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

Abstract:In this paper we introduce some continuous and irresolute maps called

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Abstract: Recently,we introduced "An unification of certain generalized Geometric polynomial Set T n (x1,x2,x3,x4) ,with the help of generating function which contains Appell function of four variables in the notation of Burchnall and Choundy [4] associated with Lauricella function. This generated hypergeometric polynomial Set covers as many as thirty four orthogonal and non -orthogonal
polynomials.In the present paper an attempt has been made to express a Triple finite integral representation of the polynomial set T n (x1,x2,x3,x4).
Key words:-Appell function, Lauricella form, Generalized hypergeometric polynomial.

[1]. Agarwal, R.P. (1965):An extension of Meijer's G-function, Proc. Nat. Institute Sci. India, 31, a, 536-546.
[2]. Abdul Halim, N and:A characterization of Laguerre polynomials,
AI_Salam, W.A. (1964) Rend, Sem, Univ., padova, 34,176 -179.
[3]. Agarwal, B.D. and:On a multivariate polynomials system

Abstract: This paper is concerned with the determination of temperature and displacement of a half space bounding surface due to thermal shock. This paper deals with the place boundary of the half-space is free of stress and is subjected to a thermal shock. Moreover , the perturbation method is employed with the thermoelastic coupling facter ԑ as the perturbation parameter. The Laplace transform and its inverse with very small thermoelastic coupling facter ԑ are used. The deformation field is obtained for small values of time. 𝑃𝑎𝑟𝑖𝑎 7 has formulated different types of thermal boundary condition problems.

[1] ATKINSON,K.E.(1976); A survey of Numerical Methods for the solution of Fredholm-Integral Equation of the Second – Kind Society of Industial and applied Mathematics, Philadelphia,Pa.

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[3] SNEDDON,I.N.(1972); The Use of Integral Transform, McGraw Hill, New-York. [4] SOKOLNIKOFF, I.S. (1956); Mathematical theory of Elasticity, McGraw Hill Book Co.

[5] WASTON, G.N. (1978); A Treatise on the Theory of Bessel Functions, 2nd Edn.C.U.P.

[6] NOWACKI, W. (1986); Thermoelasticity, 2nd End. Pergamon Press.

Abstract:The aim of this research paper was to derive the value of, and analyze π using purely basic geometrical and trigonometric methods. The derivation has been proposed after studying regular polygons and observing the similarity of an infinite sided regular polygon with a circle. Several test cases with the formula derived have been checked to verify this derivation and apart from raw calculation of data, an alternate verification using calculus has also been shown. Keywords: Pi, Regular Polygons, Geometrical Derivation.

[1]. Archimedes; http://itech.fgcu.edu/faculty/clindsey/mhf4404/archimedes/archimedes.html [2]. Archimedes; Little Heath, Sir Thomas; (2002). The Works of Archimedes. Courier Corporation. ISBN - 0-486-42084-1.

Abstract: In the present paper we have formulated the renal blood flow along the capillaries in case of renal disease Diabetes . keeping in the view the nature of renal circulatory system in human body. P.N.Pandey and V.Upadhyay have considered the blood flow has two phased one of which is that of red blood cells and other is plasma. According to Fahreaus-Lindqvist effect the blood flow in two separated layers while passing through capillaries. The plasma layer which flows along the surface of the capillaries contains almost no blood cells. The second layer the core layer containing blood cells which flows in plasma along the axis of capillary. We have collected a clinical data in case of Diabetes for hematocrit v/s blood pressure. The graphical presentation for particular parametric value is much closed to the clinical observation.

[1]. International journal of innovative Research in electrical , Electronic , Instrumentation and Control Engg. Vol.-1st, Issue-1 2013
[2] Cotran , RS S ; Kumar , Cotran, RS S.; Kumar, Vinay; Fausto, Nelson; Robbins, Stanley L.; Abbas, Abul K. (2005). Robbins and
Cotran pathologic basis of disease. St. Louis, MO: Elsevier Saunders.ISBN 0-7216-0187-1.
[3]. Cotran , RS S ; kumar , VInay, Fausto ,Nelson ; Robins , Stanley L.; Abbas Abdul K (2005) Robbins and Catron Pathologic basis of
disease .St. Louis , MO ; Elsevier Saunders .ISBN 0-7216-0187-1
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,1992, 21-43
[5]. Madsen KM , Tisher CC . Anotomy of kidney . In Brenner BM ,ed. Brenner and Rector's .The kidney , 7th ed. Vol.-1Pheladelphia
:Saunders, 2004,3-72

Abstract:In this paper we have indicated and analyzed a mathematical model of unemployment. In this nonlinear mathematical model we focused on three dynamic variables (i) Number of unemployed persons ,(ii) Number of employed persons and (iii) Number of newly created vacancies by intermediation of government and private sector. We assumed the situation that unemployed persons are also trying for their independent work and create chances for self employment. We studied stability of equilibrium point of the model. Numerical simulation is also given to compare with analytical result.
Keywords: dynamic variables, employed person, self employment, Unemployed person.

