Mathematics / Matematik
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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, 2024) İdiz, F.; Tanoǧlu, G.; Aghazadeh, N.In 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. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.Article Citation - WoS: 11Citation - Scopus: 8Local Well-Posedness of the Higher-Order Nonlinear Schrödinger Equation on the Half-Line: Single-Boundary Condition Case(Wiley, 2024) Alkın, A.; Mantzavinos, D.; Özsarı, T.We establish local well-posedness in the sense of Hadamard for a certain third-order nonlinear Schrödinger equation with a multiterm linear part and a general power nonlinearity, known as higher-order nonlinear Schrödinger equation, formulated on the half-line (Formula presented.). We consider the scenario of associated coefficients such that only one boundary condition is required and hence assume a general nonhomogeneous boundary datum of Dirichlet type at (Formula presented.). Our functional framework centers around fractional Sobolev spaces (Formula presented.) with respect to the spatial variable. We treat both high regularity ((Formula presented.)) and low regularity ((Formula presented.)) solutions: in the former setting, the relevant nonlinearity can be handled via the Banach algebra property; in the latter setting, however, this is no longer the case and, instead, delicate Strichartz estimates must be established. This task is especially challenging in the framework of nonhomogeneous initial-boundary value problems, as it involves proving boundary-type Strichartz estimates that are not common in the study of Cauchy (initial value) problems. The linear analysis, which forms the core of this work, crucially relies on a weak solution formulation defined through the novel solution formulae obtained via the Fokas method (also known as the unified transform) for the associated forced linear problem. In this connection, we note that the higher-order Schrödinger equation comes with an increased level of difficulty due to the presence of more than one spatial derivatives in the linear part of the equation. This feature manifests itself via several complications throughout the analysis, including (i) analyticity issues related to complex square roots, which require careful treatment of branch cuts and deformations of integration contours; (ii) singularities that emerge upon changes of variables in the Fourier analysis arguments; and (iii) complicated oscillatory kernels in the weak solution formula for the linear initial-boundary value problem, which require a subtle analysis of the dispersion in terms of the regularity of the boundary data. The present work provides a first, complete treatment via the Fokas method of a nonhomogeneous initial-boundary value problem for a partial differential equation associated with a multiterm linear differential operator. © 2023 Wiley Periodicals LLC.Article Citation - WoS: 553Citation - Scopus: 799Measurements of the Higgs Boson Production and Decay Rates and Constraints on Its Couplings From a Combined Atlas and CMS Analysis of the LHC pp Collision Data at √s=7 and 8 TeV(Springer, 2016) Aad, G.; Abbott, B.; Abdallah, J.; Abdinov, O.; Abeloos, B.; Aben, R.; Woods, N.Combined ATLAS and CMS measurements of the Higgs boson production and decay rates, as well as constraints on its couplings to vector bosons and fermions, are presented. The combination is based on the analysis of five production processes, namely gluon fusion, vector boson fusion, and associated production with a W or a Z boson or a pair of top quarks, and of the six decay modes H -> ZZ; WW, gamma gamma; tau tau; bb, and mu mu. All results are reported assuming a value of 125: 09 GeV for the Higgs boson mass, the result of the combined measurement by the ATLAS and CMS experiments. The analysis uses the CERN LHC proton-proton collision data recorded by the ATLAS and CMS experiments in 2011 and 2012, corresponding to integrated luminosities per experiment of approximately 5 fb(-1) at root s = 7TeV and 20 fb(-1) at root s = 8TeV. The Higgs boson production and decay rates measured by the two experiments are combined within the context of three generic parameterisations: two based on cross sections and branching fractions, and one on ratios of coupling modifiers. Several interpretations of the measurements with more model-dependent parameterisations are also given. The combined signal yield relative to the Standard Model prediction is measured to be 1.09 +/- 0.11. The combined measurements lead to observed significances for the vector boson fusion production process and for the H -> tau tau decay of 5.4 and 5.5 standard deviations, respectively. The data are consistent with the Standard Model predictions for all parameterisations considered.Article Citation - WoS: 13Citation - Scopus: 14Search for R-Parity Violating Decays of a Top Squark in Proton–proton Collisions at √s=8 Tev(Elsevier B.V., 2016) Khachatryan, V.; Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Asilar, E.; Bergauer, T.; Gomez, G.The results of a search for a supersymmetric partner of the top quark (top squark), pair-produced in proton–proton collisions at s=8 TeV, are presented. The search, which focuses on R-parity violating, chargino-mediated decays of the top squark, is performed in final states with low missing transverse momentum, two oppositely charged electrons or muons, and at least five jets. The analysis uses a data sample corresponding to an integrated luminosity of 19.7 fb−1 collected with the CMS detector at the LHC in 2012. The data are found to be in agreement with the standard model expectation, and upper limits are placed on the top squark pair production cross section at 95% confidence level. Assuming a 100% branching fraction for the top squark decay chain, t˜→tχ˜1 ±,χ˜1 ±→ℓ±+jj, top squark masses less than 890 (1000) GeV for the electron (muon) channel are excluded for the first time in models with a single nonzero R-parity violating coupling λijk ′ (i,j,k≤2), where i,j,k correspond to the three generations. © 2016 The Author(s)Article Citation - WoS: 81Citation - Scopus: 88Search for Neutral Resonances Decaying Into a Z Boson and a Pair of B Jets or Τ Leptons(Elsevier B.V., 2016) Khachatryan, V.; Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Asilar, E.; Bergauer, T.; Garcia-Ferrero, J.A search is performed for a new resonance decaying into a lighter resonance and a Z boson. Two channels are studied, targeting the decay of the lighter resonance into either a pair of oppositely charged τ leptons or a bb‾ pair. The Z boson is identified via its decays to electrons or muons. The search exploits data collected by the CMS experiment at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 19.8 fb−1. No significant deviations are observed from the standard model expectation and limits are set on production cross sections and parameters of two-Higgs-doublet models. © 2016 The AuthorArticle Citation - WoS: 8Citation - Scopus: 9Search for Supersymmetry in Electroweak Production With Photons and Large Missing Transverse Energy in Pp Collisions at √s=8tev(Elsevier B.V., 2016) Khachatryan, V.; Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Asilar, E.; Bergauer, T.; Fernandez, M.Results are reported from a search for supersymmetry with gauge-mediated supersymmetry breaking in electroweak production. Final states with photons and large missing transverse energy (ET miss) were examined. The data sample was collected in pp collisions at s=8TeV with the CMS detector at the LHC and corresponds to 7.4fb−1. The analysis focuses on scenarios in which the lightest neutralino has bino- or wino-like components, resulting in decays to photons and gravitinos, where the gravitinos escape undetected. The data were obtained using a specially designed trigger with dedicated low thresholds, providing good sensitivity to signatures with photons, ET miss, and low hadronic energy. No excess of events over the standard model expectation is observed. The results are interpreted using the model of general gauge mediation. With the wino mass fixed at 10GeV above that of the bino, wino masses below 710GeV are excluded at 95% confidence level. Constraints are also set in the context of two simplified models, for which the analysis sets the lowest cross section limits on the electroweak production of supersymmetric particles. © 2016 The AuthorArticle Citation - WoS: 23Citation - Scopus: 26Search for Supersymmetry in Events With Soft Leptons, Low Jet Multiplicity, and Missing Transverse Energy in Proton–proton Collisions at √s=8 Tev(Elsevier B.V., 2016) Khachatryan, V.; Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Asilar, E.; Bergauer, T.; Palencia Cortezon, E.Results are presented from a search for supersymmetric particles in scenarios with small mass splittings. The data sample corresponds to 19.7 fb−1 of proton–proton collisions recorded by the CMS experiment at s=8 TeV. The search targets top squark (t˜) pair production