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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


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