deletions | additions       diff --git a/Nonlinear irreversible kinetics.tex b/Nonlinear irreversible kinetics.tex  index c772046..6cde4ca 100644  --- a/Nonlinear irreversible kinetics.tex  +++ b/Nonlinear irreversible kinetics.tex 
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\displaystyle -\frac{d}{dt}\ln S_1(t) & \text{if } i = 1 \\[3pt]  \displaystyle +\frac{d}{dt}\frac{1}{S_i(t)^{i-1}} & \text{if } i \geq 2.  \end{cases}  \end{equation}For example, in the case of the $i^{th}$-order reaction, the traditional integrated rate law and a rate ``constant'', $k_i(t)\to\omega$, is  \begin{equation}  \frac{1}{C_i(t)^{i-1}} = \frac{1}{C_i(0)^{i-1}}+(i-1)\omega t.  \end{equation}  Normalizing the concentration profile, by comparing the concentration at a time $t$ to the initial concentration, leads to the survival function  \begin{equation}  S_i(t) = \sqrt[i-1]{\frac{1}{1+(i-1)\omega tC_i(0)^{i-1}}},  \end{equation}  In traditional kinetics, the rate coefficient of irreversible decay is assumed constant, in which case $k(t)\to\omega$. However, this will not be the case when the kinetics are statically or dynamically disordered. In these cases, we will use the above definitions of $k(t)$.