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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


The Devil in the Detail

Mary Orr

in Flaubert's Tentation: Remapping Nineteenth-Century French Histories of Religion and Science

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199258581
eISBN:
9780191718083
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199258581.003.0007
Subject:
Literature, World Literature, 19th-century and Victorian Literature

Devil's rides into space are a well‐worked topos in literature, but this chapter points out for the first time their literal realities in the Montgolfier balloons and Garnarin's parachute that ... More


f i v e The Universal Natural History The Purposiveness of Nature

Martin Schöneld

in The Philosophy of the Young Kant: The Precritical Project

Published in print:
2000
Published Online:
May 2006
ISBN:
9780195132182
eISBN:
9780199786336
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195132181.003.0006
Subject:
Philosophy, History of Philosophy

This chapter explores Kant’s second book, Universal Natural History and Theory of the Heavens (1755). Section 1 describes the context of the book and Kant’s critique of static and anthropocentric ... More


Harmonic Morphisms Between Riemannian Manifolds

Paul Baird and John C. Wood

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198503620
eISBN:
9780191708435
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198503620.001.0001
Subject:
Mathematics, Pure Mathematics

Harmonic morphisms are maps which preserve Laplace's equation. More explicitly, a map between Riemannian manifolds is called a harmonic morphism if its composition with any locally defined harmonic ... More


HARMONIC FUNCTIONS IN R n

Leon Ehrenpreis

in The Universality of the Radon Transform

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198509783
eISBN:
9780191709166
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509783.003.0003
Subject:
Mathematics, Mathematical Physics

This chapter looks at a variation of “harmonic function” which was introduced by Chevalley. Ordinary harmonic functions are solutions of the Laplace equation; Chevalley harmonic functions are ... More


DIFFUSION REGISTRATION

Jan Modersitzki

in Numerical Methods for Image Registration

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198528418
eISBN:
9780191713583
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528418.003.0011
Subject:
Mathematics, Applied Mathematics

A gradient-based regularization for registration is introduced, and a fast and stable implementation is developed. In contrast to the physically motivated elastic and fluid registrations, the ... More


OBJECTIVE BAYESIANISM

Jon Williamson

in Bayesian Nets and Causality: Philosophical and Computational Foundations

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198530794
eISBN:
9780191712982
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530794.003.0005
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

Objective Bayesianism imposes two norms on degrees of belief: degrees of belief should be constrained by empirical information and they should otherwise be as equivocal as possible. The origins of ... More


BEGINNING OF THE PRO-SUBJECTIVE APPROACH

Shoutir Kishore Chatterjee

in Statistical Thought: A Perspective and History

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525318
eISBN:
9780191711657
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525318.003.0007
Subject:
Mathematics, Probability / Statistics

Around the middle of the 18th century, Bayes conceived the idea of treating an unknown parameter as a subjective random variable distributed according to a prior, and inferring about it from its ... More


PRO-SUBJECTIVE APPROACH LOSES AS SAMPLING THEORY GAINS GROUND

Shoutir Kishore Chatterjee

in Statistical Thought: A Perspective and History

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525318
eISBN:
9780191711657
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525318.003.0008
Subject:
Mathematics, Probability / Statistics

In the first half of the 19th century, Laplace, Gauss, and a number of other contributors enriched statistical thought. The quest for a suitable model for the distribution of observational errors led ... More


Probability

Athol Fitzgibbons

in Keynes's Vision: A New Political Economy

Published in print:
1990
Published Online:
November 2003
ISBN:
9780198283201
eISBN:
9780191596254
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198283202.003.0002
Subject:
Economics and Finance, History of Economic Thought

Introduces Keynes's philosophy of probability, including his critiques of David Hume and Laplace, and the reason for his emphasis on non‐quantitative probabilities.


