Brillinger, David R.; Robinson, Enders A.; Schoenberg, Frederic P. (Eds.)

Time Series Analysis and Applications to Geophysical Systems

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.

Dokken, Tor; Juttler, Bert (Eds.)

Computational Methods for Algebraic Spline Surfaces
ESF Exploratory Workshop Schlos Weinberg at Kefermarkt, Austria, 2003 Revised Papers

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.

Ruiz-Tolosa, Juan R. , Castillo, Enrique

From Vectors to Tensors

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



Stroock, Daniel W.

An Introduction to Markov Processes

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


Back, K., Bielecki, T.R., Hipp, C., Peng, S., Schachermayer, W.
Frittelli, Marco; Runggaldier, Wolfgang (Eds.)

Stochastic Methods in Finance
Lectures given at the C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy, July 6-12, 2003

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


Deitmar, Anton

A First Course in Harmonic Analysis

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 * Plancheralfs Theorem * Matrix Groups * The Representations of SU(2) * The Peter-Weyl Theorem * The Heisenberg Group * The Riemann Zeta Function * Haar Integration * Bibliography * Index

Komornik, Vilmos, Loreti, Paola

Fourier Series in Control Theory

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.