Grabisch, M., Orsay, France
Murofushi, T., Tokyo Institute of Technology, Yokohama, Japan
Sugeno, M., Tokyo Institute of Technology, Yokohama, Japan
(Eds.)
2000. XIV, 477 pp. 76 figs., 41 tabs.
3-7908-1258-7
Concepts similar to fuzzy measure have been introduced
independently in many domains: in non-expected utility
theory, cooperative game theory, complexity analysis, measure
theory, etc. This book reflects all these facets. It
gathers survey papers written by leading researchers in the
field, covering a selection of most significant topics.
The first part is devoted to fundamental and theoretical
material, while the second part deals with more applied
topics such as decision making and pattern recognition. The book
is of interest to researchers in decision making,
artificial intelligence, applied mathematics, mathematical social
sciences, etc.
Keywords: Fuzzy Logic, Measures and Integrals, Decision Theory,
Pattern Recognition
Contents: P. Wakker: Foreword.- M. Grabisch, T. Murofushi, M.
Sugeno: Preface.- Theory: T. Murofushi, M.
Sugeno: Fuzzy Measures and Fuzzy Integrals.- D. Denneberg:
Non-additive Measure and Integral, Basic
Concepts and Their Role for Applications.- M. Grabisch: The
Interaction and M?bius Representations of Fuzzy
Measures on Finite Spaces, k-Additive Measures: A Survey.- K.
Fujimoto, T. Murofushi: Hierarchical
Decomposition of the Choquet Integral.- I. Kramosil: Towards
Generalized Belief Functions.- G. De Cooman:
Integration in Possibility Theory.- Z. Wang, K. Xu: On the
Autocontinuity of Set Functions.- E. Pap:
Pseudo-convolution and Its Applications.- P. Benvenuti, R.
Mesiar: Integrals with Respect to a General Fuzzy
Measure.- D. Butnariu, E.P. Klement: Measures on Triangular
Norm-based Tribes: Properties and Integral
Representations.- J.-L. Marichal: On Choquet and Sugeno Integrals
as Aggregation Functions.- H. Imaoka:
Comparison between Three Fuzzy Integrals.- Applications: A.
Chateauneuf, M. Cohen: Choquet Expected
Utility Model: A New Approach to Individual Behavior under
Uncertainty and to Social Welfare.- D. Dubois, H.
Prade, R. Sabbadin: Qualitative Decision Theory with Sugeno
Integrals.- T. Murofushi, M. Sugeno: The Choquet
Integral in Multicriteria Decision Making.- M. Grabisch, M.
Roubens. Application of the Choquet Integral in
Multicriteria Decision Making.- S.H. Kwon, M. Sugeno: A
Hierarchical Subjective Evaluation Model Using
Non-monotonic Fuzzy Measures and the Choquet Integral.- J.F.
Peters III, L. Han, S. Ramana: The Choquet
Integral in a Rough Software Cost Decision System.- M. Grabisch:
Fuzzy Integral for Classification and Feature
Extraction.- J.M. Keller, P.D. Gader, A.K. Hocaoglu: Fuzzy
Integrals in Image Processing and Recognition.- Z.
Wang, G.J. Klir, J. Swan-Stone, K. Xu: An Algorithm for
Calculating Natural Extensions with Respect to Lower
Probabilities.
Series: Studies in Fuzziness and Soft Computing.VOL. 40
Radjavi, H., Dalhousie University, Halifax, NS,
Canada
Rosenthal, P., University of Toronto, ON, Canada
2000. Approx. 200 pp.
0-387-98467-4
A collection of matrices is said to be triangularizable if there
is an invertible matrix S such that S1 AS is upper
triangular for every A in the collection. This generalization of
commutativity is the subject of many classical
theorems due to Engel, Kolchin, Kaplansky, McCoy and others. The
concept has been extended to collections of
bounded linear operators on Banach spaces: such a collection is
defined to be triangularizable if there is a maximal
chain of subspaces of the Banach space, each of which is
invariant under every member of the collection. Most of
the classical results have been generalized to compact operators,
and there are also recent theorems in the
finite-dimensional case. This book is the first comprehensive
treatment of triangularizability in both the finite and
infinite-dimensional cases. It contains numerous very recent
results and new proofs of many of the classical
theorems. It provides a thorough background for research in both
the linear-algebraic and operator-theoretic
aspects of triangularizability and related areas. More generally,
the book will be useful to anyone interested in
matrices or operators, as many of the results are linked to other
topics such as spectral mapping theorems,
properties of spectral radii and traces, and the structure of
semigroups and algebras of operators. It is essentially
self-contained modulo solid courses in linear algebra (for the
first half) and functional analysis (for the second
half), and is therefore suitable as a text or reference for a
graduate course.
Contents: 1: Algebras of Matrices. 2: Semigroups of Matrices. 3:
Semigroups over Fields of Characteristic Zero.
4: Semigroups of Non-negative Matrices. 5: Compact Operators and
Invariant Subspaces. 6: Algebras of Compact
Operators. 7: Semigroups of Compact Operators. 8: Bounded
Operators.
Series: Universitext.
