Abstract The statistical distribution of the phase of a quasi-harmonic signal has been theoretically investigated. An analytical expression for the probability density function of this distribution has been obtained for the first time, and the distribution has been shown to be a two-parameter one and to be determined by the following parameters: the signal-to-noise ratio and the deviation of the current

Abstract Model reduction methods allow to significantly decrease the time required to solve a large ODE system in some cases by performing all calculations in a vector space of significantly lower dimension than the original one. These methods frequently require apriori information about the structure of the solution, possibly obtained by solving the same system for different values of parameters.

Abstract An estimate is obtained for the increased integrability of the gradient of the solution to the Zaremba problem in a bounded plane domain with a Lipschitz boundary and rapidly alternating Dirichlet and Neumann boundary conditions, with an increased integrability exponent independent of the frequency of the boundary condition change.

Abstract We formulate a general statement of the problem of defining invariant measures with certain properties and suggest an ergodic method of perturbations for describing such measures.

Abstract New properties of convex infinitely differentiable functions related to extremal problems are established. It is shown that, in a neighborhood of the solution, even if the Hessian matrix is singular at the solution point of the function to be minimized, the gradient of the objective function belongs to the image of its second derivative. Due to this new property of convex functions, Newtonian

Abstract The integrability of certain classes of homogeneous dynamical systems on the tangent bundles of four-dimensional manifolds is shown. The force fields involved in the systems lead to dissipation of variable sign and generalize previously considered fields.

Abstract It has been known for more than a decade that, if a self-similar arc \(\gamma \) can be shifted along itself by similarity maps that are arbitrarily close to identity, then \(\gamma \) is a straight line segment. We extend this statement to the class of self-affine arcs and prove that each self-affine arc admitting affine shifts that may be arbitrarily close to identity is a segment of a parabola

An Erratum to this paper has been published: https://doi.org/10.1134/S1064562421330012

An Erratum to this paper has been published: https://doi.org/10.1134/S1064562421010087

Abstract We propose analogues of the classical Kolmogorov–Smirnov and omega-squared tests for goodness-of-fit testing of distribution tails. The consistency of the proposed tests on wide alternatives is proved both in the framework of censored data statistics and in the framework of statistics of extremes.

Abstract An asymptotic analysis of the eigenvalues and eigenfunctions in the Orr–Sommerfeld problem is carried out in the case when the velocity of the main plane-parallel shear flow in a layer of a Newtonian viscous fluid is low in a certain measure. The eigenvalues and corresponding eigenfunctions in the layer at rest are used as a zero approximation. For their perturbations, explicit analytical

Abstract We establish two-sided estimates for the proximity, as \(t \to \infty \), of the Poisson integral representing the solution of the Cauchy problem for the heat equation to modified Tikhonov–Stieltjes means of the initial function. Order-sharp two-sided estimates in some classes of initial functions are described.

Abstract— We study the equiconvergence of spectral decompositions for two Sturm–Liouville operators on the interval [0, π] generated by the differential expressions \({{l}_{1}}(y) = - y'' + {{q}_{1}}(x)y\) and \({{l}_{2}} = - y'' + {{q}_{2}}(x)y\) and the same Birkhoff-regular boundary conditions. The potentials are assumed to be singular in the sense that \({{q}_{j}}(x) = u_{j}^{'}(x)\), \({{u}_{j}}

Abstract Let \(\mathcal{M}\) be an atomless semifinite von Neumann algebra equipped with a faithful normal semifinite trace τ (or else, an atomic von Neumann algebra with all atoms having the same trace) acting on a separable Hilbert space \(\mathcal{H}\). Let \(E(\mathcal{M},\tau )\) be a separable symmetric space of τ-measurable operators, whose norm is not proportional to the Hilbert norm ||⋅||2

Abstract The existence of functions the Fourier–Walsh series of which are universal in the sense of signs for the class of almost everywhere finite measurable functions, and the structure of such functions is described.

Abstract A numerical-asymptotic approach is used to solve some coefficient inverse problems of tracer diffusion in the atmosphere. An asymptotic solution of the direct problem for an effective prognostic equation in the near-field zone of the source is obtained via a rigorous asymptotic analysis of a multidimensional singularly perturbed reaction–diffusion–advection problem. This solution is used as

Abstract Theorems on the uniqueness and existence of solutions to problems of scattering electromagnetic waves by bounded three-dimensional inhomogeneous anisotropic bodies, including lossless ones with discontinuities in the parameters of the medium, are proved.

