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Gröbner-Shirshov bases and embedding of a semigroup in a group
E. G. Karpuz,A. S. Cevik,F. Ates,J. Koppitz 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.4
The main goal of this paper is to show that if a group G has a Gröbner-Shirshov basis that satisfies the condition R+, then the semigroup P having positive rules in < as a dening relation embeds in this group G. As a corollary of our result, we obtain that the semigroup B+ n+1 of braids can be embedded in the braid group. The main goal of this paper is to show that if a group G has a Grobner-Shirshov basis that satisfies the condition R+, then the semigroup P having positive rules in < as a dening relation embeds in this group G. As a corollary of our result, we obtain that the semigroup B+ n+1 of braids can be embedded in the braid group.
Fiber reinforced concrete corbels: Modeling shear strength via symbolic regression
Ahmet E Kurtoglu,Mehmet E Gulsan,Hussein A Abdi,Mohammed A Kamil,Abdulkadir Cevik 사단법인 한국계산역학회 2017 Computers and Concrete, An International Journal Vol.20 No.1
In this study, a novel application of symbolic regression (SR) is employed for the prediction of ultimate shear strength of steel fiber reinforced (SFRC) and glass fiber reinforced (GFRC) corbels without stirrups, for the first time in the literature. A database is created using the test results (42 tests) conducted by the authors of current paper as well as the previous studies available in the literature. A symbolic regression based empirical formulation is proposed using this database. The formulation is unique in a way that it has the capability to predict the shear strength of both SFRC and GFRC corbels. The performance of proposed model is tested against randomly selected testing set. Additionally, a parametric study with a wide range of variables is carried out to test the effect of each parameter on the shear strength. The results confirm the high prediction capacity of proposed model.
COMPUTATION OF ADRIATIC INDICES OF CERTAIN OPERATORS OF REGULAR AND COMPLETE BIPARTITE GRAPHS
V. Lokesha,M. MANJUNATH,B. Chaluvaraju,K. M. Devendraiah,I. N. Cangul,A. S. CEVIK 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.2
A topological index of a graph G is a numerical parameter related to G which characterizes its molecular topology and used for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR). Adriatic indices are bond-additive topological indices. They are analyzed on the testing sets provided by the Inernational Academy of Mathematical Chemistry (IAMC) and it has been shown that they have good predictive properties in many cases. In this paper, we study the certain adriatic indices of regular and complete bipartite graphs using some graph operators.
Neuro-Fuzzy modeling of torsional strength of RC beams
A. Cevik,R. Saracoglu,M.H. Arslan 사단법인 한국계산역학회 2012 Computers and Concrete, An International Journal Vol.9 No.6
This paper presents Neuro-Fuzzy (NF) based empirical modelling of torsional strength of RC beams for the first time in literature. The proposed model is based on fuzzy rules. The experimental database used for NF modelling is collected from the literature consisting of 76 RC beam tests. The input variables in the developed rule based on NF model are cross-sectional area of beams, dimensions of closed stirrups, spacing of stirrups, cross-sectional area of one-leg of closed stirrup, yield strength of stirrup and longitudinal reinforcement, steel ratio of stirrups, steel ratio of longitudinal reinforcement and concrete compressive strength. According to the selected variables, the formulated NFs were trained by using 60 of the 76 sample beams. Then, the method was tested with the other 16 sample beams. The accuracy rates were found to be about 96% for total set. The performance of accuracy of proposed NF model is furthermore compared with existing design codes by using the same database and found to be by far more accurate. The use of NF provided an alternative way for estimating the torsional strength of RC beams. The outcomes of this study are quite satisfactory which may serve NF approach to be widely used in further applications in the field of reinforced concrete structures.
