Skip to main content
SpringerLink
Log in

On the new distribution generalizing the Gibbs, Bose-Einstein, and Pareto distributions

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

A distribution corresponding to a parastatistic and generalizing the Gibbs, Bose-Einstein, and Pareto distributions as well as rank distributions is given.

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. L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory, 2nd ed. (Nauka, Moscow, 1964; translation of the 1st ed., Pergamon Press, London-Paris and Addison-Wesley Publishing Co., Inc., Reading, Mass., 1958).

    Google Scholar 

  2. V. P. Maslov, “On the appearance of the λ-point in a weakly nonideal Bose gas and the two-liquid Thiess-Landau model,” Russian J. Math. Phys. 16(2), 146–172 (2009).

    Article  MATH  Google Scholar 

  3. Mathematical Encyclopedia (Soviet Encyclopedia, Moscow, 1977), Vol. 1 [in Russian].

  4. V. V. Kozlov, Thermal Equilibrium According to Gibbs and Poincar’e (Institute for Computer Studies, Moscow, 2002) [in Russian].

    Google Scholar 

  5. Ludwig Boltzmann: Papers and Speeches (Nauka, Moscow, 1970) [in Russian].

  6. V. P. Maslov, Quantum Economics (Moscow, Nauka, 2005) [in Russian].

    Google Scholar 

  7. 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 78(6), 870–877 (2005) [Math. Notes 78 (5–6), 807–813 (2005)].

    Google Scholar 

  8. V. P. Maslov. “Asymptotics with respect to a large number of fermions (or bosons) and their strong interaction with phonons and a quantized field,” Russian J. Math. Phys. 6(4), 409–425 (1999).

    MATH  Google Scholar 

  9. V. P. Maslov. Mathematical Conception of Gas Theory, arXiv:0812.4669, 29 Dec 2008.

  10. V. P. Maslov. “A new distribution generalizing the Bose-Einstein distribution,” Teoret. Mat. Fiz. 159(2), 319–320 (2009) [Theoret. and Math. Phys. 159 (2), 684–685 (2009)].

    Google Scholar 

  11. V. P. Maslov, “Nonlinear averages in economics,” Mat. Zametki 78(3), 377–395 (2005) [Math. Notes 78 (3–4), 347–363 (2005)].

    MathSciNet  Google Scholar 

  12. V. P. Maslov and V. E. Nazaikinskii, “On the distribution of integer random variables satisfying two linear relations, II,” Mat. Zametki 84(1), 69–98 (2008) [Math. Notes 84 (1), 73–99 (2008)].

    MathSciNet  Google Scholar 

  13. H. G. Schuster. Deterministic Chaos: An Introduction (Physik-Verlag, Meinheim, 1984; Mir, Moscow, 1988).

    MATH  Google Scholar 

  14. V. P. Maslov, Threshold Levels in Economics, arXiv:0903.4783v2 [q-fin.ST], 3 Apr 2009.

  15. V. P. Maslov, “New concept of the nucleation process,” Teoret. Mat. Fiz. 156(1), 159–160 (2008) [Theoret. and Math. Phys. 156 (1), 1101–1102 (2008)].

    MathSciNet  Google Scholar 

  16. M. E. Newman. Power Laws, Pareto Distributions, and Zipf’s Law, arXiv:cond-mat/0412004v2, 9 Jan 2005.

  17. V.P. Maslov, “Theorems on the debt crisis and the occurrence of inflation,” Math. Notes 85(1–2), 146–150 (2009).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    V. P. Maslov

Authors
  1. V. P. Maslov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. P. Maslov.

Additional information

The text was submitted by the author for the English version of the journal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maslov, V.P. On the new distribution generalizing the Gibbs, Bose-Einstein, and Pareto distributions. Math Notes 85, 613–622 (2009). https://doi.org/10.1134/S0001434609050010

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434609050010

Key words

Search

Navigation