iosr-Jm   Volume-4 ~ Issue-2

Abstract :In this paper Laminar MHD flow in the entrance region of a plane channel with dissipation under the influence of transverse magnetic field. The motion of laminar conducting fluid between two parallel plates is considered. The channel has height of 2a and a width of d. A rectangular coordinate system is placed on channel with the origin at the center of channel at the left hand edge. The flow problem is described by means of partial differential equations and solutions are obtained by the use of a finite difference technique. The velocity, temperature and pressure profiles are shown in graphs and their behaviour is discussed for the different values of magnetic field parameter M and Eckert Number Ek for fixed Prandtl Number Pr.
Keywords -Laminar Flow, MHD Plane Channel

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Abstract :In this paper a mathematical analysis of effect of couple stresses on magneto hydrodynamic (MHD) flow past a parallel plate channel of viscous, incompressible and electrically conducting fluid in the presence of porous medium has been studied. An exact solution of the dimensionless governing equations has been obtained by using method of perturbation technique. The effects on velocity, discharge between the plates and wall shear are studied for different parameters like Hartmann number, Reynolds number, pulsation, time, porosity parameter, pulsation frequency and reported graphically to show the interesting aspect of the solution.
Keywords: Couple stresses, Magneto hydrodynamics (MHD), poiseuille flow, porous medium

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Abstract :In this paper, we investigate some distributive and absorption properties of operations on soft sets.
Keyword: Soft sets operations, Distributivity, Absorption.

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[3] D. Pei and D. Miao, From Soft Sets to Information Systems, in Granular Computing, 2005 IEEE International Conference, Vol. 2 p.
617–621.
[4] Fu Li, Notes on the Soft Operations, ARPN Journal of Systems and Software, Vol. 1 no. 6 (2011), 205–208.
[5] K. Qin and Z. Hong, On Soft Equality, Journal of Computational and Applied Mathematics, 234 (2010), 1347–1355.
[6] M.I. Ali, F. Feng, X. Liu, W.K. Min, M. Shabir, On Some New Operations on Soft Set Theory, Computers and Mathematics with
Applications, 57 (2009), 1547–1553.
[7] P.K. Maji, R. Biswas, A.R. Roy, Soft Set Theory, Computers and Mathematics with Applications, 45 (2003), 555–562.

Abstract :The present model discusses the drug distribution in the layers of human dermal parts. We have considered tissue absorption rate of drug is decreasing function of drug concentration, also considered linear shape functions for approximating element wise approximate solution by Finite Element Method (FEM).In this method each region is referred to as an element and the process of subdividing a domain into a finite number of elements is referred to as discretization. Elements are connected at specific points, called nodes, and the assembly process requires that the solution be continuous along common boundaries of adjacent elements. MATLAB Software used for numerical calculation.
Keyword: Transdermal Drug Delivery System, Diffusion Equation, Finite Element Method

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Abstract :Many cell types encode signals in the frequency component of calcium oscillations. In non-excitable cells calcium oscillations are induced by calcium influx from inositol trisphosphate receptors (IP3R) or/and ryanodine receptors (RyR). The frequency of Calcium oscillations induced in such cases is primarily by the way intracellular stores like endoplasmic reticulum, sarco-endoplasmic reticulum are refilled. Sarco-endoplasmic reticulum calcium ATPase (SERCA) is the major pathway by which this refilling process is effected. Most of the mathematical models proposed thus far used Michaelis-Menten kinetics to formulate SERCA pump. In this paper more emphasis has been given over the mathematical formulation of SERCA pump. In particular reverse quasi steady-state approximation (rQSSA) is used to formulate SERCA pump. Comprehensive comparative analysis is performed with the previous SERCA pump formulation. An apparent increase in frequency and amplitude of calcium oscillation is observed.
Keyword: SERCA, Michelis-Menten, rQSSA, Enzyme Kinetics.

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Abstract :This study adopted and analyzed a SEIV (Susceptible, Exposed, Infected, and Vaccinated) vaccination model with general non-linear incidence rate and waning preventive vaccine. Thereafter the Basic Reproduction Number of the disease free equilibrium was found and simulated, it was found to be globally asymptotically stable. The epidemic free equilibrium was also found, analyzed using the Bellman and Cooke's Theorem. The result of the analyses was simulated using MATLAB and found that it is Stable on probability points of the vaccine waning period from 1.0 down to 0.3 and unstable on the points 0.2 and 0.1. Which is logical, that is, as the vaccine efficacy decreases so does the stability of the model.
Keyword: Basic Reproductive Number, Disease Free Equilibrium, Epidemic Free Equilibrium, Stability, Vaccine.

[1] R. Naresh, S. Panduy, A.K. Misra, Analysis of Vaccination model for carrier dependent infectious diseases with environmental
effects. Journal of Non-linear Analysis: Modeling and control, 13 (3), 2008, 331-350.
[2] C.P. Farrington, On Vaccine Efficacy and Reproduction numbers, Journal of Mathematics and Bioscience, 185, 2003 89-109.
[3] A.B. Gumel, S.M. Moghadas, A qualitative Study of a Vaccination Model with Non-Linear Incidence. Journal of Appl. Math.
Comp, 143, 2003, 409-419.
[4] C.M. Kribs-Zaleta, J.X. Velasco-Hernandez, A Simple Vaccination Model With Multiple Epidemic States, Math. Biosc. 164, 2000,
183-201.
[5] B. shulgin, L. Stone, Z. Agur, Pulse Vaccination Strategy in the SIR Epidemic Model. Bull Math. Biol. (1998) 60, pp. 1123-1148.
[6] L-M. Cai, X-Z. Li, Analysis of a SEIV Epidemic Model With Non-Linear Incidence Rate, Applied Mathematical Modelling (2008),
doi: 10.1016/j.apm.2008.01.005
[7] J.K. Matt and R. Pejman, Modelling Infectious Diseases in Human and Animals, New Jersey, Princeton and Oxford, 2008.
[8] J. Jia and ping Li, Global Analysis of Human SVEIR Epidemic Model with Partial Immunity, Mathematica Aeterna, (2011), Vol 1
pp. 547-561
[9] M. De La Sen, S. Alonso-Quesada and A. Ibeas, Observer based Vaccination for a SEIR Epidemic Model with Time Varying Total
Population, International Conference on Circuits, Systems and Simulation (IPCSIT), (2011) Vol. 7, pp.11-22. IACSIT Press
Singapore.
[10] M. De La Sen, S. Alonso-Quesada and A. Ibeas, On the Equilibrium Points and Some Properties of a SVEIRS Epidemic Model.
Proceedings of the World Congress on Engineering (2011) Vol. III, London UK.

Abstract :In this paper, we can use Stirling's interpolation to compute the mean and gauss curvatures for any surface z = f(x, y) at any point (x0, y0).
Keyword: Differential geometry, Gauss curvature, Mathematica program, Mean curvature, Stirling's interpolation.

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