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Abstract:

In this paper thermal stresses in an aeolotropic thin rotating annular disc under transient shearing strees applied on the outer edge are derived when the modulus of elasticity and the coefficient of thermal expansion very expansion very exponentially as the nth power of the radial distance from the center of the circular disk, corresponding result for homogeneous case are deduced as a special case and and found in agreement with the previous results. Numberical results are presented in a tabular from and graphically.

Keywords:

thermal stresses,thermal expansion,aeolotropic,shearing stress,

Refference:

I. De,A.And Choudhury, M.’Thermal stress in a non-homogeneous thin rotating annular circular disk having transient shearing stress applied on the outer edge.’ Bulletin of Calcutta Mathematical society. Vol-98,No-6,pp-128-128(2006).

II. Gogulwar, V.S and Deshmukh, K.C., “Thermal stresses in a thin circular plate with heat sources”,  Journal of Indian Academy of Mathematics, Vol-27,No-1,pp-129-141(2005).

III. Ghosh, R.E. On the loaded elastic half space with a depth varying poisson ratio. ZAMP,  Vol-20, No-5, pp-691,(1969).

IV. Love ,A.E.H. ‘A treatise on the mathematical theory of elasticity’ 2nd Edn, Dover publication, New York (1944).

V. Mollah, S.A.  “thermal stress in non-homogeneous circular dise of varying thickness rotating about a central axix.” Pure and applied mathematical science, Vol-3, No-12, pp-(55-60) (1976).

VI. Mollah, S.A. ‘Stresses in an in-homogeneous circular dise with axial hole of transversely isotropic material.’ Journal of Indian Mathematical science, Vol-1, No-2, pp-5-10 (1990).

VII. Mollah, S.A. ‘Thermal stress in a non-homogeneous thin rotating circular disk having transient shearing stress applied on the outer edge.’ Gaiit, Journal of Bangladesh Mathematical Society, Vol-1, No-1,pp-59. (1990).

VIII. Timoshenko, S. and goodier, J.N. Theory of Elasticity, 2nd edition, McGraw-Hill, pp-406-434(1955).

IX. Wankhede, P.C., “On the Quasi static thermal stresses in a circular plate”, Indian Journal of pure and Applied Mathematics, Vol-13, No-11, pp-1273-1277 (1982).

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Abstract:

In this artical, an approximate technique has been presented for obtaining the analytical approximate solutions of second order strongly  nonlinear differential systems with small damping and slowly varying coefficients based on the He's homotopy perturbation and the extended from of the Krylov-bogoliubov-Mitroppolskii method. An example is given to illustrate the efficiency and implementation of the presented method. The first order analytical approximate solutions obtained by the presented method show a good  agreement with the corresponding numerical solutions for the several damping effects.

Keywords:

doffing equation ,damping effect ,homotopy perturbation ,varying coefficients ,

Refference:

I.  Krylov N.N and Bogoliubov N.N., Introduction to nonlinear mechanics, princeton  University Press, New Jersey, 1947.

II. Bogoliubov N.N and Mitropolskii Yu., Asymptotic methods in the theory of nonlinear oscillation, Gordan and Breach, New York,1961.

III. Mitropolskii Yu. A,. Problems on asymptotic methods of non-stationary oscillations(in Russian), Izdat, Nauka, Moscow, 1964.

IV. Nayfeh A.H., Introduction to Perturbation Techniques, Wiley, New York,1981.

V. Murdock J.A., Perturbations: Theory and Methods, Wiley, New York, 1991.

VI. Hall H.S.and Knight S.R ., Higher Algebra, Radha Publishing house, culcutta,(Indian Edition) , pp-480-438, 1992.

VII. Lim C.W. and Wu B.S., A new analytical approach to the Duffing harmonic oscillator. Physics Letters A 311(2003) 365-373.

VIII. He Ji-Huan, homotopy perturbation technique, Computer Methods in applied Mechanies and Engineering. 178(1999) 257-262.

IX. He Ji.Huan, coupling method of a homotopy perturbation technique and a perturbation technique for nonlinear problems, International Journal of Nonliner Machanies, 35 (2000) 37-43.

X. He J.H., New interpreetation of homotopy perturbation method, International Journal of Modern Physics B, Vol.20, No.18 (2006) 2561-2568.

