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.

We study finite-sheeted covering mappings from compact connected spaces onto compact connected groups. For such a covering mapping we consider a method of supplying its covering space by a group structure. The covering space endowed with that group structure is a topological group, and a given covering mapping turns into a homomorphism of compact connected groups.

Let \({\cal K}\) be a root class of groups closed under taking quotient groups, G be a free product of groups A and B with amalgamated subgroups H and K. Let also H be normal in A, K be normal in B, and AutG(H) denote the set of automorphisms of H induced by all inner automorphisms of G. We prove a criterion for G to be residually a \({\cal K}\)-group provided AutG(H) is an abelian group or it satisfies

In this paper, we propose a program for studying Radon transforms in accordance with the computational (numerical) diameter (C(N)D) scheme by applying the uniform distribution theory. The main result is that Radon transforms are qualified as optimal among all possible linear functionals that are used to extract numerical information for generating a computational aggregate.

We give an application of so-called grand Lebesgue and grand Sobolev spaces, intensively studied during last decades, to partial differential equations. In the case of unbounded domains such spaces are defined using so-called grandizers. Under some natural assumptions on the choice of grandizers, we prove the existence, in some grand Sobolev space, of a solution to the equation Pm(D)u(x) = f(x), x

The notion of weekly uniform distribution of arithmetical functions was introduced by W. Narckiewicz. For many functions in various papers, the problem of existence of such distribution was solved, and asymptotic formulas for frequency of hits of function values in residue classes coprime with a module were established. These asymptotic formulas contained, as a rule, only principal part of the asymptotics

We study linear differential games described by a system of linear differential equations with delay subject to certain integral constraints imposed on players’ controls. We propose several approaches to establishing sufficient conditions for the solvability of the linear pursuit problem in the delay system.

We show that if a three-dimensional linear conjugation problem has two particular solutions with coinciding ratios of boundary values of two their components, then its general solution can be obtained in closed form.

We investigate the problem of asymptotic stability for nonstationary switched systems. The direct Lyapunov method is used. It is assumed that for any mode a comparison equation in the Bernoulli form is constructed for the considered system. Sufficient conditions on the nonstationary coefficients of the comparison equations and the switching law are found to guarantee the asymptotic stability of the