Abstract For problems related to radiative heat conduction, an algorithm is proposed that is well adapted to the architecture of systems with extramassive parallelism. According to the underlying method, a term with a small parameter multiplying the second time derivative is included in the model describing the process. Examples of numerical results obtained using this model on detailed spatial meshes

Abstract For an autonomous model of the motion of a nonlinear viscous fluid, we study the limiting behavior of its weak solutions as time tends to infinity. Namely, the existence of weak solutions on the positive half-axis is established, the trajectory space corresponding to the solutions of this model is determined, and the existence of a minimum trajectory attractor and, then, a global attractor

Abstract Inverse problems of fracture exploration seismology are solved using machine learning methods. A single fracture of fixed size and subvertical orientation is considered in the two-dimensional case. The spatial position and the inclination angle of the fracture are determined using a neural network. The training set consists of solutions of direct problems produced by the grid-characteristic

Abstract A one-parameter family of global solutions of a two-dimensional hyperbolic differential-difference equation with an operator acting with respect to a space variable is constructed. A theorem is proved stating that the resulting solutions are classical for all parameter values if the symbol of the difference operator of the equation has a positive real part. Classes of equations for which this

Abstract A theorem about the behavior of Cauchy-type integrals at the endpoints of the integration contour and at discontinuity points of the density is stated, and its application to boundary value problems for 2n-order parabolic equations with a changing direction of time are described. The theory of singular equations, along with the smoothness of the initial data, makes it possible to specify necessary

Abstract The existence of a weak solution for the Navier–Stokes-alpha model with temperature-dependent viscosity is proved using the topological approximation method for the study of hydrodynamic problems.

Abstract For the numerical solution of the Cauchy problem with multiple poles, we propose a reciprocal function method. In the case of first-order poles, it makes it possible to continue the solution through the poles and to determine the solution and the pole positions with good accuracy. The method allows one to employ conventional explicit and implicit schemes, for example, explicit Runge–Kutta

Abstract We consider C1-functions defined on two-step Carnot groups with a sub-Lorentzian structure defined by one horizontal direction with a negative squared length along it, and prove a nonholonomic coarea formula. A result of interest in itself concerns the correctness of the problem statement, namely, the level sets have to be spacelike.

Abstract We study a two-dimensional vector logarithmic-potential equilibrium problem with the Nikishin matrix of interaction. A constructive method for finding the supports of a vector equilibrium measure is given. The densities of the components of the equilibrium measure are expressed in terms of an algebraic function that is explicitly written out. The problem is motivated by the study of the convergence

Abstract Given a sum of a finite number of independent random variables, the asymptotic behavior of its distributions and densities at infinity is investigated in the case when the densities or tails of these distributions decrease faster than the densities or tails of gamma distributions.

Abstract Result on the uniform, over the entire real line, equiconvergence of spectral expansions related to the self-adjoint extension of a general differential operation of any even order with coefficients from the one-dimensional Kato class, with the Fourier integral expansion is presented. The statement is based on the obtained uniform estimates for the spectral function of this operator.

Abstract Following V.I. Arnold, we define the stochasticity parameter S(U) of a set \(U \subseteq {{\mathbb{Z}}_{M}}\) to be the sum of squares of consecutive distances between the elements of U. The stochasticity parameter of the set RM of quadratic residues modulo M is studied. We compare \(S({{R}_{M}})\) with the average value \(s(k) = s(k,M)\) of S(U) over all subsets of \(U \subseteq {{\mathbb{Z}}_{M}}\)

Abstract The evolution of a system of mutually gravitating particles is considered taking into account the energy loss in collisions. Collisions can be described in various ways. One can use the theory of inelastic impact of solids with Newton’s recovery coefficient for the relative velocity of bouncing particles. In numerical implementation, the main difficulty of this approach is to track and refine

Abstract Two approaches are suggested for constructing a probabilistic approximation of the evolution operator e–itH, where \(H = \tfrac{{{{{( - 1)}}^{m}}}}{{(2m)!}}\tfrac{{{{d}^{{2m}}}}}{{d{{x}^{{2m}}}}}\), in the strong operator topology. In the first approach, the approximating operators have the form of expectations of functionals of a certain Poisson point field, while, in the second approach

