Mathematics / Matematik
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Article Citation - WoS: 54Citation - Scopus: 59Measurement of the WZ Production Cross Section in pp Collisions at S=13 TeV(Elsevier, 2017) Khachatryan, V.; Sirunyan, A. M.; Tumasyan, A.; Adam, W.; Asilar, E.; Bergauer, T.; Woods, N.The WZ production cross section in proton-proton collisions at root s = 13 Tev is measured with the CMS experiment at the LHC using a data sample corresponding to an integrated luminosity of 2.3 fb(-1). The measurement is performed in the leptonic decay modes WZ -> lVl'l', where l,l'=e,mu. The measured cross section for the range 60<m (l'l') <120 GeV is sigma(pp -> WZ) = 39.9 +/- 3.2(stat)(2.9)(-3.1)(syst)+/- 0.4(theo)+/- 1.3(lumi)pb, consistent with the standard model prediction.Article Citation - WoS: 7Citation - Scopus: 7Structure and Stability of Bimodal Systems in R-3: Part 1(Azerbaijan National Academy of Sciences, 2014) Eldem, Vasfi; Şahan, GökhanIn this paper, the structure and global asymptotic stability of bimodal systems in R3 are investigated under a set of assumptions which simplify the geometric structure. It is basically shown that one of the assumptions being used reduces the stability problem in R3 to the stability problem in R2. However, structural analysis shows that the behavior of the trajectories changes radically upon the change of the parameters of individual subsystems. The approach taken is based on the classification of the trajectories of bimodal systems as i) the trajectories which change modes finite number of times as t ? ?, and ii) the trajectories which change modes infinite number of times as t ? ?. Finally, it is noted that this approach can be used without some of the assumptions for all bimodal systems in R3, and for bimodal systems in Rn. © 2014, Azerbaijan National Academy of Sciences. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3Reconstruction of Generalized Impedance Functions for 3d Acoustic Scattering(Academic Press Inc., 2019) Ivanyshyn Yaman, OlhaWe consider the inverse obstacle scattering problem of determining both of the surface impedance functions from far field measurements for a few incident plane waves at a fixed frequency. The reconstruction algorithm we propose is based on an iteratively regularized Newton-type method and nonlinear integral equations. The mathematical foundation of the method is presented and the feasibility is illustrated by numerical examples. (C) 2019 Elsevier Inc. All rights reserved.Article Citation - WoS: 20Citation - Scopus: 23One-Dimensional Semirelativistic Hamiltonian With Multiple Dirac Delta Potentials(American Physical Society, 2017) Erman, Fatih; Gadella, Manuel; Uncu, HaydarIn this paper, we consider the one-dimensional semirelativistic Schrdinger equation for a particle interacting with N Dirac delta potentials. Using the heat kernel techniques, we establish a resolvent formula in terms of an N x N matrix, called the principal matrix. This matrix essentially includes all the information about the spectrum of the problem. We study the bound state spectrum by working out the eigenvalues of the principal matrix. With the help of the Feynman-Hellmann theorem, we analyze how the bound state energies change with respect to the parameters in the model. We also prove that there are at most N bound states and explicitly derive the bound state wave function. The bound state problem for the two-center case is particularly investigated. We show that the ground state energy is bounded below, and there exists a selfadjoint Hamiltonian associated with the resolvent formula. Moreover, we prove that the ground state is nondegenerate. The scattering problem for N centers is analyzed by exactly solving the semirelativistic Lippmann-Schwinger equation. The reflection and the transmission coefficients are numerically and asymptotically computed for the two- center case. We observe the so-called threshold anomaly for two symmetrically located centers. The semirelativistic version of the Kronig-Penney model is shortly discussed, and the band gap structure of the spectrum is illustrated. The bound state and scattering problems in the massless case are also discussed. Furthermore, the reflection and the transmission coefficients for the two delta potentials in this particular case are analytically found. Finally, we solve the renormalization group equations and compute the beta function nonperturbatively.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 Citation - WoS: 11Citation - Scopus: 10Pseudo-Backstepping and Its Application To the Control of Korteweg-De Vries Equation From the Right Endpoint on a Finite Domain(Society for Industrial and Applied Mathematics Publications, 2019) Özsarı, Türker; Batal, AhmetIn this paper, we design Dirichlet-Neumann boundary feedback controllers for the Korteweg-de Vries equation that act at the right endpoint of the domain. The length of the domain is allowed to be critical. Constructing backstepping controllers that act at the right endpoint of the domain is more challenging than its left endpoint counterpart. The standard application of the backstepping method fails, because corresponding kernel models become overdetermined. In order to deal with this difficulty, we introduce the pseudo-backstepping method, which uses a pseudo-kernel that satisfies all but one desirable boundary condition. Moreover, various norms of the pseudo-kernel can be controlled through a parameter in one of its boundary conditions. We prove that the boundary controllers constructed via this pseudo-kernel still exponentially