Browsing by Author "Karpuz, Eylem Güzel"
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Publication A presentation and some finiteness conditions for a new version of the schiitzenberger product of monoids(Tübitak Bilimsel ve Teknolojik Araştırma Kurumu, 2016-01-01) Karpuz, Eylem Güzel; Ateş, Firat; Cevik, Ahmet Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7111-3462; 0000-0002-0700-5774; ABA-6206-2020In 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.Item Determination of genus of normal subgroups of discrete groups(Amer Inst Physics, 2010) Karpuz, Eylem Güzel; Ateş, Fırat; Psihoyios, G.; Tsitouras, C.; Cangül, İsmail Naci; Demirci, Musa; Yurttaş, Aysun; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; AAG-8470-2021; J-3505-2017; 57189022403; 23566581100; 37090056000In this work, subgroups of a special class of discrete subgroups of PLS(2, R), namely the ones of the first kind with genus 0, have been studied. We establish a technique to compute the genus of these subgroups in terms of the genus of easier groups. The method established here can be used for triangle groups, surface groups and Hecke groups (including the well-known modular group).Item Finite derivation type for graph products of monoids(University of Nis, 2015-06-20) Karpuz, Eylem Güzel; Ateş, Fırat; Çevik, A. Sinan; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017; ABA-6206-2020; 57189022403The aim of this paper is to show that the class of monoids of finite derivation type is closed under graph products.Item Generalization for Estrada index(Amer Inst Physics, 2010) Güngör, Ayşe Dilek; Çevik, Ahmet Sinan; Karpuz, Eylem Güzel; Ateş, Fırat; Psihoyios, G.; Tsitouras, C.; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017; 57189022403In 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.Item The graph based on Grobner-Shirshov bases of groups(Springer, 2013-03-26) Karpuz, Eylem Güzel; Ateş, Fırat; Çevik, Ahmet Sinan; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0700-5774; 0000-0002-0700-5774; J-3505-2017; ABA-6206-2020; 57189022403Let 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.Item A new example of deficiency one groups(Amer Inst Physics, 2010) Çevik, Ahmet Sinan; Güngör, Dilek; Karpuz, Eylem Güzel; Ateş, Fırat; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017; 57189022403The 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.Item The next step of the word problem over monoids(Elsevier Science, 2011-10) Karpuz, Eylem Güzel; Ateş, Fırat; Çevik, Ahmet Sinan; Maden, Ayşe Dilek Güngör; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/MatematikBölümü.; 0000-0002-0700-5774; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017; 57189022403It 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.Item On the efficiency of semi-direct products of finite cyclic monoids by one-relator monoids(Amer Inst Physics, 2010) Ateş, Fırat; Karpuz, Eylem Güzel; Güngör, Ayşe Dilek Maden; Çevik, Ahmet Sinan; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017; 57189022403In this paper we give necessary and sufficient conditions for the efficiency of a standard presentation for the semi-direct product of finite cyclic monoids by one-relator monoids.Item On the norms of Toeplitz and Hankel matrices with Pell numbers(Amer Inst Physics, 2010) Karpuz, Eylem Güzel; Ateş, Fırat; Güngör, Ayşe Dilek; Çevik, Ahmet Sinan; Cangül, Naci İsmail; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017; 57189022403Let us define A = [a(ij)](i,j=0)(n-1) and B = [b(ij)](i,j=0)(n-1) as n x n Toeplitz and Hankel matrices, respectively, such that a(ij) = Pi-j and b(ij) = Pi+j, where P denotes the Pell number. We present upper and lower bounds for the spectral norms of these matrices.Item Some fixed-point results on (generalized) Bruck-Reilly-extensions of monoids(Springer, 2013-03-29) Karpuz, Eylem Güzel; Çevik, Ahmet Sinan; Koppitz, Jörg; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0700-5774; 0000-0002-0700-5774; J-3505-2017; ABA-6206-2020; 57189022403In this paper, we determine necessary and sufficient conditions for Bruck-Reilly and generalized Bruck-Reilly *-extensions of arbitrary monoids to be regular, coregular and strongly pi-inverse. These semigroup classes have applications in various field of mathematics, such as matrix theory, discrete mathematics and p-adic analysis (especially in operator theory). In addition, while regularity and coregularity have so many applications in the meaning of boundaries (again in operator theory), inverse monoids and Bruck-Reilly extensions contain a mixture fixed-point results of algebra, topology and geometry within the purposes of this journal.