Vol 30, No 2 (2024)

In a recent article by V.V. Kapustin a de Branges space, whose element is an expression containing the Riemann xi function, was constructed; the canonical system with a diagonal Hamiltonian and the generalized Fourier transform corresponding to the space were found. In this article we present a similar de Branges space with some preferred modifications and we provide formulas related to it; we also write down the Hamiltonian and the generalized Fourier transform.

The article is devoted to the peculiarities of stability change of slow invariant manifolds of singularly perturbed systems of ordinary differential equations. It should be noted that the change of stability of invariant manifolds can proceed according to different scenarios. In addition to two well-known scenarios of this phenomenon, one more scenario is considered in this paper. To demonstrate the peculiarities of the stability change of slow invariant manifolds under this scenario, a number of examples are proposed. The existence theorem of an exact invariant manifold with stability change for some class of singularly perturbed systems of ordinary differential equations is obtained

Studies have been carried out of the influence of temperature stresses on the frequencies of natural oscillations rectangular plates under different fastening conditions using analytical methods and computer modeling using the finite element method. It has been established that with increasing temperature the frequency of natural oscillations decreases. The presence of temperature stresses has significant influence on the change in oscillation frequency. The lowest ones undergo the greatest change frequencies. In addition, the shape of the vibrations changes with increasing temperature

Currently, there is a problem of depletion of easily produce oil. In order to maintain hydrocarbon production rates, hard-to-recover reserves are being brought into development, a significant part of which are extra-heavy oil, the production of which takes a relatively small share in the global oilfield due to the complexity of the process. The methods existing at the moment do not allow extracting heavy and extra-heavy oil from reservoirs with a sufficient degree of efficiency. The use of such a method as microwave impact has not been widely used in the oilfield, because modeling is necessary to determine the optimal parameters of the impact. It is difficult with the number of problems associated with the complexity of the method. This article deals with the modeling of the process of microwave impact to improve the efficiency of the oil production process. The article is devoted to modeling the process of ultra-high-frequency wave impact on the oil reservoir, considering the physical and chemical parameters of fluids in the reservoir, such as thermal conductivity, dielectric permeability of oil and water (considering its salinity) in the reservoir. In the framework of the method using microwave impact for the first time determined the amount of shielding by the pipe material of this impact and determined the optimal parameters of the radiation source and the parameters of well pipe structures for effective impact on oil reservoirs. The aim of the work is to determine the optimal parameters of the source of microwaves to achieve cost-effective values of oil recovery factor. In this work the physical and mathematical model of microwave impact on the reservoir, based on the laws of electrodynamics and the density of volumetric heat generation in this equation is applied. The dependence of the magnitude of screening of microwave radiation by the production well pipe on its thickness and the dependence of the magnitude of screening of radiation by the production well pipe on the thickness of the perforation slot in this pipe and the dependence of the radius of penetration of electromagnetic waves into the formation on the absorption factor of electromagnetic radiation in the formation are obtained. The paper establishes the existence of a minimum radius of penetration of microwave radiation into the formation to achieve cost-effective values of oil recovery factor over 30%, which is 57 m, and also determined the absorption factor of microwave radiation in the formation, which allows to achieve the specified value of the radius of penetration of microwave radiation into the formation.