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

This article is cited in 10 scientific papers (total in 10 papers)

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
Received: 01.11.2006

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

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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. V. P. Maslov, “Zeroth-order phase transitions and Zipf law quantization”, Theoret. and Math. Phys., 150:1 (2007), 102–122  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    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  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    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  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Maslov V. P., Maslova T. V., “Synergetics and architecture”, Russ. J. Math. Phys., 15:1 (2008), 102–121  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Maslov V. P., “Theorems on the debt crisis and the occurrence of inflation”, Math. Notes, 85:1-2 (2009), 146–150  crossref  zmath  isi  elib  scopus
    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  crossref  zmath  isi  elib  scopus
    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  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    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  crossref  mathscinet  zmath  isi
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