iosr-Jm   Volume-10 ~ Issue-3 ~ May-June 2014

Abstract: In this paper, we studied the effect of thermal in Stokes' second problem for unsteady second grade fluid flow through porous medium. The expressions for the velocity field and the temperature field are obtained analytically. The effects of various emerging parameters on the velocity field and temperature field are studied through graphs in detail.

Keywords: Thermal Effects, Fluid Flow, Porous Medium

[1] C. Argento and D. Bouvard, A Ray Tracing Method for Evaluating the Radiative Heat Transfer in Porous Medium", Int. J. Heat
Mass Transfer, 39(1996),3175-3180.
[2] S. Asghar, T. Hayat and A.M. Siddiqui, Moving boundary in a non-Newtonian fluid, Int. J. Nonlinear Mech., 37(2002), 75–80.
[3] C.I. Chen, C.K. Chen and Y.T. Yang, Unsteady unidirectional flow of an Oldroyd-B fluid in a circular duct with different given
volume flow rate conditions. Heat and Mass Transfer, 40(2004), 203–209.
[4] H. Chen and C. Chen, Free convection flow of non-newtonian fluids along a vertical plate embedded in a porous medium, Journal
of Heat Transfer, 110(1988), 257-260.
[5] R.V. Dharmadhikari,andD.D.Kale, Flow of non-newtonian fluids through porous media, Chem. Eng. Sci., 40(1985), 527-529.
[6] J.E. Dunn and K.R. Rajagopal, Fluids of differential type: critical review and thermodynamic analysis, Int. J. Engng. Sci.,
33(1995), 689-729.

Abstract: This paper deals with the study of CR-submanifolds of a nearly trans-hyperbolic Sasakian manifold with a quarter symmetric non-metric connection. We study parallel distribution relating to   vertical CRsubmanifolds of a nearly trans-hyperbolic Sasakian manifold with quarter symmetric non-metric connection. Further, we obtain the parallel distributions on CR-submanifolds.

[1]. Bejancu, CR-submsnifolds of a Kaehler manifold. I, Proc. Amer. Math. Soc. 69 (1978), 135-142.
[2]. A. Bejancu, Geometry of CR-submanifolds, D. Reidel Publishing Company, Holland, 1986.
[3]. M. Kobayashi, CR-submanifolds of Sasakian manifold, Tensor (N.S.) 35 (1981), no. 3, 297-307.
[4]. J. A. Oubina, New class of almost contact metric structures, Publ. Math. Debrecen, 32 (1985), 187-193.
[5]. C. Gherghe, Harmonicity on nearly trans-Sasaki manifolds, Demonstratio Math. 33(2000), no. 1, 151-157.
[6]. M. H. Shahid, CR-submanifolds of a trans-Sasakian manifold, Indian J. Pure Appl. Math. 22 (1991), 1007-1012.

Abstract: We have observed numbers to progress in natural order. These numbers can be arranged in a sequence and a generalised equation can be given to predict further coming numbers. Their sum or differences can be obtained by using equations. Here, the numbers are arranged in order of columns, rows and heights as in an array and their general equations to determine their positions and other operations are given.
Key -words: Column, Frequency, Harmonic, Height, Period, Row

[1]. As it is a direct conjecture, so there are no references.

Abstract: A numerical solution for the free convective, unsteady, laminar convective heat and mass transfer in a viscoelastic fluid along a semi-infinite vertical plate with radiation and chemical reaction is presented. The Walters-B liquid model is employed to simulate medical creams and other rheological liquids encountered in biotechnology and chemical engineering. This rheological model introduces supplementary terms into the momentum conservation equation. The dimensionless unsteady, coupled, and non-linear partial differential conservation equations for the boundary layer regime are solved by an efficient, accurate and unconditionally stable finite difference scheme of the Crank-Nicolson type. The velocity, temperature, and concentration fields have been studied for the effect of Prandtl number, viscoelasticity parameter, Schmidt number, radiation parameter, chemical reaction parameter and buoyancy parameters. The local skin-friction, Nusselt number and Sherwood number are also presented and analyzed graphically. It is observed that, when the viscoelasticity parameter increases, the velocity increases close to the plate surface. An increase in Schmidt number is observed to significantly decrease both velocity and concentration.
Key words: unsteady viscoelastic flow, semi-infinite vertical plate, Walters-B short-memory mode, finite difference method, radiation and chemical reaction.

