Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article Citation - WoS: 4Citation - Scopus: 4On Schrödinger Operators Modified by Δ Interactions(Academic Press, 2023) Akbaş, Kaya Güven; Erman, Fatih; Turgut, O. TeomanWe study the spectral properties of a Schrödinger operator H0 modified by δ interactions and show explicitly how the poles of the new Green's function are rearranged relative to the poles of original Green's function of H0. We prove that the new bound state energies are interlaced between the old ones, and the ground state energy is always lowered if the δ interaction is attractive. We also derive an alternative perturbative method of finding the bound state energies and wave functions under the assumption of a small coupling constant in a somewhat heuristic manner. We further show that these results can be extended to cases in which a renormalization process is required. We consider the possible extensions of our results to the multi center case, to δ interaction supported on curves, and to the case, where the particle is moving in a compact two-dimensional manifold under the influence of δ interaction. Finally, the semi-relativistic extension of the last problem has been studied explicitly. © 2023 Elsevier Inc.Article The Adjoint Reidemeister Torsion for Compact 3-Manifolds Admitting a Unique Decomposition(TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2023) Erdal, Esma DiricanLet M be a triangulated, oriented, connected compact 3 -manifold with a connected nonempty boundary. Such a manifold admits a unique decomposition into △ -prime 3 -manifolds. In this paper, we show that the adjoint Reidemeister torsion has a multiplicative property on the disk sum decomposition of compact 3 -manifolds without a corrective term.Article Citation - Scopus: 2Analysis of the Logistic Growth Model With Taylor Matrix and Collocation Method(Etamaths Publishing, 2023) Çelik, Elçin; Uçar, DenizEarly analysis of infectious diseases is very important in the spread of the disease. The main aim of this study is to make important predictions and inferences for Covid 19, which is the current epidemic disease, with mathematical modeling and numerical solution methods. So we deal with the logistic growth model. We obtain carrying capacity and growth rate with Turkey epidemic data. The obtained growth rate and carrying capacity is used in the Taylor collocation method. With this method, we estimate and making predictions close to reality with Maple. We also show the estimates made with the help of graphics and tables. © 2023 the author(s).Article Citation - WoS: 4Citation - Scopus: 4A New Numerical Algorithm Based on Quintic B-Spline and Adaptive Time Integrator for Cou- Pled Burger's Equation(Tabriz University, 2023) Çiçek, Yeşim; Gücüyenen Kaymak, Nurcan; Bahar, Ersin; Gürarslan, Gürhan; Tanoğlu, GamzeIn this article, the coupled Burger's equation which is one of the known systems of the nonlinear parabolic partial differential equations is studied. The method presented here is based on a combination of the quintic B-spline and a high order time integration scheme known as adaptive Runge-Kutta method. First of all, the application of the new algorithm on the coupled Burger's equation is presented. Then, the convergence of the algorithm is studied in a theorem. Finally, to test the efficiency of the new method, coupled Burger's equations in literature are studied. We observed that the presented method has better accuracy and efficiency compared to the other methods in the literature. © 2023 University of Tabriz. All Rights Reserved.Article Citation - WoS: 3Citation - Scopus: 3Dispersion Estimates for the Boundary Integral Operator Associated With the Fourth Order Schrödinger Equation Posed on the Half Line(Element d.o.o., 2022) Özsarı, Türker; Alkan, Kıvılcım; Kalimeris, KonstantinosIn this paper, we prove dispersion estimates for the boundary integral operator associated with the fourth order Schr¨odinger equation posed on the half line. Proofs of such estimates for domains with boundaries are rare and generally require highly technical approaches, as opposed to our simple treatment which is based on constructing a boundary integral operator of oscillatory nature via the Fokas method. Our method is uniform and can be extended to other higher order partial differential equations where the main equation possibly involves more than one spatial derivatives.Article Discrete Fractional Integrals, Lattice Points on Short Arcs, and Diophantine Approximation(TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2022) Temur, FarukRecently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the scope of those results by extending boundedness to bivariate quadratic polynomials. We achieve this in part by establishing connections to problems on concentration of lattice points on short arcs of conics, whence we study discrete fractional integrals and lattice point concentration from a unified perspective via tools of sieving and diophantine approximation, and prove theorems that are of interest to researchers in both subjects.Article Citation - WoS: 8Citation - Scopus: 8Invariants of Bonded Knotoids and Applications To Protein Folding(MDPI, 2022) Güğümcü, Neslihan; Gabrovsek, Bostjan; Kauffman, Louis H.In this paper, we study knotoids with extra graphical structure (bonded knotoids) in the settings of rigid vertex and topological vertex graphs. We construct bonded knotoid invariants by applying tangle insertion and unplugging at bonding sites of a bonded knotoid. We demonstrate that our invariants can be used for the analysis of the topological structure of proteins.Article Citation - WoS: 2Citation - Scopus: 2An Iterative Method for Interaction of Hydro-Elastic Waves With Several Vertical Cylinders of Circular Cross-Sections(MDPI, 2022) Dişibüyük, Nazile Buğurcan; Yılmaz, Oğuz; Korobkin, A. A.; Khabakhpasheva, TatyanaThe problem of ice loads acting on multiple vertical cylinders of circular cross-sections frozen in an ice cover of infinite extent is studied. The loads are caused by a flexural-gravity wave propagating in the ice cover towards the rigid bottom-mounted cylinders. This is a three-dimensional linearized problem of hydroelasticity with finite water depth. The flow under the ice is potential and incompressible. The problem is solved by the vertical mode method combined with an iterative method. The velocity potential is written with respect to each cylinder and is expanded into the Fourier series. The algorithm of the problem solving is reduced to calculations of the Fourier coefficients of the velocity potential. Numerical results for the forces acting on four circular cylinders are presented for different ice thicknesses, incident wave angles and cylinder spacing. The obtained wave forces are compared with the results by others. Good agreement is reported.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: 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.