Item description for Associative Functions: Triangular Norms And Copulas by Claudi Alsina, Maurice J Frank & Berthold Schweizer...
The functional equation of associativity is the topic of Abel's first contribution to Crelle's Journal. Seventy years later, it was featured as the second part of Hilbert's Fifth Problem, and it was solved under successively weaker hypotheses by Brouwer (1909), Cartan (1930) and Aczel (1949). In 1958, B Schweizer and A Sklar showed that the "triangular norms" introduced by Menger in his definition of a probabilistic metric space should be associative; and in their book Probabilistic Metric Spaces, they presented the basic properties of such triangular norms and the closely related copulas. Since then, the study of these two classes of functions has been evolving at an ever-increasing pace and the results have been applied in fields such as statistics, information theory, fuzzy set theory, multi-valued and quantum logic, hydrology, and economics, in particular, risk analysis. This book presents the foundations of the subject of associative functions on real intervals. It brings together results that have been widely scattered in the literature and adds much new material. In the process, virtually all the standard techniques for solving functional equations in one and several variables come into play. Thus, the book can serve as an advanced undergraduate or graduate text on functional equations.
Promise Angels is dedicated to bringing you great books at great prices. Whether you read for entertainment, to learn, or for literacy - you will find what you want at promiseangels.com!
Studio: World Scientific Publishing Company
Est. Packaging Dimensions: Length: 8.98" Width: 6.14" Height: 0.87" Weight: 1.28 lbs.
Release Date Feb 22, 2006
Publisher World Scientific Publishing Company
ISBN 9812566716 ISBN13 9789812566713
Availability 0 units.
More About Claudi Alsina, Maurice J Frank & Berthold Schweizer
Claudi Alsina received his B.A. and Ph.D. in mathematics from the University of Barcelona. His post-doctoral studies were at the University of Massachusetts, Amherst. He is Professor of Mathematics at the Technical University of Catalonia and has developed a wide range of international activities, research papers, publications and hundreds of lectures on mathematics and mathematics education. His latest books include Associative Functions: Triangular Norms and Copulas with M. J. Frank and B. Schweizer, WSP, 2006; Math Made Visual. Creating Images for Understanding Mathematics with Roger B. Nelsen, MAA, 2006; Vitaminas Matematicas and El Club de la Hipotenusa, Ariel, 2008.
Claudi Alsina has an academic affiliation as follows - Universitat Politecnica de Catalunya, Barcelona Universitat Polit??cni.