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 Mat. Zametki, 2006, Volume 80, Issue 6, Pages 856–863 (Mi mz3362)

Negative asymptotic topological dimension, a new condensate, and their relation to the quantized Zipf law

V. P. Maslov

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: We introduce the notion of weight for the asymptotic topological dimension. Planck's formula for black-body radiation is refined. We introduce the notion of negative asymptotic topological dimension (of hole dimension). The condensate in the hole dimension is applied to the quantized Zipf law for frequency dictionaries (obtained earlier by the author).

DOI: https://doi.org/10.4213/mzm3362

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English version:
Mathematical Notes, 2006, 80:6, 806–813

Bibliographic databases:

UDC: 519

Citation: V. P. Maslov, “Negative asymptotic topological dimension, a new condensate, and their relation to the quantized Zipf law”, Mat. Zametki, 80:6 (2006), 856–863; Math. Notes, 80:6 (2006), 806–813

Citation in format AMSBIB
\Bibitem{Mas06} \by V.~P.~Maslov \paper Negative asymptotic topological dimension, a new condensate, and their relation to the quantized Zipf law \jour Mat. Zametki \yr 2006 \vol 80 \issue 6 \pages 856--863 \mathnet{http://mi.mathnet.ru/mz3362} \crossref{https://doi.org/10.4213/mzm3362} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2311613} \zmath{https://zbmath.org/?q=an:1137.81022} \elib{http://elibrary.ru/item.asp?id=9429649} \transl \jour Math. Notes \yr 2006 \vol 80 \issue 6 \pages 806--813 \crossref{https://doi.org/10.1007/s11006-006-0203-7} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000243368900022} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33845615535} 

• http://mi.mathnet.ru/eng/mz3362
• https://doi.org/10.4213/mzm3362
• http://mi.mathnet.ru/eng/mz/v80/i6/p856

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. P. Maslov, “General Notion of a Topological Space of Negative Dimension and Quantization of Its Density”, Math. Notes, 81:1 (2007), 140–144
2. V. P. Maslov, “Densities of Lattices Corresponding to Spaces of Positive, Negative, and Variational Dimension, and Their Application to Time Series”, Math. Notes, 81:1 (2007), 222–233
3. V. P. Maslov, “Zeroth-order phase transitions and Zipf law quantization”, Theoret. and Math. Phys., 150:1 (2007), 102–122
4. Maslov V. P., “Quantization of topological spaces of negative dimension, parastatistics, and distribution of dependent random variables”, Dokl. Math., 75:3 (2007), 424–427
5. Maslov V. P., “Revision of probability theory from the point of view of quantum statistics”, Russ. J. Math. Phys., 14:1 (2007), 66–95
6. Maslov V. P., Maslova T. V., “Synergetics and architecture”, Russ. J. Math. Phys., 15:1 (2008), 102–121
7. Maslov V. P., “Theorems on the debt crisis and the occurrence of inflation”, Math. Notes, 85:1-2 (2009), 146–150
8. Maslov V. P., Maslova T.V., “On the boundedness law for the number of words in an overabundant dictionary”, Math. Notes, 85:1-2 (2009), 296–301
9. Maslov V. P., “Theory of chaos and its application to the crisis of debts and the origin of inflation”, Russ. J. Math. Phys., 16:1 (2009), 103
10. Maslov V., “Dequantization, Statistical Mechanics and Econophysics”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, ed. Litvinov G. Sergeev S., Amer Mathematical Soc, 2009, 239–279
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