iosr-Jm   Volume-11 ~ Issue-4 ~ July-Aug 2015

Abstract: This paper presents the implementation of the new iterative method proposed by Daftardar-Gejji and Jafari (DGJ method) [V. Daftardar-Gejji, H. Jafari, An iterative method for solving non linear functional equations, J. Math. Anal. Appl. 316 (2006) 753-763] to solve the linear and nonlinear heat-like and wave-like equations with variable coefficients in one and higher dimensional spaces. The solution is obtained in the series form that converge to the exact solution with easily computed components. The DGJ method has many attractive features such as being derivative-free, overcome the difficulty arising in calculating Adomian polynomials to handle the nonlinear terms in Adomian Decomposition Method (ADM).

[1]. A.M. Wazwaz, Linear And Nonlinear Integral Equations Methods And Applications (Beijing And Springer-Verlag Berlin
Heidelberg, 2011.
[2]. A.M.Wazwaz, A. Gorguis, Exact Solutions For Heat-Like And Wave-Like Equations With Variable Coefficients, Applied
Mathematics And Computation, 149, 2004, 15-29.
[3]. Da-Hua Shou, Ji-Huan He, Beyond Adomian Method: The Variational Iteration Method For Solving Heatlike And Wave-Like
Equations With Variable Coefficients, Physics Letters, A 372, 2008, 233-237.
[4]. A. K. Alomari., M. S. M. Noorani, R. Nazar, Solutions Of Heat-Like And Wave-Like Equations With Variable Coefficients By
Means Of The Homotopy Analysis Method, Chineses Physics Letters, 25, 2008, 589-592.
[5]. L. Jin, Homotopy Perturbation Method For Solving Partial Differential Equations With Variable Coefficients, International Journal
Of Contemporary Mathematical Sciences, 3, 2008, 1395-1407.

Abstract: A study has been made on Couette flow of a generalized second grade fluid through a porous medium with suction. The approximate solution of the governing equation has been obtained by Variational Iteration Method. The effects of fractional calculus parameter β, porosity parameter 𝜎 and the parameter 𝜂 on primary and secondary velocities have been illustrated graphically. It is found that both the primary and the secondary velocities decrease against the distance from the lower plate with the increase in the value of the fractional calculus parameter β.

Keywords: Couette flow, porous medium, variational iteration method, Caputo operator.

[1]. D. Bose, U. Basu, Unsteady Incompressible Flow of a Generalised Oldroyed-B Fluid between Two Infinite Parallel plates., World Journal of Mechanics, 3(2), 2013,146-151.
[2]. J.H. He, Some Asymptotic Methods for Strongly Nonlinear Equations, International Journal of Modern Physics B, 20(10), 2006, 1141-199.
[3]. J. H. He , Approximate Analytical Solution for Seepage Flow with Fractional Derivatives in Porous Media, Computer Methods in AppliedMechanics and Engineering, 167(1),1998, 57-68.
[4]. J. H. He, Variational Iteration Method for Autonomous Ordinary Differential Systems, Applied Mathematics and Computation, 114(2), 000, 115-123.
[5]. D. Bose, U. Basu, Incompressible Viscoelastic Flow of a Generalised Oldroyed-B Fluid through Porous Medium between Two Infinite arallel Plates in a Rotating System., International Journal of Computer Application, 79(1), 2013, 13-20.

Abstract: In this paper a study has been carried out using crisp and fuzzy inventory model for the deteriorating items under trapezoidal fuzzy numbers when the supplier offered price discount to the retailer at the time of replenishment. In this model the deterioration rate is constant. Many researchers suggested, demand rate in the inventory models are constant, exponential (increase/decrease) and linearly increasing / decreasing demand patterns.. In practical situation, quadratic demand rate is more realistic.. In this paper, an inventory model is developed in crisp and fuzzy environment. This paper investigates the feasibility of regular order and special order offered by the supplier in which to maximize the total cost saving. Numerical example and sensitivity analysis carried out in fuzzy environment

[1]. Zadeh L A. Fuzzy sets. Information Control; Vol 8. 1965. P. 338-353
[2]. Jain R, Decision making in the presence of fuzzy variables, IIIE Transactions on systems;Man and cybernectics; Vol 17, 1976.p. 698-703.
[3]. Zimmerman H J.Using fuzzy sets in Operations; European Journal of Operations R esearch ,Vol, 13.1983.p. 201-206
[4]. Dutta D and Pawan Kumar . Fuzzy inventory model without shortages using trapezoidal fuzzy number with sensitivity analysis; IOSR- journal of Mathematics; Vol 4(3) Nov -Dec 2012. P. 32-37.
[5]. Dutta D and Pawan Kumar , Optimal policy for an inventory model without shortages considering fuzziness in demand, holding cost and ordering cost, International journal of Advanced Innovation and Research; Vol 2(2). 2013. P. 320-325.