XI. Belendez A., Hernandez A., Beledez T., Fernandez E., Alvarez M.L. and Neipp C., Application of Homotopy perturbation method to Duffing hrmonic  oscillator, International Journal of Nonlinear Science and Numerical Simulation 8(1) (2007) 78-88.

XII. Hu H., Solution of a quadratic nonlinear oscillator by the method of harmonic balance, Journal of Sound and Vibrartion 293 (2006) 462-468.

XIII. Roy K.C. and Alam M. Shamsul, Effect of higher approximation of Krylov-  Bogoliubov- Mitropolskii solution and matched asymptotic differential systems with slowly varying coefficients and damping near to a turning point, Viennam journal of mechanics, VAST, vol.26, 182-192 (2004).

XIV. Arya J.C. and Bojadziev G.N., Time depended oscillating system with damping, slowly varying parameters and delay, Acta Mechanica, vol.41 (1981) 109-119.

XV. Bojadziev G.N., Damped nonlinear oscillations modeled by a 3- dimensional differential system, Acta Mech. 48 (1983) 193-201.

XVI. Alam M. Shamsul, Azad M. Abul Kalam and Hoque M.A., A general Struble’s technique for solving an nth order weakly nonlinear differential system with damping, International Journal of Nonlinear Mechanies, 41 (2006) 905-918.

XVII. Uddin M. Alhaz and Sattar M. Abdus, An approximate techique for solving strongly nonlinear differential system with damping system with damping effects, Indian Journal of Mathematices, (Submitted,2010).,

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Abstract:

The aim of the present paper is to investigate the influence of autofrettage on stress distribution and load bearing capacity of a thick spherical shell. Appling the maximum shear stress Theory and distortion energy theory an analytical equation for optimum radius c of elastic-plasic juncture, c(opt) is deduced in autofrettage technology. It revealed that the autofrettage increases the pressure inside the wall of a thing spherical shell that it can contain.

Keywords:

autofrettage,stress distribution,shear strees,elastic-plastic juncture,

Refference:

I. Harvey JF Theory and desing of pressure vessels. New York: Van Nostrand Reinhold Company Ltd, 1985

II. Brownell LE, Young EH. Process equipment design. New York: John Wiley & sons, 1959.

III. Yu G. Chemical pressure vessel and equipment (in Chinese). Beijing: Chemical Industries Press, 1980.

IV. Boresi Ap, Sidebottom OM, Seely FB, Smith JOI. Advanced machanies of materials, 3rd edn New York: John Wiley & sons, 1978.

V. Kong.F.Determining the opimum radius of the elastic-plastic junction, RC, for thick wall Autofrettage cylinder by graphic method, (in Chinese). Petrochemical equipment, 1986;15:11.

VI. Timashenko S. Strenth of materials, New York: Van Nostrand Reinrand Company Ltd,1978.

VII. Rao Singiresu S: Engineering optimization.

VIII. Srinath, L.S.: Advance Machanics of solied, of materials, Tata McGraw-Hill Publising Company Ltd, New Delihi,1998.

IX. Zhu, Ruilin and Yang Jinlai, International Journal of Pressure Vessel and piping 75 (1998) 443-446.

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Abstract:

In this paper the author generalize several results of normal near lattices in terms of n-ideals. It has been proved that the near lattices of finitely generated principal n-ideals Pn(S) is normal if and only if each prime n-ideals. Also if  and only if

Keywords:

nearlattics,ideals ,normal nearlattics,

Refference:

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Abstract:

The object of the present paper is to investigate the joint effect of couple-stress and gravity on the propagation of waves in an elastic layer. It is found that the velocity of propagation of waves in an elastic layer increases due to the presence of couple-stress and the effect of gravity has some effect on the wave velocity when the length of the wave is small compared with the thickness of the layer. It is clear from the phase velocity equation that joint effect of couple-stresses and gravity is superposing effect when this two are acting separately.

Keywords:

elastic layer,couple-stress ,gravity,wave propagation,

Refference:

I. Voigt, W (1887): Theorestische studien iibet die elasticitats varhattnisse der krystalle–I,II. Abh.. Konigh Ges Derwise. Gottingen 34.

II. Cosserat, E and Cosserat, F. (1909): Theore das Crops-Deformations. Willy, New York. pp.44-45, 273-81.

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

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

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

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

VII.De, S.N. and Sengupta, P.R. (1974): J. Acoust. Soc. Amer., vol.55. no.5,pp.919-21.

