Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Widths and Entropy of Sets of Smooth Functions on Compact Homogeneous Manifolds(Tubitak, 2021) LEVESLEY, Jeremy; KUSHPEL, Alexander; Taş, KenanWe develop a general method to calculate entropy and n-widths of sets of smooth functions on an arbitrary compact homogeneous Riemannian manifold Md . Our method is essentially based on a detailed study of geometric characteristics of norms induced by subspaces of harmonics on Md . This approach has been developed in the cycle of works [1, 2, 10–19]. The method’s possibilities are not confined to the statements proved but can be applied in studying more general problems. As an application, we establish sharp orders of entropy and n-widths of Sobolev’s classes Wγ p ( Md ) and their generalisations in Lq ( Md ) for any 1 < p, q < ∞. In the case p, q = 1, ∞ sharp in the power scale estimates are presented.Article An Algebraic Stability Test for Fractional Order Time Delay Systems(Balikesir University, 2020) Özyetkin, Münevver Mine; Baleanu, DumitruIn this study, an algebraic stability test procedure is presented for fractionalorder time delay systems. This method is based on the principle of eliminatingtime delay. The stability test of fractional order systems cannot be examineddirectly using classical methods such as Routh-Hurwitz, because such systemsdo not have analytical solutions. When a system contains the square roots ofs, it is seen that there is a double value function of s. In this study, a stabilitytest procedure is applied to systems including ps and/or different fractionaldegrees such as s where 0 < α < 1, and αǫR. For this purpose, the integerorder equivalents of fractional order terms are first used and then the stabilitytest is applied to the system by eliminating time delay. Thanks to the proposedmethod , it is not necessary to use approximations instead of time delay termsuch as Pad´e. Thus, the stability test procedure does not require the solutionof higher order equations.Article A Behavioral Perspective on Price Convergence via Perturbed Metric Spaces with an Extended Contraction(Association of Mathematicians (MATDER), 2026) Bilazeroğlu, ŞeymaIn this study, we examine how investors update their price forecasts over time within a "perturbated metric space," which incorporates behavioral influences and market friction. Classical metric structures are inadequate when the measured distance changes with perceived deviations. Therefore, a new structure is proposed in which the measured distance is modified by perceived deviations. In this context, the existence of a fixed point is guaranteed through an extended contraction inequality, and the convergence behavior of the model is analyzed using different examples. Simulations established under different linear and nonlinear update functions demonstrate that the model can reflect both slow and fast market behaviors that reach equilibrium. The proposed approach mathematically demonstrates that investors can reach a common price expectation in the long run, even with heterogeneous psychological responses.