## CURVATURE REGISTRATION

*Jan Modersitzki*

### in Numerical Methods for Image Registration

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0012
- Subject:
- Mathematics, Applied Mathematics

Elastic, fluid, and diffusion registrations are sensitive to affine linear displacements. As a consequence, an affine linear pre-registration is unavoidable. The second order derivatives-based ... More

## Conclusion

*Tom W. N. Parker*

### in Proportional Form in the Sonnets of the Sidney Circle: Loving in Truth

- Published in print:
- 1998
- Published Online:
- October 2011
- ISBN:
- 9780198184430
- eISBN:
- 9780191674259
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198184430.003.0008
- Subject:
- Literature, Poetry, 16th-century and Renaissance Literature

This conclusion concludes that the frequency in the reiterations of particular sets of numbers within the sonnet sequences of the Sidney circle is an enough conviction that intentional patterning did ... More

## Ptolemy's Philosophy

*Jacqueline Feke*

- Published in print:
- 2018
- Published Online:
- May 2019
- ISBN:
- 9780691179582
- eISBN:
- 9780691184036
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691179582.001.0001
- Subject:
- Philosophy, Philosophy of Science

The Greco-Roman mathematician Claudius Ptolemy is one of the most significant figures in the history of science. He is remembered today for his astronomy, but his philosophy is almost entirely lost ... More

## HARMONIC FUNCTIONS AND RADON TRANSFORM ON ALGEBRAIC VARIETIES

*Leon Ehrenpreis*

### in The Universality of the Radon Transform

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198509783
- eISBN:
- 9780191709166
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509783.003.0004
- Subject:
- Mathematics, Mathematical Physics

This chapter looks at a variation of the “harmonic function” introduced by Chevalley. It deals with a noncompact version of the theory described in Chapter 3 (which deals with a compact version). One ... More

## Prolongationl Functions

*Fred Lerdahl*

### in Tonal Pitch Space

- Published in print:
- 2005
- Published Online:
- May 2008
- ISBN:
- 9780195178296
- eISBN:
- 9780199870370
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195178296.003.0005
- Subject:
- Music, Theory, Analysis, Composition

This chapter elaborates a new approach to tonal and harmonic function. To do this, it establishes a frame of reference; so it first develops a tonic-finding method, based on the principle of the ... More

## Analysis

*Robert Carl*

### in Terry Riley's in C

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780195325287
- eISBN:
- 9780199869428
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195325287.003.0004
- Subject:
- Music, Popular, History, American

This chapter analyzes In C as a score in its own right, that is, an “endogenous” analysis. Though hailed as a breakthrough work of “open form,” In C is also a conventionally notated score, albeit ... More

## Introduction

*Robert Alicki and Mark Fannes*

### in Quantum Dynamical Systems

- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198504009
- eISBN:
- 9780191708503
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504009.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This introductory chapter outlines the basic ideas of the book using two simple examples: the quantum harmonic oscillator as a prototype of an integrable system versus the quantum Arnold cat map ... More

## Boundaries and Geometries

*Gary A. Glatzmaier*

### in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0010
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter examines how boundary and geometry affect convection. It begins with a discussion of how one can implement “absorbing” top and bottom boundaries, which reduce the large-amplitude ... More

## Liquid Crystals and Harmonic Maps in Polyhedral Domains

*Apala Majumdar, Jonathan Robbins, and Maxim Zyskin*

### in Analysis and Stochastics of Growth Processes and Interface Models

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199239252
- eISBN:
- 9780191716911
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199239252.003.0014
- Subject:
- Mathematics, Probability / Statistics, Analysis

This chapter is concerned with harmonic maps from a polyhedron to the unit two-sphere, which provide a model of nematic liquid crystals in bistable displays. This chapter looks at the Dirichlet ... More

## Harmonic Morphisms Between Riemannian Manifolds

*Paul Baird and John C. Wood*

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198503620
- eISBN:
- 9780191708435
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198503620.001.0001
- Subject:
- Mathematics, Pure Mathematics

Harmonic morphisms are maps which preserve Laplace's equation. More explicitly, a map between Riemannian manifolds is called a harmonic morphism if its composition with any locally defined harmonic ... More

## Curvature considerations

*Paul Baird and John C. Wood*

### in Harmonic Morphisms Between Riemannian Manifolds

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198503620
- eISBN:
- 9780191708435
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198503620.003.0011
- Subject:
- Mathematics, Pure Mathematics

