
Russian Journal of Mathematical Physics [SJR: 0.858] [HI: 24] [0 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 15318621  ISSN (Online) 10619208 Published by SpringerVerlag [2329 journals] 
 Doubledeck structure of the boundary layer in the problem of flow in an
axially symmetric pipe with small irregularities on the wall for large
Reynolds numbers Authors: V. G. Danilov; R. K. Gaydukov
Pages: 1  18
Abstract: The problem of flow of a viscous incompressible fluid in an axially symmetric pipe with small irregularities on the wall is considered. An asymptotic solution of the problem with the doubledeck structure of the boundary layer and the unperturbed flow in the environment (the “core flow”) is obtained. The results of flow numerical simulation in the thin and “thick” boundary layers are given.
PubDate: 20170101
DOI: 10.1134/s1061920817010010
Issue No: Vol. 24, No. 1 (2017)
 Authors: V. G. Danilov; R. K. Gaydukov
 Mathematical quantum Yang–Mills theory revisited
 Authors: A. Dynin
Pages: 19  36
Abstract: A mathematically rigorous relativistic quantum Yang–Mills theory with an arbitrary semisimple compact gauge Lie group is set up in the Hamiltonian canonical formalism. The theory is nonperturbative, without cutoffs, and agrees with the causality and stability principles. This paper presents a fully revised, simplified, and corrected version of the corresponding material in the previous papers Dynin ([11] and [12]). The principal result is established anew: due to the quartic selfinteraction term in the Yang–Mills Lagrangian along with the semisimplicity of the gauge group, the quantum Yang–Mills energy spectrum has a positive mass gap. Furthermore, the quantum Yang–Mills Hamiltonian has a countable orthogonal eigenbasis in a Fock space, so that the quantum Yang–Mills spectrum is point and countable. In addition, a fine structure of the spectrum is elucidated.
PubDate: 20170101
DOI: 10.1134/s1061920817010022
Issue No: Vol. 24, No. 1 (2017)
 Authors: A. Dynin
 Tsallis p , q deformed Touchard polynomials and Stirling numbers
 Authors: O. Herscovici; T. Mansour
Pages: 37  50
Abstract: In this paper, we develop and investigate a new twoparametrized deformation of the Touchard polynomials, based on the definition of the NEXT qexponential function of Tsallis. We obtain new generalizations of the Stirling numbers of the second kind and of the binomial coefficients and represent two new statistics for the set partitions.
PubDate: 20170101
DOI: 10.1134/s1061920817010034
Issue No: Vol. 24, No. 1 (2017)
 Authors: O. Herscovici; T. Mansour
 Global transformations preserving Sturm–Liouville spectral data
 Authors: H. Isozaki; E. L. Korotyaev
Pages: 51  68
Abstract: We show the existence of a real analytic isomorphism between the space of the impedance function ρ of the Sturm–Liouville problem −ρ −2(ρ 2 f′)′ +uf on (0, 1), where u is a function of ρ, ρ′, ρ″, and that of potential p of the Schrödinger equation −y″ +py on (0, 1), keeping their boundary conditions and spectral data. This mapping is associated with the classical Liouville transformation f → ρf, and yields a global isomorphism between solutions of inverse problems for the Sturm–Liouville equations of the impedance form and those of the Schrödinger equations.
PubDate: 20170101
DOI: 10.1134/s1061920817010046
Issue No: Vol. 24, No. 1 (2017)
 Authors: H. Isozaki; E. L. Korotyaev
 On λBell polynomials associated with umbral calculus
 Authors: T. Kim; D. S. Kim
Pages: 69  78
Abstract: In this paper, we introduce some new λBell polynomials and Bell polynomials of the second kind and investigate properties of these polynomials. Using our investigation, we derive some new identities for the two kinds of λBell polynomials arising from umbral calculus.
PubDate: 20170101
DOI: 10.1134/s1061920817010058
Issue No: Vol. 24, No. 1 (2017)
 Authors: T. Kim; D. S. Kim
 From the N body problem to Euler equations
 Authors: A. A. Lykov; V. A. Malyshev
Pages: 79  95
Abstract: This paper contains a rigorous mathematical example of direct derivation of the system of Euler hydrodynamic equations from the Hamiltonian equations for an N point particle system as N → ∞. “Direct” means that the following standard tools are not used in the proof: stochastic dynamics, thermodynamics, Boltzmann kinetic equations, and the correlation functions approach due to Bogolyubov.
