The following problems are solved for systems of differential equations with periodic or aperiodic impulses, when uncertain disturbances are taken into account: estimating the set of solutions with initial data from a given ellipsoid in the form of an evolving invariant ellipsoid; the synthesis problem of continuous-impulse control, providing finite time boundedness of the original system with respect

The initial-boundary value problem for the wave equation is considered in the three-dimensional half-space. The oscillation process is initiated by the initial data and the boundary mode. We prove a theorem of existence and uniqueness of the solution; it is presented in the form of the generalized Kirchhoff formula. This work can be considered as a generalization to the three-dimensional case of the

To analyze the deformation process of layered structural elements of inelastic materials, an approach is proposed that makes it easier to solve the problem with complex types of loading. In this method, the package is homogenized, basing on its replacement by a plate with a homogeneous structure through the thickness, the mechanical characteristics of which are determined by identification methods

We solve the problem of constructing a conformal mapping from the upper half-plane onto a circular polygon with cusps (\(2\pi\) angles). We determine preimages of the polygon vertices and accessory parameters using the generalization of P.P. Kufarev's method of finding parameters in the Schwartz–Christoffel integral. The method is based on the chordal Loewner equation. The problem of finding the parameters

A simple right-alternative superalgebra whose even part has zero multiplication is called singular. In the paper, finite-dimensional algebraically generated singular superalgebras with non-degenerate switch are introduced and studied. A special case of such algebras, namely, linearly generated superalgebras, was previously classified by the authors. The construction of the extended double is given

The angle between the asymptotic lines―and generally between the lines of the Chebyshev network―on surfaces of constant curvature is usually analytically interpreted as a solution of the second-order partial differential equation. For surfaces of constant negative curvature in Euclidean space, this is the sine-Gordon equation. Conversely, surfaces of constant negative curvature are used to construct

In this paper, we study maximal operators associated with some singular surfaces in the space \(\mathbb{R}^{3}.\) We prove the boundedness of these operators in \(L^{p}\), when a surface is given by parametric equations.

Let k be an integer greater than or equal to 2. The ring R is said to be k-good if every element of R is the sum of k invertible elements of R. We have showed that the ring of formal row-finite matrices will be k-good if all rings from its main diagonal are k-good. Some applications of this result are given, in particular, to the problem of k-goodness of the ring of endomorphisms of decomposable module

We study a system of equations of dynamics of a thermoviscoelastic continuous medium with an Oldroyd-type rheological relation, which generalizes a Navier–Stokes–Fourier system. In the planar case, we prove the unique existence of strong solutions. The proof is based on the construction of Galerkin approximations and their strong estimates, which provide the corresponding limit passage.

In the half-space, we obtain a coercive a priori estimation of solutions to the boundary value problem for a degenerate pseudodifferential equation. The left-hand side of the equation is the sum of a pseudo-differential operator with degeneracy, constructed by a special integral transform, and the differentiation operator. The a priori estimation is obtained in special weight spaces of Sobolev type

This paper is devoted to the study of the topological dimension of the set of solutions of the operator inclusion of the form \(A(x)\in\lambda F(x)\), where A is a bounded linear surjective operator, and F is a multi-valued Lipschitz map with closed convex images. The resulting theorem establishes a connection between the dimension of the kernel of the operator A and the dimension of the set of solutions

In this paper, we discuss several versions of discrete Ricci flow on closed two dimensional surfaces. As it was shown by Hamilton and Chow, on a closed surface, the Ricci flow converges to the metric of a constant curvature for any initial metric. The discrete version of the Ricci flow introduced by Chow and Luo has the same property. This discretization is defined for so called circle packing metrics

In this paper, we study the initial–boundary value problem for an alpha-model, which describes the motion of weakly concentrated aqueous polymer solutions. We consider the mathematical model with a rheological relation, satisfying the objectivity principle. On the base of the topological approximation approach for studying hydrodynamic problems, we prove the existence of weak solutions to the alpha-model

We study the qualitative dynamics of weak solutions for the modified Kelvin–Voigt model based on the theory of pullback-attractors of trajectory spaces. First, for the studied model, an auxiliary problem is considered, its solvability in the weak sense is proved, and solution estimates are established. Then, on the basis of the obtained estimates of the solutions, a family of trajectory spaces is determined

A priori estimates of weak solutions to a problem of dynamics of viscoelastic continuous medium with memory along trajectories of velocity field and nonhomogenous condition on the boundary is established.

