A.Z. Petrov divided 4-metrics of signature 0 into 6 types, which later began to be denoted by I, D, O, II, N, III. However, in the case of (anti-)self-duality, the \(\lambda\)-matrix, on the basis of which Petrov built his classification, acquires specificity. First, the determinant of this \(\lambda\)-matrix has a root 0 of multiplicity at least 3. Second, the multiplicity of this root cannot be 5

We consider a boundary value problem for a system of the fourth order pseudo-hyperbolic equations with nonlocal condition on a rectangular domain. By introducing a new unknown function, the considered problem is reduced to an equivalent nonlocal problem with integral condition for a system of hyperbolic integro-differential equations of the second order. We propose an algorithm for finding an approximate

In this paper, we study approximative properties of partial sums of a conjugate Fourier series with respect to a certain system of Chebyshev – Markov algebraic fractions. We cite the main results obtained in known works devoted to studying approximations of conjugate functions in polynomial and rational cases. We introduce a system of Chebyshev – Markov algebraic fractions and construct the corresponding

Let \(\mathbb{C}\) be the complex plane, E be a measurable subset of a segment \([0, R]\) of the positive semiaxis \(\mathbb{R}^+\), and \(u\not\equiv - \infty\) be a subharmonic function on \(\mathbb{C}\). The main result of this article is an upper estimate of the integral of the module \(|u|\) over a subset of E through the maximum of the function u on a circle of radius R centered at zero and the

We consider sequences of Genocchi numbers of the first and the second kind. For these numbers, an approach based on their representation using sequences of polynomials is developed. Based on this approach, for these numbers some identities generalizing the known identities are constructed.

This article considers a dynamical system with delay described by a differential equation with partial derivatives of hyperbolic type and delay with respect to a time variable. We establish in Theorem 3.1 the k(t)-stability of weak solution under suitable initial conditions in \(\mathbb{R}^n, n>4\) by introducing appropriate Lyapunov functions.

We study the question of determining all those parameters for which all positive solutions to the logistic equation with delay tend to zero as \(t \to \infty\). The well-known Wright conjecture [1] on the estimation of the set of such parameters is proved. A methodology is developed that makes it possible to sequentially refine this estimate.

We state a new problem for a fourth-order factorized differential equation, whose operator is the product of first- and third-order differential operators, and prove its unique solvability. We construct the solution in terms of the Riemann function of the corresponding third-order pseudoparabolic differential operator, determining one of functions that enter in the formula for the problem solution

We consider an inverse boundary-value problem for a aerohydrodynamical cascade of profiles streamlined by a potential flow of an incompressible inviscid fluid. It is required to find the shape of the profile of the cascade, by a given velocity distribution as a function of the arc abscissa, and determine the period of the cascade.

For any partition \(\sigma\) of the set \(\mathbb{P}\) of all primes, it is proved that if a subgroup H of a finite \(3^{'}\)-group G is \(\sigma\)-subnormal in \(\) for any \(x \in G\), then H is \(\sigma\)-subnormal in G.

The paper devoted to different aspects of the theory of nonlinear mean random variables, i.e., the geometric mean, harmonic mean, and average power.

In this work we consider isolation from side in different degree structures, in particular, in the 2-computably enumerable wtt-degrees and in low Turing degrees. Intuitively, a 2-computably enumerable degree is isolated from side if all computably enumerable degrees from its lower cone are bounded from above by some computably enumerable degree which is incomparable with the given one. It is proved

The alternative bimodules over semisimple artinian algebras are studied. A bimodule is called almost reducible if it is a direct sum of an associative subbimodule and a completely reducible subbimodule. It is proved that if a semisimple algebra cannot be homomorphically mapped onto an associative division algebra, then an alternative bimodule above it is almost reducible. An example of an alternative

In this paper, we found sufficient conditions, under fulfillment of which the maximum principle for the solution of a second order partial differential elliptic equation in the unit circle meets maximum principle. It is proved that if a quasiconformality coefficient of such function satisfies certain boundary conditions, then this function meets maximum principle. While proving the main result, we

An initial-boundary value problem is considered, which describes the linear vibrations of a viscous stratified fluid in a bounded vessel with elastic membrane. We find sufficient existence conditions for a strong (with respect to the time variable) solution of the initial-boundary value problem describing the evolution of the specified hydrodynamics system.

