# Theoretical and applied problems of Physics and Mathematics

# Stationary Magnetic Interactional Magnetization Waves in Ferromagnetic with Easy-Axis Anisotropy

Results of research have shown that in regular ferrite-garnet films with perpendicular lightweight anisotropy in parallel to the film plane magnetic field long-wave inhomogeneous magnetic configuration of harmonic type can be created and observed. Field removes devolution in the direction of magnetization and promotes the formation of inhomogeneous magnetic configuration. During the work it was thought that the magnetic field is close to the critical value at which film homogeneously magnetization happens.

# Compact spherical vortex model

Spherical vortex with only radial distribution and also to derive self-similar equation for the vortex’s difusion and it’s solution. The investigations are theoretical ones. The obtained results are the following ones. Any of the vortical flows that has zero radial velocity is always helical one. Meridianal and azimuthal velocity components have the same distributions (are invariant). The vorticity field compensation condition for spherical coordinates does not result into vortex compactness as it is for cylindrical vortexes.

# Blade Shape and Cross Section’s Curvature Influence Parameters of the Rotor’s Rotational Noise

The aim of this work is to study the influence of the blade shape and curvature changing of characteristics of the helicopter’s rotational noise. To this end, we consider 4-digits NASA profiles whose rotational noise is compared with one of the parabolic blade. Calculations results show that 4-digits blade generated rotational noise of higher level and its distribution on the blade’s shape are smooth in comparison with noise distribution of parabolic blade. However, the parabolic blade has more expressive maximum of noise level than the 4-digits blade.

# Reflection of Surface Spin Waves from the Interface of Uniaxial and Biaxial Ferromagnets in a Planar Magnetic Field

The article investigates the reflection of surface spin waves passing through an interface of uniaxial and biaxial ferromagnets in a planar external magnetic field directed along the hard axis of ferromagnet. The problem is solved in the formalism of spin density based on equations of Landau-Lifshitz in the absence of dissipation in the system.

# Reconstruction of Hardronic Jets with Clustering Algorithms and Modern Statistical Methods of Data Analysis in High Energy Physics

In a wide range of statistical data processing in high energy physics jet clustering algorithms and applications for function minimization are used. The aim of the study is to validate the acceptability of the programs and FastJet and MINUIT, that provide a powerful tool for finding jets from data and Monte Carlo models after the selection of events and for the subsequent approximation method of least squares.

# Structure of a Set of Orthogonal Projections Connected with Cycle and Antenna

In this paper we study algebras of Temperley–Lieb type generated by orthogonal projections connected with unicyclic graph which is a cycle with the antenna. The goal of the paper is to study representations in a Hilbert space of such algebras in the simplest case and to comprehensively describe the set parameters when such representations exist. The simplest algebra corresponds to unicyclic connected graph which is a cycle connected by an edge by one separate vertex.

# Stochastic Integral and Stochastic Derivative Connected with a Lévy Progress

The extended stochastic integral with respect to a Lévy process and the corresponding Hida stochastic derivative have many applications in the stochastic analysis, in particular, in the theory of stochastic differential and integral equations.

# Conditions of Existense and Uniqueness of Solutions of Parabola-Hyperbolic Equation with Nonolocal Boundary Conditions

Processes described with parabola-hyperbolic differential equations are crucial in the theory of mathematical physics. The article deals with the heterogeneous parabola-hyperbolic equation with nonlocal boundary conditions. To further investigate this class of problems, we need to find its classical solution. We show the system of eigenfunctions and associated functions of the boundary value problem.

# An Estimate for the Rate of Convergence in the Central Limit Theorem for Integrals of Shot Noise Processes

In this paper, we study the rate of convergence of the normalized integrals of stationary shot noise processes in the central limit theorem. More precisely, we establish an estimate for the distance between pre-limit distribution functions of the normalized integrals and limit Gaussian one. The key machinery of the proof is the study of convergence rates in terms of characteristic functions with a subsequent use of Berry–Esseen bound. We also give an analogous estimate of convergence rates in Lévy metric and an estimate for integrals with explicit normalization.

# Periodogram Estimator Properties of the Parameters of the Regression Model with Strongly Dependent Noise

The problem of detection of hidden periodicities is considered in the paper. In the capacity of useful signal model the harmonic oscillation observed on the background of random noise, that is a local functional of Gaussian strongly dependent stationary process is taken. For estimation of unknown angular frequency and amplitude of harmonic oscillation periodogram estimator is chosen, for which sufficient conditions of asymptotic normality are obtained and limit normal distribution is found.