iosr-Jm   Volume-11 ~ Issue-6 ~ Nov-Dec 2015

Abstract:The unsteady hydromagnetic boundary layer flow of an incompressible and electrically conducting fluid through a porous medium bounded by a moving surface has been considered. It is assumed that the moving surface has a velocity profile with respect to time and fluid flow is taken under the influence of a transverse magnetic field. The similarity solution is used to transform the system of partial differential equations, describing the problem under consideration, into a boundary value problem of coupled ordinary differential
equations and an efficient numerical technique is implemented to solve the reduced system. The effects of the parameters such as Magnetic parameter, Prandtl number and Eckert number are discussed graphically on velocity and temperature distributions.
Keywords: Boundary layer, Heat and Mass transfer, Hydromagnetic Field, Similarity solution, Unsteady

[1]. Nield, D.A. and A. Bejan, 2006. Convection in Porous Media (3rd Edn.). Springer, New York.
[2]. Vafai, K. 2005. Handbook of Porous Media (2nd Edn.). Taylor & Francis, New York.
[3]. Ingham, D.B. and I. Pop, 2005. Transport Phenomena in Porous Media III. Elsevier, Oxford.
[4]. Vadasz, P., 2008. Emerging Topics in Heat and Mass Transfer in Porous Media. Springer, New York.
[5]. Cheng, W.T. and C.H. Lin, 2007. Melting effect on mixed convective heat transfer with aiding and opposing external flows from
the vertical plate in a liquidsaturated porous medium. Int. J. Heat MassTransfer 50: 3026-3034.
[6]. C. D. S. Devi, H. S. Takhar, G. Nath, "Unsteady mixed convection flow in stagnation region adjacent to a vertical surface," Heat
Mass Transfer, 26(1991) 71-79.

Abstract: Man has hitherto devised several manual methods to solve the problems of multiplying numbers. The Egyptians and the Russians methods are part of the several ways. In this research some of the old methods of multiplications were analyzed and some new ones were discovered, developed and formulated by the author. This paper presents to the world, new manual ways of multiplying numbers. Keywords: New methods, Old methods, Egyptian method, Russian method, Common method, Multiplication, Manual, Numbers, Whole Numbers, Decimal, Formulae,

1]. David - Osugwu M.N (1979). Understanding mathematics for Nigeria, revised edition, p.16.
[2]. Macrae M.F et al (2000), New General Mathematics, Longman,p.13.
[3]. O` Connor J.J., Robertson E.F. (2000), Egyptian multiplication. Retrieved from: http://www.history.mcs.st-andrews.ac.uk/HistTopics/Egyptian_papyri.html
[4]. [11, May2004].
[5]. Tapson F. (2004), Russian peasant method of multiplication. Retrievedfrom: http://www.ex.ac.uk/trol/trol/trolfg.pdf [11, May,2004].

Abstract:Hyperbolic activation function is examined for its ability to accelerate the performance of doing data mining by using a technique named as Reverse Analysis method. In this paper, we describe how Hopfield network perform better with hyperbolic activation function and able to induce logical rules from large database by using reverse analysis method: given the values of the connections of a network, we hope to determine what logical rules are entrenched in the database. We limit our analysis to Horn clauses. The analysis for this study was simulated using Microsoft Visual C++ software, 2010 Express.
Keywords: Reverse analysis, data mining, hyperbolic activation function, neural network

[1] Wan Abdullah, W.A.T. (1992) Logic Programming on a Neural Network. Int .J. Intelligent Sys, 7, pp 513-519.

[2] Wan Abdullah, W.A.T. (1991) Neural Network logic. Proc of the workshop held in Elba International Physics Center, Italy, pp 135-142.

[3] Sathasivam, S (2006) Logic Mining In Neural Networks. PHD Thesis. University of Malaya.

[4] J.J. Hopfield, Neural Networks and Physical Systems with Emergent Collective Computational Abilities. Proceedings. Natl. Acad. Sci. USA. , 79(1982), 2554-2558.

