Abstract Since the second half of the twentieth century, wide studies of Sobolev-type equations are undertaken. These equations contain items that are derivatives with respect to time of the second order derivatives of the unknown function with respect to space variables. They can describe nonstationary processes in semiconductors, in plasm, phenomena in hydrodinamics and other ones. Notice that wide

Abstract In this paper we study a spectral problem with spectral parameter in the boundary condition. This problem arises when solving boundary value problems for mixed type equations using the spectral method. We analyze the system of root functions of this problem and proof two theorems about basis properties of this system. The biortogonal system is constructed and uniform convergence of spectral

Abstract We consider the coupled processes of thermohydrodynamics and heat conduction and construct a variational model of such coupled problems using four-dimensional space-time continuum where time is an equal coordinate along with spatial coordinates. In this consideration 3D subspace of generalized four-dimensional pseudo-continuum is associated with three-dimension deformed media. In the general

Abstract The present paper aims to develop geometrical approach for finite incompatible deformations arising in growing solids. The phenomena of incompatibility is modeled by specific affine connection on material manifold, referred to as material connection. It provides complete description of local incompatible deformations for simple materials. Meanwhile, the differential-geometric representation

Abstract The viscoelastic behavior of anisotropic composite is studied in this paper. Constitutive relations and equilibrium equations are derived for a Kirchhoff plate using general linear viscoelasticity constitutive relations for the anisotropic case. The derived model parameters—plate stiffnesses—are experimental functions. An approach to these parameters identification is given for certain cases

Abstract The paper studies the properties of the previously proposed method for assimilating observational data into a hydrodynamic model, which is an author’s version of the generalized Kalman filter. This method generalizes the well-known ensemble Kalman filter method. The equations of the generalized Kalman filter are extended to the case when the initial hydrodynamic model is biased relative to

Abstract We study the unique solvability of the mixed biharmonic problem with the Steklov-type and Farwig conditions on the boundary in the exterior of a compact set under the assumption that generalized solutions of this problem has a bounded Dirichlet integral with weight \(|x|^{a}\). Depending on the value of the parameter \(a\), we obtained uniqueness (non-uniqueness) theorems of this problem or

Abstract The problem of the mechanics of cracks in an orthotropic plate is considered. A general solution form is proposed as a generalized Papkovich–Neuber representation for the plane problem of the theory of elasticity of an orthotropic body. This representation allows us to write the general solution in displacements through two vector potentials satisfying the generalized harmonic equations. The

Abstract A method is proposed of evaluation of symbol and/or bit error probabilities for coherent receiving of multipositional signal constructions in communication channel with fadings, which are described with the help of classical and generalized models Multiple-Wave with Diffuse Power (MWDP) fading and of additive white Gaussian noise (AWGN). This method uses the hypergeometric functions of several

Abstract Linear ordinary differential equations of the second order of a general view are considered with In variable factors (input equations) reduced to the self-interfaced form. The common decision Each input equation, by means of the integral formula, it is represented through the common decision The accompanying equation of the same type, but with constant factors. It is considered that the general

Abstract The motion equations of the micropolar theory of elasticity in displacements and rotations represented by the matrix differential tensor-operator for any inhomogeneous anisotropic materials. As a particular case the micropolar isotropic homogeneous materials with a center of symmetry is considered. In this case, the matrix differential tensor-operator of cofactors to the matrix differential

Abstract In this paper we consider existence and uniqueness of the three-dimensional static boundary-value problems in the framework of so-called gradient-incomplete strain-gradient elasticity. We call the strain-gradient elasticity model gradient-incomplete such model where the considered strain energy density depends on displacements and only on some specific partial derivatives of displacements

Abstract In this paper we present analytical solutions for the cantilever beam bending problems obtained in the non-classical electroelasticity theory with strain and electric field gradient effects. We show that considered model allows to provide the refined analysis for the electric field distribution around the supproted end of the cantilever taking into account the extended number of boundary conditions

Abstract The application of artificial intelligence algorithms for data analysis, characteristics, and metrics of scientific information resources are considered. In this paper, we discuss how metrics are related to assessment of scientific publication components and whether metrics are related to fundamental knowledge. It was noted that the characteristics of professional scientific activity are evaluated

Abstract A generalized Eshelby problem of arbitrary order in the gradient elasticity for a multilayer inclusions of spherical shape with a polynomial strain field at infinity is considered. For this problem we propose a constructive method of solution in a closed finite form, using generalized Papkovich–Neuber representation and the system of canonical potentials based on harmonic polynomials. We use

