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The Decomposition of Global Conformal Invariants (AM-182)

Spyros Alexakis

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153476
eISBN:
9781400842728
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153476.001.0001
Subject:
Mathematics, Geometry / Topology

This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question ... More


FINITELY PRESENTED SOLUBLE GROUPS

John C. Lennox and Derek J. S. Robinson

in The Theory of Infinite Soluble Groups

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198507284
eISBN:
9780191709326
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507284.003.0011
Subject:
Mathematics, Pure Mathematics

This chapter talks about finitely presented soluble groups, constructible soluble groups, embedding in finitely presented metabelian groups, coherent soluble groups, and Bieri-Strebel invariants.


Understanding Polynomial Equations in n Unknowns

Victor J. Katz and Karen Hunger Parshall

in Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691149059
eISBN:
9781400850525
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149059.003.0012
Subject:
Mathematics, History of Mathematics

This chapter examines the search for simultaneous solutions which eventually led to the creation of whole new algebraic constructs over the course of the eighteenth and nineteenth centuries. The ... 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


APPLICATIONS OF THE TOPOLOGICAL STRING/GAUGE THEORY CORRESPONDENCE

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter considers two applications of the topological string/gauge theory correspondence. The first application is to Chern-Simons knot and link invariants, and the second application is to ... More


CHERN–SIMONS THEORY AND KNOT INVARIANTS

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents various aspects of Chern-Simons theory. In a groundbreaking paper, Witten (1989) showed that Chern-Simons gauge theory, which is a quantum field theory in three dimensions, ... More


TOPOLOGICAL STRINGS

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Type-A and type-B topological sigma models are two topological field theories in two dimensions. Although they contain a lot of information in genus 0, they turn out to be trivial for g > 1. This is ... More


REPRINT STATISTICAL MECHANICS WITH TOPOLOGICAL CONSTRAINTS: II

S. F. Edwards

in Stealing the Gold: A celebration of the pioneering physics of Sam Edwards

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528531
eISBN:
9780191713415
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528531.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents a paper showing that the full specification of an assembly of long flexible molecules, needed for a statistical-mechanical study, requires an infinite set of topological ... More


NOTES ON ‘STATISTICAL MECHANICS WITH TOPOLOGICAL CONSTRAINTS: I & II’

Edward Witten

in Stealing the Gold: A celebration of the pioneering physics of Sam Edwards

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528531
eISBN:
9780191713415
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528531.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses Edwards' early work trying to devise a convenient description of topological constraint in order to study the statistical physics of cross-linked polymers, which is related to ... More


The Structure of Complex Networks: Theory and Applications

Ernesto Estrada

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199591756
eISBN:
9780191774959
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199591756.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book is devoted to the analysis of the structure of complex networks by combining results from algebraic, topological, and extremal graph theory with statistical and molecular physics, as well ... More


Direct methods of crystal-structure determination

Peter Main

in Crystal Structure Analysis: Principles and Practice

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199219469
eISBN:
9780191722516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219469.003.0010
Subject:
Physics, Crystallography

Reflection phases are essential for crystal structure solution but are not available experimentally. They can be estimated from probability and other relationships derived from known or assumed ... More


The Theory of Materials Failure

Richard M. Christensen

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199662111
eISBN:
9780191748387
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199662111.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

This book provides a complete and comprehensive development of failure theory for homogeneous materials. The resultant failure criteria to be used for applications with isotropic materials are ... More


Meter as a Kind of Attentional Behavior

Justin London

in Hearing in Time: Psychological Aspects of Musical Meter

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199744374
eISBN:
9780199949632
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199744374.003.0001
Subject:
Music, Psychology of Music, Theory, Analysis, Composition

Meter is defined as musically-specific form of entrainment, the synchronization of attention and/or other behaviors (especially motor behaviors) with periodic rhythms in the environment. This ... More


Momentum Space Topology Protected By Symmetry

VOLOVIK GRIGORY E.

in The Universe in a Helium Droplet

Published in print:
2009
Published Online:
January 2010
ISBN:
9780199564842
eISBN:
9780191709906
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199564842.003.0012
Subject:
Physics, Condensed Matter Physics / Materials, Particle Physics / Astrophysics / Cosmology

In some fermionic systems the total topological charge of the Fermi point vanishes. However, the discrete symmetry may produce the nonzero p-space topological invariant, which protects the nodal ... More


Three-Generation Mixing

Carlo Giunti and Chung W. Kim

in Fundamentals of Neutrino Physics and Astrophysics

Published in print:
2007
Published Online:
January 2010
ISBN:
9780198508717
eISBN:
9780191708862
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508717.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses the physics of three-generation mixing and explains in detail the following: diagonalization of the mass matrix, physical parameters in the mixing matrix, parameterization of ... More


Particle Motion in Curved Spacetime

Valeri P. Frolov and Andrei Zelnikov

in Introduction to Black Hole Physics

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199692293
eISBN:
9780191731860
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199692293.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Particle motion in a curved spacetime is considered. The Lagrangian and Hamiltonian form of the equation of motion of a relativistic particle are described. We discuss here also the Hamilton‐Jacobi ... More


Invariants of four-manifolds with flows via cohomological field theory

Hugo Garcia-Compeân, Roberto Santos-Silva, and Alberto Verjovsky

Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)

in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159294
eISBN:
9781400851317
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159294.003.0023
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter argues that the Jones–Witten invariants can be generalized for smooth, nonsingular vector fields with invariant probability measure on three-manifolds, thus giving rise to new invariants ... More


Top-Down Versus Bottom-Up Processing of Biological Motion

Ian M. Thornton

in People Watching: Social, Perceptual, and Neurophysiological Studies of Body Perception

Published in print:
2012
Published Online:
January 2013
ISBN:
9780195393705
eISBN:
9780199979271
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195393705.003.0003
Subject:
Psychology, Cognitive Psychology

While the visual perception of biological motion is traditionally thought to rely on top-down or stimulus-driven processes that operate locally over space and time, this chapter reviews evidence ... More


Learning from input

John R Taylor

in The Mental Corpus: How language is represented in the mind

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199290802
eISBN:
9780191741388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199290802.003.0009
Subject:
Linguistics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics

How do speakers learn from input? In the case of phoneme acquisition, it is argued that speakers notice and record statistical properties of the input. The recency effect provides further insight ... More


Scalar Invariants

Charles Fefferman and C. Robin Graham

in The Ambient Metric (AM-178)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153131
eISBN:
9781400840588
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153131.003.0009
Subject:
Mathematics, Geometry / Topology

This chapter shows how to derive a characterization of scalar invariants of conformal structures by reduction to the relevant results of [BEGr]. In [FG], the authors conjectured that when n is odd, ... More


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