[5] Sathasivam, S. and Wan Abdullah, W.A.T. (2010) The Satisfiabilty Aspect of Logic on Little Hopfield Network. ISSN 1450-223X (7), pp.90-105 [6] Joya, G, Atencia, M.A. and Sandoval, F. (2002) Hopfield neural networks for optimization: study of the different dynamics, Neurocomputing 43, Amsterdam: Elsevier Science B.V pp.219-237

Abstract:Since the inception of the Internet and the integration of email technology into our personal and work lives especially in academics, our ways of communication began to metamorphose. The Internet, which is consortium computer networks, is transforming educational processes and interpersonal communication especially through Social Networks. Young people, born into a world of laptops and cell phones, text messaging and tweeting, continually spend time exposed to digital technology and streaming so much that they perhaps experience fundamentally different brain development that favors constant communication and multitasking.

[1] Small, G. & Vorgan, G. (2009, Oct). "IBrain: How technology changes the way we think." Scientific American. [On-line]. Available : http://www.scientificamerican.com/article/your-ibrain/ [May 26, 2015]
[2] Lin, Judy. (2008, Oct). "Research shows that Internet is rewiring our brains." NEWSROOM UCLA. [On-line]. Available: http://newsroom.ucla.edu/stories/081015_gary-small-ibrain [April 21, 2015]
[3] Prensky, Marc (2001,Jan). "Digital Natives, Digital Immigrants Part 1", On the Horizon. [On-line]. 9 ( 5), pp.1 – 6. Available: http://dx.doi.org/10.1108/10748120110424816 [Sep 22, 2015]
[4] Jantsch, John(2010,May). "Social Network: The definition of social media. Duct Tape Marketing. [On-line]. Available: http://www.ducttapemarketing.com/blog/the-definition-of-social-media/ [July 29, 2015]
[5] Brian Solis (2007,Jun). "Social networks." Brian Solis: http://www.briansolis.com/2007/06/defining-social-media/ [Jul 29, 2015]
[6] Anon. (2010). "Location-Based Social Networking Marketing White Paper." Anvil Media Inc. [On-line]. Available: http://www.anvilmediainc.com/wp-content/uploads/location-based-social-networking-white-paper.pdf [Aug 20, 2015]

Abstract: In this study, a quadratic regression model and a two layered layer recurrent neural network (TLLRNN) method were used to model forecasting performance of the daily crude oil production data of the Nigerian National Petroleum Corporation (NNPC). The two methods were applied on the difference series and log difference series of the NNPC series. The results indicates that the two layered layer recurrent neural network model have better forecasting per-formance greater than the quadratic regression method based on the mean error square sense. The root mean square error (RMSE) and the mean absolute error (MAE) were applied to ascertain the assertion that the two layered layer recurrent neural network method have better forecasting performance greater than the quadratic regression method. The outcome of the analysis also indicates that modeling forecasting performance of the NNPC data with the log dif-ference series of the data gives greater forecasting performances than modeling with the difference series of the NNPC data irrespective of the method used in modeling with the series.

[1] M. Baghebo, T. O. Atima, The impact of petroleum on economic growth in nigeria, Global Business and Economics Research Journal 2 (2013) 102–115.
[2] J. Neter, M. H. Kutner, C. J. Nachtsheim, W. Wasserman, Applied linear statistical models, volume 4, Irwin Chicago, 1996.
[3] R. W. Farebrother, Non-linear curve fitting and the true method of least squares, Journal of the Royal Statistical Society: Series D (The Statistician) 47 (1998) 137–147.
[4] R. Tobia, An introduction to least squares regression, SAS Institution Inc (1999).
[5] L. M. Healy, Logistic regression: An overview, Eastern Michigan University, College of Technology. In Proceeding of COT 7 (2006) 30–37.
[6] J. L. Elman, Finding structure in time, Cognitive science 14 (1990) 179–211.
[7] A. C. Tsoi, A. Back, Discrete time recurrent neural network architectures: A unifying review, Neurocomputing 15 (1997) 183–223.

Abstract:The main object of this paper to introduce T-pre-compact space. And a good pre operator.
Key words: T-pre compact, good pre-operator.

[1]. S. Kasahara "operation-compact spaces ", Mathematic Japonica , 24(1979),97-105.
[2]. N. G. Mansour ,H. K. Moussa "T-pre-operators" ,IOSR-JM ,5(2013),56-65.
[3]. E.Rosas ,J.Vielma "operator compact and operator connected spaces" ,Scientiae Mathematicas (2) (1999),203-208.
[4]. E.Rosas ,J.Vielma "operator compactification of Topological spaces", Divulgaciones Mathematicas , vol.8,No.2 (2000),163-167.