On the first Zagreb index and multiplicative Zagreb coindices of graphs
Das, Kinkar Ch.,Akgunes, Nihat,Togan, Muge,Yurttas, Aysun,Cangul, I. Naci,Cevik, A. Sinan De Gruyter Open 2016 Analele Stiintifice ale Universitatii Ovidius Cons Vol.24 No.1
<P>For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as M-1(G) = Sigma v(i is an element of V(G))d(C)(v(i))(2), where d(G) (v(i)) is the degree of vertex v(i), in G. Recently Xu et al. introduced two graphical invariants (Pi) over bar (1) (G) = Pi v(i)v(j is an element of E(G)) (dG (v(i))+dG (v(j))) and (Pi) over bar (2)(G) = Pi(vivj is an element of E(G)) (dG (v(i))+dG (v(j))) named as first multiplicative Zagreb coindex and second multiplicative Zagreb coindex, respectively. The Narumi-Katayama index of a graph G, denoted by NK(G), is equal to the product of the degrees of the vertices of G, that is, NK(G) = Pi(n)(i=1) d(G) (v(i)). The irregularity index t(G) of G is defined as the num=1 ber of distinct terms in the degree sequence of G. In this paper, we give some lower and upper bounds on the first Zagreb index M-1(G) of graphs and trees in terms of number of vertices, irregularity index, maximum degree, and characterize the extremal graphs. Moreover, we obtain some lower and upper bounds on the (first and second) multiplicative Zagreb coindices of graphs and characterize the extremal graphs. Finally, we present some relations between first Zagreb index and NarumiKatayama index, and (first and second) multiplicative Zagreb index and coindices of graphs.</P>
GENERALIZATION OF q-APOSTOL-TYPE EULERIAN NUMBERS AND POLYNOMIALS, AND THEIR INTERPOLATION FUNCTIONS
I. N. Cangul,A. S. Cevik,Y. Simsek 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.2
In a recent paper [16], generating functions in terms of non- negative real parameters, q-Eulerian type polynomials and numbers (or q-Apostol type Frobenius-Euler numbers and polynomials) have been constructed by Y. Simsek. Additionally, some identities for these poly- nomials and numbers based on the generating functions and functional equations have been derived. Finally, a multiplication formula for the generalized Apostol type Frobenius-Euler polynomials has been given. In this paper, as a continuing study of [16], we will essentially present generalizations of the above material and, dierently from aforemen- tioned paper, we will express the interpolation functions related to these numbers and polynomials.
VL Status Index and Co-index of Connected Graphs
V. Lokesha,S. Suvarna,A. Sinan Cevik 장전수학회 2021 Proceedings of the Jangjeon mathematical society Vol.24 No.3
The status σG(u) of a vertex u in a connected graph G is defined as the sum of the distances between u and all other vertices of G. In this paper some relations over VL status index and VL status co-index of connected graphs are established. Furthermore distinguished examples for k-transmission regular graphs and nanostructures of VL status indices are computed.
Some properties on the tensor product of graphs obtained by monogenic semigroups
Akgunes, N.,Das, K.Ch.,Sinan Cevik, A. Elsevier [etc.] 2014 Applied Mathematics and Computation Vol.235 No.-
In Das et al. (2013) [8], a new graph Γ(S<SUB>M</SUB>) on monogenic semigroups S<SUB>M</SUB> (with zero) having elements {0,x,x<SUP>2</SUP>,x<SUP>3</SUP>,...,x<SUP>n</SUP>} has been recently defined. The vertices are the non-zero elements x,x<SUP>2</SUP>,x<SUP>3</SUP>,...,x<SUP>n</SUP> and, for 1≤i,j≤n, any two distinct vertices x<SUP>i</SUP> and x<SUP>j</SUP> are adjacent if x<SUP>i</SUP>x<SUP>j</SUP>=0 in S<SUB>M</SUB>. As a continuing study, in Akgunes et al. (2014) [3], it has been investigated some well known indices (first Zagreb index, second Zagreb index, Randic index, geometric-arithmetic index, atom-bond connectivity index, Wiener index, Harary index, first and second Zagreb eccentricity indices, eccentric connectivity index, the degree distance) over Γ(S<SUB>M</SUB>). In the light of above references, our main aim in this paper is to extend these studies over Γ(S<SUB>M</SUB>) to the tensor product. In detail, we will investigate the diameter, radius, girth, maximum and minimum degree, chromatic number, clique number and domination number for the tensor product of any two (not necessarily different) graphs Γ(S<SUB>M</SUB><SUP>1</SUP>) and Γ(S<SUB>M</SUB><SUP>2</SUP>).
New classifications over wreath products of groups
S. N. Noyan,A. S. Cevik 장전수학회 2023 Proceedings of the Jangjeon mathematical society Vol.26 No.2
New classifications over wreath products of groups
New results on the F-index of graphs based on Corona-type products of graphs
V. Lokesha,S. Jain,A. S. CEVIK,I. N. Cangul 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.2
In mathematical chemistry, graph operations act in very essential roles since some chemical graphs can be derived from some simpler graphs by applying dierent graph operations. Among all products of graphs, the corona product of two graphs is one of the most useful product. In this paper the explicit interpretation for F-index of dif- ferent forms of corona products involving Zagreb indices, graph size and order are obtained.