deletions | additions       diff --git a/$n^{th}$-order decay.tex b/$n^{th}$-order decay.tex  index 9a60b04..337ae37 100644  --- a/$n^{th}$-order decay.tex  +++ b/$n^{th}$-order decay.tex 
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\begin{equation}  \frac{\mathcal{J}_n(\Delta t)}{\Delta t} = \int_{t_i}^{t_f}{(n-1)^2\omega^2}([A_0]^{n-1})^{2} dt  \end{equation}  The inequality becomes  \begin{equation}  (n-1)^2\omega^2([A_0]^{n-1})^2\Delta t^2-[(n-1)\omega[A_0]^{n-1}\Delta t]^2\geq0  \end{equation}  Again, we see that when Both the length squared and the divergence are $(n-1)^2\omega^2([A_0]^{n-1})^2\Delta t^2$:  the bound $(n-1)^2\omega^2([A_0]^{n-1})^{2}\Delta t^2=[(n-1)\omega[A_0]^{n-1}\Delta t]^2$ holds, holds when  there is no static or dynamic disorder, and a single rate coefficient can be defined is sufficient  for the irreversible decay process.