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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


Postprocessing

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter explains how to write a postprocessing code, and more specifically how to study the nonlinear simulations using computer graphics and analysis. It first considers how to compute and ... 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


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


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