Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Now showing 1 - 10 of 12
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    A New Hamiltonian System
    (Academic Press inc Elsevier Science, 2020) Ugurlu, Ekin
    This 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: 6
    Citation - Scopus: 6
    The Radii of Sections of Origin-Symmetric Convex Bodies and Their Applications
    (Academic Press inc Elsevier Science, 2021) Tas, Kenan; Kushpel, Alexander
    Let 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: 22
    Citation - Scopus: 27
    On Multiplication in Finite Fields
    (Academic Press inc Elsevier Science, 2010) Ozbudak, Ferruh; Cenk, Murat
    We 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: 158
    Citation - Scopus: 181
    Hamiltonian 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: 4
    Citation - Scopus: 4
    On 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: 4
    Citation - Scopus: 4
    Singular Hamiltonian System With Several Spectral Parameters Ii: Odd-Order Case
    (Academic Press inc Elsevier Science, 2019) Ugurlu, Ekin
    In 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, Fatma
    We 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: 5
    Citation - Scopus: 5
    Singular Hamiltonian System With Several Spectral Parameters
    (Academic Press inc Elsevier Science, 2018) Ugurlu, Ekin
    In 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: 61
    Citation - Scopus: 70
    Tau 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.
  • Article
    Decoupling Structure of the Principal Sigma Model-Maxwell Interactions
    (Academic Press inc Elsevier Science, 2008) Yilmaz, Nejat T.
    The principal sigma model and Abelian gauge fields coupling is studied. By expressing the first-order formulation of the gauge field equations an implicit on-shell scalar-gauge field decoupling structure is revealed. It is also shown that due to this decoupling structure the scalars of the theory belong to the pure sigma model and the gauge fields sector consists of a number of coupled Maxwell theories with currents partially induced by the scalars. (C) 2008 Elsevier Inc. All rights reserved.