Charles Boyer and Krzysztof Galicki
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198564959
- eISBN:
- 9780191713712
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198564959.001.0001
- Subject:
- Mathematics, Geometry / Topology
Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate relationship between Sasakian and Kähler geometries, especially when the Kähler structure is that of an ...
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Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate relationship between Sasakian and Kähler geometries, especially when the Kähler structure is that of an algebraic variety. The book is divided into three parts. The first five chapters carefully prepare the stage for the proper introduction of the subject. After a brief discussion of G-structures, the reader is introduced to the theory of Riemannian foliations. A concise review of complex and Kähler geometry precedes a fairly detailed treatment of compact complex Kähler orbifolds. A discussion of the existence and obstruction theory of Kähler-Einstein metrics (Monge-Ampère problem) on complex compact orbifolds follows. The second part gives a careful discussion of contact structures in the Riemannian setting. Compact quasi-regular Sasakian manifolds emerge here as algebraic objects: they are orbifold circle bundles over compact projective algebraic orbifolds. After a discussion of symmetries of Sasakian manifolds in Chapter 8, the book looks at Sasakian structures on links of isolated hypersurface singularities in Chapter 9. What follows is a study of compact Sasakian manifolds in dimensions three and five focusing on the important notion of positivity. The latter is crucial in understanding the existence of Sasaki-Einstein and 3-Sasakian metrics, which are studied in Chapters 11 and 13. Chapter 12 gives a fairly brief description of quaternionic geometry which is a prerequisite for Chapter 13. The study of Sasaki-Einstein geometry was the original motivation for the book. The final chapter on Killing spinors discusses the properties of Sasaki-Einstein manifolds, which allow them to play an important role as certain models in the supersymmetric field theories of theoretical physics.Less
Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate relationship between Sasakian and Kähler geometries, especially when the Kähler structure is that of an algebraic variety. The book is divided into three parts. The first five chapters carefully prepare the stage for the proper introduction of the subject. After a brief discussion of G-structures, the reader is introduced to the theory of Riemannian foliations. A concise review of complex and Kähler geometry precedes a fairly detailed treatment of compact complex Kähler orbifolds. A discussion of the existence and obstruction theory of Kähler-Einstein metrics (Monge-Ampère problem) on complex compact orbifolds follows. The second part gives a careful discussion of contact structures in the Riemannian setting. Compact quasi-regular Sasakian manifolds emerge here as algebraic objects: they are orbifold circle bundles over compact projective algebraic orbifolds. After a discussion of symmetries of Sasakian manifolds in Chapter 8, the book looks at Sasakian structures on links of isolated hypersurface singularities in Chapter 9. What follows is a study of compact Sasakian manifolds in dimensions three and five focusing on the important notion of positivity. The latter is crucial in understanding the existence of Sasaki-Einstein and 3-Sasakian metrics, which are studied in Chapters 11 and 13. Chapter 12 gives a fairly brief description of quaternionic geometry which is a prerequisite for Chapter 13. The study of Sasaki-Einstein geometry was the original motivation for the book. The final chapter on Killing spinors discusses the properties of Sasaki-Einstein manifolds, which allow them to play an important role as certain models in the supersymmetric field theories of theoretical physics.
Lawrence C. Becker
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199917549
- eISBN:
- 9780199950454
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199917549.001.0001
- Subject:
- Philosophy, Moral Philosophy
This book introduces an unconventional set of background ideas for future philosophical work on normative theories of basic justice. The organizing concept is habilitation–the process of equipping a ...
