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.

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

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 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 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

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

We establish the structure of normal subgroups in θ-Frattini extensions, where θ is a subgroup functor. For a local Fitting structure \( \mathfrak{F} \) containing all nilpotent groups, it is shown that, in a soluble group, the crossing of \( \mathfrak{F} \)-abnormal maximal θ -subgroups not containing \( \mathfrak{F} \)-radicals and not belonging to \( \mathfrak{F} \) coincides with the crossing of

A recurrence algorithm for finding particular solutions of the resonant equation of the fourth order connected with the generalization of Laguerre and Legendre polynomials is constructed and substantiated. For this purpose, we use the general theorem on the representation of particular solutions of resonant equations in Banach spaces proved by Makarov in 1976. An example of the general solution of

For linear functional-differential equations of retarded and neutral types with infinitely many deviations and self-adjoint operator coefficients, we establish necessary and sufficient conditions for the absolute instability of the trivial solutions.

The main aim of the present paper is to investigate the conditions under which the nonnegative solutions blow-up for the parabolic problem \( \frac{\partial u}{\partial t}=-{\left(-\Delta \right)}^{\frac{\alpha }{2}}u+\frac{c}{{\left|x\right|}^{\alpha }}u\kern1em \mathrm{in}\kern1em {\mathrm{\mathbb{R}}}^{\mathrm{d}}\times \left(0,T\right), \) where 0 < α < min(2, d), \( {\left(-\Delta \right)}^{\frac{\alpha

We propose a method for the construction of exact solutions to the nonlinear heat equation based on the classical method of separation of variables and its generalization. We consider substitutions, which reduce the nonlinear heat equation to a system of two ordinary differential equations and construct the classes of exact solutions by the method of generalized separation of variables.

We study the asymptotic behavior of the solutions of a boundary-value problem with boundary jumps for linear integrodifferential equations of the third order with small parameters at the two higher derivatives. The asymptotic convergence of the solution of a singularly perturbed integrodifferential boundary-value problem to the solution of the corresponding modified degenerate boundary-value problem

We study Virasoro-type extensions of the q-deformed Witt Hom–Lie superalgebras. Moreover, we provide the cohomology of q-deformed Witt–Virasoro superalgebras of the Hom type.

We study a second-order parallel symmetric tensor in an 𝒮-manifold and show that there is no semiparallel hypersurface in the 𝒮-space forms \( {\tilde{M}}^{2n+s}(c) \) with c ≠ s.

We consider continuous-time risk models with m-dependent claim sizes and constant interest rate. Under certain special conditions, we obtain the upper bound for the infinite-time ruin probability. Our approach is based on the martingale methods.

We establish the conditions of existence and determine the general structure of solutions of resonant and iterative equations in Banach spaces and propose their algorithmic realization.

We study the existence and uniqueness of solutions for an analog of the Frankl-type boundary-value problem for a parabolic-hyperbolic-type equation. The uniqueness of the solution is proved by using the principle of extremum, whereas the existence is proved by the method of integral equations.

We introduce a new subclass of meromorphic Bazilevič-type functions defined with the help of a differential operator. We study some interesting properties of functions from this class, such as the arc length, the growth of coefficients, and the integral representations of functions.

Dzyadyk’s method of generalized moment representations is used to construct and study bivariate twopoint Padé-type approximants.

For systems hyperbolic in Shilov’s sense whose coefficients are continuous functions of time, we study the properties of the Green function in S-type spaces. For systems of this kind in the indicated spaces, we prove that the Cauchy problem is correctly solvable. It is shown that, for any β > 1, the space \( {S}_0^{\beta \prime } \) of Gelfand and Shilov distributions from the class of well-posedness

We study the problem of nonoverlapping domains with free poles on radial systems. Our main results strengthen and generalize several known results obtained in the investigation of this problem earlier.

We establish the exact-order estimates for the approximation of the classes \( {S}_{1,\theta}^rB\left({\mathrm{\mathbb{R}}}^d\right) \) by entire functions of exponential type such that the supports of their Fourier transforms lie in a step hyperbolic cross. The error of approximation is estimated in the metric of the Lebesgue space Lq(ℝd), 1 < q ≤ ∞ .

We establish necessary and sufficient conditions for the existence of dynamic regulators guaranteeing the prescribed estimation of the weighted level of damping of bounded disturbances and the asymptotic stability of linear descriptor systems. An algorithm for the construction of these regulators in the problems of robust stabilization and generalized H∞-optimization is proposed for the descriptor

We propose a classification of finite local nearrings with multiplicative Shmidt group. Moreover, it is shown that there are no nearrings with identity on the Shmidt groups.

Our aim is to establish some new integral formulas involving -functions associated with Laguerretype polynomials. We also show that the main results presented in the paper are general by demonstrating 18 integral formulas that involve simpler known functions, e.g., the generalized hypergeometric function pFq in a fairly systematic way.

For systems of linear differential equations whose dimension can be lowered, we estimate the growth of meromorphic vector solutions. As an essentially new feature, we can mention the fact that no additional restrictions are imposed on the order of growth of the coefficients of the system.

We propose a mathematical model for the diffusion of opinions, which eventually leads to the attainment of the state of consensus. The theory of conflict dynamical systems with attractive interaction is used for the construction of a model. The behavior of the model in the case of making binary decisions is described in detail and the behavior of trajectories in the decision-making model with many

The correct solvability of a nonlocal multipoint (in time) problem for the evolution equations with differentiation operators of infinite order is established for an infinite time interval and an initial function, which is an element of the space of generalized functions of the type W′. The properties of the fundamental solution and the behavior of the solution as t → +∞ are investigated.

We establish asymptotic bounds for the solutions of functional and functional-differential equations with linearly transformed arguments and constant delays.

We determine some classes of left modules satisfying the radical formula in a noncommutative ring. We also show that, under a certain condition, a finitely generated module over an HNP -ring (a generalization of the Dedekind domain) both satisfies the radical formula and can be decomposed into a direct sum of torsion and extending modules.

We propose a numerical method for the solution of linear boundary-value problems for systems of integrodifferential equations. The method is based on the approximation of the integral term by a cubic spline and the reduction of the original problem to a linear boundary-value problem for a system of loaded differential equations. We also propose new algorithms for finding the numerical solutions and

We obtain new conditions for the existence of bounded solutions of nonlinear discrete equations with the use of local linear approximation of these equations.

Following the line of investigation in [Linear Algebra Appl., 487, 22–42 (2015)], for y ∈ ℝ and a sequence x = (xn) ∈ ℓ∞, we define a new notion of density δg with respect to a weight function g of indices of the elements xn close to y, where g : ℕ → [0, ∞)is such that g(n) → ∞and n/g(n)0. We present the relationships between the densities δg of indices of (xn) and the variation of the Cesàrolimit