Russian Journal of Mathematical Physics最新文献

Left and right-inverse (delta)-suns and left and right (gamma)-suns are studied in asymmetric spaces. Sufficient conditions for the existence of best approximation and solarity of sets are obtained in the uniformly convex asymmetric spaces.

DOI 10.1134/S1061920824030166

The paper deals with the formal short-wavelength asymptotic solutions describing the acoustic eigenoscillations in a vessel having a hard bottom, filled in by an acoustic medium, and covered by a thin elastic membrane. The solutions are localized in the medium near the line of the rigid contact of the membrane covering the vessel with the edge of the vessel. The coefficients in the asymptotic expansion of the solutions satisfy a recurrent sequence of solvable problems, whereas the frequencies, for which such nontrivial formal solutions exist, obey an asymptotic ‘quantization-type condition.

DOI 10.1134/S1061920824030105

In this paper, we introduce the generalized product Hausdorff operator and study the boundedness of this operator on product two-weighted Morrey, Morrey–Herz spaces. As consequences, we obtain some results about the bounds of product Hausdorff operator associated with the Opdam–Cherednik transform and the sharp bounds for the product weighted Hardy–Littlewood average operator and the product Hardy–Cesàro operator on such spaces.

DOI 10.1134/S1061920824030063

The paper deals with the spectral localization in a model problem of singular perturbation theory and the role of the Stokes phenomenon in this context. We study some typical properties of the asymptotic distribution of eigenvalues and, in particular, topologically different types of the spectral configurations in the semiclassical approximation. In this setting the question naturally arises about the corresponding spectral dynamics and the deformation of the actual limit spectral configurations.

DOI 10.1134/S1061920824030026

We study real-valued asymptotic solutions of the discrete Painlevé equation of second type (dPII)

In the case of (n/nu = O(1)), and as (ntoinfty), the asymptotics is nonuniform. Near the point (n= 2nu), an inner transition layer occurs, which matches regular asymptotics to the left and to the right of this point. The matching procedure involves classical Painlevé II transcendents. The asymptotics are applied to discrete gap probabilities and random matrix theory.

DOI 10.1134/S1061920824030130

Using Maslov’s canonical operator in the Cauchy problem for a Dirac equation, we consider the asymptotics of the solution of the Cauchy problem in which the potential depends irregularly on a small parameter.

DOI 10.1134/S1061920824030014

In this paper, we prove that the vorticity belongs to (L^{infty}(0,T;L^2(Omega))) for 3D incompressible Navier–Stokes equation with space-periodic boundary conditions, then the existence of a global smooth solution is obtained. Our approach is to construct a set of auxiliary systems to approximate the original system of vorticity equation.

This paper deals with the study of initial and final value theorems by means of fractional Hankel wavelet transform function and afterwards tempered distributions.

In 2008, Spivey found a recurrence relation for the Bell numbers (phi_{n}). We consider the probabilistic (r)-Bell polynomials associated with (Y), (phi_{n,r}^{Y}(x)), which are a probabilistic extension of the (r)-Bell polynomials. Here (Y) is a random variable whose moment generating function exists in some neighborhood of the origin and (phi_{n}=phi_{n,0}^{1}(1)). The aim of this paper is to generalize the relation for the Bell numbers to that for the probabilistic (r)-Bell polynomials associated with (Y).