It is shown that typical compact submanifolds of Rⁿ are nowhere differentiable with integer box dimensions.

We consider a discrete model of operation of an insurance company whose initial capital can take any integer value. In this statement, the problem of nonruin probability is naturally solved by the Wiener – Hopf method. ...

We represent a solution of an inhomogeneous second-order differential equation with two delays by using matrix functions under the assumption that the linear parts are given by permutable matrices.

We construct a faithful self-similar action of the discrete Heisenberg group with the following properties: This action is self-replicating, finite-state, level-transitive, and noncontracting. Moreover, there exist orbital ...

The separation problem for a family of Borel and Baire G-powers of shift measures on R is studied for an arbitrary infinite additive group G using the technique developed in [Kuipers L., Niederreiter H. Uniform distribution ...

We obtain certain subordinations and superordinations results involving a new operator. By means of the new introduced operator Cλp,n(a, c)f(z), for certain multivalent functions in the open unit disc, we establish ...

We prove that certain means of quadratic partial sums of the two-dimensional Walsh–Fourier series are uniformly bounded operators acting from the Hardy space Hp to the space Lp for 0 < p < 1.

For a group G and a natural number m, a subset A of G is called m-thin if, for each finite subset F of G, there exists a finite subset K of G such that |Fg ∩ A| ≤ m for all g ∈ G \ K. We show that each m-thin subset of an ...

We prove that if the metric of a 3-dimensional α-Sasakian manifold is a Ricci soliton, then it is either of constant curvature or of constant scalar curvature. We also establish some properties of the potential vector field ...