Basing on the theory of positively invertible matrices, we study certain questions of the exponential 2p-stability \((1 \le p < \infty )\) of systems of Itô linear differential equations with bounded delays and impulse actions on certain solution components. We apply the ideas and methods developed by N.V. Azbelev and his followers for studying the stability of deterministic functional differential

In the present work, we discover some new congruences modulo 5 for \(p_r(n)\), the general partition function by restricting r to some sequence of negative integers. Our emphasis throughout this paper is to exhibit the use of q-identities to generate the congruences for \(p_r(n)\).

In this paper, we study the regular solvability (in Sobolev spaces) of transmission problems for parabolic second-order systems with conjugation conditions of non-ideal contact type. The solution of such a problem has all generalized derivatives entering in the equation that are summable with some power \(p\in (1,\infty)\). One can express limit values of conormal derivatives at the interface in terms

We prove a combinatorial identity containing k-order differences of sequences, as well as binomial coefficients. The Euler summation operation implies the calculation of all order differences of terms of the initial series. The regularity of the summing function means the coincidence with the “ordinary” sum of the series, provided that this sum exists. The proved combinatorial identity allows one to

Using the fundamental basis of the field \(L_9=\mathbb{Q} (2\cos(\pi/9)),\) the form \(N_{L_9}(\gamma)=f(x, y, z)\) is found and the Diophantine equation \(f(x,y,z)=a\) is solved. A similar scheme is used to construct the form \(N_{L_7}(\gamma)=g(x,y,z)\). The Diophantine equation \(g (x, y, z)=a\) is solved.

In this article, we consider orthogonally additive operators defined on a vector lattice E and taking value in a Banach space X. We say that an orthogonally additive operator \(T:E\to X\) is narrow if for every \(e\in E\) and \(\varepsilon>0\) there exists a decomposition \(e=e_1\sqcup e_2\) of e into a sum of two disjoint fragments e1 and e2 such that \(\|Te_1-Te_2\|<\varepsilon\). It is proved that

Let D be a hexagon having a pair of parallel sides, equal in length, and L be a half of its boundary. We study solvability of a seven-element sum-difference equation equation in the class of functions holomorphic outside L and vanishing at infinity. Their boundary values satisfy the Hölder condition on every compact not containing the nodes. At the nodes they have at most logarithmic singularities

We consider the realization of Boolean functions by the circuits of unreliable elements in a complete finite basis containing some pairs of functions. We assume that all elements of a circuit are exposed to the faults type 0 at the outputs with probability \(\varepsilon \in (0,1/2)\) independently of each other. We prove that almost any Boolean function can be implemented by an asymptotically optimal

In hyperbolic space, we consider the Cauchy problem for the aggregation equation. Non-negative initial function is bounded and summable. We prove the existence of a weak solution on a small time interval. In the case where the kernel of the integral operator is smooth and rapidly decreases at infinity, the existence of a bounded solution on an arbitrary time interval is proved.

The technical (practical) stability problem for a set of trajectories of discrete systems on a metric space of nonempty convex compact sets in \(\Bbb R ^ n\) is considered. On the basis of known results of convex geometry and comparison method, an approach of constructing the auxiliary Lyapunov functionals for the study of technical stability in terms of two measures of evolutionary equations with

The equivalence of weak solvability of initial boundary value problems for the Jeffries-Oldroyd model and one integro-differential system with memory is established. The proofs of the statements are essentially based on the properties of regular Lagrangian flows.

We apply new approach for the Goursat and Cauchy problems with additional recovering of coefficients of equation for selection of the cases of solvability of these problems in quadratures. Instead of introduction of additional boundary value conditions we offer restrictions on the structure of the equation connected with possibility of its factorization.

Riemannian manifolds of sign-definite sectional curvature have been studied by many mathematicians due to the close relationship between the curvature and the topology of a Riemannian manifold.We study Riemannian manifolds whose metric connection is a connection with vectorial torsion. The class of such connections contains the Levi-Civita connection. Although the curvature tensor of such a connection

We obtain sharp inequalities of Jackson-Stechkin type between the best approximations \({E_{n - s - 1}}\left( {{f^{\left( s \right)}}} \right)\left( {s = \overline {0,r} ,r \inℕ } \right)\) of successive derivatives \({f^{\left( s \right)}}\left( {s = \overline {0,r} ,r \inℕ } \right)\) of analytic in the disk U functions f ∈ L2(U). Two the following restrictions on f are considered:$${{\rm{\Omega

There is a complete classification of dimetric phenomenologically symmetric geometries of two sets (DPS GTS’s) of rank (n +1, 2), n = 1, 2, …. One can see from this classification that some geometries include geometries of the preceding rank. Such an embedding can be established (or disproved) by solving the corresponding functional equation that express the fact of embedding of geometries in terms

