# datetime bounds derivations

1. datetime ranges from start and stop

   symbol | description | unit | variable name
   --- | --- | --- | ---
   \(t^{B}(l)\) | datetime boundaries (\(l \in \{1,2\}\)) | \(s\) since 2000-01-01 | datetime_bounds {:,2}
   \(t_{e}\) | datetime stop | \(s\) since 2000-01-01 | datetime_stop {:}
   \(t_{s}\) | datetime start | \(s\) since 2000-01-01 | datetime_start {:}

   The pattern : for the dimensions can represent {time}, or no dimension at all.

   \begin{eqnarray} \phi^{B}(1) & = & t_{s} \\ \phi^{B}(2) & = & t_{e} \end{eqnarray}