Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis Dynamical Systems on Time Scales(Izmir Institute of Technology, 2007) Dündar, Veli; Ufuktepe, ÜnalIn this thesis, we have studied dynamical systems on time scales. Firstly, we give basic definitions and theorems about the time scales and dynamical systems. We present Floquet theory and stability criterion on periodic discrete Hamiltonian systems. We introduce the Hilger complex plane and exponential function on time scales. This exponential function is shown to satisfy an initial value problem involving a first order linear dynamic equation. Uniqueness and existence theorems are presented. And then we give stability criterion, Lyapunov transformations and a unified Floquet theory for periodic time scales. We try to collect studies (Bohner and Peterson 2001), (Dacunha 2005), (Ahlbrandt and Ridenhour 2003) about Dynamical Systems On Time Scales.Master Thesis Analytic Functions on Time Scales(Izmir Institute of Technology, 2007) Kapçak, Sinan; Ufuktepe, ÜnalThe concept of analyticity for complex functions on time scale complex plane was introduced by Bohner and Guseinov in 2005. They developed completely delta differentiability, delta analytic functions on products of two time scales, and Cauchy Riemann equations for delta case. In this thesis, beside the paper of Bohner and Guseinov, we worked on continuous, discrete and semi-discrete analytic functions and developed completely nabla differentiability, nabla analytic functions on products of two time scales, and Cauchy-Riemann equations for nabla case.Master Thesis Oscillation Theory for Second Order Differential Equations and Dynamic Equations on Time Scales(Izmir Institute of Technology, 2004) Yantır, Ahmet; Ufuktepe, Ünal; Ufuktepe, ÜnalThis thesis provides the oscillation criteria for second order linear differential equations and dynamic equations on time scales. We establish the comparison theorems and oscillation criteria for selfadjoint and non-self adjoint equations and systems of first order ordinary differential equations. Then we prove the fundamental results concerning the dynamic equations: existence and uniqueness theorem and disconjugacy criteria.