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Publication Open Access A class of Banach algebras whose duals have the Schur property(TÜBİTAK, 1999) Mustafayev, H.; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of SciencesCall a commutative Banach algebra A a γ-algebra if it contains a bounded group Λ such that aco(Λ) contains a multiple of the unit ball of A. In this paper, first by exhibiting several concrete examples, we show that the class of γ-algebras is quite rich. Then, for a γ-algebra A, we prove that A* has the Schur property iff the Gelfand spectrum Σ of A is scattered iff A* = ap(A) iff A* = Span(Σ).
Publication Metadata only A class of banach algebras whose duals have the schur property(Scientific and Technical research Council of Turkey - TUBITAK/Türkiye Bilimsel ve Teknik Araştırma Kurumu, 1999) Mustafayev, Heybetkulu; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/ACall a commutative Banach algebra A a γ-algebra if it contains a bounded group Λ such that aco(Λ) contains a multiple of the unit ball of A. In this paper, first by exhibiting several concrete examples, we show that the class of γ-algebras is quite rich. Then, for a γ-algebra A, we prove that A* has the Schur property iff the Gelfand spectrum Σ of A is scattered iff A* = ap(A) iff A* = Span(Σ).Publication Metadata only A fredholm alternative-like result on power bounded operators(Scientific Technical Research Council Turkey-Tubitak, 2011) Yavuz, Onur; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/ALet X be a complex Banach space and T:X\rightarrow X be a power bounded operator, i.e., \sup_{n \geq 0}\ T^n\Publication Metadata only A radiological study on the topographical relationships between the vestibular, cochlear and facial nerves(Atatürk Üniversitesi, 2012) Ünel, Sacide; Yılmaz, Mehmet; Albayram, Sait; Kiriş, Adem; Işık, Zehra; Işıldak, Hüseyin; Savaş, Yıldıray; Keser, Zafer; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/AObjective: The purpose of our study was to investigate the topographical relationship between these nerves along their course from the brainstem through the internal acoustic canal IAC in the living human brain using MR imaging. Materials and Methods: We performed three-dimensional gradient echo balanced Fast Field Echo (3D bFFE) sequence oblique parasagittal MR imaging in 73 healthy subjects. The IACs were analyzed from the brainstem end of the IAC to the fundus in contiguous sections. At five levels, the topographical relationships between the facial and vestibulocochlear nerves (VCN) were recorded. In the lateral portions of the IACs where they separated from each other, the relative sizes of the individual nerves were examined. Results: In general, the facial nerve (FN), which is a round structure, is located anteriorly and superiorly to the vestibulocochlear nerve throughout its course. The vestibulocochlear nerve is usually rectangular; however, it was found to be round and at times triangular in shape near the brainstem, before it became crescent-shaped at the porus in 89% of the cases. The superior vestibular nerve kept its posterosuperior position in the canal, and the inferior vestibular nerve (IVN) and the cochlear nerve (CN) travelled inferior to it. The superior and inferior vestibular nerves were divided by the falciform crest in 53% of the cases. The inferior vestibular nerve was the smallest nerve in 52% of the cases, and the cochlear nerve was the largest in 36% of the cases. Conclusion: To the best of our knowledge, this study is the largest in vivo MR study, and most of our findings differ from previous cadaver studies. Determination of these topographical relationships may facilitate our understanding of the complicated physiological relationships between the 7th and 8th nerve complexes during surgery in this region. / Öz: Amaç: Bizim amacımız, yaşayan insanlarda MR görüntülemeyi kullanarak, bu sinirlerin beyin sapından, internal akustik kanala kadar olan kısmında topografik ilişkilerini araştırmaktır. Gereç ve Yöntem: Yetmiş üç sağlıklı bireyde 3D gradient echo balanced fast field echo (3D bFFE) sekans oblik parasagittal MR inceleme yaptık. İAK, beyin sapından İAK’ın bitimindeki fundusa kadar, ardışık kesitlerle analiz edildi. Beş seviyede fasiyal ve vestibülokoklear sinirin topografik ilişkileri kaydedildi. İAK’ın lateral bölümünde (sinirin kendi içinde bölümlere ayrıldığı kısımda) sinirlerin rölatif boyutları değerlendirildi. Bulgular: Genel olarak fasiyal sinir, yuvarlak bir yapıda, anterior yerleşimli ve tüm seyri boyunca vestibulokoklear sinirin süperiorundadır. Vestibulokoklear sinir ıklıkla dikdörtgen şeklindedir. Fakat bazen beyin sapına yakın kısımda yuvarlak ve nadiren üçgen şeklinde ve vakaların %89’unda porusda kresentrik yapıdadır. Superior vestibuler sinir kanal içinde posterosüperior pozisyonunu korur ve inferior vestibüler sinir ve koklear sinir superior vestibüler sinirin altından geçer. Süperior ve inferior vestibüler sinirler vakaların %53’ünde falsiform krest tarafından bölünür. İnferior vestibüler sinir vakaların %52’sinde en küçük, koklear sinir vakaların %36’sında en geniş olarak izlenmiştir. Sonuç: Bildiğimiz kadarıyla, bu en büyük in vivo MR çalışması olup, bulgularımızın çoğu önceki kadavra çalışmalarından farklıdır.Publication Metadata only Cosmological adiabatic geometric phase of a scalar field in a Bianchi spacetime(Scientific and Technological Research Council of Turkey, 2000) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231A two-component formulation of the Klein-Gordon equation is used to investigate the cyclic and noncyclic adiabatic geometric phases due to spatially homogeneous (Bianchi) cosmological models. It is shown that no adiabatic geometric phases arise for Bianchi type I models. For general Bianchi type IX models the problem of the adiabatic geometric phase is shown to be equivalent to the one for nuclear quadrupole interactions of a spin. For these models nontrivial non-Abelian adiabatic geometrical phases may occur in general.Publication Metadata only Cyles in 2-factorizations of Kn(Anadolu Üniversitesi, 2002) N/A; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252This work studies cycles in 2-faetorizations of K n (undireeted complete graph with n vertices) and gives a complete solution (with three possible exceptions) of the problem of constructing 2-factorizations of K n containing a specified number of 8-cycles, for both n even and odd. / Bu çalışmada n köşeli tam graflardaki döngüler problemi işlenmekte, tek ve çift köşeli tam graflardaki 8-döngü sayısı problemine (üç olası istisna ile) çözüm verilmektedir.Publication Open Access Divisor function and bounds in domains with enough primes(Hacettepe Üniversitesi, 2019) Department of Mathematics; Göral, Haydar; Master Student; Department of Mathematics; College of SciencesIn this note, first we show that there is no uniform divisor bound for the Bezout identity using Dirichlet's theorem on arithmetic progressions. Then, we discuss for which rings the absolute value bound for the Bezout identity is not trivial and the answer depends on the number of small primes in the ring.Publication Metadata only Explicit realization of pseudo-Hermitian and quasi-Hermitian quantum mechanics for two-level systems(TÜBİTAK , 2006) N/A; Department of Mathematics; N/A; Mostafazadeh, Ali; Özçelik, Seher; Faculty Member; Master Student; Department of Mathematics; College of Sciences; Graduate School of Sciences and Engineering; 4231; N/AWe give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators η-, and η+-pseudo-Hermitian operators acting in ℂ2. The latter represent the physical observables of a model whose Hamiltonian and Hubert space are respectively H and ℂ2 endowed with the inner product defined by η+. Our calculations allows for a direct demonstration of the fact that the choice of an irreducible family of observables fixes the metric operator up to a multiplicative factor.Publication Metadata only Frequency of nerve root sleeve cysts in autosomal dominant polycystic kidney disease(Galenos Publ House, 2016) Asik, Murat; Tufan, Fatih; Akpinar, Timur Selcuk; Akalin, Nilgul; Tunc, Necmeddin; Hasiloglu, Zehra Isik; Altiparmak, Mehmet Riza; Ecder, Tevfik; Albayram, Sait; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/ABackground: There is sporadic data about the occurrence of spinal meningeal cysts in patients with autosomal dominant polycystic kidney disease ( ADPKD). We suggest that there is a relationship with the frequency and size of spinal meningeal cysts and headache, intracranial aneurysms, and cerebrospinal fluid leakage in patients with ADPKD. Aim: To investigate the relationship with spinal meningeal cyst, cerebrospinal fluid leakage, and headache in patients with ADPKD. Study Design: Cross-sectional study. Methods: We enrolled 50 patients with ADPKD and 37 healthy volunteers. This cross-sectional study included patients with ADPKD and matched healthy volunteers. Magnetic resonance imaging myelography was performed using the 3D-T2 HASTE technique in an MRI scanner. We questioned our subjects regarding presence of headache and evaluated headache severity using a visual analog scale. The relationship between the number and size of spinal men-ingeal cysts with headache, intracranial aneurysms, and liver cysts was also investigated. Results: Spinal meningeal cysts were more numerous and larger in patients than in controls (14.8 +/- 11.6 vs. 6.4 +/- 4.6 cysts respectively, p<0.001, 68.3 +/- 49.3 vs. 25.4 +/- 20.1 mm, p<0.001, respectively). Spinal cyst number and size were similar in APDKD patients with or without intracranial aneurysms. Headache score was correlated with the size and number of spinal meningeal cysts. This was valid only in patients with ADPKD. Conclusion: Abnormality involving the vessel wall in ADPKD may explain the increased number of spinal meningeal cysts in ADPKD. Moreover, leakage of cerebrospinal fluid secondary to spinal meningeal cyst may be responsible for recurrent severe headache by causing spontaneous intracranial hypotension in these patients.Publication Metadata only Large deformations of helices(İstanbul Technical University (İTÜ) / İstanbul Teknik Üniversitesi (İTÜ), 1992) Aköz, Yalçın; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822N/A