In the case where either r = 2, k = 1 or r = 3, k = 1, 2, for any q, p ≥ 1, β ∈ [0, 2π), and a Lebesgue-measurable set B ⊂ I2π ≔ [−π/2, 3π/2], μB ≤ β, we prove a sharp Kolmogorov–Remez-type inequality \( {\left\Vert {f}^{(k)}\right\Vert}_q\le \frac{\left\Vert \varphi r-k\right\Vert q}{E_0{{\left(\varphi r\right)}_L^{\alpha}}_p\left({I}_{2\uppi}/{B}_{2m}\right)}{\left\Vert f\right\Vert}_{L_p}^{\alp

We describe the asymptotic behavior of the logarithms of entire functions of improved regular growth with zeros on a finite system of rays in the metric of Lq[0, 2𝜋].

We study translation-invariant Gibbs measures for the Blume–Capel model with wand on a Cayley tree of order k. We find the exact critical value 𝜃cr = 1 such that, for 𝜃 ≥ 𝜃cr , there exists a unique translation-invariant Gibbs measure and, for 0 < 𝜃 < 𝜃cr , there are exactly three translation-invariant Gibbs measures in the presence of a wand in the analyzed model. In addition, we study the problem

We prove that each totally disconnected closed subset E of a domain G in the complex plane is removable for analytic functions f(z) defined in G \ E and such that, for any point z0 𝜖 E, the real or imaginary part of f(z) vanishes at z0.

We study three-dimensional trans-Sasakian manifolds admitting η-Ricci solitons. Actually, we investigate manifolds whose Ricci tensor satisfy some special conditions, such as cyclic parallelity, Ricci semisymmetry, and 𝜙-Ricci semisymmetry, after reviewing the properties of the second-order parallel tensors on these manifolds. We determine the form of the Riemann curvature tensor for trans-Sasakian

We study the relationship between the class of entire functions of completely regular growth of order 𝜌 and the class of entire functions with bounded l-index, where l(z) = |z|𝜌−1 + 1 for |z| ≥ 1. Possible applications of these functions in the analytic theory of differential equations are considered. We formulate three new problems on the existence of functions with given properties that belong

We establish approximation properties of Cesàro (C,−α,−β) means with α, β 𝜖 (0, 1) for the Vilenkin–Fourier series. This result enables one to establish a condition sufficient for the convergence of the means \( {\sigma}_{n,m}^{-\alpha, -\beta } \) (x, y, f) to f(x, y) in the Lp-metric.

We approximate ε-isometries of the unit sphere in \( {\ell}_2^n \) and \( {\ell}_{\infty}^n \) by linear isometries.

We obtain vector analogs of the Abel and Dirichlet criteria.

We consider the Stark operator \( T=-\frac{d^2}{dx^2}+x+q(x) \) on the semiaxis 0 ≤ x < ∞ with Dirichlet boundary condition at the origin. By the method of transformation operators, we study the direct and inverse spectral problems, deduce the main integral equation for the inverse problem, and prove that this equation is uniquely solvable. We also propose an effective algorithm of reconstruction of

We introduce a (p, q)-analog of the poly-Euler polynomials and numbers by using the (p, q)-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We present several combinatorial identities and properties of these new polynomials and also show some relations with (p, q)-poly-Bernoulli polynomials and (p, q)-poly-Cauchy polynomials. The (p, q)-analogs

We prove some results on the existence and uniqueness of fixed points defined on a b-metric space endowed with an arbitrary binary relation. As applications, we obtain some statements on the coincidence of points involving a pair of mappings. Our results generalize, extend, modify and unify several well-known results and, especially, the results obtained by Alam and Imdad [J. Fixed Point Theory Appl

We consider a boundary-value problem for degenerate equations with discontinuous coefficients and establish the unique strong solvability (almost everywhere) of this problem in the corresponding weighted Sobolev space.

