Skip to main content
SpringerLink
Log in

Densities of lattices corresponding to spaces of positive, negative, and variational dimension, and their application to time series

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Mathematical Encyclopaedia, Ed. by Yu. V. Prokhorov (Soviet Encyclopaedia, Moscow, 1988) [in Russian].

    Google Scholar 

  2. Yu. I. Manin, The Notion of Dimension in Geometry and Algebra, arXiv: math. AG/0502016 (2005).

  3. V. P. Maslov, “Negative asymptotic topological dimension, new condensate, and their connection with the quantized Zipf law,” Mat. Zametki [Math. Notes] 80(6), 856–863 (2006).

    Google Scholar 

  4. V. P. Maslov, “The general notion of topological spaces of negative dimension and quantization of their density,” Mat. Zametki [Math. Notes] 81(1), 157–160 (2007).

    Google Scholar 

  5. V. P. Maslov, Negative Dimension in General and Asymptotic Topology, arXiv: math. GM/0612543 (2006).

  6. V. P. Maslov, Dimension of Holes and High-Temperature Condensate in Bose-Einstein Statistics, arXiv: physics/0612182 (2006).

  7. V. P. Maslov, “Quantum Linguistic Statistics,” Russ. J. Math. Phys. 13(3), 315–325 (2006).

    Article  MATH  Google Scholar 

  8. V. P. Belavkin and V. P. Maslov, “Design of the optimal dynamic analyzer: Mathematical aspects of sound and visual pattern recognition,” in Mathematical Aspects of Computer Engineering, Ed. by V. P. Maslov and K. A. Volosov (Mir, Moscow, 1988), pp. 146–237.

    Google Scholar 

  9. G. Shafer and V. Vovk, Probability and Finance. It’s Only a Game!, in Wiley Series in Probability and Statistics (Wiley, New York, 2001).

    Google Scholar 

  10. V. P. Maslov, “Nonlinear mean in economics,” Mat. Zametki [Math. Notes] 78(3), 377–395 (2005).

    Google Scholar 

  11. V. P. Maslov, “On a general theorem of set theory leading to the Gibbs, Bose-Einstein, and Pareto distributions as well as to the Zipf-Mandelbrot law for the stock market,” Mat. Zametki [Math. Notes] 78(6), 870–877 (2005).

    Google Scholar 

  12. V. P. Maslov, “The lack-of-preference law and the corresponding distributions in frequency probability theory,” Mat. Zametki [Math. Notes] 80(2), 220–230 (2006).

    Google Scholar 

  13. V. P. Maslov, On a general theorem of number theory leading to the Gibbs, Bose-Einstein, and Pareto distributions as well as to the Zipf-Mandelbrot law for the stock market, arXiv: physics/0601005 (2006).

  14. V. P. Maslov and T. V. Maslova, Rank Distributions in Semiotics, arXiv: math. PR/0612540 (2006).

  15. U. Frisch, Turbulence. The legacy of A. N. Kolmogorov. (Cambridge University Press, Cambridge, 1995; FAZIS, Moscow, 1998).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Russia

    V. P. Maslov

Authors
  1. V. P. Maslov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V. P. Maslov, 2007, published in Matematicheskie Zametki, 2007, Vol. 81, No. 2, pp. 251–264.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maslov, V.P. Densities of lattices corresponding to spaces of positive, negative, and variational dimension, and their application to time series. Math Notes 81, 222–233 (2007). https://doi.org/10.1134/S0001434607010257

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434607010257

Key words

Search

Navigation