The Mathematics of Growth Against Limits

Abstract

The single step growth against limit equation is introduced and its consequences (s curves) are briefly explored. The possibility of sudden jumps (violations) from one growth limit curve to another is recognized and formulated. The full model featuring stochastic violations is developed. An integral equation governing the time evolution of probability density of growth is derived. The integral equation is reduced to a dispersion relation which is used to calculate the velocities of the first three moments of the growth probability density. The improvements in airliner performance over the years is analyzed by decomposition of certain economic data against the models parameters.

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