The derivation is made possible by careful investigation on the system configuration and precise calibration of involved system parameters.
Stemming from a one-dimensional approach and thanks to a compact notation for the a priori kinematic field approximation over the beam cross-section, the model derivation is made general regardless the approximation order.
For simplicity, the derivation is made for the form (2), but it is straight-forward to generalise to (1) also.
The derivations were made by assuming that the significant part of the concentration profile within a pellet may be represented by a parabolic expression over a spatial domain which expands with time.
Different derivations are made for cantilevered pipes, where the centreline is assumed inextensible, and for pipes with both ends fixed; it is shown that the derivations, the origin of the various terms and the structure of the equations are distinctly different in these two cases.
A more formal derivation of this model was made later by Nicholas Kaldor, who is largely credited for its exposition.
The selection of 450 patients for the derivation and validation cohorts was made to minimize the burden for the investigators during manual medical record review while ensuring a robust sample size for both subsets.
In the above derivations, the paraxial assumption was made for the rays passing through the refractive planes.
Since derivation was so easy, no attempt was made to increase or exactly quantify the efficiency.
In [40, 41], progress was made toward a rigorous derivation of Tanaka's capacity formula.
