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

Abstract: Queue is the study of traffic behavior near a certain section where demand exceeds available capacity. Queue can be seen in many situations, boarding a bus, train or plane traffic signal etc. Mobility is an in dispensable activity of our daily lives and traffic congestion is one popular approach to mobility. In this paper we discuss the Markovian modelling of vehicular traffic congestion in Nagercoil junction and Marthandam junction at kanayakumari district. Queuing theory analytic methodologies, simulation and Chi- square distribution are applied and parameters such as average arrival rate and service rate are calculated based on the data obtained at the Marthandam and Nagercoil junctions on daily basis for six days in a week. Keywords: Queuing system, Poisson process, Markov process, Chi - square distribution, exponential distribution

[1]. Dr.S.P Gupta &Dr.M.P Gupta, Business Statistics, Sultan Chand & Sons, New Delhi.
[2]. Mehdi, J (2003) Stochastic Models in Queuing theory, second Edition, Esevier, Berlin.
[3]. Gross, D.and Harris. C. (1998) Fundamentals, 3rd Edition, John Wiley.
[4]. Kendall D.G.Stochastic process occurring in the theory of queuing analysis by the method of the imbedded Markov chain. The Annals of Mathematical statistics 1953. 24(3).
[5]. Irene K.V.A Simulation approach to the design of the single – server Queuing system. Department of mathematics and statistics, University of Cape coast 2008.
[6]. Gerlough D.C and Schuhl A. Use of Poisson distribution in High Way Traffic and the probability theory .Applied to distribution of vehicles on Two – lane High way. New York, Columbia University press 1955.
[7]. Agbonia F.O. Road traffic Congestion and the quest for effective transportation Proceedings of the National Conference of Nigerian society of Engineers in Calaba 2011.

Abstract: Numerical methods have been formulated for the numerical approximation of real two dimensional integrals. The truncation error associated with the methods has been analyzed using the Taylors' series expansion. The methods have been verified by considering standard examples.

Keywords: Approximation rules, Degree of precision, Taylors' series expansion.

[1]. Davis,P.J. & Rabinowitz,P. Methods of numerical integration(2nd edn.),Academic Press,London,1984.
[2]. Monegato,G., The numerical evaluation of one dimensional Cauchy principal value integrals,computing,29,1982,337-354.
[3]. Monegato,G., convergence of product formulas for the numerical evaluation of cetain two dimensional CPV integral, Numer.Math., 43(2),1984,161-173.
[4]. Nayak,M.M.,Acharya,M. and Acharya,B.P., Numerical evaluation of two dimensional Cauchy principal value integrals,Appl.Math. and Comp.,225,2013,807-810.
[5]. Squire,W.,Numerical evaluation of a class of singular double integrals by symmetric pairing, Int.J.Numer.Methods Engg.,10(3),1976,703-708.
[6]. Theocaris,P.S. and Kazantzakis,J.V., On the numerical evaluation of two and three dimensional Cauchy principal value integrals,Acta Mech.,39,1981,105-115.
[7]. Theocaris,P.S.,Modified Gauss-Legendre,Lobatto and Radau cubature formulas for the numerical evaluation of 2-D singular integrals, Int.J. Math.Math. Sci,6(3), 1983, 567-587.

Abstract:The groups of much attention for which the Diffie - Hellman problem may be hard and used securely are the multiplicative group * p F , (Z/nZ)* and the group of rational points on an elliptic curve over a finite field. These groups involve large key sizes or expensive arithmetic operations. In this paper we consider the group of Lucas sequences and describe the generalization of discrete log problem to the group of Lucas sequences and adapt the baby-step giant-step algorithm to the generalization. For the computations we implement fast computing methods proposed by Smith.
Key word: Discrete Log Problem, Lucas Sequences, Public Key Cryptography.

[1]. W. Diffie and M.E. Hellman, "New directions in cryptography", IEEE Trans. Inform. Theory, IT-22(6):644-654, 1976.
[2]. T. ElGamal, "A public key cryptosystem and a signature scheme based on discrete logarithms", IEEE Trans. Inform. Theory,
31(4):469-472, 1985.
[3]. Marc Gysin, "The Discrete Logarithm Problem for Lucas Sequences and a New Class of Weak RSA Moduli", The University of
Wollongong, NSW 2522.
[4]. Peter J. Smith and Michael J.J. Lennon, "A New Public Key System", LUC Partners, Auckland UniServices Ltd, The University of
Auckland, Private Bag 92019m Auckland, New Zealand.
[5]. B.Ravitheja, "RSA-Like Cryptosystem based on the Lucas Sequence", dissertation, 2015.

