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Abstract:

In this paper, it is proved that the notions of point wise semi-continuity and quasicontinuity are the same even when the mapping is not globally semi-continuity. The concept of removable quasicontinuity at a point is introdeced with some of its applications [Theorem 4.1]. Finally, a set of sufficient conditions for a topological space to be a Baire space is formulated. In particular, it was shown that if every mappimg from a topological space X to an infinite T2 space is quasicontinuity  then X is a Baire space.

Keywords:

baire space,topological space,quasicontinuity,

Refference:

I.  Biswas, N. Atti Accad. Naz. Lincei. Sci.Fis. Mat. Natur. Series 8. Vol 48(1970), 399

II. Crossely, S.G. and Hildebra, S.K. Texas J. Sci.22(1971), 99-112.

III. Das, P. Prgr. M.M., Vol.2, No.1(1973),33-34.

IV.Das , P.I.J.M.M., Vol.2,No.1(1974),31-44

V. Dasgupta, H. and Lahiri, B.K. Acta Ciencia Indica. Vol.XII m No.1(1986),35-39.

VII. Ghose, S.R. and dasgupta, H.Bull.Cal.Math.Soc.97(2005),(4),283-296.

VIII. Halfer, E.Proc. Amer. Math.Soc. 11(1960), 688-691.

IX. Husain, T.Prace, Mathematyczne.10(1966),1-7.

X. Kuratowski, K. Topology, Academic Press. Vol1,1966.

XI. Levine, N. Amer.Math.Monthly.70(1963),36-41.

XII. Lin, S-Y.T. and Lin, Y-F.T. Canad. Bull.21 (1978), 183-186.

XIII. Long, P.E. Amer.Math.Monthly.76(1969, 930-932.

XIV. Long, P.E. Charles, E.Merril Publ. Co., Columbus, Ohio, 1971.

XV. Neubrunn, T.Math. Slovaca 26(1976),97-99

XVI. Neubrunnova, A.Mat. Cas. 23(1973)374-380

XVII. Tong, Jing Cheng Internet. J.Math. and Math.Sci. Vol.7(1983) No.1, 197-199.

XVIII. Tong,Jing Cheng Internet. J.Math. And Math. Sci. Vol.7(1984) No.3, 619-620

XIX. Wilansky, A. Topology for analysis, Ginn, Walthham, Mass, 1970.

 

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Abstract:

An over-damped solution of a nonlinear system has been investigated by multiple time scale method when one of the roots of the roots of the unperturbed equation is much smaller then the outhers. The anymptotic solunion shows excellent agreement with the numerical solution. An example is givin to biological system.

Keywords:

multiple time scale,over-damped process biological system,

Refference:

I. Bogoliubov, N.N. and Yu. Mitropolskii, “Asymptotic Methods in the theory of nonlinear osillation,” Gordan and Breach, New York, 1961.

II. Bojadziev, G.N., “Damped nonlinear oscillations modeled by a 3-dimensional system”, Acta Mechanica, Vol.48, pp.193-201, 1983.

III.FitzHugh, R., Impulse and physiological states in theoretical models of nerve membrane”, J. Biophys., Vol.1 pp.445-466,1961.

IV.Goh. B.S., Global stability in many species systems, The American Naturalist, Vol.111, pp.135-143, 1977.

V. Hsu, I.D., and  Kazarinoff, “An applicable Hopf bifurcation formula and instabity of small periodic solution of the field-noice modle” , J.Math. Anal.Applic., Vol.55, pp.61-89, 1976.

VI. Kalam A.A., M.Samsuzzoha, M.Ali Akbar and M.Alhaj, “KBM asymptotic method for over-damped processes in biological and biochemical system.” GANIT, Bangladesh Math.Soc., Vol.26, pp.1-10,2006.

VII. Krylov,  N.N. and N.N. Bogoliubov, “Introduction to nonlinear mechanics”. Princeton University Press New Jersey, 1947.

