It is established which functional bases of the first-order differential invariants of the splitting and non-splitting subgroups of the Poincaré group $P(1,4)$ are invariant under the subgroups of the extended Galilei group ...

In this note we consider sets of linear extensions of dynamical systems on a torus. We examine regularity of the systems by means of a given sign-changing Lyapunov function. The main result of the paper is to give ...

Let $D$ be a regular closed set in the open subspace $G ⊂ ℝ^n$ and $C^m(D)$ be the space of functions $f|_D$ such that $f ∈ C^m(G)$. The representation formulas for locally defined operators mapping $C^m(D)$ into $C^0(D)$ ...

We present an example of the Riemann integrable multifunction which is discontinuous at each point with respect to the Hausdorff metric. The constructed multifunction is neither lower nor upper semicontinuous.

The present paper gives a historical account on extending the factorial function to complex numbers by Gauss.

The harmonic Dirichlet problem in a planar domain with smooth cracks of an arbitrary shape is considered in case, when the solution is not continuous at the ends of the cracks. The well-posed formulation of the problem ...

The present article is a survey of our last results. We establish best possible estimates of the weak solutions to the transmission problem near conical boundary point. We study this problem for the Laplace operator ...

Optimal design problem for 2D composite materials with different circular inclusions is studied on the base of the potential method combined with functional equation method. Exact geometric description of the optimal ...

The Bergman kernels of multiply connected domains are related with proper holomorphic maps onto the unit disc. We study multiply connected planar domains and represent conformal equivalence of the Bell representative ...