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Case of less than two degrees of freedom, negative pressure, and the Fermi—Dirac distribution for a hard liquid
Mathematical notes. 2015. Vol. 98. No. 1-2. P. 138-157.
The notion of ideal liquid for the number of degrees of freedom less than 2, i.e., γ < 0, is introduced. The values of the pressure P and of the compressibility factor Z on the spinodal in the negative pressure region for the van der Waals equation determine the value of γ, γ(T) < 0, for μ = 0. For(Formula presented.), a relationship with the van der Waals equation is established. © 2015, Pleiades Publishing, Ltd.
49606783, Russian Journal of Mathematical Physics 2019 Vol. 26 No. 1 P. 50-54
In this paper, a physical and mathematical interpretation of the passage from the
Bose distribution to the Fermi distribution of nuclear matter is presented. We consider the
notion of "coat" and introduce the notion of "lacunary indeterminacy", which is a region
that contains a neighborhood of the activity a = 0 and is the boundary between the Bose
particle ...
Added: August 24, 2019
49606783, Maslova T. V., Mathematical notes 2014 Vol. 95 No. 6 P. 881-885
After the work of Irving Fisher, who formulated the main law of economics as an analog of the Claiperon--Clausius--Mendeleev relation corresponding to the Boltzmann--Maxwell ideal gas, the authors have developed this approach on the basis of the general principles of UD-statistics by assigning to the nominal interest rate the role of the chemical potential mu ...
Added: December 21, 2014
Maslov V., Mathematical notes 2012 Vol. 92 No. 3 P. 402-411
Negative pressure also means negative energy and, therefore, “holes”, antiparticles. Continuation across infinity to negative energies is accomplished by using a parastatistical correction to the Bose-Einstein distribution. ...
Added: January 17, 2013
Maslov V., Mathematical notes 2015 Vol. 97 No. 5-6 P. 909-918
We obtain a distribution of Fermi-Dirac type for a hard liquid at temperatures less than the Frenkel temperature TF for P ≥ 0 and Z ≥ 0. For the van der Waals model, one has TF = (33/25)Tc. © 2015, Pleiades Publishing, Ltd.. ...
Added: September 7, 2015
Maslov V., Mathematical notes 2017 Vol. 101 No. 4 P. 660-665
In the paper “The relationship between the Fermi–Dirac distribution and statistical
distributions in languages” (This issue of “Math. Notes”), the Bose–Einstein and Fermi–Dirac
distributions are considered in connectionwith frequency distributions in languages in the context of
the author’s approach to thermodynamics and number theory problems. The present article presents
certain clarifications of certain notions used in that approach, in ...
Added: October 28, 2018
49606783, Mathematical notes 2014 Vol. 96 No. 3 P. 403-415
In this paper, we refine some of the original notions, such as the number of degrees of freedom, for an arbitrary temperature
and an ideal Boltzmann--Maxwell gas. Using the van der Waals model, we illustrate the notion of Frenkel temperature,
which separates soft and rigid liquid. ...
Added: December 21, 2014
Маслов Виктор Павлович, Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2015 Т. 462 № 1 С. 30-34
A new distribution corresponding to thermodynamics in supercritical and subcritical regions and in the region of negative pressure is considered. ...
Added: September 8, 2015
49606783, Mathematical notes 2010 Vol. 87 No. 5 P. 728-737
The well-known empiric Van der Waals equation contains two constants characterizing a given gas, so that, in general, it depends on the characteristic interaction of particles of the given gas. In this paper, equations depending on three defining constants, are constructed on the basis of he mathematically rigorous results obtained by the author in recent ...
Added: April 13, 2012
49606783, Mathematical notes 2013 Vol. 93 No. 1-2 P. 102-136
In this paper we systematically present a new approach to classical thermodynamics, using asymptotic distribution from number theory and generalizing the Bose-Einstein distribution. The phase transition from gas to liquid, the thermodynamics of fluids, as well as the behavior of liquids under negative pressure are elucidated. ...
Added: April 1, 2013
49606783, Maslova T. V., Mathematical notes 2015 Vol. 98 No. 1-2 P. 343-347
Added: October 7, 2015
The boundary of a volume as a trap ensuring the phase transition in an ideal gas at low temperatures
49606783, Mathematical notes 2012 Vol. 92 No. 5-6 P. 657-663
It is shown that reflection from the boundary of a volume containing a gas plays a significant role in the occurrence of the second phase, and the corresponding correction (related to this effect) to the results obtained by the author in previous papers dealing with the theory of the new ideal gas is given. ...
Added: February 12, 2013
49606783, Mathematical notes 2014 Vol. 96 No. 6 P. 977-982
We give a geometric interpretation of the thermodynamic potential, free and internal energy, and enthalpy in terms of a Lagrangian manifold in the phase space of pairs (T, -S), (-mu, N), and (P,V) of intensive and extensive variables.
The Lagrangian manifold is viewed as the dequantization of the tunnel canonical operator. With this approach, the critical point ...
Added: December 24, 2014
49606783, Mathematical notes 2013 Vol. 94 No. 5 P. 722-813
In the present paper, we describe an approach to thermodynamics that does not involve Bogolyubov chains or Gibbs ensembles. We present isotherms, isochores, and isobars of various pure gases, as well as binodals, i.e., lines along which gas becomes liquid, and spinodals (endpoints of isotherms). We study supercritical phenomena for values of temperature and pressure ...
Added: December 23, 2013
49606783, Mathematical notes 2014 Vol. 96 No. 1 P. 50-67
This paper presents UD-statistics almost coinciding with Gentile statistics for negative chemical potentials, but having another extension in the case of positive chemical potentials. The physical meaning of the metamorphosis of the phase transition of the third kind to the phase transition of the first kind is explained. The coincidence of isochores and isotherms in the supercritical ...
Added: December 21, 2014
191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90
It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...
Added: September 23, 2016
Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624
Added: February 27, 2013
Ilyashenko Y., Яковенко С. Ю., М. : МЦНМО, 2013
Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...
Added: February 5, 2014
Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70
A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...
Added: July 19, 2014
Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...
Added: November 1, 2019
Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
Added: December 4, 2017
Sinelshchikov D., Кудряшов Н. А., Theoretical and Mathematical Physics 2018 Vol. 196 No. 2 P. 1230-1240
We study a family of nonautonomous generalized Liénard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I Painlevé–Gambier equations. As a result, we find four criteria of equivalence, which give four integrable families of Liénard-type equations. We demonstrate that these criteria can be used to construct ...
Added: February 9, 2019
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Kolokolov I., Lebedev V., Sizov G. A., Journal of Experimental and Theoretical Physics 2011 Vol. 140 No. 2 P. 387-400
We analyze magnetic kinematic dynamo in a conducting fluid where the stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field ...
Added: February 2, 2017