iosr-Jm   Volume-10 ~ Issue-1 ~ Jan-Feb 2014

Abstract: A mathematical model has been developed for studying the effect of porous medium on pulsatile inclined two layered blood flow with magnetic field with periodic body acceleration.Considering the Blood as couple stresses, non-Newtonian, and incompressible fluid. Finite Hankel and Laplace transform are used to analytical expression for the velocity profile and flow rate. The effect of various parameters associated with this flow problem such as porosity, Hartmann number, pressure gradient, body acceleration, gravitational parameter and inclination angle on the velocity distribution is analysed by plotting the graph. It is found that velocity decreases with the increase of the Hartmann number and the reverse behavior is noticed for the pressure gradient and body acceleration. It is also observed that the velocity profile increases with the increase of the permeability of the porous medium.

Keywords: Pulsatile blood flow, Permeability of porous medium, Magnetic field, Body acceleration.

[1] Agarwal, R. and Varshney.N.K., The effect of magnetic field of pulsatile inclined two layered blood flow with periodic body acceleration, International journal of mechanical Engineering Research. 3(3), 2013, 187-196 .
[2] Agarwal, R. and Varshney, N. K., Inclined arterial MHD pulsatile blood flow through a porous medium with periodic body acceleration, Jour. PAS, Mathematical Science. 17, 2011, 304-313.
[3] Amos, E. and Ogulu, A.,Magnetic effect on pulsatile flow in a constricted axisymmetric tube, Indian J. Pure and appl. Math. 34(9), 2003, 1315-1326.
[4] Astarita, G., Marrucii and Palumbo,G., Non-Newtonian gravity flow on inclined surface, Ind. Engg. Chem. Fundam. 3, 1964, 333.
[5] Chaturani, P. and Palanisamy, V., Casson fluid model for pulsatile flow of blood under periodic body acceleration, Biorheology, 27, 1990, 619-630.
[6] Chaturani, P. and Palanisamy V., Pulsatile flow of Power-law fluid model for blood flow under periodic body acceleration, Biorheology. 27, 1990, 747-758.

Abstract: The sequence spaces 0 w( p) ,w ( p) and w ( p)  were introduced and studied by I.J. Maddox [1,2,3,4]. In [8,9,10] , the authors have introduced sequence spaces 0 c (u,v, p) ,c(u,v, p) , l (u,v, p)  and l(u,v, p) and established some properties. In this paper we introduce the sequence spaces w(u,v; p) , 0 w (u,v; p) and w (u,v; p)  ; study some properties, find  - dual of w(u,v; p) . We also characterize the matrix classes wu,v; p, l   , wu,v; p,c  and     0 w u,v; p ,c .

Key Words: Paranormed sequence spaces,  - dual, matrix transformation, generalized weighted mean. AMS classification : 40

[1] I.J. Maddox, Paranormed sequence spaces generated by infinite matrices, Proc. Cambridge Philos. Soc.64(1968) 335-340
[2] I.J. Maddox, Spaces of Strongly summable sequences, Quart. J. Math. Oxford 18(2) (1967) 345-355
[3] C.G. Lascarides, I.J. Maddox, Matrix transformation between some classes of sequences, Proc. Cambrige Philos. Soc. (1970) 99-
104
[4] I.J. Maddox, Some properties of paranormed sequence spaces, London J. Math. Soc.2, 1(1969) 316-322
[5] S. Simons , The sequence spaces l( p )  and m( p )  Proc. Lond. Math. Soc. 15 (3) (1965) 422-436
[6] B. Choudhary, S.K. Mishra, On Kothe-Toeplitz duals of certain sequence spaces and their matrix transformations, Indian J. Pure
Appl. Math 24(5) (1993) 291-301

Abstract: In this paper we introduce the concept of -sg* -open sets and discuss some of their basic properties.

Key words: -sg*-open sets and -sg*-regular operation. AMS Classification: 54 A 05

[1] K. Balachandran P.Sundaram and H.Maki, On generalized continuous maps in topological spaces. Mem. Fac. Sci. Kochi Univ. Ser. A. Math, 12 (1991), 5.13.
[2] P. Bhattacharyya and B.K. Lahiri, Semi – generalized closed sets in topology, Indian J. Math., 29 (1987), 376 – 382.
[3] S.G. Crossely and S.K. Hildebrand, Semi closure, Texas. J. Sci., 22 (1971), 99 – 122.
[4] W. Dunham, T spaces, Kyungpook Math J., 17 (1977), 161 – 169.
[5] W.Dunham, A new closure operator for non – T1 – topologies, Kyungopook. Math. J., 22 (1982) , 55 – 60.

