## NON-PARAMETRIC IMAGE 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/9780198528418.003.0008
- Subject:
- Mathematics, Applied Mathematics

This chapter introduces non-parametric registrations. The idea behind this type of registration is to come up with an appropriate measure both for the similarity as well as for the likelihood of a ... More

## Numerical Solution

*W. Otto Friesen and Jonathon A. Friesen*

### in NeuroDynamix II: Concepts of Neurophysiology Illustrated by Computer Simulations

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780195371833
- eISBN:
- 9780199865178
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195371833.003.0024
- Subject:
- Psychology, Cognitive Neuroscience

This chapter describes the method for numerical integration of the equations that underlie NeuroDynamix II models.

## Outlook

*Sergey N. Dorogovtsev*

### in Lectures on Complex Networks

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199548927
- eISBN:
- 9780191720574
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199548927.003.0015
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In this concluding section of the text, the three major milestones marking the history of the exploration of networks are indicated. These are: Leonhard Euler's work (1735), the introduction of ... More

## o n e The Vis Viva Debate Kant's Starting Point

*Martin Schönfeld*

### 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:
- 10.1093/0195132181.003.0002
- Subject:
- Philosophy, History of Philosophy

This chapter explores the context of Kant’s first and original puzzle: what actually is force? It is an account of the debate over kinetic energy (Leibniz’s “living force” or vis viva) and the ... More

## s e v e n The Physical Monadology and theElements 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:
- 10.1093/0195132181.003.0008
- Subject:
- Philosophy, History of Philosophy

This chapter explores Kant’s professorial thesis, The Joint Use of Metaphysics and Geometry in Natural Philosophy, the First Example of Which Contains the Physical Monadology (1756). Section 1 ... More

## n i n e The Newtonian Program of thePrize Essay and Kant's Crisis The Struggle for Freedom

*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:
- 10.1093/0195132181.003.0010
- Subject:
- Philosophy, History of Philosophy

This chapter explores the aftermath of Only Possible Argument and the Prize Essay (1764). Section 1 examines the curious preface of Kant’s third book, the exchange with Mendelssohn, and Kant’s ... More

## Catalan Numbers with Applications

*Thomas Koshy*

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

Fibonacci and Lucas sequences are “two shining stars in the vast array of integer sequences,” and because of their ubiquitousness, tendency to appear in quite unexpected and unrelated places, ... More

## HYPERBOLIC CONSERVATION LAWS

*George Em Karniadakis and Spencer J. Sherwin*

### in Spectral/hp Element Methods for Computational Fluid Dynamics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198528692
- eISBN:
- 9780191713491
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528692.003.0010
- Subject:
- Mathematics, Numerical Analysis

This chapter discusses compressible Euler and Navier-Stokes equations as well as general hyperbolic conservation laws. The principle issue is how effectively to use the high-order expansions of the ... More

## RADON TRANSFORM AS THE INTERRELATION OF GEOMETRY AND ANALYSIS

*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/9780198509783.003.0008
- Subject:
- Mathematics, Mathematical Physics

This chapter deals with various questions which are related to the Radon transform, for example, the analog for forms, Selberg's trace formula. It gives a sharpening of the classical Euler-Maclaurin ... More

## THE MATHEMATICAL SETTING

*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/9780198528418.003.0003
- Subject:
- Mathematics, Applied Mathematics

The basic mathematical notation is introduced, including formal definitions of images and digital images, midpoint and meshpoint grids. Local and global interpolation techniques such as ... More

## ELASTIC 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/9780198528418.003.0009
- Subject:
- Mathematics, Applied Mathematics

This chapter introduces elastic registration using the general framework introduced in Chapter 8. A physical motivation for this particular regularizer is given. The two images are viewed as two ... More

## Partial differential equations for fluids

*Bijan Mohammadi and Olivier Pironneau*

### in Applied Shape Optimization for Fluids

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199546909
- eISBN:
- 9780191720482
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546909.003.0003
- Subject:
- Mathematics, Mathematical Physics

This chapter describes the governing equations considered throughout the book. The equations of fluid dynamics are recalled, together with the k-epsilon turbulence model, which is used later on for ... More

## Relativistic Fluids

*Yvonne Choquet-Bruhat*

### in General Relativity and the Einstein Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0009
- Subject:
- Mathematics, Applied Mathematics

This chapter presents general properties of perfect fluids. When appropriate definitions are given, some of these properties generalize well-known properties of non-relativistic perfect fluids. ... More

## Introduction: From Pipeline Economics to Computational Economics

*Ramon Marimon and Andrew Scott*

### in Computational Methods for the Study of Dynamic Economies

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199248278
- eISBN:
- 9780191596605
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199248273.003.0001
- Subject:
- Economics and Finance, Macro- and Monetary Economics

Starts by looking at the advances in macroeconomics that have been made since A. W. Phillips's 1958 Economica paper and his physical economic model (made of piping and valves) designed to teach ... More

## RELATIVISTIC HYDRODYNAMICS

*Miguel Alcubierre*

### in Introduction to 3+1 Numerical Relativity

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199205677
- eISBN:
- 9780191709371
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199205677.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the derivation of dynamical equations governing the motion of a perfect fluid, known as the Euler equations, both in the special and general relativistic cases. It considers ... More

## The Fortunes of a Mechanical Model for Natural Philosophy

*Stephen Gaukroger*

### in The Collapse of Mechanism and the Rise of Sensibility: Science and the Shaping of Modernity, 1680-1760

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199594931
- eISBN:
- 9780191595745
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199594931.003.0009
- Subject:
- Philosophy, Philosophy of Science, General

The basic assumption of ‘rational mechanics’ was that all natural philosophy was mechanics, and that, as mechanics was pursued with greater and greater detail and sophistication, the rest of natural ... More

## Fluid Dynamics: Part 1: Classical Fluid Dynamics

*Anatoly I. Ruban and Jitesh S. B. Gajjar*

- Published in print:
- 2014
- Published Online:
- August 2014
- ISBN:
- 9780199681730
- eISBN:
- 9780191761607
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199681730.001.0001
- Subject:
- Physics, Soft Matter / Biological Physics

This book, the first of a four-part series on fluid dynamics, consists of four chapters on classical theory suitable for an introductory undergraduate course. Chapter 1 discusses the continuum ... More

## The rigid body

*S. G. Rajeev*

### in Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199670857
- eISBN:
- 9780191775154
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670857.003.0005
- Subject:
- Physics, Atomic, Laser, and Optical Physics

In this chapter, the moment of inertia is defined and Euler's equations for the rigid body are derived. They can be solved in terms of Jacobi elliptic functions.

## Hamilton–Jacobi theory

*S. G. Rajeev*

### in Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199670857
- eISBN:
- 9780191775154
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670857.003.0009
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter derives the Hamilton-Jacobi equation. Euler's two centre problem is solved by using separation of variables in the elliptical co-ordinate system. The connection to the eikonal equation ... More

## The Consequences of Extensivity

*Robert H. Swendsen*

### in An Introduction to Statistical Mechanics and Thermodynamics

- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199646944
- eISBN:
- 9780191775123
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199646944.003.0013
- Subject:
- Physics, Condensed Matter Physics / Materials

Although extensivity is not an essential property of thermodynamic systems, it is a very useful concept for analysing the properties of materials when we can ignore surface and boundary effects. This ... More