iosr-Jm   Volume-12 ~ Issue-1 ~ Jan-Feb 2016

Abstract: Recently, Esi [2] defined the statistical analogue for double difference sequences x=(x_k,l) as follows: A double sequence x=(x_k,l) is said to be P- statistically Δ−convergent to L provided for each

[1]. Esi, A. Lacunary statistical convergence of difference double sequences. Acta Universitatis Apulensis, 28(2011), 143-148.
[2]. Esi, A. On some new difference double sequence spaces via Orlicz function. Journal of Advanced Studies in Topology, 2(2) (2011), 16-25.
[3]. Fast, H. Sur la convergence statistique, Colleg. Math, 2(1951), 241-244.
[4]. Freedman, A. R., Sember, I. J. & Raphael, M. Some Ces𝑎 ro type summability spaces, Proc. London Math. Soc. 37(1978), 508-520. [5]. Hamilton, H. J. Transformations of multiple sequences. Duke Math. J., 2 (1936), 29-60.
[6]. Mursaleen, M. & Edely, O. H. Statistical convergence of double sequences. J. Math. Anal. Appl., 288(1) (2003), 223-231.
[7]. Pringsheim, A. On the theory of doubly infinite sequences of numbers, Math. Ann., 53(1900), 289-321.
[8]. Robison, G. M. Divergent double sequences and series. Amer. Math. Soc. Trans, 28(1926), 50-73.

Abstract: In this paper, the nonlinear dynamical systems are solved by using the homotopy analysis method (HAM).The approximation solution of this equation is calculated in the form ofa series which its components are computed easily. The existence anduniqueness of the solution and the convergence of the proposed methodare proved.The results obtained here demonstrate that the HAM is an effective and robust technique for nonlinear dynamical systems.Nonlinear dynamical systems are omnipresent in numerous practical engineering and mathematics problems. It is hardly to seek the exact solutions in normal circumstances. However, the development of analytical methods can provide an all-embracing understanding for the systems

Key words: Nonlinear dynamical system; Homotopy Analysis Method Mathematics Subject classification: 53C; 58Z05

[1]. S. J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method,Chapman and Hall/CRC Press, Boca Raton,
(2003).
[2]. S. J. Liao and A. Campo, Analytic solutions of the tempreraturedistrbution inBlasius Viscous flow problems, J. Fluid Mech., 453 (2002), 411-425.
[3]. S. J. Liao, Notes on the homotopy analysis method, some definitions and theorems,Commun. in Nonlinear Sci. and Numer. Simulat., 14 (2009), 983-997.
[4]. S. J. Liao, An explicit totally analytic approximation of Blasiusvisous flowproblems, Int. J. Non-Linear Mech., 34 (1999), 759-778.
[5]. S. J. Liao, The proposed homotopy analysis technique for the solution of nonlinearproblems, PhD thesis, Shanghai Jiao Tong University, (1992).
[6]. S. J. Liao, Beyond perturbation, a review on the basic ideas of the homotopyanalysis method and its applications AdV Mech., 38 (2008), 1-34.

Abstract:In this paper we study the concept of almost asymptotically lacunary statistical over probabilistic p metric spaces defined by sequence of Orlicz functions and discuss some general topological properties of above sequence spaces.

[1]. T. Apostol, Mathematical Analysis, Addison-Wesley , London, 1978.
[2]. A. Esi , On some triple almost lacunary sequence spaces defined by Orlicz functions, Research and Reviews:Discrete Mathematical
Structures, 1(2), (2014), 16-25.
[3]. A. Esi and M. Necdet Catalbas,Almost convergence of triple sequences, Global Journal of Mathematical Analysis, 2(1),
(2014), 6-10.
[4]. A. Esi and E. Sava»s, On lacunary statistically convergent triple sequences in probabilistic normed space,Appl.Math.and Inf.Sci.,
9 (5) , (2015), 2529-2534.
[5]. A.Esi , Statistical convergence of triple sequences in topological groups, Annals of the University of Craiova, Mathematics and
Computer Science Series , 40(1), (2013), 29-33.
[6]. E. Savas and A. Esi,Statistical convergence of triple sequences on probabilistic normed space ,Annals of the University of Craiova,
Mathematics and Computer Science Series, 39 No(2), (2012), 226-236.
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New York , 1981.

Abstract:The Poker test is considered one of the important statistical randomness tests. This test, for independence, is based on the frequency in which certain digits are repeated in a series of numbers. In this paper we will attempt to generalize the binary poker test to be suitable to applied on not only binary sequences, in another word, the generalized poker test could be applied on digital (m-) sequences (for m≥2). The generalized poker test called Grouped poker test.

