WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7150

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Department: search.filters.department.İzmir Institute of Technology. MathematicsPublisher: search.filters.publisher.TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu

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  • Article
    Discrete Fractional Integrals, Lattice Points on Short Arcs, and Diophantine Approximation
    (TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2022) Temur, Faruk; Temur, Faruk; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    Recently 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: 1
    Citation - Scopus: 1
    Stability in Commutative Rings
    (TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2020) Ay Saylam, Başak; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    Let 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?