Browsing 2005 by Title

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  • Maximality of affine group, and hidden graph cryptosystems 
    Ustimenko, Vasiliy A. (Луганский национальный университет им. Т. Шевченко, 2005)
    We describe a new algebraic-combinatorial method of public key encryption with a certain similarity to the well known Imai-Matsumoto. We use the general idea to treat vertices of a linguistic graph (see [21] and further ...
  • Miniversal deformations of chains of linear mappings 
    Gaiduk, T. N.; Sergeichuk, V. V.; Zharko, N. A. (Луганский национальный университет им. Т. Шевченко, 2005)
    V.I. Arnold gave a miniversal deformation of matrices of linear operators; that is, a simple canonical form, to which not only a given square matrix A, but also the family of all matrices close to A, can be reduced by ...
  • On bounded m-reducibilities 
    Belyaev, Vladimir N. (Луганский национальный университет им. Т. Шевченко, 2005)
    Conditions for classes F1, F0 of non-decreasing total one-place arithmetic functions to define reducibility m [R1 R0 ] {(A,B)|A,B N & (9 r.f. h)(9f1 2 F1)(9f0 2 F0) [A h m B & f0 E h E f1]} where k E l means that ...
  • On mappings of terms determined by hypersubstitutions 
    Koppitz, J¨org; Shtrakov, Slavcho (ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)
    The extensions of hypersubstitutions are mappings on the set of all terms. In the present paper we characterize all hypersubstitutions which provide bijections on the set of all terms. The set of all such hypersubstitutions ...
  • On posets of width two with positive Tits form 
    Bondarenko, Vitalij M.; Styopochkina, Marina V. (Луганский национальный университет им. Т. Шевченко, 2005)
    We give a complete description of the finite posets of width two with the Tits form to be positive. This problem arises in studying the categories of representations of posets of finite type.
  • On representation type of a pair of posets with involution 
    Bondarenko, Vitalij M. (Луганский национальный университет им. Т. Шевченко, 2004)
    In this paper we consider the problem on classifying the representations of a pair of posets with involution. We prove that if one of these is a chain of length at least 4 with trivial involution and the other is with ...
  • On square-Hamiltonian graphs 
    Protasova, K. D. (ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)
    A finite connected graph G is called square-Hamiltonian if G2 is Hamiltonian. We prove that any join of the family of Hamiltonian graphs by tree is square-Hamiltonian. Applying this statement we show that the line graph ...
  • On strongly graded Gorestein orders 
    Theohari-Apostolidi, Th.; Vavatsoulas, H. (Луганский национальный университет им. Т. Шевченко, 2005)
    Let G be a finite group and let = g2G g be a strongly G-graded R-algebra, where R is a commutative ring with unity. We prove that if R is a Dedekind domain with quotient field K, is an R-order in a separable K-algebra ...
  • On the mean square of the Epstein zeta-function 
    Savastru, O. V.; Varbanets, P. D. (Луганский национальный университет им. Т. Шевченко, 2005)
    We consider the second power moment of the Epstein zeta-function and construct the asymptotic formula in special case, when '0(u, v) = u2 + Av2, A > 0, A 1, 2(mod 4) and '0(u, v) belongs to the one-class kind G0 of the ...
  • Realizations of affine Lie algebras 
    Futorny, Vyacheslav (Луганский национальный университет им. Т. Шевченко, 2005)
    This is an expository paper on some realizations of affine Lie algebras and their representations in terms of differential operators. In particular we recall the classical construction of Wakimoto modules and its recent ...
  • Some properties of primitive matrices over Bezout B-domain 
    Shchedryk, V. P. (Луганский национальный университет им. Т. Шевченко, 2005)
    The properties of primitive matrices (matrices for which the greatest common divisor of the minors of maximal order is equal to 1) over Bezout B - domain, i.e. commutative domain finitely generated principal ideal in which ...
  • Steiner P-algebras 
    Chakrabarti, Sucheta (Луганский национальный университет им. Т. Шевченко, 2005)
    General algebraic systems are able to formalize problems of different branches of mathematics from the algebraic point of view by establishing the connectivity between them. It has lots of applications in theoretical ...
  • Ternary Hopf algebras 
    Zekoviс, Biljana (ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)
    In this paper we introduce the notion of a ternary Hopf algebra and prove that it can be embedded into a universal enveloping Hopf algebra.
  • Topological semigroups of matrix units 
    Gutik, Oleg V.; Pavlyk, Kateryna P. (ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)
    We prove that the semigroup of matrix units is stable. Compact, countably compact and pseudocompact topologies on the infinite semigroup of matrix units B such that (B , ) is a semitopological (inverse) semigroup are ...
  • Two-generated graded algebras 
    Shirikov, Evgenij N. (ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)
    The paper is devoted to classification of two-generated graded algebras. We show that under some general assumptions there exist two classes of these algebras, namely quantum polynomials and Jordanian plane. We study prime ...
  • Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups 
    Sushchansky, Vitaly I.; Netreba, Nataliya V. (Луганский национальный университет им. Т. Шевченко, 2005)
    We define a wreath product of a Lie algebra L with the one-dimensional Lie algebra L1 over Fp and determine some properties of this wreath product. We prove that the Lie algebra associated with the Sylow p-subgroup of ...

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