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A FIXED POINT THEOREM IN GENERALIZED METRIC SPACES

Authors:

M.K.BOSE , R. TIWARI

DOI NO:

https://doi.org/10.26782/jmcms.2010.07.00001

Abstract:

In this article we prove a fixed point theorem in generalized metric spaces.

Keywords:

Refference:

1) Branciari A., A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (1-2) (2000), 31-37.
2) Lahiri B. K., Saha P.. and Tiwari R. A generalized metric space is not Hausdroff, Rev. Bull. Cal. Math. Soc., 6(2) (2008), 177-178.

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CURVE REPRESENTATION OF DSA GENERAL INDEX WITH THE HELP OF WAVELET FUNCTIONS

Authors:

M.M. Rahman, M. Das, M.G. Arif, M.A. Hossen, M.E. Karim

DOI NO:

https://doi.org/10.26782/jmcms.2010.07.00002

Abstract:

In this study, we collected the monthly raw data form DSE (Dhaka Stock Exchange) and we analyzed the data based on curve fitting. We represented this curve in wavelet form, especially in the form of Haar wavelet representation.

Keywords:

Refference:

1) Addition, Pual S. (2002): he Illustrade Wavelet Transform Handbook, Institution of physics.
2) Charles, C. (1991): Wavelet Theory, Academic Press, Cambridge, MA.
3) Christensen, O. (2004): Approximation Theory, From Taylor Polynomials to Wavelet Birrkhauser, Boston.
4) Daubechies, I. (1992)): Ten Lectures on Wavelets. SIAM, Philadelphia, pa.
5) Debnath, L. 2002): Wavelet transformation and their application, Birkhauser, Boston.
6) Mallat, S. (1999): A wavelet Tour of Signal Processing. Academi Press, New York.
7) Mayer, Y. (1993): Wavelets: their past and their future, Progress in Wavelet Analysis and its Application Gif-su-Yvette, pp 9-18.
8) Strang, G. (1989): Wavelets and Dilation Equations: A brief introduction. AM Review, 31: 614-627.
9) Wells, R.O. (1993): Parametrizing Smooth Compactly Supported Wavelets. Transform American Mathematical Society, 338(2): 919-931.
10) Walnut, D.F. (2001 0: An Introduction to Wavelet Analysis BiRkhuser, Boston.
11) Wojtaszczyk, P. (1997): A Mathematical Introduction to Wavelet, Cambridge University press, Cambridge, U. K.

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RATE OF CHANGE OF VORTICITY COVARIANCE IN MHD TURBULENT FLOW OF FLUID IN A ROTATING SYSTEM

Authors:

M.L. Rahman

DOI NO:

https://doi.org/10.26782/jmcms.2010.07.00003

Abstract:

In the paper, the rate of change of vorticity covariance in MHD turbulent flow of dusty fluid in a rotating system is studied. The results obtained show that the defining scalers (………………………..) of the rate of change of vorticity covariance of MHD turbulent flow depend on the defining sclars, W,T,R,P and F of the tensors  (……………………………..) already defined in the problem.

Keywords:

Refference:

1) Taylor, G.I. (1935) “Statistical theory of turbulence”, Proc.Roy.Soc.London,A151,421
2) Chandrasekhar, S. (1951). “The invariant theory of isotropic turbulence in magneto-hydrodynamics’,Proc.Roy.Soc.London,A204,435
3) Chandrasekhar, S. (1955a). “A theory of Turbulence”, Proc.Roy.Soc.London,A229, 1
4) Chandrasekhar, S. (1955b). “Hydromagnetic Turbulence-1 a deductive theory”, Proc.Roy.Soc.London,A233,322
5) Jain .C. (1962). “Pressure fluctuations within isotropic turbulence”, Mathematic Student,30,185
6) Saffman, P.G.(1962). On the stability of Laminar flow of a dusty gas”, J.Fuid Mech., 13, 120
7) Hinze, J.O (1975). Turbulence,McGraw Hill,New York
8) Stanisic, M.M. 1985).Mathematical theory of turbulence”,Springer-Verlag,New York
9) Kishore,N. and Sinha, A.(1988).”Rate of change of vorticity covariance in dusty fluid turbulence”,Astrophysics and Space Science,146,53
10) Kishore, N. and Gosefid,Y.T. (1988). “Effect of coriolis force on acceleration covariance in MHD turbulence”, Astrophysics and Space Science,150,89.
11) Sinha, A.(1988).’’Effect of dust particles on acceleration covariance of ordinary turbulence”,J. Scientific Research,.H.U.,38,7
12) Kishore,N. and Sarker,S.A. (1989).” Rate of change of vorticity covariance in MHD turbulence”, Presented in the 5th Mathematical Conference,B.H.U
13) Kishore,N. and Sarker,S.A. (1920).” International journal of energy research,V14,573-577.

