Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
Browse
100 results
Search Results
Article Citation - Scopus: 1Level Set Estimates for the Discrete Frequency Function(Springer Verlag, 2019) Temur, FarukWe introduce the discrete frequency function as a possible new approach to understanding the discrete Hardy-Littlewood maximal function. Considering that the discrete Hardy-Littlewood maximal function is given at each integer by the supremum of averages over intervals of integer length, we define the discrete frequency function at that integer as the value at which the supremum is attained. After verifying that the function is well-defined, we investigate size and smoothness properties of this function.Article On the Structure of Modules Defined by Opposites of Fp Injectivity(Springer Verlag, 2019) Büyükaşık, Engin; Kafkas Demirci, GizemLet R be a ring with unity and let MR and RN be right and left modules,respectively. The module MR is said to be absolutely RN-pure if M circle times NL circle times N is amonomorphism for every extension LR of MR. For a module MR, the subpurity domain of MR is defined to be the collection of all modules RN, such that MR is absolutely RN-pure. Clearly, MR is absolutely RF-pure for every flat module RF and that MR is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, MR is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. We characterize the structure of t.f.b.s. modules over commutative hereditary Noetherian rings. We prove that a module M is t.f.b.s. over a commutative hereditary Noetherian ring if and only if M/Z(M) is t.f.b.s. if and only if Hom(M/Z(M),S)0 for each singular simple module S. Prufer domains are characterized as those domains all of whose nonzero finitely generated ideals are t.f.b.s.Article Citation - WoS: 6Citation - Scopus: 7Integrable Systems From Inelastic Curve Flows in 2-And 3-Dimensional Minkowski Space(Taylor & Francis, 2016) Alkan, Kıvılcım; Anco, Stephen C.Integrable systems are derived from inelastic flows of timelike, spacelike, and null curves in 2-and 3- dimensional Minkowski space. The derivation uses a Lorentzian version of a geometrical moving frame method which is known to yield the modified Korteveg-de Vries (mKdV) equation and the nonlinear Schrodinger (NLS) equation in 2- and 3- dimensional Euclidean space, respectively. In 2-dimensional Minkowski space, time-like/space-like inelastic curve flows are shown to yield the defocusing mKdV equation and its bi-Hamiltonian integrability structure, while inelastic null curve flows are shown to give rise to Burgers' equation and its symmetry integrability structure. In 3-dimensional Minkowski space, the complex defocusing mKdV equation and the NLS equation along with their bi-Hamiltonian integrability structures are obtained from timelike inelastic curve flows, whereas spacelike inelastic curve flows yield an interesting variant of these two integrable equations in which complex numbers are replaced by hyperbolic (split-complex) numbers.Article Citation - WoS: 3Citation - Scopus: 3Blow-Up of Solutions of Nonlinear Schrödinger Equations With Oscillating Nonlinearities(American Institute of Mathematical Sciences, 2019) Özsarı, TürkerThe finite time blow-up of solutions for 1-D NLS with oscillating nonlinearities is shown in two domains: (1) the whole real line where the nonlinear source is acting in the interior of the domain and (2) the right half-line where the nonlinear source is placed at the boundary point. The distinctive feature of this work is that the initial energy is allowed to be non-negative and the momentum is allowed to be infinite in contrast to the previous literature on the blow-up of solutions with time dependent nonlinearities. The common finite momentum assumption is removed by using a compactly supported or rapidly decaying weight function in virial identities - an idea borrowed from [18]. At the end of the paper, a numerical example satisfying the theory is provided.Article A Supplement To the Paper of Zayed Et Al. [optik, 170 (2018) 339-341](Elsevier, 2019) Aslan, İsmailIt seems that the results obtained by the so-called Khater method contain computational or print errors. We look at this issue from a different point of a view, namely, from a theoretical side. We prove our claim by a formal direct approach instead of back substitution (trial and error) approach.Article The Frequency Function and Its Connections To the Lebesgue Points and the Hardy-Littlewood Maximal Function(TÜBİTAK, 2019) Temur, FarukThe aim of this work is to extend the recent work of the author on the discrete frequency function to the more