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PHYSICS (576 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  [2352 journals]
  • Localized asymptotic solutions of the wave equation with variable velocity
           on the simplest graphs
    • Authors: A. I. Allilueva; A. I. Shafarevich
      Pages: 279 - 289
      Abstract: Abstract The asymptotic behavior of the Cauchy problem for the wave equation with variable velocity and localized initial conditions on the line, semi-axis, and an infinite starlike graph is described. The solution consists of a short-wave and long-wave parts; the shortwave part moves along the characteristics, while the long-wave part satisfies the Goursat or Darboux problem. In the case of a star-like graph, the distribution of energy with respect to the edges is discussed; this distribution depends on the arrangement of the eigensubspaces of the unitary matrix that defines the boundary condition at the vertex of the star.
      PubDate: 2017-07-01
      DOI: 10.1134/s1061920817030013
      Issue No: Vol. 24, No. 3 (2017)
  • Correction to the leading term of asymptotics in the problem of counting
           the number of points moving on a metric tree
    • Authors: V. L. Chernyshev; A. A. Tolchennikov
      Pages: 290 - 298
      Abstract: Abstract In the problem of determining the asymptotics for the number of points moving along a metric tree, a polynomial approximation that uses Barnes’ multiple Bernoulli polynomials is found. The connection between the second term of the asymptotic expansion and the graph structure is discussed.
      PubDate: 2017-07-01
      DOI: 10.1134/s1061920817030025
      Issue No: Vol. 24, No. 3 (2017)
  • On some properties of multidimensional hyperbolic quasi-gasdynamic systems
           of equations
    • Authors: B. N. Chetverushkin; A. A. Zlotnik
      Pages: 299 - 309
      Abstract: Abstract We study a multidimensional hyperbolic quasi-gasdynamic (HQGD) system of equations containing terms with a regularizing parameter τ > 0 and 2nd order space and time derivatives; the body force is taken into account. We transform it to a form close to the compressible Navier–Stokes system of equations. Then we derive the entropy balance equation and show that the entropy production is similar to the latter system plus a term of the order of O(τ2). We analyze an equation for the total entropy as well. We also show that the corresponding residuals in the HQGD equations with respect to the compressible Navier–Stokes ones are of the order of O(τ2) too. Finally we treat the simplified barotropic HQGD system of equations with the general state equation and the stationary potential body force and obtain the corresponding results for it.
      PubDate: 2017-07-01
      DOI: 10.1134/s1061920817030037
      Issue No: Vol. 24, No. 3 (2017)
  • Exact and asymptotic solutions of the Cauchy–Poisson problem with
           localized initial conditions and a constant function of the bottom
    • Authors: S. Yu. Dobrokhotov; S. Ya. Sekerzh-Zen’kovich; A. A. Tolchennikov
      Pages: 310 - 321
      Abstract: Abstract In the paper, the asymptotic solutions for a problem of Cauchy–Poisson type with localized initial conditions are constructed. The bottom of the basin under consideration which was constant before the perturbation, is instantly perturbed at the initial time moment by a spatially localized function. Simplifications of the corresponding formulas are presented inside and outside the vicinity of the leading front, as well as in the case of a special choice of the initial condition. It is shown that, in the vicinity of the leading front, the asymptotic solution coincides with the asymptotic solution of the linear Boussinesq equation.
      PubDate: 2017-07-01
      DOI: 10.1134/s1061920817030049
      Issue No: Vol. 24, No. 3 (2017)
  • Constitutive relations in multidimensional isotropic elasticity and their
           restrictions to subspaces of lower dimensions
    • Authors: D.V. Georgievskii
      Pages: 322 - 325
      Abstract: Abstract The mechanical meaning and the relationships among material constants in an n-dimensional isotropic elastic medium are discussed. The restrictions of the constitutive relations (Hooke’s law) to subspaces of lower dimension caused by the conditions that an m-dimensional strain state or an m-dimensional stress state (1 ≤ m < n) is realized in the medium. Both the terminology and the general idea of the mathematical construction are chosen by analogy with the case n = 3 and m = 2, which is well known in the classical plane problem of elasticity theory. The quintuples of elastic constants of the same medium that enter both the n-dimensional relations and the relations written out for any m-dimensional restriction are expressed in terms of one another. These expressions in terms of the known constants, for example, of a three-dimensional medium, i.e., the classical elastic constants, enable us to judge the material properties of this medium immersed in a space of larger dimension.
