Title page for etd-0122105-211845


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URN etd-0122105-211845
Author Shing-Yuan Kung
Author's Email Address kungsy@math.nsysu.edu.tw
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Department Applied Mathematics
Year 2004
Semester 1
Degree Master
Type of Document
Language English
Title Density functions with extremal antiperiodic eigenvalues and related topics
Date of Defense 2005-01-07
Page Count 31
Keyword
  • Density functions
  • eigenvalue
  • Abstract In this thesis, we prove 2 theorems. First let ρ0 be
    a minimizing (or maximizing) density function for the first
    antiperiodic eigenvalue λ1' in E[h,H,M], then ρ0=hχ(a,b)+Hχ[0,π]/(a,b) (or ρ0=Hχ(a,b)+hχ[0,π]/(a,b)) a.e. Finally, we prove minλ1'=minμ1=minν1 where μ1 and ν1 are the first Dirichlet and second Neumann eigenvalues, respectively. Furthermore, we determine the jump point X0 of ρ0 and the corresponding eigenvalue λ1', assuming that ρ0 is symmetric about π/2 We derive the nonlinear equations for this jump point X0 and λ1',then use Mathematica to solve the equations numerically.
    Advisory Committee
  • Tzon-Tzer Lu - chair
  • Chiu-Ya Lan - co-chair
  • W.C.Lian - co-chair
  • Chun-Kong Law - advisor
  • Files
  • etd-0122105-211845.pdf
  • indicate access worldwide
    Date of Submission 2005-01-22

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