Therefore, the mathematical model must not only be able to reproduce the experimentally observed systems behavior at the points of time of the experiments but also be able to extrapolate the systems behavior between the experimentally observed time points.
However, it is also visible that for the sorbents with higher water affinity, i.e., CSIII or PEG, the structure of the plotted surface shows discontinuous behavior at those points, where the sample temperature is higher than the packing temperature, which is most likely caused by water condensing on the sorbent surface, influencing the precision and accuracy of the measurement.
Thus, the material behavior at the material point can be modeled in an elegant, natural and simple way.
At the lowest, which is yet by several orders larger than the atomic scale, constitutive behavior at the material point is described using traditional continuum equations.
Questions related to its operator norm function and its behavior at the critical point for norm continuity or compactness or differentiability are studied.
The method uses experimentally determined values of Henry's coefficient and a theoretically predicted value of behavior at the critical point of water to provide data that can be fitted by a semi-empirical correlation.
By using this method we not only solve a center-focus problem, but also at the same time, we open a class of differential systems, which do not have to be polynomial differential systems, with the same qualitative behavior at the critical point.
In particular, it is important to properly simulate the behavior at the branch point of PYR, where the reaction rate through PDH, ν PDH must be the negative function of ArcA (or phosphorylated ArcA, ArcA-P), while the reaction rate through pyruvate formate lyase (Pfl), ν Pfl is the positive function with respect to ArcA and Fnr, where PYR is converted to formate (FOR) and AcCoA (Figure 7).