PubDate: 20170101
DOI: 10.1134/s106192081701006x
Issue No: Vol. 24, No. 1 (2017)
 Authors: A. A. Lykov; V. A. Malyshev
 A generalized number theory problem applied to ideal liquids and to
terminological lexis Authors: V. P. Maslov; T. V. Maslova
Pages: 96  110
Abstract: We consider the notion of number of degrees of freedom in number theory and thermodynamics. This notion is applied to notions of terminology such as terms, slogans, themes, rules, and regulations. Prohibitions are interpreted as restrictions on the number of degrees of freedom. We present a theorem on the small number of degrees of freedom as a consequence of the generalized partitio numerorum problem. We analyze the relationship between thermodynamically ideal liquids with the lexical background that a term acquires in the process of communication. Examples showing how this background may be enhanced are considered. We discuss the question of the coagulation of drops in connection with the forecast of analogs of the gasideal liquid phase transition in socialpolitical processes.
PubDate: 20170101
DOI: 10.1134/s1061920817010071
Issue No: Vol. 24, No. 1 (2017)
 Authors: V. P. Maslov; T. V. Maslova
 Differentialgeometric structures associated with Lagrangians
corresponding to scalar physical fields Authors: A. K. Rybnikov
Pages: 111  121
Abstract: The paper is devoted to the investigation, using the method of Cartan–Laptev, of the differentialgeometric structure associated with a Lagrangian L, depending on a function z of the variables t, x 1,...,x n and its partial derivatives. Lagrangians of this kind are considered in theoretical physics (in field theory). Here t is interpreted as time, and x 1,...,x n as spatial variables. The state of the field is characterized by a function z(t, x 1,..., x n ) (a field function) satisfying the Euler equation, which corresponds to the variational problem for the action integral. In the present paper, the variables z(t, x 1,..., x n are regarded as adapted local coordinates of a bundle of general type M with ndimensional fibers and 1dimensional base (here the variable t is simultaneously a local coordinate on the base). If we agree to call t time, and a typical fiber an ndimensional space, then M can be called the spatiotemporal bundle manifold. We consider the variables t, x 1,...,x n , z (i.e., the variables t, x 1,...,x n with the added variable z) as adapted local coordinates in the bundle H over the fibered base M. The Lagrangian L, which is a coefficient in the differential form of the variational action integral in the integrand, is a relative invariant given on the manifold J 1 H (the manifold of 1jets of the bundle H). In the present paper, we construct a tensor with components Λ00, Λ0i , Λ ij (Λ ij = Λ ji ) which is generated by the fundamental object of the structure associated with the Lagrangian. This tensor is an invariant (with respect to admissible transformations the variables t, x 1,...,x n , z) analog of the energymomentum tensor of the classical theory of physical fields. We construct an invariant I, a vector G i , and a bivalent tensor G jk generated by the Lagrangian. We also construct a relative invariant of E (in the paper, we call it the Euler relative invariant) such that the equation E = 0 is an invariant form of the Euler equation for the variational action integral. For this reason, a nonvariational interpretation of the Euler equation becomes possible. Moreover, we construct a connection in the principal bundle with base J 2 H (the variety of 2jets of the bundle H) and with the structure group GL(n) generated by the structure associated with the Lagrangian.
PubDate: 20170101
DOI: 10.1134/s1061920817010083
Issue No: Vol. 24, No. 1 (2017)
 Authors: A. K. Rybnikov
 Norms in group algebras of finite groups under inducing
 Authors: A. I. Shtern
Pages: 122  123
Abstract: We compare norms of an element of a group algebra of a normal subgroup of a finite group in a representation of the normal subgroup and the corresponding induced representation (under the natural embedding of the group algebra of the normal subgroup in the group algebra of the entire group).
PubDate: 20170101
DOI: 10.1134/s1061920817010095
Issue No: Vol. 24, No. 1 (2017)
 Authors: A. I. Shtern
 A new class of Abelian theorems for the Mehler–Fock transforms
 Authors: H. M. Srivastava; B. J. González; E. R. Negrín
Pages: 124  126
Abstract: The main object of this paper is to derive several new Abelian theorems for the Mehler–Fock transforms. The results presented here are compared with those given earlier by R. S. Pathak and R. N. Pandey [Math. Soc. 3 (1987), 91–95]. Some applications and particular cases are also considered.