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This book introduces an unconventional set of background ideas for future philosophical work on normative theories of basic justice. The organizing concept is habilitation–the process of equipping a person or thing with functional abilities or capacities. The specific proposals drawn from the concept of habilitation are independent of any particular set of distributive principles. The result is a framework for theory that includes a metric for the pursuit of basic justice, but not a normative theory of it. The basic idea is that receiving and providing habilitation is a lifelong necessity for human beings, from the nearly helpless newborn state through the struggle to survive and thrive thereafter, even into the most severe diminishments of old age. This lifelong human necessity underlies all questions about basic justice, and the possibilities for habilitation define the circumstances under which those questions arise. Focusing on the circumstances of habilitation calls attention to the central role of physical and psychological health. Without basic good health in both domains, it is not possible to cope with the habilitative demands of one’s physical and psychological endowments, and one’s physical and social environments. And for human beings, a particular aspect of human health effectively sums up these matters: namely, human agency, the nature and extent of the ability to act effectively. The book proposes, specifically, that normative theories of basic justice adopt the habilitation framework. What then appears to follow is that the most plausible comprehensive metric for assessing progress toward basic justice will be the level and distribution of basic good health. Moreover, achieving robustly healthy agency will be the most plausible tactical target for making progress toward basic justice–again, no matter what one’s favored distributive principles might be.Less
This book introduces an unconventional set of background ideas for future philosophical work on normative theories of basic justice. The organizing concept is habilitation–the process of equipping a person or thing with functional abilities or capacities. The specific proposals drawn from the concept of habilitation are independent of any particular set of distributive principles. The result is a framework for theory that includes a metric for the pursuit of basic justice, but not a normative theory of it. The basic idea is that receiving and providing habilitation is a lifelong necessity for human beings, from the nearly helpless newborn state through the struggle to survive and thrive thereafter, even into the most severe diminishments of old age. This lifelong human necessity underlies all questions about basic justice, and the possibilities for habilitation define the circumstances under which those questions arise. Focusing on the circumstances of habilitation calls attention to the central role of physical and psychological health. Without basic good health in both domains, it is not possible to cope with the habilitative demands of one’s physical and psychological endowments, and one’s physical and social environments. And for human beings, a particular aspect of human health effectively sums up these matters: namely, human agency, the nature and extent of the ability to act effectively. The book proposes, specifically, that normative theories of basic justice adopt the habilitation framework. What then appears to follow is that the most plausible comprehensive metric for assessing progress toward basic justice will be the level and distribution of basic good health. Moreover, achieving robustly healthy agency will be the most plausible tactical target for making progress toward basic justice–again, no matter what one’s favored distributive principles might be.
DONALD A. MARCHAND, WILLIAM J. KETTINGER, and JOHN D. ROLLINS
- Published in print:
- 2002
- Published Online:
- January 2010
- ISBN:
- 9780199252213
- eISBN:
- 9780191714276
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199252213.003.0010
- Subject:
- Business and Management, Information Technology
This chapter provides an overview of the key management conclusions that can be derived from this book. It presents the key directions which will be pursued further regarding management practices and ...
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This chapter provides an overview of the key management conclusions that can be derived from this book. It presents the key directions which will be pursued further regarding management practices and strategies to measure and manage IO to improve business performance in the future.Less
This chapter provides an overview of the key management conclusions that can be derived from this book. It presents the key directions which will be pursued further regarding management practices and strategies to measure and manage IO to improve business performance in the future.
Justin London
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780195160819
- eISBN:
- 9780199786763
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195160819.001.0001
- Subject:
- Psychology, Cognitive Psychology
This book develops a theory of musical meter based on psychological research in temporal perception, cognition, and motor behavior. Meter is regarded as a kind of entrainment, a synchronization of ...
More
This book develops a theory of musical meter based on psychological research in temporal perception, cognition, and motor behavior. Meter is regarded as a kind of entrainment, a synchronization of attention and actions to the rhythms of the environment. Drawing on research on the ability to make durational discriminations and categorizations at various tempos, the “speed limits” for meter are given: the inter-onset interval for metric elements must be greater than 100ms (10 per second) and less than 1.5-2.00 seconds. Care is taken to distinguish rhythms or patterns of duration from meters, the listener/performer's complex patterns of expectation and attention. It is thus shown that metric behaviors are highly tempo-dependent. Ambiguities may arise when a rhythmic pattern may be regarded under more than one meter, and conflicts may arise when a pattern of durations contradicts the ongoing meter. The theoretical core of the book is its development of a set of metric well-formedness constraints, which limit the temporal range and organization of patterns of metric entrainment. A consideration of the rhythmic practices of various non-western cultures, including some African and Indian music, leads to an additional well-formedness constraint, that of maximal evenness. This allows for meters that involve uneven (i.e., non-isochronous) beats. The book concludes with the many meters hypothesis, which proposes that a large number of expressively timed temporal templates are acquired, which are readily used when listening in familiar musical contexts.Less
This book develops a theory of musical meter based on psychological research in temporal perception, cognition, and motor behavior. Meter is regarded as a kind of entrainment, a synchronization of attention and actions to the rhythms of the environment. Drawing on research on the ability to make durational discriminations and categorizations at various tempos, the “speed limits” for meter are given: the inter-onset interval for metric elements must be greater than 100ms (10 per second) and less than 1.5-2.00 seconds. Care is taken to distinguish rhythms or patterns of duration from meters, the listener/performer's complex patterns of expectation and attention. It is thus shown that metric behaviors are highly tempo-dependent. Ambiguities may arise when a rhythmic pattern may be regarded under more than one meter, and conflicts may arise when a pattern of durations contradicts the ongoing meter. The theoretical core of the book is its development of a set of metric well-formedness constraints, which limit the temporal range and organization of patterns of metric entrainment. A consideration of the rhythmic practices of various non-western cultures, including some African and Indian music, leads to an additional well-formedness constraint, that of maximal evenness. This allows for meters that involve uneven (i.e., non-isochronous) beats. The book concludes with the many meters hypothesis, which proposes that a large number of expressively timed temporal templates are acquired, which are readily used when listening in familiar musical contexts.