Abstract The paper presents a plane regular fractal Peano curve with a Euclidean square-to-line ratio (L2-locality) of \(5\frac{{43}}{{73}}\), which is minimal among all known curves of this class. The presented curve has a fractal genus of 25. Performed calculations allow us to state that all the other regular curves with a fractal genus not exceeding 36 have a strictly greater square-to-line ratio

Abstract This paper summarizes the results of studies of the laminar–turbulent transition in some fluid and gas dynamics problems obtained by applying numerical methods and methods of chaotic dynamics. The following problems are analyzed: 2D and 3D Kolmogorov problems in a periodic domain, 3D Rayleigh–Benard convection in rectangular domains, 3D backward-facing step flow, and development of 3D Rayleigh–Taylor

Abstract This paper shows the integrability of certain classes of odd-order dynamical systems that are homogeneous with respect to some of the variables and in which a system on the tangent bundle of smooth manifolds is distinguished. In this case, the force fields have dissipation of different signs and generalize previously considered cases.

Abstract In a complex Banach algebra that is not assumed to be commutative, nth-order linear differential equations with constant coefficients are considered. The corresponding algebraic characteristic equation of the nth degree is assumed to have n distinct roots for which the Vandermonde matrix is invertible. Analogues of Sylvester’s and Vieta’s theorems are proved, and a contour integral of Cauchy

Abstract Recently, we introduced a new class of bounded potentials of the one-dimensional stationary Schrödinger operator on the real axis, and a corresponding family of solutions of the KdV hierarchy. These potentials, which we call primitive, are obtained as limits of rapidly decreasing reflectionless potentials, or multisoliton solutions of KdV. In this note, we introduce generalized primitive potentials

Abstract Multiplicative estimates for the Lp-norms of derivatives on a domain with flexible cone condition are established.

Abstract— Scalar real Riccati equations with coefficients expandable in convergent power series in a neighborhood of infinity are considered. Extendable solutions to equations of this kind are studied. Methods of power geometry are used to obtain conditions for asymptotic series expansions of these solutions.

Abstract A linear control system described by a system of differential-difference equations of neutral type with several delays and variable matrix coefficients is considered. The relationship between the variational problem for a nonlocal functional describing the multidimensional control system with delays and the corresponding boundary value problem for the system of differential-difference equations

Abstract An impulse nonlinear problem admitting discontinuous solutions that are functions of bounded variation is studied. This problem models the deformation of a discontinuous string (chains of strings fastened together by springs) with elastic supports in the form of linear and nonlinear springs (for example, springs with different turns, whose deformations do not obey Hooke’s law). The model is

Abstract Average values over integral points on a three-dimensional sphere with an arbitrary smooth weight function are studied. For them, an expansion of the mean product of two L-series associated with the Hecke basis in spaces of holomorphic parabolic forms of integer even weight with respect to the congruence subgroup Γ0(4) is obtained.

Abstract It is proved that an artificial neural network with smooth activation functions and without bottlenecks is a Morse function for almost all, with respect to the Lebesgue measure, sets of weights.

Abstract In the framework of Zhuravlev’s algebraic approach to classification problems, a linear model of algorithms is investigated (estimates of class membership are generated by linear regressions). The possibility of weakening the completeness requirement (obtaining an arbitrary estimation matrix) in order to obtain any classification of a fixed set of objects by using special decision rules is

Abstract The fluctuations of the number of scattering and multiplying particles in a random medium are investigated as functions of time. For this purpose, randomized Monte Carlo algorithms for estimating the probabilistic moments of the corresponding exponential asymptotic parameter are constructed.

Abstract A uniqueness theorem for reconstruction of an nth-order differential operator with nonseparated boundary conditions from several spectra is proved. This theorem is based on the results of E.A. Baranova.

Abstract For a nonnegative square matrix, a method of constructing a stability indicator in the form of a polynomial in matrix coefficients is presented. Additionally, an algorithm for indicator calculation is described and the relationship of the resulting indicator with determinants of some matrices built on the basis of the original one is demonstrated.

