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: 7Citation - Scopus: 8Invariants of Multi-Linkoids(Springer Basel Ag, 2023) Gabrovsek, Bostjan; Güğümcü, NeslihanIn this paper, we extend the definition of a knotoid to multilinkoids that consist of a finite number of knot and knotoid components. We study invariants of multi-linkoids, such as the Kauffman bracket polynomial, ordered bracket polynomial, the Kauffman skein module, and the T-invariant in relation with generalized T-graphs.Article Citation - WoS: 1Citation - Scopus: 1Initial Stages of Gravity-Driven Flow of Two Fluids of Equal Depth(American Institute of Physics, 2023) Korobkin, Alexander; Yılmaz, OğuzShort-time behavior of gravity-driven free surface flow of two fluids of equal depth and different densities is studied. Initially, the fluids are at rest and separated with a vertical rigid plate of negligible thickness. Then, the plate disappears suddenly and a gravity-driven flow of the fluids starts. The flow in an early stage is described by the potential theory. The initial flow in the leading order is described by a linear problem, which is solved by the Fourier series method. The motions of the interface between the fluids and their free surfaces are investigated. The singular behaviors of the velocity field at the bottom point, where the interface meets the rigid bottom, and the top point, where the interface meets both free surfaces, are analyzed in detail. The flow velocity is shown to be log-singular at the bottom point. The leading-order inner asymptotic solution is constructed in a small vicinity of this point. It is shown that the flow close to the bottom point is self-similar. The motion of the interface is independent of any parameters, including the density ratio, of the problem in specially stretched variables. In the limiting case of negligible density of one of the fluids, the results of the classical dam break problem are recovered. The Lagrangian representation is employed to capture the behavior of the interface and the free surfaces at the top, where the fluid interface meets the free surfaces. The shapes of the free surfaces and the interface in the leading order computed by using the Lagrangian variables show a jump discontinuity of the free surface near the top point where the free surfaces and the interface meet. Inner region formulation is derived near the top point.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 - Scopus: 3Stabilization of Higher Order Schrödinger Equations on a Finite Interval: Part Ii(American Institute of Mathematical Sciences, 2022) Özsarı, Türker; Yılmaz, Kemal CemBackstepping based controller and observer models were designed for higher order linear and nonlinear Schrödinger equations on a finite interval in [3] where the controller was assumed to be acting from the left endpoint of the medium. In this companion paper, we further the analysis by considering boundary controller(s) acting at the right endpoint of the domain. It turns out that the problem is more challenging in this scenario as the associated boundary value problem for the backstepping kernel becomes overdetermined and lacks a smooth solution. The latter is essential to switch back and forth between the original plant and the so called target system. To overcome this difficulty we rely on the strategy of using an imperfect kernel, namely one of the boundary conditions in kernel PDE model is disregarded. The drawback is that one loses rapid stabilization in comparison with the left endpoint con-trollability. Nevertheless, the exponential decay of the L2-norm with a certain rate still holds. The observer design is associated with new challenges from the point of view of wellposedness and one has to prove smoothing properties for an associated initial boundary value problem with inhomogeneous boundary data. This problem is solved by using Laplace transform in time. However, the Bromwich integral that inverts the transformed solution is associated with certain analyticity issues which are treated through a subtle analysis. Numerical algorithms and simulations verifying the theoretical results are given.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: 8Citation - Scopus: 8Stabilization of Higher Order Schrödinger Equations on a Finite Interval: Part I(American Institute of Mathematical Sciences, 2021) Batal, Ahmet; Özsarı, Türker; Yılmaz, Kemal CemWe study the backstepping stabilization of higher order linear and nonlinear Schrödinger equations on a finite interval, where the boundary feedback acts from the left Dirichlet boundary condition. The plant is stabilized with a prescribed rate of decay. The construction of the backstepping kernel is based on a challenging successive approximation analysis. This contrasts with the case of second order pdes. Second, we consider the case where the full state of the system cannot be measured at all times but some partial information such as measurements of a boundary trace are available. For this problem, we simultaneously construct an observer and the associated backstepping controller which is capable of stabilizing the original plant. Wellposedness and regularity results are provided for all pde models. Although the linear part of the model is similar to the KdV equation, the power type nonlinearity brings additional difficulties. We give two examples of boundary conditions and partial measurements. We also present numerical algorithms and simulations verifying our theoretical results to the fullest extent. Our numerical approach is novel in the sense that we solve the target systems first and obtain the solution to the feedback system by using the bounded invertibility of the backstepping transformation. © 2021, American Institute of Mathematical Sciences. All rights reserved.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.