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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 153, Number 2, Pages 262–270
DOI: https://doi.org/10.4213/tmf6137 (Mi tmf6137) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Nonstandard analysis, parastatistics, and fractals

V. P. Maslov

M. V. Lomonosov Moscow State University
Full-text PDF (418 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf6137
Abstract: To estimate divergent integrals, it is convenient, on one hand, to use ideas of nonstandard analysis and, on the other hand, to approximate the integral with a special lattice model that can be interpreted as space quantization. We apply these methods in the case of noninteger (fractal) and negative (hole) dimensions and present some refined formulas, in particular, for the spectrum of flicker noise.
Keywords: nonstandard analysis, parastatistics, flicker noise, space quantization.
Received: 02.07.2007
English version:
Theoretical and Mathematical Physics, 2007, Volume 153, Issue 2, Pages 1575–1581
DOI: https://doi.org/10.1007/s11232-007-0133-x
Bibliographic databases:
Language: Russian
Citation: V. P. Maslov, “Nonstandard analysis, parastatistics, and fractals”, TMF, 153:2 (2007), 262–270; Theoret. and Math. Phys., 153:2 (2007), 1575–1581
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6137
  • https://doi.org/10.4213/tmf6137
  • https://www.mathnet.ru/eng/tmf/v153/i2/p262
    • This publication is cited in the following 4 articles:
    1. Rovenchak A., “Models of Frequency Spectrum in Texts Based on Quantum Distributions in Fractional Space Dimensions”, 2015 20th International Conference on Control Systems and Computer Science (CSCS) (Bucharest, Romania), eds. Dumitrache I., Florea A., Pop F., Dumitrascu A., IEEE, 2015, 645–649  crossref  isi  scopus
    2. Rovenchak A., “Complex-Valued Fractional Statistics for D-Dimensional Harmonic Oscillators”, Phys. Lett. A, 378:3 (2014), 100–108  crossref  mathscinet  adsnasa  isi  scopus
    3. A. E. Gutman, S. S. Kutateladze, Yu. G. Reshetnyak, “Cofinite numbers, nonstandard analysis, and mechanics”, J. Appl. Industr. Math., 4:2 (2010), 191–193  mathnet  crossref  mathscinet  elib
    4. Rovenchak A., “Harmonically Trapped Bosons on the Sierpiriski Carpet”, Acta Physica Polonica A, 118:4 (2010), 531–533  crossref  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:1260
    Full-text PDF :510
    References:146
    First page:24
     
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