Abstract Let \(\mathcal{M}\) be a quasivariety generated by a relatively free group in a class of nilpotent groups of step \(\leq 2\) with commutator subgroups of prime exponent \(p,\) \(p\neq 2.\) A class \(L(\mathcal{M})\) of all groups \(G\) the normal closure of any element in which belongs to \(\mathcal{M}\) is called the Levi class generated by \(\mathcal{M}.\) It is proved that \(L(\mathcal{M})\)

Abstract The relevance of the topic is determined by the search for the transcendental frequency equations that are reduced to algebraic and the influence of both boundary conditions at the edges of a rectangular plate and geometric and mechanical characters on the inherent oscillatory frequencies of rectangular flat elements is considered and the previous results for a rectangular plate whose material

Abstract In the one-dimensional domain it is studied the unique solvability of a class of integro-differential equations with logarithmic singularity in the kernels. The solution of the considering integro-differential equations with logarithmic singularity in the kernels on dependent of roots of corresponding characteristic equations is obtained in an explicit form. The first part of paper deals with

Abstract The class \(\mathfrak{K}\) of all connected unars with stagnant element being their single knot element is considered. Structure of the endomorphism semigroups of unars from \(\mathfrak{K}\) is described.

Abstract The work is devoted to the fundamental problem of studying the solvability of the initial-boundary value problem for a pseudo-parabolic equation (also called Sobolev type equations) with a fairly smooth boundary. In this paper, the initial-boundary value problem for a quasilinear equation of a pseudoparabolic type with a nonlinear Neumann–Dirichlet boundary condition is studied. From a physical

Abstract In the paper we provide some polynomial identities for finite-dimensional algebras. A list of well known single polynomial identities is exposed and the classification of all two-dimensional algebras with respect to these identities is given.

Abstract The article discusses the problems about the main scenarios of dynamical systems’ local bifurcations described by non-autonomous differential equations with periodic right-hand side. New formulae for calculating Lyapunov quantities are proposed. The proposed formulae are obtained on the basis of the general operator method for studying local bifurcations and do not require a transition to

Abstract This paper is devoted to the problem (Glaz, Vinsonhaler, Wickless): When a \(p\)-local torsion-free group is determined by the collection of its splitting rings? For \(p\)-local torsion-free groups with quadratic and cubic minimal splitting fields necessary and sufficient condition has been found according to which \(p\)-local group \(G\) is determined by the collection of its splitting rings

Abstract Loday and Ronco introduced the notion of a trioid. We construct a trioid which is isomorphic to the free \(n\)-nilpotent trioid, and characterize the least dimonoid congruences and the least semigroup congruence on it. We also study separately singly generated free \(n\)-nilpotent trioids.

Abstract It is studied a regularization of systems of linear Volterra integral equations of the third kind with continuous kernel degenerated at points of the given segment on the diagonal. The determinant of the matrix outside the integral disappears at the starting point or at the end of the segment. Regularizing Lavrent’ev type operator is constructed that preserves the property of Volterra equation

Abstract Let \(\mathcal{K}\) be a class of groups closed under taking subgroups, direct products of a finite number of factors, and quotient groups. Let also \(G\) be a generalized direct product of two groups with amalgamated subgroups. We obtain necessary and sufficient conditions for \(G\) to be residually a \(\mathcal{K}\)-group. These results generalize and strengthen the known conditions for

Abstract A modification of the parameterization method is proposed to solve a linear two-point boundary value problem for a Fredholm integro-differential equation. The domain of the problem is partitioned and additional parameters are set as the values of the solution at interior points of the partition subintervals. Definition of a regular pair consisting of a partition and chosen interior points

Abstract It is proved that for two different classes of torsion-free abelian groups the direct decomposability properties coincide with respect to the quotients of indecomposable summands over their regulators. The method used is embedding almost rigid groups as fully invariant subgroups in some Butler groups of infinite rank with determination of their decomposition theory.

Abstract We consider the second boundary-value problem for a third-order equation with multiple characteristics containing the second derivative with respect to time in a rectangular domain. Uniqueness of the solution is proved by the energy integral method. The Green’s function is constructed for the second boundary-value problem, through which an explicit solution of the problem is written.

