Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article Citation - WoS: 9Citation - Scopus: 8A Numerical Method Based on Legendre Wavelet and Quasilinearization Technique for Fractional Lane-Emden Type Equations(Springer, 2023) İdiz, Fatih; Tanoğlu, Gamze; Aghazadeh, NasserIn 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.Article Citation - WoS: 9Citation - Scopus: 8Taylor Wavelets Collocation Technique for Solving Fractional Nonlinear Singular Pdes(Springer, 2022) Aghazadeh, Nasser; Mohammadi, Amir; Tanoğlu, GamzeA novel technique has been introduced to solve the Emden-Fowler equations. It has been derived from the Taylor wavelets collocation method. The proposed scheme has been successfully implemented in order to solve the singular equations. The singular problem converts to a system of algebraic equations that can be solved numerically. Moreover, the technique is very effective to remove the strong singularity point at x = 0. The numerical experiments have been checked out with the exact and approximate solutions that have been achieved by others including the Adomian decomposition method (Wazwaz in Appl Math Comput 166:638-651, 2005), Modified Homotopy Perturbation Method (Singh et al. J Math Chem 54(4):918-931, 2016). Also, the error analysis of the technique has been considered.Article A Reliable and Fast Mesh-Free Solver for the Telegraph Equation(Springer, 2022) İmamoğlu Karabaş, Neslişah; Korkut, Sıla Övgü; Gürarslan, Gürhan; Tanoğlu, GamzeIn the presented study, the hyperbolic telegraph equation is taken as the focus point. To solve such an equation, an accurate, reliable, and efficient method has been proposed. The developed method is mainly based on the combination of a kind of mesh-free method and an adaptive method. Multiquadric radial basis function mesh-free method is considered on spatial domain and the adaptive fifth-order Runge–Kutta method is used on time domain. The validity and the performance of the proposed method have been checked on several test problems. The approximate solutions are compared with the exact solution, it is shown that the proposed method has more preferable to the other methods in the literature.Article Citation - WoS: 21Citation - Scopus: 28Angular Analysis of the Decay B+-> K*(892)(+)mu(+)mu(-) in Proton-Proton Collisions at Root S=8 Tev(Springer, 2021) CMS Collaboration; Karapınar, GülerAngular distributions of the decay B+-> K*(892)(+)mu(+)mu(-) are studied using events collected with the CMS detector in root s = 8 TeV proton-proton collisions at the LHC, corresponding to an integrated luminosity of 20.0 fb(-1). The forward-backward asymmetry of the muons and the longitudinal polarization of the K*(892)(+) meson are determined as a function of the square of the dimuon invariant mass. These are the first results from this exclusive decay mode and are in agreement with a standard model prediction.Article Citation - WoS: 4Citation - Scopus: 4Quantum Invariants of Knotoids(Springer, 2021) Güğümcü, Neslihan; Kauffman, Louis H.In this paper, we construct quantum invariants for knotoid diagrams in R-2. The diagrams are arranged with respect to a given direction in the plane (Morse knotoids). A Morse knotoid diagram can be decomposed into basic elementary diagrams each of which is associated to a matrix that yields solutions of the quantum Yang-Baxter equation. We recover the bracket polynomial, and define the rotational bracket polynomial, the binary bracket polynomial, the Alexander polynomial, the generalized Alexander polynomial and an infinity of specializations of the Homflypt polynomial for Morse knotoids via quantum state sum models.Article Citation - WoS: 137Citation - Scopus: 174Search for Narrow and Broad Dijet Resonances in Proton-Proton Collisions at ?s=13 Tev and Constraints on Dark Matter Mediators and Other New Particles(Springer, 2018) CMS Collaboration; Karapınar, GülerSearches for resonances decaying into pairs of jets are performed using proton-proton collision data collected at s=13 TeV corresponding to an integrated luminosity of up to 36 fb−1. A low-mass search, for resonances with masses between 0.6 and 1.6 TeV, is performed based on events with dijets reconstructed at the trigger level from calorimeter information. A high-mass search, for resonances with masses above 1.6 TeV, is performed using dijets reconstructed offline with a particle-flow algorithm. The dijet mass spectrum is well described by a smooth parameterization and no evidence for the production of new particles is observed. Upper limits at 95% confidence level are reported on the production cross section for narrow resonances with masses above 0.6 TeV. In the context of specific models, the limits exclude string resonances with masses below 7.7 TeV, scalar diquarks below 7.2 TeV, axigluons and colorons below 6.1 TeV, excited quarks below 6.0 TeV, color-octet scalars below 3.4 TeV, W′ bosons below 3.3 TeV, Z′ bosons below 2.7 TeV, Randall-Sundrum gravitons below 1.8 TeV and in the range 1.9 to 2.5 TeV, and dark matter mediators below 2.6 TeV. The limits on both vector and axial-vector mediators, in a simplified model of interactions between quarks and