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Anomalies in Quantum Field Theory

Reinhold A. Bertlmann

Published in print:
2000
Published Online:
January 2010
ISBN:
9780198507628
eISBN:
9780191706400
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507628.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The anomaly, which forms the central part of this book, is the failure of classical symmetry to survive the process of quantization and regularization. The study of anomalies is the key to a deeper ... More


Inverse Problems

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/9780198508885.003.0014
Subject:
Mathematics, Numerical Analysis

This final chapter introduces an inverse electromagnetic reconstruction problem of finding the shape of a scatterer from far field data. It focuses on the Linear Sampling Method that reduces the ... More


Well-posed hybrid systems and their properties

Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel

in Hybrid Dynamical Systems: Modeling, Stability, and Robustness

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153896
eISBN:
9781400842636
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153896.003.0006
Subject:
Mathematics, Applied Mathematics

This chapter defines nominally well-posed hybrid systems and well-posed hybrid systems to be those hybrid systems, vaguely speaking, for which graphical limits of graphically convergent sequences of ... More


Summary and Further Consequences

Philomen Probert

in Ancient Greek Accentuation: Synchronic Patterns, Frequency Effects, and Prehistory

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199279609
eISBN:
9780191707292
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199279609.003.0014
Subject:
Classical Studies, Literary Studies: Classical, Early, and Medieval

This chapter draws together results and suggests that the accentual stability of very frequent words and of words containing frequent and synchronically recognized suffixes both result from the ... More


Inverted Operations

D. Gary Miller

in Language Change and Linguistic Theory, Volume I: Approaches, Methodology, and Sound Change

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199583423
eISBN:
9780191723438
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199583423.003.0008
Subject:
Linguistics, Historical Linguistics, Theoretical Linguistics

To avoid some token of speech perceived as negative by an emulated segment of the population, speakers alter proper forms in hypercorrection, e.g. pseudocorrective replacement, inversion. Alleged ... More


Mayhem: Post-War Crime and Violence in Britain, 1748-53

Nicholas Rogers

Published in print:
2013
Published Online:
October 2013
ISBN:
9780300169621
eISBN:
9780300189063
Item type:
book
Publisher:
Yale University Press
DOI:
10.12987/yale/9780300169621.001.0001
Subject:
History, British and Irish Early Modern History

After the end of the War of Austrian Succession in 1748, thousands of unemployed, including soldiers and seamen, found themselves on the streets of London ready to roister and steal. This book ... More


REGULARIZATION OF FIELD THEORY AND CHIRAL ANOMALIES

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/9780198529132.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter illustrates the regularization of field theory by taking quantum electrodynamics (QED) as an example, showing that the mass of the photon remains at 0 even after higher-order quantum ... More


Schrödinger equation on a lattice

Efstratios Manousakis

in Practical Quantum Mechanics: Modern Tools and Applications

Published in print:
2015
Published Online:
December 2015
ISBN:
9780198749349
eISBN:
9780191813474
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198749349.003.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter begins by studying the one-dimensional time-dependent Schrödinger equation. In order to do this the chapter discretizes the spatial coordinates, and thus the differential equation ... More


Back to the Schrödinger equation on a lattice

Efstratios Manousakis

in Practical Quantum Mechanics: Modern Tools and Applications

Published in print:
2015
Published Online:
December 2015
ISBN:
9780198749349
eISBN:
9780191813474
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198749349.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter goes back to the discrete lattice in order to transform the basis to momentum eigenstates. In addition, the chapter takes the continuum limit of space and we recover known relations and ... More


Introduction

M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko

in Advances in the Casimir Effect

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199238743
eISBN:
9780191716461
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199238743.003.0001
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This introductory chapter discusses the general physical foundations of the Casimir effect as manifestation of the existence of zero-point vacuum oscillations. Connections between the Casimir force, ... More


Simple Models of the Casimir Effect

M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko

in Advances in the Casimir Effect

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199238743
eISBN:
9780191716461
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199238743.003.0002
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter discusses several basic ideas and methods related to the calculation of the Casimir energies and forces using some simple models. The simplicity of these models means that cumbersome ... More


