## Reading between the lines: John Wallis's Arithmetica infinitorum

*Jacqueline A. Stedall*

### in A Discourse Concerning Algebra: English Algebra to 1685

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198524953
- eISBN:
- 9780191711886
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198524953.003.0006
- Subject:
- Mathematics, History of Mathematics

At the beginning of his mathematical career, John Wallis embarked on the work that was to be published in 1656 as the Arithmetica infinitorum. The book was his masterpiece and over the following ten ... More

## Discrete State‐Space Methods for the Study of Dynamic Economies

*Craig Burnside*

### 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:
- 10.1093/0199248273.003.0005
- Subject:
- Economics and Finance, Macro- and Monetary Economics

A number of numerical methods are discussed for solving dynamic stochastic general equilibrium models that fall within the common category of discrete state‐space methods. These methods can be ... More

## Quantum tomography

*J. C. Garrison and R. Y. Chiao*

### in Quantum Optics

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198508861
- eISBN:
- 9780191708640
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508861.003.0018
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter begins with a review of classical tomography, which reconstructs hidden structures inside an object by successive transmissions of an X-ray beam at different angles and lateral ... More

## Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

*Klaus Boehmer*

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577040
- eISBN:
- 9780191595172
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577040.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, and create an exciting interplay. Other books discuss nonlinearity by a very few important ... More

## Basic Theory

*Walter Gautschi*

### in Title Pages

- Published in print:
- 2004
- Published Online:
- November 2020
- ISBN:
- 9780198506720
- eISBN:
- 9780191916571
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198506720.003.0003
- Subject:
- Computer Science, Mathematical Theory of Computation

This introductory chapter is to present a quick review of material on orthogonal polynomials that is particularly relevant to computation. Proofs of most results are ... More

## Nonconforming finite element methods

*Klaus Böhmer*

### in Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577040
- eISBN:
- 9780191595172
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577040.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Nonconforming FEMs avoid the strong restrictions of conforming FEMs. So discontinuous ansatz and test functions, approximate test integrals, and strong forms are admitted. This allows the proof of ... More

## Heterogeneous Logic

*Jon Barwise and John Etchemendy*

### in Logical Reasoning with Diagrams

- Published in print:
- 1996
- Published Online:
- November 2020
- ISBN:
- 9780195104271
- eISBN:
- 9780197560983
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195104271.003.0014
- Subject:
- Computer Science, Computer Architecture and Logic Design

A major concern to the founders of modern logic—Frege, Peirce, Russell, and Hilbert—was to give an account of the logical structure of valid reasoning. ... More

## Radiative Transfer in a Scattering Atmosphere

*R. M. Goody and Y. L. Yung*

### in Atmospheric Radiation: Theoretical Basis

- Published in print:
- 1989
- Published Online:
- November 2020
- ISBN:
- 9780195051346
- eISBN:
- 9780197560976
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195051346.003.0010
- Subject:
- Earth Sciences and Geography, Atmospheric Sciences

The source function for scattering, (2.32), is more complicated than a thermal source function on two accounts: it is not a function of local conditions alone, but ... More

## The Hamilton–Jacobi equation

*Gleb L. Kotkin and Valeriy G. Serbo*

### in Exploring Classical Mechanics: A Collection of 350+ Solved Problems for Students, Lecturers, and Researchers - Second Revised and Enlarged English Edition

- Published in print:
- 2020
- Published Online:
- October 2020
- ISBN:
- 9780198853787
- eISBN:
- 9780191888236
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198853787.003.0012
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter discusses the motion of particles which are scattered by and fall towards the center of the dipol, the motion of a particle in the Coulomb and the constant electric fields, and a ... More

## Random Processes and Fields

*Ilya Polyak*

### in Computational Statistics in Climatology

- Published in print:
- 1996
- Published Online:
- November 2020
- ISBN:
- 9780195099997
- eISBN:
- 9780197560938
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195099997.003.0005
- Subject:
- Computer Science, Mathematical Theory of Computation

In this chapter, the nonparametric methods of estimating the spectra and correlation functions of stationary processes and homogeneous fields are considered. It is ... More

## Signal Recovery

*Robert J Marks II*

### in Handbook of Fourier Analysis & Its Applications

- Published in print:
- 2009
- Published Online:
- November 2020
- ISBN:
- 9780195335927
- eISBN:
- 9780197562567
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195335927.003.0015
- Subject:
- Computer Science, Mathematical Theory of Computation

The literature on the recovery of signals and images is vast (e.g., [23, 110, 112, 257, 391, 439, 791, 795, 933, 934, 937, 945, 956, 1104, 1324, 1494, 1495, 1551]). In ... More

