Exact(30)
which is the first condition in (1.9).
Let (alpha_{i}) satisfy the first condition in (16).
which, together with the first condition in (3.20), implies that (3.19) holds.
This means, by the first condition in (13), that ∑ ∞ H ( k, v ) = ∞.
The first condition in both reducers' algorithm takes care of this situation.
For this graph, the first condition in Definition 3.2 means S, T are jointly nondecreasing with respect to this order.
Similar(30)
In what follows, without of loss generality, we shall assume that the first conditions in (4.34) hold with (i=2), (j=1).
This is equivalent to the second condition in (3.19).
If the second condition in (4.6) is fulfilled, we use the dual arguments.
Assume the converse, that is, the second condition in (3.7) does not hold.
Get x n k n through (18) and x nm through the third condition in (17) 5.
Write better and faster with AI suggestions while staying true to your unique style.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com