The concept of multivalued linear operators—or linear relations—is the one of the most exciting and influential fields of research in modern mathematics. Applications of this theory can be found in economic theory, noncooperative games, artificial intelligence, medicine, and more. This new book focuses on the theory of linear relations, responding to the lack of resources exclusively dealing with the spectral theory of multivalued linear operators. The subject of this book is the study of linear relations over real or complex Banach spaces. The main purposes are the definitions and characterization of different kinds of spectra and extending the notions of spectra that are considered for the usual one single-valued operator bounded or not bounded. The volume introduces the theory of pseudospectra of multivalued linear operators. The main topics include demicompact linear relations, essential spectra of linear relation, pseudospectra, and essential pseudospectra of linear relations. The volume will be very useful for researchers since it represents not only a collection of a previously heterogeneous material but is also an innovation through several extensions. Beginning graduate students who wish to enter the field of spectral theory of multivalued linear operators will benefit from the material covered, and expert readers will also find sources of inspiration.

This book provides a systematic and uniform presentation of elimination methods and the underlying theories, along the central line of decomposing arbitrary systems of polynomials into triangular systems of various kinds. Highlighting methods based on triangular sets, the book also covers the theory and techniques of resultants and Gröbner bases. The methods and their efficiency are illustrated by fully worked out examples and their applications to selected problems such as from polynomial ideal theory, automated theorem proving in geometry and the qualitative study of differential equations. The reader will find the formally described algorithms ready for immediate implementation and applicable to many other problems. Suitable as a graduate text, this book offers an indispensable reference for everyone interested in mathematical computation, computer algebra (software), and systems of algebraic equations.

The second edition of this popular book brings students fully up to date with the latest methods and techniques in choice analysis. Comprehensive yet accessible, it offers a unique introduction to anyone interested in understanding how to model and forecast the range of choices made by individuals and groups. In addition to a complete rewrite of several chapters, new topics covered include ordered choice, scaled MNL, generalized mixed logit, latent class models, group decision making, heuristics and attribute processing strategies, expected utility theory, and prospect theoretic applications. Many additional case studies are used to illustrate the applications of choice analysis with extensive command syntax provided for all Nlogit applications and datasets available online. With its unique blend of theory, estimation, and application, this book has broad appeal to all those interested in choice modeling methods and will be a valuable resource for students as well as researchers, professionals, and consultants.

This book constitutes the refereed proceedings of the Joint German/Austrian Conference on Artificial Intelligence, KI 2001, held in Vienna, Austria in September 2001. The 29 revised full technical papers presented together with one invited paper and four posters of industrial papers were carefully reviewed and selected from 79 submissions. All current aspects in AI are addressed, ranging from theoretical and foundational issues to industrial applications.