Charles P. Boyer and Krzysztof Galicki
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198564959
- eISBN:
- 9780191713712
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198564959.003.0012
- Subject:
- Mathematics, Geometry / Topology
This chapter is central to the whole book and perhaps the main reason and justification for it. Much of it is based on a new method for proving the existence of Einstein metrics on odd dimensional ...
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This chapter is central to the whole book and perhaps the main reason and justification for it. Much of it is based on a new method for proving the existence of Einstein metrics on odd dimensional manifolds, which is an orbifold version of the Kobayashi bundle construction. The key ingredient comes from the fact that links of isolated hypersurface singularities obtained from weighted homogeneous polynomials admit Sasakian structures. The focus is on the five-dimensional case where several classification results are described. Although a complete classification is perhaps not within reach, the material of this chapter gives a really good grasp of Sasaki-Einstein geometry in dimension five. One of the more important results of this chapter describes the plethora of Sasaki-Einstein metrics and their moduli that naturally occur, in particular, on many odd dimensional homotopy spheres, including exotic spheres. Toric Sasaki-Einstein manifolds are also discussed in some detail as they provide a unique source of irregular Sasaki-Einstein structures. Other important topics include extremal Sasaki metrics, Sasaki-Futaki character, and the Bishop and Lichnerowicz obstructions. The chapter ends with a brief discussion of Sasakian-η-Einsteinmetrics.Less
This chapter is central to the whole book and perhaps the main reason and justification for it. Much of it is based on a new method for proving the existence of Einstein metrics on odd dimensional manifolds, which is an orbifold version of the Kobayashi bundle construction. The key ingredient comes from the fact that links of isolated hypersurface singularities obtained from weighted homogeneous polynomials admit Sasakian structures. The focus is on the five-dimensional case where several classification results are described. Although a complete classification is perhaps not within reach, the material of this chapter gives a really good grasp of Sasaki-Einstein geometry in dimension five. One of the more important results of this chapter describes the plethora of Sasaki-Einstein metrics and their moduli that naturally occur, in particular, on many odd dimensional homotopy spheres, including exotic spheres. Toric Sasaki-Einstein manifolds are also discussed in some detail as they provide a unique source of irregular Sasaki-Einstein structures. Other important topics include extremal Sasaki metrics, Sasaki-Futaki character, and the Bishop and Lichnerowicz obstructions. The chapter ends with a brief discussion of Sasakian-η-Einsteinmetrics.
Rory Fox
- Published in print:
- 2006
- Published Online:
- May 2006
- ISBN:
- 9780199285754
- eISBN:
- 9780191603563
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199285756.001.0001
- Subject:
- Philosophy, Philosophy of Religion
This book examines 13th century views about time, particularly the views of Thomas Aquinas and his contemporaries in the middle of the century. As medieval thinkers considered time to be just another ...
