TR Dizin İndeksli Yayınlar / TR Dizin Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7149
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Article Biquandle Power Brackets of Oriented Links(Tubitak Scientific & Technological Research Council Turkey, 2025) Gügümcü, Neslihan; Nelson, SamIn this paper, we introduce biquandle power brackets, an infinite family of invariants of oriented links containing the classical skein invariants and the quandle and biquandle 2-cocycle invariants as special cases. Biquandle power brackets are generalizations of biquandle brackets in which the values of Kauffman states also depend on the biquandle colors they admit. We provide example computations and discuss the relationship between these new invariants and the previous cases.Article The Adjoint Reidemeister Torsion for Compact 3-Manifolds Admitting a Unique Decomposition(TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2023) Erdal, Esma DiricanLet M be a triangulated, oriented, connected compact 3 -manifold with a connected nonempty boundary. Such a manifold admits a unique decomposition into △ -prime 3 -manifolds. In this paper, we show that the adjoint Reidemeister torsion has a multiplicative property on the disk sum decomposition of compact 3 -manifolds without a corrective term.Article Citation - WoS: 1Citation - Scopus: 1Resting Electroencephalography Differences Between Eyes-Closed and Eyes-Open Conditions in Children With Subclinical Hypothyroidism(AVES, 2023) Bayazıt, Onur; Kahya, Mehmet Cemal; Çatlı, Gönül; Kocaaslan Atlı, Sibel; Olgaç Dündar, Nihal; Erdoğan, Uğraş; Evirgen Esin, NurObjective: Electroencephalography changes that occur during the transition from eyes-closed to the eyes-open state in resting condition are related to the early phase of sensory processing and are defined as activation. The present study aimed to reveal the potential deteriorations that may occur in the initial period of sensory processing in resting electroencephalography between children with subclinical hypothyroidism and a control group. Materials and Methods: Electroencephalographies of 15 children with subclinical hypothy-roidism and 15 healthy children aged 10 to 17 years were recorded for 2 minutes for EC and 2 minutes for eyes-open conditions in resting state. Absolute electroencephalography band powers (μV2) within the delta, theta, alpha, and beta frequency bands were calculated in Fz, Cz, Pz, and Oz electrodes, respectively, for eyes-closed and eyes-open conditions. Results: The results show that, although there was no noteworthy difference between the powers of the electroencephalography frequency bands of children with subclinical hypothyroidism and healthy children during the eyes-open condition, the alpha powers of the control group were significantly higher in all electrodes during the eyes-closed condition. Furthermore, the powers of all frequency bands were observed to decrease in the eyes-open condition in the control group. However, the same net decrease was not observed in the frequency powers of children with subclinical hypothyroidism. Conclusion: According to the results of this study, children with subclinical hypothyroidism may experience information processing impairments starting in the early stages of sensory processing. © 2023, AVES. All rights reserved.Article Discrete Fractional Integrals, Lattice Points on Short Arcs, and Diophantine Approximation(TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2022) Temur, FarukRecently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the scope of those results by extending boundedness to bivariate quadratic polynomials. We achieve this in part by establishing connections to problems on concentration of lattice points on short arcs of conics, whence we study discrete fractional integrals and lattice point concentration from a unified perspective via tools of sieving and diophantine approximation, and prove theorems that are of interest to researchers in both subjects.Article Citation - WoS: 1Citation - Scopus: 1Stability in Commutative Rings(TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2020) Ay Saylam, BaşakLet R be a commutative ring with zero-divisors and I an ideal of R. I is said to be ES-stable if JI = $I^2$ for some invertible ideal J ? I , and I is said to be a weakly ES-stable ideal if there is an invertible fractional ideal J and an idempotent fractional ideal E of R such that I = JE . We prove useful facts for weakly ES-stability