Jump to ContentJump to Main Navigation

You are looking at 1-20 of 146 items

  • Keywords: tensor x
Clear All Modify Search

View:

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


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


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


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


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


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


A Systems Approach to the Aging Brain: Neuroanatomic Changes, Their Modifiers, and Cognitive Correlates

Naftali Raz and Kristen M. Kennedy

in Imaging the Aging Brain

Published in print:
2009
Published Online:
February 2010
ISBN:
9780195328875
eISBN:
9780199864836
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195328875.003.0004
Subject:
Neuroscience, Techniques, Development

Success in diagnosing and treating age-related brain disease depends on understanding normative and optimal aging of the brain. Neuroimaging studies of healthy adults reveal differential brain ... More


Preliminaries to Main Results

Joram Lindenstrauss, David Preiss, and Tiˇser Jaroslav

in Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153551
eISBN:
9781400842698
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153551.003.0009
Subject:
Mathematics, Analysis

This chapter presents a number of results and notions that will be used in subsequent chapters. In particular, it considers the concept of regular differentiability and the lemma on deformation of ... More


Classification of Mumford-Tate Subdomains

Mark Green, Phillip Griffiths, and Matt Kerr

in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691154244
eISBN:
9781400842735
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691154244.003.0008
Subject:
Mathematics, Analysis

This chapter develops an algorithm for determining all Mumford-Tate subdomains of a given period domain. The result is applied to the classification of all complex multiplication Hodge structures (CM ... 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


Lorentz Geometry

Yvonne Choquet-Bruhat

in General Relativity and the Einstein Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.003.0001
Subject:
Mathematics, Applied Mathematics

This chapter presents a survey of the basic definitions of Riemannian and Lorentzian differential geometry used in this book. The first nine sections use the simplest formulations, in local ... More


Tensors in special relativity

Ta-Pei Cheng

in Relativity, Gravitation and Cosmology: A Basic Introduction

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199573639
eISBN:
9780191722448
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573639.003.0012
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Tensors in a general coordinate system are introduced. When a tensor is expanded in terms of a set of basis (or inverse basis) vectors, the coefficients of expansion are its contravariant (or ... More


Tensors in general relativity

Ta-Pei Cheng

in Relativity, Gravitation and Cosmology: A Basic Introduction

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199573639
eISBN:
9780191722448
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573639.003.0013
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Differentiation of tensor components in a curved space must be handled with extra care. By adding another term (related to Christoffel symbols) to the ordinary derivative operator, we can form a ... More


Mobility of Frenkel Excitons

Vladimir M. Agranovich

in Excitations in Organic Solids

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199234417
eISBN:
9780191715426
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199234417.003.0014
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter discusses the different regimes of mobility of Frenkel excitons. The diffusion equation and diffusion-related quantities (diffusion coefficient/length, diffusion constant, exciton mean ... More


Field Quantization and Vacuum Energy in the Presence of Boundaries

M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko

in Advances in the Casimir Effect

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199238743
eISBN:
9780191716461
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199238743.003.0003
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

From the standpoint of quantum field theory, the Casimir effect is related to the vacuum polarization that arises in quantization volumes restricted by boundaries or in spaces with nontrivial ... More


Polaritons: Excitonic States Taking Account of Retardation

Vladimir M. Agranovich

in Excitations in Organic Solids

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199234417
eISBN:
9780191715426
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199234417.003.0004
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter presents the microscopical theory of polaritons, being coherent superposition of one exciton and one transverse photon state. The dispersion of polaritons including the effect of spatial ... More


View: