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

Problems about continuability of solutions to real autonomous systems of equations in total differentials and about reducibility of such systems to many-dimensional dynamical systems are investigated. The reducibility criterion is proved. We receive conditions at which the reducible total differential equation system has orbits–torus-cylinders. We give examples. We note when the received outcomes can

In this paper, we consider natural generalizations of properties of the linkedness of families (of sets) and the supercompactness of topological spaces. In the first case, we analyze the “multiple” linkedness, assuming the nonemptiness of the intersection of sets from subfamilies, whose cardinality does not exceed some given positive integer \(\mathbf{n}\). In the second case, we study the question

With the help of Cauchy-type integrals, a new derivation of integral equations for solving logarithmic potential problems is given. A variant of the inverse logarithmic potential problem with two starlike solutions is analyzed; it contains fewer parameters than those considered by I.M. Rapoport. A criterion for the interior simple layer potential to be identically constant is obtained.

The aim of the paper is to describe the structure of complete Lorentzian foliations \((M, F)\) of codimension two on n-dimensional closed manifolds. We prove that a foliation \((M, F)\) is either Riemannian or of constant transversal curvature and describe its structure. We obtain a criterion which reduces the chaos problem in a foliation \((M, F)\) both to the chaos problem of the smooth action of

It is known that when a multivariate probability distribution has a “big” conditional quantile that is fully reproducible when narrowed to uni-variate quantiles, then the respective quantile differential equation is completely integrable. Yet the converse is not true in general. In this paper, we show that, provided that certain conditions are satisfied, from the given completely integrable quantile

One-dimensional movement of tensioned viscous material stream is considered. With the help of the laws of mass and momentum conservation it is shown that the stationary flow is characterized by exponential decrease of stream width and corresponding increase of stream velocity. Equations for perturbations of station variables are derived, which depend on the defining parameter. This parameter characterizes

A problem for a composite differential equation with singular integro-functional operators is investigated. The theorems of uniqueness and existence of a twice continuously differentiable solution are proved.

The work is devoted to the proof of the uniqueness and existence of solution to local and nonlocal problems with an integral gluing condition for a loaded parabolic-hyperbolic type equation with differential and integral operators of fractional order, in which the trace of the solution appears in the Erdelyi–Kober integral operator. Using the method of energy integrals, the uniqueness of the solution

In this paper, we consider dynamic properties of a delay logistic equation. In the first section, by using bifurcation methods we study the local behavior of solutions to the initial equation. We pay the main attention to studying the dependence of dynamic properties of solutions on small perturbations with a large delay. We construct special nonlinear parabolic-type equations, whose local dynamics

In this work, we study the general solution of a second-order partial differential equation in a Banach space with a potential singular on the manifolds.

We consider a three-dimensional Riemann boundary value problem which has two particular solutions such that, for one of the components, the ratios of the boundary values coincide on the conjugation contour. It is shown that, under certain restrictions on the elements of the matrix coefficient of the problem, its general solution can be obtained in a closed form.

Let \(\Gamma\) be a closed smooth Jordan curve in the complex plane \(\mathbb{C}\),G be a bounded domain in \(\mathbb{C}\) with the boundary \(\Gamma\), and let \(\overline{G}=G\cup\Gamma\). We study functions that are continuous in \(\mathbb{C}\setminus G\) and harmonic in \(\mathbb{C}\setminus\overline{G}\) that grow more slowly than the function \(|z|^2\) at \(z\to\infty\). It is shown that, if

In this paper, we prove the possibility of using the inverse scattering problem method for integrating an mKdV equation with a self-consistent source in the class of finite density functions in the case when the corresponding spectral problem has moving simple eigenvalues.

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