## 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