## System Control and Rough Paths

*Terry Lyons and Zhongmin Qian*

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198506485
- eISBN:
- 9780191709395
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506485.001.0001
- Subject:
- Mathematics, Probability / Statistics

Systems evolve and interact, and when they do this in a continuous way, differential equations can be used to provide accurate mathematical models for the interaction or reaction of the controlled ... More

## *AN INTRODUCTION TO THE LOCALIZATION METHOD OF Γ-CONVERGENCE

*Andrea Braides*

### in Gamma-Convergence for Beginners

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198507840
- eISBN:
- 9780191709890
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507840.003.0017
- Subject:
- Mathematics, Applied Mathematics

This chapter provides an introduction to the localization method of Gamma-convergence. It presents a brief account of the localization methods of Gamma-convergence that allows for the proof of ... More

## Path Integrals and Quantum Anomalies

*Kazuo Fujikawa and Hiroshi Suzuki*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198529132
- eISBN:
- 9780191712821
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198529132.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This book provides an introduction to the path integral formulation of quantum field theory and its applications to the analyses of symmetry breaking by the quantization procedure. This symmetry ... More

## The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

*Helmut Hofmann*

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.001.0001
- Subject:
- Physics, Nuclear and Plasma Physics

This book offers a survey of nuclear physics at low energies and discusses similarities to mesoscopic systems. It addresses systems at finite excitations of the internal degrees of freedom where ... More

## Formal means

*Helmut Hofmann*

### in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.003.0026
- Subject:
- Physics, Nuclear and Plasma Physics

This chapter elucidates various mathematical formulas. Based on expressions for Gaussian integrals in one and many dimensions, the methods of stationary phase and steepest descent are deduced, ... More

## CONCLUDING REMARKS

*Kazuo Fujikawa and Hiroshi Suzuki*

### in Path Integrals and Quantum Anomalies

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198529132
- eISBN:
- 9780191712821
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198529132.003.0011
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter considers a possible intuitive explanation of quantum breaking of symmetries as well as the subjects which are not discussed in the main chapters, such as the descent formula for gauge ... More

## Integral Pluralism: Beyond Culture Wars

*Fred Dallmayr*

- Published in print:
- 2010
- Published Online:
- September 2011
- ISBN:
- 9780813125718
- eISBN:
- 9780813135397
- Item type:
- book

- Publisher:
- University Press of Kentucky
- DOI:
- 10.5810/kentucky/9780813125718.001.0001
- Subject:
- Political Science, International Relations and Politics

In addition to war, terrorism, and unchecked military violence, modernity is also subject to less visible but no less venomous conflicts. Global in nature, these “culture wars” exacerbate the ... More

## INTEGRAL PROBLEMS

*Andrea Braides*

### in Gamma-Convergence for Beginners

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198507840
- eISBN:
- 9780191709890
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507840.003.0003
- Subject:
- Mathematics, Applied Mathematics

This chapter deals with integral problems. Using examples, it illustrates the need to use weak topologies to obtain compactness and coerciveness conditions. The sufficiency and necessity of the ... More

## Contentious Politics in Western Europe and the United States

*Sidney Tarrow*

### in Governing Europe

- Published in print:
- 2003
- Published Online:
- November 2003
- ISBN:
- 9780199250158
- eISBN:
- 9780191599439
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199250154.003.0014
- Subject:
- Political Science, European Union

The first part of this chapter examines the four main types of political contention outlined in the introduction to it: expressive contention, reformist contention, integral contention and communal ... More

## Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

*Xiao-Gang Wen*

- Published in print:
- 2007
- Published Online:
- February 2010
- ISBN:
- 9780199227259
- eISBN:
- 9780191713019
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227259.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been an emergence of a new ... More

## Path Integrals in Quantum Mechanics

*Jean Zinn-Justin*

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals. They share the algebraic properties of ... More

## Integral principles

*JESPER LÜTZEN*

### in Mechanistic Images in Geometric Form: Heinrich Hertz's 'Principles of Mechanics'

- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567370
- eISBN:
- 9780191717925
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567370.003.0021
- Subject:
- Physics, History of Physics

In his book Principles of Mechanics, Heinrich Hertz treats integral principles in three parts. First, he discusses the properties of geodesics and their relation to straightest paths in a purely ... More

## Two-Dimensional Granular Gases

*Nikolai V. Brilliantov and Thorsten Pöschel*

### in Kinetic Theory of Granular Gases

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198530381
- eISBN:
- 9780191713057
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530381.003.0016
- Subject:
- Physics, Condensed Matter Physics / Materials

It has been shown for molecular fluids that the velocity-time correlation function in ddimensions exhibits a power-law dependence for t >> 1. This function reveals a long time tail compared with an ... More

## Integration

*James Davidson*

### in Stochastic Limit Theory: An Introduction for Econometricians

- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198774037
- eISBN:
- 9780191596117
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774036.003.0004
- Subject:
- Economics and Finance, Econometrics

The concept of an abstract integral is developed from first principles. Riemann‐Stieltjes and Lebesgue‐Stieltjes integrals are defined. The monotone convergence theorem, fundamental properties of ... More

## Kirchhoff‐Type Formulas and Integral Equations in Green–Lindsay Theory

*Józef Ignaczak and Martin Ostoja‐Starzewski*

### in Thermoelasticity with Finite Wave Speeds

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199541645
- eISBN:
- 9780191716164
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199541645.003.0008
- Subject:
- Mathematics, Applied Mathematics, Mathematical Physics

This chapter begins with a demonstration how one can obtain the Kirchhoff type integral representation of the fundamental solutions for the G‐L theory in a 3‐D bounded region. These representations ... 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

## Scattering by a Buried Object

*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/9780198508885.003.0012
- Subject:
- Mathematics, Numerical Analysis

This chapter presents a model problem for scattering by a buried object. The ground is modeled by a two-layered medium (the air and the earth) with a planar interface. For the two-layered medium, it ... 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

## INTRODUCTION

*Terry Lyons and Zhongmin Qian*

### in System Control and Rough Paths

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198506485
- eISBN:
- 9780191709395
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506485.003.0001
- Subject:
- Mathematics, Probability / Statistics

The concept of a differential equation controlled by a rough path can be motivated by quite simple examples. One such example is a linear system driven by two-dimensional noise. This example is ... More

## ROUGH PATHS

*Terry Lyons and Zhongmin Qian*

### in System Control and Rough Paths

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198506485
- eISBN:
- 9780191709395
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506485.003.0003
- Subject:
- Mathematics, Probability / Statistics

This chapter defines rough paths. If the path has good smoothness properties, then its chords (the Abelian version of the description) provide an adequate description and can be used to predict its ... More