Abstract The paper studies the problem of approximate construction of eigenvalues and multipliers of linear (autonomous and periodic) Hamiltonian systems depending on a small parameter in the main critical cases. New formulas for the asymptotic (in powers of a small parameter) representation of the eigenvalues and multipliers of the task are proposed. The obtained formulas allow us to effectively study

Abstract In this paper, the unique solvability of the Cauchy problem for a generalized hyperbolic Gellersted equation with two lines of degeneracy of different order is studied. A modified initial problem is formulated. By using the Riemann method the solution of this problem is constructed in an explicit form inside characteristic triangle. The constructed Riemann function is expressed by special

Abstract In this work, we investigate Frankl-type problem with integral conjugating condition for a mixed type equation consisting of sub-diffusion and wave equations. A uniqueness and the existence of formulated problem have been proved using energy integrals and the method of integral equations, imposing certain conditions on given data.

Abstract In this paper we study a new problem for a parabolic-hyperbolic equation with fractional order Caputo operator in rectangular domain. There are many works devoted to study problems for the second order mixed parabolic-hyperbolic and elliptic-hyperbolic type equations in rectangular domains with two gluing conditions with respect to second argument and with boundary value conditions on all

Abstract This paper aims to prove the Riesz basisness of root functions of the non-selfadjoint a discontinuous Sturm–Liouville operator with periodic boundary condition which are not strong regular and with conjugate conditions. It is assumed that the potentials of differential operator are complex valued and continuously differentiable functions and both conjugate conditions have different finite

Abstract It is well-known that every c.e. Turing degree is the degree of categoricity of a rigid structure. In this work we study the possibility of extension of this result to properly 2-c.e. degrees. We found a condition such that if a \(\Delta^{0}_{2}\)-degree is a degree of categoricity of a rigid structure and satisfies this condition then it must be c.e. Also we show that degrees of non-categoricity

Abstract Due to complexity of the systems and processes it addresses, the development of computational quantum physics is influenced by the progress in computing technology. Here we overview the evolution, from the late 1980s to the current year 2020, of the algorithms used to simulate dynamics of quantum systems. We put the emphasis on implementation aspects and computational resource scaling with

Abstract The results of numerical modeling of white dwarf mergers on massive parallel supercomputers using a AVX-512 technique are presented. A hydrodynamic model of white dwarfs closed by a star equation of state and supplemented by a Poisson equation for the gravitational potential is constructed. This paper presents a modification based on a local linear reconstruction of the solution of the Rusanov

Abstract Polynomial completeness of an operation guarantees that deciding solvability of equations over this operation is an NP-complete problem. Thus this property is beneficial from the viewpoint of cryptographic applications. We propose an algorithm for verification of polynomial completeness of quasigroups and analyse efficiency of its serial and parallel implementations.

Abstract One of the approaches to the study of the information structure of algorithms is the analysis of information graphs. These are complex objects, the understanding of the structure of which can significantly facilitate their visualization. However, it is difficult to visualize large graphs, while maintaining clarity of the information structure of the algorithm is generally very difficult. Therefore

Abstract High-performance computing takes a very important place in modern scientific research process. And since all scientists want to solve their problems faster, it is very important to speed up these computations. For these purposes, new algorithms are being developed, new HPC systems appear, etc. However, quite little attention is paid to the efficiency of high-performance computations, which

Abstract This article discusses the capabilities of layered ‘‘2.5D’’ schemes in ultrasound tomography, in which the emitters and detectors are located in the same plane. The primary application of this method is medical imaging technology for early-stage breast cancer diagnosis. The inverse problem of tomographic image reconstruction is posed as a coefficient inverse problem for the wave equation,

Abstract Modern vector architectures are tend to be equipped with high-bandwidth memory, what makes them an interesting candidate for solving large-scale graph processing problems. However, highly irregular structure of real-world graphs makes it extremely challenging to map fundamental graph-processing problems on vector systems. This paper describes the world-first attempt, aimed to create efficient

Abstract Attenuation is widespread in the Earth’s interior. However, there are several models where viscoelastic formations comprise as few as 10 to 20 % of the volume. They include near-surface and sea-bottom formation due to the low consolidation of the sediments, oil and gas reservoirs due to fluid saturation, etc. At the same time, the major part of the medium is ideally elastic. In this situation

Abstract In this paper, a scalable iterative projection-type algorithm for solving non-stationary systems of linear inequalities is considered. A non-stationary system is understood as a large-scale system of inequalities in which coefficients and constant terms can change during the calculation process. The proposed parallel algorithm uses the concept of pseudo-projection which generalizes the notion

Abstract We present a numerical investigation of the fracture connectivity effect on attenuation of seismic waves propagating in fractured porous fluid-saturated media. We design an algorithm for statistical modeling to generate fracture systems with prescribed percolation length. Generated statistical realizations of the fractured systems are then analyzed to evaluate the fracture-cluster length-scale