Symplectic matrices are subject to certain conditions that are inherent to the Jacobian matrices of transformations preserving the Hamiltonian form of differential equations. A formula is derived which parameterizes symplectic matrices by symmetric matrices. An analogy is drawn between the obtained formula and the Cayley formula that connects orthogonal and antisymmetric matrices. It is shown that

In the paper, we apply the notion of local group in the context of operator algebras, and propose C*-algebraic constructions related to local groups. For a local group we define the concepts of *-representation and strong *-representation which are related to each other with the help of the extension of the local group. The structure of local group allows us to define the regular representation, which

We prove the completeness in L2(D) of the family of all pairwise products of solutions to the Helmholtz equation that are regular in a bounded domain D ⊂ ℝ3 and fundamental solutions to this equation with singularities at points located on the straight line \({\cal L} \subset {ℝ^3},\overline D \cap {\cal L} = \emptyset \).

We study the problem of acceleration of GCD algorithms for natural numbers based on the approximating k-ary algorithm. We suggest a new scheme of the approximating algorithm implementation ensuring the value of the reduction coefficient ρ = Ai/Bi equal or exceeding k where k is a regulated parameter of computation not exceeding the size of a computer word. This approach ensures a significant advantage

We propose a spherical and a hyperbolic (on the Lobachevskii plane) analogues for the Koch curve and the Koch snowflake. The formulae describing metric characteristics of these fractals are given. We also suggest the method of construction for these curves with the help of the groups of rigid motions of the spaces in question.

We describe the structure of a perspective integral damping coating consisting (with respect to the thickness) of two layers of a viscoelastic material with a thin reinforcing layer in-between. We propose a four-layer finite element model with fourteen degrees of freedom for a plate with a mentioned damping coating. This model allows us to take into account the effect of transversal compression of

A.M. Lyapunov proved inequality, which enables us to estimate distance between two consecutive zeros a and b of the solution of linear differential equation of the second order x″(t) + q(t)x(t) = 0, where q(t) is a continuous for t ∈ [a, b] function. In the present paper we solve analogous problem for the linear differential equation x″(t) + p(t)x′(t) + q(t)x(t) = 0. The obtained inequality is applicable

A class of discrete-time filters (systems) is selected, the frequency characteristics of which are functions of the Markov-Stieltjes type. A description of these filters is given in terms of their system function and impulse response. The properties of stationarity, causality, stability, and reversibility are investigated. A wide class of filters with rational transfer functions is indicated, which

We investigate the structure of the essential spectrum of one three particle model operator H. We prove the existence of negative eigenvalues of the operator H and obtain the estimate for a number of negative eigenvalues of the operator H.

The article describes a new type of Gaussian fields on a two-dimensional 2-adic space, invariant under the translation group and group of scaling transformations (self-similar random fields). Fields are characterized by quadratic characteristic functionals defined by homogeneous generalized functions on a 2-adic space. The properties of the proposed generalized homogeneous functions are investigated

There is given the formulation and the solution of the inverse boundary value problem of the plane theory of elasticity in this paper. The solution is reduced to finding the Taylor coefficients for the function which maps the unit dick onto the unknown domain.

In this paper we consider the Schwartz module of entire functions of exponential type having polynomial growth along the real axis. This module is equipped with the non-metrizable locally convex topology. We establish that any principal submodule is the set of limits of converging sequences which members are polynomials multiplied by the generator of the submodule. We also obtain a weight weak localizability

Let τ be a faithful normal semifinite trace on a von Neumann algebra. We establish the Leibniz criterion for sign-alternating series of τ-measurable operators and present an analogue of the criterion of series “sandwich” series for τ-measurable operators. We prove a refinement of this criterion for the τ-compact case. In terms of measure convergence topology, the criterion of τ-compactness of an arbitrary

The formulation of the acoustoelasticity problem is given on the basis of refined motion equations of orthotropic plates. These equations are constructed in the first approximation by reducing the three-dimensional equations of the theory of elasticity to the two-dimensional equations of the theory of plates, where the approximation of the transverse tangential stresses and the transverse reduction

A coincidence point of a pair of mappings is an element, at which these mappings take on the same value. Coincidence points of mappings of partially ordered spaces were studied by A.V. Arutyunov, E.S. Zhukovskiy, and S.E. Zhukovskiy (see Topology and its Applications, 2015, V. 179, No. 1, p. 13–33); they proved, in particular, that an orderly covering mapping and a monotone one, both acting from a

