Archive

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).

AN APPROXIMATE TECHNIQUE TO DUFFING EQUATION WITH SMALL DAMPING AND SLOWLY VARYING COEFFICIENT

Authors:

M.Alhaz Uddin , M.Abdus Satter

DOI NO:

https://doi.org/10.26782/jmcms.2011.01.00002

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).,

AUTOFRETTAGE OF A THICK SPHERICAL SHELL

Authors:

Sujoy Saha , Samar C. Mondal , Prabir Chandra Bhattacharyya

DOI NO:

https://doi.org/10.26782/jmcms.2011.01.00003

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.

NEAR LATTICE OF FINITELY GENERATED PRINCIPAL N-IDEALS WHICH FORMS A NORMAL NEARLATTICE

Authors:

M.S.Raihan

DOI NO:

https://doi.org/10.26782/jmcms.2011.01.00004

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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THE EFFECT OF COUPLE STRESS AND GRAVITY ON THE PROPAGATION OF WAVES IN AN ELASTIC LAYER

Authors:

Prabir Chandra Bhattacharyya

DOI NO:

https://doi.org/10.26782/jmcms.2011.01.00005

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.

TIME SERIES ANALYSIS AND MATHEMATICAL MODELING OF GENERAL INDEX OF DSE

Authors:

Moumita Das, M.M. Rahman, M.G. Arif, M.M. Hossen, A. Polin

DOI NO:

https://doi.org/10.26782/jmcms.2011.01.00006

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.

RELATIVE DEFECTS OF A SPECIAL TYPE OF DIFFERENTIAL POLYNOMIAL

Authors:

Sanjib Kumar Dutta , Sanjib Mondal

DOI NO:

https://doi.org/10.26782/jmcms.2011.01.00007

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.

A MATHEMATICAL ANALYSIS ON BLOOD FLOW THROUGH AN ARTERY WITH A BRANCH CAPILLARY

Authors:

S.P.Nanda , B.Basu Mallik

DOI NO:

https://doi.org/10.26782/jmcms.2011.07.00001

Abstract:

The paper is devoted to a theoretical study for the distribution of axial velocity for blood flow in a branch capillary emerging out of a parent artery at various locations of the branch. The results are computed for various values of r and the angle made by the parent artery and the branch capillary. Also due attention is given to the variation of n (fluid index). The output is compared with the results in the previous similar investigations. A theoretical estimate for the velocity of blood for various non negative values of the fluid index parameter and yield stress in different locations of the branch capillary is presented.

Keywords:

branch capillary,artery,fluid index,yield stress,

Refference:

1) Misra J. C., Chakravarty S. Flow on arteries in the presence of stenosis. Journal of Biomechanics.19:907-18(1986).

2) Misra J. C.,Adhikary S.D.,G.C. Shit. Multiphase flow of blood through arteries with a branch capillary: A theoretical study. Journal of Mechanics in Medicine and Biology, Vol. 7,No.4,395-417(2007).

3) Chaturani P,Prahlad RN. Blood flow in tapered tubes with rheological applications. Biorheology,22:303-314(1985).

4) Misra JC, Patra MK,Misra SC. A Non-Newtonian fluid model for blood flow through arteries under stenotic conditions. Journal of Biomechanics, 26:137-143(1993).

5) Misra JC, Shit GC. Blood flow through arteries in a pathological state: A theoretical study. International journal of Engineering Science, 44:662-671(2006).

6) Misra JC, Ghosh SK. Pulsatile flow of a viscous fluid through a porous elastic vessel of variable cross section: A mathematical model for hemodynamic flows. Comput Math Appl, 46:447-457(2003).

7) Misra JC, Ghosh SK. Pulsative flow of a couple stress fluid through narrow porous tube of elliptical cross section :A model for blood flow in a stenosed arteriole. Engineering Simulation, 15:849-864(1998).

8) Misra JC, Kar BK. A Mathematical analysis of blood flow from a feeding artery into a branch capillary. Math Comput Model, 15(6):9-18(1991).

9) Misra JC, Ghosh SK. Flow of a Casson fluid in a narrow tube with a side branch. International journal of Engineering Science, 38:2045-2077(2000).

10) Whitmore RL. Rheology of the Circulation,Pergamon Press,New York,1968.

11) Merill EW. Rheology of blood, Physiological Review, 49(4):863-888,1969.