in scenarios with mass differences Δm=m(t˜)−m(χ˜1 0) below the W-boson mass and with top-squark decays in the four-body mode (t˜→bℓνχ˜1 0), where the neutralino (χ˜1 0) is assumed to be the lightest supersymmetric particle (LSP). The signature includes a high transverse momentum (pT) jet associated with initial-state radiation, one or two low-pT leptons, and significant missing transverse energy. The event yields observed in data are consistent with the expected background contributions from standard model processes. Limits are set on the cross section for top squark pair production as a function of the t˜ and LSP masses. Assuming a 100% branching fraction for the four-body decay mode, top-squark masses below 316 GeV are excluded for Δm=25 GeV at 95% CL. The dilepton data are also interpreted under the assumption of chargino–neutralino production, with subsequent decays to sleptons or sneutrinos. Assuming a difference between the common χ˜1 +/χ˜2 0 mass and the LSP mass of 20 GeV and a τ-enriched decay scenario, masses in the range m(χ˜1 +)<307 GeV are excluded at 95% CL. © 2016 The AuthorArticle Citation - WoS: 24Citation - Scopus: 34Measurement of Spin Correlations in Tt‾ Production Using the Matrix Element Method in the Muon+jets Final State in Pp Collisions at √s=8 Tev(Elsevier B.V., 2016) Khachatryan, V.; Karapınar, Güler; Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Asilar, E.; Bergauer, T.; Cuevas, J.The consistency of the spin correlation strength in top quark pair production with the standard model (SM) prediction is tested in the muon+jets final state. The events are selected from pp collisions, collected by the CMS detector, at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 19.7 fb−1. The data are compared with the expectation for the spin correlation predicted by the SM and with the expectation of no correlation. Using a template fit method, the fraction of events that show SM spin correlations is measured to be 0.72±0.08(stat)−0.13 +0.15(syst), representing the most precise measurement of this quantity in the muon+jets final state to date. © 2016 The AuthorArticle Citation - WoS: 34Citation - Scopus: 37Search for a Low-Mass Pseudoscalar Higgs Boson Produced in Association With a Bb‾ Pair in Pp Collisions at √s=8 Tev(Elsevier B.V., 2016) Khachatryan, V.; Karapınar, Güler; Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Asilar, E.; Bergauer, T.; Fernandez Menendez, J.A search is reported for a light pseudoscalar Higgs boson decaying to a pair of τ leptons, produced in association with a bb‾ pair, in the context of two-Higgs-doublet models. The results are based on pp collision data at a centre-of-mass energy of 8 TeV collected by the CMS experiment at the LHC and corresponding to an integrated luminosity of 19.7 fb−1. Pseudoscalar boson masses between 25 and 80 GeV are probed. No evidence for a pseudoscalar boson is found and upper limits are set on the product of cross section and branching fraction to τ pairs between 7 and 39 pb at the 95% confidence level. This excludes pseudoscalar A bosons with masses between 25 and 80 GeV, with SM-like Higgs boson negative couplings to down-type fermions, produced in association with bb‾ pairs, in Type II, two-Higgs-doublet models. © 2016 The Author(s)Article Citation - WoS: 40Citation - Scopus: 41Search for Supersymmetry in the Multijet and Missing Transverse Momentum Final State in Pp Collisions at 13 Tev(Elsevier B.V., 2016) Khachatryan, V.; Karapınar, Güler; Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Asilar, E.; Bergauer, T.; Castineiras De Saa, J.R.A search for new physics is performed based on all-hadronic events with large missing transverse momentum produced in proton–proton collisions at s=13 TeV. The data sample, corresponding to an integrated luminosity of 2.3 fb−1, was collected with the CMS detector at the CERN LHC in 2015. The data are examined in search regions of jet multiplicity, tagged bottom quark jet multiplicity, missing transverse momentum, and the scalar sum of jet transverse momenta. The observed numbers of events in all search regions are found to be consistent with the expectations from standard model processes. Exclusion limits are presented for simplified supersymmetric models of gluino pair production. Depending on the assumed gluino decay mechanism, and for a massless, weakly interacting, lightest neutralino, lower limits on the gluino mass from 1440 to 1600 GeV are obtained, significantly extending previous limits. © 2016 The Author