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Abstract:

Based on the Struble technique, a simple formula is presented for obtaining approximate solutions of over-damped nonlinear differential systems when one of the roots of the unperturbed equation is much smaller than the other roots. The method is easier than the existing perturbation techniques. An example is given to biological system.

Keywords:

over-damped,perturbation techniques,biological system,

Refference:

I.Krylov N.N and Bogoliubov N.N, Introduction to Nonlinear Mechanics, Princeton University press, New Jersey 1947.

II.Bogoliubov N.N, Mitropolskii Yu. A., Asymptotic Methods in theTheory of Nonlinear Oscillation, Gordan and Breach, New York, 1961.

III.Cunningham W.J., Introduction to Nonlinear Analysis, McGraw-Hill Book Company, 1958.

IV.MinorskN. y, Introduction to Nonlinear Mechanics, J .E. Edwards, Ann Arbor, Michigan, 1947.

V.Nayfeh A. H., Perturbation Methods, J. Wiley, New York, 1973.

VI.Popov I. P., “A generalization of the Bogoliubov asymptotic method in the theory of nonlinear oscillations”, Dokl.Akad. Nauk SSSR 111 (1956), 308-310 (in Russian).

VII.Murty I. S. N., Deekshatulu B. L. and Krisna G., “General asymptotic method of Krylov-Bogoliubov for over-damped nonlinear system”, J. Frank Inst. 288 (1969), 49-46.

VIII.Alam Shamsul M., “Asymptotic methods for second-order over-damped and critically damped nonlinear system”, Soochow J. Math, 27 (2001), 187-200.

IX.Alam Shamsul M., “Method of solution to the n-th order over-damped nonlinear systems under some special conditions”, Bull. Call. Math. Soc., 94(6) (2002), 437-440.

X.Alam Shamsul M.,, “Method of solution to the order over-damped nonlinear systems with varying coefficients under some special conditions”, Bull. Call. Math. Soc., 96(5) (2004), 419-426.

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

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

XIII.Hsu, I. D. and Kazarinoff, “An applicable Hopf bifurcation formula and instabity of small periodic solution of the field-noise model”, J. math. Anal. Applic., Vol. 55, pp. 61-89, 1976.

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

XV.Lotka, A. J., “The growth of mixed population”, J. Wsah. Acad. Sci. Vol. 22, pp. 461-469, 1932.

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

XVII.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.

XVIII.Alam Shamsul M., Azad Abul Kalam M. and Hoque M. A., “A general Struble’s technique for solving an n-th order weakly non-linear differential system with damping”, Journal of Non-Linear Mechanics, Vol. 41, pp.905-918, 2006

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Abstract:

The natural frequencies of an annular plate of exponentially varying thickness under the action of a hydrostatic in-plane force have been studied on the basis of the classical theory of plates. The governing differential equation has been obtained and solved. The effects of in-plane force parameter, radii ratio and taper constants on the frequency parameter have been investigated for two different boundary conditions. Critical buckling loads have been computed for different values of taper constant and radii ratio for both the plates.

Keywords:

annular plate,critical buckling loads, taper constant,

Refference:

I.Conway, H. D. ‘Nonaxial bending of ring plate of varying thickness’, J. appl. Mech., vol. 25, pp. 386-88 (1958),

II.Gallegojuarez, J. A. ‘Axisymmetric vibrations of circular plates with stepped thickness’, J. Sound Vibr., vol. 26, pp. 411-416 (1973).

III.Gupta, U. S. and Lal, R. ‘Buckling and vibrations of circular plates of variable thickness’, J. Sound. Vibr., vol. 58, pp. 501-507 (1978).

IV.Gupta, U. S. and Lal, R. ‘Buckling and vibrations of circular plates of parabolically varying thickness’, Indian J. pure appl. Math., vol. 11, no. 2, pp. 149-159 (1980).

V.Gupta, U. S. and Lal, R. ‘Transverse vibrations of nonuniform rectangular plates on elastic foundation.’ J. Sound Vibr., vol. 61, pp. 127-133 (1978).

