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Algebraic and Geometric Surgery

Andrew Ranicki

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198509240
eISBN:
9780191708725
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509240.001.0001
Subject:
Mathematics, Geometry / Topology

This book is an introduction to surgery theory, the standard algebraic topology classification method for manifolds of dimension greater than 4. It is aimed at those who have already been on a basic ... More


THE EVEN-DIMENSIONAL SURGERY OBSTRUCTION

Andrew Ranicki

in Algebraic and Geometric Surgery

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198509240
eISBN:
9780191708725
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509240.003.0011
Subject:
Mathematics, Geometry / Topology

This chapter gives the algebraic construction and geometric properties of the even-dimensional surgery obstruction groups. It includes quadratic and kernel forms.


Finite Sample Moments

Aman Ullah

in Finite Sample Econometrics

Published in print:
2004
Published Online:
August 2004
ISBN:
9780198774471
eISBN:
9780191601347
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774478.003.0002
Subject:
Economics and Finance, Econometrics

This chapter derives techniques for obtaining exact and approximate moments of a function of random vector/matrix. A special case of the function considered is the ratio of quadratic forms, which ... More


*SOME COMMENTS ON VECTORIAL PROBLEMS

Andrea Braides

in Gamma-Convergence for Beginners

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198507840
eISBN:
9780191709890
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507840.003.0013
Subject:
Mathematics, Applied Mathematics

This chapter shows that some notions used in a one-dimensional setting can be extended to higher dimensions and vector problems if properly modified. In particular, convexity requirements for lower ... More


Matching Moments and Model Reduction View

Jörg Liesen and Zdenek Strakos

in Krylov Subspace Methods: Principles and Analysis

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199655410
eISBN:
9780191744174
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199655410.003.0003
Subject:
Mathematics, Applied Mathematics, Algebra

The projected system matrix in Krylov subspace methods consists of moments of the original system matrix with respect to the initial residual(s). This hints that Krylov subspace methods can be viewed ... More


Classical groups

Adam M. Bincer

in Lie Groups and Lie Algebras: A Physicist's Perspective

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199662920
eISBN:
9780191745492
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199662920.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Classical groups consist of the orthogonal, the unitary and the symplectic groups. These groups can be defined in terms of linear transformations that leave invariant certain quadratic forms. It ... More


Lagrangian Mechanics

Jennifer Coopersmith

in The Lazy Universe: An Introduction to the Principle of Least Action

Published in print:
2017
Published Online:
June 2017
ISBN:
9780198743040
eISBN:
9780191802966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198743040.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

It is demonstrated how d’Alembert’s Principle can be used as the basis for a more general mechanics – Lagrangian Mechanics. How this leads to Hamilton’s Principle (the Principle of Least Action) is ... More


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