      PubDate: 2017-07-01
      DOI: 10.1134/s1061920817030050
      Issue No: Vol. 24, No. 3 (2017)
  • Magneto-dimensional resonance. Pseudospin phase and hidden quantum number
    • Authors: M. V. Karasev
      Pages: 326 - 335
      Abstract: Abstract The Schrödinger operator for a spinless charge inside a layer with parabolic confinement profile and homogeneous magnetic field is considered. The Lorentz (cyclotron) and the confinement frequencies are assumed to be equal to each other. After inclination of the layer normal from the magnetic field direction there appears a pseudospin su(2)-field removing the resonance degeneracy of Landau levels. Under deviations of the layer surface from the plane shape, a longitudinal geometric current is created. In circulations around surface warping, there is a nontrivial quantum phase transition generated by an element of the π1-homotopy group and a hidden degree of freedom (spectral degeneracy) associated with a “charge” of geometric poles on the layer. The quantization rule contains an additional parity index related to the algebraic number of geometric poles and the Landau level number. The resonance pseudospin phase-shift represents an example of general Aharonov–Bohm type topologic phenomena in quantum (semiclassical or adiabatic) systems with delta-function singularities in symplectic structure.
      PubDate: 2017-07-01
      DOI: 10.1134/s1061920817030062
      Issue No: Vol. 24, No. 3 (2017)
  • Asymptotic completeness of scattering in the nonlinear Lamb system for
           nonzero mass
    • Authors: A. I. Komech; A. E. Merzon
      Pages: 336 - 346
      Abstract: Abstract We establish the asymptotic completeness in the nonlinear Lamb system with nonzero mass for hyperbolic stationary states. For the proof, we construct a trajectory of a reduced equation (which is a nonlinear nonautonomous ODE) converging to a hyperbolic stationary point, using the Banach space Inverse Function Theorem and a priori estimates. We give a counterexample showing that the hyperbolicity condition is essential.
      PubDate: 2017-07-01
      DOI: 10.1134/s1061920817030074
      Issue No: Vol. 24, No. 3 (2017)
  • Topological complexity of certain classes of C *-algebras
    • Authors: A. I. Korchagin
      Pages: 347 - 353
      Abstract: Abstract We compute the topological complexity for some important classes of noncommutative C*-algebras: AF algebras, AI algebras, and even Cuntz algebras.
      PubDate: 2017-07-01
      DOI: 10.1134/s1061920817030086
      Issue No: Vol. 24, No. 3 (2017)
  • A model of classical thermodynamics based on the partition theory of
           integers, Earth gravitation, and semiclassical asymptotics. I
    • Authors: V. P. Maslov
      Pages: 354 - 372
      Abstract: Abstract In the paper, a new construction of the theory of partitions of integers is proposed. The author defines entropy as the natural logarithm of the number of partitions of a number M into natural summands with repetitions allowed p(M) and repetitions forbidden q(M). The passage from ln p(M) to lnq(M) through the mesoscopic values M → 0 is studied. The topological transition from the mesoscopic lower levels of the Bohr–Kalckar construction to the macroscopic levels corresponding to the critical number of neutrons according to the consequence of Einstein’s inequality M ≤ c N c , where c is determined for the particles of the given atomic nucleus. The role of quantum mechanics in establishing the new world outlook in physics is analyzed. It is pointed out that the main equations of thermodynamics in the volume “Statistical Physics” of the Landau–Lifshits treatise are obtained without appealing to the so-called “three main principles of thermodynamics”. It is also pointed out that Niels Bohr’s liquid model of the nucleus does not involve any interaction of particles in the form of attraction and is based on the presence of a common potential trough for all elements of the nucleus. The author constructs a new approach to thermodynamics, using quantum mechanics and the Earth’s gravitational attraction as a common potential trough.
      PubDate: 2017-07-01
      DOI: 10.1134/s1061920817030098
      Issue No: Vol. 24, No. 3 (2017)
  • Representations associated to quasirepresentations of amenable groups with
           zero multiplication of defect operators
    • Authors: A. I. Shtern
      Pages: 373 - 375
      Abstract: Abstract A direct construction of representations associated to dual quasirepresentations with zero multiplication of defect operators for amenable groups is given.
      PubDate: 2017-07-01
      DOI: 10.1134/s1061920817030104
      Issue No: Vol. 24, No. 3 (2017)
  • Widths of weighted Sobolev classes with constraints f ( a ) = · · · = f
           ( k-1 )( a ) = f ( k )( b ) = · · · = f ( r-1 )( b ) = 0 and the
           spectra of nonlinear differential equations
    • Authors: A. A. Vasil’eva
      Pages: 376 - 398
      Abstract: Abstract In this paper we prove that the Kolmogorov widths of the weighted Sobolev class W p,g r,k [a, b] with restrictions f(a) = · · · = f( k-1)(a) = f( k )(b) = · · · = f( r-1)(b) = 0 in the weighted Lebesgue space L q,v [a, b] coincide with the spectral numbers of some nonlinear differential equation. We assume that 1 < q ≤ p < ∞, the weights are positive almost everywhere, and the Sobolev class is compactly embedded in the space L q,v [a, b].
