Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Conference Object On the Relativistic Supersymmetric Quantum Mechanics(Springer Verlag, 2002) Mir-Kasimov, Rufat M.; Kasım, Rıfat MirThe present paper is devoted to the one-dimensional relativistic supersymmetric quantum mechanics (RSUSYQM). A short formulation of RSUSYQM is given. We show that RSUSYQM is a q-deformed non-relativistic SUSYQM. Two simple examples are given.Conference Object Measure on Time Scales With Mathematica(Springer Verlag, 2006) Ufuktepe, Ünal; Yantır, AhmetIn this paper we study the Lebesgue Delta-measure on time scales. We refer to [3, 4] for the main notions and facts from the general measure and Lebesgue Delta integral theory. The objective of this paper is to show how the main concepts of Mathematica can be applied to fundamentals of Lebesgue Delta- and Lebesgue Delta- measure on an arbitrary time scale and also on a discrete time scale whose rule is given by the reader. As the time scale theory is investigated in two parts, by means of alpha and rho operators, we named the measures on time scales by the set function DMeasure and NMeasure respectively for arbitrary time scales.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: 102Citation - Scopus: 153Search for Additional Neutral Mssm Higgs Bosons in the ? ? Final State in Proton-Proton Collisions at ?s=13 Tev(Springer Verlag, 2018) CMS Collaboration; Karapınar, GülerA search is presented for additional neutral Higgs bosons in the τ τ final state in proton-proton collisions at the LHC. The search is performed in the context of the minimal supersymmetric extension of the standard model (MSSM), using the data collected with the CMS detector in 2016 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb−1. To enhance the sensitivity to neutral MSSM Higgs bosons, the search includes production of the Higgs boson in association with b quarks. No significant deviation above the expected background is observed. Model-independent limits at 95% confidence level (CL) are set on the product of the branching fraction for the decay into τ leptons and the cross section for the production via gluon fusion or in association with b quarks. These limits range from 18 pb at 90 GeV to 3.5 fb at 3.2 TeV for gluon fusion and from 15 pb (at 90 GeV) to 2.5 fb (at 3.2 TeV) for production in association with b quarks, assuming a narrow width resonance. In the mh hod + scenario these limits translate into a 95% CL exclusion of tan β > 6 for neutral Higgs boson masses below 250 GeV, where tan β is the ratio of the vacuum expectation values of the neutral components of the two Higgs doublets. The 95% CL exclusion contour reaches 1.6 TeV for tan β = 60.Article Citation - WoS: 14Citation - Scopus: 35Search for a Heavy Resonance Decaying Into a Z Boson and a Z or W Boson in 2l2q Final States at ?s=13 Tev(Springer Verlag, 2018) CMS Collaboration; Karapınar, GülerA search has been performed for heavy resonances decaying to ZZ or ZW in 2ℓ2q final states, with two charged leptons (ℓ = e, μ) produced by the decay of a Z boson, and two quarks produced by the decay of a W or Z boson. The analysis is sensitive to resonances with masses in the range from 400 to 4500 GeV. Two categories are defined based on the merged or resolved reconstruction of the hadronically decaying vector boson, optimized for high- and low-mass resonances, respectively. The search is based on data collected during 2016 by the CMS experiment at the LHC in proton-proton collisions with a center-of-mass energy of s=13 TeV, corresponding to an integrated luminosity of 35.9 fb−1. No excess is observed in the data above the standard model background expectation. Upper limits on the production cross section of heavy, narrow spin-1 and spin-2 resonances are derived as a function of the resonance mass, and exclusion limits on the production of W′ bosons and bulk graviton particles are calculated in the framework of the heavy vector triplet model and warped extra dimensions, respectively.Article Citation - WoS: 11Citation - Scopus: 45Search for Z? Resonances Using Leptonic and Hadronic Final States in Proton-Proton Collisions at ?s=13 Tev(Springer Verlag, 2018) CMS Collaboration; Karapınar, GülerA search is presented for resonances decaying to a Z boson and a photon. The analysis is based on data from proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb−1, and collected with the CMS detector at the LHC in 2016. Two decay modes of the Z boson are investigated. In