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Theoretical development of the velocity potential equation for compressible flow and its various consequences has been presented. The geometrical interpretation of potential equation and conformal mapping technique are discussed where the mappings link the flow around a circular cylinder of a slender airfoil. The lift and drag coefficients are determined for the slender airfoils based on the Mach number and compressibility effects. The calculated lift coefficients show that with the increasing of attack angle it increases linearly and a higher lift coefficient is found for a smaller Mach number for any certain attack angle. Similarly, the drag profiles are determined which are exponentially decreased with the increasing of Mach number for any fixed attack angle. The calculated and experimental data on the lift and drag coefficients over the slender airfoil surface are compared and found in good agreement. [ABSTRACT FROM AUTHOR]

This paper aims to estimate the basic reproduction number for Avian Influenza outbreak in local and global poultry industries. In this concern, we apply the SEIAVR compartmental model which is developed based on the well-known SEIR model. The SEIAVR model provides the mathematical formulations of the basic reproduction number, final size relationship and a relationship between these two phenomena. The developed model Equations are solved numerically with the help of Range-Kutta method and the values of initial parameters are taken from the several literatures and reports. The calculated result of basic reproduction number shows that it is locally and globally stable if it is less than and greater than one at disease free equilibrium and at endemic equilibrium, respectively. Furthermore, we have compared among the calculated susceptive, expose, infective, removal, virus and asymptotic compartments where infection rate and expose period are observed very sensitive compared to other parameters. In addition, the model result of infective is compared with the field data and other's model where the present model shows good performance against the field data. [ABSTRACT FROM AUTHOR]