Daniel Bertrand, Benjamin Enriquez, Claude Mitschi, Claude Sabbah, Reinhard Schaefke, Editors
Differential Equations and Quantum Groups
Andrey A. Bolibrukh Memorial Volume
IRMA Lectures in Mathematics and Theoretical Physics Vol. 9
ISBN 978-3-03719-020-3
December 2006, 302 pages, softcover, 17.0 cm x 24.0 cm.
44.50 Euro
This special volume is dedicated to the memory of Andrey A.
Bolibrukh. It contains two expository articles devoted to some
aspects of Bolibrukh's work, followed by ten refereed research
articles.
Topics cover complex linear and nonlinear differential equations
and quantum groups: monodromy, Fuchsian linear systems, Riemann--Hilbert
problem, differential Galois theory, differential algebraic
groups, multisummability, isomonodromy, Painleve equations,
Schlesinger equations, integrable systems, KZ equations, complex
reflection groups, root systems.
Contents
Garnett, John
Bounded Analytic Functions
Series: Graduate Texts in Mathematics , Vol. 236
Originally published by Academic Press, 1981
Revised 1st ed., 2007, XIV, 466 p., 31 illus., Hardcover
ISBN-10: 0-387-33621-4
ISBN-13: 978-0-387-33621-3
About this textbook
This book is an account of the theory of Hardy spaces in one
dimension, with emphasis on some of the exciting developments of
the past two decades or so. The last seven of the ten chapters
are devoted in the main to these recent developments. The motif
of the theory of Hardy spaces is the interplay between real,
complex, and abstract analysis. While paying proper attention to
each of the three aspects, the author has underscored the
effectiveness of the methods coming from real analysis, many of
them developed as part of a program to extend the theory to
Euclidean spaces, where the complex methods are not available.
Table of contents
Preliminaries.- H_P Spaces.- Conjugate Functions.- Some Extremal
Problems.- Some Uniform Algebra.- Bounded Mean Oscillation.-
Interpolating Sequences.- The Corona Construction.- Douglas
Algebras.- Interpolating Sequences and Maximal Ideals.-
Bibliography.- Index.
Ray, Urmie
Automorphic Forms and Lie Superalgebras
Series: Algebra and Applications , Vol. 5
2006, X, 290 p., Hardcover
ISBN-10: 1-4020-5009-7
ISBN-13: 978-1-4020-5009-1
About this book
A principal ingredient in the proof of the Moonshine Theorem,
connecting the Monster group to modular forms, is the infinite
dimensional Lie algebra of physical states of a chiral string on
an orbifold of a 26 dimensional torus, called the Monster Lie
algebra. It is a Borcherds-Kac-Moody Lie algebra with Lorentzian
root lattice; and has an associated automorphic form having a
product expansion describing its structure. Lie superalgebras are
generalizations of Lie algebras, useful for depicting
supersymmetry ? the symmetry relating fermions and bosons. Most
known examples of Lie superalgebras with a related automorphic
form such as the Fake Monster Lie algebra whose reflection group
is given by the Leech lattice arise from (super)string theory and
can be derived from lattice vertex algebras. The No-Ghost Theorem
from dual resonance theory and a conjecture of Berger-Li-Sarnak
on the eigenvalues of the hyperbolic Laplacian provide strong
evidence that they are of rank at most 26.
The aim of this book is to give the reader the tools to
understand the ongoing classification and construction project of
this class of Lie superalgebras and is ideal for a graduate
course. The necessary background is given within chapters or in
appendices.
Written for:
Graduate students or researchers, in particular from the fields
of Algebra, Number Theory, Conformal Field Theory and Geometry.
Padula, Mariarosaria; Zanghirati, Luisa (Eds.)
Hyperbolic Problems and Regularity Questions
Series: Trends in Mathematics
2007, VI, 231 p., Hardcover
ISBN-10: 3-7643-7450-0
ISBN-13: 978-3-7643-7450-1
About this book
This book discusses new challenges in the quickly developing
field of hyperbolic problems. Particular emphasis lies on the
interaction between nonlinear partial differential equations,
functional analysis and applied analysis as well as mechanics.