ON FINITELY GENERATED N-IDEALS WHICH FORM RELATIVELY STONE LATTICES

Authors:

M. Ayub , A.S.A.Noor

DOI NO:

https://doi.org/10.26782/jmcms.2011.07.00002

Abstract:

Set of all finitely generated n-ideals of is a lattice, denoted by . In this paper the author has characterized those which form relatively Stone lattices. It has been shown that is relatively Stone if and only if for any two incomparable prime n-ideals and of .

Keywords:

lattice,finitely generated ideals,stone lattices,

Refference:

1. Ali M. Ayub, A Study on Finitely generated n-ideals of a lattice, Ph.D Thesis, 2000.
2. Cornish W. H., Normal lattices, J. Austral. Math. Soc. 14(1972), 200-215.
3. Gratzer G., Lattice theory, First Concepts and distributive lattices, Freeman, San Francisco, 1971.
4. Latif M.A. and Noor A.S.A, n-ideals of a lattice, The Rajshahi University Studies (Part B), 22 (1994), 173-180.
5. Mandelker M., Relative annihilators in lattices, Duke Math. J. 40(1970), 377- 386.
6. Noor A. S. A. and Ali M. Ayub, Relative annihilators around a neutral element of a lattice, The Rajshahi University studies(part B), 28(2000), 141-146.
7. Noor A. S. A. and Latif M.A., Finitely generated n-ideals of a lattice, SEA Bull, Math. 22 (1998), 73-79.
8. Varlet J., Relative annihilators in semilattices, Bull. Austral. Math. Soc. 9(1973), 169- 185

CORRELATION OF MONTHLY TEMPERATURE AND RAINFALL BETWEEN THE CONSECUTIVE MONTHS OF THE MONSOON SEASON

Authors:

Maitreyi. Roy , Abir Chatterjee

DOI NO:

https://doi.org/10.26782/jmcms.2011.07.00003

Abstract:

A novel techniques for the operation of analog ICs at low operational voltage has been presented in this paper. Cascode techniques has been chosen as it reduces ratio errors due to input and output voltage difference. Over and above this method provides constant current over wide output voltage swing.

Keywords:

analog ICs,operational voltage,voltage difference,voltage swing,constant current,

Refference:

1) Chandraskashan A P , “ low power CMOS digital design “ , IEEE journal
of solid state circuits, VOL 27 P P 473-483, april 1992
2) Chandraskashen A P, “A low power chipset portable multimedia
application”, proceeding IEEE, P P ( 82-83 ) 1984. ISSCC, PP82-83, 1994
3) Takanashi etal M “ A 60 new MPEG4 video codec using clustered voltage scaling with variable voltage supply voltage scheme”- IEEE journal of solid state circuit, Vol-33 IW:11,SS PP 1772-1780 November 1998

LOW POWER OPERATION OF ANALOG ICS

Authors:

Munnujahan Ara , Moumita Das, Samah Ghanem, M. M. Rahman

DOI NO:

https://doi.org/10.26782/jmcms.2011.07.00004

Abstract:

Keywords:

meteorological parameter,correlation,bulb temperature,maximum and minimum temperature.,

Refference:

1) Ara, M. M., Hossain, M. A., and Alam 2005. Surface dry bulb temperature and its trend over Bangladesh, Journal of Bangladesh Academy of Science, 29(1):29-40.
2) Karmakar, S. and Nessa, J. 1997. Climate change and its impacts on natural disasters and SW-monsoon in Bangladesh and the Bay of Bengal. Journal of Bangladesh Academy of Sciences, 21:127-136.
3) Karmaker, S. and Shrestha, M. L. 2000. Recent Climate Change in Bangladesh, Report No. 4, SAARC Meteorological Research Center (SMRC), Dhaka, Bangladesh, 43:138-140.
4) Das, P. K. 1995. The Monsoon. 3rd edition, New Delhi: National Book, Press trust of India.
5) Hussain, M. A. and Sultana, N. 1996. Rainfall distribution over Bangladesh stations during the monsoon months in the absence of depressions and cyclonic storms, Scientific Journal, 47:339-348.
6) Chowdhury, M.H.K. and Debsharma, S.K. 1992. “Climate change in Bangladesh – A statistical review”, Report on IOC-UNEP Workshop on Impacts of Sea Level Rise due to Global Warming, NOAMI, held during 16-19 November in Bangladesh, 15.
7) WMO/UNDP/BGD/79/013, 1986. Bangladesh Meteorological Department climatological data and charts (1961-80), Tech. Note no.9.