PubDate: 20170101
DOI: 10.1134/s1061920817010101
Issue No: Vol. 24, No. 1 (2017)
 Authors: H. M. Srivastava; B. J. González; E. R. Negrín
 Propagation of a linear wave created by a spatially localized perturbation
in a regular lattice and punctured Lagrangian manifolds Authors: S. Yu. Dobrokhotov; V. E. Nazaikinskii
Pages: 127  133
Abstract: The following results are obtained for the Cauchy problem with localized initial data for the crystal lattice vibration equations with continuous and discrete time: (i) the asymptotics of the solution is determined by Lagrangian manifolds with singularities (“punctured” Lagrangian manifolds); (ii) Maslov’s canonical operator is defined on such manifolds as a modification of a new representation recently obtained for the canonical operator by the present authors together with A. I. Shafarevich (Dokl. Ross. Akad. Nauk 46 (6), 641–644 (2016)); (iii) the projection of the Lagrangian manifold onto the configuration plane specifies a bounded oscillation region, whose boundary (which is naturally referred to as the leading edge front) is determined by the Hamiltonians corresponding to the limit wave equations; (iv) the leading edge front is a special caustic, which possibly contains stronger focal points. These observations, together with earlier results, lead to efficient formulas for the wave field in a neighborhood of the leading edge front.
PubDate: 20170101
DOI: 10.1134/s1061920817010113
Issue No: Vol. 24, No. 1 (2017)
 Authors: S. Yu. Dobrokhotov; V. E. Nazaikinskii
 On the biharmonic Steklov problem in weighted spaces
 Authors: H. A. Matevossian
Pages: 134  138
Abstract: We study the unique solvability of the Steklov problem for the biharmonic equation in unbounded domains under the assumption that a generalized solution of this problem has a bounded Dirichlet integral with weight x a . Depending on the value of the parameter a, we prove uniqueness theorems or present exact formulas for the dimension of the solution space of the Steklov problem in the exterior of a compact set and in a halfspace.
PubDate: 20170101
DOI: 10.1134/s1061920817010125
Issue No: Vol. 24, No. 1 (2017)
 Authors: H. A. Matevossian
 Asymptotic support of localized solutions of the linearized system of
magnetohydrodynamics Authors: A. I. Allilueva; A. I. Shafarevich
Pages: 425  430
Abstract: The asymptotic behavior of solutions of the Cauchy problem for the linearized system of magnetohydrodynamic equations with initial conditions localized near a twodimensional surface was obtained by the authors earlier. Here, this asymptotic behavior is refined.
PubDate: 20161001
DOI: 10.1134/s1061920816040014
Issue No: Vol. 23, No. 4 (2016)
 Authors: A. I. Allilueva; A. I. Shafarevich
 Rigid body dynamics in nonEuclidean spaces
 Authors: A. V. Borisov; I. S. Mamaev
Pages: 431  454
Abstract: In this paper, we focus on the study of twodimensional plate dynamics on the Lobachevskii plane L 2. First of all, we consider the free motion of such a plate, which is a pseudospherical analog of dynamics of the Euler top, and also present an analog of the Euler–Poisson equations enabling us to study the motion of the body in potential force fields having rotational symmetry. We present a series of integrable cases, having analogs in Euclidean space, for different fields. Moreover, in the paper, a partial qualitative analysis of the dynamics of free motion of a plate under arbitrary initial conditions is made and a number of computer illustrations are presented which show a substantial difference of the motion from the case of Euclidean space. The study undertaken in the present paper leads to interesting physical consequences, which enable us to detect the influence of curvature on the body dynamics.
PubDate: 20161001
DOI: 10.1134/s1061920816040026
Issue No: Vol. 23, No. 4 (2016)
 Authors: A. V. Borisov; I. S. Mamaev
 Generalized compatibility equations for tensors of high ranks in
multidimensional continuum mechanics Authors: D. V. Georgievskii
Pages: 475  483
Abstract: Compatibility equations are derived for the components of generalized strains of rank m associated with generalized displacements of rank m − 1 by analogs of Cauchy kinematic relations in ndimensional space (multidimensional continuous medium) (m ≥ 1, n ≥ 2). These relations can be written in the form of equating to zero all components of the incompatibility tensor of rank m(n − 2) or its dual generalized Riemann–Christoffel tensor of rank 2m. The number of independent components of these tensors is found; this number coincides with that of compatibility equations in terms of generalized strains or stresses. The inequivalence of the full system of compatibility equations to any of its weakened subsystems is discussed, together with diverse formulations of boundary value problems in generalized stresses in which the number of equations in a domain can exceed the number of unknowns.
