iosr-Jm   Volume-12 ~ Issue-5 ~ Sep-Oct 2016

Abstract: In this paper, we determine the partially balanced incomplete block designs and association scheme which are formed by the minimum dominating sets of the graphs C3 ◦ K3, we determine the number of minimum dominating sets of graph G = Cn ◦ K3 and prove that the set of all mini- mum dominating sets of G = Cn ◦K3 forms a partially balanced incomplete block design with two association scheme. Finally we generalize the results for the graph H ◦ K3.

Keywords: Minimum dominating sets, association schemes, PBIB designs

[1]. Anwar Alwardi and N. D. Soner, Partial balanced incomplete block designs arising from some minimal dominating sets of SRNT graphs, International Journal of Mathematical Archive 2(2) (2011), 233-235.
[2]. P. J . Cameron and J . H. Van Lint, Designs, graphs, Codes and their links, vol. 22 of London Mathematical Society Student Texts, Cambridge University Press, Cambridge, 1991.
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[4]. V. R. Kulli and S. C. Sigarkanti, Further results on the neighborhood number of a graph. Indian J. Pure and Appl. Math.23 (8) (1992) 575 -577.
[5]. E. Sampathkumar and P. S. Neeralagi, The neighborhood number of a graph, Indian J. Pure and Appl. Math.16 (2) (1985) 126 - 132.

Abstract: A class of approximate solutions of stationary exterior fields of Einstein-Maxwell (EM) equations are obtained by expanding the metric in powers of a certain parameter and solving explicitly the first few orders in terms of four harmonic functions. Previously these approximate solutions in closed form were found upto third order. In the present paper we obtain new fourth order equations and find their approximate solutions for the particular choice of the harmonic functions. The harmonic functions are so chosen that all the approximate solutions obtained are asymptotically flat. Here some relations obtained are claimed to be a 'laboratory' with which future attempts at exact solutions in terms of harmonic functions may be tested.

Keywords: Einstein-Maxwell equations, Physical Interpretation, Approximate Solutions

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Abstract: This paper focuses on the derivation of one-sixth hybrid block method for the general solution of first order initial values problems of ordinary differential equations. The new proposed method was derived by using the approach of collocation and interpolation of Chebyshev polynomials, approximate solution at some selected points to get a continuous linear multistep method, which was evaluated at some off-grid points to generate hybrid linear multistep methods. Basic properties of the proposed method wasexamined and the method found to be zero-stable, consistent and convergent.........

Keywords: Hybrid block methods, first order initial values problems, collocation and interpolation, approximate solutions, consistent and zero stability

[1] Abbas S., Derivations of New Block Method for the Numerical Solution of First Order IVPs,International Journal of Computer Mathematics, Vol. 64, (1997), pp. 11-25.
[2] Adesanya A. O., Odekunle M. R. and James A. A., Starting Hybrid Stomer-Cowell More Accurately by Hybrid Adams Method for the Solution of First Order Ordinary Differential Equation, European Journal of Scientific Research, Vol. 77 No. 4, (2012), pp. 580-588.
[3] Areo E. A., Ademiluyi R. A. and Babatola P. O. , Three-Step Hybrid Linear Multistep Method for the Solution of First Order Initial Value Problems in Ordinary Differential Equations, J.N.A.M.P, Vol. 19, (2011), pp. 261-266.
[4] Areo, E.A. and Omojola, M. O., A New One-Twelfth Step Continuous Block Method for the Solution of Modeled Problems of Ordinary Differential Equation, American Journal of Computational Mathematics, Volume 5 (2015), pp. 447-457.
[5] Areo, E.A. and Adeniyi R. B. (2013), "A Self-Starting Linear Multistep Method for Direct Solution of Second Order Differential Equations", International Journal of Pure and Applied Mathematics, Bulgaria, Vol. 82, No. 3 pp. 345-364.

Abstract: Stochastic stability of Markov chains has an almost complete theory and forms a foundation for several other general techniques. A fuzzy Markov system is proposed and describe both determined and random behavior of complex dynamic systems. In this paper we study the ergodic behavior of a fuzzy Markov chain, and Consequently their weak and strong ergodic behavior.

Keywords: Fuzzy Markov Chain, Fuzzy Transition Probability Matrix, Non-Stationary Markov chain.

