http://dspace.nbuv.gov.ua:80/handle/123456789/150345 Wed, 22 Apr 2026 12:59:58 GMT 2026-04-22T12:59:58Z http://dspace.nbuv.gov.ua:80/bitstream/id/448091/ http://dspace.nbuv.gov.ua:80/handle/123456789/150345 http://dspace.nbuv.gov.ua:80/handle/123456789/157399 On closed rational functions in several variables Petravchuk, A.P.; Iena, O.G. Let K = K¯ be a field of characteristic zero. An element ϕ ∈ K(x1,... ,xn) is called a closed rational function if the subfield K(ϕ) is algebraically closed in the field K(x1,... ,xn). We prove that a rational function ϕ = f/g is closed if f and g are algebraically independent and at least one of them is irreducible. We also show that a rational function ϕ = f/g is closed if and only if the pencil αf + βg contains only finitely many reducible hypersurfaces. Some sufficient conditions for a polynomial to be irreducible are given. Mon, 01 Jan 2007 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/157399 2007-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/157398 On classification of CM modules over hypersurface singularities Bondarenko, V.V. This article is devoted to a special case of classification problem for Cohen-Macaulay modules over hypersurface singularities. Mon, 01 Jan 2007 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/157398 2007-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/157376 Characterization of clones of boolean operations by identities Butkote, R.; Denecke, K. In [4] the authors characterized all clones of Boolean operations (Boolean clones) by functional terms. In this paper we consider a Galois connection between operations and equations and characterize all Boolean clones by using of identities. For each Boolean clone we obtain a set of equations with the property that an operation f belongs to this clone if and only if it satisfies these equations. Mon, 01 Jan 2007 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/157376 2007-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/157371 Self-similar groups and finite Gelfand pairs D’Angeli, D.; Donno, A. We study the Basilica group B, the iterated monodromy group I of the complex polynomial z 2 + i and the Hanoi Towers group H(3). The first two groups act on the binary rooted tree, the third one on the ternary rooted tree. We prove that the action of B, I and H(3) on each level is 2-points homogeneous with respect to the ultrametric distance. This gives rise to symmetric Gelfand pairs: we then compute the corresponding spherical functions. In the case of B and H(3) this result can also be obtained by using the strong property that the rigid stabilizers of the vertices of the first level of the tree act spherically transitively on the respective subtrees. On the other hand, this property does not hold in the case of I. Mon, 01 Jan 2007 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/157371 2007-01-01T00:00:00Z