## 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