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PHYSICS (579 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]
  • 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)
  • Identities for Apostol-type Frobenius–Euler polynomials resulting from
           the study of a nonlinear operator
    • Authors: A. Bayad; T. Kim
      Pages: 164 - 171
      Abstract: Abstract We introduce a special nonlinear differential operator and, using its properties, reduce higher-order Frobenius–Euler Apostol-type polynomials to a finite series of first-order Apostol-type Frobenius–Euler polynomials and Stirling numbers. Interesting identities are established.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020023
      Issue No: Vol. 23, No. 2 (2016)
  • Belavkin filtering with squeezed light sources
    • Authors: A. Dąbrowska; J. Gough
      Pages: 172 - 184
      Abstract: Abstract We derive the filtering equation for Markovian systems undergoing homodyne measurement in the situation where the output processes being monitored are squeezed. The filtering theory applies to case where the system is driven by Fock noise (that is, quantum input processes in a coherent state) and where the output is mixed with a squeezed signal. It also applies to the case of a system driven by squeezed noise, but here there is a physical restriction to emission/absorption coupling only. For the special case of a cavity mode where the dynamics is linear, we are able to derive explicitly the filtered estimate π t (a) for the mode annihilator a based on the homodyne quadrature observations up to time t.'
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020035
      Issue No: Vol. 23, No. 2 (2016)
  • Asymptotic analysis of evolution of a neck in extended thin rigid plastic
    • Authors: D. V. Georgievskii; B. E. Pobedrya
      Pages: 200 - 206
      Abstract: Abstract We carry out an asymptotic analysis with natural small geometric parameter of the stress-strain state realized under the stretch of a rigid-plastic rod of round section and of a flat sheet infinite in one direction, taking into account the presence of areas of thinning (a neck) and thickening with respect to the medium size. In examples, we stress qualitative effects of possible inertia-free development of a neck.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020059
      Issue No: Vol. 23, No. 2 (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)
  • A finite-dimensional version of Fredholm representations
    • Authors: V. Manuilov
      Pages: 219 - 224
      Abstract: Abstract We consider pairs of mappings from a discrete group Γ to the unitary group. The deficiencies of these mappings from being homomorphisms may be great, but if they are close to each other, then we call such pairs balanced. We show that balanced pairs determine elements in the K 0 group of the classifying space of the group. We also show that a Fredholm representation of Γ determines balanced pairs.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020072
      Issue No: Vol. 23, No. 2 (2016)
  • Propagation and interaction of solitons for nonintegrable equations
    • Authors: G. Omel’yanov
      Pages: 225 - 243
      Abstract: Abstract We describe an approach to the construction of multi-soliton asymptotic solutions for nonintegrable equations. The general idea is realized in the case of N waves, N = 1, 2, 3, and for the KdV-type equation with nonlinearity u 4. A brief review of asymptotic methods as well as results of numerical simulation are included.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020084
      Issue No: Vol. 23, No. 2 (2016)
  • On the distribution of energy of localized solutions of the Schrödinger
           equation that propagate along symmetric quantum graphs
    • Authors: A. I. Shafarevich
      Pages: 244 - 250
      Abstract: Abstract From the point of view of applications to quantum mechanics, it is natural to pose a question concerning the distribution of energy of localized solutions of a nonstationary Schrödinger equation over the graph (in other words, the probability to find a quantum particle in a given area). This problem is apparently very complicated for general graphs, because the energy distribution is much more sensitive to the form of boundary conditions and to the initial state than the asymptotic behavior of the number of localized functions. Below, we present initial results concerning the distribution of energy in the case of symmetric quantum graphs (this means that the Schrödinger operators on different edges have the same structure). For general local self-adjoint boundary conditions, we describe the process of onestep scattering of the localized solutions and obtain a simple general result of the distribution of energy. Some special cases and specific examples are discussed.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020096
      Issue No: Vol. 23, No. 2 (2016)
  • On rational functions of first-class complexity
    • Authors: M. Stepanova
      Pages: 251 - 256
      Abstract: Abstract It is proved that, for every rational function of two variables P(x, y) of analytic complexity one, there is either a representation of the form f(a(x) + b(y)) or a representation of the form f(a(x)b(y)), where f(x), a(x), b(x) are nonconstant rational functions of a single variable. Here, if P(x, y) is a polynomial, then f(x), a(x), and b(x) are nonconstant polynomials of a single variable.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020102
      Issue No: Vol. 23, No. 2 (2016)
  • Bloch principle for elliptic differential operators with periodic
    • Authors: V. V. Zhikov; S. E. Pastukhova
      Pages: 257 - 277
      Abstract: Abstract Differential operators corresponding to elliptic equations of divergent type with 1-periodic coefficients are considered. The equations are put in Sobolev spaces with an arbitrary 1-periodic Borel measure on the entire space R d . In the study of the spectrum of operators of this kind, the Bloch principle is of fundamental importance. According to this principle, all points of the desired spectrum are obtained when studying the equation on the unit cube with quasiperiodic boundary conditions. The proof of the Bloch principle for problems in the above formulation is proved, in several versions of the principle. Examples of the application of the principle to finding the spectrum of specific operators, for example, for the Laplacian in a weighted space or on a singular structure of lattice type.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020114
      Issue No: Vol. 23, No. 2 (2016)
  • Thermodynamics, idempotent analysis, and tropical geometry as a return to
    • Authors: V. P. Maslov
      Pages: 278 - 280
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020126
      Issue No: Vol. 23, No. 2 (2016)
  • Absence of two Paley–Wiener properties for semisimple Lie groups of
           real rank one
    • Authors: A. I. Shtern
      Pages: 281 - 282
      Abstract: Abstract The weak Paley–Wiener property and the topological Paley–Wiener property for connected semisimple Lie groups of real rank one with finite center are discussed.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020138
      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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