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Nonstandard analysis, parastatistics, and fractals

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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.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    V. P. Maslov

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  1. V. P. Maslov
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Correspondence to V. P. Maslov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 2, pp. 262–270, November, 2007.

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Maslov, V.P. Nonstandard analysis, parastatistics, and fractals. Theor Math Phys 153, 1575–1581 (2007). https://doi.org/10.1007/s11232-007-0133-x

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  • DOI: https://doi.org/10.1007/s11232-007-0133-x

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