deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 209e825..70d0282 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
...
In this work we expand on this idea providing more generality and utility to the theory by generalizing to higher-order kinetics. For this work we propose a generalization of our previous first order irreversible decay kinetics to higher orders, with complete framework analyzing any $n^{th}$ order system with this description. In this work we propose a method for studying these more complex cases in chemical kinetics proposing theory to analyze disorder in $n^{th}$ order kinetics and provide detailed proof-of-principle analyses for second order kinetics for irreversible decay phenomena. We then connect this theory to previously accepted work on first order kinetics showing how the model simplifies in a consistent manner when working with first order models.  We consider the irreversibleelementary  reaction types \begin{equation}  A^i \to \mathrm{products}\quad\quad\textrm{for}\quad i=1,2,3,\ldots,n  \end{equation}  with the differential  rate laws \begin{equation}  \frac{dC_{A^i}(t)}{dt} \frac{dC_i(t)}{dt}  = k_i(t)C_{A^i}(t). k_i(t)\left[C_i(t)\right]^i.  \end{equation}  Experimentalists deduce rate laws from Experimental  data corresponding corresponds  to the integrated form of the  rate law. law, a concentration profile.  For example, in the case of  the $i^{th}$-order reaction reaction,  the traditional integrated rate law, with $k_i(t)\to\omega$ law and a rate ``constant'', $k_i(t)\to\omega$,  is \begin{equation}  \frac{1}{C_A(t)^{i-1}} \frac{1}{C_i(t)^{i-1}}  = \frac{1}{C_A(0)^{i-1}}+(i-1)\omega \frac{1}{C_i(0)^{i-1}}+(i-1)\omega  t. \end{equation}  Survival functions are Normalizing  the input to our theory. They are a measure of concentration profile, by comparing  the concentration of species $A$  at a time $t$compared  to the initial concentration concentration, leads to the survival function  \begin{equation}  S_i(t) = \frac{C_{A^i}(t)}{C_{A^i}(0)} \frac{C_i(t)}{C_i(0)}  = \sqrt[i-1]{\frac{1}{1+(i-1)\omega tC_{A^i}(0)^{i-1}}}, tC_i(0)^{i-1}}},  \end{equation}  which come from we will use as  the integrated rate law. input to our theory.