We define a topological characteristic, the fixed point index with respect to a convex closed subset of a Banach space for a class of completely fundamentally restrictible multivalued maps which can be represented as a composition of maps with aspheric values. This class includes, in particular, maps which are condensing with respect to a monotone nonsingular measure of noncompactness. Maps of this

Functional-differential operators with involution \(\nu(x)=1-x\), related to integral operators whose kernels can have points of discontinuity on the lines \(t=x\) and \(t=1-x\) and to Dirac and Sturm–Liouville operators, are used in the study of these operators and various applications. This paper provides a survey on the spectral properties of such operators with involution and their applications

It is shown that the metric on the union of the sets X and Y defines a Hilbert \(C^*\)-module over the uniform Roe algebra of the space X with a fixed metric dX. A number of examples of such Hilbert \(C^*\)-modules are described.

The paper is devoted to some modification of the theory of guiding potentials in such a way that it becomes applicable to investigation of ordinary differential equations on finite-dimensional non-compact smooth manifolds. Two constructions of the topological index on manifolds are described―for the maps of manifolds and for tangent and cotangent vector fields. On the basis of this modification we

In this paper, we study geometric and topological properties of harmonic homogeneous polynomials. Based on the study of zero-level lines of such polynomials on the unit sphere, we introduce the notion of their topological type. We describe topological types of harmonic polynomials up to the third degree inclusive. In the case of complex-valued harmonic polynomials, we consider distributions of their

Finite-dimensional Lie algebras with trivial Killing form are studied. The main properties of the Killing form are specified, a series of examples of Lie algebras with trivial or non-trivial Killing form are given. A classification of Lie algebras of dimension \(\le 5\) with trivial Killing form is given. Some results are found about the space of all Lie algebras with trivial Killing form.

In the work, new concepts are introduced: an admissible index, an almost perfect system of functions. Using these concepts for an arbitrary system of power series of Laurent type, a criterion for the uniqueness of a polyorthogonal polynomial associated with this system is formulated and proved. The explicit form of this polynomial is found, as well as the explicit form of polynomials in the numerator

We study the Tricomi boundary value problem for the Lavrent'ev–Bitsadze advanced-retarded equation of the mixed type. This problem is uniquely solvable.

We consider the multidimensional integral operators with homogeneous kernels of degree \((-n)\) and trigonometric coefficients of a special type. For these operators, we obtain the necessary and sufficient conditions of Fredholmness and we calculate the index.

We propose a form of writing solutions to linear difference equations which eliminates the need for information on the multiplicity of the roots of the corresponding characteristic equations.

In the Timoshenko shear model, we investigate the solvability of a geometrically nonlinear boundary value problem for arbitrary inhomogeneous isotropic shallow elastic shells with free edges. Our method is based on integral representations for generalized displacements containing arbitrary holomorphic functions. The holomorphic functions are found from some boundary conditions on the generalized displacements

We investigate the category of regular coverings of a given smooth principal bundle. A covering map of one principal bundle to another principal bundle is understood as a morphism in the category of principal bundles consisting of covering maps of their structural groups, total spaces and bases. The main results are: the construction of an invariant of a regular covering, which is a subsequence of

In this paper, we state the Darboux problem and give the definition of the Riemann–Hadamard function for a third-order equation with dominant partial derivative (the Bianchi equation). Basing on the possibility of explicitly representing the Riemann function for a certain class of Bianchi equations of the third order, which are equivalent with respect to function, we establish sufficient conditions

We study the inverse problem for a mixed type equation with the Riemann–Liouville and Caputo operator in a rectangular domain. A criterion for the uniqueness and existence of a solution to the inverse problem is established. The solution to the problem is constructed in the form of the sum of a series of eigenfunctions of the corresponding one-dimensional spectral problem. It is proved that the unique

Based on the solution of the first initial-boundary value problem for an inhomogeneous two-dimensional heat equation, we state and study inverse problems, whose right-hand sides contain unknown factors depending on spatial and time variables. Preliminarily, we explicitly construct a solution to the direct initial-boundary-value problem. We prove the uniqueness of the solution to direct and inverse

In this paper, series of exponential monomials are considered. We study conditions on sequences of indices such that the existence domains of the sum of these series coincide with their convergence domains.