VI.Jain, R. K. ‘Vibrations of circular plates of variable thickness under an in-plane force’, J. Sound Vibr., vol. 23, pp. 407-414 (1972).

VII.Leissa, A. W., Vibration of plates, NASA AP-160 (1669).

VIII.Rosen, A. and Libai, A. ‘Transverse vibrations of compressed annular plates’, J. Sound Vib., vol. 40, pp. 149-153 (1975).

IX.Soni, S. R., and Amba-Rao, C. L. ‘Axisymmetric vibrations of annular plates of variable thickness’, J. Sound Vib., vol. 38, pp. 465-473 (1975).

X.Tomar, J. S. and Gupta, D. C. ‘Free vibrations of an infinite plate of patrebolically varying thickness on elastic foundation.’ J. Sound Vib.,vol. 47, pp. 143-146 (1976).

XI.Volgel, S. M. and Skinner, D. W. ‘Natural frequencies of transversely vibrating uniform annular plates.’ J appl. Mech., vol. 32, pp. 926-931 (1965).

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Abstract:

n most recent time worrying epidemic was HIV, Influenza, Tuberculosis etc. While there are many complicating factors, simple mathematical models can provide much insight into the dynamics of disease epidemics and help officials make decisions about public health policy in this subject matter. We shall discuss two of the classical and still much used, deterministic epidemiological models which are responsible for spreading diseases in an area. We shall then consider a reaction-diffusion model, Fisher’s equation, a new integro-differential equation model for the spread of an epidemic in space and to evaluate strategies to control an epidemic.

Keywords:

epidemiological models ,reaction-diffusion model, Fisher’s equation,public health policy,

Refference:

I. Bailey N.T., The mathematical Theory of Infectious Disease (2nd edition), Charles Griffin and co. Ltd (1975)

II. Anderson R.M. and R.M. May. Infectious Diseases of Humans: Dynamics and Control. Oxford UniversityPress, Oxford, UK, 1991.

III. Bailey N.T.J.. The Mathematical Theory of Infectious Diseases. Hafner, New York, 2nd Edition, 1975.

IV. Banks R.B.. Growth and Diffusion Phenomena. Springer-Verlag, New York, 1994.

V. Daley D.J. and Gani J.. Epidemic Modelling: An Introduction. Cambridge University Press, Cambridge,UK, 1999.

VI. Murray J.D., Mathematical Biology. Springer-Verlag, New York, 2nd Edition, 1993.

VII.SIR model: Online experiments with JSX Graph (http://jsxgraph.unibayreuth.de/wiki/index/Epidemiology:_The_SIR_model)

VIII. Capasso V., The ,mathematical structure of Epidemic system, Springer Varlag (1993)

IX. Trottier, H.,& Phillippe, P. (2001). Deterministic modeling of Infectious diseases : Theory and methods. The Internet Journal of Infectious Diseases. Retrieved Dec. 3,2007, from http://www.ispub.com/ostio/index.php?xmlFilePath=journals/ ijid/volln2/model.xml.

X. Brauer, F.& Castillo-Chavez,C.(2001). Mathematical Models in Population Biology and Epidemiology.NY: Springer.

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Abstract:

Four concepts of T1 –Supra Fuzzy Topological spaces are introduced and studied in this paper. We also establish some relationships among them and study some other properties of these spaces.

Keywords:

Fuzzy set,Topological space,Supra Fuzzy Topological space,

Refference:

I.Zadeh L. A. Fuzzy sets. Information and control 8, 338-353, 1965.

II.Chang C. L. Fuzzy topological spaces; J. Math. Anal Appl. 24, 182-192,1968.

III.Lowen R. Fuzzy topological spaces and fuzzy compactness; J. Math. Anal. Appl. 56(1976), 621-633.

IV.Wong C. K. Fuzzy points and local properties of Fuzzy topology ; J. Math. Anal . Appl. 46, 316-328, 1974.

V.Srivastava A. K. and Ali D. M. A comparison of some FT2 concepts, Fuzzy sets and system 23, 289-294, 1987.

VI.Ali D. M. A note on T0 and R0 fuzzy topological spaces, Proc. Math. Soc. B.H.U. Vol. 3, 165-167, 1987.

