Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Department: search.filters.department.İzmir Institute of Technology. MathematicsSubject: search.filters.subject.Fractals

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  • Article
    Citation - WoS: 7
    Citation - Scopus: 8
    Q-Analytic Functions, Fractals and Generalized Analytic Functions
    (IOP Publishing Ltd., 2014) Pashaev, Oktay; Nalcı, Şengül
    We introduce a new class of complex functions of complex argument which we call q-analytic functions. These functions satisfy q-Cauchy-Riemann equations and have real and imaginary parts as q-harmonic functions. We show that q-analytic functions are not the analytic functions. However some of these complex functions fall in the class of generalized analytic functions. As a main example we study the complex q-binomial functions and their integral representation as a solution of the D-bar problem. In terms of these functions the complex q-analytic fractal, satisfying the self-similar q-difference equation is derived. A new type of quantum states as q-analytic coherent states and corresponding q-analytic Fock-Bargmann representation are constructed. As an application, we solve quantum q-oscillator problem in this representation, and show that the wave functions of quantum states are given by complex q-binomials.
  • Conference Object
    Citation - WoS: 8
    Citation - Scopus: 11
    Two-Circles Theorem, Q-Periodic Functions and Entangled Qubit States
    (IOP Publishing Ltd., 2014) Pashaev, Oktay
    For arbitrary hydrodynamic flow in circular annulus we introduce the two circle theorem, allowing us to construct the flow from a given one in infinite plane. Our construction is based on q-periodic analytic functions for complex potential, leading to fixed scale-invariant complex velocity, where q is determined by geometry of the region. Self-similar fractal structure of the flow with q-periodic modulation as solution of q-difference equation is studied. For one point vortex problem in circular annulus by fixing singular points we find solution in terms of q-elementary functions. Considering image points in complex plane as a phase space for qubit coherent states we construct Fibonacci and Lucas type entangled N-qubit states. Complex Fibonacci curve related to this construction shows reach set of geometric patterns.