2003 Approx. 500 p. Hardcover
3-540-00296-0
Reactive systems are becoming more and more
important for
essentially all areas of technical and professional
activities as
well as for many areas of everyday life.
The design of these
systems is a great challenge and requires
sound compromises
between safety and time-to-market. To meet
these needs, early
design phases nowadays include verification
of given
specifications against system descriptions
to find potential
design errors as early as possible.
This book is devoted to the foundation of
the most popular formal
methods for the specification and verification
of reactive
systems. In particular, the ƒÊ-calculus,
omega-automata, and
temporal logics are covered in full detail;
their relationship
and state-of-the-art verification procedures
based on these
formal approaches are presented. Furthermore,
the advantages and
disadvantages of the formalisms from particular
points of view
are analyzed. Most results are given with
detailed proofs, so
that the presentation is almost self-contained.
This book is targeted to advanced students,
lecturers and
researchers in the area of formal methods.
Keywords: Model Checking, Reactive Systems,
Specification,
Temporal Logic, Verification
Contents:
Introduction.- A Unified Specification Language.-
Fixpoint
Calculi.- Finite Automata.- Temporal Logics.-
Monadic Predicate
Logics.- Conclusions.- Index.
Series: Texts in Theoretical Computer Science.
An EATCS Series.
2003 Approx. 550 p. 113 illus. Hardcover
0-387-00173-5
The aim of this monograph is to give a unified
account of the
classical topics in fixed point theory that
lie on the border-line
of topology and non-linear functional analysis,
emphasizing the
topological developments related to the Leray-Schauder
theory.
The first part of this book is based on "Fixed
Point Theory
I" which was published by PWN, Warsaw
in 1982. The second
part follows the outline conceived by Andrzej
Granas and the late
James Dugundji. The completion of this work
has been awaited for
many years by researchers in this area.
"If the authors do equally well with
the second volume they
will have produced the best monograph in
this particular field."
Math Reviews
Contents: Elementary Fixed Point Theorems.-
Theorem of Borsuk and
Topological Transversality.- Homology and
Fixed Points.- Leray-Schauder
Degree and Fixed Point Index.- The Lefschetz-Hopf
Theory.-
Selected Topics.- Index.
Series: Springer Monographs in Mathematics.
2003 Approx. 625 p. Hardcover
0-387-95447-3
The book describes the history of Jordan
algebras, and describes
in full mathematical detail the recent structure
theory for
Jordan algebras of arbitrary dimension due
to Efim Zelmanov. To
keep the exposition elementary, the structure
theory is developed
for linear Jordan algebras (where the scalar
ring contains 1/2,
avoiding the nuisancy distractions of characteristic
2), though
the modern quadratic methods are used throughout.
Both the
quadratic methods and the Zelmanov results
go beyond the previous
textbooks on Jordan Theory, written in the
1960's and early 1980's
before the theory reached its final form.
The book is written to
serve either as a text for a 2nd year graduate
course, or for
independent reading, for students who need
or wish to know a bit
about Jordan algebras. It is not primarily
aimed at experts or
students going on to do research in the area,
and no knowledge is
required beyond standard first-year graduate
algebra courses.
General students of algebra can profit from
exposure to
nonassociative algebras, and students or
professional
mathematicians working in areas such as Lie
algebras,
differential geometry (symmetric spaces or
bounded symmetric
domains), functional analysis (JB algebras
and triples), or
exceptional groups and geometry (related
to the 27-dimensional
Albert algebra) can also profit from acquaintance
with the
material. Jordan algebras crop up in many
surprising settings,
and find application to a variety of mathematical
areas.
Contents: Introduction.- A Brief Survey of
Jordan Theory: Origin
of the Species; The Search for the Exceptional
Algebras; Was sind
und was sollen die Jordan Algebren? Connections
with Lie Algebras
and Groups; The Jordan River; Connections
with the Real World;
Connections with the Complex World.- The
Historical Perspective:
An Historical Survey of Jordan Structure
Theory: Jordan Algebras
in Physical Antiquity; Jordan Algebras in
the Algebraic
Renaissance; Jordan Algebras in the Enlightenment;
The Classical
Theory; The Final Classical Formulation;
The Classical Methods;
The Russian Revolution: 1977-1983; Zelmanov's
Exceptional Methods.-
The Classical Theory: The Category of Jordan
Algebras; The
Category of Alternative Algebras; Three Special
Examples; Jordan
Algebras of Cubic Forms; Two Basic Principles;
Invertibility;
Isotopes; Peirce Decomposition; Off-Diagonal
Rules; Peirce
Consequences; Spin Coordinatization; Hermitian
Coordinatization;
Multiple Peirce Decomposition; Multiple Peirce
Consequences;
Hermitian Symmetries; The Coordinate Algebra;
Jacobson
Coordinatization; Von Neumann Regularity;
Inner Simplicity;
Capacity; Herstein-Kleinfeld-Osborn.
Series: Universitext.
1st ed. 1980. Corr. 14th printing 2003 X,
351 pp. 34 figs.
Hardcover
0-387-90459-X
Designed for students having no previous
experience with rigorous
proofs, this text can be used immediately
after standard calculus
courses. It is highly recommended for anyone
planning to study
advanced analysis, as well as for future
secondary school
teachers. A limited number of concepts involving
the real line
and functions on the real line are studied,
while many abstract
ideas, such as metric spaces and ordered
systems, are avoided
completely. A thorough treatment of sequences
of numbers is used
as a basis for studying standard calculus
topics, and optional
sections invite students to study such topics
as metric spaces
and Riemann-Stieltjes integrals.
Keywords: Differentialrechnung, Integralrechnung
Contents: Introduction.- Sequences.- Continuity.-
Sequences and
Series of Functions.- Differentiation.- Integration.-
Appendix on
Set Notation.- Selected Hints and Answers.-
References.- Symbols
Index.- Index.
Series: Undergraduate Texts in Mathematics.