Abstract We study the following version of the mean periodic extension problem. (i) Suppose that \(T \in \mathcal{E}'({{\mathbb{R}}^{n}})\), n ≥ 2, and E is a nonempty closed subset of \({{\mathbb{R}}^{n}}\). What conditions guarantee that, for a function f ∈ C(E), there is a function \(F \in C({{\mathbb{R}}^{n}})\) coinciding with f on E such that \(F * T = 0\) in \({{\mathbb{R}}^{n}}\)? (ii) If such

Abstract Integro-differential equations with unbounded operator coefficients in a Hilbert space are studied. The equations under consideration are abstract hyperbolic equations perturbed by terms containing Volterra integral operators. These equations are operator models of integro-differential equations with partial derivatives arising in the theory of viscoelasticity, thermal physics, and homogenization

Abstract Classes of exact solutions corresponding to vortex and potential flows are presented within the framework of a hydrodynamic model describing flows of a viscous incompressible fluid. The study of exact solutions is a prerequisite for creating a core simulator, which is associated with modeling fluid dynamics in a porous medium and the response of the field to dynamic influences in order to

Abstract We introduce the concept of the uniform width of a contact circuit. For each Boolean function, we find the minimal possible value of the uniform width of a contact circuit implementing this function. We prove constructively that this value does not exceed 3. We also establish that, for almost all Boolean functions on n variables, it equals 3.

Abstract Signal structures based on OFDM signals and error-correcting codes resistant to the influence of spectrum-concentrated noise are described. An algorithm for receiving such signal structures with the use of weight functions is presented. It is shown by theoretic analysis and simulations that the class of Kravchenko weight functions based on atomic functions represents nearly optimal windows

Abstract—We give a solution to the Kolmogorov problem on uniqueness of probability solutions to a parabolic Fokker–Planck–Kolmogorov equation.

Abstract The elastic effects on an artificial ice island produced by drill impacts and the pressure of structures located on the island are numerically modeled. The problem is solved numerically by applying the grid-characteristic method with interpolation on structured and unstructured meshes. The grid-characteristic method most accurately describes dynamic processes in exploration seismology problems

Abstract Let E be a nonseparable rearrangement invariant space, and let E0 denote the closure of the set of all bounded functions in E. We study elements of E orthogonal to the subspace E0, i.e., elements \(x \in E\) such that \({{\left\| x \right\|}_{E}} \leqslant {{\left\| {x + y} \right\|}_{E}}\) for any \(y \in {{E}_{0}}\).

Abstract The saturation and weak saturation numbers of Kneser graphs with clique patterns are estimated.

Abstract An important generalization of Borsuk’s classical problem of partitioning sets into parts of smaller diameter is studied. New upper and lower bounds for the Borsuk numbers are found.

Abstract For an extremal functional interpolation problem first considered by Yu.N. Subbotin, the explicit form of the extremal interpolation constants is calculated in terms of the Favard constants in the spaces Lp, \(p = 1,3{\text{/}}2,2\). Simple efficient recurrence formulas are obtained to calculate the Favard constants, and formulas for calculating these constants in terms of the Euler numbers

Abstract— An interpolation theorem for spaces of functions of positive smoothness on a domain with flexible cone condition is established.

Abstract A new model of laminar vibrational combustion is constructed relying on a thermodynamic analysis of the combustion process. Two combustion modes, detonation and deflagration, are modeled. The nature of their origin depending on the structure of the standard chemical potential is established, and a numerical experiment concerning the onset of these combustion modes is carried out. By controlling

Abstract We consider a completely integrable Hamiltonian system with two degrees of freedom that describes the dynamics of a Lagrange top with a vibrating suspension point. The results of a stability analysis of equilibrium positions are clearly presented. It turns out that, in the case of a vibrating suspension point, both equilibrium positions can be unstable, which corresponds to the existence of

Abstract Moment methods in Krylov subspaces for solving symmetric systems of linear algebraic equations (SLAEs) are considered. A family of iterative algorithms is proposed based on generalized Lanczos orthogonalization with an initial vector \({{v}^{0}}\) chosen regardless of the initial residual. By applying this approach, a series of SLAEs with the same matrix, but with different right-hand sides

Abstract We obtain a complete description of cubic polynomials f over algebraic number fields \(\mathbb{K}\) of degree \(3\) over \(\mathbb{Q}\) for which the continued fraction expansion of \(\sqrt f \) in the field of formal power series \(\mathbb{K}((x))\) is periodic. We also prove a finiteness theorem for cubic polynomials \(f \in K[x]\) with a periodic expansion of \(\sqrt f \) for extensions

