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.

Abstract: The aim of this paper is to introduce a decompositions namely supra bT- locally closed sets and define supra bT-locally continuous functions. This paper also discussed some of their properties.

Keyword S-BTLC set, S-BTL- continuous,S-BTL- irresolute.

[1] D.Andrijevic",On b- open sets" , mat.Vesnik 48(1996), no.1-2,59-64.

[2] Arokiarani .I, Balachandran. K and Ganster .M, " Regular Generalized locallyclosed sets and RGL-continuous functions", Indian J.pure appl. Math., 28 (5): May(1997) 661-669.

[3] Bharathi. S, Bhuvaneswari.K,and Chandramathi.N, "Generalization of locally b- closed sets",International Journal of Applied Engineering Research,Volume 2,(2011) No 2.

[4] Bourbaki, "General Topology", Part I, Addison – Wesley(Reading,Mass) (1996).

[5] Devi.R., Sampathkumar S. & Caldas M.," On supra -open sets and S- continuous functions", General Mathematics, 16(2),(2008),77-84.

[6] Ganster M.& Reilly I.L.," Locally closed sets and LC continuous functions", International J.Math. and Math.Sci.,12,(1989)417-424.

[7] Krishnaveni.K and Vigneshwaran.M, "On bT-Closed sets in supra topological Spaces, On supra bT- closed sets in supra topological spaces", International journal of Mathematical Archive-4(2),2013,1-6.

[8] A.S.Mashhour, A.A.Allam, F.S.Mohamoud and F.H.Khedr,"On supra topological spaces", Indian J.Pure and Appl.Math.No.4, 14 (1983),502- 510.

[9] Ravi.O., Ramkumar. G & Kamaraj .M ,"On supra g-closed sets", International Journal of Advances in pure and Applied Mathematics, 1(2), [2010] 52-66.

[10] O.R. Sayed and Takashi Noiri," On b-open sets and supra b- Continuity on opological spaces", European Journal of Pure and applied Mathematics, 3(2)(2010), 295-302.

Abstract: This paper aims at identifying an effective and appropriate method of calculating the cost of transporting goods from several supply centers to several demand centers out of many available methods. Transportation algorithms of North-West corner method (NWCM), Least Cost Method (LCM), Vogel's Approximation Method (VAM) and Optimality Test were carried out to estimate the cost of transporting produced newspaper from production center to ware-houses using Statistical software called TORA. The results revealed that: NWCM = 36,689,050.00, LCM = 55,250,034.00, VAM = 29,097,700.00 and Optimal solution = 19,566,332.00. It was discovered that Vogel's Approximation method gives the transportation cost that closer to optimal solution. Also, the study revealed that a production center should be created at northern part of Nigeria to replace the dummy supply center used in the analysis, so as to make production capacity equal to requirement.

Key Words: algorithm, transportation, optimal solution, degeneracy, dummy.

[1]. Gass, SI (1990). On solving the transportation problem. Journal of Operational Research Society, 41(4), 291-297.
[2]. Lucey T. (1981). Quantitative Techniques, Ashford Colour Press (Fifth edition), Great Britain.
[3]. Moskowlt, H. (1979). Operation Research Techniques for Management, Macmillian Publication C. In. (second edition), New York, U.S.A.
[4]. Oseni B. A and Ayansola O .A (2011). Quantitative Analysis Made Easy, Highland Publishers), Nigeria.
[5]. Prof. G. Srinivasan (2009). Fundamentals of Operations Research (A YouTube Video Tutorial). Department of Management Studies, IIT Madras.
[6]. Richard Bronson et al. (1997) Theory and Problems of Operation Research, Publisher: McGraw-
[7]. Hill USA.
[8]. Sharma J.K. (2009) Operation Research (Theory and Application) 4th Edition, Macmillan
[9]. Publisher, Indian
[10]. Sudhakar V. J and Arunsankar .N (2012). A new approach for finding an Optimal Solution for Transportation Problem (Euro Journals Publishing) India pp. 254 – 257

Abstract: In the present paper a volume flexible production inventory model is developed for deteriorating items with time dependent demand rate. The demand rate is taken as cubic function of time and production rate is decision variable. Production cost becomes a function of production rate. Unit production cost is depending upon material cost, Labor cost and tool or die cost. The deteriorating of unit in an inventory system is taken to weibull distribution. Shortage with partially backlogged are allowed a very natural phenomenon in inventory model.

