Series: Operator Theory: Advances and Applications , Vol. 177
2007, Approx. 350 p., Hardcover
ISBN: 978-3-7643-8400-5
About this book
This book brings together all available results about the theory
of algebraic multiplicities, from the most classic results, like
the Jordan Theorem, to the most recent developments, like the
uniqueness theorem and the construction of the multiplicity for
non-analytic families. Part I (first three chapters) is a classic
course on finite-dimensional spectral theory, Part II (the next
eight chapters) presents the most general results available about
the existence and uniqueness of algebraic multiplicities for real
non-analytic operator matrices and families, and Part III (last
chapter) transfers these results from linear to nonlinear
analysis. The text is as self-contained as possible and suitable
for students at the advanced undergraduate or beginning graduate
level.
Written for:
Advanced undergraduate and graduate students; researchers in
mathematics, mathematical physics and physics
Table of contents
Preface.- I. Finite-dimensional Classic Spectral Theory - The
Jordan Theorem - Operator Calculus - Spectral Projections.- II.
Algebraic Multiplicities - Transversalization, Polynomial
Factorization, Uniqueness, Jordan Chains, Smith Form, Logarithmic
Residues - Analytic and Classical Families. Stability - Spectral
Theorem for Matrix Polynomials - Further Developments.- III.
Nonlinear Spectral Theory.- Bibliography.- Index.
Series: Springer Series in Statistics
2007, XII, 264 p., Hardcover
ISBN: 978-0-387-70897-3
About this book
A wide variety of processes occur on multiple scales, either
naturally or as a consequence of measurement. This book contains
methodology for the analysis of data that arise from such
multiscale processes. The book brings together a number of recent
developments and makes them accessible to a wider audience.
Taking a Bayesian approach allows for full accounting of
uncertainty, and also addresses the delicate issue of uncertainty
at multiple scales. The Bayesian approach also facilitates the
use of knowledge from prior experience or data, and these methods
can handle different amounts of prior knowledge at different
scales, as often occurs in practice.
The book is aimed at statisticians, applied mathematicians, and
engineers working on problems dealing with multiscale processes
in time and/or space, such as in engineering, finance, and
environmetrics. The book will also be of interest to those
working on multiscale computation research. The main
prerequisites are knowledge of Bayesian statistics and basic
Markov chain Monte Carlo methods. A number of real-world examples
are thoroughly analyzed in order to demonstrate the methods and
to assist the readers in applying these methods to their own work.
To further assist readers, the authors are making source code (for
R) available for many of the basic methods discussed herein.
Table of contents
Introduction.-Models for Spatial Data.-Illustrative Example.-Convolution
Methods.-Wavelet Methods.-Overview on Explicit Multiscale Models.-Gaussian
Multiscale Models on Trees.-Hidden Markov Models on Trees.-Mass
Balanced Multiscale Models on Trees.-Multiscale Random Fields.-Multiscale
Time Series.-Change of Support Models.-Implicit Computationally-Linked
Model Overview.-Metropolis-Coupled Methods.-Genetic Algorithms.-Soil
Permeability Estimation.-Single Photon Emission Computed
Tomography Example.-Conclusions.
Series: Graduate Texts in Mathematics , Vol. 242
Originally published by Wiley, 1999
2nd ed., 2007, Approx. 675 p., Hardcover
ISBN: 978-0-387-71567-4
Due: September 2007
"The text is geared to the needs of the beginning graduate
student, covering with complete, well-written proofs the usual
major branches of groups, rings, fields, and modules...[n]one of
the material one expects in a book like this is missing, and the
level of detail is appropriate for its intended audience."
- Alberto Delgado, MathSciNet
"This text promotes the conceptual understanding of algebra
as a whole, and that with great methodological mastery. Although
the presentation is predominantly abstract...it nevertheless
features a careful selection of important examples, together with
a remarkably detailed and strategically skillful elaboration of
the more sophisticated, abstract theories."
