2004, XIII, 376 p., Softcover
ISBN: 3-7643-2416-3
About this book
Since the publication of the first edition of this seminar book
in 1994, the theory and applications of extremes and rare events
have enjoyed an enormous and still increasing interest. The
intention of the book is to give a mathematically oriented
development of the theory of rare events underlying various
applications. This characteristic of the book was strengthened in
the second edition by incorporating various new results on about
130 additional pages. Part II, which has been added in the second
edition, discusses recent developments in multivariate extreme
value theory. Particularly notable is a new spectral
decomposition of multivariate distributions in univariate ones
which makes multivariate questions more accessible in theory and
practice. One of the most innovative and fruitful topics during
the last decades was the introduction of generalized Pareto
distributions in the univariate extreme value theory. Such a
statistical modelling of extremes is now systematically developed
in the multivariate framework.
Written for:
Graduate and postgraduate students, researchers in Number Theory,
Probability Theory and Statistics, statisticians; geophysicists,
biologists
Table of contents
Functional Laws of Small Numbers.- ExtremeValueTheory.-
Estimation of Conditional Curves.- Basic Theory of Multivariate
Maxima.- Multivariate Extremes: The Pickands Approach.- The
Pickands Approach in the Bivariate Case.- Multivariate Extremes:
Supplementary Concepts and Results.- Introduction to the Non IID
Case.- Extremes of Random Sequences.- Extremes of Gaussian
Processes.- Extensions for Rare Events.- Statistics of Extremes.
Series : Applied and Numerical Harmonic Analysis
2004, XVI, 509 p., Hardcover
ISBN: 3-7643-4105-X
A Birkhauser book
About this textbook
This self-contained book provides a basic foundation for
students, practitioners, and researchers interested in some of
the diverse new areas of multiscale (geo)potential theory. New
mathematical methods are developed enabling the gravitational
potential of a planetary body to be modeled and analyzed using a
continuous flow of observations from land or satellite devices.
Harmonic wavelet methods are introduced, as well as fast
computational schemes and various numerical test examples. The
work is divided into two main parts: Part I treats well-posed
boundary-value problems of potential theory and elasticity; Part
II examines ill-posed problems such as satellite-to-satellite
tracking, satellite gravity gradiometry, and gravimetry. Both
sections demonstrate how multiresolution representations yield
Runge?Walsh type solutions that are both accurate in
approximation and tractable in computation. Topic and key
features: * Comprehensive coverage of topics which, thus far, are
only scattered in journal articles and conference proceedings *
Important applications and developments for future satellite
scenarios; new modelling techniques involving low-orbiting
satellites * Multiscale approaches for numerous geoscientific
problems, including geoidal determination, magnetic field
reconstruction, deformation analysis, and density variation
modelling * Multilevel stabilization procedures for
regularization * Treatment of the real Earthfs shape as well as
a spherical Earth model * Modern methods of constructive
approximation * Exercises at the end of each chapter and an
appendix with hints to their solutions Models and methods
presented show how various large- and small-scale processes may
be addressed by a single geoscientific modelling framework for
potential determination. Multiscale Potential Theory may be used
as a textbook for graduate-level courses in geomathematics,
applied mathematics, and geophysics. The book is also an up-to-date
reference text for geoscientists, applied mathematicians, and
engineers.