Abstract: The aim of this research is to find a proof of the elusive side angle side (SAS) theorem of Euclid on the congruence of triangles using the cross section of a double cone. It is known that the SAS theorem has remained analytically unproved for over 2000 years. The method used for over 2000 years for proving this very important side angle side (SAS) theorem of Euclid has been the method of superposition whereby two triangles are tested for congruence by applying one to the other.

[1]. Abbott, P. (`1988). Teach Yourself Geometry. Hodder and Stoughton Educational, Great Britain.
[2]. Bass, E. et al (1988). Geometry, Prentice-Hall, Inc. New Jersey
[3]. Bergamini, D. (1970), Mathematics, Time-Life Books, New York
[4]. Bouwsma, W. D. (1972), Geometry for Teachers, McMillan Company, New York.
[5]. Durell C. V. (1961), A New Geometry for Schools, G. Bell and Sons Ltd, London.

Abstract: In this paper we study the existence of a unique continuous function y=y(x) on I=(a, a+h] solution for the fractional differential equationy()(x)=λ f(y(x)) and y(-1)(a)=,  is some constant 0<≤1,, using Banach fixed point theorem.

[1] V. Lakshmikantham, S. Leela and J. Vasundhara; theory of fractional dynamic systems, Cambridge Academic publishes,
Cambridge 2009.
[2] Sabatier, J.; Agrawal, O.P.; Tenveiro Machado, J. A; Advances in Fractional calculus; the oretical Developments and application in
physics and Engineering, springer, 2007.
[3] O. K. Jaractat, A. A-omari, S. Momani, Existence of the mild solution for fractional semi linear initial value problem. Mon linear
Analysis, 2008.
[4] A. A. Kilbas,H. M. Srirastara, J. J Trujillo, theory and applications of fractional differential equations, Elsevier, Amsterdam, 2006.
[5] M. Mater, on existence and uniqueness of the mild solution for fractional integro-differential equations, Journal of integral
equations and applications, 2011.

Abstract: The main aim of this paper is to introduce and study the notion of Size-biased discrete two-parameter Poisson-Lindley (SBDTPPL) distribution. Besides deriving its p.m.f., some of its properties and the expressions for raw and central moments, coefficients of skewness and kurtosis have been obtained. We have explored its moment equations and maximum likelihood estimators. A simulation study has been proposed in the end.

Key Words: Size-biased Poisson-Lindley distribution, Compounding; raw and central moments; maximum likelihood estimators; Fisher's scoring method.

[1]. Adhikari, T.R. and Srivastava, R.S. (2013): A Size-biased Poisson-Lindley Distribution, International Journal of Mathematical Modeling and Physical Sciences, Vol. 01 (3), pp. 1-5.
[2]. Adhikari, T.R. and Srivastava, R.S. (2014): Poisson-Size-biased Lindley Distribution,International Journal of Scientific and Research Publication, Vol. 4 (3), pp. 1-6.
[3]. Bakouch, H.S., Al-Zahrani, B.M., Al-Shomrani, A.A., Marchi, A.A. and Louzada, F. (2012) An Extended Lindley Distribution. Journal of the Korean Statistical Society, Vol. 41, No 1, pp. 75-85.
[4]. Barlow, R.E. and Proschan, F. (1981): Statistical Theory of Reliability and Life Testing, Silver Spring, MD: To Begin with.
[5]. Beall, G. (1940). The fit and significance of contagious distributions when applied to observations on larva insects. Ecology 21, 460-474.

Abstract: We study the effect of monopole field on gravitational collapse of radiating Dyon solution in non-spherical topology. Our main aim is to investigate the possibility of cosmic censorship violation in non-spherical gravitational collapse of radiating dyon solution in the presence of monopole field. It is shown that the final outcome of the collapse depends sensitively on the electric and magnetic charge parameters. The graphs with respect to the charge and monopole field show that the singularity is to be naked. It is an interesting feature emerges that the strength of naked singularity is weak curvature singularity. Though the naked singularity is weak one may conclude that the non-spherical gravitational collapse of monopole radiating Dyon solution violets the CCH.

Keywords: Cosmic censorship, gravitational collapse, naked singularity, radiating Dyon solution.

