## 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

## 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

## 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.

## 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