iosr-Jm   Volume-3 ~ Issue-1

Abstract :The main purpose of this paper is to give the relationship between hypergeometric series and the Lucas sequence. A variety of representations in terms of finite sums and infinite series involving coefficients are obtained. While many of them are well known and some identities appear to be now.

[1] A.K.Agarwal, ``On a new kind of numbers", The Fibonacci Quarterly, Vol 28(3), ( 1990), 194-199 .
[2] G.E. Andrews, Richard Askey, Ranjan Roy ``Special Functions",Cambridge University press 1999.
[3] W.N. Bailey.`` Generalized Hypergeometric Series". Cambrige: Cambridge University Press, 1935.
[4] C.Jordan. ``Calculus of Finite Differences". New York : Chelsea, 1950.
[5] Thomas Koshy. ``Fibonacci and Lucas Numbers with Applications", 2001.
[6] E.D. Rainville. ``Special Functions", New York : Macmillan, 1967.
[7] J.Riordan. ``Cambinatorial Identities". Huntington. New York: Krieger, 1979.
[8] M.Abramowitz and I.A.Stegun. ``Handbook of Mathematical Functions". Washington, D.C.: National Bureau of standards, 1964.

Abstract:The present paper studies a new class of numbers. Results obtained in this paper are a table, recurrence relations, generating functions and Summation formulas for these new class of numbers . Many results reduce to their corresponding results for the Catalan numbers .

[1] A.K.Agarwal, ``On a new kind of numbers", The Fibonacci Quarterly, Vol 28(3), ( 1990), 194-199 .
[2] C.Jordan. ``Calculus of Finite Differences". New York : Chelsea, 1950.
[3] J.Riordan. ``Cambinatorial Identities". Huntington. New York:Krieger, 1979
[4] E.D. Rainville. ``Special Functions", New York : Macmillan, 1967.

Abstract: layer of Rivlin-Ericksen viscoelastic fluid heated from below is considered in the presence of uniform vertical magnetic field. Following the linearized stability theory and normal mode analysis, the paper mathematically established the condition for characterizing the oscillatory motions which may be neutral or unstable, for any combination of perfectly conducting, free and rigid boundaries at the top and bottom of the fluid. It is established that all non-decaying slow motions starting from rest, in a Rivlin-Ericksen viscoelastic fluid of infinite horizontal extension and finite vertical depth, which is acted upon by uniform vertical magnetic field opposite to gravity and a constant vertical adverse free and rigid boundaries and the exact solutions of the problem investigated in closed form, are not obtainable. temperature gradient, are necessarily non-oscillatory, in the regime...........

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Abstract: A Moving Mesh method is proposed for numerical solution of one dimensional non linear Burgers Equation with homogeneous Dirichlets boundary conditions. Discretization of derivatives is obtained by forward Euler, Backward Euler and central difference formula. We proved that the method is stable in 2 L norm. Numerical solutions of one dimensional non linear Burgers equation obtained by Modified average method with Moving mesh are bounded. Numerical solutions are given in different domains for different values of t and constant of diffusivity k. AMS subject classification:-65M12
Keywords: Burgers equation, Moving mesh, Modified average Method, Discretization , Stability

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Abstract: The interval [I,C0] where I is the indiscrete closure operator and C0 is the co-finite closure operator on a set X is a complete sublattice of the lattice of all closure operators on X. In this paper, we determine a class of automorphisms of the lattice [I,C0] and characterize the group of automorphisms on [I,C0] when X is finite. Mathematics Subject Classification: 54A05
Keywords: lattice of all closure operators on a set X, infra closure operator, atomistic lattice, lattice
isomorphism, lattice automorphism, reflexive relation.

[1] Baby Chacko, Some Lattice Theoretic Problems Related to Set Topology and Fuzzy Topology, Thesis for Ph.D. Degree, University
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Abstract:In this paper we analyze the Laminar MHD flow in the entrance region of an annular channel under the influence of transverse magnetic field. The motion of the fluid is between the two insulating cylinders which are concentric. The origin of the coordinate system is located at the extreme left of the channel along the central line of the cylinders, z is the coordinate which increases in the down stream direction, r is the radial coordinate and θ is the angular coordinate and is perpendicular to the (r,z) plane. The flow problem is described by means of partial differential equations and the solutions are obtained by using an implicit finite difference technique. The velocity, temperature and pressure profiles are obtained and their behavior is disc ussed computationally for different values of governing parameters like magnetic field parameter M and Prandtl number Pr.
Keywords: Laminar flow, MHD, Annular channel.

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Abstract: In the present paper, we obtain three fractional derivative formulae (FDF). The first involves the product of a general class of polynomials and the multivariable A -function. The second of a general class of polynomials and two multivariable A -functions and has been obtained with the help of the generalized Leibnitz rule for fractional derivatives. The last FDF also involves the product of a general class of polynomials and the multivariable A -function but it is obtained by the application of the first FDF twice and it involves two independent variables instead of one. Two polynomials and the functions involved in all our fractional derivative formulae as well as their arguments which are of the type   x x    are quite general in nature. These formulae, besides being of very general character have been put in a compact form avoiding the< occurrence of infinite series and thus making them useful in applications. Our findings provide interesting unifications and extensions of a number of (new and known) results. For the sake of illustration, we give here exact references to the results to the results (in essence) of six research papers [3,4,12,13,14,15] that follow as particular cases of our findings. In the end, we record a new fractional derivative formula involving the product of the Hermite polynomials and the product of r different Whittakar functions as a simple special case of our first formula.
Key words: Reimann-Liouville and Erdelyi-Kober fractional operatore, Fractional derivative formulae, General class of polynomials, Multivariable A -function, Generalized Leibnitz rule.

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