[1]. Abdel-Rehim W. M. F., Ismail I. A. and Morsy E., "Testing Randomness: Poker Test with Hands of Three Numbers", Journal of Computer Science 8 (8): 1353-1357, ISSN 1549-3636, 2012.
[2]. Stewart, W. J., "Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling", 1st Edn., Princeton University Press, Princeton, ISBN-10: 0691140626, pp: 758, 2009.
[3]. Ali F. H, Mohammed, S. A. and Shammran, M. A., "Generalize the Randomness Tests to Test the Digital Sequences Produced from Digital Stream Cipher Systems", Iraqi Journal for Science, Baghdad University, College of Science, 2009.
[4]. Beker, H. and Piper, F., "Cipher Systems: The Protection of Communications", John Wiley & Sons, New York, 1982.
[5]. Gustafson, H., Dawson, E., Nielsen, L. and Caelli, W., "A Computer Package for Measuring the Strength of Encryption Algorithms", Computers & Security, 13, 687–697, 1994.

Abstract:The present paper is focusing on the order, size and degree of the nodes of the interval-valued fuzzy graphs, which are isomorphic. Isomorphism between Interval-valued fuzzy graphs is proved to be an equivalence relation, whereas the Weak isomorphism is proved to be a partial order. Few properties of interval valued fuzzy graphs, which are self complementary, are discussed.

[1]. A. Nagoorgani, K. Radha, Isomorphism on fuzzy graphs, International J. Computational Math. Sci. 2 (2008) 190-196.
[2]. A. Perchant, I. Bloch, Fuzzy morphisms between graphs, Fuzzy Sets Syst. 128 (2002) 149-168.
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[4]. A. A. Talebi, H. Rashmanlou Annals of Fuzzy Mathematics and Informatics Volume x, No. x, (Month 201y), pp. 1–xx ISSN: 2093– 9310 (print version) ISSN: 2287–6235 (electronic version) http://www.afmi.or.kr @FMI °c Kyung Moon Sa Co. Isomorphism on interval-valued fuzzy graphs.
[5]. F. Harary, Graph Theory, 3rd Edition, Addison-Wesley, Reading, MA, 1972.

Abstract:A circulant graph 𝐶𝑛 (𝑅) is said to have the Cayley Isomorphism (CI) property if whenever...

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[3] P.J. Davis, Circulant Matrices, Wiley, New York, 1979.
[4] B. Elspas and J. Turner, Graphs with circulant adjacency matrices, J. Combinatorial Theory, 9 (1970), 297-307.
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Abstract:An analytical study of momentum and heat transfer characteristics with/without suction/blowing of a reacting laminar flow in a horizontal channel filled with saturated porous media with both isothermal and isoflux boundary conditions has been carried out. The problem was studied under the Arrhenius reaction, viscous dissipation and suction. The dimensional ordinary differential equations governing the flow and the heat transfer characteristics are converted into dimensionless ordinary differential equations. The system is solved analytically using the method of undetermined coefficients and the series solution through perturbation method. Details of velocities and temperature fields for various values of the governing parameters of the problems are presented. The contoured graphical results plotted with the numerical results display the effects of various flow parameters such as thesuction/injection Reynolds number, Re, Darcy number, Da, ratio of the effective viscosity of porous region to the viscosity of the fluid, M, Brinkman number, Br, Peclet number, Pe and the Frank-Kamenetskii parameter, β due to Arrhenius kinetic term on the velocity and temperature profileswith the two distinct wall conditions.

[1]. A.K. Al-Hadrami, L. Elliot and D.B.Ingham, A New Model for Viscous Dissipation inPorous Media Across a Range of Permeability Values, Transport Porous Media, 53, 2003, 117-122.
[2]. S.A. Al-Sanea, Mixed convection heat transfer along a continuously moving heated vertical plate with suction or injection, Int. J. Heat Mass Transfer, 47, 2004, 1445–1465.
[3]. O.T. Amumeji, Analysis of a Non-Reacting Laminar Fluid Flow with Viscous Dissipation through a Porous Channel Formed by Two Parallel Horizontal Permeable Walls.Journal of Natural Sciences Research, 5( 7), 2015, 7-20.
[4]. R.O. Ayeni, On the explosion of chain thermal reactions, Journal of Austrialian Mathematical Society, 24, 1982, 194-202.
[5]. A.L. Braslow,History of Suction-type Laminar Flow control with emphasis on Flight Research American Institute of Aeronautics and Astronautics, Washington D.C, 1999.