[1]. Abad, P.L. (1996): Optimal pricing and lot sizing under conditions of perishabilityand partial backlogging. Management Science, 42(8), 1093-1104.
[2]. Aggarwal, S.P. and Jain, V. (2001): Optimal inventory management for exponentially increasing demand with deterioration. International Journal of Management and Systems, 17(1), 1-10.
[3]. Balkhi, Z.T. and Benkherouf, L. (1996): A production lot size inventory model for deteriorating items and arbitrary production and demand rate. European Journal of Operational Research, 92, 302-309.
[4]. Chang, H.J. and Dye, C.Y. (1999): An EOQ model for deteriorating items with time varying demand and partial backlogging. Journal of the Operational Research Society, 50(11), 1176-1182.
[5]. Chung, K.T. (2000): The inventory replenishment policy for deteriorating items under permissible delay in payments. Opsearch, 37(4), 267-281.
[6]. Chu, P. and Chung, K.J. (2004): The sensitivity of the inventory model with partial backorders. European Journal of Operational Research, 152, 289-295.
[7]. Gallego,G(1993):Reduced Production rate in the economic lot scheduling problem, International Journal of Production Research,316,1035-1046.
[8]. Giri, B.C. and Chaudhuri, K.S. (1998): Deterministic models of perishable inventory with stock dependent demand rate and non-linear holding cost. European Journal of Operational Research, 105, 467-474.
[9]. Giri, B.C. and Yun, W.Y. (2005): Optimal lot sizing for an unreliable production system under partial backlogging and at most two failures in a production cycle. International Journal of Production Economics, 95(2), 229-243.
[10]. Hollier, R.H. and Mak, K.L. (1983): Inventory replenishment policies for deteriorating items in a declining market. International Journal of Production Economics, 21, 813-826.

Abstract: In the labelling of graphs one of the types is cordial labelling. In this we label the vertices 0 or 1 and then every edge will have a label 0 or 1 if the end vertices of the edge have same or different labellings respectively. Here we are going find whether a k-regular bipartite graph can be cordial for different values of k.

[1] L.CAI,X.ZHU, (2001), "Gaming coloring index of graphs", Journal of graph theory, 36, 144-155
[2] XUDING ZHU, (1999), "The game coloring number of planar graphs", Journal of Combinatorial Theory Series B, 75, 245-258
[3] H. YEH, XUDING ZHUING, (2003), "4-colorable, 6-regular toroidal graphs", Discrete Mathematics, 273, 1-3,261-274
[4] X.ZHU, (2006), "Recent development in circular coloring of graphs", Topics in discrete mathematics, spinger 5, 497-550
[5] H.CHANG, X.ZHU, (2008), "Coloring games on outerplanar graphs & trees", Discrete mathematics,doi10.1016/j.disc, 9 -15
[6] H. HAJIABLOHASSAN, X. ZHU, (2003),: The circular chromatic number and mycielski construction", Journal of graph
theory,404, 106-115.

Abstract: - Aim of this study is to investigate the effect of magnetic field on blood flow in cylindrical artery through porous medium. In this paper blood is considered elastico viscous, Non Newtonian fluid and flow is assumed as fully developed and laminar. Laplace transforms and Finite Hankel Transforms are used to obtain the analytical expression for velocity profile, flow rate and fluid acceleration. The effect of magnetic field on velocity and fluid acceleration has been discussed with the help of graphs. It is found that velocity distribution, flow rate and fluid acceleration of blood in cylindrical artery decrease as magnetic field increases.

Keywords: - Elastico Viscous fluid, Laminar flow, porous medium, fully developed flow, Laplace transforms and Finite Hankel Transform

[1] G. Ahmadi and R. Manvi, "Equation of motion for viscous flow through a regis porous medium" Indian J. Tech. 9, 1971, PP441-444.

[2] R.K. Dash,K.N. Mehta and G. Jayarman . "Casson fluid flow in a pipe filled with a homogeneous porous medium." Int. J. Eng. Sci. 34, 2006, PP 1145-1156.

[3] R. Ponalgusammy,"Blood flow through an artery with mild stenosis." A two layered model, different shapes of stenosis and slip velocity at the wall." Journal of applied science, Vol.7 (2007) PP 1071-1077

[4] P. Nagarani and G. Sarojamma, "Effect of body acceleration on pulsatile flow of casson fluid through a mild stenosed artery." Korea- Australia Rheology Journal volume -20, (2008). PP189-196.

[5] Devajyoty Biswas and Uday Shankar Chakraborty, "Pulsatile flow of blood in a constricted artery with body acceleration." AAM vol.4 No. 2 December 2009 PP 329-342.

[6] Sanjeev Kumar and Archana Dixit, "Mathematical model for the effect of body acceleration on blood flow in time dependent stenosed artery." International Journal of stability and fluid mechanics. Jan-2010 Vol. 1 No.-1 PP 103-115.

[7] J.C. Mishra, A. Sinha and G.C. Shit," Mathematical modelling of blood flow in a porous vessel having double stenosis in the presence of magnetic field.", international journal of biomathematics. June 2011 Vol 4 No.2 pp 207-225.

[8] N.K. Varshney and Raja Agarwal, "MHD pulsatile flow of couple stress fluid through an inclined circular tube with periodic body acceleration." Journal purvanchal academy of sciences, 2011 vol 17 pp 277-293.

[9] Anil Kumar, C.L. Varshney, Veer Pal Singh, "Mathematical modelling of blood flow in elastic viscus fluid under periodic body acceleration with porous effect." IJMR vol 1 issue 03 sept. 2012.

Abstract:In this paper, the terms chained ternary semigroup, cancellable clement , cancellative ternary semigroup, A-regular element, π- regular element, π- invertible element, noetherian ternary semigroup are introduced.

