03407nam a22004215i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001600167072002300183082001400206100003300220245014200253250001200395264006700407300004700474336002600521337002600547338003600573347002400609490004600633505068700679520130901366650001602675650001602691650003602707700002802743700003002771710003402801773002002835776003602855830004602891856004802937978-0-387-68276-1DE-He21320180115171410.0cr nn 008mamaa140218s2011 xxu| s |||| 0|eng d a97803876827617 a10.1007/978-0-387-68276-12doi 4aQA276-280 7aPBT2bicssc 7aMAT0290002bisacsh04a519.52231 aMarshall, Albert W.eauthor.10aInequalities: Theory of Majorization and Its Applicationsh[electronic resource] /cby Albert W. Marshall, Ingram Olkin, Barry C. Arnold. aSecond. 1aNew York, NY :bSpringer New York :bImprint: Springer,c2011. aXXVIII, 909 p. 60 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aSpringer Series in Statistics,x0172-73970 aIntroduction -- Doubly Stochastic Matrices -- Schur-Convex Functions -- Equivalent Conditions for Majorization -- Preservation and Generation of Majorization -- Rearrangements and Majorization -- Combinatorial Analysis -- Geometric Inequalities -- Matrix Theory -- Numerical Analysis -- Stochastic Majorizations -- Probabilistic, Statistical, and Other Applications -- Additional Statistical Applications -- Orderings Extending Majorization -- Multivariate Majorization -- Convex Functions and Some Classical Inequalities -- Stochastic Ordering -- Total Positivity -- Matrix Factorizations, Compounds, Direct Products, and M-Matrices -- Extremal Representations of Matrix Functions. aThis book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative, coherent, well written and, most importantly, a pleasure to read. … This work is a valuable resource!” (Mathematical Reviews). “The authors … present an extremely rich collection of inequalities in a remarkably coherent and unified approach. The book is a major work on inequalities, rich in content and original in organization.” (Siam Review). “The appearance of … Inequalities in 1979 had a great impact on the mathematical sciences. By showing how a single concept unified a staggering amount of material from widely diverse disciplines–probability, geometry, statistics, operations research, etc.–this work was a revelation to those of us who had been trying to make sense of his own corner of this material.” (Linear Algebra and its Applications). This greatly expanded new edition includes recent research on stochastic, multivariate and group majorization, Lorenz order, and applications in physics and chemistry, in economics and political science, in matrix inequalities, and in probability and statistics. The reference list has almost doubled. 0aStatistics.14aStatistics.24aStatistical Theory and Methods.1 aOlkin, Ingram.eauthor.1 aArnold, Barry C.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387400877 0aSpringer Series in Statistics,x0172-739740uhttp://dx.doi.org/10.1007/978-0-387-68276-1