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Abstract: It is shown that period, rank and order of the (a,b) -Fibonacci sequence remain invariant by extension to the generalized (a,b,c,d) -Lucas sequence provided a specific determinant is relatively prime to the modulus. Given an odd prime modulus p and the p 1 exceptional (a,b) -Lucas sequences, for which p divides the discriminant of these sequences, we determine the corresponding periods and relate them to those of the (a,b) -Fibonacci sequence. The results can be viewed as extended versions of classical results by Wall in case (a,b)  (1,1)

Keywords: Fibonacci number, Lucas number, period, order, rank, order

[1]. R.A. Dunlap, The Golden Ratio and Fibonacci Numbers (World Scientific, Singapore, 1997).
[2]. T. Koshy, Fibonacci and Lucas Numbers with Applications (2nd ed.) (J. Wiley, New York, 2015).
[3]. A.P. Stakhov, The Mathematics of Harmony (Series on Knots and Everything, Vol. 22, World Scientific, Singapore, 2009).
[4]. G. Cerda-Morales, On generalized Fibonacci and Lucas numbers by matrix methods, Hacettepe Journal of Mathematics and
Statistics 42(2), 2013, 173-179.
[5]. Th. Jeffery and R. Pereira, Divisibility properties of the Fibonacci, Lucas, and related sequences, ISRN Algebra, Vol. 2014, Article
ID 730325, 2014, 5 p.

Abstract: In this paper, an efficient generalized of cosh (ξ) expansion method is proposed to seek traveling wave solutions of the derivative Schrödinger equation. The traveling wave solutions are expressed in terms of the hyperbolic and trigonometric functions. It is shown that the method is straightforward and effective for solving nonlinear evolution equations in mathematical physics.

Keywords: Generalized of cosh (ξ) Expansion Method; Exact Solutions; Derivative Schrödinger Equation.

[1]. M. Wang, X. Li,and J.Zhang (2008).The 𝐺′𝐺 expansion mathod and travelling wave solutions of nonlinear evolution equations in mathematical physics, Physics Letters A, Vol. 372, no. 4,:417-423.
[2]. Mohammad Ali Bashir, Alaaedin Amin Moussa (2014). New Approach of 𝐺′𝐺 Expansion Method. Applications to KdV Equation, Journal of Mathematics Research, Vol. 6, No. 1: 24-31.
[3]. L.X.Li, E.q.Li and M. wang (2010).The 𝐺′𝐺,1𝐺 expansion method and its application to travelling wave solutions of the Zakharov equation, Applied Mathematics B, Vol. 25, No. 4:454-462.
[4]. M Ali Akbar and Norhashidah Hj Mohd Ali (2014).Solitary wave solutions of the fourth order Boussinesq equation through 𝑒𝑥𝑝 −𝜙 𝜉 the expansion method, Springer plus ,3:344.

Abstract: The aim of this research paper is to establish some new linear generating relations involving.

Keywords: ........

[1] Srivastava, H. M., Gupta, K. C. and Goyal, S. P.: The H-function of one and two variables with applications, South Assian Publishers, New Delhi, 1982.
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[3] Shrivastava, Shweta and Shrivastava, B. M. L.: Some new generating relations and identities for H-function, Vijnana Parishad Anusandhan Patrika, Vol. 49, No.1, January, 2006, p. 63-77.,3:344.

Abstract: We investigate the channeling radiation characteristics of positrons channeled in single-walled carbon nanotubes (SWCNTs). The channeled positrons move along the nanotube axis, (z-axis), with energies (10-500) MeV. This study covers SWCNTs with different chiral indices (n,m). The energy eigenvalues, in a plane normal to the nanotube axis (xy-plane), of relativistic positron channeled through SWCNTs has been used to calculate the emitted photon energy in the forward direction, i.e.....

Keywords: Channeling Radiation; Carbon nanotubes; Relativistic positron beams..

[1] M. A. Kumakhov, Phys. Lett. 57A, 17,1976, Dokl.Akad.SSSR,230,1077 ,1976.
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single-walled carbon nanotubes". Accepted for publication in Egypt. J. Solids.2016.s ,3:344.

Abstract: Double-diffusive convection in a couple-stress fluid in the presence of uniform vertical magnetic field through porous medium using linearized stability theory and normal mode analysis is studied. For the case of stationary convection, the stable solute gradient, magnetic field and couple-stress are found to have stabilizing effects whereas medium permeability has destabilizing effect on the system. The dispersion relation is also analyzed analytically. Further, it is found that the solute gradient and uniform magnetic field introduce oscillatory modes in the system, which was non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained..

Keywords: couple-stress fluid, double-diffusive convection, linearized stability theory, porous medium, uniform vertical magnetic field,

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Abstract: In this paper, symmetric hexagonal Fuzzy Transportation Problem (FTP) is introduced with fuzzy demand and supply and an optimal solution is obtained for the same. This is done by using a numerical problem which clearly defines the fuzzy transportation problem.

Keywords: Ranking, Symmetric Hexagonal fuzzy number, Transportation problem..

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