Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 2Citation - Scopus: 1Basic Calculus on Time Scale With Mathematica(Springer Verlag, 2003) Yantır, Ahmet; Ufuktepe, ÜnalMathematical modeling of time dependent systems are always interesting for applied mathematicians. First continuous and then discrete mathematical modeling are built during the mathematical development from ancient to the modern times. By the discovery of the time scales, the problem of irregular controlling of time dependent systems is solved in 1990's. In this paper, we explain the derivative of functions on time scales and the solutions of some basic calculus problems by using Mathematica. © Springer-Verlag Berlin Heidelberg 2003.Conference Object Citation - WoS: 5Citation - Scopus: 6Quantum Calculus of Classical Vortex Images, Integrable Models and Quantum States(IOP Publishing Ltd., 2016) Pashaev, OktayFrom two circle theorem described in terms of q-periodic functions, in the limit q→1 we have derived the strip theorem and the stream function for N vortex problem. For regular N-vortex polygon we find compact expression for the velocity of uniform rotation and show that it represents a nonlinear oscillator. We describe q-dispersive extensions of the linear and nonlinear Schrodinger equations, as well as the q-semiclassical expansions in terms of Bernoulli and Euler polynomials. Different kind of q-analytic functions are introduced, including the pq-analytic and the golden analytic functions.Article Citation - WoS: 6Citation - Scopus: 6Cleavage Induced Rows of Missing Atoms on Znte (110) Surface(American Physical Society, 2013) Çelebi, Cem; Arı, Ozan; Senger, Ramazan TuğrulCleavage induced rows of linear vacancy structures on p-doped ZnTe (110) surface are studied at room temperature by using cross-sectional scanning tunneling microscopy (X-STM). The oscillating contrast superimposed on the Te-driven occupied states neighboring to the vacancy cores are characterized at the atomic scale in order to determine the type of the missing component on the ZnTe surface matrix. We identify three major intensity distributions associated with different vacancy states. The X-STM images of three possible configurations comprising Zn only, Te only, and ZnTe binary vacancy structures on the ZnTe surface are modeled by using ab initio density functional theory calculations. The comparison of the X-STM measurements of each individual vacancy state to the corresponding theoretical simulation showed that unlike the Te vacancy, which leads to a local depression, the absence of Zn only or ZnTe binary gives rise to hillock features on the neighboring Te states of the ZnTe (110) cleaved surface. The theoretical STM images calculated for an undoped ZnTe crystal imply that possible doping-related effects on vacancy-induced features can be disregarded for interpreting the experimentally observed vacancy structures in our samples.Conference Object Citation - WoS: 6Citation - Scopus: 6Vortex Images, Q-Calculus and Entangled Coherent States(IOP Publishing Ltd., 2012) Pashaev, OktayThe two circles theorem for hydrodynamic flow in annular domain bounded by two concentric circles is derived. Complex potential and velocity of the flow are represented as q-periodic functions and rewritten in terms of the Jackson q-integral. This theorem generalizes the Milne-Thomson one circle theorem and reduces to the last on in the limit q → ∞. By this theorem problem of vortex images in annular domain between coaxial cylinders is solved in terms of q-elementary functions. An infinite set of images, as symmetric points under two circles, is determined completely by poles of the q-logarithmic function, where dimensionless parameter q = r 2 2/r 1 2 is given by square ratio of the cylinder radii. Motivated by Möbius transformation for symmetrical points under generalized circle in complex plain, the system of symmetric spin coherent states corresponding to antipodal qubit states is introduced. By these states we construct the maximally entangled orthonormal two qubit spin coherent state basis, in the limiting case reducible to the Bell basis. Average energy of XYZ model in these states, describing finite localized structure with characteristic extremum points, appears as an energy surface in maximally entangled two qubit space. Generalizations to three and higher multiple qubits are found. We show that our entangled N qubit states are determined by set of complex Fibonacci and Lucas polynomials and corresponding Binet-Fibonacci q-calculus.