Packaging value-forming function

Calibration curves were fitted, and EC50 values were derived using the nonlinear regression package pro Fit 5.5 (QuantumSoft, Zurich, Switzerland). The results of the calibration curve measurements were fitted to a sigmoidal dose-response function of the following form with a slope faetor of 1 ... 

We have called the package "Miscellaneous RealOnly" to avoid the complex solutions that might otherwise be returned. We have also taken just the solutions from the last CSTR by using solns[[2n — 1]], solns[[2n]]. Now we can use the "listability" of this function cstr[n] and Map it down a vector of values for n. The infix form for Map is / and so we use it as follows ... 

When the same process is used on a waste stream of (necessarily) unknown composition, separation efficiencies cannot be measured directly. With the possible exception of comingling between HDPE and impact-modified forms of PP, the separations are quite sharp. The recovered polymers are functionally pure and have good economic value. Dissolution times are somewhat faster than for virgin pellets due to the thin cross-sections typical of plastics packaging. 

As we see, special Bessel functions are included in the equations. Despite an outward difficult look of those equations they are completely usable to calculate kinetic curves of substances B and C. Bessel functions values for given parameters values could be computed with the help of mathematic packages. Let us pint, that Maple s built-in functions Bessell(0,x), Bessell(l,x), BesselK (0,x), BesselK(l,x) have their Mathcad-analogs in the form of built-in functions I0(x), Il(x), K0(x), Kl(x) correspondingly. 

A brief discussion is perhaps in order on the selected form for representing the equation set as in Eq. (10.25). Some numerical packages used to solve differential equations require that a set of functions be defined that return the derivative values of the differential equations when evaluated. This has several disadvantages. First such a formulation does not allow one to have a set of equations expressed in terms of combinations of the derivative terms. Second, the general case of nonlinear derivative terms or transcendental functions precludes such a simple formulation. Lastly, some important sets of equations, as discussed later, are formulated in terms of a combined set of differential and algebraic equations where some equations do not have a derivative term. These important cases can not be handled if the defining equation formulism simply requires the return of the derivative value. The form selected for representation here has no such limitations and is in keeping with other problem formulations in this work where equations were coded such that the function returns zero when satisfied by a set of solution variables. 

---