In Civ3 we need to drop science slider in the last turn before knowing a tech lest wasting beakers. Is this still true in Civ4?

No, extra carries over to the next tech...

yep it carries over. thank you firaxis! that really is something that reduces micromanagement. :) (same for hammers btw)

yep it carries over. thank you firaxis! that really is something that reduces micromanagement. :) (same for hammers btw)
And if you change techs & production builds without finishing them, the research / hammers aren't lost.

Hammers do decay over time I think, to prevent the case where you (say) build 10 different units to within one turn of completion then queue them to be finished-off one-a-turn for 10 turns.

Oh damn! It carries over? I didnt know that! I just kept lowering it! Well, at least I get more gold that way... but damn, I didnt know! :-/

I've been wondering about this. thanks for the Q&A.

Research decays too, but only by a tiny amount. Know from the Future Tech I had 0% research on - out of 6,000 beakers, it decayed 3 beakers a turn.