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UNSTEADY MHD FLOW OF GENERALIZED VISCO-ELASTIC OLDROYD FLUID UNDER TIME-DEPENDENT BODY FORCE THROUGH A POROUS CONCENTRIC CIRCULAR CYLINDRICAL DUCT

Authors:

M.S. Uddin

DOI NO:

https://doi.org/10.26782/jmcms.2010.07.00004

Abstract:

The aim of present paper is the investigation of the unsteady unidirectional flow of an incompressible generalized visco-elastic Oldroyd type fluid between porous concentric cylindrical duct under the action of a transverse magnetic field with time dependent body force. Here we have calculated the velocity profile of a fluid element of the problem theoretically and graphically. From the analysis of this fluid motion, the dynamics of the ordinary viscous fluid is also discussed.

Keywords:

Refference:

1) Lamb H., : Hydrodynamics, New York, over Pub, Inc (1945).
2) Cowling T.., Magneto hydrodynamics, Inter-Science, Pub. Inc New York (1957)
3) Carslaw H.S. and Jager .C., : Operational Method in Applied math, Dover Pub. Inc ew York (1949).
4) Das K.K., : Proc Math. Soc, BHU. 7 (1991), 35-39.
5) Sengupta P.R., and Mahapatra J. Roy, : Rev. Roum. Sci Tech. Mec. Appl (1971), 1023-1031.
6) Chakraborty G. and Sengupta P.R.,: Proc. Inter-AMSE Conference Signals, Data, System, New Delhi (India) ABSE press, Vol 4 1991), 83-92.
7) Ghose B.C., Sengupta P.R. : Proc Math. Soc., BHU. 9 (1993), 89-95.
8) Cabannes . : Theoretical magneto fluid dynamics, academic press. New York and London.
9) Chandrasekhar S.,: Hydrodynamics and Hydromantic stability, Cambridge University press, (1961).
10) Rlvlin R.S. and .Ericksen J.L, : J.R. at Mech. Anul 1955).
11) Reiner M., : Amer J. Math. Soc (1945).
12) Goldroyd J., : Proc. Roy. Soc. (1950), 200-523.
13) Das K.K. and Sengupta P.R. : Unsteady flow of a conducting viscousfluid through a straight tube, proc. Nat. Aead. Aci. India (1993).
14) Chakraborty G. and Sengupta P.R. : MHD flow of two immiscible visco-elastic Rivlin’s-Erickson fluids through a non-conducting rectangular channel, Journal of physics, Vol.42 (1992, 525-531.

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SOME RESULTS ON THE MAXIMUM TERMS OF COMPOSITE ENTIRE FUNCTIONS

Authors:

Sanjib Kumar Datta , Somnath Mandal

DOI NO:

https://doi.org/10.26782/jmcms.2010.07.00005

Abstract:

The aim of this paper is to compare the maximum term of composition of two entire functions with their corresponding left and right factors.

Keywords:

Refference:

1) Singh, A.P.: On maximum term of composition of functions, Proc. Nat.Acad. Sci. India, 59A (1989), pp.103-115.
2) Singh, A.P.: On maximum modulus and maximum term of composition of entire functions, Indian J. Pure Appl. Math., 22(12), December(1991), pp.1019-1026.
3) Valiron, .: Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, 1949.

