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Fourier analysis in diffraction and image formation

Christopher Hammond

in The Basics of Crystallography and Diffraction

Published in print:
2015
Published Online:
August 2015
ISBN:
9780198738671
eISBN:
9780191801938
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198738671.003.0013
Subject:
Physics, Crystallography: Physics, Condensed Matter Physics / Materials

This chapter starts with the Fourier series and Fourier transforms, and the representation of periodic functions. It then looks at Fourier analysis in crystallography. It details electron density, ... More


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)

Bas Edixhoven and Jean-Marc Couveignes (eds)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691142012
eISBN:
9781400839001
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142012.001.0001
Subject:
Mathematics, Number Theory

Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's ... More


Electron-density maps

David Blow

in Outline of Crystallography for Biologists

Published in print:
2002
Published Online:
November 2020
ISBN:
9780198510512
eISBN:
9780191919244
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198510512.003.0016
Subject:
Chemistry, Crystallography: Chemistry

When everything has been done to make the phases as good as possible, the time has come to examine the image of the structure in the form of an ... More


Capabilities and Merits of Long-term Bio-optical Moorings

John Marra

in Ocean Optics

Published in print:
1994
Published Online:
November 2020
ISBN:
9780195068436
eISBN:
9780197560235
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195068436.003.0014
Subject:
Earth Sciences and Geography, Oceanography and Hydrology

There are primarily three ways in which the ocean can be sampled. First, depth profiles of water properties can be collected. The sampling resolution for depth ... More


Digital Filters

Ilya Polyak

in Title Pages

Published in print:
1996
Published Online:
November 2020
ISBN:
9780195099997
eISBN:
9780197560938
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195099997.003.0003
Subject:
Computer Science, Mathematical Theory of Computation

In this chapter, several systems of digital filters are presented. The first system consists of regressive smoothing filters, which are a direct consequence of the ... More


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