Abstract:The steady flow of an incompressible viscous fluid above an infinite rotating disk in a porous medium is studied with heat transfer. Numerical solutions of the nonlinear governing equations which govern the hydrodynamics and energy transfer are obtained and solved using Crank Nicolson method. The effect of the porosity of the medium on the velocity and temperature distributions is considered.
Key Words: Energy transfer, Heat transfer, Porous medium, Rotating disk and Viscous fluid..

[1] T.vonKarman,Uberlaminareundturbulentereibung,ZAMM,1(4),pp.233–235,1921. [2] W. G. Cochran, The flow due to a rotating disk, P. Camb. Philos. Soc., 30(3), pp. 365–375, 1934. [3] E.R.Benton,Ontheflowduetoarotatingdisk,J.FluidMech.,24(4),pp.781–800,1966. [4] K. Millsaps, K. Pohlhausen, Heat transfer by laminar flow from a rotating disk, J. Aeronaut. Sci., 19, pp.120–126, 1952. [5] E. M. Sparrow, J. L. Gregg, Mass transfer, flow, and heat transfer about a rotating disk,ASMEJ.HeatTransfer,pp.294-302,Nov.1960. [6] H.A.Attia,UnsteadyMHDflowneararotatingporousdiskwithuniformsuctionorinjection,FluidDyn.Res.,23,pp.283–290, 1998. [7] H. A. Attia, A. L. Aboul-Hassan, Effect of Hall current on the unsteady MHD flow due to a rotating disk with uniform suction or injection, Appl. Math. Model., 25(12), pp. 1089–1098, 2001.

Abstract:In this article, a new method of analysis of the differential equations on the sphere using Leapfrog method is presented. To illustrate the effectiveness of the Leapfrog method, an example of the dif ferential equations on the sphere has been considered and the solutions were obtained using methods taken taken from the literature [17] and Leapfrog method. The obtained discrete solutions are compared with the exact solutions of the differential equations on the sphere. Solution graphs for the differential equations on the sphere have been presented in the graphical form to show the efficiency of this Leapfrog method. This Leapfrog method can be easily implemented in a digital computer and the solution can be obtained for any length of time.

Keywords: Differential equations, system of differential equations, Differential equations on the sphere, Single-term Haar wavelet series, Leapfrog Method..

[1] E. Hairer and G. Wanner, ―Solving ordinary differential equations I: Non-stiff problems‖, 2nd Ed., Springer-Verlag, Berlin, (1996).
[2] S. Karunanithi, S. Chakravarthy and S. Sekar, ―Comparison of Leapfrog and single term Haar wavelet series method to solve the second order linear system with singular-A‖, Journal of Mathematical and Computational Sciences, vol. 4, no. 4, 2014, pp. 804-816.
[3] S. Karunanithi, S. Chakravarthy and S. Sekar, ―A Study on Second-Order Linear Singular Systems using Leapfrog Method‖, International Journal of Scientific & Engineering Research, vol. 5, issue 8, August-2014, pp. 747-750.
[4] S. Sekar and K. Prabhavathi, ―Numerical solution of first order linear fuzzy differential equations using Leapfrog method‖, IOSR Journal of Mathematics, vol. 10, no. 5 Ver. I, (Sep-Oct. 2014), pp. 07-12.
[5] S. Sekar and K. Prabhavathi, ―Numerical Solution of Second Order Fuzzy Differential Equations by Leapfrog Method‖, International Journal of Mathematics Trends and Technology, vol. 16, no. 2, 2014, pp. 74-78.
[6] S. Sekar and K. Prabhavathi, ―Numerical Strategies for the nth –order fuzzy differential equations by Leapfrog Method‖, International Journal of Mathematical Archive, vol. 6, no. 1, 2014, pp. 162-168..

Abstract:We have investigated strange quark matter attached to the string cloud with bulk viscous fluid for higher dimensional Friedman-Robertson-Walker (FRW) universe in Self Creation Cosmology (SCC). We have obtained zero string density (𝜌𝑠 = 0) in this model. Our solutions agree with the studies of Reddy, Sahoo- Mishra and Mohanty et al. in four dimensions.
Keywords: FRW universe, higher dimension, bulk viscous, string cloud, strange quark matter, Self creation cosmology, deceleration parameter..