Let \(\mathbb{R}^n\) be a Euclidean space of dimension \(n\geq 2\). For a domain \(G\subset \mathbb{R}^n\), we denote by \(V_r(G)\) the set of functions \(f\in L_{\mathrm{loc}}(G)\) having zero integrals over all closed balls of radius r contained in G (if domain G does not contain such balls, we set \(V_r(G)=L_{\mathrm{loc}}(G)\)). Let E be a nonempty subset of \(\mathbb{R}^n\). In this paper we study

We introduce the notion of an L-massive subset in a noncompact Riemannian manifold and study properties of such subsets. It is proved that a semilinear elliptic equation on a noncompact Riemannian manifold has a nontrivial bounded solution if and only if there exists an L-massive subset in this manifold. A similar assertion is also proved for solutions of semilinear equations with finite energy integral

In this paper, we develop a new method for studying the inhomogeneous vector Riemann–Hilbert boundary value problem (which is also called the Riemann boundary value problem) in the Wiener algebra of order two. The method consists in reducing the Riemann problem to a truncated Wiener–Hopf equation (to a convolution equation on a finite interval). The idea of the method was proposed by the author in

Avkhadiev's classes consist of holomorphic functions with a two-sided restriction on the module of the derivative. We study these classes in domains different from the unit disk. For the images of the domains under the mappings of Avkhadiev's classes, we find conditions providing the uniqueness of critical point of the conformal radius. We use an analogue of the concept that Lehto applied to study

The purpose of this paper is to give new sufficient conditions for solving numerically a generalized spectrum problem known in the literature as the problem of spectrum approximation of quadratic operator pencils. The new sufficient conditions obtained here are weaker than the norm convergence and the collectively compact convergence, thus they extend some previous results existing in the literature

The approximate calculation of integrals is a common part of research in various fields of mathematics, primarily in the theory of approximations and computational mathematics. In its turn, within the theory of numerical integration, distinctions take place depending on the features of the integrand, the scale of which is “Quadrature (cubature) formulas” and “Theory of oscillations”. This article belongs

We propose an algorithm for construction of quadrature formulas for linear operators acting on periodic functions. For analytic functions, the order of accuracy of quadrature formulas grows unboundedly with the growth of the number of the grid nodes. Within rather general restrictions on the kernels of linear operators, an exponential estimate of a quadrature formula is proved. To exemplify, we find

In this paper, we consider the problem of recovery of solutions to a generalized Cauchy–Riemann system in an unbounded subdomain of a multidimensional space from their values on a part of the domain boundary. With the help of the Carleman–Yarmukhamedov matrix method we construct an approximate solution to this problem.

We introduce the notion of a completely solvable complex real-holomorphic system of biholomorphisms and prove that such a system forms a discrete dynamical system. Then we define functional invariants and find the dimension of the basis of nondegenerate absolute invariants for the class of systems in question in general position. Finally, we obtain criteria of boundedness of the number of compact invariant

Based on the synthesis of the method of vector Lyapunov functions and the method of complete sets of guiding functions, we obtain sufficient conditions for the existence of Poisson bounded solutions to systems of differential equations, as well as solutions which are partially bounded in the Poisson sense.

We consider the inverse boundary value problem of aero-hydrodynamical lattices. It is necessary to find the shape of the profile of a lattice streamlined by a potential flow of an incompressible non-viscous liquid, when the distribution of the velocity value on the profile is given as a function of the abscissa of the profile point (chord diagram); the lattice period and the ratio of complex liquid

In the present work, using the Carleman function, a harmonic function and its derivatives are restored by the Cauchy data on a part of the boundary of the region. It is shown that the effective construction of the Carleman function is equivalent to the construction of a regularized solution to the Cauchy problem. We assume that a solution to the problem exists and is continuously differentiable in

In this paper, we establish some generalized inequalities of the Hermite–Hadamard type using fractional Riemann–Liouville integrals for the class of s-convex functions in the first and second sense. We assume that second derivatives of these functions are convex and take on values at intermediate points of the interval under consideration. We prove that this approach reduces the absolute error of Hadamard-type

In the unit disk, we consider the Hilbert boundary value problem. Its coefficient is assumed to be Hölder continuous everywhere on the unit circle excluding a finite set of points. At these points, the argument of the coefficient has non-removable discontinuity of logarithmic order. We obtain formulas for the general solution and fully describe the solvability of the problem in the class of functions

It is proved: if \(\phi(\tau,\xi)\) is a scalar continuous real function of arguments \(\tau\in [a_{(n-1)},\ b_{(n-1)}]\subset R^{n-1},\) \(\xi \in [a,\ b]\subset R^{1}\) and \(\phi(\tau,a)\phi(\tau,b)<0\) for all \(\tau,\) then for all \(\varepsilon >0\) there exists a continuous function \(\phi_{0}(\tau,\xi)\) such that \(|\phi(\tau,\xi)-\phi_{0}(\tau,\xi)|<\varepsilon,\) and the equation \(\phi_{0}(\tau

The double- and simple-layer potentials play an important role in solving boundary value problems for elliptic equations. The desired solution represents a potential of a certain layer with unknown density. One finds it with the help of the theory of Fredholm integral equations of the second kind. The potential, in turn, is expressed via the fundamental solution to the given elliptic equation. At present

In this paper, we consider the functions, which are represented as trigonometric series with Fourier coefficients general monotone with respect to subsequences. For these functions, estimates of the norms and modules of smoothness are given.

