http://dspace.nbuv.gov.ua:80/handle/123456789/150388 2026-04-22T18:36:45Z http://dspace.nbuv.gov.ua:80/handle/123456789/157998 On characteristic properties of semigroups Bondarenko, V.M.; Zaciha, Ya.V. Let K be a class of semigroups and P be a set of general properties of semigroups. We call a subset Q of P characteristic for a semigroup S ∈ K if, up to isomorphism and antiisomorphism, S is the only semigroup in K, which satisfies all the properties from Q. The set of properties P is called char-complete for K if for any S ∈ K the set of all properties P ∈ P, which hold for the semigroup S, is characteristic for S. We indicate a 7-element set of properties of semigroups which is a minimal char-complete set for the class of semigroups of order 3. 2015-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154900 On algebraic graph theory and non-bijective multivariate maps in cryptography Ustimenko, V. Special family of non-bijective multivariate maps Fn of Zmⁿ into itself is constructed for n=2,3,… and composite m. The map Fn is injective on Ωn={x|x₁+x₂+…xn ∈ Zm∗} and solution of the equation Fn(x)=b,x∈Ωn can be reduced to the solution of equation zr=α, z∈Zm∗, (r,ϕ(m))=1. The ``hidden RSA cryptosystem'' is proposed. Similar construction is suggested for the case Ωn=Zm∗ⁿ. 2015-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154756 New families of Jacobsthal and Jacobsthal-Lucas numbers Catarino, P.; Vasco, P.; Campos, H.; Aires, A.P.; Borges, A. In this paper we present new families of sequences that generalize the Jacobsthal and the Jacobsthal-Lucas numbers and establish some identities. We also give a generating function for a particular case of the sequences presented. 2015-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154755 On characteristic properties of semigroups Bondarenko, V.M.; Zaciha, Y.V. Let K be a class of semigroups and P be a set of general properties of semigroups. We call a subset Q of P cha\-racteristic for a semigroup S∈ K if, up to isomorphism and anti-isomorphism, S is the only semigroup in K, which satisfies all the properties from Q. The set of properties P is called char-complete for K if for any S∈ K the set of all properties P∈ P, which hold for the semigroup S, is characteristic for S. We indicate a 7-element set of properties of semigroups which is a minimal char-complete setfor the class of semigroups of order 3. 2015-01-01T00:00:00Z