VIII. Lefwver, R.and G. Nicolis, “Chemical instabilities and sustained oscillations”.J.Theor.Biol., Vol.30, pp.267-248, 1971.

IX. Lotka, A.J., “The growth of mixed popluation”, J. Wash. Acad. Sci. Vol.22, pp.461-469, 1932.

X. Murty, L.S.N. and B.L. Deekshatulu, “Method of variation of paeameters for over-damped nonlinear systems”, J.Control . Vol.9(3), pp.259-266, 1969.

XI. Murty, I.S.N., B.L.Deekshatulu and G. Krishna, “On asymptotic method of krylov-Bogoliubov for over-damped nonlinear systems”, J.Frak. Inst. Vol.288,pp.49-65, 1969.

XII. Popov, I.P. “A  generalization of the Bogoliubov asymptiotic method in the theory of nonlinear oscillation(In Russian).”, Dokl. Akad. Nauk. SSSR. Vol.3,pp.308-310, 1956.

XIII. Sattar. M.A., “An asymptotic method for second order critically damped nonlinear equation”. J.Frank.Inst. Vol.321,pp.109-113, 1986.

XIV. Shamsul Alam M., “An asymptotic method for second order over-damped and critically damped nonlinear systems”. Soochow Journal of Math. Vol.27(2), pp. 187-200, 2001.

XV.Shamsul Alam, M., “A unified Krylov-Bogoliubov-Mitropolskii method for solving n-order systems”, J.Franklin Inst., Vol.339, pp.239-248, 2002.

XVI. Shamsul Alam M., “On some special conditions of over-damped nonlinear systems”, Soochow Journal of Math. Vol.29(2),pp.181-190, 2003.

XVII.Shamsul Alam, M., M. Abul Kalam Azad and M.A. Hoque “A general Struble’s technique for solving an n-th order weakly nonlinear differential system with damping”, Int. J. Nonlinear Mech., Vol.41,pp.905-918, 2006.

XVIII. Troy, W.C., “Oscillating Phenomena in nerve condition equation”, Ph.D.Dissertation, SUNY at Buffelo, 1974.

XIX. Volterra, V., “Variazioni e fluttuazioni del numero d’individue in species animali conviventi”, Memorie del R. Comitato Talassografico Italiano, Vol.131, pp.1-142, 1927.

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Abstract:

The object of present praper is to investigate one- dimensional dynamical problem of coupled thermo- elasticity in a semi infinite elastic non - simple medium when its surface is under suddenly applied constant pressure. The solution of the problem has been deduced using Laplace transfrom in Bromwich integral from. The author determined the value of the surface displacements in  non - simple medium for small values of time t numerically and presented graphically.

Keywords:

thermo-elasticity,non-simple medium,surface displacements,

Refference:

I. Chen. P.J., & Gurtin, M.E. (1968): ZAMP, Vol. 19, pp.614.

II. Chen, P.J., Gurtin, M.E. & Williams, W.O. (1969): ZAMP, Vol.20,PP.107.

III. Nowacki, W. (1962) : “Thermoelasticity” Addison Wesley Publising Co.pp.5,8,11,40,133,159, N.Y..

IV. Iesan, D. (1970): ZAMP, Vol.21,pp.583.

V. Chakraborty, S.(1972) : Bulletin of calcutta Mathematical Society, Vol.64, pp.129.

VI. Erdelyi, A. (1954) : Tales of Integral Transforms, McGraw Hill Book col. Inc Vol.1, New York.

VII. Das, N.C., Lahiri, A., & Bhakta , P.C. , Bull. Cal. Math. Soc., 90, pp-235-250 (1998)

VIII. Kar, T.K., Lahiri, A., J.Math., NBU., Vol-1, No.-2, (2008), pp-165-172.

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Abstract:

The object of the present paper is to investigate the propagation of waves in an elastic layer immersed in an infinite liquid and under the influence of gravity. The corresponding velocity equation has been derived. In the limiting case the wave velocity equation so obtained is in good agreement with the corresponding classical problem when gravitational effects are vanishing small.