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This book examines 13th century views about time, particularly the views of Thomas Aquinas and his contemporaries in the middle of the century. As medieval thinkers considered time to be just another duration alongside the durations of aeviternity (the aevum) and eternity, the scope of the study covers all three durations, culminating in an examination of God’s relationship to time. Chapter 1 opens the discussion by examining some of the key language and terminology which 13th century thinkers used. Chapters 2-5 examine the topological properties of time: the properties that determine its shape and structure. Chapter 6 investigates the metrical properties of time: the properties pertaining to time when it is considered as a measure. Chapter 7 looks at the criteria, factors, and language which 13th century thinkers typically took as entailing that a particular would be in time. Chapter 8 explores how 13th century thinkers discussed existence outside of time, particularly as it was applied to aeviternity and aeviternal beings. Chapter 9 examines the content of the medieval concept of eternity, and how these ideas are best rendered in contemporary language. Chapter 10 examines the specific question of how 13th century thinkers viewed God’s relationship to time.Less
This book examines 13th century views about time, particularly the views of Thomas Aquinas and his contemporaries in the middle of the century. As medieval thinkers considered time to be just another duration alongside the durations of aeviternity (the aevum) and eternity, the scope of the study covers all three durations, culminating in an examination of God’s relationship to time. Chapter 1 opens the discussion by examining some of the key language and terminology which 13th century thinkers used. Chapters 2-5 examine the topological properties of time: the properties that determine its shape and structure. Chapter 6 investigates the metrical properties of time: the properties pertaining to time when it is considered as a measure. Chapter 7 looks at the criteria, factors, and language which 13th century thinkers typically took as entailing that a particular would be in time. Chapter 8 explores how 13th century thinkers discussed existence outside of time, particularly as it was applied to aeviternity and aeviternal beings. Chapter 9 examines the content of the medieval concept of eternity, and how these ideas are best rendered in contemporary language. Chapter 10 examines the specific question of how 13th century thinkers viewed God’s relationship to time.
Sharan Jagpal
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780195371055
- eISBN:
- 9780199870745
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195371055.003.0017
- Subject:
- Business and Management, Marketing
This chapter shows how the multiproduct/multiagent firm should design compensation plans for its sales force. It distinguishes between the differential effects of experience (productivity), ...
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This chapter shows how the multiproduct/multiagent firm should design compensation plans for its sales force. It distinguishes between the differential effects of experience (productivity), heterogeneous risk attitudes among salespersons, and the firm's market segmentation policies. In addition, it shows how marketing-finance fusion allows multiproduct and multiagent firms to measure changes in sales force productivity using an objective metric (not sales revenue).Less
This chapter shows how the multiproduct/multiagent firm should design compensation plans for its sales force. It distinguishes between the differential effects of experience (productivity), heterogeneous risk attitudes among salespersons, and the firm's market segmentation policies. In addition, it shows how marketing-finance fusion allows multiproduct and multiagent firms to measure changes in sales force productivity using an objective metric (not sales revenue).
Sharan Jagpal
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780195371055
- eISBN:
- 9780199870745
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195371055.003.0019
- Subject:
- Business and Management, Marketing
This chapter discusses the conditions under which brand equity can exist and whether brand equity implies charging high prices. It evaluates the use of standard metrics for measuring brand equity ...
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This chapter discusses the conditions under which brand equity can exist and whether brand equity implies charging high prices. It evaluates the use of standard metrics for measuring brand equity (e.g., Tobin's q-ratio and the multiplier method). Following this, it proposes an integrated marketing-finance fusion method for measuring brand equity that combines behavioral and financial data and allows for competitive effects at different levels in the supply chain and for differential market growth rates.Less
This chapter discusses the conditions under which brand equity can exist and whether brand equity implies charging high prices. It evaluates the use of standard metrics for measuring brand equity (e.g., Tobin's q-ratio and the multiplier method). Following this, it proposes an integrated marketing-finance fusion method for measuring brand equity that combines behavioral and financial data and allows for competitive effects at different levels in the supply chain and for differential market growth rates.
Sharan Jagpal
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780195371055
- eISBN:
- 9780199870745
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195371055.003.0023
- Subject:
- Business and Management, Marketing
This chapter shows how multinational firms can use marketing-finance fusion to choose international strategies. It discusses the pros and cons of international diversification to privately and ...
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This chapter shows how multinational firms can use marketing-finance fusion to choose international strategies. It discusses the pros and cons of international diversification to privately and publicly held firms, whether or not the firm should choose country-specific product designs, how the firm should measure and reward the performances of its country managers, what type of organizational structure the firm should use, how the firm should choose an outsourcing strategy, and what performance metrics the firm should use to measure and reward managerial performance in its outsourcing centers.Less
This chapter shows how multinational firms can use marketing-finance fusion to choose international strategies. It discusses the pros and cons of international diversification to privately and publicly held firms, whether or not the firm should choose country-specific product designs, how the firm should measure and reward the performances of its country managers, what type of organizational structure the firm should use, how the firm should choose an outsourcing strategy, and what performance metrics the firm should use to measure and reward managerial performance in its outsourcing centers.
