[see also: considerable, important, substantial]
This can result in a significant loss of smoothness.
It is important to recognize that there is a significant subclass of vector fields for which the ambiguity alluded to above disappears.
In all our analysis, only the order of magnitude of $P$ will be significant.
Their result gives no information when $k$ is large, whereas (5) is significant regardless of the size of $k$.
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