Written for:
Researchers in functional analysis, PDE, fluid dynamics and
differential geometry
Table of Contents
Holmes, Mark H.
Introduction to Numerical Methods in Differential Equations
Series: Texts in Applied Mathematics , Vol. 52
2007, X, 230 p., Hardcover
ISBN-10: 0-387-30891-1
ISBN-13: 978-0-387-30891-3
About this textbook
This book shows how to derive, test and analyze numerical methods
for solving differential equations, including both ordinary and
partial differential equations. The objective is that students
learn to solve differential equations numerically and understand
the mathematical and computational issues that arise when this is
done. Includes an extensive collection of exercises, which
develop both the analytical and computational aspects of the
material. In addition to more than 100 illustrations, the book
includes a large collection of supplemental material: exercise
sets, MATLAB computer codes for both student and instructor,
lecture slides and movies.
Table of contents
Initial Value Problems.- Two-Point Boundary Value Problems.-
Diffusion Problems.- Advection Equation.- Numerical Wave
Propagation.- Elliptic Problems.- Appendix.- References.- Index.
Aziz-Alaoui, M.A.; Bertelle, C. (Eds.)
Emergent Properties in Natural and Artificial Dynamical
Systems
Series: Understanding Complex Systems
2006, X, 281 p., 101 illus., 16 in colour, Hardcover
ISBN-10: 3-540-34822-0
ISBN-13: 978-3-540-34822-1
About this book
An important part of the science of complexity is the study of
emergent properties arising through dynamical processes in
various types of natural and artificial systems. This is the aim
of this book, which is the outcome of a discussion meeting within
the first European conference on complex systems. It presents
multidisciplinary approaches for getting representations of
complex systems and using different methods to extract emergent
structures. This carefully edited book studies emergent features
such as self organization, synchronization, opening on stability
and robustness properties. Invariant techniques are presented
which can express global emergent properties in dynamical and in
temporal evolution systems. This book demonstrates how artificial
systems such as a distributed platform can be used for simulation
used to search emergent placement during simulation execution.
Table of contents
Part I General Introduction.- Part II Natural Systems Modeling.-
Part III Dynamic Systems & Synchronization.- Part IV Decision
Support System.- Part V Spline Functions.
Jonathan D. H. Smith Iowa State University, Ames, Iowa
An Introduction to Quasigroups and Their Representations
ISBN: 1584885378
Publication Date: 11/15/2006
Number of Pages: 352
・Discusses various permutation group actions on the underlying set of a quasigroup that result from the quasigroup structure-a critical tool of quasigroup theory
・Describes basic as well as more advanced homogeneous space and permutation representation concepts, such as Lagrange's theorem and Burnside's lemma
・Encompasses many aspects of character theory, from conjugacy classes and linear characters through superschemes and permutation characters to analytical characters
・Examines several applications of quasigroup module theory, including the indexing of nonassociative powers, the exponent of a quasigroup, and the construction of free commutative Moufang loops
・Contains summaries of category theory, universal algebra, and coalgebras
・Includes exercises at the end of each chapter to link theories with applications
Collecting results scattered throughout the literature into one source, An Introduction to Quasigroups and Their Representations shows how representation theories for groups are capable of extending to general quasigroups and illustrates the added depth and richness that result from this extension.
To fully understand representation theory, the first three chapters provide a foundation in the theory of quasigroups and loops, covering special classes, the combinatorial multiplication group, universal stabilizers, and quasigroup analogues of abelian groups. Subsequent chapters deal with the three main branches of representation theory-permutation representations of quasigroups, combinatorial character theory, and quasigroup module theory. Each chapter includes exercises and examples to demonstrate how the theories discussed relate to practical applications. The book concludes with appendices that summarize some essential topics from category theory, universal algebra, and coalgebras.
Long overshadowed by general group theory, quasigroups have become increasingly important in combinatorics, cryptography, algebra, and physics. Covering key research problems, An Introduction to Quasigroups and Their Representations proves that you can apply group representation theories to quasigroups as well.
Table of contents