Abstract: In this paper, we introduced a new (more general and comprehensive) definition of similar ruled surfaces with variable transformations in Euclidean 3-space. Some important results on similar striction curves and similar ruled surfaces are obtained. Furthermore, we have been proved that: a family of k-slant helices is a family of similar curves with variable transformations.MSC: 53A04.

Keywords: Ruled surfaces, Frenet frame, Euclidean 3-space.

[1]. A.T. Ali, H.S. Abdel Aziz and A.H. Sorour, Ruled Surfaces Generated by Some Special Curves in Euclidean 3-Space, J. Egyptian Math. Soc. 21, (2013), 285–294.
[2]. A.T. Ali, New special curves and its spherical indicatrix, Glob. J. Adv. Res. Class. Mod. Geom. 1(2), (2012), 28–38.
[3]. M. Barros, General helices and a theorem of Lancret, Proc. Amer. Math. Soc. 125, (1997), 1503–1509.
[4]. O. Bektas and S. Yuce, Special Smarandache curves according to Darboux frame in E3, (2012), ArXiv:1203.4830v1 [math.GM].
[5]. M.F. El-Sabbagh and A.T. Ali, Similar curves with variable transformation, Konuralp J. Math. 1(2), (2013), 80–90.
[6]. A. Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, Second ed., Boca Raton, FL: Crc Press, (1993).

Abstract: Many researchers in Nigeria have made efforts during the past decades to determine the significant demographic characteristics associated with child mortality using multiple linear regression, logistics model, Cox proportional hazard model and so on but little has been done using Frailty Models which incorporates the term frailty which measures the unobserved heterogeneity among under-five children at individual level.Using the 2008 NDHS, this study is aimed at investigating frailty among individuals, determining those demographic characteristics responsible for under-five child mortality and hazard rates in Nigeria.

[1]. Animashaun, A. (1977). Measles and blindness in Nigerian children. Nigeria Journal of Pediatrics, 4 (1), 10-13.
[2]. Ayeni, O. & Oduntan, S. O. (1980). Infant mortality rates and trends in Nigerian rural populations. Journal of Tropical Pediatrics and Environmental Child Health, 26 (1), 7-10.
[3]. Chukwu A.U. (1998). Impact of Infant and Child mortality on spacing by parity. An analysis based on Cox proportional hazards models. Dissertation, Department of Statistics, University of Ibadan, Nigeria.
[4]. Cox, D.R. (1972). Regression models and life-tables. Journal of Royal Statistical Society Series B (Methodological) 34(20): 187-220, http://www.jstor.org/stable/2985181
[5]. Das Gupta, M. (1990). Death clustering, mother's education and determinants of child mortality in rural Punjab, India. Population Studies 44.3: 489-505

Abstract: Without any doubt, Indicators derived from mortality rates give a clear representation of the overall population health. One of such indicators is maternal mortality. This work discusses Logistic regression and Artificial Neural Network model and the application of these models in predicting maternal mortality. 276 records (ranging from 2003 to 2012) on mother's age, mode of delivery, parity, sex of the baby, baby's weight at birth, nature of complication (independent variables) and mother's status (dependent variable) were collected from the medical record department of the University College Hospital Ibadan. Logistic regression model was used to check for the risk factor associated with maternal mortality.

[1]. Central Intelligence Agency (CIA): retrieved from http://www.cia.gov/library/publications
[2]. Eftekhar B. et al (2005) "Comparison of ANN and Logistic Regression Model for Prediction of Mortality in Head Trauma Based on Clinical data. Available at ‟http://www.biomedcentral.com/1472_6947/15/3.
[3]. Everitt B.S and Skrondal A (2010) "The Cambridge Dictionary of Statistics‟
[4]. 5th Edition. Cambridge University Press, New York. ISBN-13 978-0-511-78827-7. Available at www.cambridge.org/9780521766999.
[5]. Fabayo C.O (2010) "Maternal and Child Health for Health Workers.‟ Samadex Printing Press, Ilorin, Nigeria. ISBN 978_187_301_9.

