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Mat. Zametki, 2005, Volume 78, Issue 3, Pages 377–395 (Mi mz2595)  

This article is cited in 30 scientific papers (total in 30 papers)

Nonlinear Averages in Economics

V. P. Maslov

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: Kolmogorov nonlinear averaging is complemented by a natural axiom. For this averaging, we prove a theorem on large deviations as well as establish the relationship to the tunnel canonical operator.


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English version:
Mathematical Notes, 2005, 78:3, 347–363

Bibliographic databases:

UDC: 519
Received: 30.05.2005

Citation: V. P. Maslov, “Nonlinear Averages in Economics”, Mat. Zametki, 78:3 (2005), 377–395; Math. Notes, 78:3 (2005), 347–363

Citation in format AMSBIB
\by V.~P.~Maslov
\paper Nonlinear Averages in Economics
\jour Mat. Zametki
\yr 2005
\vol 78
\issue 3
\pages 377--395
\jour Math. Notes
\yr 2005
\vol 78
\issue 3
\pages 347--363

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    This publication is cited in the following articles:
    1. 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”, Math. Notes, 78:6 (2005), 807–813  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. P. Maslov, “Refinement of the Gibbs and Bose–Einstein Distributions”, Theoret. and Math. Phys., 145:3 (2005), 1749–1752  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Maslov V. P., “Nonlinear averaging of entropy in number theory and a generalized law of large numbers”, Dokl. Math., 72:3 (2005), 925-929  mathscinet  zmath  isi  elib
    4. Maslov V. P., “Refinement of Zipf's law for frequency dictionaries”, Dokl. Math., 72:3 (2005), 942-945  zmath  isi  elib
    5. Maslov V. P., “The Zipf-Mandelbrot law: Quantization and an application to the stock market”, Russ. J. Math. Phys., 12:4 (2005), 483–488  crossref  mathscinet  zmath  isi  elib  scopus
    6. Maslov V. P., “The large deviations law in number theory, computable functions of several arguments, and decoding”, Dokl. Math., 72:2 (2005), 766–770  zmath  isi  elib
    7. Maslov V. P., “On the principle of increasing complexity in portfolio formation on the stock exchange”, Dokl. Math., 72:2 (2005), 718–722  zmath  isi  elib
    8. V. P. Maslov, “The Lack-of-Preference Law and the Corresponding Distributions in Frequency Probability Theory”, Math. Notes, 80:2 (2006), 214–223  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. V. P. Maslov, “On a new rank distribution”, Math. Notes, 80:3 (2006), 447–448  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. V. P. Maslov, “Negative asymptotic topological dimension, a new condensate, and their relation to the quantized Zipf law”, Math. Notes, 80:6 (2006), 806–813  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. Maslov V. P., “Quantum linguistic statistics”, Russ. J. Math. Phys., 13:3 (2006), 315–325  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    12. V. P. Maslov, “Zeroth-order phase transitions and Zipf law quantization”, Theoret. and Math. Phys., 150:1 (2007), 102–122  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    13. V. P. Maslov, “General Notion of a Topological Space of Negative Dimension and Quantization of Its Density”, Math. Notes, 81:1 (2007), 140–144  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    14. V. P. Maslov, “Densities of Lattices Corresponding to Spaces of Positive, Negative, and Variational Dimension, and Their Application to Time Series”, Math. Notes, 81:1 (2007), 222–233  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. Maslov V. P., “Revision of probability theory from the point of view of quantum statistics”, Russ. J. Math. Phys., 14:1 (2007), 66–95  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    16. V. P. Maslov, “Quasithermodynamics and a Correction to the Stefan–Boltzmann Law”, Math. Notes, 83:1 (2008), 72–79  mathnet  crossref  crossref  mathscinet  zmath  isi
    17. V. P. Maslov, “Transition to the Condensate State for Classical Gases and Clusterization”, Math. Notes, 84:6 (2008), 785–813  mathnet  crossref  crossref  mathscinet  isi
    18. Maslov V. P., “New Look at Thermodynamics of Gas and at Clusterization”, Russ. J. Math. Phys., 15:4 (2008), 493–510  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    19. 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  scopus
    20. Maslov V. P., “On the new distribution generalizing the Gibbs, Bose–Einstein, and Pareto distributions”, Math. Notes, 85:5-6 (2009), 613–622  crossref  zmath  isi  elib  scopus
    21. Dyakonov K. M., “Kolmogorov averages and approximate identities”, Constr. Approx., 30:1 (2009), 17–31  crossref  mathscinet  zmath  isi  elib  scopus
    22. Maslov V. P., “Thermodynamics of fluids for imperfect gases with Lennard-Jones interaction potential. I”, Math. Notes, 86:3–4 (2009), 522–529  crossref  zmath  isi  elib  scopus
    23. Maslov V. P., “Phase transitions of the first and second kind as economic crises. Abstract thermodynamics of fluids”, Russ. J. Math. Phys., 16:3 (2009), 323–344  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    24. Maslov V., “Dequantization, Statistical Mechanics and Econophysics”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, ed. Litvinov G. Sergeev S., Amer Mathematical Soc, 2009, 239–279  crossref  mathscinet  zmath  isi
    25. M. A. Guzev, E. Yu. Nikitina, “Rangovyi analiz Ugolovnogo Kodeksa RF (na primere ekonomicheskikh prestuplenii)”, Dalnevost. matem. zhurn., 10:2 (2010), 117–129  mathnet
    26. M. A. Guzev, A. A. Dmitriev, “On the Critical Points of the Kolmogorov Mean with Constraints on the Mean of the Arguments”, Math. Notes, 98:2 (2015), 237–250  mathnet  crossref  crossref  mathscinet  isi  elib
    27. Zegarlinski B., “Linear and Nonlinear Dissipative Dynamics”, Rep. Math. Phys., 77:3 (2016), 377–397  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    28. M. A. Guzev, G. Sh. Tsitsiashvili, M. A. Osipova, “Zaschita setevoi struktury avtonomnymi apparatami”, Dalnevost. matem. zhurn., 18:2 (2018), 177–182  mathnet
    29. Guzev M.A., Tsitsiashvili G.S., Osipova M.A., “The Object Detection By Autonomous Apparatus as a Solution of the Buffon Needle Problem”, Math. Mech. Complex Syst., 7:2 (2019), 189–201  crossref  mathscinet  isi
    30. A. V. Lebedev, “Zakony bolshikh chisel dlya nekotorykh abstraktnykh srednikh”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2021, no. 3, 50–53  mathnet
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