datetime derivations

1. datetime from start/stop

   symbol	description	unit	variable name
   \(t\)	datetime (mid point)	\(s\) since 2000-01-01	datetime {:}
   \(t_{e}\)	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.

   \[t = \frac{t_{s} + t_{e}}{2}\]

2. datetime from range

   symbol	description	unit	variable name
   \(t\)	datetime (mid point)	\(s\) since 2000-01-01	datetime {:}
   \(t^{B}(l)\)	datetime boundaries (\(l \in \{1,2\}\))	\(s\) since 2000-01-01	datetime_bounds {:,2}

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

   \[t = \frac{t^{B}(1) + t^{B}(2)}{2}\]