (Kedar nath ,Ram nath publication2015)
[5]. Operation Research by J. K. Sharma (Gautam Budha Technical University and Macmillan Publications India 2012)

Abstract: A non-polynomial interpolating function considered by Ayinde and Ibijola (2015) was modified and utilized to develop an improved numerical scheme for solving first order initial value problems in ordinary differential equations. The scheme was implemented in MATLAB and tested on four problems; all our numerical results show better approximations of the analytical solutions.

Key words: Non-polynomial, Single-step and Multistep.

[1]. Kama, P. and Ibijola, E. A. (2000). On a New-Step Method for Numerical Integration of Ordinary Differential Equations. International Journal of Computer Mathematics. 78(3-4)
[2]. Ibijola, E. A. (1997). New Schemes for Numerical Integration of Special Initial Value Problems in Ordinary Differential Equations. Ph. D. Thesis, University of Benin, Nigeria.
[3]. Ogunrinde, R. B., Fadugba, S. E. and Okunlola, J. T. (2012). On Some Numerical Methods for Solving Initial Value Problems in ODEs. IORS Journal of Mathematics(IORSJM). 1(3): 25-31.
[4]. Ogunderi, R. B. and Olaosebikan, T. E. (2016). Development of a Numerical Scheme. American Journal of Computational Mathematics, 6:49-54.
[5]. Ayinde, S. O. and Ibijola, E. A. (2015). A New Numerical Method for Solving First Order Differential Equations. American Journal of Applied Mathematics and Statistics, 3(4):156-160.
[6]. Kamruzzaman, M. and Hassan, M. M. (2018). A New Numerical Approach for Solving Initial Value Problems of Ordinary Differential Equations. Annals of Pure and Applied Mathematics, 17(2):157-162.

Abstract: Analytical model of degrading systems based on Finite Markov Chains is defined. This model is analyzed within the finite time horizon for recoverable, partially recoverable, and non-recoverable degrading systems. The set of critical states is identified. This set forms some base for the implementation of a bounded probabilistic analysis of the investigated degrading system.

Key Word: degrading systems, finite time horizon, Finite Markov Chains, bounded probabilistic analysis.

[1]. R. Barlow, L. Hunter. Optimum preventive maintenance policies. Operations Research. 1960; 8 (1): 90-100.
[2]. T. Nakagawa. Advanced reliability models and maintenance policies. 2008; Springer-Verlag London Limited).
[3]. B. de Jonge, P. A. Scarf. A review on maintenance optimization. European Journal of Operational Research. 2020; 285 (3): 805- 824.
[4]. B. Dowdeswell, R. Sinha, S. G. MacDonell. Finding faults: A scoping study of fault diagnostics for Industrial Cyber-Physical Systems. Journal of Systems and Software. 2020; 168, Article 110638, https://doi.org/10.1016/j.jss.2020.110638
[5]. S. Nikam, R. Ingle. Survey of research challenges in Cyber Physical Systems. International Journal of Computer Science and Information Security. 2017; 15 (11): 192-199.

Abstract: The place of an asymptotic sequence in real life problems have not been properly understood by researchers and scholars.In this paper we exemplified the definition of asymptotic sequence to transcendental
functions.Numerical experiments simplifies the place of asymptotic sequence to the functions.

Key Words; Asymptotics, Sequences, and Transcendental functions.

[1]. Ali HasanNayfeh,Perturbation Methods,(1.42):[8-12],1973.
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[5]. Professor Amazigo, J C:M.s.c Note on AsymptoticMethod,University of Nigeria Nsukka.2015.

Abstract: In this paper, some topological properties, especially those that associated with compactness properties as in.....

Keywords: - closed set, Z – closed set, Lindelöf space, Extremely disconnected space, Paracompact space, hereditary disconnected

[1]. Hausdorff F. Mengenlehre, 3rd ed. Springer, Berlin, 1927.
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[3]. Ahmad Al – Omari and Takashi Noiri. "On z – compact spaces and some functions" BOI. Soc. Paran, Math, V. 36 (2018), 121 -130.
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[5]. Beshimou R.B. and Savarova D.T. "Topological properties of Hyperspaces" Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol 2: ISS. 1, Article 2. 2019..

Abstract: Dillip Kumar Dash and Nduka Wolu (2020) proved using the concept of Euler Phi Function that for all , divides the sum of all elements of , the set of all positive integers less than where the positive integers are relatively prime to . Our work gives the converse of this result as a direct implication of a generalised property of integers which we have also stated and proved. This further enables the conclusion that for any prime integer greater than , divides the sum of all integers less than if and only if is relatively prime to . A computerized illustration for generating values of coprime to test the result is also given..

Key Word: Prime, Co-Prime, Integers, Euler Totients Function, Relatively Prime, Mutually Prime

[1]. Bialostocki, A (1998). An Application of Elementary Group Theory to Central Solitaire, the College Mathematics Journal, May 1998: 208-212.
[2]. Dillip Kumar Dash ,Nduka Wonu (2020). An introduction of a novel group theorem to Abstract Algebra. International Journal of Scientific and Innovative Mathematical Research (IJSIMR), Volume 8, Issue 3, 2020, PP 1-2. www.arcjournals.org
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Abstract: Time and again, systems described by differential equations are so complex that purely analytical solutions of the equations are not very easy to come by. Therefore, in this paper, we develop a collocation method using Laguerre polynomials as basis function to approximate two-point second-order linear boundary value problems with Dirichlet and Neumann boundary conditions in ordinary differential equations. The collocation method developed is implemented in MAPLE 17 in conjunction with MATLAB R2014a through six illustrative examples. Absolute errors are equally estimated. From the result, we observed that the accuracy of the collocation method constructed increases with the use of more terms of the Laguerre polynomials as basis function. Based on the careful observations from the numerical experiment, it may be concluded here that the collocation method developed.......

Key words: Linear Boundary Value Problems, Collocation, Laguerre polynomials.

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[2]. Bongsoo, J. (2008). Two-point Boundary Value Problems by the extended Adomian Decomposition Method. Journal of Computational and Applied Mathematics,219(1), 253-262.
[3]. Caglar, H., Caglar, N.,&Elfaituri, K. (2006). B-Spline Interpolation Compared with Finite Difference, Finite Element and Finite Volume Methods Applied to Boundary Value Problems. Applied Mathematics and Computation,175(1), 72-79.
[4]. Dolapci, I. T. (2004). Chebyshev Collocation Method for Solving Linear Differential Equations. Mathematics and Computational Applications, 9(1), 107-115.
[5]. Emad, H. A., Abdelhalim, E.,& Randolph, R. (2012). Advances in the Adomian Decomposition Method for Solving Two-point Nonlinear Boundary Value Problems with Neumann Boundary Conditions. Computer and Mathematics with Applications, 63, 1056-1065.