at short (或 a moment's) notice

with little warning or time for preparation

临时通知，提前很短时间通知

tours may be cancelled at short notice.

旅行可能会临时通知取消。

put someone on notice (或 serve notice)

warn someone of something about or likely to occur, especially in a formal or threatening manner

正式警告（某人某事将会或可能发生）；正告

we're going to put foreign governments on notice that we want a change of trade policy.

我们将要警告外国政府我们要改变贸易政策。

take no notice

pay no attention to someone or something

不注意

take notice

pay attention; show signs of interest

注意；有兴趣