[H]e always found it hard to give up anything he had set his heart on, no matter how trivial.

There's a website that can be a good learning reinforcement.

A result by Liskevich and Perelmuter from 1995 yields the optimal angle of analyticity for symmetric submarkovian semigroups on L_p, 1

In this latter or northern offthrow, nearly the whole of Peeblesshire consists, and the general dip or inclination of its rocks is accordingly northerly, or more strictly, towards north-north-west.