Sharan Jagpal
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780195371055
- eISBN:
- 9780199870745
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195371055.003.0005
- Subject:
- Business and Management, Marketing
This chapter examines the conditions under which the multiproduct firm should use market share as a metric for resource allocation. It distinguishes short- and long-run effects, analyze the effects ...
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This chapter examines the conditions under which the multiproduct firm should use market share as a metric for resource allocation. It distinguishes short- and long-run effects, analyze the effects of competition, and show how the discount rate affects the firm's revenue- and volume-based market shares. In particular, it shows how the firm can use marketing-finance fusion to choose the optimal performance metrics for managers so that they focus on maximizing long-run performance.Less
This chapter examines the conditions under which the multiproduct firm should use market share as a metric for resource allocation. It distinguishes short- and long-run effects, analyze the effects of competition, and show how the discount rate affects the firm's revenue- and volume-based market shares. In particular, it shows how the firm can use marketing-finance fusion to choose the optimal performance metrics for managers so that they focus on maximizing long-run performance.
Rory Fox
- Published in print:
- 2006
- Published Online:
- May 2006
- ISBN:
- 9780199285754
- eISBN:
- 9780191603563
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199285756.003.0007
- Subject:
- Philosophy, Philosophy of Religion
This chapter examines 13th century views on issues of measurement, particularly temporal measurement. It shows that 13th century thinkers distinguished between a variety of ways in which the word ...
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This chapter examines 13th century views on issues of measurement, particularly temporal measurement. It shows that 13th century thinkers distinguished between a variety of ways in which the word ‘measure’ (mensura) could be used; distinguishing between Platonic senses which were typically used to compare particulars in relation to their ontological perfection, and Aristotelian senses of the word ‘measure’ which were used to give an account of the metric of time. When applying measurement theory, 13th century thinkers would typically distinguish between the intrinsic and extrinsic measure. The intrinsic measure was the ‘subject’ of a particular kind of measure; the perfect standard which was the actual measure used in measuring other particulars of that same kind. When it came to carrying out actual measurements, the extrinsic measure was the ruler or clock, or other type of measure, which was an instance of the perfect standard laid down by the intrinsic measure, and which could then be used in concrete practical situations to carry out actual measurements.Less
This chapter examines 13th century views on issues of measurement, particularly temporal measurement. It shows that 13th century thinkers distinguished between a variety of ways in which the word ‘measure’ (mensura) could be used; distinguishing between Platonic senses which were typically used to compare particulars in relation to their ontological perfection, and Aristotelian senses of the word ‘measure’ which were used to give an account of the metric of time. When applying measurement theory, 13th century thinkers would typically distinguish between the intrinsic and extrinsic measure. The intrinsic measure was the ‘subject’ of a particular kind of measure; the perfect standard which was the actual measure used in measuring other particulars of that same kind. When it came to carrying out actual measurements, the extrinsic measure was the ruler or clock, or other type of measure, which was an instance of the perfect standard laid down by the intrinsic measure, and which could then be used in concrete practical situations to carry out actual measurements.
Craig Bourne
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199212804
- eISBN:
- 9780191707094
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199212804.003.0008
- Subject:
- Philosophy, Metaphysics/Epistemology
Some tense theorists think that the expansion of the universe can be used to define an absolute cosmic time that then serves to define the notion of absolute simultaneity required by tense theories. ...
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Some tense theorists think that the expansion of the universe can be used to define an absolute cosmic time that then serves to define the notion of absolute simultaneity required by tense theories. I show how Mellor's argument against this strategy fails. Clarifying the strategy leads to an exposition of the Robertson‐Walker metric, which describes such expanding universes. I identify the real reasons why we should reject this way of defining absolute simultaneity and temporal becoming.Less
Some tense theorists think that the expansion of the universe can be used to define an absolute cosmic time that then serves to define the notion of absolute simultaneity required by tense theories. I show how Mellor's argument against this strategy fails. Clarifying the strategy leads to an exposition of the Robertson‐Walker metric, which describes such expanding universes. I identify the real reasons why we should reject this way of defining absolute simultaneity and temporal becoming.
