iosr-Jm   Volume-10 ~ Issue-2 ~ Mar-Apr 2014

Abstract: The concept of fuzzy sub ℓ-ternary near ring of a ℓ-ternary near ring and some examples are presented. Some of their properties are derived.
Keywords: Fuzzy subset, ℓ-ternary near ring, Fuzzy sub ℓ-ternary near ring.

[1] S.Abou Zaid, On fuzzy sub near rings and ideals, Fuzzy Sets and Systems, 44(1991), No.1 139-146.
[2] G. Birkhoff, On the Lattice Theory of Ideals, Bull. Amer. Society, 40(1934), 613-619.
[3] T.K. Dutta and S. Kar, A Note on Regular Ternary Semirings, Kyungpook Math, Vol.46, No.3,(2006), 357-365.
[4] George Gratzer, General Lattice Theory, Birkhauser Verlag, 1978.
[5] Kavikumar, Azme Khamis and Young Bae Jun, World Academy of science, Engineering Technology, 31(2009).

Abstract: In this paper, deals with the two a single server vocation queueing model with feed back. In which the server provides two types of service and each arriving customer has the option of choosing either type is studied.
Keywords: Pn(1) , Pn(2) , Vn , Wq, Lq , λ, t.

[1]. Choudhury , G., (2003). Some aspects of an M/G/1 queueing system with optional second service, TOP, 11, 141-150.
[2]. Thangaraj, V.and Vanitha, S. (2009). A two phase M/G/1 feedback queue with multiple server vacation , Stochastic Analysis and
Applications , 27, 1231-1245.
[3]. Krishnakumar, B., Vijayakumar, A.and Arivudainambi,D., (2002).An M/G/1 retrial queueing system with two phase service and
preemptive resume, Annals of Operations Research , 113,61-79.
[4]. Jewkes, E.M. and Buzacott, J.A., (1991). Flow time distributions in a K class M/G/1 spriority feedback queue, queueing systems, 8,
183-202.
[5]. Thangaraj,V.and Vanitha, S., (2010). A single server M/G/1 feedback queue with two types of service having general distribution,
international Mathematical Forum,1,15-33.

Abstract: The purpose of this paper is to define the notion of an interval valued Intuitionistic Fuzzy R-ideal (briefly, an i-v IF R-ideal) of a BCI – algebra. Necessary and sufficient conditions for an i-v Intuitionistic Fuzzy R-ideal are stated. Cartesian product of i-v Fuzzy ideals are discussed.

[1]. K.T Atanassov, intuitionisticfuzzy sets and systems, 20(1986), 87-96
[2]. K.T Atanassov, intuitionisticfuzzy sets. Theory and applications, studies in fuzziness and soft computing, 35.Heidelberg; physica-verlag
[3]. R.Biswas, Rosenfeld's fuzzy subgroups with interval-valued membership functions, fuzzy sets and systems 63(1994), no.1,87-90
[4]. S.M. Hong, Y.B.Kim and G.I.Kim, fuzzy BCI-sub algebras with interval-valued membership functions, math japonica, 40(2)(1993)199-202

Abstract: In this paper, we obtain a new version of the proof of n1 n and the Legendre duplicating formulas for positive integer n, by using a simple analytical technique

Key words: gamma function, factorial and Legendre duplicating formulas

[1] Askey, R. A.; Roy, R. (2010), "Gamma function", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F. et al., NIST
Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0521192255, MR2723248
[2] James D. Bonnar, The Gamma Function. CreateSpace Publishing, Seattle, 2010. ISBN 978-1463694296. A thorough and systematic
book devoted entirely to the subject of the gamma function.
[3] Nico M. Temme, "Special Functions: An Introduction to the Classical Functions of Mathematical Physics", John Wiley & Sons,
New York, ISBN 0-471-11313-1,1996.
[4] Okunuga A. Solomon, "Differential Equation: Topic on special function", WIM publications, Lagos Nigeria, ISBN 978-36375-5-3,
2008

Abstract: In this paper, we obtain a further refinement of Van der Corput's inequality using an analytical technique.

Key words and phrases: Refinement, Van der Corput's inequality, Harmonic number.

[1]. B. Ch. Yang, 1 (2005), On an extension and a refinement of Van der Corput's inquality, Chinese Quart. J. Math, 22, 5 pages
[2]. Da-Wei Niu, J. Cao and Feng Qi, A refinement of van der Corput's inequality, J. Inequal. Pure Appl. Math. 7 (2006), no. 4, Article
127; Available online at http://www.emis.de/journals/JIPAM/article744.html.
[3]. J Cao, Da-Wei Niu and Feng Qi, An extension and a refinement of van der Corput's inequality, Internat. J. Math. Math. Sci. 2006
(2006), Article ID 70786, 10 pages; Available online at http://dx.doi.org/10.1155/IJMMS/2006/70786
[4]. F. Qi, J. Cao, and D.-W. Niu, A generalization of van der Corput's inequality, RGMIA Res. Rep. Coll. 10 (2007), Suppl., Article 5;
Available online at http://rgmia.org/v10(E).php.

