Yazar "Karpuz, Eylem G." seçeneğine göre listele

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    Conjugacy for Free Groups under Split Extensions
    (AMER INST PHYSICS, 2011) Cevik, A. Sinan; Karpuz, Eylem G.; Ates, Firat
    At the present paper we show that conjugacy is preserved and reflected by the natural homomorphism defined from a semigroup S to a group G, where G defines split extensions of some free groups. The main idea in the proofs is based on a geometrical structure as applied in the paper [8].
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    The Efficiency of the Semi-Direct Products of Free Abelian Monoid with Rank n by the Infinite Cyclic Monoid
    (AMER INST PHYSICS, 2011) Ates, Firat; Karpuz, Eylem G.; Cevik, A. Sinan
    In this paper we give necessary and sufficient conditions for the efficiency of the semi-direct product of free abelian monoid with rank n by the infinite cyclic monoid.
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    Generalization for Estrada Index
    (Amer Inst Physics, 2010) Güngör, Ayşe Dilek; Çevik, Ahmet Sinan; Karpuz, Eylem G.; Ateş, Fırat; Cangül, İsmail Naci
    In this paper the Estrada index of Hermite matrix is firstly defined and investigated. In fact this is a natural generalization of Estrada, distance Estrada and Laplacian Estrada indices. Thus all properties about them can be handled by this new index.
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    Generalized Bruck-Reilly *-extension as a new example of a monoid with a non-finitely generated group of units
    (Selcuk University Research Center of Applied Mathematics, 2010) Karpuz, Eylem G.
    We present a new example of a finitely presented monoid, namely Bruck-Reilly extension of generalized Bruck-Reilly ?-extension of free group with infinite rank, the group of units of which is not finitely generated.
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    The graph based on Grobner-Shirshov bases of groups
    (SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Karpuz, Eylem G.; Ates, Firat; Cevik, A. Sinan; Cangul, I. Naci
    Let us consider groups G(1) = Z(k) * (Z(m) * Z(n)), G(2) = Z(k) x (Z(m) * Z(n)), G(3) = Z(k) * (Z(m) x Z(n)), G(4) = (Z(k) * Z(l)) * (Z(m) * Z(n)) and G(5) = (Z(k) * Z(l)) x (Z(m) * Z(n)), where k, l, m, n = 2. In this paper, by defining a new graph Gamma(G(i)) based on the Grobner-Shirshov bases over groups G(i), where 1 <= i <= 5, we calculate the diameter, maximum and minimum degrees, girth, chromatic number, clique number, domination number, degree sequence and irregularity index of Gamma(G(i)). Since graph theoretical studies (including such above graph parameters) consist of some fixed point techniques, they have been applied in such fields as chemistry (in the meaning of atoms, molecules, energy etc.) and engineering (in the meaning of signal processing etc.), game theory and physics. In addition, the Grobner-Shirshov basis and the presentations of algebraic structures contain a mixture of algebra, topology and geometry within the purposes of this journal.
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    Grobner-Shirshov bases of some monoids
    (ELSEVIER SCIENCE BV, 2011) Ates, Firat; Karpuz, Eylem G.; Kocapinar, Canan; Cevik, A. Sinan
    The main goal of this paper is to define Grobner-Shirshov bases for some monoids. Therefore, after giving some preliminary material, we first give Grobner-Shirshov bases for graphs and Schutzenberger products of monoids in separate sections. In the final section, we further present a Grobner-Shirshov basis for a Rees matrix semigroup. (C) 2011 Elsevier B.V. All rights reserved.
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    A New Example of Deficiency One Groups
    (Amer Inst Physics, 2010) Çevik, A. Sinan; Güngör, A. Dilek; Karpuz, Eylem G.; Ateş, Fırat; Cangül, I. Naci
    The main purpose of this paper is to present a new example of deficiency one groups by considering the split extension of a finite cyclic group by a free abelian group having rank two.
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    A Note on the Grobner-Shirshov Bases over Ad-hoc Extensions of Groups
    (UNIV NIS, FAC SCI MATH, 2016) Karpuz, Eylem G.; Ates, Firat; Urlu, Nurten; Cevik, A. Sinan; Cangul, I. Naci
    The main goal of this paper is to obtain (non-commutative) Grobner-Shirshov bases for monoid presentations of the knit product of cyclic groups and the iterated semidirect product of free groups. Each of the results here will give a new algorithm for getting normal forms of the elements of these groups, and hence a new algorithm for solving the word problem over them.
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    Two-Sided Crossed Products of Groups
    (UNIV NIS, FAC SCI MATH, 2016) Cetinalp, Esra K.; Karpuz, Eylem G.; Ates, Firat; Cevik, A. Sinan
    In this paper, we first define a new version of the crossed product of groups under the name of two-sided crossed product. Then we present a generating and relator sets for this new product over cyclic groups. In a separate section, by using the monoid presentation of the two-sided crossed product of cyclic groups, we obtain the complete rewriting system and normal forms of elements of this new group construction.