deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 29d71fe..37117bf 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
\begin{equation}\label{eq:system_equivalent_flux_density}  SEFD = {\frac{T_{sys}}{\frac{\eta_a A}{2k_B}}}  \end{equation}  where $T_{sys}$ is the system temperature including contributions from receiver noise, feed losses, spillover, atmospheric emission, galactic background and cosmic background (Crane & Napier 1989). $k_B = 1.380 \times 10^{-23}$ Joule $K^{-1}$ is the Boltzmann constant, $A$ is the antenna collecting area, and $\eta_a$ is the antenna efficiency with \begin{equation}\label{eq:antenna_efficiency}  \eta_a $\eta_a  = \eta_{surface} \cdot \eta_{blockage} \cdot \eta_{spillover} \cdot \eta_{taper} \eta_{taper}$.  \end{equation}  \subsection{Minimize Operations Costs}  \subsubsection{Minimize Maintenance Costs} 
...