V. P. Maslov, V. E. Nazaikinskii, “Conjugate Variables in Analytic Number Theory. Phase Space and Lagrangian Manifolds”, Math. Notes, 100:3 (2016), 421

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Matematicheskie Zametki, 2016, Volume 100, Issue 3, paper published in the English version journal (Mi mzm11421)

This article is cited in 10 scientific papers (total in 10 papers)

Papers published in the English version of the journal

Conjugate Variables in Analytic Number Theory. Phase Space and Lagrangian Manifolds

V. P. Maslov^ab, V. E. Nazaikinskii^bc

^a National Research University Higher School of Economics, Moscow, Russia
^b Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia
^c Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Oblast, Russia

Citations (10)

Abstract: For an arithmetic semigroup

(G, \partial)

$(G,\partial)$ , we define entropy as a function on a naturally defined continuous semigroup

\hat{G}

$\widehat G$ containing

G

$G$ . The construction is based on conditional maximization, which permits us to introduce the conjugate variables and the Lagrangian manifold corresponding to the semigroup

(G, \partial)

$(G,\partial)$ .

Keywords: arithmetic semigroup, Bose gas, entropy, volume, Lagrange multiplier, conjugate variable, Lagrangian manifold.

Funding agency
This research was carried out at IPMech RAS in the framework of the state contract “Modeling of processes in mechanics of natural hazards, mechanics of continuum, and quantum mechanics with the use of asymptotic and analytical-numerical methods.”

Received: 26.03.2016

English version:
Mathematical Notes, 2016, Volume 100, Issue 3, Pages 421–428
DOI: https://doi.org/10.1134/S000143461609008X

Bibliographic databases:

Document Type: Article

Language: English

Citation: V. P. Maslov, V. E. Nazaikinskii, “Conjugate Variables in Analytic Number Theory. Phase Space and Lagrangian Manifolds”, Math. Notes, 100:3 (2016), 421–428

Citation in format AMSBIB

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\paper Conjugate Variables in Analytic Number Theory. Phase Space and Lagrangian Manifolds

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\issue 3

\pages 421--428

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Linking options:

https://www.mathnet.ru/eng/mzm11421

This publication is cited in the following 10 articles:

V. P. Maslov, “Analytical number theory and the energy of transition of Bose gas to Fermi gas. Critical lines as boundaries of noninteracting gas (an analog of the Bose gas in classical thermodynamics)”, Russ. J. Math. Phys., 25:2 (2018), 220–232
V. P. Maslov, “Energy Corresponding to the Change of Spin”, Math. Notes, 103:4 (2018), 616–620
V. P. Maslov, “Rotation of a Neutron in the Coat of Helium-5 as a Classical Particle for a Relatively Large Value of the Hidden Parameter $t_{\mathrm{meas}}$ ”, Math. Notes, 103:1 (2018), 67–74
V. P. Maslov, T. V. Maslova, “A generalized number theory problem applied to ideal liquids and to terminological lexis”, Russ. J. Math. Phys., 24:1 (2017), 96–110
V. P. Maslov, “A model of classical thermodynamics and mesoscopic physics based on the notion of hidden parameter, earth gravitation, and quasiclassical asymptotics. II”, Russ. J. Math. Phys., 24:4 (2017), 494–504
V. P. Maslov, “Two First Principles of Earth Surface Thermodynamics. Mesoscopy, Energy Accumulation, and the Branch Point in Boson–Fermion Transition”, Math. Notes, 102:6 (2017), 824–835
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
V. P. Maslov, “Large negative numbers in number theory, thermodynamics, information theory, and human thermodynamics”, Russ. J. Math. Phys., 23:4 (2016), 510–528
V. P. Maslov, “Modern Thermodynamics as a Branch of Mathematics (Mathematical Physics)”, Math. Notes, 100:3 (2016), 413–420
V. P. Maslov, “Tropical Topology”, Math. Notes, 100:6 (2016), 886–889

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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