We deal with the existence result for nonlinear elliptic equations of the form Au + g(x, u,∇u) = f, where the term –div (a(x, u, ∇u)) is a Leray–Lions operator from a subset of \( {W}_0^1{L}_M\left(\Omega \right) \) into its dual. The growth and coercivity conditions on the monotone vector field a are prescribed by an N-function M, which not necessarily satisfies a Δ2-condition. Therefore, we use Orlicz–Sobolev

We study the solvability of the nonlocal boundary-value problem for a differential equation with weak nonlinearity. By using the Nash–Mozer iterative scheme, we establish the solvability conditions for the posed problem in the Hilbert H¨ormander spaces of functions of several real variables, which form a refined Sobolev scale.

Assume that G is a finite group, π(G) = {s} ∪ σ, s > 2, Σ is a set of Sylow σ-subgroups in which one subgroup is taken for each pi 2 σ, and R(G) is the largest normal soluble subgroup in G (soluble radical of G). Moreover, suppose that each Sylow pi-subgroup Gpi 𝜖 Σ normalizes the s-subgroup T(i) ≠ 1 of the group G. In this case, we establish the conditions under which s divides |R(G)|.

Let G be a p-soluble group. Then G has a subnormal series whose factors are either p′-groups or Abelian p-groups. The smallest number of Abelian p-factors in all subnormal series of G of this kind is called the derived p-length of G. A subgroup H of the group G is called a Fitting subgroup if H ≤ F(G). The existence of a functional dependence of the estimate of derived p-length of a p-soluble group

We establish constructive conditions for the solvability of a linear Noetherian boundary-value problem for a matrix difference equation and propose a procedure of construction of its solutions. We suggest an original scheme of regularization of a linear Noetherian boundary-value problem for a linear degenerate system of difference equations.

We classify translation surfaces in isotropic geometry with arbitrary constant isotropic Gaussian and mean curvatures under the condition that at least one translating curve lies in the plane.

We consider a queueing system of the M/M/1 type with repeated claims in the case where the service rate depends on the loading of the system, i.e., on the number of claims in the queue waiting for service. We establish the existence conditions and the formulas for the ergodic distribution of the number of claims in the system with bounded and unbounded queues of repeated claims.

We deal with additive arithmetical semigroups and present old and new proofs for the distribution of zeros of the corresponding ζ-functions. We use these results to prove prime number theorems and a Selberg formula for semigroups of this kind.

Let p : \( \tilde{N}\to N \) be a finite covering space for nonorientable surfaces, where \( \upchi \left(\tilde{N}\right)<0 \). We study whether or not p has the Birman–Hilden property.

We establish some new extensions of Hermite–Hadamard inequality for fractional integrals and present several applications for the Beta-function.

We extend the domain of applicability of the concept of (1, 𝛼)-derivations in 3-prime near-rings by analyzing the structure and commutativity of the near-rings admitting (1, 𝛼)-derivations satisfying certain differential identities.

We study the problem of approximation of functions (ψ, β)-differentiable (in the Stepanets sense) whose (ψ, β)-derivative belongs to the class H𝛼 by biharmonic Poisson integrals in the uniform metric.

The Editor-in-Chief has retracted the article [1] because it has been published previously [2] and is therefore redundant. [The author agrees with this retraction.]

We prove the unique solvability and obtain the explicit expression for the classical solution of mixed problem in a cylindrical domain for one class of multidimensional hyperbolic-parabolic equations.

We use variational methods to study the existence and multiplicity of solutions for a nonhomogeneous p-Kirchhoff equation with the critical Sobolev exponent.

On the basis of a new approach, we prove the uniqueness theorem and construct Lavrent’ev’s regularizing operators for the solution of nonclassical linear Volterra integral equations of the first kind with nondifferentiable kernels.

We establish effective upper estimates for the maximum products of the inner radii of mutually disjoint domains in (n,m)-radial systems of points of the complex plane for all possible values of a parameter γ. We also establish conditions under which the structure of points and domains is not important for our investigations.

