The modified kinetic model can be inverted to yield information on the evolution of the distribution of layer sizes during deformation from DSC data.
Hence the function (gamma_{1}mapstoepsilon(gamma_{1})) and (gamma_{1}mapsto epsilon(gamma_{2})) can locally be inverted to yield a function (epsilonmapstogamma_{1} epsilon)) and (epsilonmapstogamma_{2} epsilon)).
If {x k } is an implosion-free sequence, it follows that mink S k >0, so Eq. (7) can be inverted to yield the following condition for signal preservation: t geq frac{max_{k} | x_{k} - m_{k} | }{min_{k} S_{k}}.
As a result, their approach relies upon the assumption that investment, i, installed in period t only becomes productive at (t+1), so that ( i_{it}=i omega _{it},k_{it})) can be inverted to yield (omega _{it}=omega _{t}(i_{it},k_{it})), assuming increasing monotonicity of (i_{ittext ) in (omega _{it}).
In particular, their approach relied upon the assumption that investment, (i_{{ it}}), installed in period t only becomes productive at (t+1), so that (i_{{ it}} = i omega _{{ it}}; k_{{ it}})) can be inverted to yield (omega _{{ it}} = omega (i_{{ it}}; k_{{ it}})) under the assumption of increasing monotonicity of (i_{{ it}}) in (omega _{{ it}}).
This relationship can be inverted to yield p2= pm+0.5(pc−1) and p1=1− pc, establishing that they are equivalent representations.
