1. 确实无疑地：foppishly 浮华地 | for a certainty 确实无疑地 | for a change 为改变
1. Economists said business wants profits to improve and is looking for certainty about the recovery's vigor before going on a spending and hiring spree.
2. We cannot say with certainty whether the scheme's promoters in China are aware of the scheme or are simply working for a finder's fee.
3. Well, this is unexpected - a comic book about the quest for logical certainty in mathematics.