Graduate Studies in Mathematics, Volume: 90
2008; approx. 260 pp; hardcover
ISBN-13: 978-0-8218-4465-6
Expected publication date is May 2, 2008.
The arithmetic theory of quadratic forms is a rich branch of number theory that has had important applications to several areas of pure mathematics--particularly group theory and topology--as well as to cryptography and coding theory. This book is a self-contained introduction to quadratic forms that is based on graduate courses the author has taught many times. It leads the reader from foundation material up to topics of current research interest--with special attention to the theory over the integers and over polynomial rings in one variable over a field--and requires only a basic background in linear and abstract algebra as a prerequisite. Whenever possible, concrete constructions are chosen over more abstract arguments. The book includes many exercises and explicit examples, and it is appropriate as a textbook for graduate courses or for independent study. To facilitate further study, a guide to the extensive literature on quadratic forms is provided.
Readership
Graduate students interested in quadratic forms.
Table of Contents
A brief classical introduction
Quadratic spaces and lattices
Valuations, local fields, and p-adic numbers
Quadratic spaces over mathbb{Q}_p
Quadratic spaces over mathbb{Q}
Lattices over principal ideal domains
Initial integral results
Local classification of lattices
The local-global approach to lattices
Lattices over mathbb{F}_q[x]
Applications to cryptography
Further reading
Bibliography
Index
American Mathematical Society Translations--Series 2, Volume: 222
2008; approx. 238 pp; hardcover
ISBN-13: 978-0-8218-4461-8
Expected publication date is May 16, 2008.
This volume contains articles on analysis, theory of algebraic groups, partial differential equations, pseudodifferential operators, wavelets, and other areas of mathematics.
This book is suitable for a broad group of graduate students and researchers interested in the topics presented here.
Readership
Research mathematicians interested in various topics in mathematics
Table of Contents
Y. A. Alkhutov and A. N. Gordeev -- L_p-estimates for solutions to second
order parabolic equations
Y. K. Dem'yanovich -- Wavelet decompositions on nonuniform grids
A. I. Karol' -- Newton polyhedra and estimates for differential operators
N. G. Kuznetsov -- Nodal lines and uniqueness of solutions to linear water-wave problems
B. E. Kunyavskii and B. Z. Moroz -- On integral models of algebraic tori and affine toric varieties
A. I. Lipovetskii -- A geometrical approach to computation of the optimal solution to the rectangle packing problem
S. Matyukevich and P. Neittaanmaki -- Nonstationary Maxwell system with nonhomogeneous boundary conditions in domains with conical points
J. Mashreghi and E. Fricain -- Exceptional sets for the derivatives of Blaschke products
S. A. Nazarov and I. L. Sofronov -- Asymptotics of solutions and artificial boundary conditions in the transmission problem with a layer-like inhomogeneity
Contemporary Mathematics, Volume: 455
2008; approx. 455 pp; softcover
ISBN-13: 978-0-8218-4150-1
Expected publication date is May 10, 2008.
The papers in this volume cover a wide variety of topics in the geometric theory of functions of one and several complex variables, including univalent functions, conformal and quasiconformal mappings, minimal surfaces, and dynamics in infinite-dimensional spaces. In addition, there are several articles dealing with various aspects of approximation theory and partial differential equations. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, drawn by a number of leading figures in the field.
This book is co-published with Bar-Ilan University (Ramat-Gan, Israel).
Readership
Graduate students and research mathematicians interested in complex analysis, PDE, and dynamical systems.