Table of contents
Preface * Introduction * Preliminary Tools * Part I: Well-Posed
Problems * Boundary-Value Problems of Potential Theory * Boundary-Value
Problems of Elasticity * Part II: Ill-Posed Problems * Satellite
Problems * The Gravimetry Problem * Conclusion * Hints for the
Solutions of the Exercises * References * Index
2005, XII, 388 p. 152 illus., Softcover
ISBN: 3-7643-4337-0 Paperback
ISBN: 3-7643-4313-3 Hardback
About this textbook
This fairly self-contained work embraces a broad range of topics
in analysis at the graduate level, requiring only a sound
knowledge of calculus and the functions of one variable. A key
feature of this lively yet rigorous and systematic exposition is
the historical accounts of ideas and methods pertaining to the
relevant topics. Most interesting and useful are the connections
developed between analysis and other mathematical disciplines, in
this case, numerical analysis and probability theory. The text is
divided into two parts: The first examines the systems of real
and complex numbers and deals with the notion of sequences in
this context. After the presentation of natural numbers as a
subset of the reals, elements of combinatorics and a discussion
of the mathematical notion of the infinite are introduced. The
second part is dedicated to discrete processes starting with a
study of the processes of infinite summation both in the case of
numerical series and of power series.
Table of contents
Preface * Real Numbers and Natural Numbers * Sequences of Real
Numbers * Integer Numbers: Congruences, Counting and Infinity *
Complex Numbers * Polynomials, Rational Functions and
Trigonometric Polynomials * Series * Power Series * Discrete
Processes * Mathematicans and Other Scientists * Bibliographical
Notes * Index
2004, VIII, 202 p., Softcover
ISBN: 3-7643-4350-8
About this book
This work treats quantitative aspects of the approximation of
functions using positive linear operators. The theory of these
operators has been an important area of research in the last few
decades, particularly as it affects computer-aided geometric
design. In this book, the crucial role of the second order moduli
of continuity in the study of such operators is emphasized. New
and efficient methods, applicable to general operators and to
diverse concrete moduli, are presented. The advantages of these
methods consist in obtaining improved and even optimal estimates,
as well as in broadening the applicability of the results. *Additional
Topics and Features: * Examination of the multivariate
approximation case * Special focus on the Bernstein operators,
including applications, and on two new classes of Bernstein-type
operators * Many general estimates, leaving room for future
applications (e.g. the B-spline case) * Extensions to
approximation operators acting on spaces of vector functions *
Historical perspective in the form of previous significant
results This monograph will be of interest to those working in
the field of approximation or functional analysis. Requiring only
familiarity with the basics of approximation theory, the book may
serve as a good supplementary text for courses in approximation
theory, or as a reference text on the subject.
Written for:
Graduate students, postdocs and higher qualified scientists in
mathematics and computer science interested in the fields of
Geometric Modeling, Computer Aided Geometric Design, Image
Processing, Real Analysis and Approximation Theory
Series : Control Engineering
2005, Approx. 265 p. 19 illus., Hardcover
ISBN: 3-7643-3782-6
About this book
Stochastic hybrid systems represent an interesting class of
systems that can be used to model a variety of systems having
abrupt random changes in their dynamics. Such systems may be
found in manufacturing, communications, aerospace, power, and
economics systems. This work presents stochastic hybrid systems
and provides up-to-date methods and techniques for the analysis
and design of various control systems with or without
uncertainties. An introductory chapter highlights basic concepts
and practical models, which are then used to solve more advanced
problems throughout the book. Included are many numerical
examples and LMI synthesis methods and design approaches to
supplement the results developed. Specific topics covered include:
* The stochastic stability problem and its robustness * The
stabilization problem---using different controllers such as the
state feedback, output feedback, and observer-based output
feedback---and its robustness * Systems with external
disturbances * The filtering problem for the class of systems
with Markovian jump parameters; Kalman and H-infinity filtering
problems are treated and LMI conditions are developed to
synthesize the gains of these filters * Systems with singular
Markovian jump parameters "Stochastic Hybrid Systems"
may be used as a textbook for graduate-level engineering courses,
or as a reference for practicing control engineers, graduate
students, and researchers in systems and control. Prerequisites
include elementary courses in matrix theory, probability,
optimization techniques, and control systems theory.
Table of contents
Preface * Introduction * Stability Problem * Stabilization
Problem * H-infinity Control Problem * Filtering Problem *
Singular Markovian Jumping Parameters Systems * Conclusion *
Appendix: Markov Processes * Bibliography * Index