Abstract: In this paper, the three-point distribution functions for simultaneous velocity, temperature and concentration fields in dusty fluids turbulent flow undergoing a first order reaction have been studied. The various properties of constructed distribution functions have been discussed. From beginning to end of the study, the transport equation for three-point distribution function undergoing a first order reaction has been obtained. The resulting equation is compared with the previous equation which related to the distribution function by many authors and the closure difficulty is to be removed as in the case of ordinary turbulence.

Keywords: Magnetic Temperature, Concentration, Three-point distribution functions, MHD turbulent flow, First Order Reactant..

[1] Ta-You W., 1966. Kinetic Theory of Gases and Plasma. Addision Wesley Phlelishing.
[2] Lundgren T.S., 1967. Hierarchy of coupled equations for multi-point turbulence velocity distribution functions. Phys. Fluid., 10:
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[3] Kumar P. and Patel S .R .Phys. of Fluids.17,1362(1974).
[4] Kumar P.S.R and Patel S .R . , Int. J. Eng. Sci.,13.305-315(1975).
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[6] Kishore N., 1978. Distribution functions in the statistical theory of MHD turbulence of an incompressible fluid. J. Sci. Res., BHU,
28(2): 163.

Abstract: This paper proposes, a Fuzzy economic order quantity based Inventory model for Non-Instantaneous deteriorating items under trade credit period. This model aids in minimizing the Fuzzy total inventory cost by finding an optimal replenishment policy. In this model, shortages are allowed and partially backlogged. The backlogging rate varies inversely as the waiting time for the next replenishment. All the inventory costs involved here are taken as pentagonal Fuzzy numbers. Graded mean representation method is used to defuzzify the model. The model is illustrated with the help of numerical examples. Sensitivity analysis of the optimal solution with respect to various parameters of the system is carried out and the results are discussed in detail.

Keywords and Phrases: Stock and time dependent demand, Partial backlogging, Non-instantaneous deterioration, pentagonal fuzzy numbers.

[1] K.V.Geetha and R.Uthayakumar, Economic Design of inventory policy non-instantaneous deteriorating items permissible delay in payments, Journal of Computational and Applied Mathematic 233(2010)2492-2505. [2] R.Uthayakumar and K.V.Geetha , A Replenishment policy for Non-instantaneous deteriorating inventory system with partial backlogging, Tamsi Oxford Journal of Mathematical Sciences 25(3) (2009)313-332. [3] R. P. Covert and G. C. Philip, An EOQmodel for items with weibulldistribution deterioration, AIIE Transactions, 5(1973), 323-326. [4] P. M. Ghare and G. H. Schrader, A modelforexponentiallydecayinginventory system, InternationalJournal of Production Research, 21(1963), 49-46.

Abstract: The differential Transform method is one of important methods to solve the differential equations. In this paper we show to that the differential transform method (DTM) is very Hermite equation.

Keywords: Differential transform method, Bessel equation, Hermite equation.

[1] A.J.H.Jawad, H.D.Petkovic and A.Biswas, Modified simple equation method for non-linear evolution equations. (Applied Mathematics and Computer. 2010)

[2] M.Akbari.The modified simplest equation method and computational methods for differential equations (2013)

[3] E.Fan and H.zhang. A note on the homogeneous balance method.( Physics letter 1998)

[4] A.Nikolai, B.N.Loguinova. Extended simplest equation method for non-linear differential equations (Applied Mathematics and computer 2008)

Abstract: Heat and mass transfer characteristics of MHD forced convection flow over a non-isothermal stretching sheet embedded in a porous medium subjected to a heat source is investigated numerically by taking into account the Soret and Dufour effects. The velocity, temperature and concentration profiles are drawn for various values of permeability parameter, heat source parameter, magnetic field parameter, Soret and Dufour numbers, thermal stratification parameter. Numerical results of rate of flow, heat and mass transfer for different parameters are presented in tabular form and the results are depicted graphically.

Keywords: Chemical reaction, heat and mass transfer, heat source, magnetic field, Soret and Dufour effects, thermal stratification.

[1] M. A. Seddeek and A. A. Almushigeh, "Effects of radiation and variable viscosity on MHD free convective flow and mass transfer over a stretching sheet with chemical reaction," Applied Mathematics and Computation, 5(1), 2010, 181–197.

[2] R. Kandasamy, T. Hayat, and S. Obaidat, "Group theory trans-formation for Soret and Dufour effects on free convective heat and mass transfer with thermophoresis and chemical reaction over a porous stretching surface in the presence of heat source/sink," Nuclear Engineering and Design, 241(6), 2011, 2155–2161.

