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A fundamental solution to the system of equations of the poroelasticity theory in the nondissipative case is obtained. It is shown that when the porosity disappears, the obtained fundamental solution goes over to the fundamental solution of the system of equations of the theory of elasticity. The inverse problem of determining a distributed source from the system of equations of the theory of poroelasticity in terms of the free surface vibration mode is also considered. Using the method of spherical means, a formula for solutions of the considered inverse dynamic problem of the theory for poroelasticity is obtained. [ABSTRACT FROM AUTHOR]

The learning process is considering as object of optimal control, for process controlling offered sequence of innovative approaches. Given a functional structure didactic system "teacher-reader" and on this bases created cyclic structure of calculation experience. The obtained results are graphically displayed. [ABSTRACT FROM AUTHOR]

The article discusses the dynamic non-stationary filtration of gas (liquid) in the system of two interacting layers, provided that edge water moves through the developed layer. The changes in time of the position of the gas-water contact, the pressure indicators in the interacting layers are determined. The results of the computational experiment are presented in the form of tables. [ABSTRACT FROM AUTHOR]

In this paper, it is established a criteria for the unique solvability of a boundary value problem for systems of integro-differential equations with an involutive transformation when the kernel is degenerate. A modified parametrization method is applied to the study of a boundary value problem for systems of integro-differential equations with involution, and conditions for the unique solvability of the problem under consideration are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider a boundary value problem for a fourth-order differential equation of mixed type with involution and with Hilfer operator of fractional integro-differentiation in a rectangular domain. The mixed type differential equation under consideration is a fourth-order differential equation with respect to the second variable. Regarding the first variable, this equation is a fractional differential equation in the positive part of the segment and is a second-order differential equation in the negative part of the segment. Using the spectral method of separation of variables, the solution of the problem is constructed in the form of a Fourier series. Theorems on the existence and uniqueness of the problem are proved. [ABSTRACT FROM AUTHOR]

The strain of a flexible current-carrying orthotropic cone with orthotropic electrical conductivity under external mag- netic fleld and external electric current is considered in this paper; and the effect of account for the conicity when determining the stress state of current-carrying orthotropic shells in a geometrically nonlinear statement is studied. It was revealed that the interaction of magnetic induction and shearing force causes the appearance of extreme values of shell stresses. [ABSTRACT FROM AUTHOR]

Derivation of a mathematical model of oscillation processes of spatially loaded rods with account for temperature is considered in the paper. On the basis of the problem posed, using the generalized Hamilton-Ostrogradsky principle, the variations in kinetic, potential energy and work of external forces were calculated, and a nonlinear mathematical model of spatially loaded rods was derived, taking into account temperature. Based on the mathematical model, the resolving equations of spatially loaded rods with generalized natural initial and boundary conditions were derived. [ABSTRACT FROM AUTHOR]

The profile of wall shear stress in non-Newtonian fluid which power law fluid through a cosine shape stenosis is analysed in this study. This study also reveals the effect of magnetic field as an external force on wall shear stress. Wall shear stress is an important flow characteristic in order to determine the behavior of blood. The governing equations employing the blood flow in the cylindrical coordinate system and then solved by finite difference scheme in staggered grid known as Marker and Cell (MAC) method. The influence of various parameters on wall shear stress profile are evaluated via graphical results. The results show that wall shear stress increases when magnetic field applied and higher at the stenotic region. [ABSTRACT FROM AUTHOR]

In the article, using the method of computational experiments on a computer, the influence of the method for calculating the values of the thermal conductivity coefficient at the nodes of the difference grid on the numerical solutions of a one-dimensional nonlinear problem of heat conduction according to explicit and implicit conservative difference schemes is investigated. The thermal conductivity is a power-law function of temperature. [ABSTRACT FROM AUTHOR]

