Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article On pseudo semisimple rings(World Scientific Publishing Co. Pte Ltd, 2013) Büyükaşık, Engin; Mohamed, Saad H.; Mutlu, HaticeA necessary and sufficient condition is obtained for a right pseudo semisimple ring to be left pseudo semisimple. It is proved that a right pseudo semisimple ring is an internal exchange ring. It is also proved that a right and left pseudo semisimple ring is an SSP ringArticle Citation - WoS: 5Citation - Scopus: 3Rings Over Which Flat Covers of Simple Modules Are Projective(World Scientific Publishing Co. Pte Ltd, 2012) Büyükaşık, EnginLet R be a ring with identity. We prove that, the flat cover of any simple right R-module is projective if and only if R is semilocal and J(R) is cotorsion if and only if R is semilocal and any indecomposable flat right R-module with unique maximal submodule is projective.Article Citation - WoS: 11Citation - Scopus: 10A Stabilizing Subgrid for Convection-Diffusion Problem(World Scientific Publishing Co. Pte Ltd, 2006) Neslitürk, Ali İhsanA stabilizing subgrid which consists of a single additional node in each triangular element is analyzed by solving the convection-diffusion problem, especially in the case of small diffusion. The choice of the location of the subgrid node is based on minimizing the residual of a local problem inside each element. We study convergence properties of the method under consideration and its connection with previously suggested stabilizing subgrids. We prove that the standard Galerkin finite element solution on augmented grid produces a discrete solution that satisfy the same a priori error estimates that are typically obtained with SUPG and RFB methods. Some numerical experiments that confirm the theoretical findings are also presented.Article Citation - WoS: 4Citation - Scopus: 5On the Number of Bound States of Point Interactions on Hyperbolic Manifolds(World Scientific Publishing Co. Pte Ltd, 2017) Erman, FatihWe study the bound state problem for N attractive point Dirac δ-interactions in two- and three-dimensional Riemannian manifolds. We give a sufficient condition for the Hamiltonian to have N bound states and give an explicit criterion for it in hyperbolic manifolds ℍ2 and ℍ3. Furthermore, we study the same spectral problem for a relativistic extension of the model on ℝ2 and ℍ2.Article Citation - WoS: 11Citation - Scopus: 10Entanglement in Two Qubit Magnetic Models With Dm Antisymmetric Anisotropic Exchange Interaction(World Scientific Publishing Co. Pte Ltd, 2010) Gürkan, Zeynep Nilhan; Pashaev, OktayIn the present paper, an influence of the anisotropic antisymmetric exchange interaction, the DzialoshinskiiMoriya (DM) interaction, on entanglement of two qubits in various magnetic spin models, including the pure DM model and the most general XYZ model, are studied. We find that the time evolution generated by DM interaction can implement the SWAP gate and discuss realistic quasi-one-dimensional magnets where it can be realized. It is shown that inclusion of the DM interaction to any Heisenberg model creates, when it does not exist, or strengthens, when it exists, the entanglement. We give physical explanation of these results by studying the ground state of the systems at T = 0. Nonanalytic dependence of the concurrence on the DM interaction and its relation with quantum phase transition is indicated. Our results show that spin models with the DM coupling have some potential applications in quantum computations and the DM interaction could be an efficient control parameter of entanglement. © 2010 World Scientific Publishing Company.Conference Object New Casimir Energy Calculations(World Scientific Publishing Co. Pte Ltd, 2007) Ahmedov, Hadji; Duru, İsmail HakkıNew Casimir energy results for massless scalar field in some 3 -dimensional cavities are presented. We attempted to discuss the correlation between the sign and the magnitude of the energy and the shape of the cavities. Sign of the Casimir energy known to be dependent on the dimension, topology and the shape of the geometry. In this note we present some new exact results for massless scalar fields in three dimensional cavities with the trivial topology. We then compare the known Casimir energy values for several three dimensional cavities. The conclusion we arrived is that the existence of the corners lowers the vacuum energy.Article Citation - WoS: 91Citation - Scopus: 91Resonance Solitons as Black Holes in Madelung Fluid(World Scientific Publishing Co. Pte Ltd, 2002) Pashaev, Oktay; Lee, Jyh HaoEnvelope solitons of the Nonlinear Schrödinger equation (NLS) under quantum potential's influence are studied. Corresponding problem is found to be integrable for an arbitrary strength, s ≠ 1, of the quantum potential. For s < 1, the model is equivalent to the usual NLS with rescaled coupling constant, while for s > 1, to the reaction-diffusion system. The last one is related to the anti-de Sitter (AdS) space valued Heisenberg model, realizing a particular gauge fixing condition of the (1 + 1)-dimensional Jackiw-Teitelboim gravity. For this gravity model, by the Madelung fluid representation we derive the acoustic form of the space-time metric. The space-time points, where dispersion changes the sign, correspond to the event horizon, while the soliton solution to the AdS black hole. Moving with the above bounded velocity, it describes evolution on the one sheet hyperboloid with nontrivial winding number, and creates under collision, the resonance states which we study by the Hirota bilinear method.