Paper author problem I'm a PhD student and I've written a paper on a numerical method, whose main contribution is a solution for piezoelectric problem. The paper uses some equations from the work of my MS degree. These equations are not the main novel parts in this paper but they are still important for the completeness of the method. I believe the paper's method is based on the work of MS and the current paper is a generalization of the MS work to a multi-physics problem. 
Of course, I will talk with my previous advisor. But before that, I would like to ask here how do we deal with such a problem basically? 


Which association of this paper belongs to? The current PhD university or the previous MS university? Or both?
I would be the first author, who will be second author and third author? My previous advisor or current advisor?
Is it possible that the previous advisor just lets us publicize without adding his name because he is also very busy and may have no time to revise this paper? (If he wants his name on the paper, he must give comments on it). 


For me, I will be the first author for sure. So I am happy to include both advisors since it has no differences on me. But the problem is about the revision of the paper: I am a little worried that, if the previous advisor is busy,his comments on this paper may come very late. It may delay the submission of the paper. He is a good professor but he is very busy.
I'll give it a try...:

The association should be your current association:


First, it's where an interested reader from abroad can find you, and
secondly, your previous association even might be unhappy if you continue to publish papers with their name on it. (Just imagine some former member - not you, of course! - publishing substandard papers!)


If there are more authors from different universities, such as your former advisor, you should mention their association, too. Sometimes that will lead to a lot of fine-print in the header... but that's not a bad thing, when it comes to publishing: it signifies the work is up to standards of two or more different associations. And many people like to see some collaboration, for a change ;)

As for arranging the authors #2..N, a host of obscure and regional rules is applied :) At some institutions, the last place is considered to be the most honorable ("the chair"), sometimes authors are listed in descending order of importance of their contribution... which without fail will cause trouble when a team wants to publish something. Some resort to alphabetical order, or even comment on the rules applied in a footnote (which is a little bit absurd). So, talk it over with you co-authors :)

If someone can't make a contribution to the publication, the correct way would be not to give them as co-author, but to identifying their contribution (if it is significant - another controversial subject) in the paper. Conversely, if you want someone as co-author who isn't directly involved, like your former advisor, she or he might almost feel obliged to force some (sometimes impractical) changes, in order to justify their co-authorship. - Again, talk to them beforehand, everything is easier that way ;)