An account for the nonlinearity effect in determining the stress-strain state of current-carrying plates and shells in a geometrically nonlinear statement is studied in this paper, using the example of a flexible current-carrying shell in a magnetic field. [ABSTRACT FROM AUTHOR]

In this paper, we consider two-dimensional generalization of an analog of parabolic equation. In the paper, by using the Fourier method, we study solvability of inverse problems with the Dirichlet condition. [ABSTRACT FROM AUTHOR]

This note discusses the definition, the history and the importance of the qualitative theory of ordinary differential equations (ODE). Although such discussions can be found in many textbooks and online lecture notes, some of the information provided are distinct and some are repeated. This article takes the union of the information and fills in the missing details by providing suitable examples from other references. The qualitative theory of ODEs are essential to complement the analytical and numerical methods. It is also required to prove qualitative properties of a dynamical system. Qualitative analysis of ODEs is also needed when exact solution, even if it can be found, is difficult to interpret or visualise. Furthermore, in some applications, only qualitative properties of the system are of interest. The qualitative methods also will provide information on the sensitivity of the system under study to perturbations of change of initial conditions and of various parameters. [ABSTRACT FROM AUTHOR]

This article is devoted to the variety of measuring antennas included in the measuring systems used for monitoring radio broadcasts. However, solutions are still being sought to create a universal antenna that allows measurements to be taken in a very wide frequency band with minimal errors. One of the possible solutions to this problem could be the creation of an antenna system consisting of several antennas operating in certain frequency ranges, but jointly covering the entire studied range of radio air. [ABSTRACT FROM AUTHOR]

In the present paper, we study the boundary value problem for a mixed parabolic-hyperbolic equation with fractional derivative and degeneration in time. Using the method of separation of variables, we prove theorems on the uniqueness and existence for the classical solution of this problem. [ABSTRACT FROM AUTHOR]

A stationary system of the two-velocity hydrodynamics with one pressure is obtained from a system of non-stationary equations of two-velocity hydrodynamics. This system is overdetermined. To solve the overdetermined problem, a new version of the method of orthogonal regularization is used. We study the regularity of the Stokes-type problem on the plane. [ABSTRACT FROM AUTHOR]

Reducing the dimension of feature space is considered to describe thematic documents. Documents are presented in the form of "object-property" tables, for the formation of which thematic dictionaries are used, usually with a volume of not more than 100 keywords. As a tool for research, we use the study of the topological properties of feature space from the values of class compactness measures based on relations between objects. [ABSTRACT FROM AUTHOR]

The paper considers the problem of assessing the quality of educational information systems in the context of the digital transformation of society. A method for determining the quality of information systems based on expert assessments is proposed. This approach differs in that it allows one to formalize qualitative assessments of the state of the system using the theory of fuzzy sets. The fuzzy quality assessment models included in the The fuzzy quality assessment models included in the methodology, as well as their corresponding algorithms, allow, on the basis of expert data, to assess the quality of educational information systems at the stage of their development, implementation and use. The implementation of the methodology makes it possible to increase the efficiency of the quality management process of educational information systems and the educational process as a whole. [ABSTRACT FROM AUTHOR]

In this paper that the estimate of the convergence rate of the remainder term in the main lemma of the theory of Galton-Watson critical branching random processes is of order O ( ln n n) , n → ∞ is proved. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problems of integral geometry on families of parabolas. We examined the application of the integral geometry problem to seismic problems. We shall get the inverse formula for the problem of integral geometry on families of parabolas. Numerical experiments demonstrate the performance of the algorithm. [ABSTRACT FROM AUTHOR]

The paper proposes a new mathematical model of economic cycles and crises, which generalizes the well-known model of Dubovsky S.V. The novelty of the proposed model lies in taking into account the effect of heredity (memory), as well as the introduction of harmonic functions responsible for the arrival of investments in fixed assets and new management technologies in innovation. The mathematical description is given using the Gerasimov-Caputo fractional derivatives, which are studied within the framework of the theory of fractional calculus. The mathematical model was investigated using the numerical method of Adams- Bashforth-Moulton (ABM), phase trajectories were constructed. It is shown that the proposed mathematical model can have both regular and chaotic regimes. [ABSTRACT FROM AUTHOR]

