Master Degree / Yüksek Lisans Tezleri

Permanent URI for this collectionhttps://hdl.handle.net/11147/3008

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Author: search.filters.author.Ufuktepe, ÜnalCOAR Access Rights: search.filters.coarAccessRights.open access

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Now showing 1 - 8 of 8
  • Master Thesis
    Applications of Petri Nets
    (Izmir Institute of Technology, 2008) Yılmaz, Buket; Ufuktepe, Ünal
    Petri nets are powerful formalism for modeling a wide range of dynamic systems and system behaviors. This thesis surveys the basic concept and application of Petri nets. The structure of Petri nets, their marking and execution and several examples of Petri net modeling. In this thesis we research into the analysis of Petri nets. Also we give the structure of Reachability graphs of Petri nets and their advantages for analyzing the Petri nets. The reachability problem for Petri nets is the problem of finding if Mn 2 R(M0) for a given marking Mn in a net (N,M0).We present several different kinds of Petri nets, together with computer tools based on Mathematica. We give the Mathematica commands for Reachability problem and also we created Mathematica commands for Incidence matrix of Petri nets. We study the concept of Petri nets and applications of Petri nets.We especially focus on Biological applications on Petri nets and we work on modeling of Hashimoto.s Thyroiditis in Petri Nets.
  • Master Thesis
    Probability Theory Applications on Time Scales
    (Izmir Institute of Technology, 2008) Kahraman, Sevcan; Ufuktepe, Ünal
    In this thesis we introduce probability theory adapted on time scales. In this study, we have modified some concepts of probability theory on time scales...Probability Function has been constructed on time scales. After providing some basic concepts of Probability Theory, the review of the fundamental concepts of time scale has been provided. Time scale unifies continuous and discrete analysis. With the help of the definition of ..Measure and the ..Probability Function, random variable has been constructed on time scale. Mathematical expectation and some probabilistic inequalities are provided to Time scale.
  • Master Thesis
    Dynamical Systems on Time Scales
    (Izmir Institute of Technology, 2007) Dündar, Veli; Ufuktepe, Ünal
    In 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, Ünal
    The 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
    Measure Theory on Times Scales
    (Izmir Institute of Technology, 2007) Deniz, Aslı; Ufuktepe, Ünal
    In this thesis, we have studied measure theory adapted to time scales. delta and nabla-measures were first defined by Guseinov in 2003, then in a further study, the relationship between Lebesgue delta-integral and Riemann delta-integral were introduced in detail by Guseinov and Bohner. In 2004, Cabada established the relationship between delta-measure and the classical Lebesgue measure, moreover, Lebesgue delta-integral and the classical Lebegue integral. Finally, deltameasurability of sets was studied by Rzezuchovsky in 2005. In this study, we have adapted basic concepts of the measure theory to time Scales, by using definitions and properties given in these papers. With the help of related papers, Lebesgue-Stieltjes measure has been constructed on time scales and the link between Lebesgue-Stieltjes measure and Lebesgue-Stieltjes delta-measure and also link between Lebesgue-Stieltjes delta-integral and Lebesgue-Stieltjes integral have taken place.
  • 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, Ünal
    This 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.
  • Master Thesis
    Edge Coloring of a Graph
    (Izmir Institute of Technology, 2004) Beşeri, Tina; Ufuktepe, Ünal
    The edge coloring problem is one of the fundamental problem on graphs which often appears in various scheduling problems like the le transfer problem on computer networks. In this thesis, we survey old and new results on the classical edge coloring as well as the generalized edge coloring problems. In addition, we developed some algorithms and modules by using Combinatorica package to color the edges of graphs with webMathematica which is the new web-based technology.
  • Master Thesis
    Vertex Coloring of a Graph
    (Izmir Institute of Technology, 2004) Bacak, Gökşen; Ufuktepe, Ünal
    Vertex coloring is the following optimization problem; given a graph, how many colors are required to color its vertices in such a way that no two adjacent vertices receive the same color? The required number of colors is called the chromatic number of G and is denoted by (G). In this thesis, we reviewed the vertex coloring concepts and theorems. The package ColorG which we have improved has many functions for dealing with graph coloring. This package uses a heuristic method due to Brelaz to color the graph so that adjacent vertices have distinct colors.