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Tensors in special relativity

Ta-Pei Cheng

in Relativity, Gravitation and Cosmology: A Basic Introduction

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199573639
eISBN:
9780191722448
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573639.003.0012
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Tensors in a general coordinate system are introduced. When a tensor is expanded in terms of a set of basis (or inverse basis) vectors, the coefficients of expansion are its contravariant (or ... More


Coordinate systems in crystallography

Paolo G. Radaelli

in Symmetry in Crystallography: Understanding the International Tables

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199550654
eISBN:
9780191775093
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199550654.003.0004
Subject:
Physics, Crystallography, Condensed Matter Physics / Materials

This chapter describes the coordinate system for defining the position of atoms and molecules (or more generically, ‘features’ in the symmetric patterns). The description is underpinned by the ... More


Type A Weyl Group Multiple Dirichlet Series

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter describes Type A Weyl group multiple Dirichlet series. It begins by defining the basic shape of the class of Weyl group multiple Dirichlet series. To do so, the following parameters are ... More


Basics of crystallography, part 1

Ulrich Müller

in Symmetry Relationships between Crystal Structures: Applications of Crystallographic Group Theory in Crystal Chemistry

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199669950
eISBN:
9780191775086
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199669950.003.0002
Subject:
Physics, Crystallography, Condensed Matter Physics / Materials

A crystal can be considered to be a finite section from an infinite ideal crystal (a crystal pattern). This is an infinite periodic, three-dimensional array of atoms. A shift by a translation vector ... More


Symmetry and reflection conditions in reciprocal space

Paolo G. Radaelli

in Symmetry in Crystallography: Understanding the International Tables

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199550654
eISBN:
9780191775093
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199550654.003.0011
Subject:
Physics, Crystallography, Condensed Matter Physics / Materials

This chapter focuses on symmetry in reciprocal space. It reviews the definitions of reciprocal space and dual (reciprocal) basis vectors (from Chapter 6), and presents the new concept of the ... More


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