Justin London
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199744374
- eISBN:
- 9780199949632
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199744374.001.0001
- Subject:
- Music, Psychology of Music, Theory, Analysis, Composition
This book develops a theory of musical meter based on psychological research in temporal perception, cognition, and motor behavior. Meter is regarded as a kind of entrainment, a synchronization of ...
More
This book develops a theory of musical meter based on psychological research in temporal perception, cognition, and motor behavior. Meter is regarded as a kind of entrainment, a synchronization of attention and actions to the rhythms of the environment. Drawing on research on the ability to make durational discriminations and categorizations at various tempos, as well as evidence from neurobiology, the “speed limits” for meter are given: the inter-onset interval for metric elements must be greater than 100ms (10 per second) and less than 1.5-2.00 seconds. Care is taken to distinguish rhythms or patterns of duration from meters, the listener/performer's complex patterns of expectation and attention. It is thus shown that metric behaviors are highly tempo-dependent. Ambiguities may arise when a rhythmic pattern may be regarded under more than one meter, and conflicts may arise when a pattern of durations contradicts the ongoing meter. The music-theoretical core of the book is its development of a set of metric well-formedness constraints, which limit the temporal range and organization of patterns of metric entrainment. A consideration of the rhythmic practices of various non-western cultures, including some African and Indian music, leads to an additional well-formedness constraint, that of maximal evenness. This allows for meters that involve uneven (i.e., non-isochronous) beats or beat subdivisions. The book concludes with the many meters hypothesis, which proposes that a large number of expressively timed temporal templates are acquired that are readily used when listening in familiar musical contexts.Less
This book develops a theory of musical meter based on psychological research in temporal perception, cognition, and motor behavior. Meter is regarded as a kind of entrainment, a synchronization of attention and actions to the rhythms of the environment. Drawing on research on the ability to make durational discriminations and categorizations at various tempos, as well as evidence from neurobiology, the “speed limits” for meter are given: the inter-onset interval for metric elements must be greater than 100ms (10 per second) and less than 1.5-2.00 seconds. Care is taken to distinguish rhythms or patterns of duration from meters, the listener/performer's complex patterns of expectation and attention. It is thus shown that metric behaviors are highly tempo-dependent. Ambiguities may arise when a rhythmic pattern may be regarded under more than one meter, and conflicts may arise when a pattern of durations contradicts the ongoing meter. The music-theoretical core of the book is its development of a set of metric well-formedness constraints, which limit the temporal range and organization of patterns of metric entrainment. A consideration of the rhythmic practices of various non-western cultures, including some African and Indian music, leads to an additional well-formedness constraint, that of maximal evenness. This allows for meters that involve uneven (i.e., non-isochronous) beats or beat subdivisions. The book concludes with the many meters hypothesis, which proposes that a large number of expressively timed temporal templates are acquired that are readily used when listening in familiar musical contexts.
Ian Carter
- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198294535
- eISBN:
- 9780191598951
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198294530.003.0011
- Subject:
- Political Science, Political Theory
A distinction should be made between the theoretical possibility of measuring freedom and the practical possibility of doing so. Most of this book has been concerned with the theoretical possibility ...
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A distinction should be made between the theoretical possibility of measuring freedom and the practical possibility of doing so. Most of this book has been concerned with the theoretical possibility of measuring freedom. Given the various practical difficulties involved in quantifying available action, some empirical indicators need to be found. Nevertheless, the search for such indicators without a theoretical understanding of that which they are intended to indicate is difficult. One possibility is to be found in a combination of an exchange-value metric (derived from the necessary relation between the possession of freedom and the de facto possession of resources) and a metric of broadly defined political freedom-types.Less
A distinction should be made between the theoretical possibility of measuring freedom and the practical possibility of doing so. Most of this book has been concerned with the theoretical possibility of measuring freedom. Given the various practical difficulties involved in quantifying available action, some empirical indicators need to be found. Nevertheless, the search for such indicators without a theoretical understanding of that which they are intended to indicate is difficult. One possibility is to be found in a combination of an exchange-value metric (derived from the necessary relation between the possession of freedom and the de facto possession of resources) and a metric of broadly defined political freedom-types.