[1]. Thibault, F., Tanguy, P. A., Power-Draw Analysis of a Coaxial Mixer with Newtonian and Non-Newtonian Fluids in the Laminar Regime, Chemical Engineering Science, 57 (2002), 18, pp. 3861-3872
[2]. Goerke, A. R., Leung, J., Wickramasinghe, S. R., Mass and Momentum Transfer in Blood Oxygenators, Chemical Engineering Science, 57 (2002), 11, pp. 2035-2046
[3]. Wang, W., Chen, G., Heat and Mass Transfer Model of Dielectric-Material-Assisted Microwave Freeze-Drying of Skim Milk with Hygroscopic Effect, Chemical Engineering Science, 60 (2005), 23, pp. 6542-6550
[4]. Vrentas, J. S., Vrentas, C. M., Axial Moment Analyses of Convective Heat and Mass Transfer Processes, Chemical Engineering Science, 51 (1996), 6, pp. 921-929
[5]. Ayazi Shamlou, P., Edwards, M. F., Heat Transfer to Viscous Newtonian and Non-Newtonian Fluids for Helical Ribbon Mixers, Chemical Engineering Science, 41 (1986), 8, pp. 1957-1967

Abstract: The Central Bank monetary policy rate is one of the monetary tools that is use to regulate liquidity in an economy. In Ghana the objectives are to ensure price stability, low inflation and also to support the Government economic objectives including growth and employment. This paper empirically models the monthly monetary policy rates from the year 2001 to 2013 using ARIMA model and the data was obtained from the website of Central Bank of Ghana. From the results, it is reveal that ARIMA(2,1,1) is appropriate for modeling the monetary policy rates of Ghana with a maximum log likelihood value of -133.49, and least AIC value of 274.98, AICc value of 275.25 and BIC value of 287.16. An ARCH LM test and Ljung-Box test on the residuals of the model revealed that the residuals are free from heteroscedasticity and serial correlation respectively. Hence, it is adequate for forecasting the monetary policy rate of Ghana.
Keywords: ARIMA, Central Bank of Ghana, Economy, Forecasting, Monetary policy rate

[1]. Bank of Ghana, Bank Monetary Policy rate, http://www.bog.gov.gh/, (accessed on April 1, 2014).
[2]. B.S. Bernanke and A. S. Blinder, The Federal Funds Rate and the Channels of Monetary Transmission, American Economic Review, 1992, 901-21.
[3]. D.M.K.N. Seneviratna and Mao Shuhua, Forecasting the Twelve Month Treasury Bill Rates in Sri Lanka: Box Jenkins Approach, IOSR Journal of Economics and Finance (IOSR-JEF) 1(1), 2013, 44 - 47.
[4]. F. Okyere and C. Mensah, Empirical Modelling and Model Selection for Forecasting Monthly Inflation of Ghana. Mathematical Theory and Modeling, 4(3), 2014, 99-106.
[5]. M. Gertler and S. Gilchrist, The Role of Credit Market Imperfections in the Monetary Transmission Mechanism: Arguments and Evidence, Scandinavian Journal of Economics, 95(1), 1993, 43-64.

Abstract:Our principle aim to study an algebraic module properties topolocically. We concern topological projective modules specially. A topological module P is called topological projective module if for all topological module epimorphism g : B  A and for all topological module morphism f :P  B, there exist a topological module morphism f*: P  A, for which the following diagram commutes: The important point of this paper is to find topological projective module from topological module given. Furthermore among results are obtained at the end of the paper.
Key words: Topological module, topological ring, topological submodule, topological projective module.

[1]. Al-Anbaki, H., 2005, "Topological Projective Modules", M.SC. Thesis, College of Education, Al-Mustanseriyah University.
[2]. Boschi, E., 2000, "Essential Subgroups of Topological Groups", Comm. In algebra, 28(10), pp.4941-4970.
[3]. Mahnoub, M.; 2002, "On Topological Modules, M.Sc. Thesis, College of Science, Al-Mustanseriyah University.
[4]. Majeed, T.H., 2013, "On Some Result of Topological Projective Modules", DJPS, Vol.(9), No.(3).
[5]. Majeed, T.H., 2014, "On On Injective Topological Modules", Journal of the College of Basic Education, Al-Mustansiriya
University, Vol.(20), No.(82).
[6]. Sahleh, H., 2006, "The v-Trace of Abelian Topological Groups", A generalization, Guilan University, Int. J., Vol.1, No.(8),
pp.381-388.

