iosr-Jm   Volume-16 ~ Issue-6 ~ Nov. – Dec. 2020

Abstract: In this work we derived and analyzed the convergence and consistency of an order eight rational integrator wherein our numerator and denominator is 4 (𝑖.𝑒 𝑚=𝑛=4) for the solution of problems in ordinary differential equations. A demonstration of the implementation of our integrator was also carried out; the result shows that our integrator is stable computationally. The integrator was observed to be A-stable, consistence and hence convergence.

Keywords: Convergence, Consistency, Gaussian Elimination, Simultaneous Linear Algebra.

[1]. Aashikpelokhai U.S.U (1991): A Class of Non Linear One Step Rational Integrator, Ph.D thesis, university of Benin, Benin City, Nigeria.
[2]. Afuwape, A.U Adesina O.A and Ebiendele E.P (2007): Periodicity and Stability results of a certain third order Non-linear Differential Equations 23, 147-15 www.emisa.de/journals.
[3]. Ebiendele, E.P (2010): On the Boundedness and Stability of Solutions of Certain Third Order Non-Linear Differential Equations Archives of Applied Science Research, 2(4), 329-337.
[4]. Ebiendele, E.P (2011): On the Stability Results for Solutions of Some Fifth Order Non-Linear Differential Equations Advances in Applied Science Research 2(5), 323-328.
[5]. Ebiendele, E.P (2013): On the Asymptotically Stability with respect to Probability Via Stochastic Matrix Valued Liapunov System Asian Journal of Fuzzy and Applied Mathematics Vol. 1(4).

Abstract: In this article,we define the modified form of Bernstein type operators based on Beta function developed by Dhawal.J. Bhatt et al. recently.We have proved these operators uniform convergence on the basis of Korovkin's theorem and rate of convergence through modulus of continuity and asymptotic behaviour is shown as Vorovnoskaja type theorem.

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Abstract: The estimation of an integral is integration. Math integrals are used to classify several useful numbers, such as regions, numbers, displacement etc. When we talk about integrals, they are commonly connected to definite integrals. For anti-derivatives, infinite integrals are used. Integration is one of the two key calculus topics in mathematics, apart from differentiation (which measures the rate of change of any function with regard to its variables, and electricity can be produced by motion by magnetism. He found that a tiny electric current flows through the wire when a magnet was pushed within a coil of copper wire. Here we discuss how integration helps in calculus and find electric field of rod along equatorial point.

Keywords: Differentiation, Integration, Vector, Scalar, Electric Field, Charge, Limit

[1]. J.Tuminaro and E. Redish, Understanding students' poor performance on mathematical problem solving in physics, in Proceedings of the Physics Education Research Conference, 2004 (unpublished).
[2]. L. Cui, A. Bennett, P. Fletcher, and N. S. Rebello, Transfer of learning from college calculus to physics courses, in Proceedings of the Annual Meeting of the National Association for Research in Science Teaching, 2006 (unpublished).
[3]. L. C. McDermott, Oersted Medal Lecture 2001: Physics education research: The key to student learning, Am. J. Phys. 69, 1127 (2001).
[4]. A. Orton, Students' understanding of integration, Educ. Stud. Math. 14, 1 (1983).
[5]. F. R. Yeatts and J. R. Hundhausen, Calculus and physics: Challenges at the interface, Am. J. Phys. 60, 716 (1992)..

Abstract: This study derives the connection between the functional power series and the inversion formula, both given in series form. The link is established by differentiation of the inversion formula showing an expression of a functional power series for the reciprocal of the derivative in terms of the function itself. 1
0.1 Mathematical Classification.

[1]. Stenlund, H.: Inversion Formula, arXiv:1008.0183v3 [math.GM] July 27 (2010)
[2]. Stenlund, H.: Functional Power Series, arXiv:1204.5992v1 [math.GM] April 24 (2012)

Abstract: We present an adaptation of the classical algorithm of the decomposition of Bender to the b-complementary multisemigroup dual problem. Despite this decomposition has been shown in literature as a good tool for dealing with high dimensional mixed-integer linear programming, that is not the case for the presented one in this paper, which is better to be solved by the simplex algorithm without partitioning. We present results from computer experiments to show that conclusion.

Keywords: Multisemigroup; Complementary; Duality; Benders Decomposition

[1]. Aráoz J. and Johnson E., "Polyhedra of Multivalued System Problems", Report No.82229-OR, Institut für Ökonometrie und Operations Research, Bonn, W. Germany (1982)
[2]. Aráoz J. and Johnson E.,"Morphic Liftings between of pairs of Integer Polyhedra", Research Report 89616OR, Int. Operations Research, Bonn 1989.
[3]. Benders, J. F., "Partitioning procedures for solving mixed variables programming problems", Numerische Mathematik, Set. 1962, 4(3): 238-252.
[4]. Madriz E., "Duality for a b-complementary multisemigroup master problem", Discrete Optimization Volume 22, Part B, November 2016, Pages 364-371
[5]. Rahmaniani R. Cranic T. G. and Rei W.,"The Benders Decomposition Algorithm: A Literature Review", CIRRELT -2016-30, June 2016, https://www.cirrelt.ca/DocumentsTravail/CIRRELT-2016-30.pdf