Abstract The MÖBIUS agent-based models (ABM) design system is presented, which allows creating efficiently scalable models with the number of agent populations up to 1 billion. The system supports dynamic changes in the number and spatial distribution of agents by simulating the processes of disappearance of agents and the emergence of new ones. The system allows one to create ABM, including populations

Abstract The present work is devoted to accelerating the NOISEtte code and lowering its memory consumption. This code for scale-resolving supercomputer simulations of compressible turbulent flows is based on higher-accuracy methods for unstructured mixed-element meshes and hierarchical MPI \(+\) OpenMP parallelization for cluster systems with manycore processors. We demonstrate modifications of the

Abstract The paper presents the results of applying the BERT representation model in the named entity recognition task (NER) for the cybersecurity domain in Russian. We compare several approaches to domain-specific NER combining BERT fine-tuning on a domain-specific text collection, general labeled data, domain-specific data augmentation, and a domain-specific annotated dataset. We showed that using

Abstract Ab initio quantum molecular dynamics simulation is used to transform a silicon dioxide crystal into silica amorphous states. Two type of amorphous states are obtained from the melts stabilized at temperatures well above the crystal melting point. The first type of amorphous states are obtained from the melts stabilized at comparably low temperatures of \(3000\) and \(4000\) K. These states

Abstract During last twenty years, the Differential evolution algorithm (DE) has proved to be one of the powerful methods to solve minimization problems for multidimensional functions. Being a member of the family of evolutionary optimization algorithms, its main principle is based upon the concepts of natural selection and mutation. In this study, we test the potential of DE to find a proper set of

Abstract Many serious medical conditions are caused by the accumulation of amyloid aggregates in tissues and organs. One of the most well-known amyloidogenic proteins is the prion protein (PrP), which may undergo conformational change between the normal cellular isoform PrPC and the aggregation-prone isoform PrPSc. Elucidation of this conformational transition is necessary for understanding the onset

Abstract This paper is concerned with investigating the capabilities of wave tomography methods via supercomputer numerical simulations on a model problem of imaging the wave velocity structure inside flat solid objects. The problem of reconstructing the velocity structure is formulated as a nonlinear coefficient inverse problem. Iterative algorithms for solving this inverse problem are based on computing

Abstract In this paper, we describe a numerical algorithm for the self-consistent simulations of surface water and sediment dynamics. The method is based on the original Lagrangian-Eulerian CSPH-TVD approach for solving the Saint-Venant and Exner equations, taking into account the physical factors essential for the understanding of the shallow water and surface soil layer motions, including complex

Abstract The present work is devoted to the development and use of supercomputer technology for modeling gas-dynamic processes using molecular dynamics methods. The relevance of the work is associated with the development of nanotechnology for the manufacture of promising nanomaterials and nanocoatings by the method of supersonic cold gasdynamic spraying. The paper proposes to consider gasdynamic processes

Abstract The described project is aimed at a complete solution to the problem of joint analysis of the properties of algorithms and features with the architecture of computing systems. This problem arose in the mid-70s of the last century, and over time, its importance in the practice of using computer systems is constantly growing. The main reason is a significant complication of the architecture

Abstract The article is devoted to the development of a method for solving the inverse problem. We considered the problem of propagation of electromagnetic wave inside the body located in free space. The method of reconstruction of the parameters inhomogeneity from a known field is applied. The numerical results of the inhomogeneity bodies is presented.

Abstract In this paper the computational algorithm for interpreting the results of hydrodynamic and thermohydrodynamic studies in non-linear filtration is proposed. The algorithm allows to determine the conductivity of the reservoir, the limiting pressure gradient, reservoir pressure and the regularization parameter. Temperature and pressure changes data, measured on a vertical well, are taken as the

Abstract The present paper considers the determination of the two-phase region boundary within a simplified version of the wide-range equations of state of water and steam by Nigmatulin–Bolotnova (EOS NB) in the case the determination is based on the temperature-dependence of the saturated vapor pressure. This version of EOS NB can be used when the temperature and pressure ranges under investigation

Abstract This article is devoted to the study of the oblique fall of an acoustic wave from a pure gas to the boundary of a multifraction gas suspension with polydisperse inclusions of different sizes and materials. A mathematical model that allows to determine the reflection coefficient when an acoustic wave falls obliquely on the interface between two media is presented. Dependencies of the reflection

Abstract The mathematical model that determines reflection and transmission of an acoustic wave at different angles of incidence through a medium containing multifractional bubbly liquid is presented. The reflection and transmission coefficients of the wave are calculated for a water–bubble liquid–water mixture. The effect of the volume content of the dispersed phase on the studied coefficients is