Springer, T.A., Mathematisch Instituut, Utrecht,
The Netherlands
Veldkamp, F.D.
2000. Approx. 170 pp.
3-540-66337-1
The 1963 G?ttingen notes of T. A. Springer are well-known in the
field but have been unavailable for some time.
This book is a translation of those notes, completely updated and
revised. The part of the book dealing with the
algebraic structures is on a fairly elementary level,
presupposing basic results from algebra. In the
group-theoretical part use is made of some results from the
theory of linear algebraic groups. The book will be
useful to mathematicians interested in octonion algebras and
Albert algebras, or in exceptional groups. It is
suitable for use in a graduate course in algebra.
Keywords: Octonions, Albert Algebras, Exceptional Groups
Contents: 1. Composition Algebras.- 2. The Automorphism Group of
an Octonion Algebra.- 3. Triality.- 4.
Twisted Composition Algebras.- 5. J-algebras and Albert
Algebras.- 6. Proper J-algebras and Twisted
Composition Algebras.- 7. Exceptional Groups.- 8. Cohomological
Invariants.
Series: Springer Monographs in Mathematics.
Thalheim, B., Technical University of Cottbus, Germany
2000. XIV, 621 S.
3-540-65470-4
Database technology and entity-relationship (ER) modeling have
meanwhile reached the level of an established
technology. This book presents the achievements of research in
this field in a comprehensive survey. It deals
with the entity-relationship model and its extensions with regard
to an integrated development and modeling of
database applications and, consequently, the specification of
structures, behavior and interaction. Apart from
research on the ER model and the syntax, semantics, and
pragmatics of database modeling the book also presents
techniques for the translation of the ER model into classical
database models and languages such as relational,
hierarchical, and network models and languages, and also into
object-oriented models. The book is of interest for
all database theoreticians as well as practitioners who are
provided with the relevant foundations of database
modeling.
Keywords: information systems, database and communication
services ; software engineering, programming,
operating systems ; commercial information technology ; DBMS ;
discrete mathematics
Contents: Introduction.- The Database Design Process.- The
Entity-Relationship Model.- Extending the
Entity-Relationship Model.- Integrity Constraints.- Operations.-
Behavior Modeling.- Applying the Theory.-
The Database Design Process in HERM.- The Translation of HERM
Schemes.- Open Problems.- References.-
Index.
Cornil, J.-M., Versailles, France
Testud, P., Versailles, France
2000. Approx. 470 pp. 105 figs.
3-540-66442-4
This book covers the needs of scientists - be they
mathematicians, physicists, chemists or engineers - in terms
of symbolic computation, and allows them to locate quickly, via a
detailed table of contents and index, the method
they require for the precise problem they are adressing.
It requires no prior experience of symbolic computation, nor
specialized mathematical knowledge, and provides
quick access to the practical use of symbolic computation
software. The organization of the book in mutually
independent chapters, each focusing on a specific topic, allows
the user to select what is of interest without
necessarily reading everything.
Keywords: Maple, scientific tools, symbolic computation
Contents: 1. What MAPLE Can Do for You.- 2. Introduction.- 3.
Arithmetic.- 4. Real Numbers - Complex
Numbers.- 5. Two-Dimensional Graphs.- 6. Equations and
Inequations.- 7. Limits and Derivatives.- 8. Truncated
Series Expansions.- 9. Differential Equations.- 10. Integration
and Summation.- 11. Three-Dimensional
Graphics.- 12. Polynomials with Rational Coefficients.- 13.
Polynomials with Irrational Coefficients.- 14. Rational
Functions.- 15. Construction of Vectors and of Matrices.- 16.
Vector Analysis and Matrix Calculus.- 17.
Systems of Linear Equations.- 18. Normalization of Matrices.- 19.
Orthogonality.- 20. Vector Analysis.- 21. The
MAPLE Objects.- 22. Working More Cleverly with the
Subexpressions.- 23. Programming: Loops and Branches.-
24. Programming: Functions and Procedures.- 25. The Mathematical
Functions.- 26. Maple Environment in
Windows.- Index.
Exner, G., Bucknell University, Lewisburg, PA, USA
2000. Approx. 220 pp. 26 figs.
0-387-98932-3
The approach here relies on two beliefs. The first is that almost
nobody fully understands calculus the first time
around. The second is that graphing calculators can be used to
simplify the theory of limits for students. This
book presents the theoretical pieces of introductory calculus,
using appropriate technology, in a style suitable to
accompany almost any first calculus text. It offers a large range
of increasingly sophisticated examples and
problems to build an understanding of the notion of limit and
other theoretical concepts. Aimed at students who
will study fields in which the understanding of calculus as a
tool is not sufficient, the text uses the "spiral
approach" of teaching, returning again and again to
difficult topics, anticipating such returns across the calculus
courses in preparation for the first analysis course. Suitable as
the "content" text for a transition to upper level
mathematics course.
Contents: Limits.- Continuity.- The Language of Theorems.-
Theorems about Continuous Functions.- Limit
Proofs.- Limit Theorems.- Which Functions are Continuous?-
Derivatives.- Theorems about the Derivative.-
Other Limits.
