Series: Lecture Notes in Mathematics , Vol. 1902
2007, VIII, 139 p., Softcover
ISBN-10: 3-540-69151-0
ISBN-13: 978-3-540-69151-8
Due: February 13, 2007
About this book
Kobayashi-hyperbolic manifolds are an object of active research
in complex geometry. In this monograph the author presents a
coherent exposition of recent results on complete
characterization of Kobayashi-hyperbolic manifolds with high-dimensional
groups of holomorphic automorphisms. These classification results
can be viewed as complex-geometric analogues of those known for
Riemannian manifolds with high-dimensional isotropy groups, that
were extensively studied in the 1950s-70s. The common feature of
the Kobayashi-hyperbolic and Riemannian cases is the properness
of the actions of the holomorphic automorphism group and the
isometry group on respective manifolds.
Table of contents
Introduction.- The Homogeneous Case.- The Case d(M)=n2.- The Case
d(m)= n2-1, n>=3.- The Case of (2,3)-Manifolds.- Proper
Actions. References.- Index.
Series: Universitext
2007, Approx. 180 p., Softcover
ISBN-10: 3-540-68375-5
ISBN-13: 978-3-540-68375-9
Due: February 13, 2007
About this textbook
This book is based on two series of lectures given at a summer
school on algebraic combinatorics at the Sophus Lie Centre in
Nordfjordeid, Norway, in June 2003, one by Peter Orlik on
hyperplane arrangements, and the other one by Volkmar Welker on
free resolutions. Both topics are essential parts of current
research in a variety of mathematical fields, and the present
book makes these sophisticated tools available for graduate
students.
Written for:
Graduate students in Mathematics
Keywords:
Gauss-Manin connections
Orlik-Solomon algebra
cellular resolutions
discrete Morse theory
hyperplane arrangements
monomial ideals
Series: Algebra and Applications , Vol. 7
2007, Approx. 365 p., Hardcover
ISBN-10: 1-4020-5809-8
ISBN-13: 978-1-4020-5809-7
Due: March 2007
About this book
Within the last decade, semigroup theoretical methods have
occurred naturally in many aspects of ring theory, algebraic
combinatorics, representation theory and their applications. In
particular, motivated by noncommutative geometry and the theory
of quantum groups, there is a growing interest in the class of
semigroup algebras and their deformations.
This work presents a comprehensive treatment of the main results
and methods of the theory of Noetherian semigroup algebras. These
general results are then applied and illustrated in the context
of important classes of algebras that arise in a variety of areas
and have been recently intensively studied. Several concrete
constructions are described in full detail, in particular
intriguing classes of quadratic algebras and algebras related to
group rings of polycyclic-by-finite groups. These give new
classes of Noetherian algebras of small Gelfand-Kirillov
dimension. The focus is on the interplay between their
combinatorics and the algebraic structure. This yields a rich
resource of examples that are of interest not only for the
noncommutative ring theorists, but also for researchers in
semigroup theory and certain aspects of group and group ring
theory. Mathematical physicists will find this work of interest
owing to the attention given to applications to the Yang-Baxter
equation.
Table of contents
1. Introduction. 2. Prerequisites on semigroup theory. 2.1
Semigroups. 2.2. Uniform semigroups. 2.3 Full linear semigroup. 2.4
Structure of linear semigroups. 2.5 Closure. 2.6 Semigroups over
a field. 3. Prerequisites on ring theory. 3.1 Noetherian rings
and rings satisfying a polynomial identity. 3.2 Prime ideals. 3.3
Group algebras of polycyclic-by-finite groups. 3.4 Graded rings.
3.5 Gelfand-Kirillov dimension. 3.6 Maximal orders. 3.7 Principal
ideal rings. 4. Algebras of submonoids of polycylic-by-finite
groups. 4.1 Ascending chain condition. 4.2 The unit group. 4.3
Almost nilpotent case. 4.4 Structure theorem. 4.5 Prime ideals of
K[S]. 4.6 Comments and problems. 5. General Noetherian semigroup
algebras. 5.1 Finite generation of the monoid. 5.2 Necessary
conditions. 5.3 Monomial semigroups and sufficient conditions. 5.4
Gelfand-Kirillov dimension. 5.5 Comments and problems. 6.
Principal ideal rings. 6.1 Group algebras. 6.2 Matrix embedding.
6.3 Finite dimensional case. 6.4 The general case. 6.5 Comments
and problems. 7. Maximal orders and Noetherian semigroup algebras.
7.1 Maximal orders and monoids. 7.2 Algebras of submonoids of
abelian-by-finite groups. 7.3 Comments and problems. 8. Monoids
of I-type. 8.1 A characterization. 8.2 Structure of monoids of I-type.