Abstract Let \({{V}_{r}}({{\mathbb{R}}^{n}})\), n ≥ 2, be the set of functions \(f \in {{L}_{{{\text{loc}}}}}({{\mathbb{R}}^{n}})\) with zero integrals over all balls in \({{\mathbb{R}}^{n}}\) of radius r. Various interpolation problems for the class \({{V}_{r}}({{\mathbb{R}}^{n}})\) are studied. In the case when the set of interpolation nodes is finite, the multiple interpolation problem is solved

Abstract We significantly improve lower bounds on the clique-chromatic numbers for some families of Johnson graphs. A new upper bound on the clique-chromatic numbers for G(n, r, r – 1) and G(n, 3, 1) is obtained. Finally, the exact value of the clique-chromatic number for G(n, 2, 1) is provided.

Abstract New bounds on the modularity of distance graphs were obtained and the exact value of modularity was calculated for G(n, 2, 1) graphs.

Abstract We study a symmetric three-level (in time) method with a weight and a symmetric vector two-level method for solving the initial-boundary value problem for a second-order hyperbolic equation with a small parameter \(\tau > 0\) multiplying the highest time derivative, where the hyperbolic equation is a perturbation of the corresponding parabolic equation. It is proved that the solutions are

Abstract The notion of a sub-Lorentzian structure with multidimensional time on Carnot–Carathéodory spaces is introduced. It is proved that classes of graph surfaces are spacelike, and a sub-Lorentzian analogue of the area formula is proved.

Abstract A two-person zero-sum positional differential game is considered in which the motion of a dynamical system is described by a nonlinear delay equation and the initial motion history is determined by a piecewise continuous function. Inequalities for directional derivatives of the value functional and inequalities for its sub- and supergradients are obtained.

Abstract New improved rates of convergence for ergodic homogeneous Markov chains are studied. Examples of comparison with classical rate bounds are provided.

Abstract The concepts of a variety of exponential MR-groups and tensor completions of groups in varieties are introduced. The relationships between free groups of a given variety under different rings of scalars are studied, and varieties of abelian MR-groups are described. Moreover, several analogues of n-class nilpotent groups are considered and compared in the category of MR-groups. It is shown

Abstract We construct the action of the restricted Weyl group on the set of principal families of orbits of a minimal parabolic subgroup over an algebraically nonclosed field. Additionally, we relate this action to the action on a polarized cotangent bundle. These results generalize the corresponding results of Knop on the action of the Weyl group on the families of Borel orbits of maximal complexity

Abstract The problem of propagation of TE-polarized electromagnetic waves in a dielectric layer is considered. The waves existing in the structure under study are classified. It is rigorously proved that, in the dielectric layer, there are no surface complex TE waves, but there are infinitely many complex leaky TE waves.

Abstract Necessary and sufficient conditions for the internal stability of formations whose dynamics are defined by linear differential equations have been obtained. The classes of admissible controls are specified as programmed controls for leaders and affine feedback controls depending on the object and leader states for followers. The conditions obtained are easy to verify and consist of (i) the

Abstract The Dirichlet problem for an elliptic functional differential equation involving a shifted and contracted argument under the Laplacian sign is studied. Sufficient conditions for the unique solvability of the problem are established. It is shown that the problem may have an infinite-dimensional solution manifold.

Abstract A combined scheme for the discontinuous Galerkin (DG) method is proposed. This scheme monotonically localizes the fronts of shock waves and simultaneously maintains increased accuracy in the regions of smoothness of the computed weak solutions. In this scheme, a nonmonotone version of the third-order DG method is used as a baseline scheme and a monotone version of this method is used as an

Abstract Today, the exploration of the Arctic region is one of the most important direction of research in our country, because large amounts of unexplored oil and gas deposits are located there. Large hydrocarbon deposits are situated within the Northern seas. Their development is complicated by gas explosions resulting from an accidental opening and further spread of the gas. Since the region with

Abstract A new method for constructing exact solutions of nonlinear equations of mathematical physics is proposed. The method is based on nonlinear integral transformations in combination with the splitting principle. The effectiveness of the method is illustrated by nonlinear reaction–diffusion equations that involve two or three arbitrary functions. New exact functional separable solutions and generalized

Abstract The problem of characterization of the bilinear Hardy inequality in discrete form is solved.

Abstract We discuss some results and problems related to the Newton–Puiseux algorithm and its generalization for nonzero characteristic obtained by the author earlier. A new method is suggested for obtaining effective estimates of the roots of a polynomial in the field of fractional power series in the case of arbitrary characteristic.

