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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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