VII.Ali D. M. Some Remarks on α-T0, α-T1 , α-T2 fuzzy topological spaces, The Journal of fuzzy mathematics, Los Angeles, Vol. 1, No. 2, 311-321,1993.

VIII.Hossain M. S. and Ali D. M. On T0 fuzzy topological spaces, J. Math and Math. Sci. Vol. 24, 95-102, 2009.

IX.Hossain M. S. and Ali D. M. On T1 fuzzy topological spaces, Ganit. J. Bangladesh Math. Soc. 24, 99-106, 2004.

X.Hossain M. S. and Ali D. M. On T2 fuzzy topological spaces, J. Bangladesh Academy of Science, 29(2),201-208, 2005.

XI.Devi R., Sampathkumar S. and Caldes M., General Mathematics, Vol. 16, Nr . 2, 77-84, 2008.

XII.Ming Pao Pu.; Ming. Ying Liu. Fuzzy topology II. Product and Quotient Spaces; J. Math. Anal. Appl. 77, 20-37, 1980.

XIII.Wong C. K. Fuzzy topology: Product and Quotient Theorem . J. Math . Anal . Appl. 45, 512-521,1974.

XIV.Azad K. K. On Fuzzy semi- continuity, Fuzzy almost continuity and Fuzzy weakly continuity; J. Math. Anal . Appl. 82(1), 14-32, 1981.

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Abstract:

The mathematical analysis presents the study of heat transfer and magneto hydrodynamic effects on pulsatile flow of blood through geometrically irregular arterial system, and its effects on cardiovascular disorder and arterial diseases. Considering the influence of magnetic field on the steno- tic artery, the effect of transverse magnetic field and multi-stenosis on the blood flow in blood vessels is studied theoretically. The blood flow is considered to be axi-symmetric with an outline of the irregular stenosis obtained from a three-dimensional casting of mild stenosed artery, so that the physical problem becomes more realistic from the physiological point of view. The MARKER AND CELL (MAC) and SUCCESSIVE –OVER-RELAXATION (SOR) methods are respectively used to solve the governing unsteady magneto-hydrodynamic equations and pressure-Poisson equation numerically. The present observations certainly have some clinical implications relating to magneto-therapy. It may help reducing the complex flow separations zones causing flow disorder and leading to the formation and propagation of the arterial diseases and cardiovascular disorders.

Keywords:

stenosis,blood flow ,heat transfer ,magnetic field,

Refference:

I. Misra, J. C., Chakravarty, S., Flow in arteries in the presence of stenosis, J. Biomech. 19 (1986), pp. 907-918.

II. Misra, J. C., Shit, G. C. and Rath, H. G.., Flow and heat transfer of a MHD viscoelastic fluid in a channel with stretching walls: some applications to haemodynamics.(computers and fluids)-37 (2008) pp.1-11.

III. Vershney Gourav, Katiyar, V. K. and Kumar Susil, Effect of magnetic field on the blood flow in artery having multiple stenosis:a numerical study.(International journal of engg.sc.and tech.) vol.2no2, 2010 , pp67-82.

IV. Mondal Prasanta Kumar, An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis40. (International journal of non-linear mechanics) (2005), pp. 151-164.

V. Chaturani, Samy, P. R. P., A study of non-Newtonian aspects of blood flow through stenosed arteries and its applications in arterial diseases, Biorheology 22 (1985), pp. 521-531.

VI. Nanda Saktipada: Mathematical Analyses of some problems of applied mechanics having application in physiological systems. Final Report, MRP-UGC (10th Plan).

VII. Sud, V.K and Sekhon, G.S. 1989 Blood flow through the human arterial system in the presence of a steady magnetic field.Phys.Med.Biol vol34,no 7 pp. 795-805 .

