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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


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