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: 11Citation - Scopus: 8Local Well-Posedness of the Higher-Order Nonlinear Schrödinger Equation on the Half-Line: Single-Boundary Condition Case(Wiley, 2023) Alkın, Aykut; Mantzavinos, Dionyssios; Özsarı, TürkerWe 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: 5Citation - Scopus: 4A New Construction Method for Keystream Generators(IEEE, 2023) Gül, Çağdaş; Kara, OrhunWe introduce a new construction method of diffusion layers for Substitution Permutation Network (SPN) structures along with its security proofs. The new method can be used in block ciphers, stream ciphers, hash functions, and sponge constructions. Moreover, we define a new stream cipher mode of operation through a fixed pseudorandom permutation and provide its security proofs in the indistinguishability model. We refer to a stream cipher as a Small Internal State Stream (SISS) cipher if its internal state size is less than twice its key size. There are not many studies about how to design and analyze SISS ciphers due to the criterion on the internal state sizes, resulting from the classical tradeoff attacks. We utilize our new mode and diffusion layer construction to design an SISS cipher having two versions, which we call DIZY. We further provide security analyses and hardware implementations of DIZY. In terms of area cost, power, and energy consumption, the hardware performance is among the best when compared to some prominent stream ciphers, especially for frame-based encryptions that need frequent initialization. Unlike recent SISS ciphers such as Sprout, Plantlet, LILLE, and Fruit; DIZY does not have a keyed update function, enabling efficient key changing. © 2005-2012 IEEE.Article Citation - WoS: 1Citation - Scopus: 1Initial Stages of a Three Dimensional Dam Break Flow(Elsevier, 2022) Fetahu, Elona; Ivanyshyn Yaman, Olha; Yılmaz, OğuzShort time behavior of a three dimensional, gravity-driven free surface flow is studied analytically and numerically. Initially the fluid is at rest, held by a vertical wall. A rectangular section of the wall suddenly disappears and the gravity driven three-dimensional flow starts. In order to describe the flow in the early stage, the potential theory is employed. Viscous effects are ignored for small times. The leading order problem is solved by using the Fourier series method and an integral equation method. Local analysis of the flow field close to the side edges of the rectangular section reveals a square root singularity. The flow velocity is also log-singular at the bottom edge of the rectangular section. In the limiting case, as the width of the rectangular section approaches infinity, the results of the classical two-dimensional dam break flow are recovered. Three dimensional effects become important closer to the side edges of the rectangular section.Article Citation - WoS: 8Citation - Scopus: 9Analysis of Covid 19 Disease With Sir Model and Taylor Matrix Method(American Institute of Mathematical Sciences, 2022) Uçar, Deniz; Çelik, ElçinCovid 19 emerged in Wuhan, China in December 2019 has continued to spread by affecting the whole world. The pandemic has affected over 328 million people with more than 5 million deaths in over 200 countries which has severely disrupted the healthcare system and halted economies of the countries. The aim of this study is to discuss the numerical solution of the SIR model on the spread of Covid 19 by the Taylor matrix and collocation method for Turkey. Predicting COVID-19 through appropriate models can help us to understand the potential spread in the population so that appropriate action can be taken to prevent further transmission and prepare health systems for medical management of the disease. We deal with Susceptible–Infected–Recovered (SIR) model. One of the proposed model’s improvements is to reflect the societal feedback on the disease and confinement features. We obtain the time dependent rate of transmission of the disease from susceptible β(t) and the rate of recovery from infectious to recovered γ using Turkey epidemic data. We apply the Taylor matrix and collocation method to the SIR model with γ, β(t) and Covid 19 data of Turkey from the date of the first case March 11, 2020 through July 3, 2021. Using this method, we focus on the evolution of the Covid 19 in Turkey. We also show the estimates with the help of graphics and Maple.Article Citation - WoS: 3Citation - Scopus: 3A Direct Method for the Low Energy Scattering Solution of Delta Shell Potentials(Springer, 2022) Erman, Fatih; Seymen, SemaA direct method for the bound states and the low energy scattering from a circular and a spherical delta shell potentials is proposed, and the results are compared with the one using the standard partial wave analysis developed for potentials with rotational symmetry. The formulation is presented in momentum space, and the scattering solutions are obtained by considering the elementary use of distributions. In this approach, the outgoing boundary conditions are imposed explicitly in contrast to the iϵ prescription often used in quantum mechanics.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: 27Citation - Scopus: 31Development and Validation of Herwig 7 Tunes From Cms Underlying-Event Measurements(Springer, 2021) Karapınar, GülerThis paper presents new sets of parameters (tunes) for the underlying-event model of the herwig 7 event generator. These parameters control the description of multiple-parton interactions (MPI) and colour reconnection in herwig 7, and are obtained from a fit to minimum-bias data collected by the CMS experiment at v s = 0.9, 7, and 13 TeV. The tunes are based on the NNPDF3.1 next-to-nextto-leading-order parton distribution function (PDF) set for the parton shower, and either a leading-order or next-to-nextto-leading-order PDF set for the simulation of MPI and the beam remnants. Predictions utilizing the tunes are produced for event shape observables in electron-positron collisions, and forminimum-bias, inclusive jet, top quark pair, and Zand Wboson events in proton-proton collisions, and are compared with data. Each of the new tunes describes the data at a reasonable level, and the tunes using a leading-order PDF for the simulation of MPI provide the best description of the data.Article Citation - WoS: 9Citation - Scopus: 15Constraints on the Initial State of Pb-Pb Collisions Via Measurements of Z-Boson Yields and Azimuthal Anisotropy at Root S(nn)=5.02 Tev(Amer Physical Soc, 2021) Karapınar, Güler; CMS CollaborationThe CMS experiment at the LHC has measured the differential cross sections of Z bosons decaying to pairs of leptons, as functions of transverse momentum and rapidity, in lead-lead collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The measured Z boson elliptic azimuthal anisotropy coefficient is compatible with zero, showing that Z bosons do not experience significant final-state interactions in the medium produced in the collision. Yields of Z bosons are compared to Glauber model predictions and are found to deviate from these expectations in peripheral collisions, indicating the presence of initial collision geometry and centrality selection effects. The precision of the measurement allows, for the first time, for a data-driven determination of the nucleon-nucleon integrated luminosity as a function of lead-lead centrality, thereby eliminating the need for its estimation based on a Glauber model.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.