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K3 Surfaces

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/9780199296866.003.0010
Subject:
Mathematics, Geometry / Topology

After abelian varieties, K3 surfaces are the second most interesting special class of varieties. These have a rich internal geometry and a highly interesting moduli theory. Paralleling the famous ... More


James’ suspension spring equations

Robert James Matthys

in Accurate Clock Pendulums

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198529712
eISBN:
9780191712791
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529712.003.0016
Subject:
Physics, History of Physics

In 1983, K. James published two useful but rather complicated equations whose purpose was to help design the suspension spring. The equations show the effect that different spring lengths, widths, ... More


Sasaki–Einstein Geometry

Charles P. Boyer and Krzysztof Galicki

in Sasakian Geometry

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.003.0012
Subject:
Mathematics, Geometry / Topology

This chapter is central to the whole book and perhaps the main reason and justification for it. Much of it is based on a new method for proving the existence of Einstein metrics on odd dimensional ... 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


Consistent Orientation of Moduli Spaces

Daniel S. Freed, Michael J. Hopkins, and Constantin Teleman

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/9780199534920.003.0019
Subject:
Mathematics, Geometry / Topology

In a series of papers by Freed, Hopkins, and Teleman (2003, 2005, 2007a) the relationship between positive energy representations of the loop group of a compact Lie group G and the twisted ... More


Smoothness and Asymptotic Smoothness

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/9780691153551.003.0008
Subject:
Mathematics, Analysis

This chapter describes the modulus of smoothness of a function in the direction of a family of subspaces and the much simpler notion of upper Fréchet differentiability. It also considers the notion ... More


Fr ´Echet Differentiability of Vector-Valued Functions

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/9780691153551.003.0013
Subject:
Mathematics, Analysis

This chapter shows that if a Banach space with a Fréchet smooth norm is asymptotically smooth with modulus o(tⁿ logⁿ⁻¹(1/t)) then every Lipschitz map of X to a space of dimension not exceeding n has ... More


The Mumford-Tate Group of a Variation of Hodge Structure

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/9780691154244.003.0004
Subject:
Mathematics, Analysis

This chapter deals with the Mumford-Tate group of a variation of Hodge structure (VHS). It begins by presenting a definition of VHS, which consists of a connected complex manifold and a locally ... More


Extensions of the Mode-Coupling Theory for the Evolution of Glassy Dynamics of Liquids

Wolfgang Götze

in Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199235346
eISBN:
9780191715600
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235346.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

It is demonstrated in this chapter that states of simple systems with density-fluctuation arrest exhibit positive static shear moduli and perfect particle localization. Approaching a generic ... More


SOLID-SOLUTION STRENGTHENING

A. S. Argon

in Strengthening Mechanisms in Crystal Plasticity

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198516002
eISBN:
9780191705717
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198516002.003.0005
Subject:
Physics, Crystallography

Incorporation of a second constituent into a pure metal offers a very flexible means of strengthening. In this chapter, the interactions of individual solute atoms with dislocations are considered in ... More


SUSY GAUGE THEORIES

John Terning

in Modern Supersymmetry: Dynamics and Duality

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567639
eISBN:
9780191718243
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567639.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter examines SUSY gauge theories. First, it looks at the role of quantum loop corrections on running couplings and masses. It then studies the space of possible vacua (the moduli space), and ... More


Arithmetic Compactifications of PEL-Type Shimura Varieties

Kai-Wen Lan

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691156545
eISBN:
9781400846016
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691156545.001.0001
Subject:
Mathematics, Geometry / Topology

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical ... More


A little elementary acoustics

G. A. D. Briggs and O. V. Kolosov

in Acoustic Microscopy: Second Edition

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199232734
eISBN:
9780191716355
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232734.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

Solids support both longitudinal and shear acoustic waves; fluids support only longitudinal waves, with attenuation proportional to the viscosity and to the square of the frequency. The longitudinal ... More


Solution of Patterson-type syntheses with the Direct methods sum function

Jordi Rius

in Structure Determination from Powder Diffraction Data

Published in print:
2006
Published Online:
January 2010
ISBN:
9780199205530
eISBN:
9780191718076
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205530.003.0013
Subject:
Physics, Condensed Matter Physics / Materials

This chapter provides a detailed mathematical definition of the Direct methods modulus sum function and its associated tangent formula (S' – TF). The latter appears to be especially well-suited to ... More


Geometry and Physics: Volume II: A Festschrift in honour of Nigel Hitchin

Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada (eds)

Published in print:
2018
Published Online:
December 2018
ISBN:
9780198802020
eISBN:
9780191869068
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198802020.001.0001
Subject:
Mathematics, Geometry / Topology

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and ... More


Geometry and Physics: Volume I: A Festschrift in honour of Nigel Hitchin

Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada (eds)

Published in print:
2018
Published Online:
December 2018
ISBN:
9780198802013
eISBN:
9780191840500
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198802013.001.0001
Subject:
Mathematics, Geometry / Topology

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and ... More


Introduction

C. M. Roland

in Viscoelastic Behavior of Rubbery Materials

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199571574
eISBN:
9780191728976
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199571574.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

This chapter describes the properties arising due to the defining feature of polymers—the enormous size of their constituent molecules. This size and the large aspect ratio of ‘macromolecules’ cause ... More


Chain dynamics

C. M. Roland

in Viscoelastic Behavior of Rubbery Materials

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199571574
eISBN:
9780191728976
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199571574.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

The slow dynamics of polymer chains involves extended spatial scales, exceeding many repeat units and making the behavior largely independent of chemical structure. This universality allows modeling ... More


Soy protein-based polymer nanocomposites

Jin Huang, Ning Lin, Yun Chen, Peter R. Chang, and Jiahui Yu

in Nanocomposites with Biodegradable Polymers: Synthesis, Properties, and Future Perspectives

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199581924
eISBN:
9780191728853
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199581924.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

The incorporation of nanofillers into soy protein materials significantly enhances tensile strength and modulus, and in some cases, contributes to a simultaneous increase in strength and elongation. ... More


Elastic soft matter

Masao Doi

in Soft Matter Physics

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199652952
eISBN:
9780191774942
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199652952.003.0003
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Elastic soft matter typically indicates rubbers and gels, which are made by introducing small amount of cross-links among polymer chains in liquid state (solutions and melts). In elastic materials, ... More


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