We study generalized convolutions for the Fourier sine and Kontorovich–Lebedev transforms$$ \left(h\underset{F_s,K}{\ast }f\right)(x) $$ in a two-parameter function space \( {L}_p^{\alpha, \beta}\left({\mathrm{\mathbb{R}}}_{+}\right) \). We obtain several estimates for the norms and prove a Young-type inequality for this generalized convolution. We also impose necessary and sufficient conditions on

We study the problem of existence and uniqueness of the solution of a three-point boundary-value problem for a differential equation of fractional order. Further, we investigate various kinds of the Ulam stability, such as the Ulam–Hyers stability, the generalized Ulam–Hyers stability, the Ulam–Hyers–Rassias stability, and the generalized Ulam–Hyers–Rassias stability for the analyzed problem. We also

We investigate the solution of the inverse problem for a linear two-dimensional parabolic equation with periodic boundary and integral overdetermination conditions. Under certain natural regularity and consistency conditions imposed on the input data, we establish the existence, uniqueness of the solution, and its continuous dependence on the data by using the generalized Fourier method. In addition

We prove a Hinich-type theorem on the existence of a model structure on a category related by adjunction to the category of differential graded modules over a graded commutative ring.

We introduce a concept of A-strongly statistical convergence for sequences of complex numbers, where A = (ank)n,k∈ℕ is an infinite matrix with nonnegative entries. A sequence (xn) is called strongly convergent to L if \( \underset{n\to \infty }{\lim }{\sum}_{k=1}^{\infty }{a}_{nk}\left|{x}_k\right.-L\left|=0\right. \) in the ordinary sense. In the definition of A-strongly statistical limit, we use

The averaging method is applied to the investigation of the problem of existence of solutions of boundary-value problems for systems of differential and integrodifferential equations. It is shown that if the averaged boundary-value problem has a solution, then the original problem also has a solution. Note that, in this case, the system obtained as a result of averaging of a system of integrodifferential

The ideas of the method of fictitious domains and homotopy are combined with an aim to reduce the solution of boundary-value problems for multidimensional partial differential equations (PDE) in domains of any shape to an exponentially convergent sequence of PDE in a parallelepiped (or, in the 2D case, in a rectangle). This enables us to decrease the required computer time due to the elimination of

We consider spectral problems related to small vibrations of a tree formed by Stieltjes strings. It is shown that the minimum number of distinct eigenvalues of this problem is equal to the maximum length (measured as the number of point masses) of paths in this tree.

We study the critical point equation (CPE) conjecture on almost Kenmotsu manifolds. First, we prove that if a three-dimensional (k, μ)'-almost Kenmotsu manifold satisfies the CPE, then the manifold is either locally isometric to the product space ℍ2(−4) × ℝ or the manifold is a Kenmotsu manifold. Further, we prove that if the metric of an almost Kenmotsu manifold with conformal Reeb foliation satisfies

We propose an S-version of Nakayama’s lemma. Let R be a commutative ring, let S be a multiplicative subset of R, and let M be an S-finite R-module. Also let I be an ideal of R. We show that if there exists t ∈ S such that tM ⊆ IM, then (t' + a)M = 0 for some t' ∈ S and a ∈ I. We also present an analog of Nakayama’s lemma for a w-ideal and an S-w-finite R-module, where R is an integral domain. Thus

We study a modified Cauchy problem for the degenerate hyperbolic equation of the second kind. First, we find the representations of the general solution of the analyzed equation for α ≤ 1. Then, by using these representations, we formulate modified Cauchy problems for all real values of α and deduce the formulas for the solution of the analyzed problems. Further, it is shown that the obtained solutions

We present sufficient conditions for the tautness modulo an analytic hypersurface of Hartogs-type domains ΩH(X) and Hartogs–Laurent-type domains Σu,v(X). We also propose a version of Eastwood’s theorem for tautness modulo an analytic hypersurface.

Five mock theta functions of S. Ramanujan are combinatorially interpreted by means of certain associated lattice path functions and antihook differences. These results provide new combinatorial interpretations of five Ramanujan mock theta functions. By using a bijection between the associated lattice path functions and the (n + t)-color partitions and then between the associated lattice path functions

We establish new properties of the solutions of a functional-differential equation with linearly transformed argument.

We construct classes of equations in a Hilbert space whose sets of solutions are invariant under a group isomorphic to a one-parameter group of unitary operators. It is shown that the unbounded solutions of these equations are unstable. The applications of the obtained results to nonlinear mechanics are presented.

