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Telecommunications have penetrated deeply into all spheres of human activity. Due to the use of digital technologies, it has become possible to transmit and receive information of various kinds in one stream (not separately). Three geostationary satellites are sufficient to provide data transmission from anywhere in the world to another point using artificial Earth satellites. Data transmission systems using the satellite should contain at least two Earth Stations and a repeater of the communication satellite. There are no means of combating any types of artificial interference in the Earth Stations equipment. The jammer, an illegitimate user, can emit a signal from any point in space within a telecommunications satellite system. The paper provides an analysis of existing methods for determining the coordinates of a radio signal source, describes a method for determining the coordinates of an radio signal source (illegitimate user) in satellite telecommunications systems using a geostationary spacecraft. The development was based on a three-position virtual antenna array, the positions of which determined the base of an irregular tetrahedron, and the radio signal source itself was its vertex. In the course of the solution, canonical equations of straight lines in space were compiled, at the intersection point of which the source of the radio signal is located. The coordinates of the radio signal source were the roots of the system, when finding the unit vectors lying on these lines.

Within the framework of the Euler equations, the possibility of achieving extreme pressure values at the inner point of a stationary flow of a nonviscous gas is considered. The flow can be non-barotropic. The well-known (G.B.Sizykh, 2018) subsonic principle of maximum pressure (SPMP) cannot be applied in transonic and supersonic flow regions. Under the conditions of the classical principle of maximum pressure by C.Truesdell (1953), there is no restriction on the values of local Mach numbers, but it has a number of features that do not allow it to be used to verify numerical calculations in the same way as it can be done when using SPMP in subsonic regions. A previously unknown principle of maximum pressure is discovered: a function of derivative flow parameters is found, which must have a certain sign (different for minimum and for maximum pressure) at the point where the pressure reaches a strict or nonstrict local extremum. This principle of maximum pressure is called general (GPMP) because its conditions do not include barotropicity, restrictions on the values of local Mach numbers, and the assumption that the gas obeys the MendeleevClapeyron equation. One of the consequences of GPMP is the conclusion that the requirement of barotropicity can be excluded from the conditions of Truesdell's principle of maximum pressure. It is proposed to use GPMP to verify numerical calculations of the ideal gas flow behind a detached shock wave formed in a supersonic flow around bodies and to verify numerical calculations of a viscous gas flow around bodies in regions remote from sources of vorticity, where the effect of viscosity can be neglected.

The nanosecond speed of information writing and reading is recognized as one of the main advantages of next-generation non-volatile ferroelectric memory based on hafnium oxide thin films. However, the kinetics of polarization switching in this material have a complex nature, and despite the high speed of internal switching, the real speed can deteriorate significantly due to various external reasons. In this work, we reveal that the domain structure and the dielectric layer formed at the electrode interface contribute significantly to the polarization switching speed of 10 nm thick Hf0.5Zr0.5O2 (HZO) film. The mechanism of speed degradation is related to the generation of charged defects in the film which accompany the formation of the interfacial dielectric layer during oxidization of the electrode. Such defects are pinning centers that prevent domain propagation upon polarization switching. To clarify this issue, we fabricate two types of similar W/HZO/TiN capacitor structures, differing only in the thickness of the electrode interlayer, and compare their ferroelectric (including local ferroelectric), dielectric, structural (including microstructural), chemical, and morphological properties, which are comprehensively investigated using several advanced techniques, in particular, hard X-ray photoelectron spectroscopy, high-resolution transmission electron microscopy, energy dispersive X-ray spectroscopy, X-ray diffraction, and electron beam induced current technique.

In the framework of the NavierStokes equations, the flow of a viscous incompressible fluid between immovable parallel permeable walls is considered, on which only the longitudinal velocity component is equal to zero. Solutions are sought in which the velocity component transverse to the plane of the plates is constant. Both stationary and non-stationary solutions are obtained, among which there is a non-trivial solution with a constant pressure and a longitudinal velocity exponentially decaying with time. These solutions show the influence on the profile of the horizontal velocity component of the removal of the boundary layer into the depth of the flow from one plate with simultaneous suction of the boundary layer on the other plate. It is established that for stationary flows the removal of the boundary layer into the depth of the flow from one plate and, with simultaneous suction of the boundary layer on the other plate, leads to an increase in the drag compared to the classical Poiseuille flow. In the case of impermeable walls, an exact non-stationary solution is obtained, the velocity profile of which at fixed times differs from the profile in the classical Poiseuille flow and, in the limit (as time tends to infinity), corresponds to rest.

