Details

Autor(en) / Beteiligte

• Marshall, Albert W.,
• Olkin, Ingram,

Titel

Inequalities : theory of majorization and its applications

Ort / Verlag

New York : Academic Press,

Erscheinungsjahr

1979

Link zum Volltext

• Elsevier Books AutoHoldings

Beschreibungen/Notizen

• Includes indexes.
• Bibliography: pages 531-552.
• Front Cover; Inequalities: Theory of Majorization and its Applications; Copyright Page; Table of Contents; Dedication; Preface; Acknowledgments; Basic Notation and Terminology; Part I: Theory of Memorization; Chapter 1. Introduction; A. Motivation and Basic Definitions; B. Majorization as a Partial Ordering; C. Order-Preserving Functions; D. Various Generalizations of Majorization; Chapter 2. Doubly Stochastic Matrices; A. Doubly Stochastic Matrices and Permutation Matrices; B. Characterization of Majorization Using Doubly Stochastic Matrices
• C. Doubly Substochastic Matrices and Weak MajorizationD. Doubly Superstochastic Matrices and Weak Majorization; E. Orderings on D; F. Proofs of Birkhoff's Theorem and Refinements; G. Classes of Doubly Stochastic Matrices; H. More Examples of Doubly Stochastic and Doubly Substochastic Matrices; I. Properties of Double Stochastic Matrices; J. Diagonal Equivalence of Nonnegative Matrices and Doubly Stochastic Matrices; Chapter 3. Schur-Convex Functions; A. Characterization of Schur-Convex Functions; B. Compositions Involving Schur-Convex Functions
• C. Some General Classes of Schur-Convex FunctionsD. Examples I. Sums of Convex Functions; E. Examples II. Products of Logarithmically Concave Functions; F. Examples III. Elementary Symmetric Functions; G. Symmetrization of Convex and Schur-Convex Functions: Muirhead's Theorem; H. Shur-Convex Functions on D and Their Extension to Rn; I. Miscellaneous Specific Examples; J. Integral Transformations Preserving Schur-Convexity; Chapter 4. Equivalent Conditions for Majorization; A. Characterization by Linear Transformations; B. Characterization in Terms of Order-Preserving Functions
• C. A Geometric CharacterizationChapter 5. Preservation and Generation of Majorization; A. Operations Preserving Majorization; B. Generation of Majorization; C. Maximal and Minimal Vectors under Constraints; D. Majorization in Integers; Chapter 6. Rearrangements and Majorization; A. Majorizations from Additions of Vectors; B. Majorizations from Functions of Vectors; C. Weak Majorizations from Rearrangements; D. L-Superadditive Functions-Properties and Examples; E. Inequalities without Majorization; F. A Relative Arrangement Partial Order; Part II: Mathematical Applications
• Chapter 7. Combinatorial AnalysisA. Some Preliminaries on Graphs, Incidence Matrices, and Networks; B. Conjugate Sequences; C. The Theorem of Gale and Ryser; D. Some Applications of the Gale-Ryser Theorem; E. s-Graphs and a Generalization of the Gale-Ryser Theorem; F. Tournaments; G. Edge Colorings in Graphs; Chapter 8. Geometric Inequalities; A. Inequalities for the Angles of a Triangle; B. Inequalities for the Sides of a Triangle; C. Inequalities for the Exradii and Altitudes; D. Inequalities for the Sides, Exradii, and Medians; E. Isoperimetric-Type Inequalities for Plane Figures
• Chapter 9. Matrix Theory
• Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying ""theory of inequalities."" For certain kinds of inequalities, the notion of majorization leads to such a theory that is sometimes extremely useful and powerful for deriving inequalities. Moreover, the derivation of an inequality by methods of majorization is often very helpful both for providing a deeper understanding and for suggesting natural generalizations.<br>Anyone wishing to employ majorization as a tool in appli
• English
• Description based on print version record.