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Root selection and dynamical systems

Christopher G. Small and Jinfang Wang

in Numerical Methods for Nonlinear Estimating Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506881
eISBN:
9780191709258
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506881.003.0007
Subject:
Mathematics, Probability / Statistics

This chapter explores the relationship between the numerical methods described in earlier chapters and the theory of dynamical systems. An estimating function defines a dynamical estimating system, ... More


A Survey of Supervaluational and Revision‐Rule Theories

Hartry Field

in Saving Truth From Paradox

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199230747
eISBN:
9780191710933
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230747.003.0012
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter begins by mentioning some weaknesses in the supervaluationist theory of the previous chapter, especially regarding compositional principles. Some of the weaknesses can be improved upon ... More


Fixed Points and Revision Rules for Conditionals

Hartry Field

in Saving Truth From Paradox

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199230747
eISBN:
9780191710933
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230747.003.0017
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter looks at two ways of meeting the goal of naïvety. Yablo's is technically simpler, but involves extreme failures of intersubstitutivity of logical truths within conditionals. The ... More


 Keeping Your Balance

Ken Binmore

in Playing for Real: Game Theory

Published in print:
2007
Published Online:
May 2007
ISBN:
9780195300574
eISBN:
9780199783748
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195300574.003.0008
Subject:
Economics and Finance, Microeconomics

This chapter focuses on the existence of Nash equilibria. The existence problem is first introduced with pure-strategy reaction curves for Noisy and Silent Duel. A proof of John Nash's existence ... More


Keeping the Fixed Points Fixed: Narrative: What to Do When Water Refuses to Boil at the Boiling Point

Hasok Chang

in Inventing Temperature: Measurement and Scientific Progress

Published in print:
2004
Published Online:
January 2005
ISBN:
9780195171273
eISBN:
9780199835003
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195171276.003.0001
Subject:
Philosophy, Philosophy of Science

This chapter draws attention to the challenges faced by the early scientists in establishing the fixed points of thermometry such as the boiling and freezing points of water. It provides a historical ... More


Dynamics in State Space: One and Two Dimensions

Robert C. Hilborn

in Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

Published in print:
2000
Published Online:
January 2010
ISBN:
9780198507239
eISBN:
9780191709340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507239.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The description of nonlinear behaviour using state space techniques is introduced in this chapter by examining systems with one or two dynamical variables, that is, the state spaces have one or two ... More


Kripke's Theory of Truth (Strong Kleene Version)

Hartry Field

in Saving Truth From Paradox

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199230747
eISBN:
9780191710933
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230747.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter is an exposition of the strong Kleene version of Kripke's fixed point semantics, and the theories of truth that can be obtained from it. Emphasis is put on the distinction between ... More


AUTOMORPHISMS OF RECURSIVELY SATURATED MODELS

Roman Kossak and James H. Schmerl

in The Structure of Models of Peano Arithmetic

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568278
eISBN:
9780191718199
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568278.003.0008
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter develops the basic theory of automorphisms of countable recursively saturated models of PA. The key results are: Smoryìnski's characterization of exponentially closed cuts, the Moving ... More


Foundations of the Mode-Coupling Theory for the Evolution of Glassy Dynamics in Liquids

Wolfgang Götze

in Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199235346
eISBN:
9780191715600
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235346.003.0004
Subject:
Physics, Condensed Matter Physics / Materials

In this chapter, mode-coupling equations of motion for a correlation-function description of the dynamics of simple liquids and colloids are derived and their mathematical properties are analysed. ... More


Introduction to Supervaluational Approaches to Paradox

Hartry Field

in Saving Truth From Paradox

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199230747
eISBN:
9780191710933
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230747.003.0011
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter examines the simplest supervaluationist fixed points, and the ‘internal’ fixed-point theories based on them. These are not gap theories; they are ‘weakly classical’ theories in that they ... More


Renormalization group and scaling

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Mean-field theory is usually taken as a first step toward understanding critical phenomena, providing an overview that reveals qualitative behaviour of physical quantities. However, it is necessary ... More


Renormalization group: General formulation

Jean Zinn-Justin

in Phase Transitions and Renormalization Group

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199227198
eISBN:
9780191711107
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227198.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the general concept of renormalization group in the spirit of the work. It studies the role of fixed points and their stability properties. It exhibits a particular fixed ... More


Truth, Paradox, and Partially Defined Predicates

Scott Soames

in Understanding Truth

Published in print:
1999
Published Online:
November 2003
ISBN:
9780195123357
eISBN:
9780199872114
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195123352.003.0007
Subject:
Philosophy, Philosophy of Language

Presents a philosophical model of partially defined predicates, illustrates how a language could come to contain them, and provides a natural way of understanding the truth predicate in which it ... More


FUNCTIONAL ITERATIONS

D. A. Bini, G. Latouche, and B. Meini

in Numerical Methods for Structured Markov Chains

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.003.0006
Subject:
Mathematics, Numerical Analysis

The major iterative algorithms based on functional iteration techniques for solving nonlinear matrix equations are described, analysed, and compared in this chapter. First, the basic concepts on ... More


General Renormalization Group. The Critical Theory Near Dimension Four

JEAN ZINN-JUSTIN

in Quantum Field Theory and Critical Phenomena

Published in print:
2002
Published Online:
January 2010
ISBN:
9780198509233
eISBN:
9780191708732
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509233.003.0025
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The RG theory, as applied to Critical Phenomena, has been developed by Kadano, Wilson, Wegner, and many others. This chapter first describes the basic renormalization group ideas in a somewhat ... More


ALTERNATIVE APPROACHES

D. A. Bini, G. Latouche, and B. Meini

in Numerical Methods for Structured Markov Chains

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.003.0008
Subject:
Mathematics, Numerical Analysis

Alternative numerical approaches for solving matrix equations associated with M/G/1-type Markov chains are considered in this chapter. A general shift technique for accelerating the convergence of ... More


SPECIALIZED STRUCTURES

D. A. Bini, G. Latouche, and B. Meini

in Numerical Methods for Structured Markov Chains

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.003.0009
Subject:
Mathematics, Numerical Analysis

Some specialized structures are investigated in this chapter and some of the algorithms in previous chapters are adapted to the specific cases. Markov chains with limited displacement (non-skip-free ... More


Intersections and Fixed Points

S. N. Afriat

in Logic of Choice and Economic Theory

Published in print:
1987
Published Online:
November 2003
ISBN:
9780198284611
eISBN:
9780191595844
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198284616.003.0031
Subject:
Economics and Finance, Microeconomics

This is the last of three chapters on general mathematics as applied to economics, and presents a treatment of intersections and fixed points. The eight sections of the chapter are: simplices and ... More


Iterating Linear Functions

David P. Feldman

in Chaos and Fractals: An Elementary Introduction

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199566433
eISBN:
9780191774966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566433.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter examines the different kinds of behaviour that arise when linear functions are iterated. It looks at a number of different linear functions, each having at most one fixed point whose ... More


Flexible Population and Avoidance of Malthusian Poverty

Michio Morishima

in Theory of Economic Growth

Published in print:
1969
Published Online:
November 2003
ISBN:
9780198281641
eISBN:
9780191596667
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198281641.003.0014
Subject:
Economics and Finance, Development, Growth, and Environmental

So far, this book has been concerned with an economy where the labour force increases at a given constant rate, independently of the real wage rate and other economic factors.. However, the rate of ... More


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