      PubDate: 2017-07-01
      DOI: 10.1134/s1061920817030116
      Issue No: Vol. 24, No. 3 (2017)
  • Optimal control of the motion of a helical body in a liquid using rotors
    • Authors: E. V. Vetchanin; I. S. Mamaev
      Pages: 399 - 411
      Abstract: Abstract The motion controlled by the rotation of three internal rotors of a body with helical symmetry in an ideal liquid is considered. The problem is to select controls that ensure the displacement of the body with minimum effort. The optimality of particular solutions found earlier is studied.
      PubDate: 2017-07-01
      DOI: 10.1134/s1061920817030128
      Issue No: Vol. 24, No. 3 (2017)
  • Example of nonexistence of a positive generalized entropy solution of a
           Cauchy problem with unbounded positive initial data
    • Authors: L. V. Gargyants
      Pages: 412 - 414
      Abstract: Abstract A Cauchy problem for a first-order quasilinear equation with polynomial flux function and exponential initial data is studied. We prove that this problem has no positive solution in the class of locally bounded functions.
      PubDate: 2017-07-01
      DOI: 10.1134/s106192081703013x
      Issue No: Vol. 24, No. 3 (2017)
  • Stabilizer of a function in the gage group
    • Authors: V. K. Beloshapka
      Pages: 148 - 152
      Abstract: Abstract It is proved that, for the dimension d of the stabilizer of an analytic function z(x, y) in the gage pseudogroup G = {z(x, y) → c(z(a(x), b(y))}, there are precisely four possibilities: (1) d = ∞ and the complexity of z is zero, (2) d = 3 and the complexity of z is equal to one, (3) d = 1 and z is equivalent the function r(x + y) − x of complexity two, (4) d = 0 in all remaining cases.
      PubDate: 2017-04-01
      DOI: 10.1134/s1061920817020029
      Issue No: Vol. 24, No. 2 (2017)
  • Generalized optical theorem to a multipole source excitation in the
           scattering theory
    • Authors: Yu. A. Eremin; A. G. Sveshnikov
      Pages: 207 - 215
      Abstract: Abstract In the present paper, the Optical Theorem is generalized to the case of a penetrable obstacle excited by a multipole of arbitrary order in the presence of a transparent substrate. This generalization allows one to test computer modules when wave scattering by lossless penetrable obstacle is considered. Besides, it enables one to evaluate the absorption cross-section by subtracting the scattering cross-section from the extinction cross-section. This seems to be important because, in this particular case, the far field does not involve a Sommerfeld integral.
      PubDate: 2017-04-01
      DOI: 10.1134/s1061920817020066
      Issue No: Vol. 24, No. 2 (2017)
  • Measures on the Hilbert space of a quantum system
    • Authors: A. Yu. Khrennikov; O. G. Smolyanov
      Pages: 234 - 240
      Abstract: Abstract The paper is the first in a series of papers on the use of measures and generalized measures in quantum theory. In particular, a survey of the proofs of equivalence of various definitions of the density operator is presented. The exposition is of algebraic nature, and analytic assumptions are usually omitted.
      PubDate: 2017-04-01
      DOI: 10.1134/s106192081702008x
      Issue No: Vol. 24, No. 2 (2017)
  • Degenerate Laplace transform and degenerate gamma function
    • Authors: T. Kim; D. S. Kim
      Pages: 241 - 248
      Abstract: Abstract In this paper, we introduce the degenerate Laplace transform and degenerate gamma function and investigate some of their properties. From our investigation, we derive some interesting formulas related to the degenerate Laplace transform and degenerate gamma function.
      PubDate: 2017-04-01
      DOI: 10.1134/s1061920817020091
      Issue No: Vol. 24, No. 2 (2017)
  • Remark concerning Maslov’s theorem on homomorphisms of topological
    • Authors: A. I. Shtern
      Pages: 261 - 262
      Abstract: Abstract Maslov’s theorem on finally continuous sequences of homomorphisms of topological groups is presented for more general passages to the limit.
      PubDate: 2017-04-01
      DOI: 10.1134/s106192081702011x
      Issue No: Vol. 24, No. 2 (2017)
  • Singular sets of surfaces
    • Authors: I. G. Tsar’kov
      Pages: 263 - 271
      Abstract: Abstract Sets of values of the metric projection for an approximatively compact subset of Hilbert space are studied. The results obtained in this way are used to study the geometry of hypersurfaces in ℝ n and their singular sets.
      PubDate: 2017-04-01
      DOI: 10.1134/s1061920817020121
      Issue No: Vol. 24, No. 2 (2017)
  • Erratum to “A new class of Abelian theorems for the
           Mehler–Fock transforms”
    • Authors: H. M. Srivastava; B. J. González; E. R. Negrín
      Pages: 278 - 278
      PubDate: 2017-04-01
      DOI: 10.1134/s1061920817020145
      Issue No: Vol. 24, No. 2 (2017)
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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