dark matter particles, are presented as functions of dark matter particle mass and coupling to quarks. Searches are also presented for broad resonances, including for the first time spin-1 resonances with intrinsic widths as large as 30% of the resonance mass. The broad resonance search improves and extends the exclusions of a dark matter mediator to larger values of its mass and coupling to quarks.Article Citation - WoS: 98Citation - Scopus: 89Measurement of the Cross Section for Top Quark Pair Production in Association With a W or Z Boson in Proton-Proton Collisions at ?s = 13 Tev(Springer, 2018) Karapınar, GülerA measurement is performed of the cross section of top quark pair production in association with a W or Z boson using proton-proton collisions at a center-of-mass energy of 13 TeV at the LHC. The data sample corresponds to an integrated luminosity of 35.9 fb−1, collected by the CMS experiment in 2016. The measurement is performed in the same-sign dilepton, three- and four-lepton final states. The production cross sections are measured to be σ(tt¯W)=0.77−0.11+0.12(stat)−0.12+0.13(syst)pb and σ(tt¯Z)=0.99−0.08+0.09(stat)−0.10+0.12(syst)pb. The expected (observed) signal significance for the t t ¯ W production in same-sign dilepton channel is found to be 4.5 (5.3) standard deviations, while for the t t ¯ Z production in three- and four-lepton channels both the expected and the observed significances are found to be in excess of 5 standard deviations. The results are in agreement with the standard model predictions and are used to constrain the Wilson coefficients for eight dimension-six operators describing new interactions that would modify t t ¯ W and t t ¯ Z production.Article Citation - WoS: 61Citation - Scopus: 67Search for Top Squark Pair Production in Pp Collisions at ?s=13 Tev Using Single Lepton Events(Springer, 2017) CMS Collaboration; Karapınar, GülerA search for top squark pair production in pp collisions at s=13 TeV is performed using events with a single isolated electron or muon, jets, and a large transverse momentum imbalance. The results are based on data collected in 2016 with the CMS detector at the LHC, corresponding to an integrated luminosity of 35.9 fb−1. No significant excess of events is observed above the expectation from standard model processes. Exclusion limits are set in the context of supersymmetric models of pair production of top squarks that decay either to a top quark and a neutralino or to a bottom quark and a chargino. Depending on the details of the model, we exclude top squarks with masses as high as 1120 GeV. Detailed information is also provided to facilitate theoretical interpretations in other scenarios of physics beyond the standard model.Article Citation - WoS: 12Citation - Scopus: 36Measurement of the Semileptonic T T ¯ + ? Production Cross Section in Pp Collisions at ?s=8 Tev(Springer, 2017) CMS Collaboration; Karapınar, GülerA measurement of the cross section for top quark-antiquark (t t ¯) pairs produced in association with a photon in proton-proton collisions at s=8 TeV is presented. The analysis uses data collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 19.7 fb1. The signal is defined as the production of a t t ¯ pair in association with a photon having a transverse energy larger than 25 GeV and an absolute pseudorapidity smaller than 1.44. The measurement is performed in the fiducial phase space corresponding to the semileptonic decay chain of the t t ¯ pair, and the cross section is measured relative to the inclusive t t ¯ pair production cross section. The fiducial cross section for associated t t ¯ pair and photon production is found to be 127 ±27 (stat+syst) fb per semileptonic final state. The measured value is in agreement with the theoretical prediction.Article Citation - WoS: 47Citation - Scopus: 70Search for Direct Production of Supersymmetric Partners of the Top Quark in the All-Jets Final State in Proton-Proton Collisions at ?s=13 Tev(Springer, 2017) Karapınar, GülerA search for direct production of top squark pairs in events with jets and large transverse momentum imbalance is presented. The data are based on proton-proton collisions at a center-of-mass energy of 13 TeV, collected with the CMS detector in 2016 at the CERN LHC, and correspond to an integrated luminosity of 35.9 fb−1. The search considers a variety of R-parity conserving supersymmetric models, including ones for which the top squark and neutralino masses are nearly degenerate. Specialized jet reconstruction tools are developed to exploit the unique characteristics of the signal topologies. With no significant excess of events observed above the standard model expectations, upper limits are set on the direct top squark pair production cross section in the context of simplified supersymmetric models for various decay hypotheses. Models with larger differences in mass between the top squark and neutralino are probed for masses up to 1040 and 500 GeV, respectively, whereas models with a more compressed mass hierarchy are probed up to 660 and 610 GeV, respectively. The smallest mass difference probed is for masses near to 550 and 540 GeV, respectively.