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The simplest cases: Dirichlet and Neumann boundary conditions

Andreas Kirsch and Natalia Grinberg

in The Factorization Method for Inverse Problems

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.003.0001
Subject:
Mathematics, Applied Mathematics

After a short derivation of the Helmholtz equation in acoustics this chapter formulates the direct scattering problem and presents results on uniqueness and existence without proofs (but gives ... More


Classical Scattering Theory

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0009
Subject:
Mathematics, Numerical Analysis

This chapter presents basic tools for studying the scattering problem. The Stratton-Chu integral representation of the electromagnetic field is derived as well as the far field pattern of the ... More


Generalized Computational Systems

Marco Giunti

in Computation, Dynamics, and Cognition

Published in print:
1997
Published Online:
November 2020
ISBN:
9780195090093
eISBN:
9780197560600
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195090093.003.0006
Subject:
Computer Science, Mathematical Theory of Computation

The definition of a computational system that I proposed in chapter 1 (definition 3) employs the concept of Turing computability. In this chapter, however, I will show ... More


The character of the fieldscape

Stephen Rippon

in Making Sense of an Historic Landscape

Published in print:
2012
Published Online:
March 2015
ISBN:
9780199533787
eISBN:
9780191804366
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:osobl/9780199533787.003.0006
Subject:
History, Ancient History / Archaeology

This chapter presents a characterization of the field-boundary patterns based on an analysis of the Ordnance Survey First Edition Six Inch maps. It discusses historic landscape character types ... More


Mathematical Dynamical Systems and Computational Systems

Marco Giunti

in Title Pages

Published in print:
1997
Published Online:
November 2020
ISBN:
9780195090093
eISBN:
9780197560600
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195090093.003.0005
Subject:
Computer Science, Mathematical Theory of Computation

The main thesis of this chapter is that a dynamical viewpoint allows us to better understand some important foundational issues of computation theory. Effective procedures are traditionally studied ... More


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