[1] C.V.Nikolopoulos, DE Tzanetis, A model for housing allocation of a homeless population due to natural disaster, Nonlinear Anal.4,2003,pp.561-579.

[2] A.K.Misra, A.K.Singh, A mathematical model for unemployment, IJTPC 4,2013 pp.2322-3138.

[3] A.K.Misra, A.K.Singh, A Delay mathematical model for the control of unemployment , Differ Equ Dyn Syst 21(3), 2013,pp.291-307. [4] N. Sirghi, M.Neamtu , Deterministic and stochastic advertising diffusion model With delay, WSEAS Transaction on system and control, 4(8), 2013,pp. 141-150.

[5] M. Neamtu, M.Pirtea, G. Mircea, D. Opris, Stochastic , Fuzzy, Hybrid delayed Dynamics Heterogeneous competitions with Product Differentiation, WSEAS Transaction on mathematics , 7(9), 2010, pp.581-591.

[6] M.Neamtu, A dynamic model for unemployment control with migration and distributed delay, Mathematical Methods in finance and business Administration,Proceeding of the International Business Administration conference, Tenerife, Spain, 1,2014, pp.23-31.

Abstract: The linear and weakly non-linear stability analyses of double diffusive electro-convention in a micropolar fluid layer heated and saluted from below and cooled from above is studied. The linear and non-linear analyses are, respectively based on normal mode technique and truncated representation of Fourier series. The influence of various parameters on the onset of convection has been analyzed in the linear case. The resulting autonomous Lorenz model obtained in non-linear analysis is solved numerically to quantify the heat and mass transforms through Nusselt and Sherwood number. It is observed that the increase in concentration of suspended particles and electric field and electric Rayleigh number increases the heat and mass transfer.
Keywords: Double diffusive convection, Micropolar fluid, Electro-convection, autonomous Lorenz model and Nusselt and Sherwood number.

1]. Ahmadi G (1976). Stability of micropolar fluid layer heated from below. International Journal of Engineering Science14, pp. 81-85.
[2]. Bhadauria BS and Palle Kiran (2014). Weak nonlinear double-diffusive magnetoconvection in a newtonian liquid under temperature modulation. International Journal of Engineering Mathematics, pp. 1-11.
[3]. Bhattacharya SP and Jena SK (1983).On the stability of hot layer of micropolar fluid.International Journal of Engineering Science21(9), pp. 1019-1024.
[4]. Chandrasekhar S (1961). Hydrodynamic and hydromagnetic stability. Oxford: Clarendon Press.
[5]. Datta AB and Sastry VUK (1976). Thermal instability of a horizontal layer of micropolar fluid heated from below. International Journal of Engineering Science14(7), pp. 631-637.
[6]. Eringen AC (1964). Simple microfluids. International Journal of Engineering Science2(2), pp. 205-217.

Abstract:Regular Convolutions Care progressions in one – to – one correspondence with sequences   p p P  of decompositions of N into arithmetical progressions (finite or infinite)and this is represented by writing C    p p P
 . In this paper we proved that any regular convolution C gives rise to a structure of meet semilattice on  ,  C  Z  and the convolution C is completely characterized by certain lattice theoretic properties of  ,  . C  Z  In particular we prove that the only regular convolution including a lattice structure on  ,  C  Z  is the Dirichlit's convolution.
Key words: convolution , Dirichlit's convolution, arithmetical progressions, relation isomorphism

[1]. G.Birkhoff. Lattice Theory, American Mathematical Society, 1967.
[2]. E.Cohen, Arithmetical functions associated with the unitary divisors of an integer, Math.Z.,74,66-80.1960.
[3]. B.A.Davey and H.A.Priestly, Introduction to lattices and order, Cambridge University Press,2002.
[4]. G.A.Gratzer. General Lattice Theory,Birkhauser,1971.
[5]. W.Narkiewicz, On a class of arithmetical convolutions,Colloq.Math., 10,81-94,1963.
[6]. U.M. Swamy andSagiSanker , Partial orders induced by convolutions, international Journal of mathematics and soft computing ,
2(1), 2011.

