datetime start derivations

1. datetime start from datetime and stop

   symbol	description	unit	variable name
   \(t\)	datetime (mid point)	\(s\) since 2000-01-01	datetime {:}
   \(t_{s}\)	datetime start	\(s\) since 2000-01-01	datetime_start {:}
   \(\Delta t\)	time duration	\(s\)	datetime_length {:}

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

   \[t_{s} = t - \frac{\Delta t}{2}\]

2. datetime start from range

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

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

   \[t_{s} = t^{B}(1)\]