## Operational Constraints in Diagrammatic Reasoning

*Atsushi Shimojima*

### in Logical Reasoning with Diagrams

- Published in print:
- 1996
- Published Online:
- November 2020
- ISBN:
- 9780195104271
- eISBN:
- 9780197560983
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195104271.003.0006
- Subject:
- Computer Science, Computer Architecture and Logic Design

Diagrammatic reasoning is reasoning whose task is partially taken over by operations on diagrams. It consists of two kinds of activities: (i) physical ... More

## Theory of Radiative Transfer

*R. M. Goody and Y. L. Yung*

### in Atmospheric Radiation: Theoretical Basis

- Published in print:
- 1989
- Published Online:
- November 2020
- ISBN:
- 9780195051346
- eISBN:
- 9780197560976
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195051346.003.0004
- Subject:
- Earth Sciences and Geography, Atmospheric Sciences

In common with astrophysical usage the word intensity will denote specific intensity of radiation, i.e., the flux of energy in a given direction per second per unit ... More

## Matching Moments and Model Reduction View

*Jörg Liesen and Zdenek Strakos*

### in Krylov Subspace Methods: Principles and Analysis

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199655410
- eISBN:
- 9780191744174
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199655410.003.0003
- Subject:
- Mathematics, Applied Mathematics, Algebra

The projected system matrix in Krylov subspace methods consists of moments of the original system matrix with respect to the initial residual(s). This hints that Krylov subspace methods can be viewed ... More

## Hidden New Analysis

*Niccolò Guicciardini*

### in Isaac Newton on Mathematical Certainty and Method

- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262013178
- eISBN:
- 9780262258869
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262013178.003.0012
- Subject:
- History, History of Science, Technology, and Medicine

This chapter presents proof that Newton developed advanced quadrature techniques, and also examines Corollary 3, Proposition 41, Book 1; and Corollary 2, Proposition 91, Book 1, of his Principia. In ... More

## Forms of Expression

### in The Good Life in the Scientific Revolution: Descartes, Pascal, Leibniz, and the Cultivation of Virtue

- Published in print:
- 2006
- Published Online:
- March 2013
- ISBN:
- 9780226409542
- eISBN:
- 9780226409566
- Item type:
- chapter

- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226409566.003.0006
- Subject:
- History, History of Science, Technology, and Medicine

This chapter considers how Leibniz came to maintain that symbolic expression could constitute legitimate knowledge. It discusses how he produced his quadrature of the circle, the terms in which he ... More

## Charting Wakean Territory

*Ciaran McMorran*

### in Joyce and Geometry

- Published in print:
- 2020
- Published Online:
- September 2020
- ISBN:
- 9780813066288
- eISBN:
- 9780813065267
- Item type:
- chapter

- Publisher:
- University Press of Florida
- DOI:
- 10.5744/florida/9780813066288.003.0005
- Subject:
- Literature, 20th-century Literature and Modernism

This chapter explores how geometry is presented as a language for describing both visual and nonvisual spaces in Finnegans Wake. It demonstrates how the Wake’s Protean visual landscape is shaped by ... More

## Computer-Aided Chemistry

*Mark Ladd*

### in Bonding, Structure and Solid-State Chemistry

- Published in print:
- 2016
- Published Online:
- May 2016
- ISBN:
- 9780198729945
- eISBN:
- 9780191818783
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198729945.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter introduces the various programs that have been devised to accompany the text, using both Python and Fortran programs, some of which are interactive. The topics that are programmed and ... More

## The Hermite–Gauss Route to LBE

*Sauro Succi*

### in The Lattice Boltzmann Equation: For Complex States of Flowing Matter

- Published in print:
- 2018
- Published Online:
- June 2018
- ISBN:
- 9780199592357
- eISBN:
- 9780191847967
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199592357.003.0015
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

This chapter describes the side-up approach to Lattice Boltzmann, namely the formal derivation from the continuum Boltzmann-(BGK) equation via Hermite projection and subsequent evaluation of the ... More

## The Hamilton–Jacobi equation

*Gleb L. Kotkin and Valeriy G. Serbo*

### in Exploring Classical Mechanics: A Collection of 350+ Solved Problems for Students, Lecturers, and Researchers - Second Revised and Enlarged English Edition

- Published in print:
- 2020
- Published Online:
- October 2020
- ISBN:
- 9780198853787
- eISBN:
- 9780191888236
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198853787.003.0025
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter discusses the motion of particles which are scattered by and fall towards the center of the dipol, the motion of a particle in the Coulomb and the constant electric fields, and a ... More