[1] D M Eardley and L Smarr, Time function in numerical relativity: Marginally bound dust collapse, Phys. Rev,. D 19, 1979, 2239-2259.
[2] D Christodoulou, Violation of cosmic censorship in gravitational collapse of a dust cloud, Commun. Math. Phys., 93, 1984, 171-195.
[3] R P A C Newman, Strength of naked singularities in Tolman-Bondi space-times, Class. Quantum Grav., 3, 1986, 527.
[4] K D Patil and U S Thool, Spherical and non-spherical gravitational collapse in Husain space-time, Int. J. Mod. Phys., D 14(6), 2005, 873-882.
[5] K D Patil, Structure of radial null geodesics in higher-dimensional dust collapse, Phys. Rev. D 67, 2003, 024017.

Abstract:Thepresentpaperdealswith multiplicative suitable mappingof A(0) ng semigroups which can become subtraction semi-groups, when a subtraction operatoris defined on them in terms of t he group composition. In Bohdan Zelinka[1]solved this problem partially by showing atomic subtraction semigrou ps canbe characterized as cancellative semigroups containing '0'. group A(0)with '0' can be made into a subtraction group if a exists.MoreoverthegreatmathematicianB.M. Schein[2] raised the problem of characterizi

[1] Bohdan Zelinka: Subtraction Semigroups, Mathematical Bohemica, Vol.120(1995), N0.4, 445-447.

[2] Schein B.M.: Difference semigroups, Communications in Algebra 20(1992), 2153-2169.

[3] Abbott, J.C.: Sets, Lattices and Boolean Algebras, Allyn and Bacon, Bosten, 1969.

[4] J. C. Beidleman, A note on Regular near-rings, J. Indian Math. Soc. 33 (1969), 207–210.

[5] J. R. Clay, The near-rings on groups of low order, Math. Z. 104 (1968), 364–371.

Abstract: Rainfall is very important for the economic growth and development of any nation; hence there is dire need to study the monthly and annual trends. This paper critically examines the mathematical study of monthly and annual rainfall patterns in Nasarawa State for 20 years (1993-2012) using data obtained from the archives of Meteorological Observatory at the College of Agriculture, Lafia, Nasarawa State. Statistical techniques like time series analysis, mean and standard deviation were employed to depict the temporal distribution of rainfall over the area. The study shows that 1996 is the wettest year, while 2010 shows a year with the lowest negative rainfall deviation. In analyzing the months for the period, it was noticed that August recorded the highest rainfall value of 2498mm which is the month where clouds pervades the sky.

Keywords: Rainfall, time series analysis, Nasarawa State, standardized anomaly index, temporal variations

[1] J.O. Ayoade, Annual rainfall trends and periodicities in Nigeria, Nigerian Geog. J., 16(2) (1973), 167-176.
[2] W.N. Adger, S. Huq, K. Brown, D. Conway and M. Hulme, Adaptation to climate change in the developing world, Progress Dev. Stud., 3(2003), 179-195.
[3] I.C. Enete and I.N. Ebenebe, Analysis of rainfall distribution over Enugu during the little dry season (1990-2005), J. Geog and Regional Planning, 2(7) (2009), 182-189.
[4] P. Hutchinson, Rainfall analysis of the Sahelian drought in the Gambia, J. Climatology, 5(1985), 665-672.
[5] S. Gregory, A note in the mean season rainfall in the Sahel, 1931-60 and 1961-80, Geography, 68(1983), 31-36.
[6] B.N. Goswami, V. Venugopal, D. Sengupa, M.S. Madhusoodanan and P.K. Xavier, Increasing trend of extremerain events over India in a warming environment, Science, 314(2006), 1442-1445.
[7] P. Guhathakurta and M. Rajeevan, Trends in the rainfall pattern over India, National Climate Centre, India, Research Report No: 2/2006, (2006).

Abstract: In this problem the distribution due to thermal source in a homogenous isotropic thermoelastic half space has been investigated by applying a combination of Laplace and Fourier transform technique in the context of Generalized theories of thermoelasticity. The inverse transform integral have been evaluated by using Cagniard method to obtain the exact closed algebraic expressions for the displacement and temperature as function of time and horizontal distances, which are valid for all epicentral distances. The displacement and temperature so obtained in the physical domain have been computed.

[1]. Cauchy, A.L., 1823: Bulletin aela societephilomathique, 177, Paris.
[2]. Duhamel , J.M.C., 1837: Second memoriesurles pheromones thermo mechaniques, J.L. EcolePolytech, 15,1-57.
[3]. Neumann, F., 1855: VorlesungenUber Die theorie der, Elastizitat der festenKorpern, Leipzig.
[4]. Voigt, w., 1887: TheoretischestudienuberElastizitatverhaltnisse der KristalleAbh; GesWiss . Gottingen,34.
[5]. Cosserat, E. and Cosserat, F., 1909: Theories des corps deformables; A. Herrman, Paris.