and investigate this stability in Noetherian-like settings. Moreover, we discuss a question of A. Mimouni on locally weakly ES-stable rings: is a locally weakly ES-stable domain of finite character weakly ES-stable?Article The Frequency Function and Its Connections To the Lebesgue Points and the Hardy-Littlewood Maximal Function(TÜBİTAK, 2019) Temur, FarukThe aim of this work is to extend the recent work of the author on the discrete frequency function to the more delicate continuous frequency function tau, and further to investigate its relations to the Hardy-Littlewood maximal function M, and to the Lebesgue points. We surmount the intricate issue of measurability of tau f by approaching it with a sequence of carefully constructed auxiliary functions for which measurability is easier to prove. After this, we give analogues of the recent results on the discrete frequency function. We then connect the points of discontinuity of Mf for f simple to the zeros of tau f, and to the non-Lebesgue points of f.Article Citation - WoS: 5Citation - Scopus: 5Convergence Analysis and Numerical Solution of the Benjamin-Bona Equation by Lie-Trotter Splitting(TUBITAK, 2018) Zürnacı, Fatma; Gücüyenen Kaymak, Nurcan; Seydaoğlu, Muaz; Tanoğlu, GamzeIn this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.Article Citation - WoS: 1Corrigendum: on Density Theorems for Rings of Krull Type With Zero Divisors(TUBITAK, 2017) Ay Saylam, BaşakThis corrigendum is written to correct some parts of the paper "On density theorems for rings of Krull type with zero divisors". The proofs of Proposition 2.4 and Proposition 4.3 are incorrect and the current note makes the appropriate corrections.Article Citation - Scopus: 2On Density Theorems for Rings of Krull Type With Zero Divisors(TUBITAK, 2014) Ay Saylam, BaşakLet R be a commutative ring and I(R) denote the multiplicative group of all invertible fractional ideals of R, ordered by A ≥ B if and only if B ⊆ A. If R is a Marot ring of Krull type, then R(Pi), where {Pi}i∈I are a collection of prime regular ideals of R, is a valuation ring and R = ∩ R(Pi) . We denote by Gi the value group of the valuation associated with R(Pi). We prove that there is an order homomorphism from I(R) into the cardinal direct sum ∐i∈I Gi and we investigate the conditions that make this monomorphism onto for R.Article Citation - Scopus: 13The Prognostic Value of Tumor-Stroma Proportion in Laryngeal Squamous Cell Carcinoma(Federation of Turkish Pathology Societies, 2013) Ünlü, Mehtat; Çetinayak, Hasan Oğuz; Önder, Devrim; Ecevit, Cenk; Akman, Fadime; İkiz, Ahmet ömer; Ada, Emel; Karaçalı, Bilge; Sarıoğlu, SülenObjective: Tumor-stroma proportion of tumor has been presented as a prognostic factor in some types of adenocarcinomas, but there is no information about squamous cell carcinomas and laryngeal carcinomas. Material and Method: Five digital images of the tumor sections were obtained from 85 laryngeal carcinomas. Proportion of epithelial tumor component and stroma were measured by a software tool, allowing the pathologists to mark 205.6 μm2 blocks on areas as carcinomatous/stromal, by clicking at the image. Totally, 3.451 mm2 tumor areas have been marked to 16.785 small square blocks for each case. Results: Median follow up was 48 months (range 3-194). The mean tumor-stroma proportion was 48.63+18.18. There was no difference for tumor-stroma proportion when tumor location, grade, stage and perinodal invasion were considered. Although the following results were statistically insignificant, the mean tumor-stroma proportion was the lowest (37.46±12.49) for subglottic carcinomas, and it was 52.41±37.47, 50.86+19.84 and 44.56±16.91 for supraglottic, transglottic and glottic cases. The tumor-stroma proportion was lowest in cases with perinodal invasion and the highest in cases without lymph node metastasis (44.72±20.23, 47.77±17.37, 50.05±17.34). Tumor-stroma proportion was higher in the basaloid subtype compared with the classical squamous cell carcinoma (53.76±14.70 and 48.63±18.38 respectively). The overall and disease-free survival analysis did not reveal significance for tumor-stroma proportion (p=0.08, p=0.38). Only pathological stage was an independent factor for overall survival (p=0.008). Conclusion: This is the first series investigating tumor-stroma proportion as a prognostic marker in laryngeal carcinomas proposing a new method, but the findings do not support tumor-stroma proportion as a prognostic marker.