deletions | additions       diff --git a/Nonlinear irreversible kinetics.tex b/Nonlinear irreversible kinetics.tex  index ddeedf9..f95d151 100644  --- a/Nonlinear irreversible kinetics.tex  +++ b/Nonlinear irreversible kinetics.tex 
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\begin{equation}  \frac{dC_i(t)}{dt} = k_i(t)\left[C_i(t)\right]^i.  \end{equation}  Experimental data corresponds is typically a concentration profile corresponding  to the integrated form of the rate law, a concentration profile. law.  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} 
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\begin{equation}  S_i(t) = \frac{C_i(t)}{C_i(0)} = \sqrt[i-1]{\frac{1}{1+(i-1)\omega tC_i(0)^{i-1}}},  \end{equation}  which we will use as the input to our theory. From the survival function, Namely,  we define the time-dependent effective  rate coefficient coefficient, $k_i(t)$,  through an appropriate time derivative depending of the survival function that depends  on thetotal  order $i$  of reaction \begin{equation}  k_i(t) \equiv  \begin{cases}