THERMAL STRESSES IN A LONG IN-HOMOGENEOUS CYLINDER WITH VARIABLE ELASTIC CONSTANTS, THERMAL CONDUCTIVITY AND THERMAL CO-EFFICIENT

Authors:

Anukul De , Ajoy Kanti Das

DOI NO:

https://doi.org/10.26782/jmcms.2011.07.00005

Abstract:

The object of this paper is to study the thermal stresses in a long in-homogeneous aelotropic cylinder with the variable thermal conductivity of the material varies as mthpower of the radial distance, the elastic constants and the coefficients of thermal expansion of the material vary as nth power of the redial distance.

Keywords:

the thermal stress, thermal expansion, redial distance,aelotropic cylinder,

Refference:

1)I.Engineering Research, Res., vol.5, No. 9, pp. 171-178, 1965.

II.De, A., Choudhury, M., ‘Thermal Stresses in a Long In-homogeneous Transversely Isotropic Elastic Annular Subject to γRay Heating’.Bulletin of Calcutta Mathematical Society, vol., No. 2, pp. 101, 2009.

III.Hearman, R. F. S., An introduction to applied anisotropic elasticity, 1961.

IV.Martin, W. T., Reissner, E., Elementary differential equation, 1958.

V.Mollah, S. H., ‘Thermal Stresses in a Long In-homogeneous Aelotropic Cylinder Subjected to γRay Heating’, Mechanika Teoretyczna Estosowana, vol. 4, pp. 27, 1989.

VI.Nowinski, J., ‘Thermoelastic Problem for an Isotropic Sphere with Temperature Dependent Properties1’, ZAMP, vol. X, pp. 565, 1959.

VII.Sharma, B., Jour. App. Mech., vol. 23, no. 4, 1956. 8)Timoshenko, S. and Goodier, J. N., Theory of elasticity, second edition, 1966.

SOME PROPERTIES OF STANDARD SUBLATTICES OF A LATTICE

Authors:

R.M.Hafizur Rahman

DOI NO:

https://doi.org/10.26782/jmcms.2011.07.00006

Abstract:

In this paper we study some properties and give some characterizations of these sublattices. Also we prove that for a central element n of a lattice, the standard n-congruences are permutable.

Keywords:

lattice, sublattices,central element,congruences,

Refference:

I. Gätzer G., and Schmidt E.T., Acta. Math. Acad. Sci. Hungar. 12, 17 (1961).

II. Grätzer G., General lattice theory, (Birkhauser Verlag, Basel, 1978).

III. Cornish W.H. and Noor A.S.A, Bull. Austral. Math. Soc. 26, 185 (1982).

IV. Fried E. and Schmidt E.T., Algebra Universalis, 5, 203 (1975).

V. Nieminen J., Commentari Mathematical Universitals Stancti Paulie 33(1), 87 (1984).

VI.Noor A.S.A. and Latif M.A., SEA Bull. Math. 4, 185 (1997).

SENSITIVITY AND ACCUARACY OF EIGENVALUES RELATIVE TO THEIR PERTURBATION

Authors:

M. A. Huda, Md. Harun-or-Roshid, A. Islam , Mst. Mumtahinah

DOI NO:

https://doi.org/10.26782/jmcms.2011.07.00007

Abstract:

The main objective of this paper is to study the sensitivity of eigenvalues in their computational domain under perturbations, and to provide a solid intuition with some numerical example as well as to represent them in graphically. The sensitivity of eigenvalues, estimated by the condition number of the matrix of eigenvectors has been discussed with some numerical example. Here, we have also demonstrated, other approaches imposing some structures on the complex eigenvalues, how this structure affects the perturbed eigenvalues as well as what kind of paths do they follow in the complex plane.

Keywords:

sensitivity,eigenvalues, perturbations,complex eigenvalues,

Refference:

I.Aripirala R. and Syrmos V. L., “Sensitivity Analysis of Stable GeneralizedLyapunov Equations,” In Proc. of the 32nd IEEE Conf. on Decision and Control, pp. 3144-3129, San Antonio, 1993.

II.Bhatia R., Eisner L. and Krause G., “Bounds for the Variation of the Rootsof a Polynomial and the Eigenvalues of a Matrix,” Linear Algebra Appl.,142, 195-209, 1990.