We have obtained systems of equations of the Burgers and the Hopf types from the system of non-stationary equations of the two-velocity hydrodynamics. Account must be taken of the fact that the energy dissipation occurs due to the viscosities of subsystems and the coefficient of inter-component friction. For a Hopf-type model, the analysis of the system of differential equations reduces in the form of traveling waves to solving a system of nonlinear ordinary differential equations. The effect of the kinetic coefficients on the propagation of nonlinear waves is clarified. [ABSTRACT FROM AUTHOR]

In the paper, we consider one boundary value problem of parabolic type with a divergent principal part when the boundary condition contains the time derivative of the unknown function with the dimension of the domain m ≥ 3. An approximate solution of the considered problem is constructed by the Galerkin method. The existence and uniqueness of a generalized solution of the problem is proved in the space H ˜ 1 , 1 (Q T). [ABSTRACT FROM AUTHOR]

In this paper, we study the conditions of global solvability and unsolvability in time of solutions to the nonlinear diffusion problem based on self-similar analysis. We constructed various self-similar solutions of the nonlinear diffusion problem in the slow diffusion case. We established critical exponents of the Fujita type and critical exponents for the global existence of the solution. Using the asymptotic formulas as the initial approximation for the iterative process, numerical calculations are performed. [ABSTRACT FROM AUTHOR]

The mathematical statement of a problem about potential movement of a liquid for dependent variables is given, features of numerical algorithm for the decision of a spatial eaday, the system of the difference equations for potential is offered, the order of calculation of sizes in a single-step method is described, the method of construction of a grid is considered. [ABSTRACT FROM AUTHOR]

The article proposes a technique for generating substitution tables for 256 elements for binary and 729 elements for ternary number systems, estimates the correlation coefficients, avalanche effect and nonlinearity (Hamming distance) of the obtained substitution tables, and also describes a computational experiment for finding the coefficients of the Algebraic Normal Form (ANF) the output functions of the table substitution for 729 values (S-box) and the estimation of its algebraic degree of nonlinearity. The resulting S-boxes can be further used as cryptographic primitives in encryption algorithms. [ABSTRACT FROM AUTHOR]

The article investigates the gamma functions of ternary logic, evaluates their features, makes the choice of the most preferable one for use as a cryptographic primitive in the encryption algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider the central limit theorem for associated random fields, invariance principles for two-parameter associated random fields, and an application of the invariance principle to the least squares estimates. [ABSTRACT FROM AUTHOR]

In the paper we consider a sequence of nearly critical branching processes with immigration. We will prove central limit theorem for fluctuation of branching processes with ϕ − mixing immigration. [ABSTRACT FROM AUTHOR]

In the paper the central limit theorem for Hilbert space-valued random fields satisfying some dependence condition is proved. [ABSTRACT FROM AUTHOR]

In the paper, we give the upper bounds for moments of branching processes in a varying environment starting with a random number of particles. [ABSTRACT FROM AUTHOR]

The pivotal aim of the present work is to obtain analytical and approximate solution for nonlinear time-fractional Swift-Hohenberg equations (FS-HEs) using the conformable residual series method (CRSM). The fractional derivative is proposed within a conformable concept. The proposed method is graceful amalgamations of the conformable residual error functions and generalized Talyor series in the sense of conformable operator. The truncated approximate solution is substituted in the nonlinear fractional model where the conformable derivative to the residual function is equal to zero. The convergence analysis is discussed to show the accuracy and efficiency of the CRSM to obtain approximate solutions for the FS-HEs. Numerical simulation with graphical representation is also given to validate and illustrate the proposed method. The obtained results indicate that the CRS technique is effective, simple, and systematic for analyzing the behavior of nonlinear partial differential equations of fractional order arisen in many areas of physics and science. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear parabolic variational inequality in noncylindrical domain is considered. Using extended Rothe's method recently achieved in [10] an approximate solution is constructed. Existence and uniqueness results are proved. Also, we present some further results and comments related to the main result. [ABSTRACT FROM AUTHOR]

