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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.

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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

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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

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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.

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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.

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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).

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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.

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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.

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Abstract:

In this paper, Fourier analysis began as an attempt to approximate periodic functions with infinite summations of trigonometric polynomials. For certain functions, these sums, known as Fourier series, converge exactly to the original function. Hereextending the result of R. Islam & M. Zaman (1999), a theorem on βνμλ,,,k summability of quadruple Fourier series has been established.

Keywords:

Fourier series,approximate periodic function,infinite summation,quadruple Fourier series,

Refference:

I.Agnew, R. P.(1957). The Lotosky method of evaluation of series, Michigan, Math, Journal, 4,105.

II.Islam, R. and Zaman, M. (1999). On νμλ,,k-summability of a triple Fourier series, Bull. Cal. Math. Soc., 91, (4) 323-332.

III.Karamata, J.(1935). Theorems sur la Sommabilite exponentialle etd, autres Sommabilities S’y rattachant, Mathematica (Cluj), 9,164.

IV.Kathal, P.D. (1969). A new criterion for Karamata summability of Fourier series, Riv. Math. Univ. Parma, Italy 10(2), 33.

V.Lal, Shyam (1997). On μλ,k-summability of a double Fourier series, Bull. Cal. Math. Soc., 89, 327.

VI.Lototsky, A.V. (1963), On a linear transformation of sequence (Russian) Ivanov, Gos, Red. Inst. Uchen, Zap., 4, 61.

VII.Vuckovic, V. (1965). The summability of Fourier series by Karamata methods, Math. Zeitchr, 89, 192.

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