GCRIS Repository Collection: Collection of Mathematics / Matematik Bölümü koleksiyonu
https://hdl.handle.net/11147/8
Collection of Mathematics / Matematik Bölümü koleksiyonu2023-12-07T12:25:36ZArithmetic progressions in certain subsets of finite fields
https://hdl.handle.net/11147/13781
Title: Arithmetic progressions in certain subsets of finite fields
Authors: Eyidoğan, Sadık; Göral, Haydar; Kutlu, Mustafa Kutay
Abstract: In this note, we focus on how many arithmetic progressions we have in certain subsets of finite fields. For this purpose, we consider the sets Sp = {t2 : t & ISIN; Fp} and Cp = {t3 : t & ISIN; Fp}, and we use the results on Gauss and Kummer sums. We prove that for any integer k & GE; 3 and for an odd prime number p, the number of k-term arithmetic progressions in Sp is given by p2 2k + R, where and ck is a computable constant depending only on k. The proof also uses finite Fourier analysis and certain types of Weil estimates. Also, we obtain some formulas that give the exact number of arithmetic progressions of length in the set Sp when & ISIN; {3,4, 5} and p is an odd prime number. For = 4, 5, our formulas are based on the number of points on2023-01-01T00:00:00ZExponential stability and boundedness of nonlinear perturbed systems by unbounded perturbation terms
https://hdl.handle.net/11147/13777
Title: Exponential stability and boundedness of nonlinear perturbed systems by unbounded perturbation terms
Authors: Şahan, Gökhan
Abstract: We study the exponential stability and boundedness problem for perturbed nonlinear time-varying systems using Lyapunov Functions with indefinite derivatives. As the limiting function for the perturbation term, we use different forms and give stability and boundedness conditions in terms of the coefficients in these bounds. Contrary to most of the available conditions, we allow the coefficients to be unbounded. But instead, we put forward a condition that requires a series produced by coefficients to be limited and exponentially decaying. We perform our results on Linear time-varying systems and generalize many of the available results. & COPY; 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.2023-01-01T00:00:00ZDual Kasch rings
https://hdl.handle.net/11147/13759
Title: Dual Kasch rings
Authors: Büyükaşık, Engin; Lomp, Christian; Yurtsever, Haydar Baran
Abstract: It is well known that a ring R is right Kasch if each simple right R-module embeds in a projective right R-module. In this paper we study the dual notion and call a ring R right dual Kasch if each simple right R-module is a homomorphic image of an injective right R-module. We prove that R is right dual Kasch if and only if every finitely generated projective right R-module is coclosed in its injective hull. Typical examples of dual Kasch rings are self-injective rings, V-rings and commutative perfect rings. Skew group rings of dual Kasch rings by finite groups are dual Kasch if the order of the group is invertible. Many examples are given to separate the notion of Kasch and dual Kasch rings. It is shown that commutative Kasch rings are dual Kasch, and a commutative ring with finite Goldie dimension is dual Kasch if and only if it is a classical ring (i.e. every element is a zero divisor or invertible). We obtain that, for a field k, a finite dimensional k-algebra is right dual Kasch if and only if it is left Kasch. We also discuss the rings over which every simple right module is a homomorphic image of its injective hull, and these rings are termed strongly dual Kasch.
Description: Article; Early Access2023-01-01T00:00:00ZThe adjoint Reidemeister torsion for compact 3-manifolds admitting a unique decomposition
https://hdl.handle.net/11147/13746
Title: The adjoint Reidemeister torsion for compact 3-manifolds admitting a unique decomposition
Authors: Dirican Erdal, Esma
Abstract: Let M be a triangulated, oriented, connected compact 3-manifold with a connected nonempty boundary. Such a manifold admits a unique decomposition into o-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.2023-01-01T00:00:00Z