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Equivalence Criteria for Fourier–Mukai Transforms

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/9780199296866.003.0007
Subject:
Mathematics, Geometry / Topology

Criteria must be developed to determine whether a given Fourier-Mukai transform is in fact an equivalence. Applying the techniques from Chapter 1, this chapter explains the fully faithfulness of a ... More


NILPOTENT 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/9780198507284.003.0002
Subject:
Mathematics, Pure Mathematics

This chapter discusses extraction of roots in nilpotent groups. Topics covered include the Mal’cev completion for a torsion-free nilpotent group, the commutator collection process, and isolators.


Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)

Umberto Zannier

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153704
eISBN:
9781400842711
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153704.001.0001
Subject:
Mathematics, Geometry / Topology

This book considers the so-called unlikely intersections, a topic that embraces well-known issues, such as Lang's and Manin–Mumford's, concerning torsion points in subvarieties of tori or abelian ... More


Circular and Thin-Wall Torsion

Sanjay Govindjee

in Engineering Mechanics of Deformable Solids: A Presentation with Exercises

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199651641
eISBN:
9780191775017
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199651641.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

This chapter introduces the fundamental kinematic assumption associated with the torsion of circular bars. It treats the equilibrium of twisted rods and examines the behaviour of elastic as well as ... More


Measurements of the Casimir Force Between Metals

M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko

in Advances in the Casimir Effect

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199238743
eISBN:
9780191716461
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199238743.003.0019
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter starts chronologically with the first measurement, by means of a torsion pendulum, in the recent phase of Casimir force experiments. Then the main breakthroughs in the measurement of the ... More


Saccades and fixations

Nicholas J. Wade and Benjamin W. Tatler

in The Moving Tablet of the Eye: The origins of modern eye movement research

Published in print:
2005
Published Online:
April 2010
ISBN:
9780198566175
eISBN:
9780191584954
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566175.003.0004
Subject:
Psychology, Cognitive Psychology

Fixations were examined before saccades were measured. Concerns were the stability of fixation and torsion of the eyes. The latter resulted in Donders' law and Listing's law, both of which were ... More


Engineering Mechanics of Deformable Solids: A Presentation with Exercises

Sanjay Govindjee

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199651641
eISBN:
9780191775017
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199651641.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

This book covers the essential elements of engineering mechanics for mechanical elements in tension-compression, torsion, and bending. Its approach emphasizes a fundamental bottom-up approach to the ... More


BROWNIAN MOTION AND NOISE

Robert M. Mazo

in Brownian Motion: Fluctuations, Dynamics, and Applications

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199556441
eISBN:
9780191705625
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556441.003.0013
Subject:
Physics, Condensed Matter Physics / Materials

This chapter treats Brownian motion as a fundamental limit on the precision of experimental measurements. As mechanical examples, the oscillations of a small mirror mounted on a torsion fibre are ... More


The Cartan structure equations

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0065
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter focuses on Cartan structure equations. It first introduces a 1-form and its exterior derivative, before turning to a study of the connection and torsion forms, thereby expressing the ... More


Integral coefficients

Claire Voisin

in Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160504
eISBN:
9781400850532
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160504.003.0006
Subject:
Mathematics, Geometry / Topology

This chapter turns to a number of birational invariants that can be defined using Z-coefficients. It is devoted in part to the study of the groups Z²ⁱ(X) measuring the failure of the Hodge conjecture ... More


Modular curves, modular forms, lattices, Galois representations

Bas Edixhoven

in Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691142012
eISBN:
9781400839001
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142012.003.0002
Subject:
Mathematics, Number Theory

This chapter provides the necessary background concerning modular curves and modular forms. It covers modular curves, modular forms, lattices and modular forms, Galois representations attached to ... More


Approximating Vf over the complex numbers

Jean-Marc Couveignes

in Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691142012
eISBN:
9781400839001
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142012.003.0012
Subject:
Mathematics, Number Theory

This chapter addresses the problem of computing torsion divisors on modular curves with an application to the explicit calculation of modular representations. The final result of the chapter is ... More


Torsion

Benson Farb and Dan Margalit

in A Primer on Mapping Class Groups (PMS-49)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691147949
eISBN:
9781400839049
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147949.003.0008
Subject:
Mathematics, Geometry / Topology

This chapter deals with finite subgroups of the mapping class group. It first explains the distinction between finite-order mapping classes and finite-order homeomorphisms, focusing on the Nielsen ... More


Some boundary-value problems for uniform isotropic incompressible materials

David J. Steigmann

in Finite Elasticity Theory

Published in print:
2017
Published Online:
December 2017
ISBN:
9780198567783
eISBN:
9780191746536
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198567783.003.0007
Subject:
Mathematics, Applied Mathematics

This chapter outlines the formulation and explicit solution of a number of simple boundary-value problems. Analysis is facilitated by the constraint of incompressibility. Examples include ... More


Winged artifacts

Wolfgang Send

in Living machines: A handbook of research in biomimetics and biohybrid systems

Published in print:
2018
Published Online:
June 2018
ISBN:
9780199674923
eISBN:
9780191842702
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199674923.003.0046
Subject:
Neuroscience, Sensory and Motor Systems, Development

Winged artifacts aim at the imitation of nature’s ingenious method to produce thrust with slim and smart-shaped flapping surfaces—the bending-torsional drive. The kinematics of these surfaces shows, ... More


Torsion of Elliptic Curves and Unlikely Intersections

Fedor Bogomolov, Hang Fu, and Yuri Tschinkel

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

Published in print:
2018
Published Online:
December 2018
ISBN:
9780198802013
eISBN:
9780191840500
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198802013.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter studies effective versions of unlikely intersections of images of torsion points of elliptic curves on the projective line.


Extension of General Relativity

Bahram Mashhoon

in Nonlocal Gravity

Published in print:
2017
Published Online:
July 2017
ISBN:
9780198803805
eISBN:
9780191842313
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198803805.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

Nonlocal general relativity (GR) requires an extension of the mathematical framework of GR. Nonlocal GR is a tetrad theory such that the orthonormal tetrad frame field of a preferred set of observers ... More


Mollusca: Gastropoda

Elena E. Voronezhskaya and Roger P. Croll

in Structure and Evolution of Invertebrate Nervous Systems

Published in print:
2015
Published Online:
March 2016
ISBN:
9780199682201
eISBN:
9780191813436
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199682201.003.0020
Subject:
Biology, Animal Biology

Gastropods comprise the second largest metazoan taxon, with about 60,000 to 80,000 living species occupying ecological niches covering the globe. Anatomy, behaviour, and development vary ... More


Fooled by Cognitive Artifacts

Edouard Machery

in Philosophy Within Its Proper Bounds

Published in print:
2017
Published Online:
August 2017
ISBN:
9780198807520
eISBN:
9780191845444
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198807520.003.0004
Subject:
Philosophy, Philosophy of Mind

Chapter 3 examines one of the two concerns often brought up against the method of cases: The judgments elicited by cases seem epistemically deficient. This concern is captured by the first argument ... More


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