Mark Casson
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199213979
- eISBN:
- 9780191707469
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213979.003.0003
- Subject:
- Business and Management, Business History, Organization Studies
The counterfactual railway system was constructed using nine heuristic principles. The most important was the Steiner Principle, which asserts that under certain conditions an optimal railway network ...
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The counterfactual railway system was constructed using nine heuristic principles. The most important was the Steiner Principle, which asserts that under certain conditions an optimal railway network is linked up by a set of spatially symmetric three-way hubs. The counterfactual network equals or exceeds the performance of the actual network according to various metrics. The counterfactual network achieves this performance with 13,000 route miles as compared to the 20,000 route miles of the actual system.Less
The counterfactual railway system was constructed using nine heuristic principles. The most important was the Steiner Principle, which asserts that under certain conditions an optimal railway network is linked up by a set of spatially symmetric three-way hubs. The counterfactual network equals or exceeds the performance of the actual network according to various metrics. The counterfactual network achieves this performance with 13,000 route miles as compared to the 20,000 route miles of the actual system.
Charles P. Boyer and Krzysztof Galicki
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198564959
- eISBN:
- 9780191713712
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198564959.003.0002
- Subject:
- Mathematics, Geometry / Topology
This chapter begins by introducing various geometries that play important roles in the way they relate to Sasakian structures. It espouses the point of view that a geometric structure is best ...
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This chapter begins by introducing various geometries that play important roles in the way they relate to Sasakian structures. It espouses the point of view that a geometric structure is best described as a G-structure which may or may not be (partially) integrable. Some selected topics include: Riemannian metrics, complex structures, symplectic structures, contact structures, quaternionic structures, group actions, pseudogroups, sheaves, bundles, connections, holonomy, curvature and integrability.Less
This chapter begins by introducing various geometries that play important roles in the way they relate to Sasakian structures. It espouses the point of view that a geometric structure is best described as a G-structure which may or may not be (partially) integrable. Some selected topics include: Riemannian metrics, complex structures, symplectic structures, contact structures, quaternionic structures, group actions, pseudogroups, sheaves, bundles, connections, holonomy, curvature and integrability.
Charles P. Boyer and Krzysztof Galicki
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198564959
- eISBN:
- 9780191713712
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198564959.003.0006
- Subject:
- Mathematics, Geometry / Topology
This chapter is a second trip into the realm of Kähler geometry, focusing on Kähler-Einstein metrics, in particular positive scalar curvature Kähler-Einstein metrics on compact Fano orbifolds, which ...
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This chapter is a second trip into the realm of Kähler geometry, focusing on Kähler-Einstein metrics, in particular positive scalar curvature Kähler-Einstein metrics on compact Fano orbifolds, which gives rise to the famous Monge-Amfipere equation. Some basic techniques such as the continuity method, Tian's invariant, and multipliers ideal sheaves are introduced. These provide for proving various existence results concerning orbifold Kähler-Einstein metrics. The Matsushima-Lichnerowicz theorem and Futaki invariant are briefly discussed in the section on obstructions.Less
This chapter is a second trip into the realm of Kähler geometry, focusing on Kähler-Einstein metrics, in particular positive scalar curvature Kähler-Einstein metrics on compact Fano orbifolds, which gives rise to the famous Monge-Amfipere equation. Some basic techniques such as the continuity method, Tian's invariant, and multipliers ideal sheaves are introduced. These provide for proving various existence results concerning orbifold Kähler-Einstein metrics. The Matsushima-Lichnerowicz theorem and Futaki invariant are briefly discussed in the section on obstructions.
Charles P. Boyer and Krzysztof Galicki
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198564959
- eISBN:
- 9780191713712
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198564959.003.0007
- Subject:
- Mathematics, Geometry / Topology
This chapter presents the necessary foundational material on almost contact, contact, and metric contact structures. The key result is an orbifold version of the famous Boothby-Wang fibration. An ...
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This chapter presents the necessary foundational material on almost contact, contact, and metric contact structures. The key result is an orbifold version of the famous Boothby-Wang fibration. An introduction of a compatible Riemannian metric naturally leads to the definition of K-contact and Sasakian structures introduced at the very end.Less
This chapter presents the necessary foundational material on almost contact, contact, and metric contact structures. The key result is an orbifold version of the famous Boothby-Wang fibration. An introduction of a compatible Riemannian metric naturally leads to the definition of K-contact and Sasakian structures introduced at the very end.
