Title page for etd-0706110-113622


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URN etd-0706110-113622
Author Bo-Yu Chen
Author's Email Address shanjinyo@hotmail.com
Statistics This thesis had been viewed 5066 times. Download 1244 times.
Department Applied Mathematics
Year 2009
Semester 2
Degree Master
Type of Document
Language zh-TW.Big5 Chinese
Title Jensen Inequality, Muirhead Inequality and
Majorization Inequality
Date of Defense 2010-06-04
Page Count 92
Keyword
  • system of distinct representatives
  • Three Chord Lemma
  • Birkhoff Theorem
  • convex function
  • concave function
  • convex hull
  • double stochastic matrix
  • Jensen Inequality
  • Lorenz Curve
  • Majorization Inequality
  • majorization
  • Muirhead Inequality
  • Muirhead condition
  • Schur concave function
  • Schur Criterion
  • Schur convex function
  • Schur Inequality
  • supporting line
  • Supporting Line Inequality
  • Abstract Chapter 1 introduces Jensen Inequality and its geometric interpretation. Some useful criteria for checking the convexity of functions are discussed. Many applications in various fields are also included.
    Chapter 2 deals with Schur Inequality, which can easily solve some problems involved symmetric inequality in three variables. The relationship between Schur Inequality and the roots and the coefficients of a cubic equation is also investigated.
    Chapter 3 presents Muirhead Inequality which is derived from the concept of majorization. It generalizes the inequality of arithmetic and geometric means.
    The equivalence of majorization and Muirhead’s condition is illustrated. Two useful tricks for applying Muirhead Inequality are provided.
    Chapter 4 handles Majorization Inequality which involves Majorization and Schur convexity, two of the most productive concepts in the theory of inequalities.
    Its applications in elementary symmetric functions, sample variance, entropy and birthday problem are considered.
    Advisory Committee
  • Mei-Hui Guo - chair
  • Mong-Na Lo Huang - co-chair
  • May-Ru Chen - co-chair
  • Fu-Chuen Chang - advisor
  • Files
  • etd-0706110-113622.pdf
  • indicate access worldwide
    Date of Submission 2010-07-06

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