[1] M. Tegmark et al. Phys. Rev. D,69, 2004, 103501-103527.
[2] G. Efstathiou, et al. Mon. Not. Roy. Astron. Soc.,330, 2002, L29- L35.
[3] N. Bilic, arXiv:0812.5050v2.
[4] C. H. Brans, R. H. Dicke, Phys. Rev., 124, 1961, 925-935.
[5] G. Lyra, Math. Z., 54, 1951, 52-64.
[6] F. S. N. Lobo, M. A. Oliviera, Phys. Rev., 80, 2009, 104012-104021.
[7] D. Saez, V. J. Ballester, Phys. Lett., A 113, 1986, 467-470.
[8] H. Yılmaz, Phys. Rev., 111, 1958, 1417-1426.
[9] G. A. Barber, Gen. Relativ. Gravit., 14, 1982, 117-136.

Abstract:Method of collocation of the differential system and interpolation of the approximate solution which is a combination of power series and exponential function at some selected grid and off-grid points to generate a linear multistep method which is implemented in block method is considered in this paper. The basic properties of the block method which include; consistency, convergence and stability interval is verified. The method is tested on some numerical experiments and found to have better stability condition and better approximation than the existing methods.
Keywords: Interpolation, Collocation, Consistent, Convergent, Block Method, Power Series.

[1] Onumanyi, P., Awoyemi, D. O., Jator, S. N. and Sirisena, U. W. (1994): New linear multistep methods with continuous coefficients
for first order initial value problems. Journal Nig.Maths.Soc.13,37 - 51.
[2] Onumanyi, P., Sirisena, U. W. and Jator, S. N. (1999): Continuous finite difference approximation for solving differential equations.
International Journal of Computer and Mathematics. 72,15 - 27.
[3] Lambert, J. D. (1973): Computational methods in ordinary differential equations.John Wiley, New York.
[4] Lambert, J. D. (1979): Safe Point methods for separable stiff systems of ordinary differential equations. UK: University of Dundee,
Department of Mathematics report No NA/31.
[5] James, A. A., Adesanya, A. O. and Fasasi, M.K. (2013):Starting order seven methods accurately for the solution of first IVPs of
first order ODEs. Progress in Applied Mathematics. 6(1), 30 - 39.
[6] James, A. A and Adesanya, A. O. (2014): A note on the construction of constant order predictor - corrector Algorithm for the
solution of. British Journal of Mathematics and Computer Science. 4(6),886 - 895.
[7] Sirisena, U. W. (1999): An accurate implementation of the butcher hybrid formula for the initial value problems in ordinary
differential equations. Nigeria Journal of Mathematics and Application. 12,199 - 206.
[8] Sirisena, U. W., Kumleng, G. M. and Yahaya, Y. A. (2004): A new Butcher type two-step block hybrid multistep method for
accurate and efficient parallel solution of ordinary differential equations. Abacus 31(2A): Maths Series, 2 - 7.

Abstract:In this paper, an iterative method proposed by Daftardar-Gejji and Jafari namely (DJM) will be presented to solve the weakly singular Volterra integral equation (WSVIE) of the second kind. This method is able to solve large class of linear and nonlinear equations effectively, more accurately and easily. In this iterative method the solution is obtained in the series form that converges to the exact solution if it exists. The main contribution of the current paper is to obtain the exact solution rather than numerical solution as done by some existing techniques.

[1]. Abdul-Majid Wazwaz, Linear and Nonlinear Intagral Equations Methods and Applications, Saint Xavier University, Higher Education Press, Beijing and Springer-Varleg Berlin Heidlberg, 2011.
[2]. P. Linz, Analytical and Numerical Methods for Volterra equations, ch. 8, SIAM, Philadelphia, 1985.
[3]. J.B. Keller, W.E. Olmstead, Temperature of a nonlinearity radiating semi-infinite solid, The Quarterly of Applied Mathematics, 29, 1972, 59–566.
[4]. N. Levinson, A nonlinear Volterra equation arising in the theory of superfluidity, Journal of Mathematical Analysis and Applications, 1, 1960, 111.
[5]. Z. Chen, W. Jiang, The exact solution of a class of Volterra integral equation with weakly singular kernel, Applied Mathematics and Computation, 217, 2011, 7515–7519.
[6]. T. Diogo, P. Lima, Superconvergence of collocation methods for a class of weakly singular Volterra integral equations, Journal of Computational and Applied Mathematics, 218, 2008, 307 – 316.