8.3 Binomial monoids are of I-type. 8.4 Decomposable monoids of I-type.
8.5 Algebras of monoids of I-type. 8.6 Comments and problems. 9.
Monoids of skew type. 9.1 Definition. 9.2 Monoids of skew type
and the cyclic condition. 9.3 Non-degenerate monoids of skew type.
9.4 Algebras of non-degenerate monoids of skew type. 9.5 The
cancellative congruence and the prime radical. 9.6 Comments and
problems. 10. Examples. 10.1 Monoids of skew type and the Gelfand-Kirillov
dimension. 10.2 Four generated monoids of skew type. 10.3
Examples of Gelfand-Kirillov dimension 2. 10.4 Non-degenerate
monoids of skew type of Gelfand-Kirillov dimension one. 10.5
Examples of maximal orders. 10.6 Comments. Bibliography. Index.
Notation.
Series: Applied Mathematical Sciences , Vol. 161
Based on volume 374 in the series Lecture Notes in Physics. Now
worked out to a full monograph.
2007, Approx. 510 p., 100 illus., Hardcover
ISBN-10: 3-540-68581-2
ISBN-13: 978-3-540-68581-4
Due: March 2007
About this book
This is a comprehensive account of the asymptotic theory of
slender vortices with diffusion cores. Addressed to both graduate
students and researchers it describes the mathematical model and
its numerical analysis. The asymptotic analysis involves two
length and two time scales. Consistency conditions and time
invariance of moments of vorticity are given and applied to
numerical solutions. The authors also describe consistency
conditions between the large circumferential and axial velocity
in the core.
Table of contents
Introduction.- Vortex Dominated Flows and General Theory.- Motion
and Decay of Vortex Filaments - Matched Asymptotics.- Nonlinear
Dynamics of Nearly Straight Vortex Filaments.- Numerical
Simulation of Slender Vortex Filaments.- Numerical Simulations of
the Merging of Vortices or Filaments.- Flow-Generated Sound.-
Sound-Generated Flow.- Epilogue.- Appendices: A. Governing
Equations for Higher-Order Solutions.- B. Second-Order Two-Time
Solutions.- C. Equations of Motion of Filaments.- D. Formulae for
the Coefficients in (6.2.74) and (6.2.75).- E. Transformations to
Filament-Attached Coordinates.- References.- Index.
Series: CMS Books in Mathematics
2007, Approx. 310 p., Softcover
ISBN-10: 0-387-68914-1
ISBN-13: 978-0-387-68914-2
Due: April 2007
About this book
One of the fundamental questions of Banach space theory is
whether every Banach space has a basis. A space with a basis
gives us the feeling of familiarity and concreteness, and perhaps
a chance to attempt the classification of all Banach spaces and
other problems.
The main goals of this book are to:
・ introduce the reader to some of the basic concepts, results
and applications of biorthogonal systems in infinite dimensional
geometry of Banach spaces, and in topology and nonlinear analysis
in Banach spaces;
・ to do so in a manner accessible to graduate students and
researchers who have a foundation in Banach space theory;
・ expose the reader to some current avenues of research in
biorthogonal systems in Banach spaces;
・ provide notes and exercises related to the topic, as well as
suggesting open problems and possible directions of research.
The intended audience will have a basic background in functional
analysis. The authors have included numerous exercises, as well
as open problems that point to possible directions of research.
Table of contents
Biorthogonal Systems in Separable Spaces.- Universality and
Szlenk Index.- Biorthogonal systems in nonseparable spaces.-
Weakly Lindelof detemined spaces.- Weakly compactly generated
spaces.- Geometry of spaces with fundamental biorthogonal systems.
Series: Graduate Texts in Mathematics , Vol. 238
2007, Approx. 550 p., Hardcover
ISBN-10: 3-540-39032-4
ISBN-13: 978-3-540-39032-9
Due: April 2007
About this textbook
Combinatorial enumeration is a readily accessible subject full of
easily stated, but sometimes tantalizingly difficult problems.
This book leads the reader in a leisurely way from the basic
notions to a variety of topics, ranging from algebra to
statistical physics. Its aim is to introduce the student to a
fascinating field, and to be a source of information for the
professional mathematician who wants to learn more about the
subject. The book is organized in three parts: Basics, Methods,
and Topics. There are 666 exercises, and as a special feature
every chapter ends with a highlight, discussing a particularly
beautiful or famous result.
Written for:
junior/senior undergraduates, beginning graduates, professional
mathematicians who want to know more about the subject
Keywords:
Polya theory
generating functions
graph and knot polynomials
hypergeometric summation
orthogonal polynomials
sieve methods
statisical physics
symmetric functions