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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


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


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


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


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


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


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


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


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


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