Abstract: In this paper, LRS bianchi type I models in the light of perfect fluid, quintessence and standard Chaplygin gas, have been studied by solving the Rosen's field equations in bimetric theory of gravitation. It is pointed out that the geometry of perfect fluid model is coincide with the geometry of quintessence model for[1, 0],q  1/ 3 and the geometry of quintessence model for q  1/ 3 is similar to geometry of standard Chaplygin gas model. All models are expanding with accelerating expansion. Other geometrical and physical properties of the model are studied. Our opinion supports the observational data that universe is continuously expanding with acceleratingexpansion.
Keywords: Cosmology, Dark Energy, Dark Matter

[1]. A.G. Riess, et al., Astrophysical Journal, 607, 2004, 665.
[2]. D.J. Eisensteinet al., Astrophysical Journal, 633, 2005, 560.
[3]. P. Astieret al., Astronomy and Astrophysics, 447, 2006, 31.
[4]. D.N. Spergel et al., Astrophysical Journal Supplement Series, 170, 2007, 3771.
[5]. A.G. Riess, A.V. Filippenko, P. Challis,A. Clocchiatti, A. Diercks, P.M.Garnavich, R.L. Gilliland, C.J. Hogan, S.Jha, R.P.Kirshner, B.Leibundgut, M.M. Phillips, D. Reiss, B.P. Schmidt, R.A. Schommer, R.C. Smith, J.Spyromilio, C. Stubbs, N.B.Suntzeff andJ.Tonry 3: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astronomical Journal, 116, 1998, 1009.

Abstract: Producer Price Indices are a key of economic indicator in most countries and price instability introduces uncertainty into economic analysis and decision making. This paper empirically models the monthly producer price inflation rates from the year 2009 to 2013 using ARIMA model and the data was obtained from the website of Ghana Statistical Service. From the results, it is revealed that ARIMA(1,1,1) is appropriate for modeling the producer price inflation rates of Ghana with a maximum log likelihood value of -163.34, and least AIC value of 332.68, AICc value of 333.11, BIC value of 338.91 and MAE value of 2.455111. An ARCH LM test and Ljung-Box test on the residuals of the model revealed that the residuals are free from heteroscedasticity and serial correlation respectively. Hence, it is adequate for forecasting the producer price inflation rates of Ghana.
Keywords: ARIMA, Ghana Statistical Service, Modelling, Producer Price Index

[1] D.M.K.N. Seneviratna and Mao Shuhua, Forecasting the Twelve Month Treasury Bill Rates in Sri Lanka: Box Jenkins Approach, IOSR Journal of Economics and Finance (IOSR-JEF) 1(1), 2013, 44 - 47.
[2] F. Okyere and C. Mensah, Empirical Modelling and Model Selection for Forecasting Monthly Inflation of Ghana. Mathematical Theory and Modeling, 4(3), 2014, 99-106.
[3] J. M. Tebbs, STAT 520 Forecasting and Time Series (University of South Carolina, Department of Statistics, Spring, 2010).
[4] J.C. Paul, S. Hoque, and M.M. Rahman, Selection of Best ARIMA Model for Forecasting Average Daily Share Price Index of Pharmaceutical Companies in Bangladesh: A case Study on Square Pharmaceutical Ltd, Global Journal of Management and Business Research, 13(3), 2013.
[5] J.T. Olajide, O.A. Ayansola, M.T. Odusina, and I.F. Oyenuga, Forecasting the Inflation Rate in Nigeria: Box Jenkins Approach, IOSR Journal of Mathematics (IOSR-JM), 3(5), 2012, 15-19.

Abstract: The object of this paper is to prove some of the properties of ( ) -paracontact Sasakian manifoldThis paper is summarized as follows: Section (1) is introductory. In Section (2) we sketch the notion of ( ) - paracontact metric manifold and ( ) -paracontact Sasakian manifold. Section (3) and (4) deals with some properties like D-totally, D -totally, mixed totally geodesic etc. CR-submanifold of an ( ) -paracontact Sasakian manifold. Section (5) and (6) gives some idea of geometry of leaves and contact CR-product . Finally we have given an example of ( ) -paracontact Sasakian manifold.
Key Words : and Phrases: ( ) -paracontact Sasakian manifold, D(D )-totally geodesic, mixed totally geodesic, contact CR-product.

