CHARACTERISTIC POLYNOMIALS OF SUBDIVISION GRAPHS

FERIHA CELIK,Musa DEMIRCI,SADIK DELEN,Ugur ANA,Ismail Naci CANGUL 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.1

Energy of a graph, rstly dened by E. Huckel is an important sub area of graph theory with numerous applications in Chemistry and Physics together with all areas they are used as fundamental methods. Schrodinger equation is a second order dierential equation which include the energy of the corresponding system. Subdivision of a graph is a method of obtaining a derived graph from a given one which helps to calculate some properties of a complex molecular graph by calculating the same for some easier molecular graph. Unlike many other areas in graph theory, to obtain a general result in spectral graph theory is indeed quite dicult and mostly impossible. In this article, as a result of this idea, the spectral polynomials and their reccurence relations of the subdivision graphs of some well-known graphs are studied. Also the energy of some subdivision graphs are obtained by using the denition of energy. A new relation for the characteristic polynomial of a cyclic graph in terms of the triangular numbers is also obtained.

Formulae and recurrence relations on spectral polynomials of some graphs

FERIHA CELIK,Ismail Naci CANGUL 장전수학회 2017 Advanced Studies in Contemporary Mathematics Vol.27 No.3

Energy of a graph, firstly defined 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. Schrödinger equation is a second order differantial equation which include the energy of the corresponding system. Here we obtain the polynomials and recurrence relations for the spectral (characteristic) polynomials of some 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.

Clinicopathologic features and survival outcomes of ocular melanoma: a series of 31 cases from a tertiary university hospital

Selin Kestel,Feriha Pınar Uyar Göçün,Betül Öğüt,Özlem Erdem 대한병리학회 2022 Journal of Pathology and Translational Medicine Vol.56 No.4

Background: We aimed to determine the effect of clinicopathologic features on overall survival among Caucasian ocular melanoma patients in the Central Anatolia region of Turkey.Methods: This single-center study included conjunctival (n = 12) and uveal (n = 19) melanoma patients diagnosed between January 2008 and March 2020. Clinicopathologic features and outcomes were reviewed retrospectively. Five cases were tested for BRAF V600 mutations with real-time polymerase chain reaction, and one case was tested with nextgeneration sequencing. Survival was calculated using the Kaplan-Meier method.Results: Thirty-one patients had a mean initial age of 58.32 years (median, 61 years; range 25 to 78 years). There were 13 male and 18 female patients. The median follow-up time was 43.5 months (range, 6 to 155 months) for conjunctival melanoma and 35 months (range, 8 to 151 months) for uveal melanoma. When this study ended, eight of the 12 conjunctival melanoma patients (66.7%) and nine of the 19 uveal melanoma patients (47.4%) had died. The presence of tumor-infiltrating lymphocytes was related to improved overall survival in conjunctival melanoma (p = .014), whereas the presence of ulceration (p = .030), lymphovascular invasion (p = .051), tumor in the left eye (p = .012), tumor thickness of > 2 mm (p = .012), and mitotic count of >1/mm² (p = .012) reduced the overall survival in conjunctival melanoma. Uveal melanoma tumors with the largest diameter of 9.1–15 mm led to the lowest overall survival among subgroups (p = .035). Involvement of the conjunctiva (p=.005) and lens (p = .003) diminished overall survival in uveal melanoma. BRAF V600 mutation was present in one case of conjunctival melanoma, GNAQ R183Q mutation was present in one case of uveal melanoma. Patients with uveal melanoma presented with an advanced pathological tumor stage compared to those with conjunctival melanoma (p = .019).Conclusions: This study confirmed the presence of tumor-infiltrating lymphocytes as a favorable factor in conjunctival melanoma and conjunctival and lens involvement as unfavorable prognostic factors in uveal melanoma for overall survival, respectively.

Multiple idiopathic external and internal resorption: Case report with cone-beam computed tomography findings

Celikten, Berkan,Uzuntas, Ceren Feriha,Kurt, Hakan Korean Academy of Oral and Maxillofacial Radiology 2014 Imaging Science in Dentistry Vol.44 No.4

Root resorption is loss of dental hard tissue as a result of clastic activities. The dental hard tissue of permanent teeth does not normally undergo resorption, except in cases of inflammation or trauma. However, there are rare cases of tooth resorption of an unknown cause, known as "idiopathic root resorption". This report would discuss a rare case of multiple idiopathic resorption in the permanent maxillary and mandibular teeth of an otherwise healthy 36-year-old male patient. In addition to a clinical examination, the patient was imaged using conventional radiography and cone-beam computed tomography (CBCT). The examinations revealed multiple external and internal resorption of the teeth in all four quadrants of the jaws with an unknown cause. Multiple root resorption is a rare clinical phenomenon that should be examined using different radiographic modalities. Cross-sectional CBCT is useful in the diagnosis and examination of such lesions.

Rotor Position Estimation Strategy Using Artificial Neural Network for a Novel Design Transverse Flux Machine

Cigdem Gundogan Turker,Feriha Erfan Kuyumcu 대한전기학회 2015 Journal of Electrical Engineering & Technology Vol.10 No.5

The E-Core Transverse Flux Machine is a different design of transverse flux machines combined with reluctance principle. Determination of the rotor position is important for the movement of the ETFM by switching the phase currents in synchronism with the inductance regions of the stator windings. It is the first time that rotor position estimation based on Artificial Neural Network (ANN) is purposed to eliminate the position sensor for the ETFM. Simulation and experimental tests are demonstrated for the feasibility of the proposed estimation algorithm for the exercise bike application of the ETFM.

Multiple idiopathic external and internal resorption: Case report with cone-beam computed tomography findings

Berkan Celikten,Ceren Feriha Uzuntas,Hakan Kurt 대한영상치의학회 2014 Imaging Science in Dentistry Vol.44 No.4

Root resorption is loss of dental hard tissue as a result of clastic activities. The dental hard tissue of permanent teeth does not normally undergo resorption, except in cases of inflammation or trauma. However, there are rare cases of tooth resorption of an unknown cause, known as "idiopathic root resorption." This report would discuss a rare case of multiple idiopathic resorption in the permanent maxillary and mandibular teeth of an otherwise healthy 36-year-old male patient. In addition to a clinical examination, the patient was imaged using conventional radiography and cone-beam computed tomography (CBCT). The examinations revealed multiple external and internal resorption of the teeth in all four quadrants of the jaws with an unknown cause. Multiple root resorption is a rare clinical phenomenon that should be examined using different radiographic modalities. Cross-sectional CBCT is useful in the diagnosis and examination of such lesions.

Rotor Position Estimation Strategy Using Artificial Neural Network for a Novel Design Transverse Flux Machine

Turker, Cigdem Gundogan,Kuyumcu, Feriha Erfan The Korean Institute of Electrical Engineers 2015 Journal of Electrical Engineering & Technology Vol.10 No.5

The E-Core Transverse Flux Machine is a different design of transverse flux machines combined with reluctance principle. Determination of the rotor position is important for the movement of the ETFM by switching the phase currents in synchronism with the inductance regions of the stator windings. It is the first time that rotor position estimation based on Artificial Neural Network (ANN) is purposed to eliminate the position sensor for the ETFM. Simulation and experimental tests are demonstrated for the feasibility of the proposed estimation algorithm for the exercise bike application of the ETFM.