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TMF, 2007, Volume 153, Number 2, Pages 262–270 (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

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

DOI: https://doi.org/10.4213/tmf6137

Full text: PDF file (418 kB)
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English version:
Theoretical and Mathematical Physics, 2007, 153:2, 1575–1581

Bibliographic databases:

Received: 02.07.2007

Citation: V. P. Maslov, “Nonstandard analysis, parastatistics, and fractals”, TMF, 153:2 (2007), 262–270; Theoret. and Math. Phys., 153:2 (2007), 1575–1581

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  • http://mi.mathnet.ru/eng/tmf/v153/i2/p262

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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. 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
    2. Rovenchak A., “Harmonically Trapped Bosons on the Sierpiriski Carpet”, Acta Physica Polonica A, 118:4 (2010), 531–533  crossref  isi  elib  scopus
    3. Rovenchak A., “Complex-Valued Fractional Statistics for D-Dimensional Harmonic Oscillators”, Phys. Lett. A, 378:3 (2014), 100–108  crossref  mathscinet  adsnasa  isi  scopus
    4. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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