deletions | additions       diff --git a/$n^{th}$-order decay.tex b/$n^{th}$-order decay.tex  index 877e0fd..58ffa15 100644  --- a/$n^{th}$-order decay.tex  +++ b/$n^{th}$-order decay.tex 
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\begin{equation}  k_n(t) \equiv (\frac{d\frac{1}{(S(t)^{n-1)}}}{dt})\equiv(n-1)\omega[A_0]^{n-1}  \end{equation}  The nonlinearity of the rate law leads to solutions that depend on concentration. As shown in equation 4, the statistical length is the integral of the cumulative time dependent rate coefficient over a period of time $\Delta{t}$. The statistical length is \begin{equation}  \mathcal{L}_n(\Delta t)^2 = \left[\int_{t_i}^{t_f}(n-1)\omega([A_0]^{n-1})dt\right]^2   \end{equation} 
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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}  Both the length squared and the divergence are $(n-1)^2\omega^2([A_0]^{n-1})^2\Delta t^2$: the bound holds when there is no static or dynamic disorder, and a single rate coefficient is sufficient for the irreversible decay process. The nonlinearity of the rate law leads to solutions that depend on concentration. This concentration dependence is also present in both $\mathcal{J}$ and $\mathcal{L}$.