## 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