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Öğe Analysis approach to finite monoids(SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Cevik, A. Sinan; Cangul, I. Naci; Simsek, YilmazIn 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.Öğe Bounds for Resistance-Distance Spectral Radius(HACETTEPE UNIV, FAC SCI, 2013) Maden, A. Dilek Gungor; Gutman, Ivan; Cevik, A. SinanLower and upper bounds as well as Nordhauss-Gaddum-type results for the resistance-distance spectral radius are obtained.Öğe Conjugacy for Free Groups under Split Extensions(AMER INST PHYSICS, 2011) Cevik, A. Sinan; Karpuz, Eylem G.; Ates, FiratAt 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].Öğe 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. SinanIn 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.Öğe Finite Derivation Type for Graph Products of Monoids(UNIV NIS, FAC SCI MATH, 2016) Karpuz, Eylem Guzel; Ates, Firat; Cangul, I. Naci; Cevik, A. SinanThe aim of this paper is to show that the class of monoids of finite derivation type is closed under graph products.Öğe A GENERALIZATION FOR THE CLIQUE AND INDEPENDENCE NUMBERS(INT LINEAR ALGEBRA SOC, 2012) Maden (Gungor), A. Dilek; Cevik, A. SinanIn this paper, lower and upper bounds for the clique and independence numbers are established in terms of the eigenvalues of the signless Laplacian matrix of a given graph G.Öğe The graph based on Grobner-Shirshov bases of groups(SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Karpuz, Eylem G.; Ates, Firat; Cevik, A. Sinan; Cangul, I. NaciLet 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.Öğe Grobner-Shirshov bases of some monoids(ELSEVIER SCIENCE BV, 2011) Ates, Firat; Karpuz, Eylem G.; Kocapinar, Canan; Cevik, A. SinanThe 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.Öğe GROBNER-SHIRSHOV BASES OF SOME WEYL GROUPS(ROCKY MT MATH CONSORTIUM, 2015) Karpuz, Eylem Guzel; Ates, Firat; Cevik, A. SinanIn 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.Öğe Knit Products of Some Groups and Their Applications(C E D A M SPA CASA EDITR DOTT ANTONIO MILANI, 2009) Ates, Firat; Cevik, A. SinanLet 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.Öğe MAJORIZATION BOUNDS FOR SIGNLESS LAPLACIAN EIGENVALUES(INT LINEAR ALGEBRA SOC, 2013) Maden, A. Dilek; Cevik, A. SinanIt is known that, for a simple graph G and a real number alpha, the quantity s(alpha)'(G) is defined as the sum of the alpha-th power of non-zero singless Laplacian eigenvalues of G. In this paper, first some majorization bounds over s(alpha)'(G) are presented in terms of the degree sequences, and number of vertices and edges of G. Additionally, a connection between s(alpha)'(G) and the first Zagreb index, in which the Holder's inequality plays a key role, is established. In the last part of the paper, some bounds (included Nordhauss-Gaddum type) for signless Laplacian Estrada index are presented.Öğe Minimality over free monoid presentations(HACETTEPE UNIV, FAC SCI, 2014) Cevik, A. Sinan; Das, Kinkar Ch.; Cangul, I. Naci; Maden, A. DilekAs 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.Öğe NEW BOUNDS FOR THE SPREAD OF THE SIGNLESS LAPLACIAN SPECTRUM(ELEMENT, 2014) Guengoer, A. Dilek Maden; Cevik, A. Sinan; Habibi, NaderThe spread of the singless Laplacian of a simple graph G is defined as SQ(G) = mu(1)(G) - mu(n)(G), where mu(1)(G) and mu(n)(G) are the maximum and minimum eigenvalues of the signless Laplacian matrix of G, respectively. In this paper, we will present some new lower and upper bounds for SQ(G) in terms of clique and independence numbers. In the final section, as an application of the theory obtained in here, we will also show some new upper bounds for the spread of the singless Laplacian of tensor products of any two simple graphs.Öğe A New Graph over Semi-Direct Products of Groups(UNIV NIS, FAC SCI MATH, 2016) Topkaya, Sercan; Cevik, A. SinanIn this paper, by establishing a new graph Gamma(G) over the semi-direct product of groups, we will first state and prove some graph-theoretical properties, namely, diameter, maximum and minimum degrees, girth, degree sequence, domination number, chromatic number, clique number of Gamma(G). In the final section we will show that Gamma(G) is actually a perfect graph.Öğe A new semigroup obtained via known ones(WORLD SCIENTIFIC PUBL CO PTE LTD, 2019) Ozalan, Nurten Urlu; Cevik, A. Sinan; Karpuz, Eylem GuzelThe goal of this paper is to establish a new class of semigroups based on both Rees matrix and completely 0-simple semigroups. We further present some fundamental properties and finiteness conditions for this new semigroup structure.Öğe 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. DilekIt 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.Öğe 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. NaciThe 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.Öğe On Average Eccentricity of Graphs(NATL ACAD SCIENCES INDIA, 2017) Das, Kinkar Ch.; Maden, A. Dilek; Cangul, I. Naci; Cevik, A. SinanThe 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.Öğe On certain topological indices of nanostructures using q(g) and r(g) operators(ANKARA UNIV, FAC SCI, 2018) Lokesha, V.; Shruti, R.; Ranjini, S.; Cevik, A. SinanThe invention of new nanostructures gives a key measurement to industry, electronics, pharmaceutical and biological therapeutics. By considering the importance of this key point, in here we compute the 2D-lattice, nanotube and nanotorus of TUC4C8[p, q] over the graphs Q(G) and R(G) in terms of certain topological indices, namely first, second and third Zagreb indices, hyper Zagreb index and forgotten topological index. These indices are numerical propensity that often characterizes the quantitative structural activity/property/toxicity relationships, and also correlates physico-chemical properties such as boiling point, melting point and stability of respective nanostructures.Öğe On Laplacian Energy(UNIV KRAGUJEVAC, FAC SCIENCE, 2013) Das, Kinkar Ch.; Gutman, Ivan; Cevik, A. Sinan; Zhou, BoLet G be a connected graph of order n with Laplacian eigenvalues mu(1) >= mu(2) >= ... >= mu(n-1) > mu(n) = 0. The Laplacian energy of the graph G is defined as LE = LE(G) = (n)Sigma(i=1)vertical bar mu(i)-2m/n vertical bar. Upper bounds for LE are obtained, in terms of n and the number of edges m.