[3] D. Pal and B. Talukdar, "Combined effects of Joule heating and chemical reaction on unsteady magnetohydrodynamic mixed convection of a viscous dissipating fluid over a vertical plate in porous media with thermal radiation," Mathematical and Computer Modelling, 54(11-12), 2011,.3016–3036.

[4] A.A.Joneidi, G.Domairry,and M.Babaelahi, "Analytical treatment of MHD free convective flow and mass transfer over a stretching sheet with chemical reaction," Journal of the Taiwan Institute of Chemical Engineers, 41(1), 2010, 35–43.

[5] S.P.Anjalidevi and R.Kandasamy, "Effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate," Heat and Mass Transfer, 35(6), 1999, 465–467.

Abstract:A group is a nonempty set equipped with one binary operation satisfying contain axioms while a ring is an algebraic structure with two binary operations namely addition and multiplication. We have tried to discuss Prime ideals, radical of rings and M-system in this paper.
Keywords: Prime ideals, m-system, Semi-prime ideal, n-system, Prime radical of the ring.

[1] Howard H.Mitchell,Proof that certain Ideals in a Cyclotomic Realm are Principal Ideals,Transactions of the American Mathematical Society, Vol.19,No.2 (Apr, 1918) pp:119-126, American Mathematical Society. [2] R.A. Dean,-Elements of Abstract Algebra, John Wiley and Sons, Inc , Newyork and LONDON. [3] Neal H. Mccoy ,-The Theory of Rings, The Macmollan Company, Newyork,LONDON. [4] H.Paley and P.M Weichsel, -A first course in Abstract Algebra, Holt,Rinehart and Winston, Inc. [5] P.F.Smith, Rings with Every Proper Images a Principal Ideal Rings,Proceedings of the American Mathematical Society, Vol.81, No.3 (Mar 1981). PP:347-352, American Mathematical Society.

Abstract: This study investigated the relationship between average personal income and genetic factors in Abia State University Teaching Hospital, Aba. The data for the study was a secondary data which constitute a sample of 500 patients. The data was observed to be normally distributed. The basic assumptions underlying the classical linear regression model which includes multi-co-linearity, autocorrelation and hetroscedasticity was verified and a linear regression model of average personal income and genetic factors was fitted. In conclusion, it was recommended for the general public to be enlightened on their average income management and the adverse health effect emanating from genetic factors so as to maintain a healthy living.

Keywords: Average personal income, Genetic factors, Multiple Regression Model and Hetroscedasticity

[1]. Adler, N. E., Boyce, T., Chesney, M. A., Cohen, S., Folkman, S., Kahn, R. L., and Syme, S. L. (1994). Socioeconomic status and health. Am. Psychol. Pp.49:15-24.
[2]. Singer, B. H., and Ryff, C. D. (1999). Hierarchies of life histories and associated risks. In N. E. Adler, M. Marmot, B. S. McEwen and J. Stewart (eds.), Socioeconomic Status and Health in Industrial Nations. New York: New York Academy of Sciences, pp. 96-115.
[3]. Adler, N. E., and Snibbe, A. C. (2003). The role of psychosocial processes in explaining The gradient between socioeconomic status and health. Curr. Directions Psychol. Sci. 12(4), 119-123.
[4]. 4. Stevens, J.,Cai,J., Pamuk, E.R.,Willamson,D.F.,Thun, M.J and wood,J.L.(1998). The effect of age on the association between body mass index and mortality.
[5]. New England Journal of Medicine. Pp.338. (1):1-7
[6]. Naidia, A.N., Neela, J. and Rai, N.P. (2009), maternal body mass index and birth weight.
[7]. Nutrition News, National Institute of Nutrition, Hyderabad. Pp12 (2):12-132

Abstract:The main aim of this paper is to present a new extension of Mittag-Leffler functions using extended Beta function. We derive several Integral representations and differentiation formulas for this new extended Mittag- Leffler function. Further, we establish Mellin transform of these functions in terms of Wright generalized hypergeometric functions.

Keywords: Mittag-Leffler function, extended Beta function, Mellin transform, Wright generalized hypergeometric functions

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(1997).
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Applied Mathematics and Computation, Vol. 159, No. 2, 589-602 (2004).
[3]. Lee, D.M, Rathie, A.K., Parmar, R.K. and Kim, Y.S., Generalization of extended beta function, hpergeometric and confluent
hpyergeometric functions, Honman Mathematical J., 33 (2), 187-206. (2011).
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[5]. Özarslan, M.A., and Yilmaz, B., The extended Mittag-Leffler function and its properties, Journal of Inequalities and Applications,
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