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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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