# Theoretical and applied problems of Physics and Mathematics

# Rank One Strong Singular Perturbation by Nonsymmetric Potential

For a rank one strong singular perturbation of a self-adjoint operator by nonsymmetric potential, we present a construction and investigated the corresponding eigenvalue problem.

# Behavior of Surface Spin Waves at Reflection from Uniaxial Multilayer Ferromagnet

The purpose of this article is to review the reflective properties of multilayer ferromagnet for surface spin waves. It was calculated the reflection coefficient of surface spin waves from multilayer ferromagnet with uniaxial magnetic anisotropy in non-ideal boundary conditions at the interface between layers. The problem is solved in the exchange approximation. Graphics shows us the dependence of the reflection coefficient on the frequency, of the external magnetic field, the exchange interaction constant and uniaxial magnetic anisotropy.

# Sound Generation by Taylor and Scully Vortexes and the Blade of the Varying Cross Section

A problem of the blade vortex interaction noise (BVI) generation has been solved for incoming flux and Taylor, Scully vortexes. Solution for this problem is a closed system of the aeroacoustical equations, which is based on perfect compressible gas model. A behavior of the generated noise has been studied for the different flow velocities and blade thicknesses. Results of the calculations show existence of the two frank regions of the sound existence on the blade shape. The first of it is more resistant for the parameters changing. The second one is a flow region of the instability.

# Inertial Stability as a Result of the Relation Between Transport and Relative Fluid Rotations

The aim of the paper is fluid inertial stability nature determination through the representation of potential (non-rotational) motion as the compensation of two rotations, transport one and relative one. Theoretical methods are used. It is based on well-known description of fluid motion as a sum of three types (Cauchy–Helmholz theorem), but uses theoretical mechanics approach. The motion is considered as a sum of transport and relative ones. Thransport angular velocity corresponds to macroscopic motion, while relative one is caused by fluid parcel deformation.

# Definition Peculiarities of Energy of Vacancy Formation In 4d-Transition Metals from First Principles

In this paper a study of the temperature dependence of the vacancy formation energy in bulk fcc 4d-transition metals Ag and Pd using DFT was presented. Peculiarity of this work is the use of experimental values of the lattice parameters for the respective temperatures. This paper discusses the various contributions to the vacancy formation energy and shows that they can play an important role. It was shown that thermal excitation has a significant impact on the vacancy formation energy at high temperatures. The possibility of the existence of the compensation effect, i.e.

# Propagation of Spin Wave Through the Anisotropic Boundary of Two Uniaxial Ferromagnets in an External Magnetic Field

This paper represents the investigation of the reflection of bulk spin waves at the interface of two uniaxial ferromagnetic media that propagate at an angle to the interface and their penetration from one ferromagnetic medium to another one. Thereby, the interaction similar to the interaction of two antiferromagnets is taken into account at the boundary interface between two media in an external constant uniform magnetic field. The problem is solved in the formalism of spin density based on equations of Landau–Lifshitz in the absence of dissipation in the system.

# Distribution of the Antiferromagnetism Vector for an Isolated Antidot and a System of Remote Antidots in Antiferromagnets

In the paper, an antiferromagnetism vector distribution in an antiferromagnetic film composed of an uniaxial or isotropic two-sublattice antiferromagnet with a set system of circular antidots is investigated. For such a system, the Landau-Lifshitz equation is written and its solution is obtained.

# Symmetry Analysis of a Class of (2+1)-Dimensional Linear Ultra-Parabolic Equations

In this paper, a class of (2+1)-dimensional linear ultra-parabolic equations of the second order is investigated by using the methods of group analysis of differential equations. The class under study generalizes a number of the classical equations of mathematical physics such as the free Kramers equation, the linear Kolmogorov equation etc. The classification of the symmetry properties of equations from the class is carried out by using the well-known Lie–Ovsiannikov algorithm.

# Minimal Systems of Generators and Relations and Properties of Wreath Products of Perfect Groups

Generators and defining relations for wreath products of perfect group which is two generating and alternating groups (m 2 times) are given. System of generators of metaperfect groups are found. Generators and defining relations for wreath products of 2-generating perfect groups were found, including alternating groups, i.e. (m 2 time). Systems of generators for metaperfect groups were investigated. A constructive proof of the minimality found system of generators was presented. It is shown that metaperfect group is not locally finite group.