Purpose of the study is to obtain formulas for such a speed of imaginary particles that the circulation of the speed of a (real) fluid along any circuit consisting of these imaginary particles changes (in the process of motion of imaginary particles) according to a given time law. (Until now, only those speeds of imaginary particles were known, at which the mentioned circulation during the motion remained unchanged). Method. Without implementation of asymptotic, numerical and other approximate methods, a rigorous analysis of the dynamic equation of motion (flow) of any continuous fluid medium, from an ideal liquid to a viscous gas, is carried out. Plane-parallel and nonswirling axisymmetric flows are considered. The concept of motion of imaginary particles is used, based on the K. Zoravsky criterion (which is also called A. A. Fridman’s theorem). Results. Formulas for the speed of imaginary particles are proposed. These formulas include the parameters of the (real) flow, their spatial derivatives and the function of time, which determines the law of the change in time of the (real fluid) velocity circulation along the contours moving together with the imaginary particles. In addition, it turned out that for a given function of time (and, as a consequence, for a given law of change in circulation with respect to time), the speed of imaginary particles is determined ambiguously. As a result, a method is proposed to change the speed and direction of motion of imaginary particles in a certain range (while maintaining the selected law of changes in circulation in time). For a viscous incompressible fluid, formulas are proposed that do not include pressure and its derivatives. Conclusion. A new Lagrangian point of view on the vorticity evolution in two-dimensional flows of fluids of all types is proposed. Formulas are obtained for the velocity of such movement of contours, at which the real fluid velocity circulation along any contour changes according to a given time law. This theoretical result can be used in computational fluid dynamics to limit the number of domains when using a gridless method for calculating flows of a viscous incompressible fluid (the method of viscous vortex domains).

Stationary flows of an ideal gas behind the detached bow shock are investigated in the general 3D case. The well-known integral invariant (V.N.Golubkin, G.B.Sizykh, 2019), generalizing the axisymmetric invariant of (L.Crocco, 1937) to asymmetric flows, is a curvilinear integral over a closed vortex line (such lines lie on isentropic surfaces), in which the integrand is the pressure divided by the vorticity. This integral takes on the same value on all (closed) vortex lines lying on one isentropic surface. It was obtained after the discovery of the fact that the vortex lines are closed in the flow behind the shock in the general 3D case. Recently, another family of closed lines behind the shock was found, lying on isentropic surfaces (G.B.Sizykh, 2020). It is given by vector linesa the vector product of the gas velocity and the gradient of the entropy function. In the general 3D case, these lines and vortex lines do not coincide. In the presented study, an attempt is made to find the integral invariant associated with closed vector lines a. Without using asymptotic, numerical and other approximate methods, the Euler equations are analyzed for the classical model of the flow of an ideal perfect gas with constant heat capacities. The concept of imaginary particles carrying the streamlines of a real gas flow, based on the HelmholtzZoravsky criterion, is used. A new integral invariant of isentropic surfaces is obtained. It is shown that the curvilinear integral over a closed vector linea, in which the integrand is the pressure divided by the projection of the vorticity on the directiona, has the same values for all lines a lying on one isentropic surface. This invariant, like another previously known integral invariant (V.N.Golubkin, G.B.Sizykh, 2019), in the particular case of non-swirling axisymmetric flows, coincides with the non-integral invariant of L.Crocco and generalizes it to the general spatial case.

A Molecular Features Set (MFS), is a result of a vast diversity of bioinformatics pipelines. The lack of a “gold standard” for most experimental data modalities makes it difficult to provide valid estimation for a particular MFS's quality. Yet, this goal can partially be achieved by analyzing inner-sample Distance Matrices (DM) and their power to distinguish between phenotypes. The quality of a DM can be assessed by summarizing its power to quantify the differences of inner-phenotype and outer-phenotype distances. This estimation of the DM quality can be construed as a measure of the MFS's quality. Here we propose Hobotnica, an approach to estimate MFSs quality by their ability to stratify data, and assign them significance scores, that allow for collating various signatures and comparing their quality for contrasting groups.

A Molecular Features Set (MFS), is a result of a vast diversity of bioinformatics pipelines. The lack of a “gold standard” for most experimental data modalities makes it difficult to provide valid estimation for a particular MFS's quality. Yet, this goal can partially be achieved by analyzing inner-sample Distance Matrices (DM) and their power to distinguish between phenotypes. The quality of a DM can be assessed by summarizing its power to quantify the differences of inner-phenotype and outer-phenotype distances. This estimation of the DM quality can be construed as a measure of the MFS's quality. Here we propose Hobotnica, an approach to estimate MFSs quality by their ability to stratify data, and assign them significance scores, that allow for collating various signatures and comparing their quality for contrasting groups.

In the framework of the Navier–Stokes equations, unsteady axisymmetric flows of a homogeneous viscous incompressible fluid, in which the axial and circumferential velocities depend only on radius and time are considered, and the radial velocity is zero. It is shown that the velocity of such flows is the sum of the velocities of two flows of a viscous incompressible fluid: axial flow (radial and circumferential velocities are zero) and circumferential flow (radial and axial velocities are zero). Axial and circumferential movements occur independently, without exerting any mutual influence. This allows us to split the boundary value problems for the type of flows under consideration containing three unknown functions (pressure, circumferential and axial velocities) into two problems, each of which contains two unknown functions (pressure and one of the velocity components). In this case, the sum of pressures of the axial and circumferential flow will be the pressure of the initial flow. The discovered possibility of splitting allows using known solutions to replenish the “reserves” of axial and circumferential exact solutions. These solutions, in its turn, can be summed in various combinations and, as a result, give the velocities and pressures of new exact solutions of the Navier–Stokes equations.

