Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article Citation - WoS: 1Citation - Scopus: 1Euler-Zagier Sums Via Trigonometric Series(Publishing House of the Romanian Academy, 2023) Çam Çelik, Şermin; Göral, HaydarIn this note, we study the evaluations of Euler sums via trigonometric series. It is a commonly believed conjecture that for an even weight greater than seven, Euler sums cannot be evaluated in terms of the special values of the Riemann zeta function. For an even weight, we reduce the evaluations of Euler sums into the evaluations of double series and integrals of products of Clausen functions. We also re-evaluate Euler sums of odd weight using a new method based on trigonometric series.Article Relativistic Dissipatons in Integrable Nonlinear Majorana Type Spinor Model(Yunnan University, 2022) Pashaev, Oktay; Lee, J. H.By method of moving frame, the relativistic integrable nonlinear model for real, Majorana type spinor fields in 1+1 dimensions is introduced and gauge equivalence of this model with Papanicolau spin model on one sheet hyperboloid is established. In terms of the so called double numbers, the model is represented also as hyperbolic complex relativistic model, in the form similar to the massive Thirring model. By using Hirota's bilinear method, the one dissipaton solution of this model is constructed. We calculate first integrals of motion for this dissipaton and show that it represents a relativistic particle with highly nonlinear mass. Analyzing resonance conditions for scattering of two relativistic dissipatons, we find a solution describing resonant property of the dissipatons.Article Class Number and the Special Values of L-Functions(Romanian Academy, 2022) Göral, HaydarWe give infinitely many explicit new representations of the class number of imag inary quadratic fields in terms of certain trigonometric series. Our result relies on a hybrid between power series and trigonometric series. Furthermore, in some cases we prove that the special values of Dirichlet L-functions can be evaluated as certain finite sums.Article Lehmer’s Conjecture Via Model Theory(Japan Academy, 2022) Göral, HaydarIn this short note, we study Lehmer's conjecture in terms of stability theory. We state Bounded Lehmer's conjecture, and we prove that if a certain formula is uniformly stable in a class of structures, then Bounded Lehmer's conjecture holds. Our proof is based on Van der Waerden's theorem from additive combinatoricsArticle Two Numerical Solutions for Solving a Mathematical Model of the Avascular Tumor Growth(Dokuz Eylül Üniversitesi, 2021) Korkut, Sıla Övgü; İmamoğlu Karabaş, Neslişah; Başbınar, YaseminObjective: Cancer which is one of the most challenging health problems overall the world is composed of various processes: tumorigenesis, angiogenesis, and metastasis. Attempting to understand the truth behind this complicated disease is one of the common objectives of many experts and researchers from different fields. To provide deeper insights any prognostic and/or diagnostic scientific contribution to this topic is so crucial. In this study, the avascular tumor growth model which is the earliest stage of tumor growth is taken into account from a mathematical point of view. The main aim is to solve the mathematical model of avascular tumor growth numerically. Methods: This study has focused on the numerical solution of the continuum mathematical model of the avascular tumor growth described by Sharrett and Chaplin. Unlike the existing recent literature, the study has focused on the methods for the temporal domain. To obtain the numerical schemes the central difference method has been used in the spatial coordinates. This discretization technique has reduced the main partial differential equation into an ordinary differential equation which will be solved successively by two alternative techniques: the 4th order Runge-Kutta method (RK4) and the three-stage strongly-stability preserving Runge-Kutta method (SSP-RK3). Results: The model has been solved by the proposed methods. The numerical results are discussed in both mathematical and biological angles. The biological compatibility of the methods is depicted in various figures. Besides biological outputs, the accuracies of the methods have been listed from a mathematical point of view. Furthermore, the rate of convergence of the proposed methods has also been discussed computationally. Conclusion: All recorded results are evidence that the proposed schemes are applicable for solving such models. Moreover, all exhibited figures have proved the biological compatibility of the methods. It is observed that the quiescent cells which are one of the most mysterious cells in clinics tend to become proliferative for the selected parameters.Article The Group of Invertible Ideals of a Prufer Ring(Indian Academy of Sciences, 2020) Saylam, Başak AyLet R be a commutative ring and I( R) denote the multiplicative group of all invertible fractional ideals of R, ordered by A <= B if and only if B subset of A. We investigatewhen there is an order homomorphism from I(R) into the cardinal direct sum G(i), where G(i)'s are value groups, if R is a Marot Prufer ring of finite character. Furthermore, over Prufer rings with zero-divisors, we investigate the conditions that make this monomorphism onto.Article Citation - WoS: 14Citation - Scopus: 12Injective modules over down-up algebras(Cambridge University Press, 2010) Carvalho, Paula A.A.B.; Lomp, Christian; Pusat, DilekThe purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian down-up algebras. We will show that the Noetherian down-up algebras A(α, β, γ) which are fully bounded are precisely those which are module-finite over a central subalgebra. We show that injective hulls of simple A(α, β, γ)-modules are locally Artinian provided the roots of X2 − αX − β are distinct roots of unity or both equal to 1.Article Citation - WoS: 9Citation - Scopus: 78Reconstruction and Identification of ? Lepton Decays To Hadrons and ?? at Cms(IOP Publishing Ltd., 2016) CMS Collaboration; Karapınar, GülerThis paper describes the algorithms used by the CMS experiment to reconstruct and identify τ → hadrons + νtau; decays during Run 1 of the LHC. The performance of the algorithms is studied in proton-proton collisions recorded at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 19.7 fb-1. The algorithms achieve an identification efficiency of 50-60%, with misidentification rates for quark and gluon jets, electrons, and muons between per mille and per cent levels.Article Citation - WoS: 208Citation - Scopus: 186Performance of Photon Reconstruction and Identification With the Cms Detector in Proton-Proton Collisions at ?s = 8 Tev(IOP Publishing Ltd., 2015) CMS Collaboration; Karapınar, GülerA description is provided of the performance of the CMS detector for photon reconstruction and identification in proton-proton collisions at a centre-of-mass energy of 8 TeV at the CERN LHC. Details are given on the reconstruction of photons from energy deposits in the electromagnetic calorimeter (ECAL) and the extraction of photon energy estimates. The reconstruction of electron tracks from photons that convert to electrons in the CMS tracker is also described, as is the optimization of the photon energy reconstruction and its accurate modelling in simulation, in the analysis of the Higgs boson decay into two photons. In the barrel section of the ECAL, an energy resolution of about 1% is achieved for unconverted or late-converting photons from Hγγ decays. Different photon identification methods are discussed and their corresponding selection efficiencies in data are compared with those found in simulated events. © CERN 2015 for the benefit of the CMS collaboration.Article Citation - WoS: 1Citation - Scopus: 1Rad-supplements in injective modules(Institute of Applied Mathematics And Mechanics of the National Academy of Sciences of Ukraine, 2016) Büyükaşık, Engin; Tribak, RachidWe introduce and study the notion of Rad-sinjective modules (i.e. modules which are Rad-supplements in their injective hulls). We compare this notion with another generalization of injective modules. We show that the class of Rad-s-injective modules is closed under finite direct sums. We characterize Rads-injective modules over several type of rings, including semilocal rings, left hereditary rings and left Harada rings. © Journal “Algebra and Discrete Mathematics”.