Mathematics / Matematik

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  • Article
    Citation - WoS: 54
    Citation - Scopus: 59
    Measurement 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
    Arithmetic Progressions in Certain Subsets of Finite Fields
    (Elsevier, 2023) Eyidoğan, Sadık; Göral, Haydar; Kutlu, Mustafa Kutay
    In this note, we focus on how many arithmetic progressions we have in certain subsets of finite fields. For this purpose, we consider the sets Sp = {t2 : t & ISIN; Fp} and Cp = {t3 : t & ISIN; Fp}, and we use the results on Gauss and Kummer sums. We prove that for any integer k & GE; 3 and for an odd prime number p, the number of k-term arithmetic progressions in Sp is given by p2 2k + R, where and ck is a computable constant depending only on k. The proof also uses finite Fourier analysis and certain types of Weil estimates. Also, we obtain some formulas that give the exact number of arithmetic progressions of length  in the set Sp when  & ISIN; {3,4, 5} and p is an odd prime number. For  = 4, 5, our formulas are based on the number of points on
  • Article
    Citation - WoS: 8
    Citation - Scopus: 7
    Exponential Stability and Boundedness of Nonlinear Perturbed Systems by Unbounded Perturbation Terms
    (Elsevier, 2023) Şahan, Gökhan
    We study the exponential stability and boundedness problem for perturbed nonlinear time-varying systems using Lyapunov Functions with indefinite derivatives. As the limiting function for the perturbation term, we use different forms and give stability and boundedness conditions in terms of the coefficients in these bounds. Contrary to most of the available conditions, we allow the coefficients to be unbounded. But instead, we put forward a condition that requires a series produced by coefficients to be limited and exponentially decaying. We perform our results on Linear time-varying systems and generalize many of the available results. & COPY; 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Plaintext Recovery and Tag Guessing Attacks on Authenticated Encryption Algorithm Colm
    (Elsevier, 2022) Ulusoy, Sırrı Erdem; Kara, Orhun; Efe, Mehmet Önder
    There are three main approaches related to cryptanalysis of Authenticated Encryption with Associated Data (AEAD) algorithms: Simulating the encryption oracle (universal forgery attack), simulating the decryption oracle (plaintext recovery attack) and producing the valid tag of a given ciphertext (tag guessing attack). In this work, we analyze the security of COLM in these approaches. COLM is one of the AEAD algorithms chosen in the final portfolio for defense-in-depth use case of the CAESAR competition. The ciphers in this portfolio are supposed to provide robust security with their multiple layered defense mechanisms. The main motivation of this work is to examine if COLM indeed satisfies defense-in-depth security. We make cryptanalysis of COLM, particularly in the chosen ciphertext attack (CCA) scenario, once its secret whitening parameter L=EK(0) is recovered. To the best of our knowledge, we give the first example of querying an EME/EMD (Encrypt-linearMix-Encrypt/Decrypt) AEAD scheme in its decryption direction for arbitrary ciphertexts, not produced previously by the oracle, namely either a forgery or tag guessing attack. We construct SEBC/SDBC (Simulation models of the Encryption/Decryption oracles of the underlying Block Cipher) of COLM, thereby forming the first examples of these models of an authenticated EME scheme simultaneously. The combination of our SEBC/SDBC is a powerful tool to mount a universal forgery attack, a tag guessing attack and a plaintext recovery attack. All of these attacks have polynomial time complexities once L is recovered in the offline phase, indicating that the security of COLM against plaintext recovery and tag guessing attacks is limited by the birthday bound. Apart from exploiting SEBC/SDBC, we mount a pair of plaintext recovery attacks and another universal forgery attack. Finally, we make some suggestions to prevent our attacks.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Initial Stages of a Three Dimensional Dam Break Flow
    (Elsevier, 2022) Fetahu, Elona; Ivanyshyn Yaman, Olha; Yılmaz, Oğuz
    Short 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.