Abstract: We show, if thenormsof k S areuniformly boundedon   n p l for a bounded   n p if and onlyifthereexists
𝑟, 1 ≤ 𝑟 < ∞,such thatthenormsin   n p l andtheclassical space r l are equivalent. A "pointwise-bounded" family of continuous linear operators from a Banach space to a normed space is "Uniformly bounded." Stated another way, let𝑋 be a Banach space and 𝑌 be a normed space. If 𝒜 is a collection of bounded linear mappings of 𝑋 into 𝑌 such that for each𝑥𝜖𝑋, 𝑠𝑢𝑝 𝐴𝑥 ; 𝐴 ∈ 𝒜 < ∞, then𝑠𝑢𝑝 𝐴 : 𝐴 ∈ 𝒜 < ∞.

Keywords: Banach space, characteristicfunction, linear mappings,Uniformly bounded.

[1] O. KOVÁČIK AND J. RÁKOSNÍK, On spaces l p x and Wk,p x , Czechoslovak Math. J., 41 (1996), 167-177.
[2] D.E. EDMUNDS AND A. NEKVINDA, Averaging operators on l pn and Lp x , Math. Inequal. Appl., Zagreb (2002), 235-
246.
[3] ALES NAKVINDA, EQUIVALENCE OF
  n p
l NORMS AND SHIFT OPERATORS, Math. Inequal.& Applications, Zagreb
(2002), 711-723.
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Abstract:Som [11 ] establishes a common fixed point theorem for R-weakly Commuting mappings in a Fuzzy metric space.The object of this Paper is to prove some fixed point theorems for occasionally Weakly compatible mappings by improving the condition of Som[11 ].

Keywords: Common fixed point ,Fuzzy metric space, Compatible maps, Occasionally weakly compatible mappings

[1] Balasubramaniam P , Muralishankar S and Pant R P , Common fixed point P Of four mappings in a fuzzy metric space ,J.Fuzzy Math.,10(2002),379.

[2] Cho, Y.J.,Fixed point in fuzzy metric space ,J. Fuzzy Math.5 (1997),949-962.

[3] Cho, Y.J.,Pathak ,H.K.,Kang,S.M.,J.S.,Common fixed point of compatible Mapping of type (β) on Fuzzy metric space, Fuzzy Sets and Systems, 93(1998),99-111.

[4 ] George A and Veeramani P , On some results in fuzzy metric space ,Fuzzy Sets and systems,64(1994),395.

[5] Grabiec G ,Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems,27(1998),385.

[6] Jain ,A.,Badshah ,V.H. and Prasad, S.K., Fixed Point theorems in Fuzzy Mertic space for Semi Compatible Mappings, Intrenational Journal of Research and Reviews in Applied Sciences,12(2012),523-526.

Abstract: An analysis is carried out to study the MHD steady two-dimensional stagnation-point flow and heat transfer from a warm, laminar liquid flow to a melting stretching sheet. The governing partial differential equations are transformed into ordinary differential equations by similarity transformation, before being solved numerically using Runge-Kutta-Fehlberg method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. Effects of the Magnetic parameter, melting parameter, stretching parameter and prandtl number on the flow and heat transfer characteristics are thoroughly examined.

Key Words: Laminar boundary layer; MHD; Runge-Kutta-Fehlberg method;Stagnation point; Prandtl Number; Nusselt number..

[1] B.C. Sakiadis, Boundary layer behavior on continuous solid surfaces: I Boundary layer equations for two dimensional and
axisymmetric flow, AIChE J. 7 (1961) 26–28.
[2] I.C. Liu, Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to a transverse
magnetic field, Int. J. Heat Mass Transfer 47 (2004) 4427–4437.
[3] S.K. Khan, M. Subhas Abel, M. Sonth Ravi, Viscoelastic MHD flow heat and mass transfer over a porous stretching sheet with
dissipation of energy and stress work, Int. J. Heat Mass Transfer 40 (2003) 47–57.
[4] R. Cortell, Effects of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a viscoelastic fluid
over a stretching sheet, Phys. Lett. A 357 (2006) 298–305.
[5] B.S. Dandapat, B. Santra, K. Vajravelu, The effects of variable fluid properties And thermo capillarity on the flow of a thin film on
an unsteady stretching sheet, Int. J. Heat Mass Transfer 50 (2007) 991–996.
[6] S. Nadeem, A. Hussain, M. Khan, HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching
sheet, Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 475–481.

Abstract: In this paper, the variational iteration method (VIM) is used to get an approximate solution for a system of two coupled nonlinear ordinary differential equations which represent the concentrations of carbon dioxide 𝐶𝑂2 and phenyl glycidyl ether. In this system there are boundary conditions of Dirichlet type and the other is a mixed set of Neumann and Dirichlet type. Our calculations evidenced by tables and figures for the analysis of the maximal error remainder values.