Abstract The connection between the number of internal zeros of nontrivial solutions to fourth-order self-adjoint boundary value problems and the inertia index of these problems is studied. We specify the types of problems for which such a connection can be established. In addition, we specify the types of problems for which a connection between the inertia index and the number of internal zeros of

Abstract A class of force evolutionary billiards is discovered that realizes important integrable Hamiltonian systems on all regular isoenergy 3-surfaces simultaneously, i.e., on the phase 4-space. It is proved that the well-known Euler and Lagrange integrable systems are billiard equivalent, although the degrees of their integrals are different (two and one).

Abstract For a system of electrodynamic equations, the inverse problem of determining an anisotropic conductivity is considered. It is supposed that the conductivity is described by a diagonal matrix σ(x) = \({\text{diag}}({{\sigma }_{1}}(x),{{\sigma }_{2}}(x)\), σ3(x)) with \(\sigma (x) = 0\) outside of the domain Ω = \(\{ x \in {{\mathbb{R}}^{3}}|\left| x \right| < R\} \), \(R > 0\), and the permittivity

Abstract We describe all Carnot algebras with growth vector (2, 3, 5, 6), their normal forms, an invariant that separates them, and a change of basis that transforms such an algebra into a normal form. For each normal form, Casimir functions and symplectic foliations on the Lie coalgebra are computed. An invariant and normal forms of left-invariant (2, 3, 5, 6)-distributions are described. A classification

Abstract Linear systems of differential equations with an invariant in the form of a positive definite quadratic form in a real Hilbert space are considered. It is assumed that the system has a simple spectrum and the eigenvectors form a complete orthonormal system. Under these assumptions, the linear system can be represented in the form of the Schrödinger equation by introducing a suitable complex

Abstract We consider smooth mappings acting from one Banach space to another and depending on a parameter belonging to a topological space. Under various regularity assumptions, sufficient conditions for the existence of global and semilocal continuous inverse and implicit functions are obtained. We consider applications of these results to the problem of continuous extension of implicit functions

Abstract A novel method for filtering images contaminated by mixed (additive-multiplicative) noise is substantiated and implemented for the first time. The method includes several stages: the formation of similar structures in 3D space, homomorphic transformation, a 3D filtering approach based on a sparse representation in the discrete cosine transform space, inverse homomorphic transformation, and

Abstract We study first-order zero–one law and the first-order convergence law for two recursive random graph models, namely, the uniform and preferential attachment models. In the uniform attachment model, a new vertex with \(m\) edges chosen uniformly is added at every moment, while, in the preferential attachment model, the distribution of second ends of these edges is not uniform, but rather the

Abstract An adaptive mesh refinement algorithm for simulations of the Navier–Stokes equations on unstructured hybrid meshes is presented. Numerical results for compressible supersonic flow around a sphere are given.

Abstract The problem of numerical modelling water purification from iron impurities is considered. The cleaning task is relevant for many industrial applications, including the development of new cleaning methods and devices for the preparation of ultrapure water. The performed mathematical study is associated with the calculations of the water flow and the transfer of contaminants in the treatment

Abstract This paper states that, for any nonzero linear form \({{h}_{0}}{{f}_{0}}(1) + {{h}_{1}}{{f}_{1}}(1)\) with integer coefficients h0, h1, there exist infinitely many p-adic fields where this form does not vanish. Here, \({{f}_{0}}(1) = \mathop \sum \limits_{n = 0}^\infty {{\left( \lambda \right)}_{n}}\) and \({{f}_{1}}\left( 1 \right) = \mathop \sum \limits_{n = 0}^\infty {{\left( {\lambda +

Abstract For an overdetermined system of nonlinear equations, a two-stage method is suggested for constructing an error-stable approximate solution. The first stage consists in constructing a regularized set of approximate solutions for finding normal quasi-solutions of the original system. At the second stage, the regularized quasi-solutions are approximated using an iterative process based on square

Abstract An autonomous object possessing a high-speed striking device is moving under observation conditions. Threatened by the device, a spatial observer has to hide behind convex fragments of the surrounding terrain. The paper describes the routes from a given movement corridor along which the object could pass remaining hidden from the observer by choosing a suitable velocity of motion.

