Series: Progress in Mathematics, Vol. 240
2005, Approx. 200 p., Hardcover
ISBN: 3-7643-7321-0
About this book
This monograph addresses perturbation methods in critical point
theory. It particularly emphasizes applications such as
semilinear elliptic problems on R^n, bifurcation from the
essential spectrum, the prescribed scalar curvature problem,
nonlinear Schroedinger equations, and singularly perturbed
elliptic problems in domains.
Table of contents
Preface.- Examples and Motivations.- Perturbation in Critical
Point Theory.- Bifurcation from the Essential Spectrum.-
Subcritical Problems.- Problems with Critical Exponent.- The
Yamabe Problem.- Problems in Conformal Geometry.- NLS.-
Singularly Perturbed Neumann Problems.- Concentration at Spheres.-
Bibliography.- Index.
1st ed. 1997. Corr. 2nd printing, 2005, Approx. 685 p. 86
illus., Hardcover
ISBN: 0-8176-4434-2
About this textbook
"There are three words that characterize this work:
thoroughness, completeness and clarity. The authors are
congratulated for taking the time to write an excellent linear
systems textbook! …The authors have used their mastery of the
subject to produce a textbook that very effectively presents the
theory of linear systems as it has evolved over the last thirty
years. The result is a comprehensive, complete and clear
exposition that serves as an excellent foundation for more
advanced topics in system theory and control."
?IEEE Transactions on Automatic Control
"In assessing the present book as a potential textbook for
our first graduate linear systems course, I find it compares very
favorably with some of the excellent texts already available….
Antsaklis and Michel have contributed an expertly written and
high quality textbook to the field and are to be congratulated….
Because of its mathematical sophistication and completeness the
present book is highly recommended for use, both as a textbook as
well as a reference."
?Automatica
Linear systems theory plays a broad and fundamental role in
electrical, mechanical, chemical and aerospace engineering,
communications, and signal processing. A thorough introduction to
systems theory with emphasis on control is presented in this self-contained
textbook.
The book examines the fundamental properties that govern the
behavior of systems by developing their mathematical descriptions.
Linear time-invariant, time-varying, continuous-time, and
discrete-time systems are covered. Rigorous development of
classic and contemporary topics in linear systems, as well as
extensive coverage of stability and polynomial matrix/fractional
representation, provide the necessary foundation for further
study of systems and control.
Linear Systems is written as a textbook for a challenging one-semester
graduate course; the book’s flexible coverage and self-contained
presentation also make it an excellent reference guide or self-study
manual.
For a treatment of linear systems that focuses primarily on the
time-invariant case using streamlined presentation of the
material with less formal and more intuitive proofs, see the
authors’ companion book entitled A Linear Systems Primer.
Table of contents
Preface.- Mathematical Descriptions of Systems.- Response of
Linear Systems.- Controllability and Observability.- State
Feedback and State Observers.- Realization Theory and Algorithms.-
Stability.- Polynomial Matrix Descriptions and Matrix Fractional
Descriptions of Systems.- Appendix: Numerical Considerations.-
Bibliography.- Index
Series: Progress in Mathematical Physics, Preliminary entry
1200
2006, Approx. 450 p., Hardcover
ISBN: 0-8176-4351-6
About this book
Homogenization is a method for modelling processes in complex
structures. These processes are far too complex for analytic and
numerical methods and are best described by PDEs with rapidly
oscillating coefficients - a technique that has become
increasingly important in the last three decades due to its
multiple applications in the areas of optimization, radiophysics,
filtration theory, rheology, elasticity theory, and other domains
of mechanics, physics, and technology.
The present monograph is a comprehensive study of homogenization
problems describing various physical processes in micro-inhomogeneous
media. From the technical viewpoint the work focuses on the
construction of nonstandard models for media characterized by
several small-scale parameters (multiscale models). A variety of
techniques are used --- specifically functional analysis, the
spectral theory for differential operators, the Laplace
transform, and, most importantly, a new variational PDE method
for studying the asymptotic behavior of solutions of stationary
boundary value problems. This new method can be applied to a wide
variety of problems.
Key topics in this systematic exposition include asymptotic
analysis, Dirichlet- and Neumann-type boundary value problems,
differential equations with rapidly oscillating coefficients,
homogenization, homogenized and non-local models. Along with
complete proofs of all main results, numerous examples of typical
structures of micro-inhomogeneous media with their corresponding
homogenized models are provided.
Applied mathematicians, advanced-level graduate students,
physicists, engineers, and specialists in mechanics will benefit
from this monograph, which may be used in the classroom or as a
comprehensive reference text.