the leptonic channels, the Z boson candidates are reconstructed using electron or muon pairs. In the hadronic channels, they are identified using a large-radius jet, containing either light-quark or b quark decay products of the Z boson, via jet substructure and advanced b quark tagging techniques. The results from these channels are combined and interpreted in terms of upper limits on the product of the production cross section and the branching fraction to Zγ for narrow and broad spin-0 resonances with masses between 0.35 and 4.0 TeV, providing thereby the most stringent limits on such resonances.Article Citation - WoS: 13Citation - Scopus: 23Search for Top Squarks Decaying Via Four-Body or Chargino-Mediated Modes in Single-Lepton Final States in Proton-Proton Collisions at ?s=13 Tev(Springer Verlag, 2018) CMS Collaboration; Karapınar, GülerA search for the pair production of the lightest supersymmetric partner of the top quark (t ˜ 1) is presented. The search focuses on a compressed scenario where the mass difference between the top squark and the lightest supersymmetric particle, often considered to be the lightest neutralino (χ˜10), is smaller than the mass of the W boson. The proton-proton collision data were recorded by the CMS experiment at a centre-of-mass energy of 13 TeV, and correspond to an integrated luminosity of 35.9 fb−1. In this search, two decay modes of the top squark are considered: a four-body decay into a bottom quark, two additional fermions, and a χ˜10; and a decay via an intermediate chargino. Events are selected using the presence of a high-momentum jet, significant missing transverse momentum, and a low transverse momentum electron or muon. Two analysis techniques are used, targeting different decay modes of the t ˜ 1: a sequential selection and a multivariate technique. No evidence for the production of top squarks is found, and mass limits at 95% confidence level are set that reach up to 560 GeV, depending on the m(t˜1)−m(χ˜10) mass difference and the decay mode.Article Citation - WoS: 10Citation - Scopus: 33Search for Dark Matter Produced in Association With a Higgs Boson Decaying To ?? or ? + ? - at ?s=13 Tev(Springer Verlag, 2018) CMS Collaboration; Karapınar, GülerA search for dark matter particles is performed by looking for events with large transverse momentum imbalance and a recoiling Higgs boson decaying to either a pair of photons or a pair of τ leptons. The search is based on proton-proton collision data at a center-of-mass energy of 13 TeV collected at the CERN LHC in 2016 and corresponding to an integrated luminosity of 35.9 fb−1. No significant excess over the expected standard model background is observed. Upper limits at 95% confidence level are presented for the product of the production cross section and branching fraction in the context of two benchmark simplified models. For the Z′-two-Higgs-doublet model (where Z′ is a new massive boson mediator) with an intermediate heavy pseudoscalar particle of mass mA = 300 GeV and mDM = 100 GeV, the Z′ masses from 550 GeV to 1265 GeV are excluded. For a baryonic Z′ model, with mDM = 1 GeV, Z′ masses up to 615 GeV are excluded. Results are also presented for the spin-independent cross section for the dark matter-nucleon interaction as a function of the mass of the dark matter particle. This is the first search for dark matter particles produced in association with a Higgs boson decaying to two τ leptonsArticle Citation - WoS: 51Citation - Scopus: 100Search for Vector-Like T and B Quark Pairs in Final States With Leptons at ?s=13 Tev(Springer Verlag, 2018) CMS Collaboration; Karapınar, GülerA search is presented for pair production of heavy vector-like T and B quarks in proton-proton collisions at s=13 TeV. The data sample corresponds to an integrated luminosity of 35.9 fb−1, collected with the CMS detector at the CERN LHC in 2016. Pair production of T quarks would result in a wide range of final states, since vector-like T quarks of charge 2e/3 are predicted to decay to bW, tZ, and tH. Likewise, vector-like B quarks are predicted to decay to tW, bZ, and bH. Three channels are considered, corresponding to final states with a single lepton, two leptons with the same sign of the electric charge, or at least three leptons. The results exclude T quarks with masses below 1140–1300 GeV and B quarks with masses below 910–1240 GeV for various branching fraction combinations, extending the reach of previous CMS searches by 200–600 GeV.