Abstract: An asymptotic analysis of an unsteady hydromagnetic boundary layer flow of an incompressible viscous conducting fluid with uniform distribution of dust particle bounded by semi-infinite plate in the presence of exponential decaying pressure gradient is investigated. The exact solutions of the boundary layer equations are obtained by asymptotic behaviour of Laplace transform treatment. The structure of velocity distribution is investigated and the effect of various physical parameters likes magnetic parameter, Ekman parameter and Hall current parameter on velocities of both fluid and dust phase are depicted graphically.

[1]. R.Tiwari and Kamal Singh, Effect of Hall current on unsteady hydromagnetic boundary layer in rotating dusty fluid, Indian J. Pure
appl. Math., 14(1) (1983) 159-165.
[2]. D.R.V. Prasada Rao and D.V.Krishna , Hall effect on unsteady hydromagnetic flow , Indian J. Pure appl. Math., 12(2) (1981) 270-
276.
[3]. Debnath.L, Effect of Hall current on unsteady Hydromagnetic flow past a porous plate in a rotating fluid system, ZAMM, 59 (1979)
469.
[4]. Oberhettinger,F. and Badii, Table of Laplace Transforms, Spinger-Verlag,Berlin, (1973).

Abstract: In this paper, concepts of smooth topology and fuzzy metric space have been introduced. We define smooth Hausdroff space and so fuzzy open ball in fuzzy metric space to get the smooth topological space which is called induced smooth topological space then we proved this fuzzy metric is smooth Hausdroof space.

[1]. C. Hua Yan, S. Zhang Guo, I-Fuzzy Topological Groups, Fuzzy Sets and Systems, V.161 (2010) 2166–2180.
[2]. H. Yia Li, F. Gui Shi, Some Separation Axioms in I-Fuzzy topological spaces, Fuzzy sets and Systems, V.159 (2008) 573-587.
[3]. H. J. Zimmermann, Fuzzy set theory and its applications, K. Nijhoff, (1985), 29.
[4]. M. Demirci, Three Topological Structure of Smooth Topological Spaces, Fuzzy Sets and Systems, V.101 (1991), 185-190.
[5]. N. Kabir, Sh. Ghasemzadeh, Separable Fuzzy Metric Spaces, Mathematical Sciences, V.3, No.1 (2009) 55-62.

Abstract: The effect of hall current onan unsteady magnetohydrodynamic flow of heat and mass transfer of an electrically conducting incompressible fluid along an infinite vertical porous plate in presence ofthermal radiation, viscous dissipationand chemical reaction has been studied.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 dimensionless governing coupled,

[1]. Abdul Maleque, Kh. and Abdur Sattar, Md., 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, 48, 4460 – 4466.
[2]. Ajay Kumar Singh, 2003. MHD Free – convection and Mass Transfer Flow with Hall Current Viscous Dissipation, Joule Heating
and Thermal Diffusion, Indian Journal of Pure and Applied Physics, 41, 24 – 35.
[3]. Anand Rao, J. and Srinivasa Raju, R., 2010. Applied Magnetic Field on Transient Free Convective Flow of an Incompressible
Viscous Dissipative Fluid in a Vertical Channel, Journal of Energy, Heat and Mass Transfer, 32, 265 – 277.
[4]. Anjali Devi, S. P., Shailendhra, K., and Hemamalini, P. T., 2011. Pulsated convective MHD flow with Hall current, heat source
and viscous dissipation along a vertical porous plate, Int. J. of App. Math. and Computation, 3(2), 141–150.
[5]. Atul Kumar Singh, Ajay Kumar Singh and N. P. Singh, N. P., 2005. Hydromagnetic free convection and Mass transfer flow with
Joule heating, thermal diffusion, Heat source and Hall current, Bulletin of the Institute of mathematics academia sinica, 33(3),
291 – 310.

Abstract: The aim of the present paper is to study the oscillatory motion of a conducting visco-elastic Oldroyd liquid of second order between two parallel flat plates under the influence of an uniform magnetic field applied perpendicularly to the flat plates. Both the plates are considered to be oscillating harmonically with different amplitudes and different frequencies. Some particular cases have also been discussed in detail. Keywords: Magnetic field, MHD, Non-Newtonian fluid, Oldroyd fluid of second order, Visco-elastic fluid.

[1]. Ferraro,V. C. A. and Plumpton, C. (1966): Magneto fluid mechanics, Larendon press, Oxford, London.
[2]. Pai, S. L. (1962): Magneto hydrodynamics and Plasma Dynamics, Prentice Hall London.
[3]. Shercliff, J. A. (1965): A Text Book of Magneto hydrodynamics, Pergamon, Press.
[4]. Sutton, G. W. and Sherman, A. (1965): Engineering Magneto hydrodynamics, Mc. Graw Hill Book Company.
[5]. Jefferey, A. (1966): Magneto hydrodynamics, Oliver and Boyd, Edinbergh and London, Newyark.

