Included in series
Studies in Logic and the Foundations of Mathematics, 150
Description
*The modern theory of algebras of binary relations, reformulated
by Tarski as an abstract, algebraic, equational theory of
relation algebras, has considerable mathematical significance,
with applications in various fields: e.g., in computer science---databases,
specification theory, AI---and in anthropology, economics,
physics, and philosophical logic.?
*This comprehensive treatment of the theory of relation algebras
and the calculus of relations is the first devoted to a
systematic development of the subject.?
Key Features:
- Presents historical milestones from a modern perspective.
- Careful, thorough, detailed guide to understanding relation
algebras.
- Includes a wealth of scholarly material --- 100 years of work
by a research community --- presented in book form for the first
time.
- Provides a framework and unified perspective of the subject.
- Roger D. Maddux is one of the world's leading experts in the
field of relation algebras.
Contents
List of Figures
Chapter 1. Foreword
Chapter 2. The Calculus of Relations
Chapter 3. Set Theory
Chapter 4. General Algebra
Chapter 5. First-Order Logic with Equality
Chapter 6. Boolean Algebras
Chapter 7. Relation Algebras
Chapter 8. Constructions
Chapter 9. SA and RA
Chapter 10. Dimension Theory
Chapter 11. Finite Integral Relation Algebras
Appendix A. Failures of J, L, and M Among 4527 Polygroups
Appendix B. 1316 Polygroups with Atoms 1', a, b, c, e
Appendix C. 3013 Polygroups with Atoms 1', a, b, c, d
Appendix.
Bibliography.
Hardbound, ISBN: 0-444-52013-9, publication date: 2006
Series: Frontiers in Mathematics
2006, Approx. 300 p., Softcover
ISBN: 3-7643-7552-3
About this book
This book intends to give an extensive treatment of the basic
theory of general near polygons. Near polygons have been
introduced about 25 years ago and have been studied intensively
in the 1980s. In recent years the subject of near polygons has
regained interest. This book discusses old and new results on
this subject. In the first part of the book, we develop the basic
theory of near polygons. We discuss three important classes of
near polygons (dense, regular and glued near polygons) and
develop the theory of valuations which is very important for
classification purposes. In the second part of the book, we
discuss recent results on the classification of dense near
polygons with three points on each line.
Table of contents
Preface.- Introduction.- Dense Near Polygons.- Regular Near
Polygons.- Glued Near Polygons.- Valuations.- The Known Slim
Dense Near Polygons.- Slim Dense Near Hexagons.- Slim Dense Near
Polygons With a Nice Chain of Convex Subpolygons.- Slim Dense
Near Octagons.- Appendices.- Bibliography.- Index.
Series: Progress in Nonlinear Differential Equations and Their
Applications, Vol. 68
2006, Approx. 200 p., Hardcover
ISBN: 3-7643-7564-7
About this book
The study of variational problems in materials science has a long
history, and it has contributed a lot in shaping our
understanding on how materials work and perform. There is,
however, a recent renewed interest in this subject as a
consequence of the fruitful interaction between mathematical
analysis and the modelling of new, technologically advanced
materials.
This volume collects articles about the study of BV vector
fields, path functionals over Wasserstein spaces, variational
approaches to quasi-static evolution, free-discontinuity problems
with applications to fracture and plasticity, systems with
hysteresis or with interfacial energies, evolution of interfaces,
multi-scale analysis in ferromagnetism and ferroelectricity,
variational techniques for the study of crystal plasticity, of
dislocations, and of concentrations in Ginzburg-Landau
functionals, concentrated contact interactions, and phase
transitions in biaxial liquid crystals.
Table of contents
Preface.- Contributions by K. Barmak, A. Braides, G. Buttazzo, V.
Chiado Piat, G. De Matteis, G. Del Piero, N. Desenzani, I.
Fragala, G. Francfort, A. Garroni, D. Kinderlehrer, I. Livshits,
G. Palatucci, D. Percivale, P. Podio-Guidugli, M.O. Rieger, S.
Ta'asan, F. Tomarelli, E. Virga, A. Visintin
2006, Approx. 685 p. 20 illus., Hardcover
ISBN: 0-8176-4480-6
About this textbook
Algebraic function fields of one variable are used in several
areas of mathematics: complex analysis, algebraic geometry, and
number theory. This text applies an arithmetic-algebraic
viewpoint to the study of function fields as part of the
algebraic theory of numbers, where a function field of one
variable is the analogue of a finite extension of Q, the field of
rational numbers. The author does not ignore the geometric and
analytic aspects of function fields, but focuses on an in-depth
examination from a number-theoretic perspective.
Table of contents
Preface.- Algebraic and Numerical Antecedents.- Algebraic
Function Fields of One Variable.- The Riemann?Roch Theorem.-
Examples.- Cohomology of Groups.- Extensions and Galois Theory.-
Congruence Function Fields.- The Riemann Hypothesis.- Constant
and Separable Extensions.- The Riemann?Hurwitz Formula.-
Introduction to Class Field Theory.- Cyclotomic Function Fields.-
Automorphisms and Galois Theory.- Notations.- References.- Index.