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I'm reading a paper by V.S. Vladimirov and I.V. Volovich and they make a particular claim which is supposed to be discussed in:

N.M. Krylov, Dokl. Akad. Nauk SSSR, 60, 687 (1947).

I have not been able to reproduce the claimed result, so, it would be nice to see what precisely is done in the reference above.

The claim is that hyperderivatives of functions on $\mathcal{A} = \mathbb{R} \oplus j\mathbb{R} \oplus j^2\mathbb{R}$ with $j^3=1$ give three dimensional wave equations. V.S. Vladimirov and I.V. Volovich do show other examples that I've been able to reproduce, but the $j^3=1$ example is elusive.

Thanks in advance for any insights.

Update:(9/13/2012) I have tried my interlibrary loan service and contacting the author, but neither has been thus far successful. I need to find the title of the article and/or the page numbers for the interlibrary loan service to try to find it. The style of reference I list above is sadly insufficient for them to locate the article.

James S. Cook
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  • You're not looking for a reference, you're looking for a precise paper you don't have access to, right? – Fernando Muro Sep 06 '12 at 05:41
  • If needed, I could look for the paper in one of the big libraries here and maybe scan it. – Thomas Riepe Sep 06 '12 at 06:19
  • this journal is only available electronically since 1996 (when the "SSSR" was dropped from the name), so a request for a copy from a library seems the only option. – Carlo Beenakker Sep 06 '12 at 10:12
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    Did you try interlibrary loan? – Igor Belegradek Sep 06 '12 at 10:35
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    Most of Russian mathematical joournals are available in electronic form here: http://www.mathnet.ru/#, but this is not the one. You can try to contact I.V.Volovich directly, his address is here: http://www.mathnet.ru/php/person.phtml?option_lang=rus&personid=8846 I am sure he will help. – Sergei Akbarov Sep 06 '12 at 11:26
  • @Fernado Muro yes, this is a specific paper which I don't have direct access, and interlibrary loan might work... haven't tried it yet. My pessimistic suspicion is that the abbreviated form of the journal reference would impede communication with my library staff... I was hopeful that it might exist open access somewhere because I've found scattered papers here and there. – James S. Cook Sep 06 '12 at 16:36
  • @ Sergei Akbarov thanks. I will try that. – James S. Cook Sep 06 '12 at 16:37
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    @James S. Cook: mathscinet (or google search) says that "Dokl. Akad. Nauk SSSR" is the abbreviation of "Doklady Akademii Nauk SSSR, Continued as Dokl. Akad. Nauk, Mathematics section translated in Soviet Math. Dokl., Soviet Phys. Dokl. and Soviet Physics Dokl." – Igor Belegradek Sep 06 '12 at 21:59
  • Thanks everybody, this has been helpful. I sent the email and I'm waiting to hear back from the interlibrary loan service here. I'll update this once something happens. – James S. Cook Sep 07 '12 at 19:30
  • @Thomas Riepe If it's not too much trouble could you look for this at your library? It would seem the other options are not working. In particular: 1.) the email was not sucessful 2.) "Library of Congress says "Other pagination is by issue, not cumulative to across the volume. Without an article title, we have nothing to look for."

    Apparently, I need the title of the article. The style of reference does not list the explicit title and I have not been able to find the title with google thus far.

     – James S. Cook Sep 14 '12 at 02:03
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    It appears that my library has this journal, in offsite storage. I've put in a request and should have the bound volumes tomorrow or early next week. Our catalog lists volume 60 with year 1948, so I also requested volumes 55-59 just in case (though from the catalog it appears 56-58 may be missing). I don't read Russian but hopefully I can transliterate well enough to tell if I'm looking at your article, and if so I'll send it to you. Is the yahoo.com address on your web page a good one to use? – Nate Eldredge Sep 14 '12 at 04:04
  • @James S. Cook - I see below that you already receive a copy, so I do not look further for it. – Thomas Riepe Sep 14 '12 at 11:21
  • @Thomas Riepe I have not obtained a copy and it is now official that neither Nate nor Carlo have it in their libraries. – James S. Cook Sep 18 '12 at 01:49
  • OK, I'll call my friends in St. Petersburg too then. It may take a few days :) If anyone gets it sooner, post here. – fedja Sep 20 '12 at 03:17

1 Answers1

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Does this sound like it?

Крылов Н.М. О кватернионах Роана Гамильтона и понятии моногенности// ДАН СССР.- 1947.- т.55, № 9. с.799-800.

In English: N.M.Krylov, On Rowan Hamilton quaternions and the notion of monogeny, Doklady Akademii Nauk SSSR (Proceedings of the Academy of Sciences of the USSR), 1947, vol. 55, no 9, pages 799-800

It disagrees with the data you have in the volume and the issue numbers but it is the closest one I could find as far as the other parameters are concerned. I do not have an access to the article either (I doubt any kind soul was patient enough to scan all old volumes of DAN) but if you confirm that the title sounds reasonable, I can try to get a scan of the article (alas, in Russian). Also, I doubt it'll have a full proof of anything there: most likely it is a short announcement (a la Comptes Rendus). However, it still may give some clues.

fedja
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    @James S. Cook: our library has this issue of DAN; I'll scan the article and email it to you this Monday (I looked before in volume 60, without finding it, so evidently I was looking in the wrong volume). – Carlo Beenakker Sep 14 '12 at 08:21
  • @fedja This does look like the right article. In Russian will do nicely. Since it sounds like Carlo has easy access, and in the interest of not duplicating the effort, If Carlo Beenakker could scan it and email it to classicalsuperfield@gmail.com then I would be grateful. Of course, I am thankful for the offers from Nate Eldrege and fedja. – James S. Cook Sep 14 '12 at 15:08
  • I'm sorry, this volume is missing from Leiden University library; what we have of Doklady Akademii Nauk was published through the French Academy of Sciences, and apparently the war years interrupted that. – Carlo Beenakker Sep 17 '12 at 09:28
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    I've just sent you an e-mail with the scan. – fedja Sep 24 '12 at 11:41
  • @fedja Success! However, that paper is apparently not about the three-dimensional real associative, unital algebra with $j^3=1$. Which is not surprising given the title you posted in this answer to start... so, I guess the right paper is somewhere... but I don't know it's title or year of publication. Fedja has kindly provided a list of all Krylov's publications so I will search that and see if I can make a less ambiguous request in the future. – James S. Cook Sep 25 '12 at 03:15