
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 [2335 journals] 
 Asymptotic support of localized solutions of the linearized system of
magnetohydrodynamics Authors: A. I. Allilueva; A. I. Shafarevich
Pages: 425  430
Abstract: 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: 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
 Asymptotic theory of linear water waves in a domain with nonuniform bottom
with rapidly oscillating sections Authors: S. Yu. Dobrokhotov; V. V. Grushin; S. A. Sergeev; B. Tirozzi
Pages: 455  474
Abstract: Abstract A linear problem for propagation of gravity waves in the basin having the bottom of a form of a smooth background with added rapid oscillations is considered. The formulas derived below are asymptotic ones; they are quite formal, and we do not discuss the problem concerning their uniformness with respect to these parameters.
PubDate: 20161001
DOI: 10.1134/s1061920816040038
Issue No: Vol. 23, No. 4 (2016)
 Authors: S. Yu. Dobrokhotov; V. V. Grushin; S. A. Sergeev; B. Tirozzi
 Generalized compatibility equations for tensors of high ranks in
multidimensional continuum mechanics Authors: D. V. Georgievskii
Pages: 475  483
Abstract: 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: 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: 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
 Large negative numbers in number theory, thermodynamics, information
theory, and human thermodynamics Authors: V. P. Maslov
Pages: 510  528
Abstract: We show how the abstract analytic number theory of Maier, Postnikov, and others can be extended to include negative numbers and apply this to thermodynamics, information theory, and human thermodynamics. In particular, we introduce a certain large number N 0 on the “zero level” with a high multiplicity number q i ≫ 1 related to the physical concept of gap in the spectrum. We introduce a general notion of “hole,” similar to the Dirac hole in physics, in the theory. We also consider analogs of thermodynamical notions in human thermodynamics, in particular, in connection with the role of the individual in history.
PubDate: 20161001
DOI: 10.1134/s1061920816040075
Issue No: Vol. 23, No. 4 (2016)
 Authors: V. P. Maslov
 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: 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: 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: 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
 Weak and strong probabilistic solutions for a stochastic quasilinear
parabolic equation with nonstandard growth Authors: Z. I. Ali; M. Sango
Pages: 283  308
Abstract: Abstract In this paper, we investigate a class of stochastic quasilinear parabolic initial boundary value problems with nonstandard growth in the functional setting of generalized Sobolev spaces. The deterministic version of the equation was first introduced and studied by Samokhin in [45] as a generalized model for polytropic filtration. We establish an existence result of weak probabilistic solutions when the forcing terms do not satisfy Lipschitz conditions. Under the Lipschitz property of the forcing terms, we obtain the uniqueness of weak probabilistic solutions. Combining the uniqueness and the famous Yamada–Watanabe result, we prove the existence of a unique strong probabilistic solution of the problem.
PubDate: 20160701
DOI: 10.1134/s1061920816030018
Issue No: Vol. 23, No. 3 (2016)
 Authors: Z. I. Ali; M. Sango
 Unique solvability of a nonstationary problem of radiativeconductive heat
exchange in a system of semitransparent bodies Authors: A. A. Amosov
Pages: 309  334
Abstract: Abstract A nonstationary initial boundary value problem describing the radiativeconductive heat exchange in a system of semitransparent bodies is considered. The radiation transfer equation with boundary conditions of mirror reflection and refraction according to the Fresnel laws is used to describe the propagation of radiation. The dependence of the radiation intensity and the optical properties of bodies on the radiation frequency is taken into account. The existence and uniqueness of a weak solution are proved. A comparison theorem is proved. Some a priori estimates for the weak solution are derived and its regularity is proved.
PubDate: 20160701
DOI: 10.1134/s106192081603002x
Issue No: Vol. 23, No. 3 (2016)
 Authors: A. A. Amosov
 On the classes H p ω and Lip (α, p ) for trigonometric series
with monotone coefficients Authors: A. P. Antonov
Pages: 335  342
Abstract: Abstract The paper is devoted to the study of a relationship between the behavior of the coefficients of trigonometric series of many variables and the smoothness of the sums of these series in the spaces L p .
PubDate: 20160701
DOI: 10.1134/s1061920816030031
Issue No: Vol. 23, No. 3 (2016)
 Authors: A. P. Antonov
 Algebraic functions of complexity one, a Weierstrass theorem, and three
arithmetic operations Authors: V. K. Beloshapka
Pages: 343  347
Abstract: Abstract The Weierstrass theorem concerning functions admitting an algebraic addition theorem enables us to give an explicit description of algebraic functions of two variables of analytical complexity one. Their description is divided into three cases: the general case, which is elliptic, and two special ones, a multiplicative and an additive one. All cases have a unified description; they are the orbits of an action of the gauge pseudogroup. The first case is a 1parameter family of orbits of “elliptic addition,” the second is the orbit of multiplication, and the third of addition. Here the multiplication and addition can be derived from the “elliptic addition” by passages to a limit. On the other hand, the elliptic orbits correspond to complex structures on the torus, the multiplicative orbit corresponds to the complex structure on the cylinder, and the additive one to that on the complex plane. This work was financially supported by the Russian Foundation for Basic Research under grants nos. 1400709a and 130112417ofim2.