Abstract: This paper has mainly focused on the relation among semisimple ring, Baer ring and Von-Neumann regular ring where it has been showed that " R is a ring then R is semi simple artinian if and only if B(R) is
a Baer ring for all infinite set  [Theorem 3.1] and " R is semisimple if and only if R is Von Neumann regular. On the other hand Von Neumann regular tends to exchange ring but conversely is not possible .In fact
we have showed the chain with semi simple ring, Baer ring and Von Neumann regular ring. We have tried to connect the semi simple ring with the properties between Baer ring and Von Neumann regular ring in terms of
row and column finite matrix rings. Result: The main result of this paper is "Let R be a ring. Then the following conditions are equivalent
1. R is semisimple artinian 2. BR is a Baer ring 3. R is von Neumann regular.

Key Word: Semi simple ring, Baer ring, Von Neumann regular ring.

[1]. J. J. Simon Finitely generated projective modules over row and column finite matrix ´ rings, J. Algebra 208 Z. 1997, 165184.
[2]. V. Camillo, F. J. Costa-Cano, and J. J. Simon, Relating properties of a ring and its ring of row and column finite matrices, J. Algebra 244 (2001), no. 2, 435-449. MR1859035 (2002i:16039).
[3]. K. C. O'Meara, The exchange property for row and column-finite matrix rings, J. Algebra 268 (2003), no. 2, 744-749. MR2009331 (2004i:16040).
[4]. J. Haefner, A. Del Rio and J. J. Simon," Isomorphism of Row and Column Finite Matrix Rings, Proc. Amer. Math. Soc. V. 125. No. 6 (1997) 1651-1658.
[5]. Pace P. Nielsen, Row and column finite matrices, Proc. Amer. Math. Soc. V. 135. No. 9 (2007) 2689-2697.

Abstract: Gibonacci sequence is a generalization of Fibonacci and Lucas sequences. In this study, we define unrestricted gibonacci quaternions by picking arbitrary elements of gibonacci sequence for the ordered basis of quaternions. After obtaining Binet formula for unrestricted gibonacci quaternions, we give generalizations of the some well – known identities..

Key Word: Gibonacci sequence; Quaternions; Binet formula

[1]. Akyigit, M., Kosal, H.H. and Tosun, M. Fibonacci generalized quaternions. Advances in Applied Clifford Algebras. 2014: 24; 631-641.
[2]. Aydin, F.T. Bicomplex Fibonacci quaternions. Chaos, Solitons & Fractals. 2018: 106; 147 – 153.
[3]. Aydin, F.T. The k-Fibonacci dual quaternions. International Journal of Mathematical Analysis. 2018: 12(8); 363 – 373.
[4]. Flaut, C. and Shpakivskiy, V. On generalized Fibonacci quaternions and Fibonacci – Narayana quaternions. Advances in Applied Clifford Algebras. 2013: 23(3); 673 – 688.
[5]. Halici, S. On Fibonacci quaternions. Advanced Applied Clifford Algebras. 2012: 22(2); 321 – 327.

Abstract: By using Krasnoselskii's fixed point theorem in cones to study the existence of periodic solutions for a higher-dimensional of second order nonlinear functional differential equations of the form...

Keywords: Periodic solution; Delay differential equations; Fixed point theorem; Parameter

[1]. Y. Liu, W. Ge, Positive solutions Positive solutions for nonlinear Duffing equations with delay and variable coefficients, Tamsui Oxf. J.
Math. sci., 20 (2004) 235-255.
[2]. W. Han, J. Ren, Some results on second-order neutral functional differential equations with infinite distributed delay, Nonlinear Anal.,
(2008), 1-14.
[3]. Y. Wang, H. Lian, W. Ge, Periodic solutions for a second order nonlinear functional differential equation, Appl. Math. Lett., (2007)
110-115.
[4]. Y. Li, L. Zhu, Periodic solutions for a class of higher-dimensional state-dependent delay functional differential equations with
feedback control. Appl. Math. Comput., (2003) 783-795.
[5]. A. Wan, D. Jiang, Existence of Positive solutions Positive solutions functional differential equations, Kyushu J. Math., 56 (2002)
193-202

Abstract: In the given paper some linear discrete-time stochastic model intended for simulation the behavior of an analyzed production system functioning in an unstable external environment is proposed.In this model
destabilizing effects on the inventory and on the external supplies of the analyzed production system are presented explicitly.The average and the second order behaviors of the proposed model is analyzed.Some twodimensional
time-invariant production system is provided, as an example.The step-by-step adaptive approach for correction the planned standard behavior of the production system functioning in the unstable external
environment is proposed.This approach is based on the assumption that the estimates of the returned or nonconforming inventory and of unforeseen changes in the deliveries of the inventory are true.

Keywords:Production systems, planning, unstable environment, discrete-time, linear stochastic model,inventory control

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1997; 48 (2): 221–224.
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based on limited shelf space. Yugoslav Journal of Operations Research. 2010; 20 (1): 55–69.
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Probability. 2009; 19 (4): 1404–1458.
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