Abstract:In this paper, we reviewed the work of Adepoju et al [1] and also corrected some mistakes in the paper. We then used this known result to obtain our own results using the well known Legendre duplicating formula.
Keywords: Holomorphic function, Osgood's theorem, Verdemonde's identity, Legendre duplicating formula and geometric progression formula.

[1]. Adepoju, J. A. and Mogbademu, A. A. (2008), "On the coefficient of holomorphic functions and the identity
" Journal of the Nigerian Association of Mathematical Physics, Vol. 13, 17-20.
[2]. Adepoju, J. A. and Yemoah, G. S. (1999), "On the Growth of the Coefficients of Holomorphic Functions in Faber Regions" Journal
Sci. Res. Dev., vol. 4, 167-174.

Abstract: The unsteady magnetohydrodynamics free convection flow of an incompressible viscous fluid past a stretching surface is analyzed by taking into an account the variable viscosity and viscous dissipation under the influence of hall currents effect. The problem is governed by coupled nonlinear partial differential equations. The coupled non-linear ordinary differential equations have been solved numerically by the implicit finite difference method. The effect of magnetic parameter M, Hall parameter m, Prandtl number Pr, Eckert number Ec, on velocity and temperature fields are investigated through graphs.

Keywords: MHD, viscous dissipation, implicit finite difference method, Hall parameter.

[1]. J.A.D. Ackroyd, Stress work effects in laminar flat-plate natural convection, J. Fluid Mech., 62(4), pp. 677–695, 1974.
[2]. B. Gebhart, Effects of viscous dissipation in natural convection, J. Fluid Mech., 14(2), pp. 225–232, 1962.
[3]. B. Gebhart, J. Mollendorf, Viscous dissipation in external natural convection flows, J. Fluid Mech., 38(1), pp. 97–107,1969.
[4]. M.A. Seddeek, "The effect of variable viscosity on hyromagnetic flow and heat transfer past a continuously moving porous boundary with radiation ," International Communications in Heat and Mass Transfer, vol. 27, no. 7, pp. 1037–1047, 2000.
[5]. M.A. Seddeek, "Effects of radiation and variable viscosity on aMHDfree convection flow past a semi infinite flat plate with an aligned magnetic field in the case of unsteady flow," International Journal of of Heat and Mass Transfer, vol. 50, no. 5-6, pp. 991–996, 2007.

Abstract: The purpose of this paper is to study the optimality of circular neighbor balanced designs for total effects when equal right and left neighbor effects are present in the model and the observation errors are correlated according to first order circular stationary autoregressive process. Few results pertaining to the optimality conditions under some specified conditions are provided and the efficiencies of circular neighbor balanced designs relative to the optimal continuous block designs are also investigated. The efficiency of the circular neighbor balanced designs is illustrated corresponding to the optimal continuous block designs.

Key Words: Auto regressive process, Block Design, Circular, Correlated observation, Equal Neighbor balanced effect, Total effect, Universal optimality.

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[2]. AI, M.-y., GE, G.-n.andCHAN, L.-y. (2007). Circular neighbor-balanced designs universally optimal for total effects.Sci. China Ser. A 50 821–828.MR2353065
[3]. AI, M., YU, Y. and HE, S. (2009). Optimality of circular neighbor-balanced designs fortotal effects with autoregressive correlated observations. J. Statist. Plann.Inference1392293–2304.MR2507991
[4]. BAILEY, R.A. and DRUILHET, P., (2004). Optimality of Neighbor-balanced designs for total effects. Ann. Statist. 32(4),1650-1661.
[5]. BOX, G.E.P., HUNTER, J.S. and HUNTER, W.G., (2005).Statistics for Experimenters. John Wiley & Sons, New Jersey.

Abstract:This work investigates the existence of a T periodic solution of the problem

[1]. Hakl, R; Lomtatidze, A and Sremr, J.O: on a boundary-value problem for for linear solutions. Masarky University, Brno (2002).
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[3]. F. Li and Z. Liang, Existence of positive periodic solution to nonlinear second order differential equations. Applied Mathematics Letters, Vol. 18, No. 11, 2005, pp. 1256-1264.
[4]. K.Q. Lan, Nonzero positive solutions of systems of boundary value problems, AMS, vol.139, No. 12, 2011, pp 4343-4349.