http://dspace.nbuv.gov.ua:80/handle/123456789/106559 Sun, 19 Apr 2026 06:30:32 GMT 2026-04-19T06:30:32Z http://dspace.nbuv.gov.ua:80/bitstream/id/317198/ http://dspace.nbuv.gov.ua:80/handle/123456789/106559 http://dspace.nbuv.gov.ua:80/handle/123456789/106592 Isometric Expansions of Quantum Algebra of Linear Bounded Operators Zolotarev, V.A. Sun, 01 Jan 2006 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/106592 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/106591 The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups Petrov, Ye.V. We consider smooth oriented hypersurfaces in 2-step nilpotent Lie groups with a left invariant metric. We derive an expression for the Laplacian of the Gauss map for such hypersurfaces in the general case and in some particular cases. In the case of CMC-hypersurface in the 2m+1-dimensional Heisenberg group we also give necessary and su cient conditions for the Gauss map to be harmonic and prove that for m = 1 all CMC-surfaces with the harmonic Gauss map are cylinders . Sun, 01 Jan 2006 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/106591 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/106590 On a Regular Hypersimplex Inscribed into the Multidimensional Cube Medianik, A.I. It is proved the existence of a regular hypersimplex inscribed into the (4n - 1)-dimensional cube under the vanishing condition of the resultant of some system of 4n - 1 algebraic equations with 4n - 1 unknown quantities. Sun, 01 Jan 2006 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/106590 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/106589 On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case Khrabustovsky, V.I. In the context of dissipative and accumulative di erential equations (which contain the spectral parameter λ nonlinearly) in a separable Hilbert space H we introduce a characteristic operator M(λ) that works as an analog of the characteristic Weyl-Titchmarsh matrix. Its existence and properties are investigated. A description of M(λ) that corresponds to separated boundary conditions is given. Analogs for Weyl functions and solutions are introduced. Weyl type inequalities for those analogs are established, which reduce to well-known inequalities in various special cases. The proofs are based on description and properties of maximal semi-definite subspaces in H² of special form that we provide while studying boundary problems for equations as above. Sun, 01 Jan 2006 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/106589 2006-01-01T00:00:00Z