PubDate: 20160701
DOI: 10.1134/s1061920816030043
Issue No: Vol. 23, No. 3 (2016)
 Authors: V. K. Beloshapka
 Semiclassical spectral series of a quantum Schrödinger operator
corresponding to a singular circle composed of equilibria Authors: V. L. Chernyshev
Pages: 348  354
Abstract: Abstract On a twodimensional surface, a Schrödinger operator is considered with a potential whose critical points form a closed curve. We pose the problem of describing the semiclassical spectral series corresponding to this curve. The standard construction for describing the spectral series corresponding to isolated nondegenerate equilibria or to periodic trajectories of Hamiltonian systems is not applicable in this situation. In the paper, a description of semiclassical solutions of the spectral problem for the quantum Schrödinger operator that correspond to nonisolated equilibria are presented and, to calculate the splitting of the eigenvalues, it turns out to be necessary to find the spectral series with a higher order of accuracy than it is usually required.
PubDate: 20160701
DOI: 10.1134/s1061920816030055
Issue No: Vol. 23, No. 3 (2016)
 Authors: V. L. Chernyshev
 Negative energy, debts, and disinformation from the viewpoint of analytic
number theory Authors: V. P. Maslov
Pages: 355  368
Abstract: Abstract The number zero and negative numbers are added to analytical number theory which includes transcendents. New solutions of Diophantine equations are applied to thermodynamics, information theory and biology.
PubDate: 20160701
DOI: 10.1134/s1061920816030067
Issue No: Vol. 23, No. 3 (2016)
 Authors: V. P. Maslov
 A series of irreducible unitary representations of a group of
diffeomorphisms of the halfline Authors: E. D. Romanov
Pages: 369  381
Abstract: Abstract We present a family of unitary representations of a group of diffeomorphisms of a finitedimensional real Euclidean space using a family of quasiinvariant measures. In the onedimensional case, for a special kind of group diffeomorphisms of the halfline, we prove the irreducibility of the representations thus obtained.
PubDate: 20160701
DOI: 10.1134/s1061920816030079
Issue No: Vol. 23, No. 3 (2016)
 Authors: E. D. Romanov
 Some families of generating functions and associated hypergeometric
transformation and reduction formulas Authors: H. M. Srivastava
Pages: 382  391
Abstract: Abstract Summation, transformation and reduction formulas for various families of hypergeometric functions in one, two and more variables are potentially useful in many diverse areas of applications. The main object of this paper is to derive several substantially more general results on this subject than those considered recently by Neethu et al. [7] in connection with Bailey’s transformation involving the Gauss hypergeometrc function 2F 1 (see [1]). The methodology used here is based essentially on some families of hypergeometric generating functions. Relevant connections of the results presented in this paper with those in the earlier works are also pointed out.
PubDate: 20160701
DOI: 10.1134/s1061920816030080
Issue No: Vol. 23, No. 3 (2016)
 Authors: H. M. Srivastava
 Embedding theorems for a weighted Sobolev class in the space L q,v with
weights having a singularity at a point: Case v ∉ L q 1 Authors: A. A. Vasil’eva
Pages: 392  424
Abstract: Abstract In the paper, embedding theorems for reduced weighted Sobolev classes in the space L q,v with weights having a singularity at a point are obtained. For a special class of weights, estimates for widths are also obtained. The case of v ∉ L q is considered.
PubDate: 20160701
DOI: 10.1134/s1061920816030092
Issue No: Vol. 23, No. 3 (2016)
 Authors: A. A. Vasil’eva
 Contribution to the symplectic structure in the quantization rule due to
noncommutativity of adiabatic parameters Authors: M. V. Karasev
Pages: 207  218
Abstract: Abstract A geometric construction of the `ala Planck action integral (quantization rule) determining adiabatic terms for fastslow systems is considered. We demonstrate that in the first (after zero) adiabatic approximation order, this geometric rule is represented by a deformed fast symplectic 2form. The deformation is controlled by the noncommutativity of the slow adiabatic parameters. In the case of one fast degree of freedom, the deformed symplectic form incorporates the contraction of the slow Poisson tensor with the adiabatic curvature. The same deformed fast symplectic structure is used to represent the improved adiabatic invariant in a geometric form.
PubDate: 20160401
DOI: 10.1134/s1061920816020060
Issue No: Vol. 23, No. 2 (2016)
 Authors: M. V. Karasev