Inequalities

Theory of Majorization and Its Applications

Edited by
  • Albert W. Marshall - Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada
  • Ingram Olkin - Department of Statistics, Stanford University, Stanford, California
Volume 143,

Pages 3-569 (1979)

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Contents

    1. Mathematics in Science and Engineering

      Page ii
    1. Front Matter

      Page iii
    1. Copyright page

      Page iv
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    1. Dedication

      Page v
    1. Preface

      Pages xiii-xv
    1. Acknowledgments

      Pages xvii-xviii
    1. Basic Notation and Terminology

      Pages xix-xx
  1. Part I Theory of Memorization

    1. Chapter 1 - Introduction

      Pages 3-17
    2. Chapter 2 - Doubly Stochastic Matrices

      Pages 18-52
    3. Chapter 3 - Schur-Convex Functions

      Pages 53-106
    4. Chapter 4 - Equivalent Conditions for Majorization

      Pages 107-114
    5. Chapter 5 - Preservation and Generation of Majorization

      Pages 115-137
    6. Chapter 6 - Rearrangements and Majorization

      Pages 138-168
  2. Part II Mathematical Applications

    1. Chapter 7 - Combinatorial Analysis

      Pages 171-191
    2. Chapter 8 - Geometric Inequalities

      Pages 192-214
    3. Chapter 9 - Matrix Theory

      Pages 215-262
    4. Chapter 10 - Numerical Analysis

      Pages 263-277
  3. Part III Stochastic Applications

    1. Chapter 11 - Stochastic Majorizations

      Pages 281-329
    2. Chapter 12 - Probabilistic and Statistical Applications

      Pages 330-384
    3. Chapter 13 - Additional Statistical Applications

      Pages 385-413
  4. Part IV Generalizations

    1. Chapter 14 - Orderings Extending Majorization

      Pages 417-428
    2. Chapter 15 - Multivariate Majorization

      Pages 429-439
  5. Part V Complementary Topics

    1. Chapter 16 - Convex Functions and Some Classical Inequalities

      Pages 443-480
    2. Chapter 17 - Stochastic Ordering

      Pages 481-486
    3. Chapter 18 - Total Positivity

      Pages 487-495
    4. Chapter 19 - Matrix Factorizations, Compounds, Direct Products, and M-Matrices

      Pages 496-508
    5. Chapter 20 - Extremal Representations of Matrix Functions

      Pages 509-519
  6. Biographies

    1. Robert Franklin Muirhead 1860–1941

      Page 521
    2. Max Otto Lorenz 1876–1959

      Pages 521-522
    3. Baron Edward Hugh John Neal Dalton 1887–1962

      Pages 522-523
    4. Issai Schur 1875–1941

      Page 524
    5. Godfrey Harold Hardy 1877–1947

      Pages 524-526
    6. John Edensor Littlewood 1885–1977

      Pages 526-527
    7. George Pólya 1887–

      Pages 527-529
    1. References

      Pages 531-552
    1. Author Index

      Pages 553-558
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    1. Subject Index

      Pages 559-569
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ISBN: 978-0-12-473750-1

ISSN: 0076-5392