iosr-Jm   Volume-6 ~ Issue-3

Abstract: In this Paper, the effect of the variation of recruitment rate on the transmission dynamics of tuberculosis was studied by modifying an existing model. While the recruitment rate into the susceptible class of the existing model is constant, in our modified model we used a varying recruitment rate. The models were analyzed analytically and numerically and these results were compared. The Disease Free Equilibrium (DFE) state of the existing model was found to be          ,0,0,0  , the DFE of the modified model was found to be ( ,0,0,0) * S where * S is arbitrary. While all the eigenvalue of the existing model are negative, one of the eigenvalues of the modified model is zero. The basic reproduction number o R of both models are established to be the same. The numerical experiments show a gradual decline in the infected and exposed populations as the recruitment rates increase in both models but the decline is more in the modified model than in the existing model. This implies that eradication will be achieved faster using the model with a varying recruitment rate.

Keywords: tuberculosis, variation, recruitment rate, constant, effect, reproduction number, stability

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Abstract:In this paper, I have invented the formulae for finding the area of an Isosceles triangle. My finding is based on pythagoras theorem.

1 Geometry concepts and Pythagoras theorem.

Abstract: This pape r d e l i n e a t e s existence, characterizations and st rong unicity of best uniform approximations in real linear 2-normed spaces. AMS Su ject Classification: 41A50, 41A52, 41A99, 41A28.

Key Words and Phrases: Best approximation, existence, 2-normed linear spaces.

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Abstract: In this paper, first we define β*-open sets and β*-interior in topological spaces.J.Antony Rex Rodrigo[3] has studied the topological properties of 𝜂 * -derived, 𝜂 * -border, 𝜂 * -frontier and 𝜂 * exterior of a set using the concept of 𝜂 * -open following M.Caldas,S.Jafari and T.Noiri[5]. By the same technique the concept of β*-derived, β*-border, β*-frontier and β*exterior of a set using the concept of β*-open sets are introduced.Some interesting results that shows the relationships between these concepts are brought about.

Key words: 𝜂 * -border, 𝜂 * -frontier and 𝜂 * exterior, β*-derived, β*-border, β*-frontier and β*exterior

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Abstract: We present the theory of Malliavin Calculus by tracing the origin of this calculus as well as giving a simple introduction to the classical variational problem. In the work, we apply the method of integration-byparts technique which lies at the core of the theory of stochastic calculus of variation as provided in Malliavin Calculus. We consider the application of this calculus to the computation of Greeks, as well as discussing the calculation of Greeks (price sensitivities) by considering a one dimensional Black-Scholes Model. The result shows that Malliavin Calculus is an important tool which provides a simple way of calculating sensitivities of financial derivatives to change in its underlying parameters such as Delta, Vega, Gamma, Rho and Theta.

[1] Bally, V., Caramellio, L. & Lombardi, L. (2010). An introduction to Malliavin Calculus and its application to finace. Lambratoire
d'analysis et de Mathématiques. Appliquées, Uviversité Paris-East, Marne-la-Vallée.
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Engineering Vol I. WCE 2011, July 6-8, London, U.K.
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South Africa.
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[9] Nualart, D.G. (2009). Lectures on Malliavin Calculus and its applications to Finance.University of Paris.
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Abstract: In this paper, we study rectangular matrices which satisfy the criteria of the Cayley-Hamilton theorem for a square matrix.Various results on  characteristic polynomials,  characteristic equations,   eigenvalues and α-minimal polynomial of rectangular matrices are proved. AMS SUBJECT CLASSIFICATION CODE: 17D20(γ,δ).

Keywords: Rectangular matrix,  characteristic polynomial,  characteristic equation,   eigenvalues and α-minimal polynomial.

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Abstract: In this paper, a numerical method for Nth - order fuzzy initial value problems (FIVP) based on Seikkala derivative of fuzzy process is studied. The fourth order Runge-Kutta method based on Centroidal Mean (RKCeM4) is used to find the numerical solution and the convergence and stability of the method is proved. This method is illustrated by solving second and third order FIVPs. The results show that the proposed method suits well to find the numerical solution of Nth – order FIVPs.

Keywords - Fuzzy numbers, Nth - order Fuzzy Initial Value Problems, Runge-Kutta method, Centroidal Mean, Lipschitz condition.

[1]. Abbasbandy. S, T. Allahviranloo, Numerical solutions of fuzzy differential equations by taylor method, Comput. Methods Appl. Math. 2 (2002) 113-124.
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Abstract: A numerical study is presented of two-dimensional laminar steady-state on megneto-hydrodynamics (MHD) free convection for heat flow patterns within trapezoidal enclosures. A finite element analysis is performed to investigate the effects of unifor heating and is also used for solving the Navier-Stokes and Energybalance equations.In this study, cold bottom walls, uniformly heated left and right (side) walls and insulated top walls with inclination angles (ф) are considered in a trapezoidal enclosure. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters, Prandtl numbers, (Pr = 0.026 - 0.7), and Rayleigh numbers (Ra = 103 – 105), Hartmann number (Ha = 50) with various tilt angles Ф = 450, 300 and 00(square).Numerical results are presented in terms of streamlines, isotherms, heat function (total heat flux) and nusselt numbers.for different Ra and Pr. As Ra increases conduction dominant region changes for different Pr. Complete heat transfer analysis is performed in terms of local and average nusselt numbers.

Keywords: Free convection, Finite element method, Trapezoidal Enclosures, Uniform heating.

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Abstract: In the present paper, we study some properties of CR-submanifolds of a nearly hyperbolic cosymplectic manifold. We also obtain some results on 𝜉−horizontal and 𝜉−vertical CR- submanifolds of a nearly hyperboliccosymplectic manifold.

Keywords: CR-submanifolds, nearlyhyperbolic cosymplectic manifold, totally geodesic,parallel distribution

[1]. A.Bejancu, CR- submanifolds of a Kaehler manifold I, Proc. Amer. Math. Soc. 69 (1978), 135-142.

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[3]. C.J. Hsu, On CR-submanifolds of Sasakian manifolds I, Math. Research Center Reports, Symposium Summer 1983, 117-140.

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[7]. C. Ozgur, M. Ahmad and A. Haseeb, CR-submanifolds of LP-Sasakian manifolds with semi-symmetric metric connection, Hacettepe J. Math. And Stat. vol. 39 (4) (2010), 489-496.

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[10]. M. Ahmad, M.D. Siddiqi and S. Rizvi, CR-submanifolds of a nearly hyperbolic Sasakian manifold admitting semi-symmetric semi-metric connection, International J. Math. Sci. &Engg.Appls., Vol. 6 (2012), 145-155.

Abstract: The purpose of the study is to get some qualitative and quantitative insight into the problem of flow in vessels under consideration where the concentration of lubrication film of plasma is present between each red cells and tube wall. This film is potentially important in region to mass transfer and to hydraulic resistance, as well as to the relative resistance times of red cells and plasma in the vessels network.

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