Abstract: We present a paper on the numerical analysis of a power-law fluid flow on a moving wall. We investigate the steady boundary-layer flow of a non-Newtonian fluid, represented by a power-law model over a moving flat plate . The governing partial differential equation is transformed into ordinary differential equation through a similarity variable. The finite difference method is employed to obtain solution of the non-linear problem. We investigate the effect of the power-law viscosity index n, and the results obtained are discussed.

Keywords: Steady boundary-layer flow; Moving plate; Non – Newtonian power- law fluid and Finite difference method.

[1] Abdelhafez,T.A;1985.Skin friction and heat transfer on a continuous flat surface moving in a parallel stream.Int.J.Heat Mass Transfer 28,pp.1234-1237.
[2] Abel,M.S;P.G.Siddheshwar and N.Mahesha,2009.Effects of thermal buoyancy and variable thermal conductivity on the MHD flow and heat transfer in a power-law fluid past a vertical stretching sheet in the presence of a non-uniform heat source.Int.J.Non-Linear Mech.44,pp.1-12.
[3] Afzal,N;A.Badaruddin and A.A.Elgarvi,1993.Momentum and transport on a continuous flat surface moving in a parallel stream.Int.J.Heat Mass Transfer 36,pp.3399-3403.
[4] Andersson,H.I.and F.Irgens,1990.Film flow of power-law fluids.In:Encyclopedia of Fluid Mechanics,Vol.9,Polymer Flow Engineering(N.P.Cheremissinoff,ed.).Gulf Publishing ,Houston.

Abstract: Binary and prime fields are being considered for practical implementation on both Elliptic and Hyperelliptic curves for software curve implementation. The main operations like scalar multiplication and group operations are compared in both hyperelliptic and elliptic cryptography. ECC and HECC are implemented on different binary fields and also compare the encryption and decryption system in discrete logarithmic problem.

[1]. Darrel Hankerson, Alfred Menezes, Scott Vanstone, 2004. "Guide to elliptic curve cryptography" Springer publication, ISBN 0-387-95273-X.
[2]. Henry Cohen and Gerhard Frey, 2006. "Handbook of Elliptic and Hyperelliptic Curve Cryptography", Chapman and Hall/CRC press.
[3]. Kakali Chatterjee, Daya Gupta, 2009. "Secure access of smart cards using elliptic curve cryptosystem", Wicom, IEEE catlog No. CFPO9WNM-CDR.
[4]. Tanja Lange, 2005. "Formula for Arithmetic on Genus 2 hyperelliptic curves" Applicable Algebra in Engineering and Computing, Volume 15.
[5]. P. Longa, Catherine Gebotys, 2009. "Novel precomputation Schemes for elliptic Curve Cryptosystems", ACNS, LNCS vol-5536, pp:71-88.
[6]. Kakali Chatterjee, Asok De, Daya Gupta, 2011. "Software implementation of Curve based Cryptography for constrained Devices. Volume 24 – No.5, June 2011.

Abstract: In this paper, we discuss a mulit dimensional stochastic differential equation model where the underlying stochastic process is a jump-diffusion process. The stochastic differential equation is represented as a Partial Integro Differential Equation(PIDE) using the Fokker Planck equation. The solution of the PIDE is obtained by the method of finite differences. The consistency, the convergence of the solution and the stability of the finite difference scheme are discussed.

[1]. .Cont & Ekaterina Voltchkova,"A finite difference scheme for option pricing in jump diffusion and exponential Levy models", Rapport Interne CMAP No., 513,(Sep2003).
[2]. David G.Feingold & .S.Varga, " Block diagonally dominant matrices and generalizations of the Gerschgorin circle theorem", Pacific J.of mathematics, vol 12 no. 4 (1962).
[3]. Oskendal.B,"Stochastic differential equations- an introduction with applications", 5th ed, Springer Verlag (2000).
[4]. A.K.Pani et al, "Numerical methods for hyperbolic and parabolic integro-differential equations", J.of integral equations and applications, vol 4 (4) 533-584, (summer 1992).
[5]. F.B.Hanson, " Applied stochastic processes and control for jump diffusions-modelling, analysis and computations", SIAM (2007).

Abstract: In this paper we introduce intuitionistic fuzzy contra regular weakly generalized open mappings and intuitionistic fuzzy contra regular weakly generalized closed mappings. We investigate some of their properties.

Keywords: Intuitionistic fuzzy topology, intuitionistic fuzzy regular weakly generalized closed mappings and intuitionistic fuzzy regular weakly generalized open mappings intuitionistic fuzzy contra regular weakly generalized closed mappings and intuitionistic fuzzy contra regular weakly generalized open mappings..

[1]. K.T.Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986), 87-96.
[2]. C.L.Chang, Fuzzy topological spaces, J.Math.Anal.Appl, 24(1968), 182-190.
[3]. D.Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy sets and systems, 88(1997), 81-89.
[4]. Joung Kon Jeon, Young Bae Jun and Jin Han Park, Intuitionistic fuzzy alpha continuity and intuitionistic fuzzy pre continuity, International journal of Mathematics and Mathematical Sciences, (2005), 3091-3101.