iosr-Jm   Volume-10 ~ Issue-1 ~ Jan-Feb 2014

Abstract: The object of the present paper is to study generalized projective -recurrent Sasakian manifolds. Here we find a relation between the associated 1-forms A and B. We also proved that the characteristic vector field and vector field associated to the 1-forms A and B are co-directional. Finally we proved that generalized projective -recurrent Sasakian manifold is of constant curvature.
Key Words: Generalized projective -recurrent, Sasakian manifold, Sectional curvature.

[1] Blair, D.E., Contact manifolds in Riemannian geometry, Lecture Notes in Math. Springer 509(1976).
[2] Bhagwat Prasad, A pseudo projective curvature tensor on a Riemannian manifolds Bull.Cal.Math.Soc., 94:3(2002), 163-166.
[3] Asli Basari, Cengizhan Murathan, Generalized -recurrent kenmotsu Manifolds, Sdu fen debiyat fakultesi, 3(1)(2008), 91-97.
[4] M.C.Chaki, On Pseudo Symmetric manifolds, Analele Stiintifice Ale Univeritatti. 33(1987), 53-58.
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Abstract: The idea of difference sequence spaces was introduced by Kizmaz [1] and then this subject has been studied and generalized by various mathematicians. In this paper we define some difference rate sequence spaces by Orlicz space of bounded sequences and establish some inclusion relations. Some properties of these spaces are studied.
Keywords: Difference sequence, Bounded sequence, Orlicz function.

[1] H.Kizmaz, On certain sequence spaces, Canad. Math. Bull., 24 (2) (1981), 169-176.
[2] M.Et and R. Colak, On some generalized difference sequence spaces, Soochow J. Math., 21 (4) (1995), 377 – 386.
[3] M. Et, On some topological properties of generalized difference sequence spaces, Int. J. Math. Math. Sci., 24 (11) (2000), 785 – 791.
[4] M. Et and F. Nuray, – Statistical convergence, Indin J. Pure Appl. Math., 32 (6) (2001), 961 – 969.
[5] R. Colak, M. Et and E. Malkowsky, Some Topics of Sequence Spaces, Lecture Notes in Mathematics. Firat University Press, Elazig, Turkey, 2004.

Abstract: The approximate solutions for the Kuramoto – Sivashinsky Equation are obtained by using the Adomain Decomposition method (ADM). The numerical examples show that the approximate solution comparing with the exact solution is accurate and effective and suitable for this kind of problem.

Keywords: Adomain Decomposition method (ADM); Kuramoto – Sivashinsky Equation.

[1] S.T. Mohyud-Din, On Numerical Solutions of Two-Dimensional Boussinesq Equations by Using Adomian Decomposition and He's Homotopy Perturbation Method,J. Applications nd Applied Mathematics,1932-9466, 2010, 1-11.
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[4] Sivashinsky, G.L., Instabilities, pattern-formation, and turbulencein flames. Ann. Rev. Fluid Mech. ,15, 1983, 179–199.
[5] Akrivis, Georgios, Smyrlis, Yiorgos-sokratis, Implicit-explicitBDF methods for the Kuramoto-Sivashinskyequation,Appl.Numer. Math. 51, 2004, 151–169.
[6] Manickam, A.V., Moudgalya, K.M., Pani, A.K., Second-ordersplitting combined with orthogonal cubic spline collocation methodfor the Kuramoto–Sivashinsky equation, Comput. Math. Appl. 35, 1998, 5–25.

Abstract: In this paper, an application of homotopy perturbation method (HPM) is applied to finding the approximate solution of nonlinear diffusion equation with convection term, We obtained the numerically solution and compared with the exact solution.The results reveal that the homotopy perturbation method is very effective, simple and very close to the exact solution.

Keywords: Diffusion equation with convection term,homotopy perturbation method.

1] J.H.He, Variational iteration method: a kind of nonlinear analytical technique: some examples,International Journal of Non-Linear Mechanics, 34, 699-708,1999.
[2] He J.H., Homotopy perturbation method: a new nonlinear analytical technique, Applied Mathematics and Computation, 135, 73-79, 2003.
[3] J.H. He, Homotopy perturbation technique,Computer Methods in Applied Mechanics and Engineering, 178, 257-262,1999.
[4] J.H.He, A coupling method of homotopy technique and perturbation technique for nonlinear problems, International Journal of Non-Linear Mechanics, 35, 37-43, 2000.
[5] J.H.He,Comparison of homotopy perturbation method and homotopy analysis method,applied Mathematics and Computation, 156, 527-539,2004.
[6] J.H. He, A review on some new recently developed nonlinear analytical techniques, International Journal of Nonlinear Sciences and Numerical Simulation,1, 51-70,2000.