Mathematics / Matematik

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Now showing 1 - 10 of 24
  • Article
    Citation - WoS: 9
    Citation - Scopus: 8
    A Numerical Method Based on Legendre Wavelet and Quasilinearization Technique for Fractional Lane-Emden Type Equations
    (Springer, 2024) İdiz, F.; Tanoǧlu, G.; Aghazadeh, N.
    In this research, we study the numerical solution of fractional Lane-Emden type equations, which emerge mainly in astrophysics applications. We propose a numerical approach making use of Legendre wavelets and the quasilinearization technique. The nonlinear term in fractional Lane-Emden type equations is iteratively linearized using the quasilinearization technique. The linearized equations are then solved using the Legendre wavelet collocation method. The proposed method is quite effective to overcome the singularity in fractional Lane-Emden type equations. Convergence and error analysis of the proposed method are given. We solve some test problems to compare the effectiveness of the proposed method with some other numerical methods in the literature. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 8
    Local Well-Posedness of the Higher-Order Nonlinear Schrödinger Equation on the Half-Line: Single-Boundary Condition Case
    (Wiley, 2024) Alkın, A.; Mantzavinos, D.; Özsarı, T.
    We establish local well-posedness in the sense of Hadamard for a certain third-order nonlinear Schrödinger equation with a multiterm linear part and a general power nonlinearity, known as higher-order nonlinear Schrödinger equation, formulated on the half-line (Formula presented.). We consider the scenario of associated coefficients such that only one boundary condition is required and hence assume a general nonhomogeneous boundary datum of Dirichlet type at (Formula presented.). Our functional framework centers around fractional Sobolev spaces (Formula presented.) with respect to the spatial variable. We treat both high regularity ((Formula presented.)) and low regularity ((Formula presented.)) solutions: in the former setting, the relevant nonlinearity can be handled via the Banach algebra property; in the latter setting, however, this is no longer the case and, instead, delicate Strichartz estimates must be established. This task is especially challenging in the framework of nonhomogeneous initial-boundary value problems, as it involves proving boundary-type Strichartz estimates that are not common in the study of Cauchy (initial value) problems. The linear analysis, which forms the core of this work, crucially relies on a weak solution formulation defined through the novel solution formulae obtained via the Fokas method (also known as the unified transform) for the associated forced linear problem. In this connection, we note that the higher-order Schrödinger equation comes with an increased level of difficulty due to the presence of more than one spatial derivatives in the linear part of the equation. This feature manifests itself via several complications throughout the analysis, including (i) analyticity issues related to complex square roots, which require careful treatment of branch cuts and deformations of integration contours; (ii) singularities that emerge upon changes of variables in the Fourier analysis arguments; and (iii) complicated oscillatory kernels in the weak solution formula for the linear initial-boundary value problem, which require a subtle analysis of the dispersion in terms of the regularity of the boundary data. The present work provides a first, complete treatment via the Fokas method of a nonhomogeneous initial-boundary value problem for a partial differential equation associated with a multiterm linear differential operator. © 2023 Wiley Periodicals LLC.
  • Conference Object
    Citation - WoS: 1
    Citation - Scopus: 4
    Uniform Asymptotic Stability by Indefinite Lyapunov Functions
    (IEEE, 2022) Sahan, Gokhan; Ozdemir, Derya
    In this work, we consider Uniform Asymptotic Stability (UAS) of nonlinear time-varying systems. We utilize an indefinite signed polynomial of Lyapunov Function (LF) for the upper bound of the derivative of LF. This special bound is especially useful for perturbation problems. Compared to the ones in the literature we improve the upper bound of the LF and its related properties. Since UAS is the first step for input to state stability (ISS) and integral ISS, it should be thought that these improvements will give rise to new advances in real-world applications as well.
  • Article
    Citation - WoS: 1
    Dedekind Harmonic Numbers
    (Indian Academy of Sciences, 2021) Altuntaş, Çağatay; Göral, Haydar
    For any number field, we define Dedekind harmonic numbers with respect to this number field. First, we show that they are not integers except finitely many of them. Then, we present a uniform and an explicit version of this result for quadratic number fields. Moreover, by assuming the Riemann hypothesis for Dedekind zeta functions, we prove that the difference of two Dedekind harmonic numbers are not integers after a while if we have enough terms, and we prove the non-integrality of Dedekind harmonic numbers for quadratic number fields in another uniform way together with an asymptotic result.
  • Conference Object
    Holomorphic Realization of Non-Commutative Space-Time and Gauge Invariance
    (IOP Publishing, 2003) Mir-Kasimov, Rufat M.
    The realization of the Poincare Lie algebra in terms of noncommutative differential calculus over the commutative algebra of functions is considered. The algebra of functions is defined on the spectrum of the unitary irreducible representations of the De Sitter group. Corresponding space-time carries the noncommutative geometry. Gauge invariance principle consistent with this noncommutative space is considered.
  • Conference Object
    Citation - Scopus: 1
    Hipokampüsün El ve Atlas Tabanlı Otomatik Bölütlenmesinin Hacimsel Olarak Karşılaştırılması
    (Institute of Electrical and Electronics Engineers Inc., 2009) Kutucu, Hakan; Eker, Çağdaş; Kitiş, Ömer; Gönül, Ali Saffet
    High-resolution Magnetic resonance imaging (MRI) is helpful in diagnosing diseases such as schizophrenia, alzheimer, dementia etc. Brain segmentation is an important preprocess in medical imaging applications. In this study we compare atlas based segmentation and manual segmentation of hippocampus for volumetric measures. A statistically difference was obtained between automatic and manual measurement. We conclude that contemporary techniques are not adequate to obtain sensitive data in some barin structures such as hippocampus core.
  • Article
    Citation - WoS: 35
    Citation - Scopus: 93
    Search for Resonant and Nonresonant Higgs Boson Pair Production in the B B ¯final State in Proton-Proton Collisions at ?s=13 Tev
    (Springer Verlag, 2018) CMS Collaboration; Karapınar, Güler
    Searches for resonant and nonresonant pair-produced Higgs bosons (HH) decaying respectively into , through either W or Z bosons, and b b ¯ are presented. The analyses are based on a sample of proton-proton collisions at s=13 TeV, collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 35.9 fb −1 . Data and predictions from the standard model are in agreement within uncertainties. For the standard model HH hypothesis, the data exclude at 95% confidence level a product of the production cross section and branching fraction larger than 72 fb, corresponding to 79 times the standard model prediction. Constraints are placed on different scenarios considering anomalous couplings, which could affect the rate and kinematics of HH production. Upper limits at 95% confidence level are set on the production cross section of narrow-width spin-0 and spin-2 particles decaying to Higgs boson pairs, the latter produced with minimal gravity-like coupling.
  • Article
    Citation - WoS: 24
    Citation - Scopus: 26
    Pseudorapidity Distributions of Charged Hadrons in Proton-Lead Collisions at ?snn=5.02 and 8.16 Tev
    (Springer Verlag, 2018) CMS Collaboration; Karapınar, Güler
    The pseudorapidity distributions of charged hadrons in proton-lead collisions at nucleon-nucleon center-of-mass energies sNN=5.02 and 8.16 TeV are presented. The measurements are based on data samples collected by the CMS experiment at the LHC. The number of primary charged hadrons produced in non-single-diffractive proton-lead collisions is determined in the pseudorapidity range |η lab | < 2.4. The charged-hadron multiplicity distributions are compared to the predictions from theoretical calculations and Monte Carlo event generators. In the center-of-mass pseudorapidity range |η cm | < 0.5, the average charged-hadron multiplicity densities 〈dN ch /dη cm 〉 |ηcm| < 0.5 are 17.31 ± 0.01 (stat) ± 0.59 (syst) and 20.10 ± 0.01 (stat) ± 0.85(syst) at sNN=5.02 and 8.16 TeV, respectively. The particle densities per participant nucleon are compared to similar measurements in proton-proton, proton-nucleus, and nucleus-nucleus collisions.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 6
    Production of Leading Charged Particles and Leading Charged-Particle Jets at Small Transverse Momenta in Pp Collisions at Sqrt(s) = 8 Tev
    (American Physical Society, 2015) CMS Collaboration; Karapınar, Güler
    The per-event yield of the highest transverse momentum charged particle and charged-particle jet, integrated above a given pTmin threshold starting at pTmin=0.8 and 1 GeV, respectively, is studied in pp collisions at s=8 TeV. The particles and the jets are measured in the pseudorapidity ranges |η|<2.4 and 1.9, respectively. The data are sensitive to the momentum scale at which parton densities saturate in the proton, to multiple partonic interactions, and to other key aspects of the transition between the soft and hard QCD regimes in hadronic collisions. © 2015 CERN, for the CMS Collaboration. Published by the American Physical Society under the terms of the »http://creativecommons.org/licenses/by/3.0/» Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
  • Conference Object
    Citation - WoS: 1
    Citation - Scopus: 1
    Enabling Cooperation, Resource Allocation and Receiver Selection Across Cells: Complementary Fractional Frequency Reuse
    (Institute of Electrical and Electronics Engineers Inc., 2013) Bakşi, Saygın; Kaya, Onur; Bıyıkoğlu, Türker
    For a multi-cell multiple access channel, we develop a comprehensive cooperative communication framework: we propose a novel complementary fractional frequency reuse (FFR) strategy tailored specifically for pairwise user cooperation, also taking into account cell sectoring. This strategy allows the cell edge users not only to pool their resources and cooperate across cells, but also to choose the best receiver. We divide the users into cooperating inner and outer user pairs, and assign each pair orthogonal resources using OFDMA. We employ pairwise bidirectional cooperation based on block Markov superposition encoding among user pairs. We derive the achievable rates, while taking into account the geometry dependent interference at the users and the receiver. We find the jointly optimal power allocation, partner selection and receiver selection strategies that maximize the sum rate of the system. We then propose a heuristic matching algorithm, which operates based only on user and receiver locations. We compare the performance of our proposed strategies with several non-cooperative models, and demonstrate that the sum rate can nearly be doubled, while using the same resources. © 2013 IEEE.