deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 5045288..d8d4fef 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
The modified equations for the equilibrium solutions become:  \begin{equation}  A_i^* + \sum_{j} \beta_{ij}A_j^* - \frac {\alpha^{AP}{\lambda_i^q {\alpha^{AP}}{\lambda_i^q}  \sum_{j<=i} P_j P_j^*  = K_a \end{equation}  \begin{equation}  P_i^* = \alpha^{AP} A_i^* + K_p  
...