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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


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


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


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


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