delicate continuous frequency function tau, and further to investigate its relations to the Hardy-Littlewood maximal function M, and to the Lebesgue points. We surmount the intricate issue of measurability of tau f by approaching it with a sequence of carefully constructed auxiliary functions for which measurability is easier to prove. After this, we give analogues of the recent results on the discrete frequency function. We then connect the points of discontinuity of Mf for f simple to the zeros of tau f, and to the non-Lebesgue points of f.Article Citation - WoS: 3Citation - Scopus: 3A Perturbative Approach To the Tunneling Phenomena(Frontiers Media S.A., 2019) Erman, Fatih; Turgut, Osman TeomanThe double-well potential is a good example, where we can compute the splitting in the bound state energy of the system due to the tunneling effect with various methods, namely path-integral, WKB, and instanton calculations. All these methods are non-perturbative and there is a common belief that it is dif fi cult to fi nd the splitting in the energy due to the barrier penetration from a perturbative analysis. However, we will illustrate by explicit examples including singular potentials (e.g., Dirac delta potentials supported by points and curves and their relativistic extensions) it is possible to fi nd the splitting in the bound state energies by developing some kind of perturbation method.Article Citation - WoS: 40Citation - Scopus: 40The Initial-Boundary Value Problem for the Biharmonic Schrödinger Equation on the Half-Line(American Institute of Mathematical Sciences, 2019) Özsarı, Türker; Yolcu, NerminWe study the local and global wellposedness of the initial-boundary value problem for the biharmonic Schrodinger equation on the half-line with inhomogeneous Dirichlet-Neumann boundary data. First, we obtain a representation formula for the solution of the linear nonhomogenenous problem by using the Fokas method (also known as the unified transform method). We use this representation formula to prove space and time estimates on the solutions of the linear model in fractional Sobolev spaces by using Fourier analysis. Secondly, we consider the nonlinear model with a power type nonlinearity and prove the local wellposedness by means of a classical contraction argument. We obtain Strichartz estimates to treat the low regularity case by using the oscillatory integral theory directly on the representation formula provided by the Fokas method. Global wellposedness of the defocusing model is established up to cubic nonlinearities by using the multiplier technique and proving hidden trace regularities.Article Multiparticle Correlations and Higher Order Harmonics in Ppb Collisions at Root S(nn)=8.16 Tev(Elsevier Ltd., 2019) Karapınar, Güler; CMS CollaborationThe elliptic and higher-order azimuthal anisotropy Fourier harmonics (v(n)) are obtained for pPb collisions at root s(NN) = 8.16 TeV over a wide range of event multiplicities based on multiparticle correlations. The data were collected by the CMS experiment during the 2016 LHC run. A sample of peripheral PbPb collisions at root s(NN) = 5.02 TeV covering a similar range of event multiplicities to the pPb results is also analyzed for comparison. The ratios of different harmonic moments are obtained for both v(2) and v(3) with high precision, which allows a direct comparison to theoretical predictions assuming a hydrodynamic evolution of the created medium with initial-state density fluctuations, particularly probing the non-Gaussian nature of initial-state fluctuations in small collision systems. The presented results provide crucial insights into the origin of collective long-range correlations observed in small collision systems.Article Citation - WoS: 19Citation - Scopus: 24Pseudorapidity and Transverse Momentum Dependence of Flow Harmonics in P Pb and Pbpb Collisions(American Physical Society, 2018) CMS Collaboration; Karapınar, GülerMeasurements of azimuthal angular correlations are presented for high-multiplicity pPb collisions at sNN=5.02TeV and peripheral PbPb collisions at sNN=2.76TeV. The data used in this work were collected with the Compact Muon Solenoid (CMS) detector at the European Organization for Nuclear Research (CERN) Large Hadron Collider (LHC). Fourier coefficients as functions of transverse momentum and pseudorapidity are studied using the scalar product method; four-, six-, and eight-particle cumulants; and the Lee-Yang zero technique. The influence of event plane decorrelation is evaluated using the scalar product method and found to account for most of the observed pseudorapidity dependence.