With a table the table caption should be an integral part so I think it is reasonable to have abbreviations in the table body as long as the abbreviations are explained in the table caption.
The same could apply to figures as well but I would go further and aim for making the graphics along self-explanatory even without its caption.
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Visit Stack Exchange As we all know, you typically abbreviate something the first time that particular term shows up in a paper.
So, perhaps a appears only ONCE in the abstract, then I shouldn't abbreviate it because then I would have defined an abbreviation that I would not have used again (given the concept of 'the abstract should be able to stand on its own).
The problem with (2) is that people will immediately think that the 'first instance' of should be abbreviated and don't immediately consider the 'stand-alone' idea so I'm either having to revise or try to put up a convincing argument for what I did.
So, my question is, what is the proper way of handling these abbreviations and is the idea of 'this piece must be able to stand on its own' valid (and if its valid, what exactly does this idea apply to)?
Additional Information: I am a computational chemist so we pretty much are forced to use the alphabet-soup of acronyms.
The abstract needs to stand on its own, and the introduction should also make sense to somebody who hasn't just read the abstract.
Additionally, as some have said, in some fields there may be abbreviations that are so generally accepted that there is no need to expand them.