Series : The IMA Volumes in Mathematics and its Applications , Vol. 139
2004, XII, 258 p. 94 illus., Hardcover
ISBN: 0-387-22311-8
About this book
Time series methods are essential tools in the analysis of many
geophysical systems. This volume, which consists of papers
presented by a select, international group of statistical and
geophysical experts at a Workshop on Time Series Analysis and
Applications to Geophysical Systems at the Institute for
Mathematics and its Applications (IMA) at the University of
Minnesota from November 12-15, 2001 as part of the IMA's Thematic
Year on Mathematics in the Geosciences, explores the application
of recent advances in time series methodology to a host of
important problems ranging from climate change to seismology. The
works in the volume deal with theoretical and methodological
issues as well as real geophysical applications, and are written
with both statistical and geophysical audiences in mind.
Important contributions to time series modeling, estimation,
prediction, and deconvolution are presented. The results are
applied to a wide range of geophysical applications including the
investigation and prediction of climatic variations, the
interpretation of seismic signals, the estimation of flooding
risk, the description of permeability in Chinese oil fields, and
the modeling of NOx decomposition from thermal power plants.
Table of contents
Interpretation of Seismic Signals.-Nonparametric deconvolution of
seismic depth phases.- State space approach to signal extraction
problems in seismology.- Improved signal transmission through
randomization.- Online analysis of seismic signals.- Temperature
Data.- Nonstationary time series analysis of monthly global
temperature anomalies.- A test for detecting changes in mean.-
Spatio-temporal modelling of temperature time series.- Modeling
North Pacific climate time series.- Assortment of Important Time
Series Problems and Applications.- Skew-elliptical time series
with application to flood risk.- Hidden periodicities anaysis and
its application in geophysics.- The innovation approach to the
identification of nonlinear causal models in time series analysis.-
Non-Gaussian time series driven by fractional Gaussian noise.-
List of workshop participants.
2004, VII, 237 p., Hardcover
ISBN: 3-540-23274-5
About this book
The papers included in this volume provide an overview of the
state of the art in approximative implicitization and various
related topics, including both the theoretical basis and the
existing computational techniques. The novel idea of approximate
implicitization has strengthened the existing link between
Computer Aided Geometric Design and classical algebraic geometry.
There is a growing interest from researchers and professionals
both in CAGD and Algebraic Geometry, to meet and combine
knowledge and ideas, with the aim to improve the solving of
industrial-type challenges, as well as to initiate new directions
for basic research. This volume will support this exchange of
ideas between the various communities.
Table of contents
Approximate Parametrisation of Confidence Sets (Zbynek Sir).-
Challenges in surface-surface intersections (Vibeke Skytt).-
Computing the topology of three-dimensional algebraic curves (G.
Gatellier, A. Labrouzy, B. Mourrain, J.P. Tecourt).- Distance
Properties of Points on Algebraic Curves (Sonia Perez-Diaz, Juana
Sendra, J.Rafael Sendra).- Distance Separation Measures Between
Parametric Curves and Surfaces Toward Intersection and Collision
Detection Applications (Gershon Elber).- Elementary Theory of Del
Pezzo Surfaces (Josef Schicho).- The Geometry of the Tangent
Developable (Pal Hermunn Johansen).- Numerical and algebraic
properties (Joab R. Winkler).- Polynomial C2 spline surfaces
guided by rational multisided patches (Kestutis Karciauskas, Jorg
Peters).- A Recursive Taylor Method for Algebraic Curves and
Surfaces (Huahao Shou, Ralph Martin, Guojin Wang, Adrian Bowyer,
Irina Voiculescu).- Self-intersection problems and approximate
implicitization (Jan B. Thomassen).- Singularities of some
projective rational surfaces (Ragni Piene).- On the Shape Effect
of a Control Point Experimenting with NURBS Surfaces (Panagiotis
Kaklis, Spyridon Dellas).- Third Order Invariants of Surfaces (Jens
Gravesen).- Universal Rational Parametrizations and Spline Curves
on Toric Surfaces (Rimvydas Krasauskas, Margarita Kazakeviciute).-
Panel discussion.
Series : Universitext
2005, XVI, 670 p., Softcover
ISBN: 3-540-22887-X
About this textbook
This textbook, deals with tensors that are treated as vectors,
and has a practical orientation. In addition to dealing with the
classical topics of tensor books, new tensor concepts are
introduced, such as the rotation of tensors, the transposer
tensor, the eigentensors, the permutation tensor structure, etc.
The book covers an existing gap between the classic theory of
tensors and the possibility of solving tensor problems with a
computer. In fact, the computational algebra is formulated in
matrix form to facilitate its implementation on computers. For
the first time tensor contraction is formulated in terms of
matrix operations. A computer package , written in Mathematica,
is available through Internet at: http://personales.unican.es/castie/tensors
that complements the book. In summary, the book is not a standard
book on tensors because of its orientation, the many novel
contributions included in it, the careful notation and the
stretching-condensing techniques used for most of the
transformations used in the book.