An Introduction to Newton's Scientific Method

William L. Harper

in Isaac Newton's Scientific Method: Turning Data into Evidence about Gravity and Cosmology

Published in print:
2011
Published Online:
May 2012
ISBN:
9780199570409
eISBN:
9780191728679
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199570409.003.0001
Subject:
Philosophy, History of Philosophy, Philosophy of Science

This chapter includes some historical background on Astronomy, mechanics and physical causes, as well as an overview of Newton’s background framework and his theoretical concept of a centripetal ... More


Newton's Methodology and the Practice of Science

William L. Harper

in Isaac Newton's Scientific Method: Turning Data into Evidence about Gravity and Cosmology

Published in print:
2011
Published Online:
May 2012
ISBN:
9780199570409
eISBN:
9780191728679
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199570409.003.0010
Subject:
Philosophy, History of Philosophy, Philosophy of Science

Part I. Distinctive features of Newton’s method: Successively more accurate approximations and increasing empirical support from measurements. Part II. The Mercury perihelion problem: A proposal to ... More


Mechanics and Astronomy

E. Brian Davies

in Science in the Looking Glass: What Do Scientists Really Know?

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199219186
eISBN:
9780191711695
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219186.003.0006
Subject:
Physics, History of Physics

This chapter considers two related topics. The first is the development of astronomy in the 16th and 17th centuries, culminating in Newton's publication of his laws of motion in 1687; the second ... More


Transport at electrodes

Kyösti Kontturi, Lasse Murtomäki, and José A. Manzanares

in Ionic Transport Processes: in Electrochemistry and Membrane Science

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199533817
eISBN:
9780191714825
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199533817.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter is concerned with transport in the vicinity of electrodes, and hence on the coupling between Faradaic electrode processes and mass transport. It covers transport in stationary and ... More


Science and Darwinism

Paul C. Gutjahr

in Charles Hodge: Guardian of American Orthodoxy

Published in print:
2011
Published Online:
May 2011
ISBN:
9780199740420
eISBN:
9780199894703
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199740420.003.0056
Subject:
Religion, Church History

Chapter fifty-six takes a close look at Hodge’s lifelong commitment and interest in science. As many as twenty percent of Repertory articles concerned themselves with science, and Hodge remained ... More


Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Christopher D. Sogge

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160757
eISBN:
9781400850549
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160757.001.0001
Subject:
Mathematics, Numerical Analysis

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. The book gives a proof of the sharp Weyl ... More


The Disappearance of History

C. A. J. Coady

in Testimony: A Philosophical Study

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198235514
eISBN:
9780191597220
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198235518.003.0011
Subject:
Philosophy, Metaphysics/Epistemology

The puzzle addressed in this chapter is most explicitly raised by Laplace, though foreshadowed by Locke, and is concerned with the supposed diminution in probative force of testimony that has passed ... More


Holder Estimates for Euclidean Models

Charles L. Epstein and Rafe1 Mazzeo

in Degenerate Diffusion Operators Arising in Population Biology (AM-185)

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157122
eISBN:
9781400846108
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157122.003.0008
Subject:
Mathematics, Probability / Statistics

This chapter presents the Hölder space estimates for Euclidean model problems. It first considers the homogeneous Cauchy problem and the inhomogeneous problem before defining the resolvent operator ... More


Deterministic Dynamics

Robert Alicki and Mark Fannes

in Quantum Dynamical Systems

Published in print:
2001
Published Online:
February 2010
ISBN:
9780198504009
eISBN:
9780191708503
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504009.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the basic mathematical facts concerning Schrödinger's equation with constant and time-dependent Hamiltonians: Stone's theorem on strongly continuous one-parameter groups of ... More


Transformation, convolution, and correlation

Bernhard Blümich

in NMR Imaging of Materials

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198526766
eISBN:
9780191709524
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526766.003.0004
Subject:
Physics, Condensed Matter Physics / Materials

Transformation, convolution, and correlation are used over and over again in nuclear magnetic resonance (NMR) spectroscopy and imaging in different contexts and sometimes with different meanings. The ... More


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