Densities of Lattices Corresponding to Spaces of Positive, Negative, and Variational Dimension,
Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 251-264.

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We prove a general theorem concerning a distribution of Bose–Einstein type. Using this theorem, we apply the notions of lattice dimension and lattice density to oscillatory time series.
Keywords: lattice density, negative dimension, time series, Bose–Einstein distribution, Hölder exponent.
Mots-clés : positive dimension, variational dimension
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V. P. Maslov. Densities of Lattices Corresponding to Spaces of Positive, Negative, and Variational Dimension,. Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 251-264. http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a8/

[1] Matematicheskii entsiklopedicheskii slovar, ed. Yu. V. Prokhorov, Sovetskaya entsiklopediya, M., 1988 | MR | Zbl

[2] Yu. I. Manin, The Notion of Dimension in Geometry and Algebra, arXiv: math.AG/0502016 | MR

[3] V. P. Maslov, “Otritsatelnaya asimptoticheskaya topologicheskaya razmernost, novyi kondensat i ikh svyaz s kvantovannym zakonom Tsipfa”, Matem. zametki, 80:6 (2006), 856–863 | MR | Zbl

[4] V. P. Maslov, “Obschee ponyatie topologicheskikh prostranstv otritsatelnoi razmernosti i kvantovannie ikh plotnostei”, Matem. zametki, 81:1 (2007), 157–160 | MR | Zbl

[5] V. P. Maslov, Negative Dimension in General and Asymptotic Topology, arXiv: math.GM/0612543

[6] V. P. Maslov, Dimension of Holes and High-Temperature Condensate in Bose–Einstein Statistics, arXiv: physics/0612182

[7] V. P. Maslov, “Quantum Linguistic Statistics”, Russ. J. Math. Phys., 13:3 (2006), 315–325 | DOI | MR | Zbl

[8] V. P. Belavkin, V. P. Maslov, “Design of the optimal dynamic analyzer: mathematical aspects of sound and visual pattern recognition”, Mathematical Aspects of Computer Engineering, eds. V. P. Maslov, K. A. Volosov, Mir, Moscow, 146–237

[9] G. Shafer, V. Vovk, Probability and Finance. It's Only a Game!, Wiley Series in Probability and Statistics, Wiley, New York, 2001 | MR | Zbl

[10] V. P. Maslov, “Nelineinoe srednee v ekonomike”, Matem. zametki, 78:3 (2005), 377–395 | MR | Zbl

[11] V. P. Maslov, “Ob odnoi obschei teoreme teorii mnozhestv, privodyaschei k raspredeleniyu Gibbsa, Boze–Einshteina, Pareto i zakonu Tsipfa–Mandelbrota dlya fondovogo rynka”, Matem. zametki, 78:6 (2005), 870–877 | MR | Zbl

[12] V. P. Maslov, “Zakon “otsutstviya predpochteniya” i sootvetstvuyuschee raspredelenie v chastotnoi teorii veroyatnostei”, Matem. zametki, 80:2 (2006), 220–230 | MR | Zbl

[13] V. P. Maslov, On a General Theorem of Number Theory Leading to the Gibbs, Bose–Einstein, and Pareto Distribution as well as to the Zipf-Mandelbrot Law for the Stock Market, arXiv: physics/0601005

[14] V. P. Maslov, T. V. Maslova, Rank Distributions in Semiotics, arXiv: math.PR/0612540

[15] U. Frish, Turbulentnost. Nasledie A. N. Kolmogorova, FAZIS, M., 1998 | MR | Zbl