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The Factorization Method for Inverse Problems

Andreas Kirsch and Natalia Grinberg

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.001.0001
Subject:
Mathematics, Applied Mathematics

This book is devoted to problems of shape identification in the context of (inverse) scattering problems and problems of impedance tomography. In contrast to traditional methods which are based on ... More


Numerical Methods for Structured Markov Chains

Dario A. Bini, Guy Latouche, and Beatrice Meini

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.001.0001
Subject:
Mathematics, Numerical Analysis

The book deals with the numerical solution of structured Markov chains which include M/G/1 and G/M/1-type Markov chains, QBD processes, non-skip-free queues, and tree-like stochastic processes and ... More


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


The factorization method for other types of inverse obstacle scattering problems

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/9780199213535.003.0002
Subject:
Mathematics, Applied Mathematics

This chapter studies some examples of inverse scattering problems in which the data operator fails to be normal. The impedance boundary condition, the reconstruction from limited-angle data, and the ... More


The mixed boundary value problem

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/9780199213535.003.0003
Subject:
Mathematics, Applied Mathematics

For the mixed boundary value problem, the scattering domain D consists of several components with different types of boundary conditions. The chapter begins by reviewing results on uniqueness and ... More


The MUSIC algorithm and scattering by an inhomogeneous medium

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/9780199213535.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter examines the case of a penetrable scatterer with an index of refraction that can be space-dependent and is assumed to be different from the constant background index. The inverse ... More


The factorization method in impedance tomography

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/9780199213535.003.0006
Subject:
Mathematics, Applied Mathematics

This chapter examines the classical problem of impedance tomography. The corresponding direct problem is a boundary value problem for a simple elliptic differential equation of second order in ... More


Dynamics and Interdependence

David F. Hendry

in Dynamic Econometrics

Published in print:
1995
Published Online:
November 2003
ISBN:
9780198283164
eISBN:
9780191596384
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198283164.003.0004
Subject:
Economics and Finance, Econometrics

When two time series are integrated but not causally related, conventional tests reject up to 80% under the null, at a 5% nominal level. This ‘nonsense regressions’ phenomenon is analysed, and ... More


PRODUCTS AND RETRACTS

Pavol Hell and Jaroslav Nešetřil

in Graphs and Homomorphisms

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528173
eISBN:
9780191713644
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528173.003.0002
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter focuses on certain basic constructions that occur frequently in the rest of the book, emphasizing the product and the retract, but also considering other constructs. These include the ... More


Harmonic morphisms from compact 3-manifolds

Paul Baird and John C. Wood

in Harmonic Morphisms Between Riemannian Manifolds

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198503620
eISBN:
9780191708435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198503620.003.0010
Subject:
Mathematics, Pure Mathematics

This chapter shows that a non-constant harmonic morphism with compact fibres from a 3-manifold endows it with the structure of a Seifert fibre space — a 3-manifold with a certain type of ... More


Harmonic morphisms with one-dimensional fibres

Paul Baird and John C. Wood

in Harmonic Morphisms Between Riemannian Manifolds

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198503620
eISBN:
9780191708435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198503620.003.0012
Subject:
Mathematics, Pure Mathematics

This chapter shows that a harmonic morphism from a manifold of dimension n+1 to a manifold of dimension n is, locally or globally, a principal bundle with a certain metric. When n = 3, in a ... More


Decomposing Muscle Activity in Motor TasksMethods and Interpretation

Lena H. Ting and Stacie A. Chvatal

in Motor Control: Theories, Experiments, and Applications

Published in print:
2010
Published Online:
January 2011
ISBN:
9780195395273
eISBN:
9780199863518
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195395273.003.0005
Subject:
Neuroscience, Sensory and Motor Systems

This chapter examines methodologies for dimensional analysis and linear decomposition of multivariate data sets, and discusses their implicit hypotheses and interpretations for muscle coordination of ... More


MATRIX EQUATIONS AND CANONICAL FACTORIZATIONS

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/9780198527688.003.0003
Subject:
Mathematics, Numerical Analysis

This chapter is concerned with infinite block Toeplitz matrices, their relationships with matrix power series and matrix Laurent power series, and the fundamental problem of solving matrix equations ... More


M/G/1-TYPE MARKOV CHAINS

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/9780198527688.003.0004
Subject:
Mathematics, Numerical Analysis

This chapter is devoted to the theoretical analysis of M/G/1-type Markov chains. Conditions for the ergodicity are given in terms of the drift. The reduction to solving a nonlinear matrix equation is ... More


Econometric Concepts

David F. Hendry

in Dynamic Econometrics

Published in print:
1995
Published Online:
November 2003
ISBN:
9780198283164
eISBN:
9780191596384
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198283164.003.0002
Subject:
Economics and Finance, Econometrics

The main concepts for empirical modelling of economic time series are explained: parameter and parameter space; constancy; structure; distributional shape; identification and observational ... More


The Theory of Reduction

David F. Hendry

in Dynamic Econometrics

Published in print:
1995
Published Online:
November 2003
ISBN:
9780198283164
eISBN:
9780191596384
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198283164.003.0009
Subject:
Economics and Finance, Econometrics

Twelve stages of reduction are delineated from the actions of agents in an economy to an econometric model. The actual measurement process induces the DGP, followed by data transformations and ... More


Totally Nonnegative Matrices

Shaun M. Fallat and Charles R. Johnson

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691121574
eISBN:
9781400839018
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691121574.001.0001
Subject:
Mathematics, Applied Mathematics

Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, ... More


Quantum algorithms

Vlatko Vedral

in Introduction to Quantum Information Science

Published in print:
2006
Published Online:
January 2010
ISBN:
9780199215706
eISBN:
9780191706783
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199215706.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

As computers get faster and faster, the size of the circuitry imprinted onto silicon chips decreases. The size of the circuitry becomes so small that its behavior is governed by the laws of quantum ... More


Hadron induced DIS

Robin Devenish and Amanda Cooper-Sarkar

in Deep Inelastic Scattering

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198506713
eISBN:
9780191709562
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506713.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter concentrates on those areas of hard scattering in hadron-hadron interactions which are important for the determination of PDFs, or which complement lepton-induced DIS. Because of the ... More


QCD and formal methods

Robin Devenish and Amanda Cooper-Sarkar

in Deep Inelastic Scattering

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198506713
eISBN:
9780191709562
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506713.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter begins with a brief introduction to quantum chromodynamics (QCD), highlighting the similarities and differences with quantum electrodynamics (QED). QCD gives a non-linear force that ... More


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