stabilize the system with the cost of a low exponential rate of decay. We show that a single Dirichlet controller is sufficient for exponential stabilization with a slower rate of decay. We also consider a second order feedback law acting at the right Dirichlet boundary condition. We show that this approach works if the main equation includes only the third order term, while the same problem remains open if the main equation involves the first order and/or the nonlinear terms. At the end of the paper, we give numerical simulations to illustrate the main result.Article Citation - WoS: 7Citation - Scopus: 7Output Feedback Stabilization of the Linearized Korteweg-De Vries Equation With Right Endpoint Controllers(Elsevier Ltd., 2019) Batal, Ahmet; Özsarı, TürkerIn this paper, we prove the output feedback stabilization for the linearized Korteweg-de Vries (KdV) equation posed on a finite domain in the case the full state of the system cannot be measured. We assume that there is a sensor at the left end point of the domain capable of measuring the first and second order boundary traces of the solution. This allows us to design a suitable observer system whose states can be used for constructing boundary feedbacks acting at the right endpoint so that both the observer and the original plant become exponentially stable. Stabilization of the original system is proved in the L-2-sense, while the convergence of the observer system to the original plant is also proved in higher order Sobolev norms. The standard backstepping approach used to construct a left endpoint controller fails and presents mathematical challenges when building right endpoint controllers due to the overdetermined nature of the related kernel models. In order to deal with this difficulty we use the method of Ozsan and Batal, (2019) which is based on using modified target systems involving extra trace terms. In addition, we show that the number of controllers and boundary measurements can be reduced to one, with the cost of a slightly lower exponential rate of decay. We provide numerical simulations illustrating the efficacy of our controllers. (C) 2019 Elsevier Ltd. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 1Discrete Fractional Integral Operators With Binary Quadratic Forms as Phase Polynomials(Academic Press, 2019) Temur, Faruk; Sert, EzgiWe give estimates on discrete fractional integral operators along binary quadratic forms. These operators have been studied for 30 years starting with the investigations of Arkhipov and Oskolkov, but efforts have concentrated on cases where the phase polynomial is translation invariant or quasi-translation invariant. This work presents the first results for operators with neither translation invariant nor quasi-translation invariant phase polynomials. (C) 2019 Elsevier Inc. All rights reserved.Article Citation - WoS: 52Citation - Scopus: 56Study of Jet Quenching With Isolated-Photon+jet Correlations in Pbpb and Pp Collisions at Snn=5.02 Tev(Elsevier Ltd., 2018) CMS Collaboration; Karapınar, GülerMeasurements of azimuthal angle and transverse momentum (pT) correlations of isolated photons and associated jets are reported for pp and PbPb collisions at sNN=5.02 TeV. The data were recorded with the CMS detector at the CERN LHC. For events containing a leading isolated photon with pT γ>40 GeV/c and an associated jet with pT jet>30 GeV/c, the photon+jet azimuthal correlation and pT imbalance in PbPb collisions are studied as functions of collision centrality and pT γ. The results are compared to pp reference data collected at the same collision energy and to predictions from several theoretical models for parton energy loss. No evidence of broadening of the photon+jet azimuthal correlations is observed, while the ratio pT jet/pT γ decreases significantly for PbPb data relative to the pp reference. All models considered agree within uncertainties with the data. The number of associated jets per photon with pT γ>80 GeV/c is observed to be shifted towards lower pT jet values in central PbPb collisions compared to pp collisions.Article Citation - WoS: 33Citation - Scopus: 75Search for an Exotic Decay of the Higgs Boson To a Pair of Light Pseudoscalars in the Final State With Two B Quarks and Two Τ Leptons in Proton–proton Collisions at S=13tev(Elsevier B.V., 2018) Sirunyan,A.M.; Tumasyan,A.; Adam,W.; Ambrogi,F.; Asilar,E.; Bergauer,T.; Adzic,P.A search for an exotic decay of the Higgs boson to a pair of light pseudoscalar bosons is performed for the first time in the final state with two b quarks and two τ leptons. The search is motivated in the context of models of physics beyond the standard model (SM), such as two Higgs doublet models extended with a complex scalar singlet (2HDM + S), which include the next-to-minimal supersymmetric SM (NMSSM). The results are based on a data set of proton–proton collisions corresponding to an integrated luminosity of 35.9fb−1, accumulated by the CMS experiment at the LHC in 2016 at a center-of-mass energy of 13TeV. Masses of the pseudoscalar boson between 15 and 60GeV are probed, and no excess of events above the SM expectation is observed. Upper limits between 3 and 12% are set on the branching fraction B(h→aa→2τ2b) assuming the SM production of the Higgs boson. Upper limits are also set on the branching fraction of the Higgs boson to two light pseudoscalar bosons in different 2HDM + S scenarios. Assuming the SM production cross section for the Higgs boson, the upper limit on this quantity is as low as 20% for a mass of the pseudoscalar of 40GeV in the NMSSM. © 2018 The Author(s)