Regularization and Renormalization of the Vacuum Energy

M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko

in Advances in the Casimir Effect

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199238743
eISBN:
9780191716461
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199238743.003.0004
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter uses the method of heat kernel expansion together with cutoff regularization to separate the divergent part of the vacuum energy. After the vacuum energy has been regularized, the ... More


Signal extraction in presence of smoothing and noise

Melvin Lax, Wei Cai, and Min Xu

in Random Processes in Physics and Finance

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.003.0015
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The problem of extracting a signal from a distorted output (that is, the solution of an inverse problem) in the presence of smoothing and noise is a ubiquitous one. It occurs in the analysis of ... More


Informal Law in Informal Settlements

Jane Matthews Glenn and Véronique Bélanger

in Law and Geography

Published in print:
2003
Published Online:
March 2012
ISBN:
9780199260744
eISBN:
9780191698675
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199260744.003.0014
Subject:
Law, Philosophy of Law

Because of the inappropriate and excessively high demands of the formal requirements associated with low-cost housing facilities in most developing countries, many of those who comprise the urban ... More


Accentual Patterns in Romance Verb Forms

Judith Meinschaefer

in Morphological Autonomy: Perspectives From Romance Inflectional Morphology

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199589982
eISBN:
9780191728884
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199589982.003.0004
Subject:
Linguistics, Syntax and Morphology, Historical Linguistics

What principles of morphology determine the locus of word stress in Spanish and Italian verb forms? It is argued that paradigmatic uniformity has played a crucial role in the evolution of verb stress ... More


Entropy Regularization

Grandvalet Yves and Bengio Yoshua

in Semi-Supervised Learning

Published in print:
2006
Published Online:
August 2013
ISBN:
9780262033589
eISBN:
9780262255899
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262033589.003.0009
Subject:
Computer Science, Machine Learning

This chapter promotes the use of entropy regularization as a means to benefit from unlabeled data in the framework of maximum a posteriori estimation. The learning criterion is derived from clearly ... More


Binary Classification under Sample Selection Bias

Hein Matthias

in Dataset Shift in Machine Learning

Published in print:
2008
Published Online:
August 2013
ISBN:
9780262170055
eISBN:
9780262255103
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262170055.003.0003
Subject:
Computer Science, Machine Learning

This chapter examines the problem of binary classification under sample selection bias from a decision-theoretic perspective. Starting from a derivation of the necessary and sufficient conditions for ... More


Multidimensional PGSE NMR

Paul T. Callaghan

in Translational Dynamics and Magnetic Resonance: Principles of Pulsed Gradient Spin Echo NMR

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199556984
eISBN:
9780191774928
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556984.003.0009
Subject:
Physics, Condensed Matter Physics / Materials, Nuclear and Plasma Physics

This chapter shows how both Fourier transformation and inverse Laplace transformation can be used in conjunction with pulsed gradient spin echo NMR, as a basis for a multidimensional ... More


Data-Dependent Regularization

Corduneanu Adrian and Jaakkola Tommi

in Semi-Supervised Learning

Published in print:
2006
Published Online:
August 2013
ISBN:
9780262033589
eISBN:
9780262255899
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262033589.003.0010
Subject:
Computer Science, Machine Learning

This chapter considers two ways of representing the topology over examples, either based on complete knowledge of the marginal density or by grouping together examples whose labels should be related. ... More


The Geometric Basis of Semi-Supervised Learning

Sindhwani Vikas, Belkin Misha, and Niyogi Partha

in Semi-Supervised Learning

Published in print:
2006
Published Online:
August 2013
ISBN:
9780262033589
eISBN:
9780262255899
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262033589.003.0012
Subject:
Computer Science, Machine Learning

This chapter presents an algorithmic framework for semi-supervised inference based on geometric properties of probability distributions. This approach brings together Laplacian-based spectral ... More


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