PubDate: 20161001
DOI: 10.1134/s106192081604004x
Issue No: Vol. 23, No. 4 (2016)
 Authors: D. V. Georgievskii
 Quantization due to breaking the commutativity of symmetries. Wobbling
oscillator and anharmonic Penning trap Authors: M. V. Karasev
Pages: 484  490
Abstract: We discuss two examples of classical mechanical systems which can become quantum either because of degeneracy of an integral of motion or because of tuning parameters at resonance. In both examples, the commutativity of the symmetry algebra is breaking, and noncommutative symmetries arise. Over the new noncommutative algebra, the system can reveal its quantum behavior including the tunneling effect. The important role is played by the creationannihilation regime for the perturbation or anharmonism. Activation of this regime sometimes needs in an additional resonance deformation (Cartan subalgebra breaking).
PubDate: 20161001
DOI: 10.1134/s1061920816040051
Issue No: Vol. 23, No. 4 (2016)
 Authors: M. V. Karasev
 Asymptotic expansions of Feynman integrals of exponentials with polynomial
exponent Authors: A. K. Kravtseva; O. G. Smolyanov; E. T. Shavgulidze
Pages: 491  509
Abstract: In the paper, an asymptotic expansion of path integrals of functionals having exponential form with polynomials in the exponent is constructed. The definition of the path integral in the sense of analytic continuation is considered.
PubDate: 20161001
DOI: 10.1134/s1061920816040063
Issue No: Vol. 23, No. 4 (2016)
 Authors: A. K. Kravtseva; O. G. Smolyanov; E. T. Shavgulidze
 Comparison of solutions of a problem of Cauchy–Poisson type under
discontinuous and smooth initial values with the marigrams of Tsunami 2011
obtained from DART stations Authors: S. Ya. SekerzhZen’kovich
Pages: 529  535
Abstract: The problem of Cauchy–Poisson type is considered in the framework of potential tsunami model with impulse cylindical compactly supported source discontinuous with respect to the radial horizontal coordinate under the assumption that the depth of the liquid is constant. An analytical solution of the problem for a special choice of values of the parameters of the source is given. The connection the solution thus obtained with nonstandard characteristics introduced by Maslov is discussed. The graphs of the time history of the free surface elevation are compared with the marigrams, received for the 2011 tsunami from the DART stations 21418, 21413, and 51407, and also with graphs calculated for the wellknown model with a “simple” source.
PubDate: 20161001
DOI: 10.1134/s1061920816040087
Issue No: Vol. 23, No. 4 (2016)
 Authors: S. Ya. SekerzhZen’kovich
 Distribution of energy of solutions of the wave equation on singular
spaces of constant curvature and on a homogeneous tree Authors: A. V. Tsvetkova
Pages: 536  550
Abstract: In the paper, the Cauchy problem for the wave equation on singular spaces of constant curvature and on an infinite homogeneous tree is studied. Two singular spaces are considered: the first one consists of a threedimensional Euclidean space to which a ray is glued, and the other is formed by two threedimensional Euclidean spaces joined by a segment. The solution of the Cauchy problem for the wave equation on these objects is described and the behavior of the energy of a wave as time tends to infinity is studied. The Cauchy problem for the wave equation on an infinite homogeneous tree is also considered, where the matching conditions for the Laplace operator at the vertices are chosen in the form generalizing the Kirchhoff conditions. The spectrum of such an operator is found, and the solution of the Cauchy problem for the wave equation is described. The behavior of wave energy as time tends to infinity is also studied.
PubDate: 20161001
DOI: 10.1134/s1061920816040099
Issue No: Vol. 23, No. 4 (2016)
 Authors: A. V. Tsvetkova
 Description of locally bounded pseudocharacters on almost connected
locally compact groups Authors: A. I. Shtern
Pages: 551  552
Abstract: A description of locally bounded pseudocharacters on almost connected locally compact groups is given.
PubDate: 20161001
DOI: 10.1134/s1061920816040105
Issue No: Vol. 23, No. 4 (2016)
 Authors: A. I. Shtern