The Mathematica Journal is no longer accepting submissions
mathematica-journal.com
mathematica-journal.com
They aren't. BUT, I would love to see something like this happen for all science journals:
1. You post a paper to arXiv (or equivalent for your field).
2. Preliminary review by whoever is interested (and is qualified to publish on arXiv themselves)
3. Interested editors of various journals contact you with a list of proposed in-depth reviewers (or just accept based on quality of existing reviews).
4. Address reviewer questions (to the extent you think valuable)
5. Post update to arXiv.
6. Editor decides to publish or pass (return to step 3).
2 and 3 are self-reinforcing effects -- why does Nature attract prestigious papers? Because it publishes prestigious papers. Why does Nature attract high-quality research? Because it is full of high-quality research.
All of this is to say that it is likely that, given a distribution of reasonably-edited arXiv-overlay journals, there's a pretty good chance that just a few of them in any given field (or at large) will attract most of the serious work
[1] https://scirate.com/arxiv/quant-ph (go to previous day to see more scites)
eLife also has started its own pipeline for invited preprints: https://elifesciences.org/about/peer-review
It's not without controversy. Especially the eLife decision to not have an accept/reject decision is controversial (https://www.nature.com/articles/d41586-023-00831-6). Personally, I think it's a good decision, there is no place for 'old-style' journals in the way science is developing.
37 titles referencing Mathematica, though all appear to be the software.
While checking past issues on the web, it's a bummer that they didn't work out how to typeset the actual Mathematica commands in the articles as text rather than the current image format. This prevents copy-pasting code, which can spend dozens of lines, making it harder to try them out. That's at least not the case in the Wolfram Comunity pages - I'm guessing those are just notebooks at their core, so much easier to do.