September 2002, ISBN 1-4020-0844-9, Hardbound
Methods in Nonlinear Integral Equations presents
several
extremely fruitful methods for the analysis
of systems and
nonlinear integral equations. They include:
fixed point methods (the
Schauder and Leray-Schauder principles),
variational methods (direct
variational methods and mountain pass theorems),
and iterative
methods (the discrete continuation principle,
upper and lower
solutions techniques, Newton's method and
the generalized
quasilinearization method). Many important
applications for
several classes of integral equations and,
in particular, for
initial and boundary value problems, are
presented to complement
the theory. Special attention is paid to
the existence and
localization of solutions in bounded domains
such as balls and
order intervals. The presentation is essentially
self-contained
and leads the reader from classical concepts
to current ideas and
methods of nonlinear analysis.
This work will be of interest to graduate
students and
theoretical and applied mathematicians in
nonlinear functional
analysis, integral equations, ordinary and
partial differential
equations, and related fields.
Contents
Preface. Notation. Overview. I: Fixed Point
Methods. 1.
Compactness in Metric Spaces. 2. Completely
Continuous Operators
on Banach Spaces. 3. Continuous Solutions
of Integral Equations
via Schauder's Theorem. 4. The Leray-Schauder
Principle and
Applications. 5. Existence Theory in LPSpaces.
References: Part I.
II: Variational Methods. 6. Positive Self-Adjoint
Operators in
Hilbert Spaces. 7. The Frechet Derivative
and Critical Points of
Extremum. 8. The Mountain Pass Theorem and
Critical Points of
Saddle Type. 9. Nontrivial Solutions of Abstract
Hammerstein
Equations. References Part II. III: Iterative
Methods. 10. The
Discrete Continuation Principle. 11. Monotone
Iterative Methods.
12. Quadratically Convergent Methods. References:
Part III. Index.
August 2002, ISBN 1-4020-7201-5, Hardbound
The goal of this publication is to provide
basic tools of
differential topology to study systems of
nonlinear equations,
and to apply them to the analysis of general
equilibrium models
with complete and incomplete markets. The
main content of general
equilibrium analysis is to study existence,
(local) uniqueness
and efficiency of equilibria. To study existence
Differential
Topology and General Equilibrium with Complete
and Incomplete
Markets combines two features. First, order
conditions (of
agents' maximization problems) and market
clearing conditions,
instead of aggregate excess demand functions.
Then the
application to that "extended system"
of a homotopy
argument, which is stated and proved in relatively
elementary
manner. Local uniqueness and smooth dependence
of the endogenous
variables from the exogenous ones are studied
using a version of
a so called parametric transversality theorem.
In a standard
general equilibrium model, all equilibria
are efficient, but that
is not the case if some imperfection, like
incomplete markets,
asymmetric information, strategic interaction,
is added. Then,
for almost all economies, equilibria are
inefficient, and an
outside institution can Pareto improve upon
the market outcome.
Those results are proved showing that a well-chosen
system of
equations has no solutions.
The target audience of Differential Topology
and General
Equilibrium with Complete and Incomplete
Markets consists of
researchers interested in economic theory.
The needed background
is multivariate analysis, basic linear algebra
and basic general
topology.
Contents
List of Figures. Acknowledgments. Introduction.
Part I. 1.
Prerequisites. 2. Manifolds in Euclidean
Spaces. 3. Differentials.
4. Regular Values. 5. Manifolds with Boundary.
6. Sard's Theorem
and Transversality. 7. Homotopy and Degree
Theory. Part II. 8.
Exchange Economies. 9. Production Economies.
10. Time,
Uncertainty and Incomplete Markets. 11. Numeraire
Assets. 12.
Nominal Assets. 13. Real Assets. 14. Restricted
Participation. 15.
Planner Intervention on the Market Outcome.
Index.
September 2002, ISBN 1-4020-0806-6, Hardbound
This book presents the recent development
of stochastic
approximation algorithms with expanding truncations
based on the
TS (trajectory-subsequence) method, a newly
developed method for
convergence analysis. This approach is so
powerful that
conditions used for guaranteeing convergence
have been
considerably weakened in comparison with
those applied in the
classical probability and ODE methods. The
general convergence
theorem is presented for sample paths and
is proved in a purely
deterministic way. The sample-path description
of theorems is
particularly convenient for applications.
