We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results ...

A free boundary problem describing a filtration process in a porous medium is considered. An unknown interface divides the filtration domain into elliptic and parabolic regions. In the parabolic region the governing equation ...

We establish several sufficient conditions for a compact spacelike surface in the 3-dimensional de Sitter space to be totally geodesic or spherical.

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 ...