Charles P. Boyer and Krzysztof Galicki
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198564959
- eISBN:
- 9780191713712
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198564959.003.0014
- Subject:
- Mathematics, Geometry / Topology
This chapter introduces a special case of Sasaki-Einstein manifolds which have a somewhat richer structure and occur only in dimensions 4m + 3. As any Sasakian manifold they are foliated by ...
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This chapter introduces a special case of Sasaki-Einstein manifolds which have a somewhat richer structure and occur only in dimensions 4m + 3. As any Sasakian manifold they are foliated by 1-dimensional leaves but now the transverse space has additional properties. In addition to a Kähler-Einstein metric, it has a complex contact structure making it into an orbifold twistor space. Furthermore, 3-Sasakian manifolds fiber as Konishi orbibundles over quaternionic Kähler orbifolds. Most of the 3-Sasakian metrics considered are obtained via symmetry reduction similar to hyper Kähler and quaternionic Kähler reduction. Indeed the three reductions are all related, so the manifolds and the metrics obtained are quite often explicit and can be studied as quotients. A detailed study and a classification of toric 3-Sasakian manifolds is presented. Some non-toric examples are also constructed as quotients as well as Konishi orbibundles over Hitchin-Tod self-dual Einstein orbifolds.Less
This chapter introduces a special case of Sasaki-Einstein manifolds which have a somewhat richer structure and occur only in dimensions 4m + 3. As any Sasakian manifold they are foliated by 1-dimensional leaves but now the transverse space has additional properties. In addition to a Kähler-Einstein metric, it has a complex contact structure making it into an orbifold twistor space. Furthermore, 3-Sasakian manifolds fiber as Konishi orbibundles over quaternionic Kähler orbifolds. Most of the 3-Sasakian metrics considered are obtained via symmetry reduction similar to hyper Kähler and quaternionic Kähler reduction. Indeed the three reductions are all related, so the manifolds and the metrics obtained are quite often explicit and can be studied as quotients. A detailed study and a classification of toric 3-Sasakian manifolds is presented. Some non-toric examples are also constructed as quotients as well as Konishi orbibundles over Hitchin-Tod self-dual Einstein orbifolds.
Paul Baird and John C. Wood
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198503620
- eISBN:
- 9780191708435
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198503620.003.0007
- Subject:
- Mathematics, Pure Mathematics
This chapter discusses how twistor methods can be used to construct nonconstant harmonic morphisms from (orientable) Einstein 4-manifolds to Riemann surfaces. It is shown that any such map induces an ...
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This chapter discusses how twistor methods can be used to construct nonconstant harmonic morphisms from (orientable) Einstein 4-manifolds to Riemann surfaces. It is shown that any such map induces an (integrable) Hermitian structure J on the 4-manifold with respect to which the map is holomorphic. The fibres of the map are ‘superminimal’, i.e., J is parallel along them. Conversely, a Hermitian structure induces (local) harmonic morphisms with these properties. Thus, the problem of finding harmonic morphisms is converted into that of finding Hermitian structures and superminimal surfaces in an Einstein 4-manifold; a problem that can be solved by twistor theory. This gives explicit constructions of all harmonic morphisms from domains of Euclidean 4-space, the 4-sphere, and complex projective 2-space to surfaces. The last section discusses harmonic morphisms from other Einstein manifolds, including the join of two complex projective 2-spaces endowed with the Page metric.Less
This chapter discusses how twistor methods can be used to construct nonconstant harmonic morphisms from (orientable) Einstein 4-manifolds to Riemann surfaces. It is shown that any such map induces an (integrable) Hermitian structure J on the 4-manifold with respect to which the map is holomorphic. The fibres of the map are ‘superminimal’, i.e., J is parallel along them. Conversely, a Hermitian structure induces (local) harmonic morphisms with these properties. Thus, the problem of finding harmonic morphisms is converted into that of finding Hermitian structures and superminimal surfaces in an Einstein 4-manifold; a problem that can be solved by twistor theory. This gives explicit constructions of all harmonic morphisms from domains of Euclidean 4-space, the 4-sphere, and complex projective 2-space to surfaces. The last section discusses harmonic morphisms from other Einstein manifolds, including the join of two complex projective 2-spaces endowed with the Page metric.