- Werner Kleinert, Zentralblatt
For the new edition, the author has completely rewritten the
text, reorganized many of the sections, and even cut or shortened
material which is no longer essential. He has added a chapter on
Ext and Tor, as well as a bit of topology.
Table of contents
Preface.- Groups.- Structure of Groups.- Rings.- Field Extensions.-
Galois Theory.- Fields with Orders or Valuations.- Commutative
Rings.- Modules.- Semisimple Rings and Modules.- Projectives and
Injectives.- Constructions.- Ext and Tor.- Algebras.- Lattices.-
Universal Algebra.-Categories.- Appendix.- References.- Further
Readings.- Index
Series: International Series of Numerical Mathematics , Vol.
156
2007, Approx. 300 p., Hardcover
ISBN: 978-3-7643-8330-5
A Birkhauser book
About this book
This book offers a detailed asymptotic analysis of some important
classes of singularly perturbed boundary value problems which are
mathematical models for various phenomena in biology, chemistry,
and engineering.
The authors are particularly interested in nonlinear problems,
which have hardly been examined so far in the literature
dedicated to singular perturbations. This book proposes to fill
in this gap, since most applications are described by nonlinear
models. Their asymptotic analysis is very interesting, but
requires special methods and tools. The treatment presented in
this volume combines some of the most successful results from
different parts of mathematics, including functional analysis,
singular perturbation theory, partial differential equations, and
evolution equations. Thus a complete justification for the
replacement of various perturbed models with corresponding
reduced models, which are simpler but in general have a different
character, is offered to the reader
Specific applications are addressed, such as propagation of
electromagnetic or mechanical waves, fluid flows, or diffusion
processes. However, the methods presented are also applicable to
other mathematical models.
The book covers mostly original results by the authors. It is
designed for researchers and graduate students.
Table of contents
Preface.- I Preliminaries.- 1. Regular and Singular Perturbations.-
2. Evolution Equations in Hilbert Spaces.-II Singularly Perturbed
Hyperbolic Problems.- 3. Presentation of the Problems.- 4.
Hyperbolic Systems with Algebraic Boundary Conditions.- 5.
Hyperbolic Systems with Dynamic Boundary Conditions.- III
Singularly Perturbed Coupled Boundary Value Problems.- 6.
Presentation of the Problems.- 7. The Stationary Case.- 8. The
Evolutionary Case.- IV Elliptic and Hyperbolic Regularizations of
Parabolic Problems.- 9. Presentation of the Problems.- 10. The
Linear Case.- 11. The Nonlinear Case
2008, Approx. 350 p., Hardcover
ISBN: 978-0-8176-4668-4
About this textbook
This text on modern harmonic analysis provides an introduction to
the subject in the context in which it is actually applied, in
particular, through complex function theory and partial
differential equations. The exposition begins with the
fundamentals of Fourier analysis, complex function theory, and
integral operators and further introduces students to cutting-edge
ideas about the Heisenberg group.
The subject is introduced through Fourier series and Hilbert
transforms, passing into singular integrals, Riesz fractional
integrals and the Calderon-Zygmund singular integrals. Function
theory of several complex variables is presented as a prelude to
the generalized Cayley transform and the Sigel upper halfspace.
Finally, the structure of the Heisenberg group, which naturally
models the structures of canonical operators of several complex
variables, is explored.
This self-contained text serves as an introduction to analysis on
the Heisenberg group. It is an ideal text for advanced
undergraduate and graduate students and will aid them in forging
new paths of research.
Table of contents
Preface.-Background in Fourier Series.-The Fourier Transform.-Fractional
and Singular Integrals.-Pseudodifferential Operators.-The Real
Variable Point of View.-Several Complex Variables.-Canonical
Integral Operators.-Boundary Behavior.-The Heisenberg Group.-Analysis
on the Heisenberg Group.-Index.