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The adequacy of the model equation in predicting optimum response values was verified effectively using experimental test data that was not used in the development of the model.
After prediction of model equation in RSM and training of artificial neurons in ANNs, the products were used for estimation of the response of the 27 experimental runs.
The usability of the model equation in a real engineering problem was also tested by a numerical solution of a differential equation obtained from the batch reactor.
After prediction of the model equation in RSM and training of the artificial neurons in ANNs, using the data of 13 experimental points, the products were used for estimation of the response of the 35 experimental points.
Our method relies on accurate, essentially noise-free, solutions of the basic microscopic kinetic equation, e.g. the Boltzmann equation or a kinetic model equation; in this paper, the BGK model and the ES-BGK model equations are considered.
As an illustration, we study the generalized parabolic Anderson model equation and prove, under mild geometric conditions, its well-posed character in Hölders spaces, in small time on a potentially unbounded 2-dimensional Riemannian manifold, for an equation driven by a weighted noise, and for all times for the linear parabolic Anderson model equation in 2-dimensional unbounded manifolds.
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We first recall the model equations in full (3+1) dimensions.
We propose a diafiltration model in a dimensionless form with normalized model equations in order to determine general features of optimal diluant utilization strategy.
Many researchers use a time-lagged or loosely coupled approach in solving the Navier Stokes equations and two-equation turbulence model equations in a time-marching method.
This method could be successfully applied to the N-S model equations in polar coordinates.
Figure 6 Exact and numerical solutions of the 2D Navier Stokes' model equations in Cartesian coordinates.
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