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Mat. Zametki, 2008, Volume 83, Issue 3, Pages 381–401 (Mi mz4526)  

This article is cited in 20 scientific papers (total in 20 papers)

On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. II

V. P. Maslova, V. E. Nazaikinskiib

a M. V. Lomonosov Moscow State University, Faculty of Physics
b A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Abstract: We continue our study of the problem on the allocation of indistinguishable particles to integer energy levels under the condition that the total energy of the system is bounded above. It is shown that the Bose condensation phenomenon can occur in this model. Systems of dimension $d<1$ (including negative dimensions) are studied.

Keywords: Bose-Einstein statistics, Bose condensate, system of negative dimension, cumulative distribution, convergence, limit distribution


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English version:
Mathematical Notes, 2008, 83:3, 345–363

Bibliographic databases:

UDC: 519.2+531.19
Received: 07.02.2008

Citation: V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. II”, Mat. Zametki, 83:3 (2008), 381–401; Math. Notes, 83:3 (2008), 345–363

Citation in format AMSBIB
\by V.~P.~Maslov, V.~E.~Nazaikinskii
\paper On the Distribution of Integer Random Variables Related by a Certain Linear Inequality.~II
\jour Mat. Zametki
\yr 2008
\vol 83
\issue 3
\pages 381--401
\jour Math. Notes
\yr 2008
\vol 83
\issue 3
\pages 345--363

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    This publication is cited in the following articles:
    1. V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Related by Two Linear Inequalities: I”, Math. Notes, 83:4 (2008), 512–529  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. P. Maslov, “Solution of the Gibbs Paradox in the Framework of Classical Mechanics (Statistical Physics) and Chrystalizations of the Gas $C_{60}$”, Math. Notes, 83:5 (2008), 716–722  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. III”, Math. Notes, 83:6 (2008), 804–820  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Satisfying Two Linear Relations”, Math. Notes, 84:1 (2008), 73–99  mathnet  crossref  crossref  mathscinet  isi  elib
    5. V. P. Maslov, “New Distributions in Classical Physics”, Math. Notes, 84:2 (2008), 290–296  mathnet  crossref  crossref  mathscinet  isi
    6. V. P. Maslov, “A correction to the Maxwell distribution and the Bose–Einstein-type distribution in classical physics”, Theoret. and Math. Phys., 157:1 (2008), 1491–1495  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. V. P. Maslov, “Clustering in an ideal gas in nanostructures as a Bose-condensation-type phenomenon in an asymptotically probabilistically quantized space”, Theoret. and Math. Phys., 157:3 (2008), 1760–1761  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    8. Maslov V.P., “On the superfluidity of classical liquid in nanotubes. IV”, Russ. J. Math. Phys., 15:2 (2008), 280–290  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    9. Maslov V.P., “On a new universal constant in ideal gas theory in a nanoporous medium”, Math. Notes, 84:3 (2008), 439–441  crossref  mathscinet  zmath  isi  elib  scopus
    10. Maslov V.P., “New theory of nucleation”, Russ. J. Math. Phys., 15:3 (2008), 332–342  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. Maslov V., “Dequantization, statistical mechanics and econophysics”, Tropical and idempotent mathematics, Contemp. Math., 495, ed. Litvinov G. Sergeev S., Amer. Math. Soc., Providence, RI, 2009, 239–279  crossref  mathscinet  zmath  isi
    12. Maslov V.P., “New global distributions in number theory and their applications”, J. Fixed Point Theory Appl., 8:1 (2010), 81–111  crossref  mathscinet  zmath  isi  scopus
    13. Maslov V.P., “Mathematical conception of “phenomenological” equilibrium thermodynamics”, Russ. J. Math. Phys., 18:4 (2011), 440–464  crossref  mathscinet  zmath  isi  elib  scopus
    14. Maslov V.P. Maslov A.V. Maslova T.V., “New paradigm in thermodynamics and its connection with economics and linguistics”, Russ. J. Math. Phys., 18:3 (2011), 329–337  crossref  mathscinet  zmath  isi  elib  scopus
    15. Maslov V.P., “New probability theory compatible with the new conception of modern thermodynamics. Economics and crisis of debts”, Russ. J. Math. Phys., 19:1 (2012), 63–100  crossref  mathscinet  zmath  isi  elib  scopus
    16. Maslov V.P., “Old Mathematical Errors in Statistical Physics”, Russ. J. Math. Phys., 20:2 (2013), 214–229  crossref  mathscinet  zmath  isi  elib  scopus
    17. Maslov V.P., “The Relationship Between the Van-der-Waals Model and the Undistinguishing Statistics of Objectively Distinguishable Objects. the New Parastatistics”, Russ. J. Math. Phys., 21:1 (2014), 99–111  crossref  mathscinet  zmath  isi  elib  scopus
    18. Maslov V.P., “Bubbles in the Negative Pressure Domain”, Russ. J. Math. Phys., 22:4 (2015), 483–490  crossref  mathscinet  zmath  isi  scopus
    19. V. P. Maslov, S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Volume and Entropy in Abstract Analytic Number Theory and Thermodynamics”, Math. Notes, 100:6 (2016), 828–834  mathnet  crossref  crossref  mathscinet  isi  elib
    20. Maslov V.P., “Negative energy, debts, and disinformation from the viewpoint of analytic number theory”, Russ. J. Math. Phys., 23:3 (2016), 355–368  crossref  mathscinet  zmath  isi  elib  scopus
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