III.Elsner L., “An Optimal Bound for the Spectral Variation of Two Matrices,”Linear” Algebr’a and Its Applications, 71:77 -80, 1985.

IV.Eslami M., “Theory of Sensitivity in Dynamic Systems,” Springer-Verlag,Berlin, 1994.

V.Holbrook J. A. R., “Spectral Variation of Normal Matrices,” LinearAlgbera Appl., 174:131-144, 1994.

VI.J.B. Hiriart-Urruty J.B. and Ye D., “Sensitivity Analysis of All Eigenvalues of aSymmetric Matrix,” Numer. Math., 70:45-72, 1992.

VII.Hewer G. and Kenney C., “The Sensitivity of the Stable LyapunovEquation,” SIAM J. Cont. Optim., 26: 321-344, 1998.

VIII.Ipsen I. C. F., “Relative Perturbation Results for Matrix Eigenvalues andSingular Values,” Acta Numer, 7:151-201, 1998.

IX.Konstanitinov M., Petkov P., GU D. W. and Mehrmann V., “Sensitivity of.General Lyapunov Equations,” Technical report 98-15, Dept. of Engineering, Leicester univ., UK, 1998.

X.Konstantinov M., Petkov P. and Angelova V., “ Sensitivity of GeneralDiscrete Algebraic Riccati Equations,” In Proc. 28 Spring Conf. of Union of Bulgar. Mathematics, pp. 128-136, Bulgaria, 1999.

XI.Moler C. B., Numerical Computing with MATLAB, February 15, 2008.

XII.Ostrowski A., “Dber die Stetigkeit von charakteristischen Wurzeln inAbhiingigkeit von den Matrizenelementen,” Jahresberichte der Deutsche Mathematische Ver”ein 60, 40-42, 1957.

XIII.Parlett B. N., “The Symmetric Eigenvalue Problem,” Prentice-Hall,Englewood Cliffs, NJ, 1980.

XIV.Rump S. M., “Estimation of the Sensitivity of Linear and NonlinearAlgebraic Problems,” Linear algebra, Appl., 153:1-34, 1991.

XV.Rajendra B., “Perturbation Bounds for Matrix Eigenvalues,” SIAM, Wiley,New York, 2007.

XVI.Sun J.G., “On the Perturbation of the Eigenvalues of a Normal Matrix,”Math. Numer. Sinica, 6 334-336, 1984.

XVII.Stewart G. W, Sun J., “Matrix Perturbation Theory,” Academic Press. Inc,New York, 2000.

XVIII.Sun J. G, “Sensitivity Analysis of the Discrete-Time Algebraic RiccatiEquation,” Lin. Alg. Appl., 275-276: 595-615, 1998.

XIX.Wilkinson J. H, “Rounding Errors in Algebraic Processes,” Prentice Hall,Englewood Cliffs, 1963.

XX.Wilkinson J., “The Algebraic Eigenvalue Problem,” Clarendon Press, Oxford, 1965.

XXI.Xu S. “Sensitivity Analysis of the Algebraic Riccati Equations,” Numer.Math., 75: 121-134, 1996.

A NOTE ON THE GROWTH PROPERTIES OF WRONSKIANS

Authors:

Sanjib Kumar Dutta , Tanmay Biswas

DOI NO:

https://doi.org/10.26782/jmcms.2011.07.00008

Abstract:

In the paper we study the comparative growth properties of composite entire and meromorphic functions on the basis of th order ( th lower order ) and order ( th lower order ) where is a slowly chang-ing function and are positive integers and

Keywords:

composite entire function,composite entire meromorphic function,comparative growth properties,

Refference:

I. Datta, S. K. and Biswas, T.: On the th order of Wronskians, Int. J. Pure Appl. Math., Vol.50, No.3 (2009), pp.373-378.

II. Hayman, W.K.: Meromorphic Functions, The Clarendon Press, Oxford (1964).

III. Juneja, O.P.: Kapoor, G.P. and Bajpai, S.K.: On the order and lower order of an entire function, J.Reine Angew. Math., 282(1976), pp.53-67.

IV. Somasundaram, D and Thamizharasi, R.: A note on the entire functions of -bounded index and -type, Indian J. Pure Appl. Math. , Vol. 19, No. 3 (1988), pp. 284-293.

V. Valiron, G.: Lectures on the general theory of integral functions, Chel-sea Publishing Company, 1949.