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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


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