In many environmental, industrial and biological processes, flows occur in a saturated porous fluid medium. The transport of substances between surface water and groundwater is a very serious problem. A mathematical model of this problem is studied here. The basis of the mathematical model is based on the interpenetrating model of two-phase media. The proposed equations make it possible to study the flow of a liquid in and outside the porous region in a uniform manner. In this case, the Navier-Stokes equation is obtained in the liquid region. In the porous region, the equations are close to the Brinkman model. In connection with the description of the flow from the standpoint of a single equation for the entire region, there is no need to set boundary conditions in the separation region (such as Beavers Joseph Saffman). Cross-border conditions arise if the Darcy model is used for the porous region. In this case, the order of the systems of equations in each area is different. On the basis of the proposed model, one-dimensional and two-dimensional problems are considered. For the numerical solution of two-dimensional problems, the SIMPLE algorithm with appropriate modifications. [ABSTRACT FROM AUTHOR]

The development of information technology is accompanied by a comprehensive transformation of the service sector, including microcredit. This sector of the Russian financial market shows steady growth annually. However, amid the high debt load on the Russian population, the availability of microcredit for most citizens, including online, has led to a high share of default disbursements of microloans in MFIs. Pressure from the regulator and a decrease in the income of Russians led the majority of MFIs to bankruptcy, while the remaining players in the microfinance market led to lower interest rates, and as a result, their margins decreased significantly. In this regard, MFIs have an urgent need to develop a scoring model that would be able to identify high-margin borrowers at the stage of applying for a microloan and "cut off" potentially defaulted borrowers. As part of this work, a methodology is proposed for clustering borrowers based on the fuzzy criterion "level of financial responsibility" and the proposed classification of borrowers. [ABSTRACT FROM AUTHOR]

Nowadays, a house has become a necessity for everyone. Most Malaysians put homeownership as one of their ultimate goals in life. Yet, homeownership is a rather complicated feat due to the many factors involved. Therefore, this study aims to determine the most significant factors to homeownership. The factors involved are financial assistance, housing performance, housing motivation, housing market and housing policy. Using a sample of 100 respondents, questionnaire surveys were distributed to obtain their feedbacks. Binary logistic regression analysis was employed in this study and the data was analyzed using IBM SPSS Statistical Software. The data analysis revealed that financial assistance and housing policy significantly influence homeownership. The study results can be beneficial for policymakers and developers in gaining a more in-depth insight of consumer needs and the factors that motivate them to own a house in Malaysia. [ABSTRACT FROM AUTHOR]

Consider a convex hull generated by a homogeneous Poisson point process in a cone on the plane. In this paper, we present a result that the area of bounded perimeters of the convex hull and the support boundary of the distribution in the cone is the sum of independent identically distributed random variables. In addition, we prove the central limit theorem for the number of vertices of the convex hull in a cone bounded by a disk of radius T as T → ∞. The known results of [1] coincide with the results obtained in the paper. [ABSTRACT FROM AUTHOR]

In the paper problems related to the fulfillment of infinite smallness condition and the validity of the Central Limit Theorems are considered for a sequence of series of independent random variables. In this case, instead of traditional condition of the Lindeberg type, the numerical characteristic introduced by I.A. Ibrahimov and L.V. Osipov is used. [ABSTRACT FROM AUTHOR]