Convergence theory
takes both observation noise and structural
error of the
regression function into consideration. Convergence
rates,
asymptotic normality and other asymptotic
properties are
presented as well. Applications of the developed
theory to global
optimization, blind channel identification,
adaptive filtering,
system parameter identification, adaptive
stabilization and other
problems arising from engineering fields
are demonstrated.
Audience: Researchers and students of both
graduate and
undergraduate levels in systems and control,
optimization, signal
processing, communication and statistics.
Contents
Preface. Acknowledgments. 1. Robbins-Monro
Algorithm. 2.
Stochastic Approximation Algorithms with
Expanding Truncations. 3.
Asymptotic Properties of Stochastic Approximation
Algorithms. 4.
Optimization by Stochastic Approximation.
5. Applications To
Signal Processing. 6. Application to Systems
and Control. 7.
Appendices. References. Index.
September 2002, ISBN 1-4020-0853-8, Hardbound
Book Series: STUDIES IN LINGUISTICS AND PHILOSOPHY
: Volume 79
Speech Acts, Mind, and Social Reality - these
are the main topics
in the work of John R. Searle, one of the
leading philosophical
figures of the present times. How language
is based on
intentionality, how intentionality in turn
is to be explicated by
means of distinctions discovered in Speech
Act Theory, and how
language and intentionality are both related
to social facts and
institutions - these are questions to be
tackled in this volume.
The contributions result from discussions
on and with John R.
Searle, containing Searle's own latest views
- including his
seminal ideas on Rationality in Action. The
collection provides a
good basis for advanced seminar debates in
Philosophy of
Language, Philosophy of Mind, and Social
Philosophy, and will
also stimulate some further research on all
of the three main
topics.
Contents and Contributors
Introduction. Speech Acts, Mind, and Social
Reality; J.R. Searle.
Interview with John R. Searle; R. Stoecker.
Speech Acts. How
Performatives Don't Work; G. Grewendorf.
Are Performative
Utterances Declarations? R.M. Harnish. Expressibility,
Explicability, and Taxonomy. Some Remarks
on the Principle of
Expressibility; F. Kannetzky. Expressing
an Intentional State; A.
Kemmerling. On the Proper Treatment of Performatives;
A.
Martinich. Why Do We Mean Something Rather
Than Nothing? C.
Plunze. What Is an Illocutionary Point? M.
Siebel. Searle on
Meaning and Action; D. Vanderveken. Mind.
Understanding
Utterances and Other Actions; T. Bartelborth,
O. Scholz.
Intrinsic Intentionality; W. Lenzen. Causal
Reduction,
Ontological Reduction, and First-Person Ontology.
Notes on
Searle's Views about Consciousness; M. Nida-Rumelin.
The Hidden
Algebra of the Mind from a Linguistic Perspective;
T. Roeper.
Identification and Misidentification; A.
Stroll. Social Reality.
Searle on Social Reality: Process Is Prior
to Product; S.B.
Barnes. On Searle's Collective Intentionality.
Some Notes; G.
Meggle. Searle's Theory of Institutional
Facts: A Program of
Critical Revision; J. Moural. True Reality
and Real Truth; D.
Sosa. Searle, Collective Intentionality,
and Social Institutions;
R. Tuomela. New Perspectives. The Classical
Model of Rationality
and Its Weaknesses; J.R. Searle. Contributors.
October 2002, ISBN 1-4020-7276-7, Hardbound
Book Series: GENETIC ALGORITHMS AND EVOLUTIONARY
COMPUTATION :
Volume 10
Evolutionary Algorithms for Embedded System
Design describes how
Evolutionary Algorithm (EA) concepts can
be applied to circuit
and system design - an area where time-to-market
demands are
critical. EAs create an interesting alternative
to other
approaches since they can be scaled with
the problem size and can
be easily run on parallel computer systems.
This book presents
several successful EA techniques and shows
how they can be
applied at different levels of the design
process. Starting on a
high-level abstraction, where software components
are dominant,
several optimization steps are demonstrated,
including DSP code
optimization and test generation. Throughout
the book, EAs are
tested on real-world applications and on
large problem instances.
For each application the main criteria for
the successful
application in the corresponding domain are
discussed. In
addition, contributions from leading international
researchers
provide the reader with a variety of perspectives,
including a
special focus on the combination of EAs with
problem specific
heuristics.
Evolutionary Algorithms for Embedded System
Design is an
excellent reference for both practitioners
working in the area of
circuit and system design and for researchers
in the field of
evolutionary concepts.