## THE NONLINEAR RADON AND FOURIER TRANSFORMS

*Leon Ehrenpreis*

### in The Universality of the Radon Transform

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198509783
- eISBN:
- 9780191709166
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509783.003.0005
- Subject:
- Mathematics, Mathematical Physics

In order to deal with the nonlinear Radon transform, this chapter introduces a new type of Fourier transform: the nonlinear Fourier transform. This can be used to analyze various nonlinear Radon ... More

## Parallel Scientific Computation: A Structured Approach using BSP and MPI

*Rob H. Bisseling*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198529392
- eISBN:
- 9780191712869
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198529392.001.0001
- Subject:
- Mathematics, Applied Mathematics

This book explains the use of the bulk synchronous parallel (BSP) model and the BSPlib communication library in parallel algorithm design and parallel programming. The main topics treated in the book ... More

## Fourier transforms and convolutions

*Dennis Sherwood and Jon Cooper*

### in Crystals, X-rays and Proteins: Comprehensive Protein Crystallography

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199559046
- eISBN:
- 9780191595028
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199559046.003.0005
- Subject:
- Physics, Crystallography

This chapter revisits the essential mathematics of integral calculus and introduces the important concept of the Fourier transform, the properties of which are elegantly demonstrated by sketching the ... More

## Crystals, X-rays and Proteins: Comprehensive Protein Crystallography

*Dennis Sherwood and Jon Cooper*

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199559046
- eISBN:
- 9780191595028
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199559046.001.0001
- Subject:
- Physics, Crystallography

This book presents a complete account of the theory of the diffraction of X-rays by crystals with particular reference to the processes of determining the structures of protein molecules. The book ... More

## STRUCTURED MATRIX ANALYSIS

*D. A. Bini, G. Latouche, and B. Meini*

### in Numerical Methods for Structured Markov Chains

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198527688
- eISBN:
- 9780191713286
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527688.003.0002
- Subject:
- Mathematics, Numerical Analysis

This chapter describes structural and computational properties which are the basis of the design and analysis of fast algorithms for the numerical solution of structured Markov chains. Toeplitz ... More

## Fourier series and Fourier transforms

*Chun Wa Wong*

### in Introduction to Mathematical Physics: Methods & Concepts

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199641390
- eISBN:
- 9780191747786
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199641390.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The Fourier expansion of an arbitrary piecewise-smooth function in the finite interval —π 〈 x 〈 π as an infinite sum of terms (a 0; a n ... More

## Diffraction

*Dennis Sherwood and Jon Cooper*

### in Crystals, X-rays and Proteins: Comprehensive Protein Crystallography

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199559046
- eISBN:
- 9780191595028
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199559046.003.0006
- Subject:
- Physics, Crystallography

This chapter covers the principles of the interaction of waves with obstacles and the manner in which information on the nature of an obstacle is contained within the resulting wave forms. The ... More

## Simulating experimental data

*Reinhard B. Neder and Thomas Proffen*

### in Diffuse Scattering and Defect Structure Simulations: A cook book using the program DISCUS

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199233694
- eISBN:
- 9780191715563
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233694.003.0004
- Subject:
- Physics, Crystallography

In most cases, simulations of disordered materials are performed to understand experimental observations, in this case diffraction data. This chapter discusses the calculation of several experimental ... More

## Solving crystal structures from HRTEM images by crystallographic image processing

*Xiaodong Zou, Sven Hovmöller, and Peter Oleynikov*

### in Electron Crystallography: Electron Microscopy and Electron Diffraction

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199580200
- eISBN:
- 9780191731211
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199580200.003.0007
- Subject:
- Physics, Crystallography

A fundamentally important feature of electron crystallography is its power in solving crystal structures directly from HRTEM images, using crystallographic image processing. With the appropriate ... More

## Fourier syntheses

*William Clegg*

### in Crystal Structure Analysis: Principles and Practice

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199219469
- eISBN:
- 9780191722516
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199219469.003.0008
- Subject:
- Physics, Crystallography

A diffraction pattern is the (forward) Fourier transform of a crystal structure, obtained physically in an experiment and mathematically from a known or model structure (providing both amplitudes and ... More