Title page for etd-0730112-120420


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URN etd-0730112-120420
Author Tui-En Wang
Author's Email Address No Public.
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Department Applied Mathematics
Year 2011
Semester 2
Degree Ph.D.
Type of Document
Language English
Title Direct and Inverse Spectral Problems on Quantum Graphs
Date of Defense 2012-06-29
Page Count 80
Keyword
  • quantum graphs
  • inverse spectral problem
  • Ambarzumyan problem
  • spectrum
  • graphene
  • Abstract Recently there is a lot of interest in the study of Sturm-Liouville problems on graphs,
    called quantum graphs. However the study on cyclic quantum graphs are scarce. In
    this thesis, we shall rst consider a characteristic function approach to the spectral
    analysis for the Schrodinger operator H acting on graphene-like graphs|in nite periodic
    hexagonal graphs with 3 distinct adjacent edges and 3 distinct potentials de ned
    on them. We apply the Floquet-Bloch theory to derive a Floquet equation with parameters
    theta_1, theta_2, whose roots de ne all the spectral values of H. Then we show that the
    spectrum of this operator is continuous. Our results generalize those of Kuchment-Post
    and Korotyaev-Lobanov. Our method is also simpler and more direct.
    Next we solve two Ambarzumyan problems, one for graphene and another for a cyclic
    graph with two vertices and 3 edges. Finally we solve an Hochstadt-Lieberman type
    inverse spectral problem for the same cyclic graph with two vertices and 3 edges.
    Keywords : quantum graphs, graphene, spectrum, Ambarzumyan problem, inverse
    spectral problem.
    Advisory Committee
  • Chao-Nien Chen - chair
  • Tzon-Tzer Lu - co-chair
  • Yung-Sze Choi - co-chair
  • Chung-Tsun Shieh - co-chair
  • Chung-Chuan Chen - co-chair
  • Chun-Kong Law - advisor
  • Files
  • etd-0730112-120420.pdf
  • Indicate in-campus at 2 year and off-campus access at 2 year.
    Date of Submission 2012-07-30

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