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Science in the Looking Glass: What Do Scientists Really Know?

E. Brian Davies

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199219186
eISBN:
9780191711695
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219186.001.0001
Subject:
Physics, History of Physics

How do scientific conjectures become laws? Why does proof mean different things in different sciences? Do numbers exist, or were they invented? Why do some laws turn out to be wrong? This book ... More


Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

Gisbert Wüstholz and Clemens Fuchs (eds)

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691193779
eISBN:
9780691197548
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691193779.001.0001
Subject:
Mathematics, Geometry / Topology

This book presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the ... More


Confined divisors

James McKernan

in Flips for 3-folds and 4-folds

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198570615
eISBN:
9780191717703
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570615.003.0007
Subject:
Mathematics, Geometry / Topology

Shokurov proposed the CCS conjecture as an intermediate step leading to his finite generation conjecture implying the existence of pl flips in all dimensions. After the work of Hacon and McKernan, ... More


Kähler Manifolds

Charles P. Boyer and Krzysztof Galicki

in Sasakian Geometry

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.003.0004
Subject:
Mathematics, Geometry / Topology

This chapter reviews some basic facts about Kähler manifolds with special emphasis on projective algebraic varieties. All standard material is covered: complex structures, curvature properties, Hodge ... More


Sasakian Structures, Killing Spinors, and Supersymmetry

Charles P. Boyer and Krzysztof Galicki

in Sasakian Geometry

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.003.0015
Subject:
Mathematics, Geometry / Topology

This chapter gives a very brief overview of the rich theory of Killing spinors describing Bär's correspondence which connects Sasaki-Einstein geometry to Berger's holonomy theorem. It is then shown ... More


THE PARTIAL ORDER OF GRAPHS AND HOMOMORPHISMS

Pavol Hell and Jaroslav Nešetřil

in Graphs and Homomorphisms

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528173
eISBN:
9780191713644
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528173.003.0003
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter considers the order homomorphisms induce on the set of all cores; this order is rich enough to represent all countable partial orders. Antichains in the homomorphism order are discussed, ... More


COLOURING—VARIATIONS ON A THEME

Pavol Hell and Jaroslav Nešetřil

in Graphs and Homomorphisms

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528173
eISBN:
9780191713644
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528173.003.0006
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter sets out certain particular classes of homomorphism problems that have been investigated as variants of graph colourings. The homomorphism perspective unifies these concepts and offers ... More


DISCOVERING CAUSAL RELATIONSHIPSH

Jon Williamson

in Bayesian Nets and Causality: Philosophical and Computational Foundations

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198530794
eISBN:
9780191712982
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530794.003.0008
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

There are two main proposals for discovering causal relationships: a hypothetico-deductive and an inductive approach. Neither account is fully satisfactory. Various specific approaches are discussed, ... More


TOWARDS A MATROID-MINOR STRUCTURE THEORY

Jim Geelen, Bert Gerards, and Geoff Whittle

in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198571278
eISBN:
9780191718885
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571278.003.0005
Subject:
Mathematics, Probability / Statistics

This chapter surveys recent work aimed at generalizing the results and techniques of the Graph Minors Project of Robertson and Seymour to matroids. Some of the most interesting and apparently ... More


3-fold flips after Shokurov

Alessio Corti

in Flips for 3-folds and 4-folds

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198570615
eISBN:
9780191717703
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570615.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter gives a concise, complete, and pedagogical proof of existence of 3-fold flips according to Shokurov. In particular, the foundation of the theory of b-divisors, algebras of rational ... More


ADVANCES ON THE ERDŐS–FABER–LOVÁSZ CONJECTURE

David Romero and Abdón S´nchez-Arroyo

in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198571278
eISBN:
9780191718885
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571278.003.0017
Subject:
Mathematics, Probability / Statistics

A hypergraph is linear if no two distinct edges intersect in more than one vertex. A well-known conjecture of Erdős, Faber, and Lovász states that if a linear hypergraph has n edges, each of size n, ... More