In the paper, Beltrami flows or helical flows are flows in which the vorticity and velocity vectors are collinear, and the proportionality coefficient between these vectors is nonzero and is the same at all points of the flow. A method is proposed that allows using known helical solutions to obtain new helical solutions of the Euler equations for an incompressible fluid. Some of these new solutions cannot be obtained by the known methods of replicating solutions by shifting and rotating the coordinate system, symmetry, scaling, cyclic permutation of the velocity and coordinate components, vector summation. The new replication method is applied to such parametric families of exact solutions in which the proportionality coefficient between velocity and vorticity remains unchanged for different values of the parameter. The essence of the method is that for such families the derivative of the velocity with respect to the parameter is also the helical velocity. The sequential differentiation of the speed of a new solution with respect to a parameter gives an endless chain of new exact solutions.

Purpose of the study is to obtain a criterion for existence of stationary solution of the complete system of equations describing the flow of ideal perfect gas for a given non-solenoidal helical velocity field. Conditions of such a criterion should contain only the components of this velocity and their derivatives. The fulfillment of conditions must be necessary and sufficient for the existence of such fields of density and pressure, which, together with the considered velocity, satisfy the complete system of equations. Methods. Without using asymptotic, numerical, and other approximate methods, the analysis of the complete system of equations of the classical model of the flow of ideal perfect gas with constant heat capacities is carried out. Results. A criterion for the existence of a solution to the complete system of equations for stationary motion of ideal perfect gas for a non-solenoidal helical velocity field is proposed, consisting of a system of equations and inequalities containing only velocity components and their derivatives. An example of a non-solenoidal helical velocity field is presented, for which, according to the proposed criterion, there is no solution to the complete system of equations. The study demonstrates that the justification of the correspondence of the velocity field to any model of fluid motion is a meaningful problem, without which this field cannot be associated with the fluid flow velocity. Conclusion. The problem of the existence of an exact solution of the complete system of equations for a given velocity field has been proposed and the solution one has been obtained for the simplest model of stationary fluid motion and a nonsolenoidal helical velocity field. It is shown that not every non-solenoidal helical velocity can be considered the velocity of a compressible fluid. The relevance of the problem posed is confirmed by an example of research (Morgulis A. et al. Comm. On Pure and Applied Math, 1995), in which the non-solenoidal helical velocity presented by the authors is unlawfully attributed to the flow of compressible fluid since the proof of the existence of corresponding solution of the complete system of equations of any model of compressible liquid is not given.

Changes in the spiritual life of modern society actualise the controversy of new writers with the fundamental ideas of Russian classical literature. The purpose of this article is to analyse the influence of certain aspects of Dostoevsky’s worldview and creative work on the poetics and issues considered in Yury Vasilievich Buida’s stories Lethe, Kazan Railway Station, and The Law of the Jungle. The authors aim to identify the similarities and differences in the depiction of the world and man, typological convergences at the level of motifs and plots, key symbols characteristic of Dostoevsky, and their new interpretation. The authors establish that the philosophical problem of the relationship between man and God, fundamental for Dostoevsky’s worldview and the question of the significance of Christian and ethical categories in society are important for the author’s concept of Buida’s works. The modern writer portrays lost people guided by primitive instincts, abiding in a peculiar space of material and spiritual poverty, but in their own way looking for God. However, to a larger extent than Dostoevsky’s characters, Buida’s characters are characterised by the acceptance of life due to their subconscious striving for light and good. The revealed images and motifs, typologically similar to the corresponding elements of Dostoevsky’s poetics, are aimed at complicating the cultural and historical context of the Jungle collection in order to clarify the social issues of boundary time and the basic concept of the book by Buida. The images of the garden, stairs, axe, stone, which have a pronounced allusive character, turn out to be connected with the existential model of the universe proposed by the modern prose writer. The motif complex of Lethe, Kazan Railway Station, The Law of the Jungle, which reveals the author’s references to classical texts, contributes to the expression of the philosophical idea of the loss of spirituality and sometimes the unconscious existence of modern man.

A Molecular Features Set (MFS), is a result of a vast diversity of bioinformatics pipelines. The lack of a “gold standard” for most experimental data modalities makes it difficult to provide valid estimation for a particular MFS's quality. Yet, this goal can partially be achieved by analyzing inner-sample Distance Matrices (DM) and their power to distinguish between phenotypes. The quality of a DM can be assessed by summarizing its power to quantify the differences of inner-phenotype and outer-phenotype distances. This estimation of the DM quality can be construed as a measure of the MFS's quality. Here we propose Hobotnica, an approach to estimate MFSs quality by their ability to stratify data, and assign them significance scores, that allow for collating various signatures and comparing their quality for contrasting groups.