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PHYSICS (583 journals)

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Journal Cover Russian Journal of Mathematical Physics
  [SJR: 0.858]   [H-I: 24]   [0 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1531-8621 - ISSN (Online) 1061-9208
   Published by Springer-Verlag Homepage  [2335 journals]
  • Asymptotic support of localized solutions of the linearized system of
    • 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 two-dimensional surface was obtained by the authors earlier. Here, this asymptotic behavior is refined.
      PubDate: 2016-10-01
      DOI: 10.1134/s1061920816040014
      Issue No: Vol. 23, No. 4 (2016)
  • Rigid body dynamics in non-Euclidean spaces
    • Authors: A. V. Borisov; I. S. Mamaev
      Pages: 431 - 454
      Abstract: Abstract In this paper, we focus on the study of two-dimensional 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: 2016-10-01
      DOI: 10.1134/s1061920816040026
      Issue No: Vol. 23, No. 4 (2016)
  • 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: 2016-10-01
      DOI: 10.1134/s1061920816040038
      Issue No: Vol. 23, No. 4 (2016)
  • 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 n-dimensional space (multi-dimensional 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: 2016-10-01
      DOI: 10.1134/s106192081604004x
      Issue No: Vol. 23, No. 4 (2016)
  • 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 creation-annihilation regime for the perturbation or anharmonism. Activation of this regime sometimes needs in an additional resonance deformation (Cartan subalgebra breaking).
      PubDate: 2016-10-01
      DOI: 10.1134/s1061920816040051
      Issue No: Vol. 23, No. 4 (2016)
  • Asymptotic expansions of Feynman integrals of exponentials with polynomial
    • 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: 2016-10-01
      DOI: 10.1134/s1061920816040063
      Issue No: Vol. 23, No. 4 (2016)
  • 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: 2016-10-01
      DOI: 10.1134/s1061920816040075
      Issue No: Vol. 23, No. 4 (2016)
  • 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. Sekerzh-Zen’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 well-known model with a “simple” source.
      PubDate: 2016-10-01
      DOI: 10.1134/s1061920816040087
      Issue No: Vol. 23, No. 4 (2016)
  • 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 three-dimensional Euclidean space to which a ray is glued, and the other is formed by two three-dimensional 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: 2016-10-01
      DOI: 10.1134/s1061920816040099
      Issue No: Vol. 23, No. 4 (2016)
  • 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: 2016-10-01
      DOI: 10.1134/s1061920816040105
      Issue No: Vol. 23, No. 4 (2016)
  • 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: 2016-07-01
      DOI: 10.1134/s1061920816030018
      Issue No: Vol. 23, No. 3 (2016)
  • Unique solvability of a nonstationary problem of radiative-conductive 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 radiative-conductive 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: 2016-07-01
      DOI: 10.1134/s106192081603002x
      Issue No: Vol. 23, No. 3 (2016)
  • 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: 2016-07-01
      DOI: 10.1134/s1061920816030031
      Issue No: Vol. 23, No. 3 (2016)
  • 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 1-parameter 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. 14-00709-a and 13-01-12417-ofi-m2.
      PubDate: 2016-07-01
      DOI: 10.1134/s1061920816030043
      Issue No: Vol. 23, No. 3 (2016)
  • 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 two-dimensional 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: 2016-07-01
      DOI: 10.1134/s1061920816030055
      Issue No: Vol. 23, No. 3 (2016)
  • 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: 2016-07-01
      DOI: 10.1134/s1061920816030067
      Issue No: Vol. 23, No. 3 (2016)
  • A series of irreducible unitary representations of a group of
           diffeomorphisms of the half-line
    • Authors: E. D. Romanov
      Pages: 369 - 381
      Abstract: Abstract We present a family of unitary representations of a group of diffeomorphisms of a finite-dimensional real Euclidean space using a family of quasi-invariant measures. In the one-dimensional case, for a special kind of group diffeomorphisms of the halfline, we prove the irreducibility of the representations thus obtained.
      PubDate: 2016-07-01
      DOI: 10.1134/s1061920816030079
      Issue No: Vol. 23, No. 3 (2016)
  • 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: 2016-07-01
      DOI: 10.1134/s1061920816030080
      Issue No: Vol. 23, No. 3 (2016)
  • 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: 2016-07-01
      DOI: 10.1134/s1061920816030092
      Issue No: Vol. 23, No. 3 (2016)
  • 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 fast-slow systems is considered. We demonstrate that in the first (after zero) adiabatic approximation order, this geometric rule is represented by a deformed fast symplectic 2-form. 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: 2016-04-01
      DOI: 10.1134/s1061920816020060
      Issue No: Vol. 23, No. 2 (2016)
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
Tel: +00 44 (0)131 4513762
Fax: +00 44 (0)131 4513327
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