Steganography develops tools and methods for hiding the fact of message transmission. The first traces of stegano-graphic methods are lost in ancient times. From detective works, various methods of secret writing between the lines of ordinary text are well known: from milk to complex chemical reagents with subsequent processing. Digital steganography is based on hid- ing or embedding additional information in digital objects while causing some distortion of these objects. In this case, text, images, audio, video, network packets, and so on can be used as objects or containers. To embed a secret message, steganographic methods rely on redundant container information or properties that the human perception system cannot distinguish. Recently, there has been a lot of progress in hiding information in a text container, since text documents are used in many organizations. Based on this, here the MS Word document is considered as a data carrier, which has various parameters, changing these parameters can achieve data integration. In the same article, we present steganography using invisible Unicode characters of the Space type, but with a different encoding. [ABSTRACT FROM AUTHOR]

In the paper, we introduce the notion of transversality for Volterra quadratic stochastic operators acting in a finite- dimensional simplex Sm−1 as the positivity condition of all principal minors of an even order of a skew-symmetric matrix A = (aki). We also study a number of properties of transversal operators that are necessary for further research. One can easily note that this definition is equivalent to the classical definition of the transversality of smooth mappings. Further, we also consider the properties of the fixed points charts of transversal operators. [ABSTRACT FROM AUTHOR]

This paper discusses properties of mathematic modeling processes described by the Cauchy problem to the double nonlinear parabolic equation with convective transfer and damping. [ABSTRACT FROM AUTHOR]

The present paper investigates the sections of cube with plane. There may be triangle, quadrant, pentagon and hexagon on the section. We investigate the algebraic method to define the sections. And we introduce new conceptions for the our method as spacial edges. All theorems are the main results of this paper. [ABSTRACT FROM AUTHOR]

The aim of this work is the search for the sufficient conditions of nonexistence of global solutions for the following nonlinear fractional differential system: { D 0 | t α 1 u + (− Δ) β 1 / 2 u = | u | p 1 | v | q 1 + f (t , x) , (t , x) ∈ ℝ + × ℝ N , D 0 | t α 2 v + (− Δ) β 2 / 2 v = | u | p 2 | v | q 2 + g (t , x) , (t , x) ∈ ℝ + × ℝ N , u (0 , x) = u 0 (x) ≥ 0 , ≢ 0 , x ∈ ℝ N , v (0 , x) = v 0 (x) ≥ 0 , ≢ 0 , x ∈ ℝ N , (1) where N ∈ ℕ, 1 ≤ βi ≤ 2, pi, qi (i = 1, 2) are real constants such that p1,q2 > 1, q1, p2 ≥ 0 and D 0 | t α i (i = 1, 2) denotes the standard Caputo fractional derivative of order αi ∈ (0,1). (− Δ) β i 2 (i = 1, 2) is the β i 2 -fractional power of the Laplacien (−Δ) defined by (− Δ) β i 2 u (x , t) = 𝔉 − 1 (| ζ | β i 𝔉 (u) (ζ)) (x , t) , where 𝔉 denotes the Fourier transform and 𝔉−1 its inverse. f and g are given functions satisfying some hypotheses which will be presented later. Our nonexistence result is obtained by using variational formulations and test functions methods. [ABSTRACT FROM AUTHOR]

In problems of population genetics, we need to study the evolution of biological systems with respect to time. In many cases, the evolution of a system is described by quadratic mappings of a simplex into itself. As is known, every quadratic stochastic operator of Volterra type given on a finite-dimensional simplex defines a certain tournament. This paper introduces the concept of a homogeneous tournament and studies the stability of fixed points of discrete dynamical systems of Volterra operators corresponding to homogeneous tournaments in the simplex S4. [ABSTRACT FROM AUTHOR]

