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In the spirit of Which journals publish expository work? please advise:

What consistently high quality journals$^1$ today publish results that would otherwise go to a pure mathematics journal if not for the included applied content,$^2$ motivation, and examples?

PNAS (if the paper is short), Lecture Notes in Mathematics (if it's long), Journal of Interdisciplinary Mathematics, SIAM subject journals, Journal of Modern Dynamics, Journal of Mathematical Biology, Bulletin of Mathematical Biology, and International Journal of General Systems (are the last three read by working mathematicians these days?) go without saying. But what about others?

To make the question answerable, please suggest a journal per answer with comments. So that others can vote on it, and an answer can be accepted eventually.

$^1$ Many applied journals are neither read nor refereed by mathematicians primarily working in mathematics. Which makes it difficult to get appropriate referees to advise on submitted papers, at all or in a timely manner. If only because of, for example, notation or terminology lag (APS journals for example). Please only suggest journals that are not especially obscure. (There are many obscure ones, with inconsistent quality. Nothing wrong with obscurity, but as you know ... arXiv by itself is often more widely read in comparison.)

$^2$ Content that is inappropriate in a pure mathematics journal for it contains sufficiently detailed applications. Yet the applications by themselves cannot be coherently published separately from the majority of the paper, which begins with and discusses a problem of primarily mathematical interest and with conventional mathematical rigour.

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  • $\begingroup$ I've never been able to really decide an answer to this question myself, after a lot of time. Splitting off the applied part into a second paper is the usual decision. But this results in it getting published later. For it would usually then go through revision and resubmission, unlike the first part. For whether the applications are clear or interesting separately is very difficult to judge as the author who wrote it as one single discussion. $\endgroup$ – Guido Jorg Jul 26 '15 at 10:13
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    $\begingroup$ scimagojr.com/… $\endgroup$ – Carlo Beenakker Jul 26 '15 at 10:17
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    $\begingroup$ I don't think I would necessarily assume that the "applied content" automatically makes the paper unsuitable for a pure math journal. If the mathematical results are of interest by themselves, then explaining how they are used in an applied context could only increase the interest, I would think. $\endgroup$ – Nate Eldredge Jul 26 '15 at 15:41
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    $\begingroup$ Math Proc Camb Phil Soc: journals.cambridge.org/action/displayJournal?jid=PSP (If it doesn't satisfy point 1 of your requirements then I don't think I want to know :) ) $\endgroup$ – Ben Green Jul 26 '15 at 19:05
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    $\begingroup$ I had exactly the same question two years ago with this paper: aimsciences.org/journals/pdfs.jsp?paperID=10624&mode=full -- I've been extremely impressed with the relatively new Journal of Computational Dynamics. I experienced high quality of anonymous reviews, a relatively quick turnaround time, and a top-notch theory-savvy editorial board. That being said, I wish they'd go open access and lose the comic sans from their website. $\endgroup$ – Vidit Nanda Jul 27 '15 at 9:58

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