Table of Contents
L. Aizenberg and N. Tarkhanov -- Stable expansions in homogeneous polynomials
S. Aizicovici, S. Reich, and A. J. Zaslavski -- Dynamics of approximate solutions to a class of evolution equations in Banach spaces
K. Astala, T. Iwaniec, G. Martin, and J. Onninen -- Schottky's theorem on conformal mappings between annuli: A play of derivatives and integrals
D. Bshouty and A. Lyzzaik -- Univalent convex functions in the positive direction of the real axis
M. Budzynska and T. Kuczumow -- The common fixed point set of commuting nonexpansive mappings in infinite products of unit balls
M. Elin, D. Shoikhet, and L. Zalcman -- Controlled approximation for some classes of holomorphic functions
M. I. Ganzburg and D. S. Lubinsky -- Best approximating entire functions
to leftvert xrightvert ^{alpha} in L_2
V. M. Gichev -- Orbits of tori extended by finite groups and their polynomial hulls: The case of connected complex orbits
D. H. Hamilton -- QC Riemann mapping theorem in space
G. Harutyunyan and B.-W. Schulze -- Boundary value problems in weighted edge spaces
H. T. Kaptanoglu and A. E. Ureyen -- Analytic properties of Besov spaces via Bergman projections
B. A. Kats -- The Cauchy integral over non-rectifiable paths
O. Kounchev and H. Render -- Holomorphic continuation via Laplace-Fourier series
Y. Krasnov -- Analytic functions in algebras
S. L. Krushkal -- Rational approximation of holomorphic functions and geometry of Grunsky inequalities
R. Kuhnau -- Quadratic forms in geometric function theory, quasiconformal extensions, Fredholm eigenvalues
A. Kytmanov -- Elimination methods of unknowns from nonlinear systems
P. Liczberski and V. V. Starkov -- On locally biholomorphic finitely valent mappings from multiply connected to simply connected domains
Y. Lutsky and V. S. Rabinovich -- Parabolic pseudodifferential operators in exponential weighted spaces
O. Makhmudov, I. Niyozov, and N. Tarkhanov -- The Cauchy problem of couple-stress elasticity
S. Myslivets -- On the zeta-function of a nonlinear system
E. Reich -- Some questions of uniqueness for extremal quasiconformal mappings
E. Saucan -- Remarks on the existence of quasimeromorphic mappings
A. Shlapunov -- On the Cauchy problem for the Cauchy-Riemann operator in Sobolev spaces
V. Strauss -- On spectral functions for commutative J-self-adjoint operator
families of the D_{kappa}^+-class
A. Ukhlov and S. K. Vodopyanov -- Mappings associated with weighted Sobolev spaces
E. Vesentini -- Inner maps and Banach algebras
A. Vidras -- Reconstructing holomorphic functions in a domain from their values on a part of its boundary
A. Weitsman -- A note on the parabolicity of minimal graphs
K. Wlodarczyk, D. Klim, and R. Kowalczyk -- Localization of fixed points and zeros for holomorphic maps in locally convex spaces and nonexpansive maps in J*-algebras
V. Zahariuta -- On harmonic polynomial interpolation
2008; approx. 287 pp; hardcover
ISBN-10: 0-8218-4440-7
ISBN-13: 978-0-8218-4440-3
Expected publication date is June 12, 2008.
Grothendieck's Resume is a landmark in functional analysis. Despite having
appeared more than a half century ago, its techniques and results are still
not widely known nor appreciated. This is due, no doubt, to the fact that
Grothendieck included practically no proofs, and the presentation is based
on the theory of the very abstract notion of tensor products. This book
aims at providing the details of Grothendieck's constructions and laying
bare how the important classes of operators are a consequence of the abstract
operations on tensor norms. Particular attention is paid to how the classical
Banach spaces (C(K)'s, Hilbert spaces, and the spaces of integrable functions)
fit naturally within the mosaic that Grothendieck constructed.
Readership
Graduate students and research mathematicians interested in abstract analysis, Banach space theory, functional analysis, and operator theory.
Table of Contents
Basics on tensor norms
The role of C(K)-spaces and L^1-spaces
otimes-norms related to Hilbert space
The fundamental theorem and its consequences
Glossary of terms
The problems of the Resume
The Blaschke selection principle and compact convex sets in finite dimensional Banach spaces
A short introduction to Banach lattices
Stonean spaces and injectivity
Epilogue
Bibliography
Author index
Index of notation
Index
Approx. 258 pages
Trim size 5 7/8 X 8 7/8 in
Copyright 2008
A title in the Monograph Series on Nonlinear Science and Complexity series.