We consider the distance function (DF), given by the caliber (the Minkowski gauge function) of a convex body, from a point to strictly, strongly, and weakly convex sets in an arbitrary Hilbert space. Some properties of the caliber of a strongly convex set and the conditions for obtaining a strict, strong, or weak convexity of Lebesgue sets for the distance function are established in accordance with

The main problem of the theory of phenomenologically symmetric geometries of two sets is that of classification of these geometries. In this paper, by means of complexification by associative hypercomplex numbers, for functions of a pair of points of some known phenomenologically symmetric geometries of two sets (PhS GTS), we find functions of a pair of points of new geometries. We also find the equations

The main result of the paper is a criterion for a sequence of points in a domain of the complex plane, giving necessary and sufficient conditions under which this sequence of points is an exact sequence of zeros of some holomorphic function whose logarithm of modulus is majored by a given subharmonic function in the domain under consideration. Our criterion for the distribution of zeros of holomorphic

We construct a reduction of the three-dimensional Darboux system for the Christoffel symbols which describes conjugate curvilinear coordinate systems. The reduction is determined by one additional algebraic condition on the Christoffel symbols. It is shown that the corresponding class of solutions of the Darboux system is parameterized by six functions of one variable (two for each of three independent

We consider the Cauchy problem for dynamic Lame systems in the cylinder GT = D × (0,T) constructed over a domain D in a three-dimensional space, where the initial data are given in some strip in the lateral surface of the cylinder. The strip has the form S × (0,T), where S is an open subset of the boundary surface of the domain D. This problem is ill-posed. Under certain requirements to the configuration

We study the geometry of locally complete similarly homogeneous ℝ-trees. We prove the existence theorem for the introduced earlier class of vertical ℝ-trees which are not strongly vertical. The analogous method is applicable to other classes of locally complete ℝ-trees.

for arbitrary continuous function f(t) on the segment [−1,1] we construct discrete Fourier sums Sn,N(f,t) on a system of polynomials forming an orthonormal system on non-uniform grids \({T_N} = \left\{{{t_j}} \right\}\matrix{{N - 1} \cr {j = 0} \cr}\) of N points from segment [−1,1] with weight Δtj=tj+1−tj. Approximation properties of the constructed partial sums Sn,N(f,t) of order n ≤ N−1 are investigated

We study the system of functions λ1+n(x) generated by the system of Laguerre functions. We express functions λ1+n(x) in terms of Laguerre polynomials \(L_n^\alpha (x)\). Using the obtained representations and asymptotic formulas for polynomials \(L_n^\alpha (x)\), we study the behavior of functions λ1+n(x) on [0,∞) with n →∞ and deduce estimates analogous to those for Laguerre functions.

We study finite-dimensional Lie algebras which have a codimension one abelian ideal and prove some their properties including those related to the structure of the space of all Lie algebras. We also compute the automorphism groups of such Lie algebras.

The work is devoted to the study of weak solvability of the optimal feedback control problem for the Voigt model with variable density. The proof is based on the approximation-topological approach. First, the solvability of the approximation problem is proved, and then, based on a priori estimates that are independent of the approximation parameter, it is shown that from the sequence of solutions of

For an open subset of the Euclidean space of dimension n we consider interior and exterior approximations by sequences of open sets. We prove convergence everywhere of the corresponding sequences of distance functions from boundary as well as convergence almost everywhere for their gradients. As applications we obtain several new Hardy-type inequalities that contain the scalar product of gradients

We study the boundedness of the composition operator in the spaces Lp(V, W1, r(Yv)). Such spaces arise when modeling the transport processes in a porous medium. It is assumed that the operator is induced by a mapping preserving the priority of the variables, which agrees with the physical requirements for the model.

We introduce a Lie triple system associated with the central isotope of (− 1, 1)-algebra. The associator ideal of (−1, 1)-algebra is nilpotent if and only if the Lie triple system is nilpotent. The relationship of the constructed Lie triple system with other known Lie triple systems is discussed.

We define holomorphic and pluri-harmonic functions in classical E. Cartan domains of the first type, and research Laplace and Hua Luogeng operators. We find a connection between these operators.

We study a one-dimensional mixed problem for the heat equation, with time advance in nonlocal and non-self-adjoint boundary conditions, describing a real physical process. Under minimal conditions on the initial data, we prove its unique solvability and obtain an explicit representation for the solution.