Natural and Mathematical Scienceshttp://hdl.handle.net/10679/3132019-08-25T20:21:07Z2019-08-25T20:21:07ZConvergence of a semi-discrete numerical method for a class of nonlocal nonlinear wave equationsErbay, Hüsnü AtaErbay, SaadetErkip, A.http://hdl.handle.net/10679/62492019-03-29T12:47:29Z2018-09-13T00:00:00ZConvergence of a semi-discrete numerical method for a class of nonlocal nonlinear wave equations
Erbay, Hüsnü Ata; Erbay, Saadet; Erkip, A.
In this article, we prove the convergence of a semi-discrete numerical method applied to a general class of nonlocal nonlinear wave equations where the nonlocality is introduced through the convolution operator in space. The most important characteristic of the numerical method is that it is directly applied to the nonlocal equation by introducing the discrete convolution operator. Starting from the continuous Cauchy problem defined on the real line, we first construct the discrete Cauchy problem on a uniform grid of the real line. Thus the semi-discretization in space of the continuous problem gives rise to an infinite system of ordinary differential equations in time. We show that the initial-value problem for this system is well-posed. We prove that solutions of the discrete problem converge uniformly to those of the continuous one as the mesh size goes to zero and that they are second-order convergent in space. We then consider a truncation of the infinite domain to a finite one. We prove that the solution of the truncated problem approximates the solution of the continuous problem when the truncated domain is sufficiently large. Finally, we present some numerical experiments that confirm numerically both the expected convergence rate of the semi-discrete scheme and the ability of the method to capture finite-time blow-up of solutions for various convolution kernels.
2018-09-13T00:00:00ZFrequently hypercyclic weighted backward shifts on spaces of real analytic functionsAnahtarcı, BerkayKarıksız, Can Dehahttp://hdl.handle.net/10679/62352019-03-27T21:31:11Z2018-01-01T00:00:00ZFrequently hypercyclic weighted backward shifts on spaces of real analytic functions
Anahtarcı, Berkay; Karıksız, Can Deha
We study frequent hypercyclicity in the case of weighted backward shift operators acting on locally convex spaces of real analytic functions. We obtain certain conditions on frequent hypercyclicity and linear chaoticity of these operators using dynamical transference principles and the frequent hypercyclicity criterion.
2018-01-01T00:00:00ZObservation of t ¯ t H productionSirunyan, A. M.Işıldak, Borahttp://hdl.handle.net/10679/62322019-03-27T21:30:45Z2018-06-04T00:00:00ZObservation of t ¯ t H production
Sirunyan, A. M.; Işıldak, Bora
The observation of Higgs boson production in association with a top quark-antiquark pair is reported, based on a combined analysis of proton-proton collision data at center-of-mass energies of root s = 7, 8, and 13 TeV, corresponding to integrated luminosities of up to 5.1, 19.7, and 35.9 fb(-1), respectively. The data were collected with the CMS detector at the CERN LHC. The results of statistically independent searches for Higgs bosons produced in conjunction with a top quark-antiquark pair and decaying to pairs of W bosons, Z bosons, photons, tau leptons, or bottom quark jets are combined to maximize sensitivity. An excess of events is observed, with a significance of 5.2 standard deviations, over the expectation from the background-only hypothesis. The corresponding expected significance from the standard model for a Higgs boson mass of 125.09 GeV is 4.2 standard deviations. The combined best fit signal strength normalized to the standard model prediction is 1.26(-0.26)(+0.31).
2018-06-04T00:00:00ZSearch for a singly produced third-generation scalar leptoquark decaying to a τ lepton and a bottom quark in proton-proton collisions at s√=13 TeVSirunyan, A. M.Işıldak, Borahttp://hdl.handle.net/10679/62292019-03-27T21:30:51Z2018-07-01T00:00:00ZSearch for a singly produced third-generation scalar leptoquark decaying to a τ lepton and a bottom quark in proton-proton collisions at s√=13 TeV
Sirunyan, A. M.; Işıldak, Bora
A search is presented for a singly produced third-generation scalar leptoquark decaying to a tau lepton and a bottom quark. Associated production of a leptoquark and a tau lepton is considered, leading to a final state with a bottom quark and two tau leptons. The search uses proton-proton collision data at a center-of-mass energy of 13 TeV recorded with the CMS detector, corresponding to an integrated luminosity of 35.9 fb(-1). Upper limits are set at 95% confidence level on the production cross section of the third-generation scalar leptoquarks as a function of their mass. From a comparison of the results with the theoretical predictions, a third-generation scalar leptoquark decaying to a tau lepton and a bottom quark, assuming unit Yukawa coupling (lambda), is excluded for masses below 740 GeV. Limits are also set on lambda of the hypothesized leptoquark as a function of its mass. Above lambda = 1.4, this result provides the best upper limit on the mass of a third-generation scalar leptoquark decaying to a tau lepton and a bottom quark.
2018-07-01T00:00:00Z