We study the complexity of initial value problems for Banach space valued ordinary differential equations in the randomized setting. The right- hand side is assumed to be r-smooth, the r-th derivatives being ϱ-Hölder ...

Sato introduced the τ-function to describe solutions to a wide class of completely integrable differential equations. Later Segal–Wilson represented it in terms of the relevant integral operators on Hardy space of the unit ...

The controllability of a slowly rotating beam clamped to a disc is considered. It is assumed that at the beginning the beam remains at the position of rest and it is supposed to rotate by the given angle to achieve a desired ...

An operator G: X → Y is said to be a Daugavet center if ||G + T|| = ||G|| + ||T|| for every rank-1 operator T: X → Y . The main result of the paper is: if G: X →! Y is a Daugavet center, Y is a subspace of a Banach space ...

We review the relations between distance matrices and isometric embeddings and give simple proofs that distance matrices de ned on euclidean and spherical spaces have all eigenvalues except one nonpositive. Several ...

We study the filters, such that for convergence with respect to this filters the Lebesgue dominated convergence theorem and the Egorov theorem on almost uniform convergence are valid (the Lebesgue filters and the Egorov ...

We study an eigenvalue distribution of the adjacency matrix A^(N,p,a) of the weighted random bipartite graph Г = ГN,p. We assume that the graph has N vertices, the ratio of parts is α(1-α), and the average number of the ...

First we note that the best polynomial approximation to jxj on the set, which consists of an interval on the positive half-axis and a point on the negative half-axis, can be given by means of the classical Chebyshev ...

The aim of the paper is to find the conditions on the function F(z), determined in the domain G and having in G continuous partial derivatives, for validity of the following statements: i) almost everywhere F(z) has the ...