I have finished writing one paper, but have not submitted it yet to a journal. I am working on a related but not identical subject, though many of the definitions and theorems are same (but they are true in a very different context compared to the first paper). Now, is it okay to use the same figures that I had used for illustrations in my first paper? What about the theorems and definitions? I feel like changing the theorem statements is not worth spending time on, but is this correct?
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Most journals require that the submitted manuscript has not been submitted total or partially to any other journal. Of course different policies apply to open access journals. If I were you I would check the journal's policy regarding this issue and contact the editors if necessary to get their opinion (probably they will require details on what will be duplicated). To the very least discuss this with your supervisor. You can find yourself in a very unpleasant position if you are not careful (not to mention having your papers rejected), as indicated by @Enthusiastic Student

ddiez
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The journal that I am targetting does not require total new content. I have checked. – Arani Sep 07 '14 at 06:16
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You have to check on both journals. And you have to be careful about self plagiarism. That being said, it is probably enough to use common sense. Imagine you are presenting in one of your manuscript a method, but an application of such method is published before the method (this happened to me). You will have to give a briefing on your method an maybe use some figure to make the point. You may reuse that figure later, assuming you have the copyright. In the case of previous results, if the main goal of both studies is not duplicated it may be again be possible (but check copyright issues). – ddiez Sep 07 '14 at 10:47
first
paper is whatever you submit first and thesecond
paper is the paper you submit after the first one. Put the theorems and all other stuff in thefirst
paper, cite thefirst
paper in thesecond
paper. Alternatively some other reasonable options could potentially be: make azero
paper with the fundamental stuff and cite it in bothfirst
andsecond
or make afull
paper and put everything in it. – Trylks Sep 05 '14 at 16:08