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## Wavelet Methods for Elliptic Partial Differential Equations

*Karsten Urban*

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780198526056
- eISBN:
- 9780191712340
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526056.001.0001
- Subject:
- Mathematics, Applied Mathematics, Mathematical Finance

Wavelets have become a powerful tool in several applications by now. Their use for the numerical solution of operator equations has been investigated more recently. By now the theoretical ... More

## Wavelets

*Karsten Urban*

### in Wavelet Methods for Elliptic Partial Differential Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780198526056
- eISBN:
- 9780191712340
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526056.003.0005
- Subject:
- Mathematics, Applied Mathematics, Mathematical Finance

Starting from a Multiresolution Analysis, wavelets are introduced as a basis for the corresponding detail spaces. The main families are introduced, namely orthogonal Daubechies' wavelets as well as ... More

## Variational methods for wavelets, with S. Dahlke

*Klaus Böhmer*

### in Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577040
- eISBN:
- 9780191595172
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577040.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 9 studies S. Dahlke studies wavelet methods. This is the first presentation in this generality and is appropriate for nonlinear problems and bifurcation for elliptic PDEs. As a consequence of ... More

## Wavelet-Galerkin Methods

*Karsten Urban*

### in Wavelet Methods for Elliptic Partial Differential Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780198526056
- eISBN:
- 9780191712340
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526056.003.0006
- Subject:
- Mathematics, Applied Mathematics, Mathematical Finance

Using wavelets as basis for the test and trial spaces of a Galerkin method allows an optimal preconditioning of the stiffness matrix. It is proven that a diagonal scaling provides such a ... More

## Wavelets on General Domains

*Karsten Urban*

### in Wavelet Methods for Elliptic Partial Differential Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780198526056
- eISBN:
- 9780191712340
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526056.003.0008
- Subject:
- Mathematics, Applied Mathematics, Mathematical Finance

The construction of wavelets on general domains is performed in three steps. This chapter starts by introducing the construction of scaling functions and wavelets on bounded univariate intervals. ... More

## Introduction

*Karsten Urban*

### in Wavelet Methods for Elliptic Partial Differential Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780198526056
- eISBN:
- 9780191712340
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526056.003.0001
- Subject:
- Mathematics, Applied Mathematics, Mathematical Finance

This chapter gives an outline of the history of wavelets, in particular with respect to their use to numerically solve partial differential equations. The scope of the book and its outline is ... More

## Adaptive Wavelet Methods

*Karsten Urban*

### in Wavelet Methods for Elliptic Partial Differential Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780198526056
- eISBN:
- 9780191712340
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526056.003.0007
- Subject:
- Mathematics, Applied Mathematics, Mathematical Finance

This chapter starts by adaptively approximating a given function and introduce the main theoretical concepts. After describing the more classical approach to adaptivity based upon a-posteriori error ... More

## Some Applications

*Karsten Urban*

### in Wavelet Methods for Elliptic Partial Differential Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780198526056
- eISBN:
- 9780191712340
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526056.003.0009
- Subject:
- Mathematics, Applied Mathematics, Mathematical Finance

Some recent applications of wavelet methods are shown. The chapter starts with the numerical realization of the WEM and consider the L-shaped domain as a model for a non-separable domain. The chapter ... More

## Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

*Klaus Boehmer*

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577040
- eISBN:
- 9780191595172
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577040.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, and create an exciting interplay. Other books discuss nonlinearity by a very few important ... More

## Transformation, convolution, and correlation

*Bernhard Blümich*

### in NMR Imaging of Materials

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198526766
- eISBN:
- 9780191709524
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526766.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials

Transformation, convolution, and correlation are used over and over again in nuclear magnetic resonance (NMR) spectroscopy and imaging in different contexts and sometimes with different meanings. The ... More

## Intermittent Vorticity, Power Spectral Scaling, and Dynamical Measures on Resting Brain Magnetic Field Fluctuations: A Pilot Study

*Arnold J. Mandell, Karen A. Selz, Tom Holroyd, Lindsay Rutter, and Richard Coppola*

### in The Dynamic Brain: An Exploration of Neuronal Variability and Its Functional Significance

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780195393798
- eISBN:
- 9780199897049
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195393798.003.0014
- Subject:
- Neuroscience, Behavioral Neuroscience, Development

A new time-dependent global MEG variable, symmetric sensor difference series, from frontal, central, parietal and temporal sensor pairs in ten task free, resting schizophrenic patients and ten age ... More

## Signal Processing

*Robert M. Stern, William J. Ray, and Karen S. Quigley*

### in Psychophysiological Recording

- Published in print:
- 2000
- Published Online:
- March 2012
- ISBN:
- 9780195113594
- eISBN:
- 9780199846962
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195113594.003.0014
- Subject:
- Psychology, Health Psychology

When considering attentional abilities, two physiological variables need to be recorded: basal (tonic) activity or event-related (phasic) activity. In general, tonic activity can be derived from the ... More

## Toward Automatic Recognition of Spontaneous Facial Actions

*Marian Stewart Bartlett, Javier R. Movellan, Gwen Littlewort, Bjorn Braathen, Mark G. Frank, and Terrence J. Sejnowski*

### in What the Face Reveals: Basic and Applied Studies of Spontaneous Expression Using the Facial Action Coding System (FACS)

- Published in print:
- 2005
- Published Online:
- March 2012
- ISBN:
- 9780195179644
- eISBN:
- 9780199847044
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195179644.003.0019
- Subject:
- Psychology, Cognitive Psychology

This chapter presents an approach for developing a fully automatic Facial Action Coding System (FACS). The approach uses state-of-the-art machine learning techniques that can be applied to ... More

## Diffraction of Light from Blood Cells

*Robert N. Compton and Michael A. Duncan*

### in Laser Experiments for Chemistry and Physics

- Published in print:
- 2015
- Published Online:
- December 2015
- ISBN:
- 9780198742975
- eISBN:
- 9780191816932
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198742975.003.0030
- Subject:
- Physics, Atomic, Laser, and Optical Physics

The picture on the front of this book shows the diffraction pattern from a laser beam passing through a pinhole. The experiment in this chapter uses Babinet’s principle to analyze the diffraction of ... More

## Microstructures and fabrics of granites

*Anne Nédélec and Jean-Luc Bouchez*

### in Granites: Petrology, Structure, Geological Setting, and Metallogeny

- Published in print:
- 2015
- Published Online:
- April 2015
- ISBN:
- 9780198705611
- eISBN:
- 9780191774515
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198705611.003.0009
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics

Microstructures in granitic rocks essentially concern quartz grains which deliver key indications on the conditions of deformation of these rocks (magmatic versus high- or low-temperature ... More

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