The curvature of the domain on various combinations of horizontal and vertical vectors is calculated for a horizontally conformal submersion and for a (submersive) harmonic morphism. It is related to ... More

## Reduction techniques

*Paul Baird and John C. Wood*

### in Harmonic Morphisms Between Riemannian Manifolds

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198503620
- eISBN:
- 9780191708435
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198503620.003.0013
- Subject:
- Mathematics, Pure Mathematics

When a map has a certain symmetry, the equations for a harmonic morphism reduce to equations in a smaller number of variables. Here, the appropriate symmetry is equivariant with respect to ... More

## Riemannian manifolds and conformality

*Paul Baird and John C. Wood*

### in Harmonic Morphisms Between Riemannian Manifolds

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198503620
- eISBN:
- 9780191708435
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198503620.003.0002
- Subject:
- Mathematics, Pure Mathematics

This chapter introduces fundamental concepts from Riemannian geometry, including the Laplacian and harmonic functions on a Riemannian manifold. The next two sections discuss weak conformality and the ... More

## Harmonic mappings between Riemannian manifolds

*Paul Baird and John C. Wood*

### in Harmonic Morphisms Between Riemannian Manifolds

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198503620
- eISBN:
- 9780191708435
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198503620.003.0003
- Subject:
- Mathematics, Pure Mathematics

A harmonic morphism between arbitrary Riemannian manifolds is a type of harmonic map. This chapter is devoted to the description of those properties of harmonic maps, which are essential to the ... More

## Holomorphic harmonic morphisms

*Paul Baird and John C. Wood*

### in Harmonic Morphisms Between Riemannian Manifolds

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198503620
- eISBN:
- 9780191708435
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198503620.003.0008
- Subject:
- Mathematics, Pure Mathematics

The first section of this chapter investigates the general question of when holomorphic maps between almost Hermitian manifolds are harmonic maps or harmonic morphisms. In particular, a holomorphic ... More

## Mathematical Models of Electromagnetism

*Peter Monk*

### in Finite Element Methods for Maxwell's Equations

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198508885
- eISBN:
- 9780191708633
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508885.003.0001
- Subject:
- Mathematics, Numerical Analysis

This chapter presents a summary of Maxwell’s equations. The time-harmonic Maxwell equations considered throughout this book are derived from the time domain system, and several linear constitutive ... More

## Chapter Nine The Whodunit Game: The Mature Style of Billy Strayhorn

*Walter van de Leur*

### in Something to Live For: The Music of Billy Strayhorn

- Published in print:
- 2002
- Published Online:
- September 2008
- ISBN:
- 9780195124484
- eISBN:
- 9780199868711
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195124484.003.0009
- Subject:
- Music, History, Western

This chapter plots the development in Strayhorn’s later arranging and composing. By the mid-1950s, Strayhorn had expanded his music writing with numerous individual elements into a mature and ... More

## Harmonia

*Jacqueline Feke*

### in Ptolemy's Philosophy

- Published in print:
- 2018
- Published Online:
- May 2019
- ISBN:
- 9780691179582
- eISBN:
- 9780691184036
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691179582.003.0005
- Subject:
- Philosophy, Philosophy of Science

In the Harmonics, Ptolemy reveals that the heavens and human souls share the same formal structure. They are characterized by the same set of ratios, the ones studied by harmonics, the mathematical ... More

## S‐Duality in HyperkäHler Hodge Theory

*TamáS Hausel*

### in The Many Facets of Geometry: A Tribute to Nigel Hitchin

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199534920
- eISBN:
- 9780191716010
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534920.003.0016
- Subject:
- Mathematics, Geometry / Topology

This chapter surveys the motivations, related results, and progress made towards the following problem, raised by Hitchin in 1995: What is the space of L2 harmonic forms on the moduli space of Higgs ... More

## Sounds and Sweet Airs

*Murray Campbell, Clive Greated, and Arnold Myers*

### in Musical Instruments: History, Technology, and Performance of Instruments of Western Music

- Published in print:
- 2004
- Published Online:
- May 2008
- ISBN:
- 9780198165040
- eISBN:
- 9780191713675
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198165040.003.0001
- Subject:
- Music, History, Western

This introductory chapter discusses how sound waves are generated by musical instruments, travel to the ear of a listener, and there evoke the sensation of music. Using the example of an orchestral ... More