Introduction: Moral Conflict, Political Liberalism, and Islamic Ethics

Andrew F. March

in Islam and Liberal Citizenship: The Search for an Overlapping Consensus

Published in print:
2009
Published Online:
May 2009
ISBN:
9780195330960
eISBN:
9780199868278
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195330960.003.0001
Subject:
Religion, Islam

This chapter states the aims of the book: its core question of the compatibility between formal Islamic doctrine and liberal citizenship It emphasizes how this book differs from historical, ... More


Methods: The Ethics of Comparative Ethics

Andrew F. March

in Islam and Liberal Citizenship: The Search for an Overlapping Consensus

Published in print:
2009
Published Online:
May 2009
ISBN:
9780195330960
eISBN:
9780199868278
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195330960.003.0003
Subject:
Religion, Islam

This chapter elaborates a methodology for engaging in what Rawls referred to as “conjecture,” here called “justificatory comparative political theory” or “comparative ethics.” It moves beyond Rawls’s ... More


Forensic Rhetoric on the Popular Stage: Shakespeare's Histories

Lorna Hutson

in The Invention of Suspicion: Law and Mimesis in Shakespeare and Renaissance Drama

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199212439
eISBN:
9780191707209
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199212439.003.0006
Subject:
Literature, Shakespeare Studies

This chapter finds continuity between the neoclassical Inns of Court drama of the 1560s and the hybrid forms of emblematic, allegorical, and episodic drama on the popular stage in the 1580s. Looking ... More


Arithmetic of Period Maps of Geometric Origin

Mark Green, Phillip Griffiths, and Matt Kerr

in Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691154244
eISBN:
9781400842735
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691154244.003.0009
Subject:
Mathematics, Analysis

This chapter considers some arithmetic aspects of period maps with a geometric origin. It focuses on the situation Φ‎ : S(ℂ) → Γ‎\D, where S parametrizes a family X → S of smooth, projective ... More


How Hard can Problems Get?

E. Brian Davies

in Science in the Looking Glass: What Do Scientists Really Know?

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199219186
eISBN:
9780191711695
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219186.003.0004
Subject:
Physics, History of Physics

This chapter describes some of the outstanding mathematical discoveries which have taken place during the last half century, focusing on what they say about how far human mathematical powers extend. ... More


In defence of John

Demetrios S. Katos

in Palladius of Helenopolis: The Origenist Advocate

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199696963
eISBN:
9780191731969
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199696963.003.0004
Subject:
Religion, Early Christian Studies, Church History

This chapter continues the analysis of the Dialogue in accordance with principles of judicial rhetoric. This chapter analyzes the rhetoric of the arguments used by Palladius to defend John by ... More


Creative Combination of Representations: Scientific Discovery and Technological Invention

Paul Thagard

in Psychology of Science: Implicit and Explicit Processes

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199753628
eISBN:
9780199950027
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199753628.003.0016
Subject:
Psychology, Cognitive Psychology, Social Psychology

This chapter describes two studies that help evaluate the combinatorial conjecture that all creativity results from combinations of mental representations. The first study examines 100 examples of ... More


Introduction

Gisbert Wüstholz and Clemens Fuchs (eds)

in Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691193779
eISBN:
9780691197548
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691193779.003.0001
Subject:
Mathematics, Geometry / Topology

This introductory chapter provides an overview of the three topics discussed in this book: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings heights and ... More


Using Significance Tests in Establishing Associations

Ezra Susser, Sharon Schwartz, Alfredo Morabia, and Evelyn J. Bromet

in Psychiatric Epidemiology: Searching for the Causes of Mental Disorders

Published in print:
2006
Published Online:
September 2009
ISBN:
9780195101812
eISBN:
9780199864096
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195101812.003.23
Subject:
Public Health and Epidemiology, Public Health, Epidemiology

Statistical significance testing can be viewed as a formal method for assessing the evidence with regard to a scientific conjecture. It reflects the degree to which we can be confident that an ... More


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