We establish strong and weak Hardy–Littlewood–Sobolev inequalities for the subadditive operators majorized by operators from a certain class of integral convolutions of the Riesz-potential type with almost monotone kernels generated both by operators of ordinary shift and by operators of generalized shift associated with the differential Laplace–Bessel operator.

A ring R is called clean (resp., uniquely clean) if every element is (uniquely represented as) the sum of an idempotent and a unit. A ring R is called strongly P-clean if every its element can be represented as the sum of an idempotent and a strongly nilpotent element, which are commuting. The class of strongly P-clean rings is a subclass of classes of semi-Boolean and strongly nil clean rings. A ring

For periodic functions of one variable in the metric spaces LΨ [0, 2π], we establish an analog of Marchaud’s inequality for multiple modules of continuity.

The problem of evaluation of the norm of a composition operator acting between the spaces of holomorphic functions is quite difficult. In the Hardy and weighted Bergman spaces, the norm of the composition operator is unknown even for the choice of a fairly simple symbol. We compute the operator norm of the composition operator acting between the space of Cauchy transforms and Zygmund-type spaces. We

We find a criterion for a commutative ring to be a weakly clean UNI ring, as well as a criterion for an exchange ring to have strongly invo-clean unit group. These two assertions somewhat improve earlier author’s results published in [Ukr. Math. J. (2017)] and [Internat. J. Algebra (2017)]

We consider a nonlocal problem for a system of partial differential equations of higher order with pulsed actions. By introducing new unknown functions, the analyzed problem is reduced to an equivalent problem including a nonlocal problem for the impulsive system of the second-order hyperbolic equations and integral relations. We propose an algorithm for finding the solutions of the equivalent problem

We recall the notion of generalized hyperbolic angle between proper and improper straight lines, which is only available in Hungarian and Esperanto. Then we summarize the generalized hyperbolic conic sections. After the investigation of real conic sections and their isoptic curves in the hyperbolic plane H2, we consider the problem of isoptic curves of generalized conic sections in the extended hyperbolic

By the method of integral and hybrid integral transforms in combination with the method of principal solutions (matrices of influence and Green matrices), we construct the integral representation of the unique exact analytic solution of a hyperbolic boundary-value problem of mathematical physics for a piecewise homogeneous hollow cylinder.

We study the asymptotic behavior of solutions to a class of abstract nonlinear stochastic evolution equations with additive noise that covers numerous 2D hydrodynamical models, such as the 2D Navier–Stokes equations, 2D Boussinesq equations, 2D MHD equations, etc., and also some 3D models, like the 3D Leray 𝛼-model. We prove the existence of random attractors for the associated continuous random dynamical

We study and solve one class of discrete matrix equations with cubic nonlinearity. The existence of a two-parameter family of monotone and bounded solutions is proved. Under certain additional conditions, we determine the asymptotic behavior of the constructed solutions. The obtained results are extended to the corresponding inhomogeneous discrete matrix equations and to some more general cases of

The conditions of existence and asymptotic representations as t ↑ 𝜔 (𝜔 ≤ + ∞) are obtained for one class of solutions of nonautonomous differential equations of the nth order asymptotically close, in a certain sense, to equations with regularly varying nonlinearities.

We consider a one-dimensional Stark operator on the semiaxis with Dirichlet boundary condition at the origin. The asymptotic behavior of eigenvalues at infinity is analyzed.

We study the relationships between the properties of nonperiodic groups and the norms of their decomposable subgroups. The influence of restrictions imposed on the norms of decomposable subgroups and on the properties of the group is analyzed under the condition that this norm is non-Dedekind and locally nilpotent. We also describe the structure of nonperiodic locally soluble groups for which the norm

We present a series of definitions and properties of lifting dynamical systems (LDS) corresponding to the notion of deterministic diffusion. We give heuristic explanations of the mechanisms of formation of deterministic diffusion in LDS and the anomalous deterministic diffusion in the case of transportation in long billiard channels with spatially periodic structures and nonideal reflection law. The

Our main aim is to introduce an iterative algorithm for the approximation of a common solution to a splitequality problem for finite families of variational inequalities and the split equality fixed-point problem. By using our iterative algorithm, we state and prove a strong convergence theorem for the approximation of an element in the intersection of the set of solutions of the split-equality problem