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Comparison of the shaping ability of novel thermally treated reciprocating instruments
Keskin, Cangul,Demiral, Murat,Sariyilmaz, Evren The Korean Academy of Conservative Dentistry 2018 Restorative Dentistry & Endodontics Vol.43 No.2
Objectives: The present study aimed to evaluate the shaping ability of 2 thermally treated nickel-titanium reciprocating systems in simulated curved canals. Materials and Methods: Forty simulated canals were prepared to apical size 25 using Reciproc Blue R25 (VDW) and WaveOne Gold Primary (Dentsply Sirona) instruments. Standard pre- and post-preparation images were taken and superimposed. The removal of resin material was measured at 5 standard points: the canal orifice, halfway between the canal orifice and the beginning of the curve, the beginning of the curve, the apex of the curve, and the end-point of the simulated canal. The data were analysed using the independent sample t-test with a 5% significance threshold. Results: The canals in which Reciproc Blue R25 was used showed a significantly greater widening than those in which WaveOne Gold was used at 4 of the 5 measurement points (p < 0.05). The Reciproc Blue R25 instrument removed significantly more resin from the inner aspect of the curve at 2 of the 5 points and similar amounts at the remaining 3 points. At the 2 apical points, there was no significant difference between the Reciproc Blue R25 and WaveOne Gold Primary instruments. Conclusion: Both instruments respected the original canal anatomy; however, WaveOne Gold resulted in a more conservative shape with less transportation.
Changing relationship between sets using convolution sums of restricted divisor functions
Ismail Naci Cangul,Daeyeoul Kim 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.3
There are real life situations in our lives where the things are changing continuously or from time to time. It is a very important problem for one whether to continue the existing relationship or to form a new one after some occasions. That is, people, companies, cities, countries, etc. may change their opinion or position rapidly. In this work, we think of the problem of changing relationships from a mathematical point of view and think of an answer. In some sense, we comment these changes as power changes. Our number theoretical model will be based on this idea. Using the convolution sum of the restricted divisor function $E$, we obtain the answer to this problem.
ON THE HIGHER-ORDER w-q-GENOCCHI NUMBERS
I. N.. Cangul,H. Ozden,V. Kurt,Y. Simsek 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.1
Main purpose of this paper is to study on higher-order w-q-Genocchi numbers and polynomials by using p-adic q-deformed fermi- onic integral on Zp. We derive some identities related to higher-order w-q- Genocchi numbers and polynomials. We also give interpolation functions of these numbers and polynomials.
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.
Bounds for matching number of fundamental realizations according to new graph invariant Omega
MERT SINAN OZ,Ismail Naci CANGUL 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.1
Matching number of a graph is one of the intensively studied areas in graph theory due to numerous applications of the matching and related notions. Recently, Delen and Cangul defined a new graph invariant denoted by which helps to determine several graph theoretical and combinatorial properties of the realizations of a given degree sequence. In this paper, using K2 deletion process, the maximum and minimum matching numbers of all so-called fundamental realizations of a given degree sequence.
Soydan,Demirci,Cangul 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.2
The object of this paper is to give a new proof of all the solutions of the Diophantine equation x² + 11m = yⁿ,in positive integers x; y with odd m > 1 and n ≥ 3.
FORGOTTEN INDEX OF GRAPHS WITH DELETED EDGES
PUSHPALATHA MAHALANK,Ismail Naci CANGUL 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.4
The forgotten index F(G) of a graph G is a degree based topological index which is defined as the sum of the cubes of the degrees of its vertices which was introduced by Furtula and Gutman in 2015. It was used in earlier works in relation with the first Zagreb index but not named until 2015. In this work, we present the effect of deleting edges from a simple graph on forgotten index is studied. In particular, some statements for the change of forgotten index of path, cycle, complete, star, complete bipartite and tadpole graphs are obtained. Also the same effect is determined for regular graphs.
SOME RECURRENCE RELATIONS FOR THE ENERGY OF CYCLE AND PATH GRAPHS
FERIHA CELIK,Ismail Naci CANGUL 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.3
Energy of a graph, rst dened by E. Hückel as the sum of absolute values of the eigenvalues of the adjacency matrix while searching for a method to obtain approximate solutions of Schrödinger equation for a class of organic molecules, is an important sub area of graph theory. This equation is a second order dierential equation which include the energy of the corresponding system. The energy of many graph types are well-known in literature. To know the energy of a molecule is an important aspect in Chemical Graph Theory. Two classes, cycles and paths, show serious dierences from others as the eigenvalues are trigonometric algebraic numbers which makes it difficult to calculate the energy of the corresponding graph. Here we obtain the polynomials and recurrence relations for the spectral polynomials of cycles and paths to nd the energy of larger graphs easier than the classical way.
Remarks on q-Bernoulli numbers associated with Daehee numbers
H. Ozden,I. N. Cangul,Y. Simsek 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.18 No.1
In this work, we study on Carlitz's type q-Bernoulli numbers, q-Frobenius-Euler numbers and Daehee numbers and polynomials. We also give p-adic integral representation of the twisted Daehee polynomials. By using this representation, we ¯nd Raabe-type multiplication formula for the twisted Daehee polynomials.
MINIMUM PENDANT DOMINATING ESTRADA INDEX OF A GRAPH
AKbar Jahanbani,Ismail Naci CANGUL 장전수학회 2020 Advanced Studies in Contemporary Mathematics Vol.30 No.4
The main purpose of this paper is to introduce the con- cept of minimum pendant dominating Estrada index of a graph. First, we compute minimum pendant dominating Estrada index for complete graph, star graph, complete bipartite graph and cocktail party graph which are amongst the most widely-used graph classes. Also, upper and lower bounds for this new index are established. Finally, the rela- tions between the new Estrada index and the new type of energy are investigated.