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The rates of reactions as a function of substrate concentration were fit to either the regular Hill equation or the Hill equation complemented with an allowance for partial substrate inhibition, as described in the Supporting Information, by means of a combination of the Nelder Mead and Marquardt nonlinear regression algorithms, as implemented in the SpectraLab software package.
We investigate the regular differential equation (2.8).
Consider the auxiliary regular differential equation.
In order to use the regular solution equation, simplified assumptions have been made concerning ΔCP, specifically, ΔCP = 0, or ΔCP = ΔS.
The solubility data was used with the calculated ideal solubility to obtain activity coefficients, which were then fitted to the van't Hoff-like regular solution equation.
For other results concerning the existence and multiplicity of positive doubly periodic solutions for a single regular telegraph equation or regular telegraph system, see, for example, the papers [13 17] and the references therein.
Also, Fig. 1 shows the exact solution (u x,t)) of the regular Harry Dym equation ((alpha = 1)) given by Mokhtari [20] for constants value of (a=4, b=1, c=1).
For the clear fluid zone, the regular Navier Stokes equation is used; and the Darcy Brinkman Forchheimer model is used for simulating flow in the porous zone.
The S50 term in eq 2 is defined in a way similar to that in the regular Hill equation: as the hth root of the apparent dissociation constant of the catalytically competent enzyme substrate complex.
Unlike regular coordinate equations, conic sections are general equations and don't necessarily have to be functions.
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