Abstract For the first time, a method is proposed for constructing a multidimensional combined shock-capturing scheme that monotonically localizes shock wave fronts and, at the same time, has increased accuracy in smoothness regions of calculated generalized solutions. In this method, the solution of the combined scheme is constructed using monotonic solutions of a bicompact scheme of the first order

Abstract For weighted directed chain-cycle graphs, an algorithm transforming one graph into another is constructed. The algorithm runs in linear time and yields a sequence of transformations with the smallest, up to an additive error, total cost. The costs of the operations of inserting and deleting an edge segment may differ from each other and from the costs of the other operations. The additive

Abstract— Analogues of the Heath-Brown and Selberg identities for three-dimensional Kloosterman sums are proved.

Abstract— The problem of the absence of global periodic solutions for a Schrödinger-type nonlinear evolution equation with a linear damping term is investigated. It is proved that when the damping coefficient is nonnegative, the problem does not have global periodic solutions for any initial data, while when it is negative, the same is valid for “sufficiently large values” of the initial data.

Abstract The aim of this paper is to find an analytical formula for the Kirchhoff index of circulant graphs \({{C}_{n}}({{s}_{1}},{{s}_{2}},\; \ldots ,\;{{s}_{k}})\) and \({{C}_{{2n}}}({{s}_{1}},{{s}_{2}},\; \ldots ,\;{{s}_{k}},n)\) with even and odd valency, respectively. The asymptotic behavior of the Kirchhoff index as n → ∞ is investigated. We proof that the Kirchhoff index of a circulant graph

Abstract We consider initial boundary value problems with boundary conditions of the first or second kind for one-dimensional (with respect to a spatial variable) Petrovskii parabolic systems of the second order with variable coefficients in a bounded domain with nonsmooth lateral boundaries. The uniqueness of regular solutions to these problems in the class of functions that are continuous in the

Abstract— A characterization of bilinear inequalities with two-dimensional rectangular Hardy operators in weighted Lebesgue spaces is given.

Abstract An effectively verifiable condition for quasipositivity of links is given. In particular, it is proven that if a quasipositive link can be represented by an alternating diagram satisfying the condition that no pair of Seifert circles is connected by a single crossing, then the diagram is positive and the link is strongly quasipositive.

Abstract The asymptotic behavior of the chromatic number of the binomial random hypergraph \(H(n,k,p)\) is studied in the case when \(k \geqslant 4\) is fixed, n tends to infinity, and p = p(n) is a function. If p = p(n) does not decrease too slowly, we prove that the chromatic number of \(H(n,k,p)\) is concentrated in two or three consecutive values, which can be found explicitly as functions of n

Abstract Let \(\zeta (s)\) and \(\beta (s)\) be the Riemann zeta function and the Dirichlet beta function. The formulas for calculating the values of \(\zeta (2m)\) and \(\beta (2m - 1)\) (\(m = 1,\;2,\; \ldots \)) are classical and well known. Our aim is to represent \(\zeta (2m + 1)\), \(\beta (2m)\), and related numbers in the form of definite integrals of elementary functions and rapidly converging

Abstract We consider a number of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set \(\Omega \). Solutions to these problems are obtained using methods of convex trigonometry. The paper includes (1) geodesics in the Finsler problem on the Lobachevsky hyperbolic plane; (2) left-invariant sub-Finsler geodesics on all unimodular 3D Lie groups (\({\text{SU}}(2)\)

Abstract We define the scale \({{\mathcal{Q}}_{p}}\), \(n - 1 < p < \infty \), of homeomorphisms of spatial domains in \({{\mathbb{R}}^{n}}\), a geometric description of which is due to the control of the behavior of the p-capacity of condensers in the image through the weighted p-capacity of the condensers in the preimage. For p = n the class \({{\mathcal{Q}}_{n}}\) of mappings contains the class

Abstract We consider the three-dimensional stationary Vlasov–Poisson system of equations with respect to the distribution function of the gravitating matter \(f = {{f}_{q}}(r,u)\), the local density \(\rho = \rho (r)\), and the Newtonian potential \(U = U(r)\), where \(r: = {\text{|}}x{\text{|}}\), \(u: = {\text{|}}v{\text{|}}\) (\((x,v) \in {{\mathbb{R}}^{3}} \times {{\mathbb{R}}^{3}}\) are the space–velocity

Abstract A mathematical model for viscous gas flow simulation with time scales bounded by the characteristic time between molecular collisions is considered. This approach is a variant of the quasi-gasdynamic system of equations, which is based on the relationship between the kinetic and macroscopic descriptions of continuous medium motion. Based on the presented model, a numerical algorithm is constructed