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O FOURTH ORDER MORE CRITICALLY DAMPED NONLINEAR DIFFERENTIAL SYSTEM

Authors:

M. Ali Akbar

DOI NO:


Abstract:

In this article an analytical approximate solution has been investigated for obtaining the transient response of fourth order more critically damped nonlinear systems. The results obtained by the presented technique agree with the numerical result obtained by the fourth order Runge-Kutta method nicely. An example is solved to illustrate the method.

Keywords:

Refference:

1) Akbar, M. A. Paul A. C. and Sattar M.A., An Asymptotic Method of Krylov-Bogoliubov for Fourth Order Over-damped Nonliner Systems, Gaint, J. angladesh Math. Soc., Vol. 22, pp. 83-96, 2002.
2) Akbar, M.A. Shamsul Alam M. and Sattar M.A., Asymptotic Method for Fourth Order Damped Nonlinear Systems, Ganit, J. Bangladesh Math. Soc. Vol. 23, pp. 41-49, 2003.
3) Akbar, M. A, Shamsul Alam M. and . Sttar M., A Simple Technique for Obtaining Certain Over-damped Solutions of an (………………………) Order Nonlinear Differential Equation, Soochow of Mathematics Vol. 31(2), pp. 291-299, 2005.
4) Bogoliubov, N. N. and Mitropolski Yu., Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordan and Breach, New York, 1961.
5) Emdadul Hoque, M., M. Takasaki, . Ishino and . Mizuon, Development of a Three Axis Active Vibration Isolator Using Zero-Power Control, IEEE/ASME Transactions on Mechatronics, 2(4), 462-470, 2006.
6) Krylov, N. . and Bogoliubov N. N., Introduction to Nonlinear Mechanics, Princeton University Press, New Jersey, 1947.
7) Mendelson, K. S., Perturbation Theory for Damped Nonlinear Oscillations, J. Math. Physics, Vol. 2, pp. 3413-3415, 1970.
8) Mizuon, T., T. Toumia and M. Takasaki, Vibration Isolation System Using Negative Stiffness, JSME International Journal, Series C, 46(3), 517-523, 2003.
9) Murty, I. S. N., Deekshatulu B. L. and Krishna G., On an Asymptotic Method of Krylov-Bogoliubov for Over-damped Nonlinear System, J. Frank. Inst., Vol. 288, pp. 49-65, 1969.
10) Murty, I. S. N., A Unified Krylov-Bogoliubov Method for Solving Second Order Nonlinear Systems, Int. J. Nonlinear Mech. Ol. 6, pp. 45-53, 1971.
11) Popov, I. P., A Generalization of the Bogoliubov Asymptotic Method in the Theory of Nonlinear Oscillations (in Russian) Dokl. Akad. SSR Vol. 3, pp. 308-310, 1956.
12) Rokibul, M. I, Akbar M. A. and Samsuzzoha ., “A New Technique for Third Order Critically Damped Non-linear Systems, “Journal of Applied Sciences Research, Vol. 4(6), pp. 695-706, 2008.
13) Rokibul M. I, Sharif ddin M., Akbar M. A, Azmol Huda M. and Hossain S. M. ., A New Technique for Fourth Order Critically Damped Nonlinear System with Some Conditions, Bull. Cal. Math. Soc., Vol. 100(5), pp. 501-514, 2008.
14) Sattar, M. A., An asymptotic Method for Second Order Critically Damped Nonlinear Equations, J. Frank. Inst., Vol. 321, pp. 109-113, 1986.
15) Shamsul Alam, M. and Sattar M. ., An Asymptotic Method for Third Order Critically Damped Nonlinear Equations, J. Mathematical and Physical Sciences, Vol. 30, pp. 291-298,1996.
16) Shamsul Alam, M., Asymptotic Methods for Second Order Over-damped and Critically Damped Nonlinear Systems, Soochow Journal of Math. Vol. 27, pp. 187-200, 2001.
17) Shamsul Alam, M. Bogoliubov’s Method for Third Order Critically Damped Nonlinear Systems, Soochow J. Math. Vol. 28, pp. 65-80, 2002.

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