We study a system of nonlinear singular integral equations with a sum-difference kernel on the positive half-line. Such a system occurs (in various representations) in many branches of mathematical physics and applied mathematics. In particular, one encounters a system of equations with a kernel representing a Gaussian distribution and with a power nonlinearity in the dynamic theory of p-adic open-closed

We (completely) determine those natural numbers n for which the full matrix ring \(\mathbb{M}_n(\mathbb{F}_2)\) and the triangular matrix ring \(\mathbb{T}_n(\mathbb{F}_2)\) over the two elements field \(\mathbb{F}_2\) are either n-torsion clean or are almost n-torsion clean, respectively. These results somewhat address and settle a question, recently posed by Danchev–Matczuk in Contemp. Math. (2019)

This work continues a series of author's papers devoted to the problems of the existence and uniqueness of positive solutions of boundary value problems for nonlinear second order functional-differential equations. We study a boundary value problem for a nonlinear second order functional-differential equation with homogeneous boundary conditions. Based on the theory of semi-ordered spaces and with

Let \(\mathcal{K}\) be a root class of groups and G be an HNN-extension of a group B with subgroups H and K associated by an isomorphism \(\varphi\colon H \to K\). We obtain certain sufficient conditions for G to be residually a \(\mathcal{K}\)-group provided the set \(\{h^{-1}(h\varphi) \mid h \in H\}\) is a normal subgroup of B or there exists an automorphism \(\alpha\) of B such that \(H\alpha =

We consider one-sided Grubbs's statistics for a normal sample of the size n. These statistics are extreme studentized deviations of the observations from the sample mean. One abnormal observation (outlier) is assumed in the sample, its number is unknown. We consider the case when the outlier differs from other observations in values of population mean and dispersion, i. e., shift and scale parameters

We show that some BMO-type spaces are invariant with respect to Hausdorff operators of a special kind (weighted Hardy–Cesáro operators). Moreover, we establish the necessary and sufficient conditions for the boundedness of such operators in spaces of functions of generalized bounded variation. We study the invariance of Hölder–Lipschitz spaces with respect to these operators.

The aim of research is to obtain new estimates of extent of irrationality for values \(\arctan \frac{1}{5}, \arctan\frac{1}{3}.\) In this article, we constructed a new integral for getting an irrationality measure of \(\arctan \frac{1}{5}\) based on the idea from work of K. Wu, 2002. We investigated the linear form generated by this integral and found that it allows to get a better estimate for this

The work is devoted to the study of derivations in group algebras using the results of combinatorial group theory. A survey of old results is given, describing derivations in group algebras as characters on an adjoint action groupoid. In this paper, new assertions are presented that make it possible to connect derivations of group algebras with the theory of ends of groups and in particular the Stallings

In this paper, we study the homogeneous vector Riemann boundary value problem (the factorization problem) from a new point of view. Namely, we reduce the Riemann problem to the truncated Wiener–Hopf equation (a convolution equation in a finite interval). We establish a connection between the problem of the factorization of a matrix function in the Wiener algebra of order two and the truncated Wiener–Hopf

Following up on the results obtained earlier, a refined nonlinear model of static deformation of sandwich plates with transversal-soft core and facings with low stiffness of transverse shear and transverse compression is constructed for the case of cylindrical bending. It is based on the use of linear approximations in thickness for deflections of the external layers, cubic approximation in thickness

According to the theory of Goldstone bosons, one of the sources of arion radiation is electromagnetic fields. However, the retarded solution of the arion field equations turns out to be inconvenient to apply, since the integrand is not equal to zero in the entire space and there are no small parameters in the problem by whose powers it can be decomposed. In this paper, based on the proved theorems

In this paper, we study the first boundary problem for a mixed-type elliptic-hyperbolic equation of the second kind in a rectangular domain. We construct the problem solution as the sum of a biorthogonal series and prove the uniqueness criterion for it. When proving the existence of the problem solution, we encounter the problem of small denominators. In this connection, we establish estimates for