Series: Undergraduate Texts in Mathematics.
Rosenblatt, M., University of California, San Diego, La Jolla, CA, USA
2000. Approx. 255 pp.
0-387-98917-X
The principal focus here is on autoregressive moving average
models and analogous random fields, with
probabilistic and statistical questions also being discussed. The
book contrasts Gaussian models with noncausal or
noninvertible (nonminimum phase) non-Gaussian models and deals
with problems of prediction and estimation. New
results for nonminimum phase non-Gaussian processes are exposited
and open questions are noted. Intended as a
text for gradutes in statistics, mathematics, engineering, the
natural sciences and economics, the only
recommendation is an initial background in probability theory and
statistics. Notes on background, history and
open problems are given at the end of the book.
Contents: Reversibility and Identifiability.- Minimum Phase
Estimation.- Homogeneous Gaussian Random
Fields.- Cumulants, Mixing and Estimation for Gaussian Fields.-
Prediction for Minimum and Nonminimum Phase
Models.- The Fluctuation of the quasi-Gaussian Likelihood.-
Random Fields.- Estimation for Possibly
Nonminimum Phase Schemes.
Series: Springer Series in Statistics.
Bunimovich, L.A., Georgia Institute of Technology,
Atlanta, GA, USA
Dani, S.G., Tata Institute of Fundamental Research, Bombay, India
Dobrushin, R.L.
Jakobson, M.V., University of Maryland, College Park, MD, USA
Kornfeld, I.P., North Dakota State University, Fargo, ND, USA
Maslova, N.B.
Pesin, Y.B., Penn State University, University Park, PA, USA
Sinai, Y.G., Princeton University, Princeton, NJ, USA
Smillie, J., Cornell University, Ithaca, NY, USA
Sukhov, Y.M., University of Cambridge, UK
Vershik, A.M., Math. Institute of the Russian Academy of
Sciences, St. Petersburg, Russia
Sinai, Y.G., Princeton University, Princeton, NJ, USA
(Ed.)
2nd enlarged and corr. ed. 2000. Approx. 470 pp.
3-540-66316-9
This EMS volume, the first edition of which was published as
Dynamical Systems II, EMS 2, sets out to familiarize
the reader to the fundamental ideas and results of modern ergodic
theory and its applications to dynamical systems
and statistical mechanics. The exposition starts from the basic
of the subject, introducing ergodicity, mixing and
entropy. The ergodic theory of smooth dynamical systems is
treated. Numerous examples are presented carefully
along with the ideas underlying the most important results.
Moreover, the book deals with the dynamical systems
of statistical mechanics, and with various kinetic equations. For
this second enlarged and revised edition,
published as Mathematical Physics I, EMS 100, two new
contributions on ergodic theory of flows on homogeneous
manifolds and on methods of algebraic geometry in the theory of
interval exchange transformations were added.
This book is compulsory reading for all mathematicians working in
this field, or wanting to learn about it.
Keywords: dynamical systems, invariant measure, ergodic theorem,
hyperbolicity, spectrum of dynamical
systems
Contents: I. General Ergodic Theory of Groups of Measure
Preserving Transformations (contributions by
I.P.Kornfeld, Ya.G.Sinai, and A.M.Vershik).- II. Ergodic Theory
of Smooth Dynamical Systems (contributions by
L.A.Bunimovich, M.V.Jakobson, Y.B.Pesin, and Ya.G.Sinai).- III.
Dynamical Systems on Homogeneous Spaces
(by S.G.Dani).- IV. The Dynamics of Billiard Flows in Rational
Polygons (by J.Smillie).- V. Dynamical Systems of
Statistical Mechanics and Kinetic Equations (contributions by
R.L.Dobrushin, N.B.Maslova, Ya.G.Sinai, and
Yu.M.Sukhov).- References.- Subject Index
Series: Encyclopaedia of Mathematical Sciences.VOL. 100
Janich, K., University of Regensburg, Germany
2000. Approx. 170 pp. 110 figs.
0-387-98649-9
Classical vector analysis deals with vector fields; the gradient,
divergence, and curl operators; line, surface, and
volume integrals; and the integral theorems of Gauss, Stokes, and
Green. Modern vector analysis distills these
into the Cartan calculus and a general form of Stokes' theorem.
This essentially modern text carefully develops
vector analysis on manifolds and reinterprets it from the
classical viewpoint (and with the classical notation) for
three-dimensional Euclidean space, then goes on to introduce de
Rham cohomology and Hodge theory. The
material is accessible to an undergraduate student with calculus,
linear algebra, and some topology as
prerequisites. The many figures, exercises with detailed hints,
and tests with answers make this book particularly
suitable for anyone studying the subject independently.
Contents: Differentiable manifolds.- Tangent vector space.-
Differential forms.- Orientability.- Integration on
manifolds.- Open manifolds.- The intuitive meaning of Stokes'
theorem.- The hat product and the definition of
Cartan's derivative.- Stokes' theorem.- Classical vector
analysis.- De Rham cohomology.- Differential forms on
Riemannian manifolds.- Calculating in coordinates.- Answers.-
References.- Index.
Series: Undergraduate Texts in Mathematics.