The problems of solvability of a nonlocal inverse boundary value problem for a mixed type pseudohyperbolic-pseudoelliptic differential equation with a spectral parameter and integral conditions are considered. The equation is characterized by the fact that it has three unknown functions: with respect to the main unknown function the equation is a mixed type differential equation; and with respect to redefinition functions it is Fredholm integral equations of the second kind. The cases of regular and irregular values of the spectral parameter are studied. By the aid of the method of the Fourier series, a nonlinear system of two countable systems of Fredholm ordinary integral equations of the second kind is obtained. From this system we prove the existence and uniqueness of the Fourier coefficients of redefinition functions. In the proof of the unique solvability of this system of two countable systems of Fredholm ordinary integral equations of the second kind the method of compressive mappings is applied. In this proof we use also the Cauchy-Schwartz inequality and the Bessel inequality. For regular values of the spectral parameter, a criterion of unique solvability of the inverse boundary value problem is established. Solutions of the inverse boundary value problem are obtained in the form of Fourier series. The convergence of the obtained Fourier series and the possibility of term-by-term differentiation of the main Fourier series are shown. In the case of irregular values of spectral parameter, it is constructed an infinite number of solutions of the inverse problem in the view of Fourier series. The results are formulated as a theorem. [ABSTRACT FROM AUTHOR]

In this article, we consider a boundary value problem for a nonlinear partial integro-differential equation of mixed type with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with positive spectral parameter in a negative rectangular domain. The partial integro-differential equation of mixed type depends on another real spectral parameter in integral part of the mixed equation. With respect to first variable this equation is a fractional integro-differential equation in the positive part of the considering segment, and is a second-order integro-differential equation with spectral parameter in the negative part of this segment. Using the Fourier series method of separation variables and Fredholm method of degenerate kernels, the solutions of nonlinear boundary value problems are constructed in the form of a Fourier series. Theorems on the existence and uniqueness of solution of the problem are proved for regular values of the spectral parameters. [ABSTRACT FROM AUTHOR]

The solvability of one class of Neumann-type problems for non homogeneous polyharmonic equation in the unit ball is investigated. It is established that the set of necessary solvability conditions of the problem obtained earlier is also a set of sufficient conditions. The obtained conditions are in the form of orthogonality of homogeneous harmonic polynomials of certain degrees to linear combinations of boundary functions with coefficients from the Neumann integer triangle. [ABSTRACT FROM AUTHOR]

Chemical graph theory are usually use in topological indices for studied their bioactivitty and physical-chemical characteristic. These topological indices mostly use in the fields of chemistry, gene therapy and other areas of applied sciences. In our article, we study the line graph of one of the families of Polyphenylene dendrimer, namely D3[n]. We also compute their topological indices of the line graph of Polyphenylene dendrimer. In additional, to makes more interesting, we analyzed and showed the behavior of above computed topological indices towards Polyphenylene dendrimer. [ABSTRACT FROM AUTHOR]

We consider a family of the discrete Schrödinger operators Hλμ, in the d (d ≥ 3)-dimensional lattice with a wide class of dispersion relation and a potential constructed by a combination of the Kronecker delta function and the shift operator, depending on two parameters. The exstence of eigenvalues, threshold eigenvalues and threshold resonances and their dependence on the parameters of the operator and dimension of the lattice are explicitly derived. [ABSTRACT FROM AUTHOR]

It is shown any hyperfinite factor has an involutive *-antiautomorphism. It is proved that a real subfactor is irreducible if and only if its enveloping factor is irreducible. Using constructed examples in the complex case, as well as using an involutive *-antiautomorphism of a W*-algebra, examples of irreducible hyperfinite real subfactors with index larger than 4 are constructed. [ABSTRACT FROM AUTHOR]

This paper examines the estimation of the best weighted approximation and (co)convex functions with varying degrees of polynomial order. There are some situations in which the estimation of the best approximation is not well equipped to deal with the (co)convex and unconstrained polynomial (COCUNP) approximation and the reduction of the control of the rate errors of approximation. The weighted Ditzian-Totik moduli of smoothness (DTMS) and Lebesgue Stieltjes integral are employed to prove. The developed estimate is able to priority unconstrained approximation. [ABSTRACT FROM AUTHOR]