iosr-Jm   Volume-6 ~ Issue-4

Abstract: The aim of this paper is to introduce Lexisearch the structure of the search algorithm does not require huge dynamic memory during execution. Mathematical programming is concerned with finding optimal solutions rather than obtaining good solutions. The Lexisearch derives its name from lexicography .This approach has been used to solve various combinatorial problems efficiently , The Assignment problem, The Travelling Salesman Problem , The job scheduling problem etc. In all these problems the lexicographic search was found to be more efficient than the Branch bound algorithms. This algorithm is deterministic and is always guaranteed to find an optimal solution.

Keywords: Introduction, Combinatorial problem , The Travelling Salesman problem, Lexisearch Method, The Lexisearch Approach, Algorithm LEXIG TSP, A Lexisearch Method Illustration of Travelling Salesman Problem, Conclusion.

[1]. M. Ramesh. "A lexisearch approach to some combinatorial programming problems", University of Hyderabad, India, 1997.
[2]. S.N.N. Pandit. "Some quantitative combinatorial search problems", Indian Institute of Technology, Kharagpur, India, 1963.
[3]. Srinivasan V. & G.L. Thompson (1973). An Algorithm for Assigning Uses to Sources in a Special Class of Transportation Problems, Op. Res., Vol. 21, No.1.

Abstract: In this paper, an implicit one-step method for numerical solution of second order Initial Value Problems of Ordinary Differential Equations has been developed by collocation and interpolation technique. The one-step method was developed using Chebyshev polynomial as basis function and, the method was augmented by the introduction of offstep points in order to bring about zero stability and upgrade the order of consistency of the new method. An advantage of the derived continuous scheme is that it can produce several outputs of solution at the off-grid points without requiring additional interpolation. Numerical examples are presented to portray the applicability and the efficiency of the method.

Keywords: Interpolation, Chebyshev polynomial, Collocation,continuous scheme.

[1] Aladeselu, V.A., Improved family of block method for special second orderinitial value problems (I.V.Ps). Journal of the Nigerian Association ofMathematical Physics, 11, 2007,153-158.

[2] Lambert, J.D., Numerical Methods for Ordinary Differential Systems(John Wiley, New York, 1991).

[3] Kayode S. J., An Improved Numerov method for Direct Solution of GeneralSecond Order Initial Value Problems of Ordinary Equations, National MathsCentre proceedings 2005.

[4] Adesanya, A.O., Anake T.A. and Oghonyon, G.J., Continuous implicit method for the solution of general second order ordinary differential equations. J. Nig. Assoc. of Math. Phys. 15, 2009, 71-78.

[5] Yahaya, Y. A. and Badmus, A. M., A Class of Collocation Methods for General Second Order Ordinary Differential Equations. African Journal ofMathematics and Computer Science research vol. 2(4), 2009, 069-072.

[6] Awoyemi, D.O., A class of Continuous Methods for general second orderinitial value problems in ordinary differential equation. International Journal of Computational Mathematics, 72, 1999, 29-37.

[7] Lambert, J.D., Computational Methods in Ordinary Differential Equations. John Wiley, New York, 1973.

[8] Jator, S.N., A Sixth Order Linear Multistep Method for the Direct Solutionof y'' = f(x, y, y'). International Journal of Pure and Applied Mathematics,40(4), 2007, 457-472.

Abstract: In this paper, we introduce the concept of N-closed maps and we obtain the basic properties and their relationships with other forms of N-closed maps in supra topological spaces.

Keywords: supra N-closed map, almost supra N-closed map, strongly supra N-closed map.

[1] R.Devi, S.Sampathkumar and M.Caldas, " On supra α open sets and sα-continuous maps, General Mathematics",
16(2)(2008),77-84.
[2] P.Krishna, Dr.J.Antony Rex Rodrigo, "On R-Closed Maps and R-Homeomorphisms in Topological Spaces", IOSR Journal
of Mathematics, 4(1)(2012),13-19.
[3] N.Levine, "Semi-open sets and Semi-continuity in topological spaces", Amer.Math.,12(1991),5-13.
[4] A.S.Mashhour, A.A.Allam, F.S.Mahmoud and F.H.Khedr, " On supra topological spaces", Indian J.Pure and
Appl.Math.,14(A)(1983),502-510.
[5] T.Noiri and O.R.Sayed, " On Ω closed sets and Ωs closed sets in topological spaces", Acta Math,4(2005),307-318.
[6] M.Trinita Pricilla and I.Arockiarani, "Some Stronger Forms of gb-continuous Functions", IOSR Journal of Engineering, 1(2),
111-117.
[7] L.Vidyarani and M.Vigneshwaran, "On Supra N-closed and sN-closed sets in Supra topological Spaces",
Internatinal Journal of Mathematical Archieve, 4(2),2013,255-259.