Series: Lecture Notes in Mathematics , Vol. 1964
2009, Approx. 345 p., Softcover
ISBN: 978-3-540-87564-2
Due: January 14, 2009
Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions. Different approaches are applied in each of these cases using different techniques. The order structure of the (extended) real number system is used for real-valued functions and measures, whereas suprema and infima are replaced with topological limits in the vector-valued case.
A novel approach employing more general structures, locally convex cones, which are natural generalizations of locally convex vector spaces, is introduced here. This setting allows developing a general theory of integration which simultaneously deals with all of the above-mentioned cases.
Introduction.- 1. Locally Convex Cones.- 2. Measures and Integrals. The General Theory.- 3. Measures on Locally Compact Spaces.- List of Symbols.- Bibliography.- Index.
Series: Understanding Complex Systems
2009, XI, 236 p. 106 illus., 54 in color., Hardcover
ISBN: 978-3-540-88072-1
Due: January 7, 2009
The concern of this book is the use of emergent computing and self-organization modelling within various applications of complex systems. The authors focus their attention both on the innovative concepts and implementations in order to model self-organizations, but also on the relevant applicative domains in which they can be used efficiently.
This book is the outcome of a workshop meeting within ESM 2006 (Eurosis), held in Toulouse, France in October 2006.
Researchers, engineers, graduate students in nonlinear dynamics, complexity
Series: Advanced Courses in Mathematics - CRM Barcelona
2009, Approx. 400 p., Softcover
ISBN: 978-3-7643-8961-1
Due: January 2009
Additive Combinatorics is a relatively recent term coined to comprehend the developments of the more classical Additive Number Theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach Conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary Additive Combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory.
This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive Combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.
Foreword.- Preface.- I. Additive Group Theory and Non-unique Factorizations - II. Sumsets and structure.- III. Thematic seminars - Contributions by Jean Marc Deshouillers, Christian Elsholtz, Gregory A. Freiman, Yahya O. Hamidoune, Norbert Hegyvari, Gyula Karoly, Melvyn B. Nathanson, Jaroslav Ne?etril, Jozsef Solymosi, Yonutz V. Stanchescu, Gilles Zemor.
Series: Universitext
Originally published with the subtitle: An Introduction with Stochastic Processes
2009, Approx. 455 p., Softcover
ISBN: 978-3-540-88232-9
Due: February 2009
The volume offers a mathematical introduction to non-life insurance and, at the same time, to a multitude of applied stochastic processes. It includes detailed discussions of the fundamental models regarding claim sizes, claim arrivals, the total claim amount, and their probabilistic properties. Throughout the volume the language of stochastic processes is used for describing the dynamics of an insurance portfolio in claim size, space and time. Special emphasis is given to the phenomena which are caused by large claims in these models. The reader learns how the underlying probabilistic structures allow determining premiums in a portfolio or in an individual policy.
The second edition contains various new chapters that illustrate the use of point process techniques in non-life insurance mathematics. Poisson processes play a central role. Detailed discussions show how Poisson processes can be used to describe complex aspects in an insurance business such as delays in reporting, the settlement of claims and claims reserving. Also the chain ladder method is explained in detail.
More than 150 figures and tables illustrate and visualize the theory. Every section ends with numerous exercises. An extensive bibliography, annotated with various comments sections with references to more advanced relevant literature, makes the volume broadly and easily accessible.
Students and lecturers of actuarial mathematics, mathematics, economics, physics, statistics, econometrics
2009, Approx. 180 p. 20 illus., Hardcover
ISBN: 978-0-387-88752-4
Due: June 2009
Supports advanced-level (Ph.D.) courses in mathematics and computer science
G. C. Rota is a distinguished figure and respected by research institutions (libraries, research departments, universities) in Europe and the USA, making this title a "long seller" in international academia
Combinatorics to Philosophy: The Legacy of G. C. Rota provides an assessment of G. C. Rotafs legacy to international research in mathematics, philosophy and computer science.
This volume includes chapters by leading researchers, as well as a number of invited research papers. Rotafs legacy connects European and Italian research communities to the USA by providing inspiration to several generations of researchers in combinatorics, philosophy and computer science.
Combinatorics to Philosophy: The Legacy of G. C. Rota is of valuable interest to research institutions and university libraries worldwide. This book is also designed for advanced-level students in computer science and mathematics.
Preface.- Introduction.- G. C. Rota Legacy.- Research Contributions: Combinatorics.- Research Contributions: Philosophy.- Index.