Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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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: 16Citation - Scopus: 16A Singular One-Dimensional Bound State Problem and Its Degeneracies(Springer Verlag, 2017) Erman, Fatih; Gadella, Manuel; Tunalı, Seçil; Uncu, HaydarWe give a brief exposition of the formulation of the bound state problem for the one-dimensional system of N attractive Dirac delta potentials, as an N× N matrix eigenvalue problem (ΦA= ωA). The main aim of this paper is to illustrate that the non-degeneracy theorem in one dimension breaks down for the equidistantly distributed Dirac delta potential, where the matrix Φ becomes a special form of the circulant matrix. We then give elementary proof that the ground state is always non-degenerate and the associated wave function may be chosen to be positive by using the Perron-Frobenius theorem. We also prove that removing a single center from the system of N delta centers shifts all the bound state energy levels upward as a simple consequence of the Cauchy interlacing theorem.Article Citation - WoS: 44Citation - Scopus: 40Measurements of the Tt¯ Production Cross Section in Lepton+jets Final States in Pp Collisions at 8 Tev and Ratio of 8 To 7 Tev Cross Sections(Springer Verlag, 2017) CMS Collaboration; Karapınar, GülerA measurement of the top quark pair production (tt¯) cross section in proton–proton collisions at the centre-of-mass energy of 8TeV is presented using data collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 19.6fb-1. This analysis is performed in the tt¯ decay channels with one isolated, high transverse momentum electron or muon and at least four jets, at least one of which is required to be identified as originating from hadronization of a b quark. The calibration of the jet energy scale and the efficiency of b jet identification are determined from data. The measured tt¯ cross section is 228.5±3.8(stat)±13.7(syst)±6.0(lumi) pb. This measurement is compared with an analysis of 7TeV data, corresponding to an integrated luminosity of 5.0fb-1, to determine the ratio of 8TeV to 7TeV cross sections, which is found to be 1.43±0.04(stat)±0.07(syst)±0.05(lumi). The measurements are in agreement with QCD predictions up to next-to-next-to-leading order.Article Citation - WoS: 17Citation - Scopus: 20Measurement of Dijet Azimuthal Decorrelation in Pp Collisions at ?s=8tev(Springer Verlag, 2016) CMS Collaboration; Karapınar, GülerA measurement of the decorrelation of azimuthal angles between the two jets with the largest transverse momenta is presented for seven regions of leading jet transverse momentum up to 2.2TeV. The analysis is based on the proton-proton collision data collected with the CMS experiment at a centre-of-mass energy of 8TeV corresponding to an integrated luminosity of 19.7fb-1. The dijet azimuthal decorrelation is caused by the radiation of additional jets and probes the dynamics of multijet production. The results are compared to fixed-order predictions of perturbative quantum chromodynamics (QCD), and to simulations using Monte Carlo event generators that include parton showers, hadronization, and multiparton interactions. Event generators with only two outgoing high transverse momentum partons fail to describe the measurement, even when supplemented with next-to-leading-order QCD corrections and parton showers. Much better agreement is achieved when at least three outgoing partons are complemented through either next-to-leading-order predictions or parton showers. This observation emphasizes the need to improve predictions for multijet production.Article Citation - WoS: 34Citation - Scopus: 26Forward–backward Asymmetry of Drell–yan Lepton Pairs in Pp Collisions at ?s = 8 Tev(Springer Verlag, 2016) CMS Collaboration; Karapınar, GülerA measurement of the forward–backward asymmetry AFB of oppositely charged lepton pairs (μμ and ee) produced via Z / γ∗ boson exchange in pp collisions at √s = 8 TeV is presented. The data sample corresponds to an integrated luminosity of 19.7 fb-1 collected with the CMS detector at the LHC. The measurement of AFB is performed for dilepton masses between 40 GeV and 2TeV and for dilepton rapidity up to 5. The AFB measurements as a function of dilepton mass and rapidity are compared with the standard model predictions.Article Citation - WoS: 18Citation - Scopus: 18Search for Lepton Flavour Violating Decays of Heavy Resonances and Quantum Black Holes To an Eµ Pair in Proton–proton Collisions at ?s = 8 Tev(Springer Verlag, 2016) CMS Collaboration; Karapınar, GülerA search for narrow resonances decaying to an electron and a muon is presented. The eμ mass spectrum is also investigated for