Table of contents
Series : Graduate Texts in Mathematics , Vol. 230
2005, XIV, 171 p., Hardcover
ISBN: 3-540-23499-3
About this textbook
This book provides a rigorous but elementary introduction to the
theory of Markov Processes on a countable state space. It should
be accessible to students with a solid undergraduate background
in mathematics, including students from engineering, economics,
physics, and biology. Topics covered are: Doeblin's theory,
general ergodic properties, and continuous time processes. A
whole chapter is devoted to reversible processes and the use of
their associated Dirichlet forms to estimate the rate of
convergence to equilibrium.
Written for:
Advanced undergraduates with strong mathematics preparation and
graduate students looking for a non-measure-theoretic, but
rigorous, introduction to Markov processes
Table of contents
Series : Lecture Notes in Mathematics
Subseries : Fondazione C.I.M.E., Firenze , Vol. 1856
2004, XIII, 307 p., Softcover
ISBN: 3-540-22953-1
About this book
This volume includes the five lecture courses given at the CIME-EMS
School on "Stochastic Methods in Finance" held in
Bressanone/Brixen, Italy 2003. It deals with innovative methods,
mainly from stochastic analysis, that play a fundamental role in
the mathematical modelling of finance and insurance: the theory
of stochastic processes, optimal and stochastic control,
stochastic differential equations, convex analysis and duality
theory. Five topics are treated in detail: Utility maximization
in incomplete markets; the theory of nonlinear expectations and
its relationship with the theory of risk measures in a dynamic
setting; credit risk modelling; the interplay between finance and
insurance; incomplete information in the context of economic
equilibrium and insider trading.
Table of contents
Series : Universitext
2nd ed., 2005, Approx. 215 p., Softcover
ISBN: 0-387-22837-3
About this textbook
From the reviews of the first edition: "This lovely book is
intended as a primer in harmonic analysis at the undergraduate
level. All the central concepts of harmonic analysis are
introduced using Riemann integral and metric spaces only. The
exercises at the end of each chapter are interesting and
challenging..." Sanjiv Kumar Gupta for MathSciNet "...
In this well-written textbook the central concepts of Harmonic
Analysis are explained in an enjoyable way, while using very
little technical background. Quite surprisingly this approach
works. It is not an exaggeration that each undergraduate student
interested in and each professor teaching Harmonic Analysis will
benefit from the streamlined and direct approach of this book."
Ferenc Moricz for Acta Scientiarum Mathematicarum This book is a
primer in harmonic analysis using an elementary approach. Its
first aim is to provide an introduction to Fourier analysis,
leading up to the Poisson Summation Formula. Secondly, it makes
the reader aware of the fact that both, the Fourier series and
the Fourier transform, are special cases of a more general theory
arising in the context of locally compact abelian groups. The
third goal of this book is to introduce the reader to the
techniques used in harmonic analysis of noncommutative groups.
There are two new chapters in this new edition. One on
distributions will complete the set of real variable methods
introduced in the first part. The other on the Heisenberg Group
provides an example of a group that is neither compact nor
abelian, yet is simple enough to easily deduce the Plancherel
Theorem. Professor Deitmar is Professor of Mathematics at the
University of T"ubingen, Germany. He is a former Heisenberg
fellow and has taught in the U.K. for some years. In his leisure
time he enjoys hiking in the mountains and practicing Aikido.
Table of contents
* Fourier Series * Hilbert Spaces * The Fourier Transform *
Distributions * Finite Abelian Groups * LCA groups * The Dual
Group * Plancheralfs Theorem * Matrix Groups * The
Representations of SU(2) * The Peter-Weyl Theorem * The
Heisenberg Group * The Riemann Zeta Function * Haar Integration *
Bibliography * Index
Series : Springer Monographs in Mathematics
2005, Approx. 240 p., Hardcover
ISBN: 0-387-22383-5
About this textbook
This book uses techniques of Fourier series and functional
analysis to deal with certain problems in differential equations.
The Fourier series and functional analysis are merely tools; the
authors' real interest lies in the differential equations that
they study. It has been known since 1967 that a wide variety of
sets {ewikt} of complex exponential functions play an important
role in the control theory of systems governed by partial
differential equations. However, this book is the first serious
attempt to gather all of the available theory of these "nonharmonic
Fourier series" in one place, combining published results
with new results by the authors, to create a unique source of
such material for practicing applied mathematicians, engineers
and other scientific professionals.
Table of contents
Preface.- Introduction.- Observation, control and stabilization.-
Well-posedness in a Riesz basis setting.- Observability of
strings.- Observability of beams.- Vector sum estimates.-
Problems on spherical domains.- Multidimensional Ingham type
theorems.- A general Ingham type theorem.- Problems with weakened
gap conditions.- References.- Index.