VIII. Mindlin, R.D. and Tiesten, H.F (1962): Effect of couple-stress in linier elasticity, Arch. Rat. Mech. Analysis, 11, 415-448.

IX. Bhattacharyya, P.C. and Sengupta, P.R.(1984): Influence of gravity on propagation of waves in composit elastic layer, Ranchi, Uni. Math. Jour. vol-15(1984)

X. Acharya, D.P., Roy, I (2008): on interface waves in second order thermo – visco elastic solid media under the influence of gravity, J.Mech. Cont.& Math. Sci., vol-3, no-3, pp-286-298.

XI. Sengupta, P.R and Ghosh, B. (1980): Effect of couple-stresses on the steady-state response to moving Loads in the semi-infinite elastic medium, J.Math. Stu., Vol-48, no-2, pp 183-200.

 

 

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Abstract:

In our study we have analyzed the market volatility in stock prices in the Dhaka stock Exchange (DSE) during 2005-2008. Frist of all the row data is collected from DSE (Dhaka Stock Exchange Deperment). Then we have analyzed the data in two way, one is based on statistical measure and the other is curve fitting. We also explor the trend of general index of DSE in the from of differential equatiol with the  help of least square method.

Keywords:

time series,market volatility,stock price,statistical measure,

Refference:

I. Ariff, M. and Finn, Finn, F.J., “Announcement Effects and Market  Efficiency in a Thin Market: an Empirical Application to the Singapore Equity Market”, Asia Pacific Journal of Management, vol.6 1989, pp.243-267.

II. Bollerslev,  T., “Generalized Autoregressive Conditional Heterpskedasticity.” , jouenal of Econometrics, Vol.31, 1986, pp.307-27.

III. Chowdhury, S.S.H. and Rahman, M.A., “On the Empirical Relation Between Macroeconomic Volatility and Stock market Volatility of Bangladesh”, The Global Journal of Finance and Economic, Vol,1, No.2, 2004, pp.209-225.

IV. Easton, S.A. and Sinclair, N.A., “The Impact of Unexpected Earning and Dividends on Abnormal Returns to Equity”, Journal of Accounting & Finance, Vol.29, 1989, pp.1-19.

V. Gordon, M.J., “Dividend, Earning, and Stock Price”, The Review of Economics and Statistics, Vol.41 1959, pp.99-105.

VI. kato, K. and Loewenstenie, U., “The Ex-Dividend-Day Behavior of Stock price: The Case of Japan”, The Review of Financial Studies, Vol.8, 1995, pp.816-847.

VII. Lee, B.S., “The Response of Stock Price to Perment and Temporary Shocks to Dividends”, Journal of Financial and Quantitative Analysis, Vol.30, 1995, pp.1-22.

VIII. Loughlin P.H., “The Effect of Dividend Policy on Changes in Stockholders, Wealth”, A PhD Thesis, Graduate School of Saint Louis University, 1982, USA.

IX. Ogden, J.P., “A Dividend Payment Effect in Stock Returns”, Financial review, Vol.29, 1994, pp.345-369.

X. Rahman, M.M., “Trend Analysis and Mathematical Modeling of General Index of Dhaka Stock Exchange”, M.Sc. Thesis, Mathematics Discipline, Khulna University, 2009, pp.64-73.

XI. Schwert, G.W. and Stambauge, R., “Expected Stock Returns and Volatility”, Journal of Financial Econamics, Vol.19, 1987.

XII. Stevens, J.L. and Jose, M.L., “The Effect of Dividend Payout, Stability, and Smoothing on Firm value”, Journal of Accounting Auditing & Finance, Vol.7 1992, pp.195-216.

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Abstract:

The aim of paper is to compare the valiron defect with the relative Navanlinna defect of a special type of differential polynomial generated by a transcndental meromorphic function.

Keywords:

valirodefect,nevanlinna defect,differential polynomial ,meromorphic function ,

Refference:

1) Hayman W.K. : Meromorphic Functions, The Clarendon Press, Oxford (1964).
2) Xiong Q.L. : A fundamental inequality in the theory of meromorphic functions and its applications, Chinese Mathematics, Vol. 9, No. 1 (1967), pp. 146-167.

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