Table of contents
Introduction
Chapter 1. The Dirichlet boundary value problem in strongly
perforated domains
1.1 Method of orthogonal projections and abstract scheme of the
Dirichlet boundary problem in strongly perforated domains
1.2 Asymptotic behavior of solutions of the Dirichlet boundary
value problem in strongly perforated domains
1.3 The Dirichlet boundary value problem in domains in random
strongly perforated domains
Chapter 2. The Dirichlet boundary value problem in domains with
complex boundary
2.1 Necessary and sufficient conditions for convergence of
solutions of the Dirichlet boundary value problem
2.2 Asymptotic behavior of solutions of variational problems for
non-quadratic functionals in domains with complex boundary
2.3 Asymptotic behavior of the potential of electrostatic field
in weakly non-linear medium with thin perfectly conducting
Filaments
Chapter 3. Strongly connected domains
3.1 Preliminary consideration
3.2 Sequences of domains satisfying the condition of strong
connectedness
3.3 Sequences of strongly connected domains of decreasing volume
Chapter 4. The Neumann boundary value problems in strongly
connected domains
4.1 Asymptotic behavior of the Neumann boundary value problems in
strongly connected domains
4.2 Calculation of the conductivity tensor for structures close
to periodic
4.3 Asymptotic behavior of the Neumann boundary value problems in
weakly connected domains
4.4 Asymptotic behavior of the Neumann boundary value problems in
domains with traps
4.5 Asymptotic behavior of the Neumann boundary value problems in
strongly connected domains of decreasing volume
Chapter 5. Non-stationary problems and spectral problems
5.1 Asymptotic behavior of solutions of a non-stationary problem
in tube domains
5.2 Asymptotic behavior of solutions of the Dirichlet boundary
value problems in varying strongly perforated domains
5.3 Asymptotic behavior of eigenvalues of boundary value problems
in strongly perforated domains
Chapter 6. Differential equations with rapidly oscillating
coefficients
6.1 Asymptotic behavior of solutions of differential equations
with coefficients, which are not uniformly elliptic
6.2 Examples of particular realizations of the homogenized
diffusion model
6.3 Asymptotic behavior of solutions of differential equations
with coefficients, which are not uniformly bounded
6.4 Example of a non-local homogenized model
6.5 Homogenized heat conductivity model for a medium containing
inclusions with high specific heat
Chapter 7. Homogenized conjugation conditions
7.1 The Dirichlet problem. The general case of surface
distribution of sets
7.2 The Neumann problem. The general case of surface distribution
of sets
7.3 Deflection of elastic plates with small inclusions
7.4 Stationary Josephson effect.
Bibliography
2005, Approx. 880 p. 82 illus., Hardcover
ISBN: 0-8176-4367-2
About this book
Named for one of the great mathematicians of the twentieth
century, Banach spaces figure prominently in the study of
functional analysis, having applications to integral and
differential equations, approximation theory, harmonic analysis,
convex geometry, numerical mathematics, analytic complexity, and
probability theory. This work, written by a distinguished
specialist in functional analysis, is devoted to a comprehensive
treatment of the history of Banach spaces and (abstract bounded)
linear operators. While other comprehensive texts on Banach
spaces focus on developments before 1950, this one is mainly
devoted to the second half of the twentieth century.
Banach space theory is presented as a part of a broad mathematics
context, using tools from such areas as set theory, topology,
algebra, combinatorics, probability theory, logic, etc. Equal
emphasis is given to both spaces and operators. Numerous examples
and counterexamples elucidate the scope of the underlying
concepts. As a stimulus for further research, the text also
contains many problems which have not been previously solved.
The book may serve as a reference and introduction for graduate
students and researchers who want to learn Banach space theory
with some historical flavor
Table of contents
Preface.- Acknowledgements.- Introduction.- The Birth of Banach
Spaces.- Historical Roots and Basic Results.- Weak Topologies.-
Classical Banach Spaces.- Basic Results from the Post-Banach
Period.- Modern Banach Space Theory ? Selected Topics.-
Miscellaneous Topics.- Mathematics is Made by Mathematicians.-
Chronology.- Quotations.- Bibliography.- Index.
Series: Operator Theory: Advances and Applications, Vol. 161
2005, Approx. 285 p., Hardcover
ISBN: 3-7643-7370-9
About this book
The present volume contains a collection of essays representing
some of the recent advances in the state space method. Methods
covered include noncommutative systems theory, new aspects of the
theory of discrete systems, discrete analogs of canonical
systems, and new applications to the theory of Bezoutiants and
convolution equations.
Table of contents
Editorial Introduction.- Discrete Analogs of Canonical Systems
with Pseudo-exponential Potential. Definitions and Formulas for
the Special Matrix Functions.- Matrix-J-unitary Noncommutative
Rational Formal Power Series.- State/Signal Linear Time-invariant
Systems Theory, Part I: Discrete Time Systems.- Conservative
Structured Noncommutative Multidimensional Linear Systems.- The
Bezout Integral Operator: Main Property and Underlying Abstract
Scheme
Series: Progress in Mathematics, Vol. 241
2005, Approx. 280 p., Hardcover
ISBN: 3-7643-7322-9
About this book
The aim of this book is to give an overview of selected topics on
the topology of singularities, with emphasis on its relations to
other branches of geometry and topology. The first chapters are
mostly devoted to complex singularities and a myriad of results
spread in a vast literature, including recent research. The
second part of the book studies real analytic singularities which
arise from the topological and geometric study of holomorphic
vector fields and foliations. In the low dimensional case these
turn out to be related to fibred links in the 3-sphere defined by
meromorphic functions.
Table of contents
Preface.- Introduction.- A Fast Trip through the Classical Theory.-
Motions in Plane Geometry and the 3-Dimensional Brieskorn
Manifolds.- 3-Dimensional Lie Groups and Surface Singularities.-
Within the Realm of the General Index Theorem.- On the Geometry
and Topology of Quadrics in CP^n.- Real Singularities and Complex
Geometry.- Real Singularities with a Milnor Fibration.- Real
Singularities and Open Book Decompositions of the 3-Sphere.-
Bibliography.- Index.