Russian Journal of Mathematical Physics最新文献

Recently, the degenerate hyperbolic functions are studied in connection with the degenerate Bernoulli and degenerate Euler numbers which were introduced by Carlitz. The aim of this paper is to derive moment representations of the fully degenerate Bernoulli and degenerate Euler polynomials associated with the Laplace random variable with parameters ((a,b)=(0,1)). In addition, we obtain the product expansions for the functions which are degenerate versions of (frac{sinh t}{t}) and (cosh t). We also obtain some new identities involving the fully degenerate Bernoulli and degenerate Euler numbers by using series expansions for certain degenerate hyperbolic functions.

DOI 10.1134/S1061920824040071

The Cauchy problem on the real axis for the Gurtin–Pipkin equation with the Rabotnov kernel is considered. For some special case, it is proved that there is no propagation front in this problem.

DOI 10.1134/S1061920824040137

We prove necessary and sufficient conditions that an ordinary unitary character on the radical of a connected locally compact group admits an extension to a locally bounded finally precontinuous one-dimensional pure pseudorepresentation of the group.

DOI 10.1134/S1061920824040149

Given an action of an infinite discrete group on a smooth manifold, we construct an equivariant Chern character in cyclic cohomolgy of the crossed product for equivariant vector bundles over fixed point submanifolds of torsion elements in the group. We use this Chern character to obtain an index formula for nonlocal elliptic operators associated with the group action.

DOI 10.1134/S1061920824040174

We study the relationship between the phase space recently introduced by Bolotin and Treschev in connection with the study of billiards with semirigid walls and the phase space arising in the construction of semiclassical asymptotics for a class of differential equations degenerating on the boundary of a domain.

DOI 10.1134/S1061920824040101

We consider a periodic boundary value problem for a singularly perturbed reaction-advection-diffusion equation in the case of a two-dimensional space variable. We construct a new interior layer-type formal asymptotics which includes an approximation of the location of the interior layer, investigate the order-preserving properties of the operators generating the asymptotics, and propose a modified procedure to obtain asymptotic lower and upper solutions. By using sufficiently precise lower and upper solutions, we prove the existence of a periodic solution with an interior layer and estimate the accuracy of its asymptotics. We also prove the asymptotic Lyapunov stability of this solution.

DOI 10.1134/S1061920824040113

Properties of local and global suns and protosuns are studied. In particular, we investigate properties of a space and a set under which the local solarity of the set implies its global solar properties. It is shown that, in CLUR-spaces, a segmented Chebyshev local sun is a sun. In particular, a Chebyshev local sun composed of an at most countable family of convex existence sets is a sun.

DOI 10.1134/S1061920824040150

The semiclassical asymptotics of the solution of the Cauchy problem for the Schrödinger equation with a delta potential localized on a surface of codimension 1 is described. The Schrödinger operator with a delta potential is defined using extension theory and specified by boundary conditions on this surface. The initial conditions are chosen in the form of a narrow peak, which is a Gaussian packet, localized in a small neighborhood of a surface of arbitrary dimension, and oscillating rapidly along it. The Maslov complex germ method is used to construct the asymptotics. The reflection of an isotropic manifold with a complex germ interacting with the delta potential is described.

DOI 10.1134/S1061920824030142

The coincidence of the ( operatorname{Ind} ) and (dim) dimensions for the first countable paracompact (sigma)-spaces is proved. This gives a positive answer to A.V. Arkhangel’skii’s question of whether the dimensions ( operatorname{ind} X), ( operatorname{Ind} X), and (dim X) are equal for the first countable spaces with a countable network.

DOI 10.1134/S1061920824030178

Let (Y) be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to study probabilistic Bernoulli polynomials of order (r) associated with (Y) and probabilistic multi-poly-Bernoulli polynomials associated with (Y). They are respectively probabilistic extensions of Bernoulli polynomials of order (r) and multi-poly-Bernoulli polynomials. We find explicit expressions, certain related identities and some properties for them. In addition, we treat the special cases of Poisson, gamma and Bernoulli random variables.

DOI 10.1134/S1061920824030087