Keywords - chained ternary semigroup, cancellable clement , cancellative ternary semigroup, noetherian ternary semigroup and ternary group.

[1] Anjaneyulu. A., On primary ideals in Semigroups - Semigroup Forum, Vol .20(1980), 129-144.
[2] Anjaneyulu. A., On Primary semigroups – Czechoslovak Mathematical Journal., 30(105)., (1980), Praha.
[3] Anjaneyulu. A., Structure and ideal theory of duo semigroups – semigroup forum., Vol.22(1981) 151-158
[4] Bourne S.G., Ideal theory in a commutative semigroup – Dessertation, John Hopkins University(1949).
[5] Clifford A.H and Preston G.B., The Algebroic Theory of Semigroups , Vol – I, American Math. Society, Province (1961).
[6] Clifford A.H and Preston G.B., The Algebroic Theory of Semigroups , Vol – II, American Math. Society, Province (1967).
[7] Giri. R. D and Wazalwar. A. K., Prime ideals and prime radicals in non-commutative semigroups – Kyungpook Mathematical
Journal, Vol.33, No.1, 37-48, June 1993.
[8] Hanumanta Rao.G, Anjaneyulu. A and Madhusudhana Rao. D., Primary ideals inTernary semigroups - International eJournal
of Mathematics and Engineering 218 (2013) 2145 – 2159.
[9] Hanumanta Rao.G, Anjaneyulu. A and Gangadhara Rao. A., Semiprimary ideals inTernary semigroups - International
Journal of Mathematical Sciences, Technology and Humanities 91 (2013) 1010 – 1025
[10] Harbans lal., Commutative semiprimary semigroups – Czechoslovak Mathematical Journal., 25(100)., (1975), 1-3.

Abstract: This paper deals with some fundamental properties of the set of strongly unique best simultaneous coapproximation in a linear 2-normed space. AMS Subject classification: 41A50,41A52,41A99, 41A28.

Keywords: Linear 2-normed space, strongly unique best coapproximation, best Simultaneous coapproximation and strongly unique best simultaneous coapproximation.

[1] Y.J.Cho, "Theory of 2-inner product spaces", Nova Science Publications, New York, 1994.

[2] J.B.Diaz and H.W.McLaughlin, On simultaneous Chebyshev approximation of a set of bounded complex-valued functions, J.Approx Theory, 2 (1969), 419-432.

[3] J.B.Diaz and H.W.McLaughlin, On simultaneous Chebyshev approximation and Chebyshev approximation with an additive weight function, J. Approx. Theory, 6 (1972), 68-72.

[4] C.B.Dunham, Simultaneous Chebyshev approximation of functions on interval, Proc.Amer.Math.Soc., 18 (1967), 472-477.

[5] Geetha S.Rao, Best coapproximation in normed linear spaces in Approximation Theory, V.C.K.Chui, L.L.Schumaker and J.D.Ward (eds.), Academic Press, New York, 1986,535-538.

[6] Geetha S.Rao and K.R.Chandrasekaran, Best coapproximation in normed linear spaces with property (Λ) , Math. Today, 2 (1984), 33-40.

[7] Geetha S.Rao and K.R.Chandrasekaran, Characterizations of elements of best coapproximation in normed linear spaces, Pure Appl. Math. Sci., 26(1987), 139-147.

[8] Geetha S.Rao and R.Saravanan, Best simultaneous coapproximation, Indian J. Math., 40 No.3, (1998), 353-362.

[9] D.S.Goel, A.S.B.Holland, C.Nasim and B.N.Sahney, On best simultaneous approximation in normed linear spaces. Canad. Math. Bull., 17 (No. 4) (1974), 523-527.

[10] D.S.Goel, A.S.B.Holland, C.Nasim, and B.N.Sahney, Characterization of an element of best Lp -simultaneous approximation, S.R.Ramanujan memorial volume, Madras, 1974, 10-14.

Abstract: In this paper numerical technique has been used to solve two dimensional steady heat flow problem with Dirichlet boundary conditions in a rectangular domain and focuses on certain numerical methods for solving PDEs; in particular, the Finite difference method (FDM), the Finite element method (FEM) and Markov chain method (MCM) are presented by using spreadsheets. Finally the numerical solutions obtained by FDM, FEM and MCM are compared with exact solution to check the accuracy of the developed scheme

Keywords - Dirichlet Conditins, Finite difference Method, Finite Element Method, Laplace Equation, Markov chain Method.

[1] Mark A. Lau, and Sastry P. Kuruganty, Spreadsheet Implementations for Solving Boundary-Value Problems in Electromagnetic, Spreadsheets in Education (eJSiE), 4(1), 2010.
[2] M. N. O. Sadiku, Elements of Electromagnetics (New York: Oxford University Press, 4th edition, 2006).
[3] A. Bernick Raj, and K. Vasudevan, Solution of Laplace equation by using Markov Chains, International Journal Contemp. Math. Sciences, 7(30), 2012, 1487 – 1493.
[4] Erwin kreyszig, Advanced Engineering Mathematics (New York: John Wiley & Sons, 10th edition, 2011).