[from sth; see also: besides, except
Apart from these two lemmas, we make no use of the results of [4].
That is---apart from the use of relaxed controls---precisely the stochastic Bellman equation.
Apart from being very involved, the proof requires the use of......
for no x apart from the unique solution of......
[Note the difference between besides, except and apart from: besides usually indicates “adding'' something, except “subtracts'', and apart from can be used in both senses; after no, nothing etc., all three can be used.]
Their centres are a distance at least N apart.
The m points x1,…,xm are regularly spaced t units apart.
What sets the case n=5 apart is the fact that homotopic embeddings in a 5-manifold need not be isotopic.