non-resonant contributions from the production of quantum black holes (QBHs). The analysis is performed using data corresponding to an integrated luminosity of 19.7 fb-1 collected in proton-proton collisions at a centre-of-mass energy of 8 TeV with the CMS detector at the LHC. With no evidence for physics beyond the standard model in the invariant mass spectrum of selected eμ pairs, upper limits are set at 95 % confidence level on the product of cross section and branching fraction for signals arising in theories with charged lepton flavour violation. In the search for narrow resonances, the resonant production of τ sneutrino in R-parity violating supersymmetry is considered. The τ sneutrino is excluded for masses below 1.28 TeV for couplings λ132= λ231= λ311 ′= 0.01 , and below 2.30 TeV for λ132= λ231= 0.07 and λ311 ′= 0.11. These are the most stringent limits to date from direct searches at high-energy colliders. In addition, the resonance searches are interpreted in terms of a model with heavy partners of the Z boson and the photon. In a framework of TeV-scale quantum gravity based on a renormalization of Newton’s constant, the search for non-resonant contributions to the eμ mass spectrum excludes QBH production below a threshold mass Mth of 1.99 TeV. In models that invoke extra dimensions, the bounds range from 2.36 TeV for one extra dimension to 3.63 TeV for six extra dimensions. This is the first search for QBHs decaying into the eμ final state. © 2016, CERN for the benefit of the CMS collaboration.Article Citation - WoS: 33Citation - Scopus: 30Search for Massive Wh Resonances Decaying Into the L?bb¯ Final State at ?s = 8 Tev(Springer Verlag, 2016) CMS Collaboration; Karapınar, GülerA search for a massive resonance W ′decaying into a W and a Higgs boson in the ℓνb b ¯ (ℓ= e , μ) final state is presented. Results are based on data corresponding to an integrated luminosity of 19.7fb - 1 of proton–proton collisions at s= 8 TeV , collected using the CMS detector at the LHC. For a high-mass (≳ 1TeV) resonance, the two bottom quarks coming from the Higgs boson decay are reconstructed as a single jet, which can be tagged by placing requirements on its substructure and flavour. Exclusion limits at 95 % confidence level are set on the production cross section of a narrow resonance decaying into WH, as a function of its mass. In the context of a little Higgs model, a lower limit on the W ′ mass of 1.4TeV is set. In a heavy vector triplet model that mimics the properties of composite Higgs models, a lower limit on the W ′ mass of 1.5TeV is set. In the context of this model, the results are combined with related searches to obtain a lower limit on the W ′ mass of 1.8TeV , the most restrictive to date for decays to a pair of standard model bosons.Article Citation - WoS: 50Citation - Scopus: 49Measurement of the Inclusive Jet Cross Section in Pp Collisions at ?s = 2.76 Tev(Springer Verlag, 2016) Karapınar, GülerThe double-differential inclusive jet cross section is measured as a function of jet transverse momentum pT and absolute rapidity |y|, using proton-proton collision data collected with the CMS experiment at the LHC, at a center-of-mass energy of √s = 2.76 TeV and corresponding to an integrated luminosity of 5.43 pb-1. Jets are reconstructed within the pT range of 74 to 592 GeV and the rapidity range |y|<3.0. The reconstructed jet spectrum is corrected for detector resolution. The measurements are compared to the theoretical prediction at next-to-leading-order QCD using different sets of parton distribution functions. This inclusive cross section measurement explores a new kinematic region and is consistent with QCD predictions. © 2016, CERN for the benefit of the CMS collaboration.Article Citation - WoS: 60Citation - Scopus: 54Measurement of the Tt¯ Production Cross Section in the All-Jets Final State in Pp Collisions at ?s = 8 Tev(Springer Verlag, 2016) CMS Collaboration; Karapınar, GülerThe cross section for (Formula presented.) production in the all-jets final state is measured in pp collisions at a centre-of-mass energy of 8 (Formula presented.) at the LHC with the CMS detector, in data corresponding to an integrated luminosity of 18.4 (Formula presented.). The inclusive cross section is found to be (Formula presented.) (Formula presented.). The normalized differential cross sections are measured as a function of the top quark transverse momenta, (Formula presented.) , and compared to predictions from quantum chromodynamics. The results are reported at detector, parton, and particle levels. In all cases, the measured top quark (Formula presented.) spectra are significantly softer than theoretical predictions. © 2016, CERN for the benefit of the CMS collaboration.