## 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

## 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

## Oblique Procrustes problems

*J. C. Gower and G. B. Dijksterhuis*

### in Procrustes Problems

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198510581
- eISBN:
- 9780191708961
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198510581.003.0006
- Subject:
- Mathematics, Probability / Statistics

This chapter considers oblique Procrustes problems where T is, or is a function of, a direction cosine matrix C. There are four possibilities and a new unified approach is developed, which determines ... 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

## Determinateness, Hyper‐Determinateness, and Super‐Determinateness

*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/9780199230747.003.0023
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This chapter is about whether we can make sense of a notion of hyper-determinacy that will transcend the hierarchy of iterations of the determinacy operators and restore paradox. To investigate this, ... More

## Hyper‐Determinacy and Revenge

*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/9780199230747.003.0028
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Do dialetheic theories do better as regard revenge problems than theories that restrict excluded middle? This chapter argues that they do not, and shows in particular that each of the revenge ... More

## Heat Transfer and Other Field Problems in Two Dimensions

*J. N. REDDY*

### in An Introduction to Nonlinear Finite Element Analysis

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198525295
- eISBN:
- 9780191711671
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525295.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter considers the use of the finite element method in analysing problems in which the coefficients of the differential equation are possibly functions of the dependent variable and its ... More

## Margins for Error in Context

*Denis Bonnay and Paul Egré*

### in Relative Truth

- Published in print:
- 2008
- Published Online:
- May 2010
- ISBN:
- 9780199234950
- eISBN:
- 9780191715846
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199234950.003.0005
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Language

Williamson's margin for error semantics for knowledge implies that knowledge cannot systematically imply knowledge of one's knowledge. Each new iteration of knowledge requires what is known to remain ... More

## Differential Equations

*Tomas Björk*

### in Arbitrage Theory in Continuous Time

- Published in print:
- 2004
- Published Online:
- October 2005
- ISBN:
- 9780199271269
- eISBN:
- 9780191602849
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199271267.003.0005
- Subject:
- Economics and Finance, Financial Economics

This chapter examines whether there exists a stochastic process X, which satisfies the stochastic differential equation (SDE) d X t = μ (t, X t) d t + σ (t, X t) d W t, X 0 = x 0. The standard method ... More

## Requirement

*Garrett Cullity*

### in The Moral Demands of Affluence

- Published in print:
- 2004
- Published Online:
- April 2005
- ISBN:
- 9780199258116
- eISBN:
- 9780191602221
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199258112.003.0011
- Subject:
- Philosophy, Moral Philosophy

We have an argument for rejecting an iterative but not an aggregative approach to the life-saving analogy. This means that, while Chs 7–9 show that certain forms of personal spending are morally ... More

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

*S. G. Rajeev*

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670857.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This book begins with the ancient parts of classical mechanics: the variational principle, Lagrangian and Hamiltonian formalisms, and Poisson brackets. The simple pendulum provides a glimpse of the ... More

## Arrays

*Mark D. LeBlanc and Betsey Dexter Dyer*

### in Perl for Exploring DNA

- Published in print:
- 2007
- Published Online:
- April 2010
- ISBN:
- 9780195305890
- eISBN:
- 9780199773862
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195305890.003.09
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

This chapter is about scaling up. It introduces a list-like data structure used to collect and manage large numbers of DNA files and sequences for analysis. Any analysis that can be done on a single ... More

## Variational methods for wavelets, with S. Dahlke

*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/9780199577040.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 9 studies S. Dahlke studies wavelet methods. This is the first presentation in this generality and is appropriate for nonlinear problems and bifurcation for elliptic PDEs. As a consequence of ... More

## Some Polyadic Quantifiers of Natural Language

*Stanley Peters*

### in Quantifiers in Language and Logic

- Published in print:
- 2008
- Published Online:
- October 2011
- ISBN:
- 9780199291267
- eISBN:
- 9780191700590
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199291267.003.0011
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

This chapter looks at some instances of polyadic natural language quantifiers, beginning with the most common way of combining monadic quantifiers, in ordinary clauses with more than one noun phrase: ... More

## Democratic Iterations: The Local, the National, and the Global

*Seyla Benhabib*

### in Another Cosmopolitanism

- Published in print:
- 2006
- Published Online:
- October 2011
- ISBN:
- 9780195183221
- eISBN:
- 9780199851041
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195183221.003.0003
- Subject:
- Philosophy, Political Philosophy

More and more human beings find themselves not sharing in the collective identity of their host countries, while enjoying certain rights and benefits as guest workers or permanent residents. The ... More

## Cosmopolitan Norms

*Jeremy Waldron*

### in Another Cosmopolitanism

- Published in print:
- 2006
- Published Online:
- October 2011
- ISBN:
- 9780195183221
- eISBN:
- 9780199851041
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195183221.003.0004
- Subject:
- Philosophy, Political Philosophy

There is a massive and so far quite mysterious difference between thinking of cosmopolitan norms as law and thinking in legal terms about the norms of an ordinary municipal system. Until one has ... More

## The limits of iteration

*Graham Priest*

### in Beyond the Limits of Thought

- Published in print:
- 2002
- Published Online:
- October 2011
- ISBN:
- 9780199254057
- eISBN:
- 9780191698194
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199254057.003.0003
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter discusses the contradiction in the limits of iteration, one of the four limits of thought. This type of limit arises when there is some operation that is applied over and over again as ... More

## Graphical Iteration

*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/9780199566433.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter describes a tool for visualising and analysing iterated functions which can be used to quickly determine the stability of all of a function's fixed points. It presents an example that ... 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

## Introducing Julia Sets

*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/9780199566433.003.0023
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter focuses on the Julia set, a collection of points that do not tend toward infinity when iterated by a function. Any initial condition that is negative will become positive after one ... More