The upper estimates and, in some special cases, the lower estimates of the rate of rational approximation of piecewise-analytic functions defined on touching continuums are established. The upper and the lower estimates ...

The handle decompositions of 1-connected smooth or piecewise linear 5-manifolds are considered. The basic notions and constructions necessary for proving further results are introduced.

New types of reduction of the Kadomtsev-Petviashvili (KP) hierarchy are considered on the basis of Sato's approach. As a result, we obtain a new multicomponent nonlinear integrable system. Bi-Hamiltonian structures for the ...

The D-function is a new topological invariant introduced by the author in [3] to classify the minimal dynamical system and to generalize Sharkovskii's theorem on the coexistence of periodic orbits. We show that the D-function ...

The paper contains a generalization of certain previous results on subharmonic extension of functions and on extension of functions in the Hardy - Orlicz classes. We give unified proofs of these results.

It is proved that, under some restrictions, a family of selfadjoint commuting operators A=(Aφ) φ ∈ Φ where Φ is a nuclear space, has a cyclic vcctor iff there exists a Hilbert space H ⊂ Φ′ of full operator-valued measure ...

Вивчені властивості узагальненої групи Вейля для α-розшарованих модулів над алгеброю Лі sl(n,C).

Досліджується система, інверсна до нелінійної динамічної системи Бенні — Каупа. Для цієї сис­теми доведено існування нескінченної ієрархії функціонально незалежних та інволютивних за­конів збереження, знайдені пара ...

A complete asymptotical solution is constructed and justified for optimal singular parabolic problems with constraint control and complete degeneration of the differential part of the operator.