Answer
The electrophile and the nucleophile, and the curved arrow mechanism are shown in the picture.
This reaction is not a Brønsted–Lowry acid–base reaction.
Work Step by Step
1) $BH_3$ is an electrophile because it accepts the lone pair of electrons and $CH_3OCH_3$ is a nucleophile because it donates the pair of electron.
The electrophile is a lewis acid and nucleophile is a lewis base.
2) The curved arrow originated from the $CH_3OCH_3$ lone pair of oxygen and goes towards the B in $BH_3$.
3) In this reaction there is no proton transfer.
Therefore, it is not a Brønsted–Lowry acid–base reaction.
