deletions | additions       diff --git a/Intro1.tex b/Intro1.tex  index 5b5db25..67b8b29 100644  --- a/Intro1.tex  +++ b/Intro1.tex 
...
Rate coefficients are a vital part of any kinetics experiment. There are many instances where the traditional kinetic model does not sufficiently describe a population decaying over time [insert citation]. The overall rate coefficient may depend of a distribution of rate coefficients, or the rate coefficient may be time dependent. These models are respectively known as static and dynamic disorder[insert citation]. Both static and dynamic disorder have mostly been studied in first order irreversible decay reactions[insert citation], but has now been studied in second, mixed second, and $n^{th}$ order irreversible decay. An inequality between two important quantities known as the statistical length and Fisher divergence is able to quantitatively measure the amount of static and dynamic disorder of a rate coefficient over a period of time time,  and is able to determine when traditional kinetics is truly valid[insert citation]. When the inequality is minimized, the statistical description of rate coefficients is also minimized, which can help one determine the best data set to use during a kinetic analysis. This inequality measures the temporal and spatial variation in the rate coefficient. When there is no static or dynamic disorder, this inequality is reduced to an equality and it is the only time where traditional kinetics is truly valid. It has recently been shown that an inequality between the statistical length squared and the divergence can numerically represent how constant a rate coefficient is of a population irreversibly decaying over time in first order[insert citation]. But not every irreversible decay reaction is first order, showing that more theory is required to quantitatively measure flucuations of rate coefficients in higher order reactions. An irreversible decay reaction may follow second order kinetics, with two of the same or different molecules, which can also be treated as a first order reaction by using a pseudo-first order rate coefficient. The focus of this research is making the inequality between statistical length and divergence, which quantitatively measures the disorder of a rate coefficient, extend to higher order reactions.  
...
\end{equation}  The second form of the inequality is the most useful, as the difference in $\mathcal{J}(\Delta t)$ and $\mathcal{L}(\Delta t)^2$ measures the variation in the rate coefficient. When the difference between these two quantities is zero, the rate coefficient is constant.   his This  inequality is derived from the first order rate law and survival function. In traditional kinetics, irreversible decay is only dependent on one rate coefficient, $\omega$, and the mechanism of the reaction. The rate law of a first order reaction of A irreversibly decaying into B is \begin{equation}  \frac{-dA}{dt}=\omega[A]  \end{equation} 
...
\begin{equation}  \int\frac{\frac{dx}{dt}}{{([A_0]-x)([B_0]-x)}}dt=k(t)  \end{equation}  And from that definition of k(t), we get can arrive at  the inequality.