Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 1Citation - Scopus: 1A New Hamiltonian System(Academic Press inc Elsevier Science, 2020) Ugurlu, EkinThis paper aims to share a new first-order differential equation that contains the continuous analogous of the orthogonal polynomials on the unit-circle. We introduce some basic results on the system and solutions of the system. Using nested-circle approach we introduce the possible number of square-integrable solutions of the system. At the end of the paper we share a limit-point criteria for the two-dimensional system of equations. (C) 2020 Elsevier Inc. All rights reserved.Article Citation - WoS: 6Citation - Scopus: 6The Radii of Sections of Origin-Symmetric Convex Bodies and Their Applications(Academic Press inc Elsevier Science, 2021) Tas, Kenan; Kushpel, AlexanderLet V and W be any convex and origin-symmetric bodies in R-n . Assume that for some A is an element of L (R-n -> R-n), det A not equal 0, V is contained in the ellipsoid A(-1)B((2))(n), where B-(2)(n) is the unit Euclidean ball. We give a lower bound for the W-radius of sections of A(-1) V in terms of the spectral radius of AA and the expectations of parallel to . parallel to(V) and parallel to . parallel to(W)0 with respect to Haar measure on Sn-1 subset of R-n. It is shown that the respective expectations are bounded as n -> infinity in many important cases. As an application we offer a new method of evaluation of n-widths of multiplier operators. As an example we establish sharp orders of n-widths of multiplier operators Lambda : L-p (M-d) -> L-q (M-d), 1 < q <= 2 <= p < infinity on compact homogeneous Riemannian manifolds M-d. Also, we apply these results to prove the existence of flat polynomials on M-d. (c) 2020 Elsevier Inc. All rights reserved.Article Citation - WoS: 22Citation - Scopus: 27On Multiplication in Finite Fields(Academic Press inc Elsevier Science, 2010) Ozbudak, Ferruh; Cenk, MuratWe present a method for multiplication in finite fields which gives multiplication algorithms with improved or best known bilinear complexities for certain finite fields. Our method generalizes some earlier methods and combines them with the recently introduced complexity notion (M) over cap (q)(l), which denotes the minimum number of multiplications needed in F-q in order to obtain the coefficients of the product of two arbitrary l-term polynomials modulo x(l) in F-q[x]. We study our method for the finite fields F(q)n, where 2 <= n <= 18 and q = 2, 3,4 and we improve or reach the currently best known bilinear complexities. We also give some applications in cryptography. (C) 2010 Published by Elsevier Inc.Article Citation - WoS: 14Citation - Scopus: 18A Validated Active Contour Method Driven by Parabolic Arc Model for Detection and Segmentation of Mitochondria(Academic Press inc Elsevier Science, 2016) Hassanpour, Reza Z.; Perkins, Guy; Tasel, Serdar F.; Mumcuoglu, Erkan U.Recent studies reveal that mitochondria take substantial responsibility in cellular functions that are closely related to aging diseases caused by degeneration of neurons. These studies emphasize that the membrane and crista morphology of a mitochondrion should receive attention in order to investigate the link between mitochondria] function and its physical structure. Electron microscope tomography (EMT) allows analysis of the inner structures of mitochondria by providing highly detailed visual data from large volumes. Computerized segmentation of mitochondria with minimum manual effort is essential to accelerate the study of mitochondrial structure/function relationships. In this work, we improved and extended our previous attempts to detect and segment mitochondria from transmission electron microcopy (TEM) images. A parabolic arc model was utilized to extract membrane structures. Then, curve energy based active contours were employed to obtain roughly outlined candidate mitochondrial regions. Finally, a validation process was applied to obtain the final segmentation data. 3D extension of the algorithm is also presented in this paper. Our method achieved an average F-score performance of 0.84. Average Dice Similarity Coefficient and boundary error were measured as 0.87 and 14 nm respectively. (C) 2016 Elsevier Inc. All rights reserved.Article Citation - WoS: 158Citation - Scopus: 181Hamiltonian Formulation of Systems With Linear Velocities Within Riemann-Liouville Fractional Derivatives(Academic Press inc Elsevier Science, 2005) Muslih, SI; Baleanu, D; Avkar, T.The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent. (c) 2004 Elsevier Inc. All rights reserved.Article Citation - WoS: 4Citation - Scopus: 4On the Optimality of the Trigonometric System(Academic Press inc Elsevier Science, 2020) Jarad, Fahd; Kushpel, A.; Tas, K.We study a new phenomenon of the behaviour of widths with respect to the optimality of trigonometric system. It is shown that the trigonometric system is optimal in the sense of Kolmogorov widths in the case of "super-high" and "super-small" smoothness but is not optimal in the intermediate cases. Bernstein's widths behave differently when compared with Kolmogorov in the case of "super-small" smoothness. However, in the case of "super-high" smoothness Kolmogorov and Bernstein widths behave similarly, i.e. are realized by trigonometric polynomials. (C) 2019 Elsevier Inc. All rights reserved.Article Citation - WoS: 4Citation - Scopus: 4Singular Hamiltonian System With Several Spectral Parameters Ii: Odd-Order Case(Academic Press inc Elsevier Science, 2019) Ugurlu, EkinIn this paper we deal with a singular Hamiltonian system of odd-order with several spectral parameters and we investigate the behavior of the solution of this system at singular point with the aid of the characteristic function theory. Moreover, some results have been introduced for the Weyl-Titchmarsh function for some special Hamiltonian systems of odd-order with several spectral parameters. (C) 2019 Elsevier Inc. All rights reserved.Article The Quaternion Group Has Ghost Number Three(Academic Press inc Elsevier Science, 2017) Aksu, Fatma Altunbulak; Green, David J.; Altunbulak Aksu, FatmaWe prove that the group algebra of the quaternion group Q(8) over any field of characteristic two has ghost number three. (C) 2016 Elsevier Inc. All rights reserved.Article Citation - WoS: 5Citation - Scopus: 5Singular Hamiltonian System With Several Spectral Parameters(Academic Press inc Elsevier Science, 2018) Ugurlu, EkinIn this paper, the Weyl-Titchmarsh theory has been constructed for the singular 2n-dimensional (even order) Hamiltonian system with several spectral parameters. In particular, we consider that the left end point of the interval is regular and the right end point of the interval is singular for the Hamiltonian system with several parameters. Using the nested circles approach, we prove that at least n-linearly independent solutions are squarly integrable with respect to some matrix functions. (C) 2018 Elsevier Inc. All rights reserved.Article Citation - WoS: 61Citation - Scopus: 70Tau Method for the Numerical Solution of a Fuzzy Fractional Kinetic Model and Its Application To the Oil Palm Frond as a Promising Source of Xylose(Academic Press inc Elsevier Science, 2015) Salahshour, S.; Baleanu, D.; Amirkhani, H.; Yunus, R.; Ahmadian, A.The Oil Palm Frond (a lignocellulosic material) is a high-yielding energy crop that can be utilized as a promising source of xylose. It holds the potential as a feedstock for bioethanol production due to being free and inexpensive in terms of collection, storage and cropping practices. The aim of the paper is to calculate the concentration and yield of xylose from the acid hydrolysis of the Oil Palm Frond through a fuzzy fractional kinetic model. The approximate solution of the derived fuzzy fractional model is achieved by using a tau method based on the fuzzy operational matrix of the generalized Laguerre polynomials. The results validate the effectiveness and applicability of the proposed solution method for solving this type of fuzzy kinetic model. (C) 2015 Elsevier Inc. All rights reserved.