Integral equations division scheme

Rubinow defined a normalized cell maturation variable, p. such that a cell will divide when / = 1. Now /x is related to the biochemical events occurring during the cell cycle in some undetermined fashion. It is, therefore, a semiempirical variable and is operationally defined in terms of measured cell cycle times. This implies that all cells divide after the cell cycle time of t hours. It is observed, however, that cell division times are scattered about a mean value. This randomness must be accounted for suitably. Most models account for this with an explicit operation in the mathematical solution by averaging cell division times over the entire population. This scheme leads to the solution of a rather difficult integral equation (see, e.g., Trucco (4)). Recently Subramarian et al. (8) have considered weighted-residual methods for more easily solving these problems. 

Division of equation [9.126] into the constituents must be done with full assurance to maintain influence of different solvents. For this reason, it is necessary to have a few isotherms of equilibrium constant dependencies on permittivity (K=f(e)T). We have developed an equation of a process depicted by scheme [9.45] after approximating each isotherm as InK vs. 1/efunction and by following approximation of these equations fore-1, e-2, e-3...e-j conditions. We then can calculate the integral value of process entropy by differentiating relationship [9.55] versus T, e.g., AG= -RTlnK ... 

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