[1] A.Bejancu, CR-submanifolds of a Kahler manifold I, Proc. Amer. Math. Soc. 89 (1978) 135-142.
[2] A.Bejancu, CR-submanifolds of a Kahler manifold II,Trans.Amer. Math. Soc. 250 (1979) 333-345
[3] A.Bejancu and K.L.Duggal, Real hypersurfaces of indefinite Kaehler manifolds, Int.J.Math.Math.Sci.16(1993), no.3, 545-556.
[4] Arindam Bhattacharyya and Bandana Das, Contact CR-Submanifolds of an Indefinite Trans-Sasakian Manifold, Int. J. Contemp.
Maths. Scinces, Vol. 6, 2011, no. 26, 1271-1282.
[5] B.O'Neill, Semi-Riemannian Geometry with application to relativity, Academic Press, 1983.
[6] D.E.Blair, Riemannian Geometry of contact and cosymplectic manifolds, Progren in Mathematics, 203. Birkhouser Boston, Inc.
place city Boston, MA, 2002.

Abstract: Numerical solutions for heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting chemically reacting viscous dissipative fluid on a continuously vertical permeable surface in the presence of a heat source, a first – order homogeneous chemical reaction and the mass flux are reported. The plate is assumed to move with a constant velocity in the direction of fluid flow. A uniform magnetic field acts perpendicular to the porous surface, which absorbs the fluid with a suction velocity varying with time. The fluid is considered to be a gray, absorbing emitting but non – scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The problem is governed by coupled non – linear partial differential equations. Dimensionless equations of the problem have been solved numerically by finite element method. The effects of flow parameters, viz. thermal Grashof number, solutal Grashof number, Hartmann number, Permeability parameter, Thermal radiation parameter, Prandtl number, Heat source parameter, Schmidt number and Eckert number on velocity, temperature and concentration fields are investigated through graphs. Skin friction, Rate of heat and mass transfer coefficients are derived, discussed numerically and presented in tabular forms. The combined heat and mass transfer plays an important role are designing chemical processing equipment, formation and dispersion of fog, distribution of temperature and< moisture over agricultural fields and groves of fruit trees, crop damage due to freezing, and environmental pollution.
Keywords: MHD, Free convection, Viscous dissipation, Porous medium, Thermal radiation, Chemical reaction and Finite element method..

[1] Abdur Sattar, Md. and Kh. Abdul Maleque, 2005. The Effects of Variable properties and Hall current on steady MHD laminar
convective fluid flow due to a porous rotating disk, Int. Journal of Heat and Mass Transfer, Vol. 48, pp. 4460 – 4466.
[2] Anjali Devi, S. P. and J. Wilfred Samuel Raj,2011. Thermo diffusion effects on unsteady hydromagnetic free convection flow
with heat and mass transfer past a moving vertical plate with time dependent suction and heat source in a slip flow regime,Int. J.
of Appl. Math. and Mech., Vol. 7, No. 21, pp. 20 – 51.
[3] Dulal Pal and Babulal Talukdar, 2010. Perturbation analysis of unsteady magnetohydro dynamic convective heat and mass
transfer in a boundary layer slip flow past a vertical permeable plate with thermal radiation and chemical reaction,
Communications in Nonlinear Science and Numerical Simulation,pp.1813 – 1830.
[4] Ibrahim, F. S., A. M. Elaiw and A. A. Bakr, 2008. Effect of the chemical reaction and radiation absorption on the unsteady MHD
free convection flow past a semi – infinite vertical permeable moving plate with heat source and suction, Communications
Nonlinear Science Numerical Simulation, Vol. 13, No. 6, pp. 1056 – 1066.
[5] Kesavaiah, D., Ch. P. V. Satyanarayana and S. Venkataramana, 2011. Effects of the chemical reaction and radiation absorption
on an unsteady MHD convective heat and mass transfer flow past a semi – infinite vertical permeable moving plate embedded in
a porous medium with heat source and suction,Int. J. of Appl. Math. and Mech., Vol. 7, No. 1, pp. 52 – 69.