Chapter 1 The algebraic prerequisites for the book are covered here and in the appendix. This chapter should be used as reference material and should be consulted as needed. A systematic treatment of algebras, coalgebras, bialgebras, Hopf algebras, and represen tations of these objects to the extent needed for the book is given. The material here not specifically cited can be found for the most part in Sweedler, 1969] in one form or another, with a few exceptions. A great deal of emphasis is placed on the coalgebra which is the dual of n x n matrices over a field. This is the most basic...

This volume contains the keynote lectures, reports on the experimental work, and papers contributed as posters at the Fifth International Workshop of the Group for Aquatic Primary Productivity (GAP). GAP workshops bring together a diverse group of scientists interested in many aspects of aquatic primary productivity and the programmes are designed to promote the sharing of expertise through joint experimental work. This time the Workshop theme was the daily growth cycle of phototrophic micro-organisms, and incorporated different aspects of growth - increase in algal biomass, specific cell...

Utility theory or, value theory in general, is certainly the cornerstone of decision theory, game theory, microecon mics, and all social and political theories which deal with public decisions. Recently the American School of utility, founded by von N eumann Morgenstern, encountered a far-going criticism by the French School of utility represented by its founder Allais. The whole basis of the theory of decisions involving risk has been shaken and put into question. Consequently, basic research in the fundamentals of utility and value theory evolved into a crisis. Like any crisis in basic...

In this volume we present some o the papers that were delivered at FUR-82 - the First International Con erence on Foundations o Utility and Risk Theory in Oslo, June 1982. The purpose o the con erence was to provide a orum within which scientists could report on interesting applications o modern decision theory and exchange ideas about controversial issues in the oundations o the theory o choice under un certainty. With that purpose in mind we have selected a mixture of applied and theoretical papers that we hope will appeal to a wide spectrum o readers rom graduate students in social science...

This volume contains twelve of my game-theoretical papers, published in the period of 1956-80. It complements my Essays on Ethics, Social Behavior, and Scientific Explanation, Reidel, 1976, and my Rational Behavior and Bargaining Equilibrium in Games and Social Situations, Cambridge University Press, 1977. These twelve papers deal with a wide range of game-theoretical problems. But there is a common intellectual thread going though all of them: they are all parts of an attempt to generalize and combine various game-theoretical solution concepts into a unified solution theory yielding...

This book offers a unified treatment of my research in the foundations of expected utility theory from around 1965 to 1980. While parts are new, the presentation draws heavily on published articles and a few chapters in my 1970 monograph on utility theory. The diverse notations and styles of the sources have of course been reconciled here, and their topics arranged in a logical sequence. The two parts of the book take their respective cues from the von Neumann-Morgenstern axiomatization of preferences between risky options and from Savage's foundational treatment of decision making under...

The quantitative revolution in geography has passed. The spirited debates of the past decades have, in one sense, been resolved by the inclusion of quantitative techniques into the typical geographer's set of methodological tools. A new decade is upon us. Throughout the quantitative revolution, geographers ransacked related disciplines and mathematics in order to find tools which might be applicable to problems of a spatial nature. The early success of Berry and Marble's Spatial Analysis and Garrison and Marble's volumes on Quantitative Geog raphy is testimony to their accomplished search....

This collection of articles contains contributions from a few of Werner Leinfellner's many friends and colleagues. Some of them are former students of Werner's. Others were colleagues of his at various American and European universities. Further, some have come to know Werner through his research, his long-standing editorship of Theory and Deci sion and his extensive participation in international conferences and congresses. The following articles are new to this volume. The areas covered are those in which Werner continues to play an active professional role. We offer them as a tribute to...

This book describes highly applicable mathematics without using calculus or limits in general. The study agrees with the opinion that the traditional calculus/analysis is not necessarily the only proper grounding for academics who wish to apply mathematics. The choice of topics is based on a desire to present those facets of mathematics which will be useful to economists and social/behavioral scientists.
The volume is divided into seven chapters. Chapter I presents a brief review of the solution of systems of linear equations by the use of matrices. Chapter III introduces the theory of...

Mathematical economics uses mathematical tools and reasoning to describe and explain economic reality. At the core of mathematical economics is general equilibrium theory. Static and Dynamic Aspects of General Disequilibrium Theory describes and analyses various general equilibrium models, treating theory from an axiomatic point of view, which may lead to a deeper understanding of problems, may help to avoid incorrect reasoning, and may improve communication within the economic science.
This volume consists of four parts, each of which is self-contained. Part I deals...