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