Yazar "Ates, Firat" 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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    Finite Derivation Type for Graph Products of Monoids
    (UNIV NIS, FAC SCI MATH, 2016) Karpuz, Eylem Guzel; Ates, Firat; Cangul, I. Naci; Cevik, A. Sinan
    The aim of this paper is to show that the class of monoids of finite derivation type is closed under graph products.
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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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    GROBNER-SHIRSHOV BASES OF SOME WEYL GROUPS
    (ROCKY MT MATH CONSORTIUM, 2015) Karpuz, Eylem Guzel; Ates, Firat; Cevik, A. Sinan
    In this paper, we obtain Crobner-Shirshov (non-commutative) bases for the n-extended affine Weyl group (W) over tilde of type A(1), elliptic Weyl groups of types A(1)((1,1)) A(1)((1,1))* and the 2-extended affine Weyl group of type A(2)((1,1)) with a generator system of a 2-toroidal sense. It gives a new algorithm for getting normal forms of elements of these groups and hence a new algorithm for solving the word problem in these groups.
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    Grobner-shirshov basis for the singular part of the brauer semigroup
    (SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, 2018) Ates, Firat; Cevik, Ahmet Sinan; Guzel Karpuz, Eylem
    In this paper, we obtain a Grobner-Shirshov (noncommutative Grobner) basis for the singular part of the Brauer semigroup. It gives an algorithm for getting normal forms and hence an algorithm for solving the word problem in these semigroups.
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    Knit Products of Some Groups and Their Applications
    (C E D A M SPA CASA EDITR DOTT ANTONIO MILANI, 2009) Ates, Firat; Cevik, A. Sinan
    Let G be a group with subgroups A and K (not necessarily normal) such that G = AK and A boolean AND K = {1}. Then G is isomorphic to the knit product, that is, the "two-sided semidirect product" of K by A. We note that knit products coincide with Zappa-Szep products (see [18]). In this paper, as an application of [2, Lemma 3.16], we first define a presentation for the knit product G where A and K are finite cyclic subgroups. Then we give an example of this presentation by considering the (extended) Hecke groups. After that, by defining the Schur multiplier of G, we present sufficient conditions for the presentation of G to be efficient. In the final part of this paper, by examining the knit product of a free group of rank n by an infinite cyclic group, we give necessary and sufficient conditions for this special knit product to be subgroup separable.
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    The next step of the word problem over monoids
    (ELSEVIER SCIENCE INC, 2011) Karpuz, E. Guzel; Ates, Firat; Cevik, A. Sinan; Cangul, I. Naci; Maden (Gungor), A. Dilek
    It is known that a group presentation P can be regarded as a 2-complex with a single 0-cell. Thus we can consider a 3-complex with a single 0-cell which is known as a 3-presentation. Similarly, we can also consider 3-presentations for monoids. In this paper, by using spherical monoid pictures, we show that there exists a finite 3-monoid-presentation which has unsolvable "generalized identity problem'' that can be thought as the next step (or one-dimension higher) of the word problem for monoids. We note that the method used in this paper has chemical and physical applications. (C) 2011 Elsevier Inc. All rights reserved.
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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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    A presentation and some finiteness conditions for a new version of the Schiitzenberger product of monoids
    (SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, 2016) Karpuz, Eylem Guzel; Ates, Firat; Cevik, Ahmet Sinan; Cangul, Ismail Naci
    In this paper we first define a new version of the Schutzenberger product for any two monoids A and B, and then, by defining a generating and relator set, we present some finite and infinite consequences of the main result. In the final part of this paper, we give necessary and sufficient conditions for this new version to be periodic and locally finite.
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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.