iosr-Jm   Volume-12 ~ Issue-4 ~ Jul-Aug 2016

Abstract: The paper describes a special recurrence relation whose expansion involve with a typical sequence of plus (+) and minus (-) signs by a process of recursive substitution. The kind of a sign at any k-th place of the expansion depends on the powers of twos in the expression of k in binary scale.

Keywords: Recurrence; sequence; binomial coefficient; compositions; positive integer in binary scale.

[1]. Andrews G.E., The Theory of Partitions, Cambridge University Press, 1998, Chapter 4, p54.
[2]. Bera Soumendra, Relationships between Ordered Compositions and Fibonacci Numbers, Journal of Mathematics Research, CCSE,
Vol. 7, No. 3, 2015.
[3]. John Riordan, Combinatorial identities, R. E. Krie

Abstract:A linear stability analysis is carried out for triple diffusive convection in Oldroyd-B liquid. The expressions of Rayleigh number for stationary and oscillatory convection has been obtained. The neutral curvesforoscillatory mode for different values of stress relaxation parameter, strain retardation parameter, solute Rayleigh numbers, ratio of diffusivity of solutes and heat diffusivity and Prandtl number has been examined. It is found that the oscillatory triple diffusive convection sets in earlier in system with Oldroyd-B liquid as compared to Newtonian liquid system.
Keywords: Triple diffusive convection, viscoelastic liquid,Oldroyd-B liquid, oscillatory convection.

[1] Pearlstein, A. J., et al., 1989, "The onset of convective instability in a triply diffusive fluid layer," J. Fluid Mech., 202, pp. 443-465.
[2] Lopez R. A., et al., 1990, "Effect of rigid boundaries on the onset of convective instability in a triply diffusive fluid layer," Phys.
Fluids A, 2, pp. 897.
[3] Rudraiah, N., and Vortmeyer, D., 1982, "The influence of permeability and of a third diffusing component upon the onset of
convection in a porous medium," Int. J. Heat and mass transfer, 25, pp. 457.
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Fluids, 28, pp. 3172.
[5] Chand, S., 2012, "Triple-Diffusive convection in a micropolarferrofluid in the presence of rotation," Int. J. Engg. Research and
Tech., 1(5), pp. 1-14.

Abstract:In the present paper, an efficient approach based on homotopy perturbation method by using natural transform is adopted to solve some linear and non-linear space-time fractional Fokker-Planck Equations (FPE) in closed form. The space and time fractional derivatives are considered in Caputo sense. The homotopy perturbation natural transform method is a combined form of natural transform, homotopy perturbation method and He's polynomials. The method gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The numerical result shows the effectiveness and good accuracy of the method.
Keywords: Fokker-Planck Equation, Caputo fractional derivative, Natural transform, Homotopy perturbation
method..

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Applications, 29(7)(1995), 103-108.
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Numer. Anal. 39(2001), 1219-1253.
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(1967), 529-539.
[5]. Chandrasekhar,S., Stochastic problem in physics and astronomy, Review of Modern Physics 15 (1943), 1-89.

Abstract: This research is an interdisciplinary study that aims to examine the cultural values of Bugisi Makassar which is involved in the interaction of the mathematics learning. This research was done at one of the schools in the city of Makassar by recording anecdotal for observing and analyzing the interactions that occur between teachers and students and also between students and students. The important recording is observing the cultural values of Bugisi Makassar that is involved in the interaction process. The result of this research shows that the dual concepts of the culture of bugis Makassar are siri' and pacce that is involved in the interaction of mathematics learning process between the interaction of teacher and students and also between students and students........
Keywords:Interactions, Siri', Pacce

[1]. Abdullah, Hamid.,1985., Manusia Bugis Makassar. Jakarta: Indti Idayu Press.
[2]. ______________., 1990., Reaktualisasi Etos Budaya Manusia Bugis. Solo: Ramadhani
[3]. Abidin, Andi Zainal., 1983. Persepsi Orang Bugis Makassar tentang Hukum, Negara dan Dunia Luar. Bandung: Penerbit Alumni.
[4]. Atweh, Bleicher & Cooper, 1998., The Construction of the Social Contex of Mathematics Classrooms: A Sosiolinguitics Analysis. Journal for Research in Mathematics Education. Volume 29, Number 1, January 1998 USA: NCTM, Inc
[5]. Cobb, Wood, & Yackel,1991., Small Group Interaction as A Source of Learning Opportunities in Second-Grade Mathematics. Journal for Research in Mathematics Education. Volume 22, Number 5, November 1991 USA: NCTM, Inc