Keywords:

elastic layer, propagation of waves,effect of gravity,

Refference:

I. Voigt, W (1887) : Theorestische Studien iiber die elasticitats varhattnisse der krystalle- I,II. Abh.Konigh Ges derwise. Gottingen 34.

II. Biot, M.A. (1965) : Mechanics of incmental deformation. Willy, New York, pp 44-45, 273-81.

III. Bromwich, T.J.I.A (1898) : Proc.London.Math.Soc.30,  98-120.

IV. Love, A.E.H (1952) : The Mathematical Theory of Elasticity, Dover, pp-164.

V. De, S.N. and Sengupta, P.R. (1974) : J. Acoust.Soc.Amer., Vol.55. No.5 pp.919-21.

VI. De, S.N. and Sengupta, P.R (1975) : Gerlands. Beitr Geophysik, Lepizing 84, 6. s 509-514.

VII. Bhattacharyya, P.C. and Sengupta, P.R. (1984) : Influence of gravity on propagation of waves in a composite elastic layer, Ranchi, Uni. Math. Jour. Vol-15(1984).

VIII. Acharya, D.P., Roy I and Chakraborty, H.S. (2008) : On interface Waves in second order thermo- visco elastic solid media under the influence of gravity, J.Math. Sci., Vol-3 No.3 (2008). pp 286-298.

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Abstract:

Following Deissler's approach the decay for the concentration fluctuation of a dilute contaminant undergoing a first order chemical reaction in MHD turbluent flow at times before the final period in a rotating system for the case of multi-point and multi-time correlation equations is studied. Two-point, two-time and three-point, correlation eqyations have been obtained and to make the set of  equations determinate, the trams containing quadruple correlations in compraison with second and third order correlation terms. The solution obtained gives the decay law for the concentration fluctuations before the final period in a rotating system.

Keywords:

MHD turbulent flow, rotating system,concentration fluctuation,

Refference:

I. S.Chandrasekher, Proc. R.Soc. London A204(1951) 435.

II. S.Corrsin J.Appl.Phys. 22(1951) 469.

III. R.G. Deissler, Phys. Fluid 1 (1958) 111.

IV.R.G. Deissler, Phys. Fluid 3(1960) 176.

V. P.Kumar and S.R. Patel, Phys, Fluid 17 (1971) 1364.

VI. P.Kumar and S.R. Patel, Int J. Eng.Soc. 13(1975) 305.

VII. A.L. Loeffler and R.G. Deissler, Int J.Heat Mass transfer 1(1961) 312.

VIII. S.R. Patel, Int J.Eng. Sci. 12(1975)159.

IX. S.A. Sarker and N. Kishore, Int J.Eng. Sci. 29 (1991)1479.

X. S.A. Sarker and M.A. Islam, Indian J.Pure and Appl. Math. 8(2001)32.

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Abstract:

This paper is concerned with the steady flow of a micropolar fluid an infinite flat plate subjected to unifrom suction.

Keywords:

micro polarfluid,steady flow, flate plate,uniform suction,

Refference:

I. Eringen, A.C. (1964)- Simple Microfluids; Int. Jour. Engng. Sci. 2, 205.

II. Hoyl, J.W. and Fabula, A.C. (1964)- The effect of additives on fluid.

III. Willson, A.J. (1969)- Basic flowes of a micropolar liquid; Appl. Sci. Res., 20,338.

IV. Willson, A.J. (1968)- The flow of a micropolar liquid layer down an inclined plane; Proc. Camb. Phil. Soc., 64,513.

V. Willson, A.J. (1970)- Boundary layer in micropolar liquid ; Proc. Camb. Phil. Soc.., 67,469.

VI. Sengupta, P.R. and Ghosh, P.C. (1982)- Asymptotic suction problem in the unsteady flow of  micropolar liquid; Journal of Technology, XXVII, 1,21.

