Theoretical and applied problems of Physics and Mathematics

Quantum-Mechanical Structures with Delta-Functional Potential

Based on the concept of quantum-mechanical impedance model, we develop the quantum-mechanical δ-inhomogeneities – δ-barrier and δ well for nanoelectronics applications. Typical models for natural and artificial quantum-mechanical structures: single, double and triple δ inhomogeneities; potential steps, wells and barriers with δ inhomogeneities, lattice of δ-inhomogeneities are considered. We obtain analytical expressions for eigenvalues of structures.

Helicopter Rotor Blade-Vortex Interaction (BVI) Noise

In this paper, a model of sound generation by blade–vortex interaction (BVI) is offered for helicopter rotor operating at subsonic regime ( ). We find the quantitative limits of its use. Based on three-dimensional non-stationary equation of small perturbations spreading, the problem of sound generation by parabolic blade and Taylor’s vortex, situated at a certain distance from the blade, is solved. To solve this problem, we use the numerical analytical method. The method allows calculating the near-field sound potential and its derivatives.

Compact Turbulent Vortex Generation: Approximate Model for Relatively Large Time Moments

The aim of research is to develop the analytical model capable o approximate description of compact turbulent vortex generation by finite power circulation source for relatively large time moments. The method is based on turbulence gradient Boussinesk model according to which turbulent viscosity coefficient has a constant value.

Features of Nematic Phase in Magnets with S = 2

This paper investigates the nematic phase of isotropic non-Heisenberg magnet with spin magnetic ion 2. The spectrum behavior of elementary excitations in the vicinity of phase transition lines with other phases is implemented in this model. To solve the site problem, we use the method of diagonalization N-level system based on employing Hubbard algebra. The research found that the nematic phase in this phase is the geometric image of “corrugated” biaxial ellipsoid because of the additional parameter β.

Effect of Magnetic Field on the Structure and Properties of Polymers and Their Composites

This paper studies the influence of magnetic field on the structure and properties of polymers and their composites. The analysis of research into the impact of magnetic fields on unfilled polymers and composites on their basis allows separate effects associated with the interaction of the polymer matrix with the magnetic field and the effects due to structuring ferromagnetic fillers. We establish that the structure of polymer composite materials changes under the impact of a magnetic field.

The Electrolyte Movement at Etching and Deposition of Metals Under Inhomogeneous Constant Magnetic Field

This paper considers the features of the electrolyte movement in the surface layer in the processes of etching and deposition of metals at a ferromagnetic electrode in the form of a ball, when it is magnetized in an external inhomogeneous magnetic field of the moderate intensity (∼ 1 kOe). The choice of an electrode in the form of a ball makes it easy to distinguish the effects of magnetic fields from the effects of a different nature due to the equivalence of all points of its surface in the absence of magnetization in this model system.

Generators and Relations of Syllows p-Subgroups of Group Sn

In this article, we investigate generators and relations of syllows subgroups of some symmetric group. It will enable studying syllows subgroups of other groups since every finite subgroup is isomorphicaly embedded in the syllows subgroup of some symmetric group. We find a set of relations for a fixed system of generators and prove that this set of relations is minimal between sets of relations. Research methods are the method of Shreier’s canonical words and rewriting process.

Group Classification of Kolmogorov Nonlinear Equations

We consider Kolmogorov nonlinear equations with an arbitrary function. The group-theoretical method is one of the methods for solving partial differential problem. Using this method, we integrate equations with a non-trivial symmetry group. Therefore, group classification is high priority. Specifically, we conduct the group classification of Kolmogorov nonlinear equations. Using obtained continuous equivalence transformations, we present nonequivalent subclasses of these equations. We calculate maximum invariance algebras for all these subclasses.

Вариационный подход к задаче Дирихле з лапласианом по мере на гильбертовом пространстве

Исследована задача Дирихле для эллиптического уравнения в области гильбертова пространства. В частности, сформулирована задача Дирихле для рассматриваемого уравнения, а также слабой версии задачи, которая подразумевает поиск слабых решений. Сформулированы и доказаны теоремы существования и единственности слабой версии первой краевой задачи и, отдельно, исходной версии поставленной задачи в совместной области определения левой и правой частей исходного уравнения. Причем слабая версия задачи решается посредством вариационного подхода.

Application of the Theory of Fractional Calculus to Integral Operators with Generalized Hypergeometric Functions

The aim of paper is to study the properties of the integral operators with generalized hypergeometric functions in the kernels, in particular, to study the conditions of existence and their boundedness, the study of compositional relations with fractional integrals. In the study of common methods used by the theory of special functions, the theory of integral transforms and operators of fractional integro-differentiation. We introduce integral operators with (τ,β)-generalized hypergeometric functions in the kernels.