Abstract Processes in the dynamics of electrically conducting fluid flows in complex heat transfer systems are mathematically modeled in detail on high-performance parallel computing systems. The study is based on the kinetically consistent magnetogasdynamic approach adjusted to this class of problems. The kinetically consistent algorithm is well adapted to the architecture of high-performance computing

Abstract Weighted grand Lebesgue spaces with mixed norms are introduced, and criteria for the boundedness of strong maximal functions and Riesz transforms in these spaces are given.

Abstract Polynomial identities and codimension growth of nonassociative algebras over a field of characteristic zero are considered. A new approach is proposed for constructing nonassociative algebras starting from a given infinite binary word. The sequence of codimensions of such an algebra is closely connected with the combinatorial complexity of the defining word. These constructions give new examples

Abstract This paper shows the possibilities of solving the Gardner problem of determining the lock-in range for multidimensional phase-locked loop models. Analytical estimates of the lock-in range for a third-order system are obtained for the first time by developing analogues of classical stability criteria for the cylindrical phase space.

Abstract Fractional Brownian motion is studied. Statistical estimators of the Hurst exponent are proposed, and their properties are examined. This stochastic process is widely used in model development, trend forecasting, and, in particular, as a special case of long-memory processes. The first model involving the Hurst exponent appeared in the British hydrologist Harold Hurst’s research published

Abstract—In this paper the generalized localization principle for the spherical partial sums of the multiple Fourier series in the L2 class is proved, that is, if f ∈ L2(TN) and f = 0 on an open set Ω ⊂ TN, then it is shown that the spherical partial sums of this function converge to zero almost-everywhere on Ω. It has been previously known that the generalized localization is not valid in Lp(TN) when

Abstract The even Radon–Kipriyanov transform (Kγ-transform) is suitable for studying problems with the Bessel singular differential operator \({{B}_{{{{\gamma }_{i}}}}} = \frac{{{{\partial }^{2}}}}{{\partial x_{i}^{2}}} + \frac{{{{\gamma }_{i}}}}{{{{x}_{i}}~}}\frac{\partial }{{\partial {{x}_{i}}}},{{\gamma }_{i}} > 0\). In this work, the odd Radon–Kipriyanov transform and the complete Radon–Kipriyanov

Abstract The optical properties of plasma are determined by the presence of a fluctuating microscopic electric field. A simple ab initio model of a plasma microfield accounting for its inhomogeneity up to an octupole term has been constructed for the first time. A comparison with experiments has shown that only this model correctly describes the observed number of spectral lines.

Abstract According to the Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form in independent random variables given another. We prove an analogue of this theorem for linear forms in two independent random variables with values in an a-adic solenoind without elements of order 2, assuming that the characteristic

Abstract A numerically implementable model of a three-dimensional homogeneous random field in a “horizontal” layer 0 < z < H is constructed assuming that the integral of the field with respect to the “vertical” coordinate z has a given infinitely divisible one-dimensional distribution and a given correlation function. An aggregate of n independent elementary horizontal layers of thickness h = H/n shifted

Abstract An original concept of building a factor model based on frames has been proposed. A method has been developed for calculating the values of factors by searching for the eigenvalues of matrices of pairwise comparisons of the degree of influence of slots. Possible applications of the factor model in the study of complex processes and systems are discussed.

Abstract The game problem of a control system approaching a target set at a fixed point in time is studied. The stability defect of a set in the position space that is weakly invariant with respect to a finite set of unification differential inclusions is estimated from below.

Abstract Observation and control problems in Banach (B)-spaces are investigated. A criterion for controllability and optimal controllability is formulated on the basis of the BUME method and the monotone mapping method. An inverse controllability problem is introduced, and an abstract maximum principle is formulated in (B)-spaces. For PDE in Hilbert (H)-spaces and for ODE in \({{\mathbb{R}}^{n}}\)

Abstract A model was constructed for reconstructing the initial stage of solidification of binary alloys treated as a nonequilibrium phase transition with a diffusion stratification mechanism. Numerical experiments concerning the self-excitation of a homogeneous state by applying a melt cooling boundary control condition were performed.