[1] S. Inoue and N. Amazaki, In organic and bioorganic chemistry of carbon dioxide (Eds., Ko-dansha Ltd.,Tokyo, 1982).
[2] S. Muthukaruppan, I. Krishnaperumal, R. Lakshmanan, Theoretical analysis of mass transfer with chemical reaction using absorption of carbon dioxide into phenyl glycidyl ether solution, Appl. Math., 3, 2012, 1179–1186.
[3] Y.S. Choe, S.W. Park, D.W. Park, K.J. Oh, S.S. Kim, Reaction kinetics of carbon dioxide with phenyl glycidyl ether by TEA–CP–MS41 catalyst, J. Jpn. Petrol. Inst., 53, 2010, 160–166.
[4] S.W. Park, D.W. Park, T.Y. Kim, M.Y. Park, K.J. Oh, Chemical kinetics of the reaction between carbon dioxide and phenyl glycidyl ether using aliquat 336 as a catalyst, Catal. Today, 98, 2004, 493–498.
[5] Y.S. Choe, K.J. Oh, M.C. Kim, S.W. Park, Chemical absorption of carbon dioxide into phenyl glycidy ether solution containing THA–CP–MS41 catalyst, Korean J. Chem. Eng., 27, 2010, 1868–1875.
[6] J.H. He, Variational iteration method for delay differential equations, Commun. Nonlinear Sci. Numer. Simul., 2 (4), 1997, 235-236.

Abstract:The objective of this paper is to study the Soret and Dufour effects on the free convection boundary layer flow of an incompressible, viscous and chemically reacting fluid over a vertical plate in the presence of viscous dissipation. The governing partial differential equations are converted to a set of ordinary differential equations using suitable similarity transformations. The resulting equations are solved analytically using homotopy analysis method (HAM). The convergence of obtained analytical solutions is explicitly discussed. The effects of various parameters on dimensionless velocity, temperature and concentration profiles are discussed
with the help of graphs. The numerical values of skin friction, Nusselt number and Sherwood number for different parameters are presented in tabular form. Our results are compared with the previously published results and are found to be in good agreement.
Keywords: Soret and Dufour effects, viscous dissipation, HAM.

[1] K. A. Helmy, MHD unsteady free convection flow past a vertical porous plate, Zeitschrift für Angewandte Mathematik und
Mechanik, 78 (4), 255-270, 1998.
[2] E. M. A. Elabashbeshy, Heat and mass transfer along a vertical plate with variable temperature and concentration in the presence of
magnetic field, International Journal of Engineering Science, 34 (5), 512-522, 1997.
[3] V. Prasad, F. A. Kulacki, M. Keyhani, Natural convection in porous media, Journal of Fluid Mechanics, 150, 89-119, 1985.
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vertical porous plate with constant heat flux, Journal of Energy Heat and Mass Transfer, 62 (9), 489-491, 1982.
[5] O. D. Makinde, Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate, International
Communications in Heat and Mass Transfer, 32 (10), 1411-1419, 2005.
[6] T. Hymavathi, B. Shankar, A quasilinearization approach to heat transfer in MHD visco-elastic fluid flow, Applied Mathematics
and Computation, 215 (6), 2045-2054, 2009.

Abstract: In this paper we investigate the effect of hall current on an unsteady magnetohydrodynamic free convective flow along a vertical porous plate with thermal radiation. The dimensionless governing coupled, non-linear boundary layer partial differential equations are solved by an efficient finite element method for velocity, temperature, concentration field and also the expression for shearing stress, Nusselt number and Sherwood number are obtained. The effect of thermal Grashof Number, solutal Grashof Number, Transpiration cooling parameter, Prandtl Number, Schmidt Number, Hartmann number, Thermal radiation parameter, Eckert number and Hall parameter on the flow field are shown through graphs and tables.

Key words: Hall current, Unsteady, MHD, Thermal radiation, FEM.

[1]. Abdul Maleque, Kh and Abdur Sattar, Md, 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, 2005, 4460 – 4466.
[2]. Ajay Kumar Singh, 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, 2003,24 – 35.
[3]. Anand Rao, J. and Srinivasa Raju, R, 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, 32,2010, 265 – 277.
[4]. Anjali Devi, S. P., Shailendhra, K., and Hemamalini, P. T, 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), 2011, 141–150.
[5]. Atul Kumar Singh, Ajay Kumar Singh and N. P. Singh, N. P, 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), 2005, 291 – 310..