VII. Gupta, P.S. and Gupta, A.S (1972)- Steady flow of Micropolar Liquids; Acta Meachanica, 15,141.

 

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Abstract:

A two dimensional natural convection flow of a viscous incompressible and electrically conducting fluid past a vertical impermeable flat plate is considered in presence of a unifrom transverse magnetic field. The governing equations are reduced to non-similar boundary layer equations by introducing coordinate transformations appropriate to the cases (i) near the leading edge (ii) in the region for away from the leading edge and (iii) for the entire regime from leading edge to down stream. the governing equations for the flow in the up stream regime are investigated by perturbation method for smaller values of the stream wise distributed magnetic field parameter. The equations governing the flow for large and for all have been investigated by employing the implicit finite difference method with Killer box scheme. The effect of prandit number pr and the magnetic filed parameter on the skin fricition as well as on the rate of heat transfer for the fluid of low prandtl number will be shown in tabular from. The effect of Pr and different level of velocity, in the boundary layer region, will also be shown graphically.

Keywords:

viscous incompressible fluid, convection flows,skin friction,heat transfer,

Refference:

I. Sparrow, E.M. and Gregg, J.L.: Buoyancy effects in forced convection flow and heat Transfer. ASME J. Appl. Mech., Vol.83, 133-134 (1959).

II. Merkin, J.H.: The effect of buoyancy forces on the boundary layer flow over semi-infinite vertical flat plate in a unifrom free stream, J. Fluid Mech., vol.35, pp.439-450 (1969).

III. Lioyd, J.R. and Sparrow, E.M, : Combined forced and free convection flow on a vartical surface. Int. J. Heat Transfer. vol.13, pp.434-438(1970).

IV. Wilks, G. and Hunt, R.: Continuous transformation computation of boundary layer equations between similarity regimes. J. Comp. Phys., vol.40, (1981).

V. Raju, M.S., Liu, X.R. and Law, C.K.: A formulation of combined forced and free convection past a horizontal and vertical surface . Int. J. Heat mass Transfer, vol.27 pp.2215-2224 (1984).

VI. Tingwei, G., Bachrun, P. and Daguent, M. (1982): Influence de la converction natural le convection force and dessus d’ume surface plane vertical vomise a un flux de rayonnement. Int. J. Heat Mass Transfer, vol.25 pp.1061-1065 (1982).

VII. Sparrow, E.M. and Cess, R.D.: Effect of magnetic filed on free convection heat transfer. Int. J. Heat Transfer, vol.3. pp.267-274 (1961).

VIII. Riley, N.: Magnetohydrodynamic free convection. J. Fluid Mech., vol.18, pp. 267-277(1964).

IX. Kuiken, H.K.: Magnetohydrodynamic free convection in a strong cross-field. J. Fluid Mech., vol.40,pp.21-38 (1970).

X. Sing, K.R. and Cowling, T.G.: Thermal convectiv in Magnetohydrodynamic boundary layer. J. Mech. Appl. Math. vol.16, pp.1-5 (1963).

XI. Crammer, E.M. and Pai, S.I.: Megnetofluid Dynamics for Engineering and applied Physicists. McGrow-Hill, New York, (1974).

XII. Wilks, G.: Magnetohydrodynamic free convection about a semi-infinite vertical plate in a strong cross-field. J. Appl. Phys., vol.27, pp.621-631, (1976).

XIII. Wilks, G. and Hunt, R: Magnetohydrodynamic free convection about a semi-infinite vertical plate at whose surface the heat flux is unifrom. J. Appl. Math. Phys. (ZAMP), vol.34, January, (1984).

XIV. Hossain, M.A. and Ahmed, M.: MHD forced and free convection boundary layer flow near the leading edge. Int. J. Heat Mass transfer, vol.33. pp.571-575 (1984).

XV. Hossain, M.A., Pop I. and Ahmed, M.: MHD Free Convection Flow From an isothermal plate inclined a small angle to the horizontal. J. Theo. Appl. Fluid Mech., Vol.1, pp.194-207, (1996).

XIV. Cebeci, T. and Bradshaw, P.: Physical and computational aspects of convective heat transfer. Springer, New York, (1984).

 

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