Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Institution Author: search.filters.institutionAuthor.Tülü, Serdar

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  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Motion of Vortices Outside a Cylinder
    (American Institute of Physics, 2010) Tülü, Serdar; Yılmaz, Oğuz
    The problem of motion of the vortices around an oscillating cylinder in the presence of a uniform flow is considered. The Hamiltonian for vortex motion for the case with no uniform flow and stationary cylinder is constructed, reduced, and constant Hamiltonian (energy) curves are plotted when the system is shown to be integrable according to Liouville. By adding uniform flow to the system and by allowing the cylinder to vibrate, we model the natural vibration of the cylinder in the flow field, which has applications in ocean engineering involving tethers or pipelines in a flow field. We conclude that in the chaotic case forces on the cylinder may be considerably larger than those on the integrable case depending on the initial positions of vortices and that complex phenomena such as chaotic capture and escape occur when the initial positions lie in a certain region.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    Weighted Bloch, Lipschitz, Zygmund, Bers, and Growth Spaces of the Ball: Bergman Projections and Characterizations
    (Elsevier Ltd., 2011) Kaptanoğlu, Hakkı Turgay; Tülü, Serdar
    We determine precise conditions for the boundedness of Bergman projections from Lebesgue classes onto the spaces in the title, which are members of the same one-parameter family of spaces. The projections provide integral representations for the functions in the spaces. We obtain many properties of the spaces as straightforward corollaries of the projections, integral representations, and isometries among the spaces. We solve the Gleason problem and an extremal problem for pointevaluations in each space. We establish maximality of these spaces among those that exhibit Mobius-type invariances and possess decent functionals. We find new Hermitiannon-Kahlerian metrics that characterize half of these spaces by Lipschitz-type inequalities.