Yazar "Cangul, I. Naci" seçeneğine göre listele

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    Analysis approach to finite monoids
    (SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Cevik, A. Sinan; Cangul, I. Naci; Simsek, Yilmaz
    In a previous paper by the authors, a new approach between algebra and analysis has been recently developed. In detail, it has been generally described how one can express some algebraic properties in terms of special generating functions. To continue the study of this approach, in here, we state and prove that the presentation which has the minimal number of generators of the split extension of two finite monogenic monoids has different sets of generating functions (such that the number of these functions is equal to the number of generators) that represent the exponent sums of the generating pictures of this presentation. This study can be thought of as a mixture of pure analysis, topology and geometry within the purposes of this journal. AMS Subject Classification: 11B68, 11S40, 12D10, 20M05, 20M50, 26C05, 26C10.
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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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    Minimality over free monoid presentations
    (HACETTEPE UNIV, FAC SCI, 2014) Cevik, A. Sinan; Das, Kinkar Ch.; Cangul, I. Naci; Maden, A. Dilek
    As a continues study of the paper [4], in here, we first state and prove the p-Cockcroft property (or, equivalently, efficiency) for a presentation, say PE, of the semi-direct product of a free abelian monoid rank two by a finite cyclic monoid. Then, in a separate section, we present sufficient conditions on a special case for PE to be minimal whilst it is inefficient.
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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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    On Average Eccentricity of Graphs
    (NATL ACAD SCIENCES INDIA, 2017) Das, Kinkar Ch.; Maden, A. Dilek; Cangul, I. Naci; Cevik, A. Sinan
    The eccentricity of a vertex is the maximum distance from it to any other vertex and the average eccentricity avec(G) of a graph G is the mean value of eccentricities of all vertices of G. In this paper we present some lower and upper bounds for the average eccentricity of a connected (molecular) graph in terms of its structural parameters such as number of vertices, diameter, clique number, independence number and the first Zagreb index. Also, we obtain a relation between average eccentricity and first Zagreb index. Moreover, we compare average eccentricity with graph energy, ABC index and index.
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    Zagreb Polynomials of Three Graph Operators
    (UNIV NIS, FAC SCI MATH, 2016) Bindusree, A. R.; Cangul, I. Naci; Lokesha, V.; Cevik, A. Sinan
    In general, the relations among Zagreb polynomials on three graph operators are discussed in this paper. Specifically, relations between Zagreb polynomials of a graph G and a graph obtained by applying the operators S(G), R(G) and Q(G) are investigated. In a separate section, the relation between Zagreb polynomial of a graph G and its corona is also described.