  • Conference Object
    Existence and Uniqueness of Solution for Discontinuous Conewise Linear Systems
    (Elsevier, 2020) Şahan, Gökhan
    In this study, we give necessary and sufficient conditions for well posedness of Conewise Linear Systems in 3-dimensional space where the vector field is allowed to be discontinuous. The conditions are stated using the subspaces derived from subsystem matrices and the results are compared with the existing conditions given in the literature. We show that even we don't have a fixed structure on system matrices as in bimodal systems, similar subspaces and numbers again determines well posedness. Copyright (C) 2020 The Authors.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 12
    An Efficient Approach for Solving Nonlinear Multidimensional Schrodinger Equations
    (Elsevier, 2021) İmamoğlu Karabaş, Neslişah; Korkut, Sıla Övgü; Tanoğlu, Gamze; Aziz, Imran; Siraj-ul-Islam
    An efficient numerical method is proposed for the solution of the nonlinear cubic Schrodinger equation. The proposed method is based on the Frechet derivative and the meshless method with radial basis functions. An important characteristic of the method is that it can be extended from one-dimensional problems to multi-dimensional ones easily. By using the Frechet derivative and Newton-Raphson technique, the nonlinear equation is converted into a set of linear algebraic equations which are solved iteratively. Numerical examples reveal that the proposed method is efficient and reliable with respect to the accuracy and stability.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    A Three Dimensional Dam Break Flow: Small Time Behavior
    (Elsevier, 2021) Fetahu, Elona; Yılmaz, Oğuz
    Small time behavior of gravity driven free surface flows resulting from the collapse of a cavity is studied. Initially there is a rigid vertical cylinder of circular cross section starting from the free surface of a liquid and ending at the rigid bottom. The cylinder disappears suddenly and gravity driven flow of the fluid starts. The flow in early stage is described by the potential theory. Attention is paid to the singular behavior of the velocity field at the intersection line between the bottom and the free surface of the cavity. The leading order linear problem is solved by the Fourier series method. The flow velocity is log-singular at the intersection line. In the limiting case where the radius and the center of the cavity approach infinity, the problem is reduced to the classical two dimensional dam break problem where the fluid is initially on one side of a vertical wall (dry bed case). The flow resulting from cavity collapse is a three dimensional dam break flow. It is concluded that the three dimensional effects are important when the radius of the cavity is small compared with its depth and that the local flow near the intersection line of the cavity is governed only by the hydrostatic pressure.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Numerical Solution of a Generalized Boundary Value Problem for the Modified Helmholtz Equation in Two Dimensions
    (Elsevier, 2021) Ivanyshyn Yaman, Olha; Özdemir, Gazi
    We propose numerical schemes for solving the boundary value problem for the modified Helmholtz equation and generalized impedance boundary condition. The approaches are based on the reduction of the problem to the boundary integral equation with a hyper-singular kernel. In the first scheme the hyper-singular integral operator is treated by splitting off the singularity technique whereas in the second scheme the idea of numerical differentiation is employed. The solvability of the boundary integral equation and convergence of the first method are established. Exponential convergence for analytic data is exhibited by numerical examples. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.Y. All rights reserved.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 6
    Dynamical Properties of Generalized Traveling Waves of Exactly Solvable Forced Burgers Equations With Variable Coefficients
    (Elsevier, 2021) Atılgan Büyükaşık, Şirin; Bozacı, Aylin
    The initial value problem for a generalized forced Burgers equation with variable coefficients U-t + ((mu)over dot(t)/mu(t))U + UUX = (1/2 mu(t))U-xx - a(t)U-x + b(t)(xU)(x) - omega(2)(t)x + f(t), x is an element of R , t > 0, is solved using Cole-Hopf linearization and Wei-Norman Lie algebraic approach for finding the evolution operator of the associated linear diffusion type equation. As a result, solution of the initial value problem is obtained in terms of a corresponding linear second-order inhomogeneous ordinary differential equation and a standard Burgers model. Then, using the translation and Galilean invariance of standard Burgers equation, families of generalized nonlinear waves propagating according to a Newtonian type equation of motion are constructed. The influence of the damping, dilatation and forcing terms on the dynamics of shocks, multi-shocks, triangular and N-shaped generalized traveling waves and rational type solutions with moving singularities is investigated. Finally, exactly solvable models with concrete time-variable coefficients are introduced and dynamical properties of certain particular solutions are discussed. (C) 2020 Elsevier B.V. All rights reserved.