Expected Release Date: Mar 2008
Key Features
Technical, but not specialistic language
About 100 illustrative Figures
Full overview on synchronization phenomena
Review of the main tools and techniques used in the field
Paradigmatic examples and experiments illustrating the basic concepts
Full Reference to the main publications existing in the literature on the subject
Related Titles
Bifurcation and Chaos in Complex Systems
Description
The origin of the word synchronization is a greek root, meaning ";to share the common time";. The original meaning of synchronization has been maintained up to now in the colloquial use of this word, as agreement or correlation in time of different processes. Historically, the analysis of synchronization phenomena in the evolution of dynamical systems has been a subject of active investigation since the earlier days of physics. Recently, the search for synchronization has moved to chaotic systems. In this latter framework, the appearance of collective (synchronized) dynamics is, in general, not trivial. Indeed, a dynamical system is called chaotic whenever its evolution sensitively depends on the initial conditions. The above said implies that two trajectories emerging from two different closeby initial conditions separate exponentially in the course of the time. As a result, chaotic systems intrinsically defy synchronization, because even two identical systems starting from slightly different initial conditions would evolve in time in a unsynchronized manner (the differences in the systems' states would grow exponentially). This is a relevant practical problem, insofar as experimental initial conditions are never known perfectly. The setting of some collective (synchronized) behavior in coupled chaotic systems has therefore a great importance and interest. The subject of the present book is to summarize the recent discoveries involving the study of synchronization in coupled chaotic systems. Not always the word synchronization is taken as having the same colloquial meaning, and one needs to specify what synchrony means in all particular contexts in which we will describe its emergence. The book describes the complete synchronization phenomenon, both for low and for high dimensional situations, and illustrates possible applications in the field of communicating with chaos. Furthermore, the book summarizes the concepts of phase synchronization, lag synchronization, imperfect phase synchronization, and generalized synchronization, describing a general transition scenario between a hierarchy of different types of synchronization for chaotic oscillators. These concepts are extended to the case of structurally different systems, of uncoupled systems subjected to a common external source, of space extended nonlinearly evolving fields, and of dynamical units networking via a complex wiring of connections, giving thus a summary of all possible situations that are encountered in real life and in technology.
Readership
Senior graduate students, Established researchers in the area
Contents
Chapter 1 * Preface Chapter 2 * Introduction Chapter 3 * Identical Systems
Chapter 4 9 Non identical Systems Chapter 5 * Structurally non equivalent
Systems Chapter 6 * Effects of noise Chapter 7 * Distributed and Extended
Systems Chapter 8 * Complex Networks
2008; 806 pp; hardcover
ISBN-13: 978-0-8218-4438-0
Expected publication date is June 4, 2008.
Undoubtedly [the book] will be for years the standard reference on symplectic geometry, analytical mechanics and symplectic methods in mathematical physics.
--Zentralblatt fur Mathematik
For many years, this book has been viewed as a classic treatment of geometric mechanics. It is known for its broad exposition of the subject, with many features that cannot be found elsewhere. The book is recommended as a textbook and as a basic reference work for the foundations of differentiable and Hamiltonian dynamics.
Readership
Graduate students interested in differential geometry and physics.
Table of Contents
Preliminaries
Differential theory
Calculus on manifolds
Analytical dynamics
Hamiltonian and Lagrangian systems
Hamiltonian systems with symmetry
Hamilton-Jacobi theory and mathematical physics
An outline of qualitative dynamics
Topological dynamics
Differentiable dynamics
Hamiltonian dynamics
Celestial mechanics
The two-body problem
The three-body problem
The general theory of dynamical systems and classical mechanics by A. N. Kolmogorov
Bibliography
Index
Glossary of symbols
Errata