## Derived Categories of Coherent Sheaves

*D. Huybrechts*

### in Fourier-Mukai Transforms in Algebraic Geometry

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199296866
- eISBN:
- 9780191711329
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296866.003.0003
- Subject:
- Mathematics, Geometry / Topology

The discussion of the previous chapter is applied to the derived category of the abelian category of coherent sheaves. The Serre functor is introduced, and particular spanning classes are ... More

## MULTI-DIMENSIONAL EXPANSION BASES

*George Em Karniadakis and Spencer J. Sherwin*

### in Spectral/hp Element Methods for Computational Fluid Dynamics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198528692
- eISBN:
- 9780191713491
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528692.003.0003
- Subject:
- Mathematics, Numerical Analysis

This chapter considers the extension of the one-dimensional formulation to two and three dimensions by the development of expansion bases in standard regions such as triangles or rectangles in two ... More

## MATERIAL DEFORMATION

*Nasr M. Ghoniem and Daniel D. Walgraef*

### in Instabilities and Self-Organization in Materials: Volume I: Fundamentals of Nanoscience, Volume II: Applications in Materials Design and Nanotechnology

- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199298686
- eISBN:
- 9780191720222
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199298686.003.0002
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter discusses the main elements of continuum theory, which will be utilized further in later sections dealing with a variety of applications. First, a basic review of vector and tensor ... More

## Diffusion MRI in Epilepsy

*Rajkumar Munian Govindan and Harry T. Chugani*

### in Neuroimaging in Epilepsy

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780195342765
- eISBN:
- 9780199863617
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195342765.003.0006
- Subject:
- Neuroscience, Disorders of the Nervous System

Diffusion MRI facilitates the measurement of water diffusion in specific spatial directions and is highly sensitive to microstructural changes in neural tissue. This chapter provides an overview of ... More

## Operator spaces

*David P. Blecher and Christian Le Merdy*

### in Operator Algebras and Their Modules: An operator space approach

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198526599
- eISBN:
- 9780191712159
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526599.003.0001
- Subject:
- Mathematics, Pure Mathematics

This chapter presents some background results about operator spaces and establishes some notations which will be used throughout this book. It can serve as a mini-course on the basics of operator ... More

## Basic theory of operator modules

*David P. Blecher and Christian Le Merdy*

### in Operator Algebras and Their Modules: An operator space approach

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198526599
- eISBN:
- 9780191712159
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526599.003.0003
- Subject:
- Mathematics, Pure Mathematics

This chapter discusses the basics of operator modules. Topics covered include Hilbert modules, operator modules over operator algebras, two module tensor products, module maps, module map extension ... More

## Selfadjointness criteria

*David P. Blecher and Christian Le Merdy*

### in Operator Algebras and Their Modules: An operator space approach

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198526599
- eISBN:
- 9780191712159
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526599.003.0007
- Subject:
- Mathematics, Pure Mathematics

This chapter discusses several interesting criteria which force an operator algebra to be selfadjoint. Such results are in some sense ‘negative’ in nature, showing that certain results or themes ... More

## Stress and elastic constants

*Erich H. Kisi and Christopher J. Howard*

### in Applications of Neutron Powder Diffraction

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780198515944
- eISBN:
- 9780191705663
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198515944.003.0011
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter highlights a different but significant application of neutron diffraction in the measurement of engineering strains. It begins by defining the stress and strain tensors, and their ... More

## GRAVITATIONAL WAVE EXTRACTION

*Miguel Alcubierre*

### in Introduction to 3+1 Numerical Relativity

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199205677
- eISBN:
- 9780191709371
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199205677.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Gravitational waves are one of the most important physical phenomena associated with the presence of strong and dynamic gravitational fields, and as such they are of great interest in numerical ... More

## SPACE AND TIME PROPERTIES

*R. E. Raab and O. L. de Lange*

### in Multipole Theory in Electromagnetism: Classical, quantum, and symmetry aspects, with applications

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198567271
- eISBN:
- 9780191717970
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567271.003.0003
- Subject:
- Physics, Atomic, Laser, and Optical Physics

Polar and axial vectors and tensors are defined in terms of their behaviour under coordinate transformations. The effect of the time-reversal operator on kets and matrix elements is considered, ... More