apart

[from sth; see also: besides, except, distinguish]

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 ......

There is a curve lying entirely in the open strip $0<\sigma<1$ apart from the endpoints such that ......

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 $x_1,\dots,x_m$ 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.



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