VIII. Walters .K. : Second order effects in elasticity, plasticity and fluid dynamics. Pergamon; 1964.

IX. Young .D.F. Shukla et.al. : Fluid mechanics of arterial stenosis, J. Biomech. Trans ASME 101 (1986) 907-918.

X. Singh Bijendra, Joshi Padma and B. K.: Blood Flow through an Artery Having Radially Non-Symmetric Mild Stenosis. Applied Mathematical Sciences, Vol. 4, 2010, no. 22, 1065 – 1072

XI. Shailesh Mishra, S.U. Siddiqui and Amit Medhavi: Blood Flow through a Composite Stenosisin an Artery with Permeable Wall. Applications and Applied Mathematics, Vol. 6, Issue 11 (June 2011) pp. 1798 – 1813.

XII. Razavi Modarres M. R., Seyedein S.H. and Shahabi P. B. : Numerical Study of Hemodynamic Wall Parameters on Pulsatile Flow through Arterial Stenosis. IUST International Journal of Engineering Science, Vol.17, No.3-4, 2006, Page 37-46.

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Abstract:

In this paper we introduce the notion of neutral convex sublattices of a lattice to generalize the concept of neutral ideals. Here we give several characterizations of these sublattices and include some of their properties.

Keywords:

lattice ,neutral ideals,neutral convex sublattices,

Refference:

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

II. Grätzer G., Notes on lattice theory,I; Magyar Tud. Akad. Mat. Kutato Int. Kozl 7 (1962), p. 191- 192.

III. Grätzer G., and Schmidt E.T., Acta. Math. Acad. Sci. Hungar. 12(1961), p. 17-86.

IV.Fried E., and Schmidt E.T., Algebra Universalis,5(1975), p. 203-211.

V. Nieminen J., Commentari Mathematical Universitals Stancti Paulie 33 (1) (1984), p. 87- 93.

VI. Hafizur Rahman R.M., Some properties of standard sublattices of a lattice, Submitted to JSR.

VII.Cornish W.H. J., Austral. Math. Soc. 14(1972), p.200-215

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Abstract:

The present study shows that the most abundant species was Amblyseius largoensis (Muma) and Amblyseius pruni Gupta among predatory mites in all the plants (tulsi, mango, chili and papaya) in post monsoon period. During premonsoon period the most dominant species were Amblyseius largoensis, Amblyseius multidentatus, (Swirski & Sheeter), Amblyseius pruni, Amblyseius coccineae Gupta. Species diversity index and species richness index were determined for aforesaid species for the period of pre and post-monsoon period and it was represented in a tabular form.

Keywords:

predatory mites,crops,species diversity index,species richness index,

Refference:

I. Bullock, J.A. 1971. The investigation of sample containing many species. I. Sample description. Biol. J.Linn. Soc., 3: 1-21.

II. Golek, Z. 1975. A study of the destruction of the fruit tree red spider mite Panonychus ulmi (Koch) on apple. Zesz. Probl. Postepow. Nouk. Rola., 171: 15-34.

III.Heip.C. 1974. A new index measuring evenness. J.Mar.Biol.Assoc. U.K., 54: 555-557

IV.Heip.C. & Engels, P. 1974. Comparing species diversity and evenness indics. J.Mar.Biol.Assoc. U.K., 54: 559-569.

V.Herbert, H.J & Butler, K.P. 1973. influence of two spotted spider mite population on photosynthesis of apple leaves. J.Econ. Entomol. 105: 263-269.

VI.Mac. Arthur. R.H.& Mac Arthur, J.W. (1961). On bird species diversity., Ecology,42: 594-598.

VII.Menhinick, E.F., 1964, A comarison of some species diversity indices applied to samples of field insects, Ecology, 45: 859-861.

VIII.Margalef, R. 1958. Information theory in ecology., Gen. Syst., 3: 36-71.

IX.Shannon, C.E., Weaver, W., 1949, The mathematical theory of communication, University of Illinois Press, Urbana. Pp. 220

X. Shree, M.P. &Nataraja, S. 1993. Infectional biomechanical and physiological changes in mulberry. Curr Sci., 65: 337-346.

XI. Simpson, C.E. & Weaner, W., 1949, Measurement of diversity, Nature 163: 688.

XII. Tamura, H. 1967, Some ecological observations on Collumbola in Sappore, Northern Japan, Journal. Fac. Sci. Hokkaido Univ. Zer. VI Zool., 16(2): 238 – 252.

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