D. Huybrechts
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199296866
- eISBN:
- 9780191711329
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296866.001.0001
- Subject:
- Mathematics, Geometry / Topology
This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this ...
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This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of the variety. Including notions from other areas, e.g., singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs and exercises are provided. The final chapter summarizes recent research directions, such as connections to orbifolds and the representation theory of finite groups via the McKay correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe.Less
This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of the variety. Including notions from other areas, e.g., singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs and exercises are provided. The final chapter summarizes recent research directions, such as connections to orbifolds and the representation theory of finite groups via the McKay correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe.
Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198566656
- eISBN:
- 9780191718014
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566656.001.0001
- Subject:
- Mathematics, Mathematical Physics
This text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis on the magnetohydrodynamics of liquid metals, on two-fluid flows, and ...
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This text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis on the magnetohydrodynamics of liquid metals, on two-fluid flows, and on a prototypical industrial application. The approach is a highly mathematical one, based on the rigorous analysis of the equations at hand, and a solid numerical analysis of the discretization methods. Up-to-date techniques, both on the theoretical side and the numerical side, are introduced to deal with the nonlinearities of the multifluid magnetohydrodynamics equations. At each stage of the exposition, examples of numerical simulations are provided, first on academic test cases to illustrate the approach, next on benchmarks well documented in the professional literature, and finally on real industrial cases. The simulation of aluminium electrolysis cells is used as a guideline throughout the book to motivate the study of a particular setting of the magnetohydrodynamics equations.Less
This text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis on the magnetohydrodynamics of liquid metals, on two-fluid flows, and on a prototypical industrial application. The approach is a highly mathematical one, based on the rigorous analysis of the equations at hand, and a solid numerical analysis of the discretization methods. Up-to-date techniques, both on the theoretical side and the numerical side, are introduced to deal with the nonlinearities of the multifluid magnetohydrodynamics equations. At each stage of the exposition, examples of numerical simulations are provided, first on academic test cases to illustrate the approach, next on benchmarks well documented in the professional literature, and finally on real industrial cases. The simulation of aluminium electrolysis cells is used as a guideline throughout the book to motivate the study of a particular setting of the magnetohydrodynamics equations.
Andrea Braides
- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198507840
- eISBN:
- 9780191709890
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507840.003.0010
- Subject:
- Mathematics, Applied Mathematics
This chapter describes the interaction between homogenization and surface terms using three examples. It shows that in some regimes, there is a separation of scales, while in other regimes the two ...
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This chapter describes the interaction between homogenization and surface terms using three examples. It shows that in some regimes, there is a separation of scales, while in other regimes the two phenomena must be considered together. The first example deals with the interaction between oscillations and phase transitions in producing surface terms. The second exhibits a different scaling of the same problem giving a limit energy finite on piecewise-Sobolev functions through phase accumulation. The third example deals with the homogenization of free-discontinuity problems.Less
This chapter describes the interaction between homogenization and surface terms using three examples. It shows that in some regimes, there is a separation of scales, while in other regimes the two phenomena must be considered together. The first example deals with the interaction between oscillations and phase transitions in producing surface terms. The second exhibits a different scaling of the same problem giving a limit energy finite on piecewise-Sobolev functions through phase accumulation. The third example deals with the homogenization of free-discontinuity problems.
D. Huybrechts
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199296866
- eISBN:
- 9780191711329
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296866.003.0012
- Subject:
- Mathematics, Geometry / Topology
This chapter completes the classification of algebraic surfaces from the point of view of their derived categories. Abelian, K3, and elliptic surfaces play a special role. For all other surfaces, the ...
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This chapter completes the classification of algebraic surfaces from the point of view of their derived categories. Abelian, K3, and elliptic surfaces play a special role. For all other surfaces, the derived category determines the isomorphism type. The reduction to minimal surfaces is due to Kawamata, and the case of elliptic surfaces was dealt with by Bridgeland and Maciocia.Less
This chapter completes the classification of algebraic surfaces from the point of view of their derived categories. Abelian, K3, and elliptic surfaces play a special role. For all other surfaces, the derived category determines the isomorphism type. The reduction to minimal surfaces is due to Kawamata, and the case of elliptic surfaces was dealt with by Bridgeland and Maciocia.
Korbinian Brodmann
- Published in print:
- 2006
- Published Online:
- May 2009
- ISBN:
- 9780195177640
- eISBN:
- 9780199864799
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195177640.003.0021
- Subject:
- Neuroscience, Sensory and Motor Systems, Behavioral Neuroscience
This chapter presents a paper published by Korbinian Brodmann in 1908, which contains the first complete description of a parcellation of the whole cortical surface, one that is still widely used ...
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This chapter presents a paper published by Korbinian Brodmann in 1908, which contains the first complete description of a parcellation of the whole cortical surface, one that is still widely used today. The paper is a shorter version of Brodmann's famous 1909 book.Less
This chapter presents a paper published by Korbinian Brodmann in 1908, which contains the first complete description of a parcellation of the whole cortical surface, one that is still widely used today. The paper is a shorter version of Brodmann's famous 1909 book.
Yuval Ginbar
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199540914
- eISBN:
- 9780191716256
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199540914.003.0007
- Subject:
- Law, Human Rights and Immigration
This chapter introduces Part II, examining the ticking bomb question as one of public, practical, morality in the real world, namely whether it is morally justifiable for democratic states facing ...
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This chapter introduces Part II, examining the ticking bomb question as one of public, practical, morality in the real world, namely whether it is morally justifiable for democratic states facing terrorism to torture in order to save many innocent lives. It outlines the parameters for discussing the question. Part II is to first address the question of whether transferring the ‘torture in a ticking bomb situation’ (TBS) moral dilemma from the private to the public sphere in itself entails a different moral solution. Secondly, the question is to be addressed of whether — accepting arguendo that torture in this situation is morally justified — states can torture in TBSs while limiting both torture and its direct and indirect harm to a morally acceptable level, or else must slide down an inevitable, and intolerable ‘slippery slope’. ‘Slippery surface’ dangers unique to the public sphere are also discussed.Less
This chapter introduces Part II, examining the ticking bomb question as one of public, practical, morality in the real world, namely whether it is morally justifiable for democratic states facing terrorism to torture in order to save many innocent lives. It outlines the parameters for discussing the question. Part II is to first address the question of whether transferring the ‘torture in a ticking bomb situation’ (TBS) moral dilemma from the private to the public sphere in itself entails a different moral solution. Secondly, the question is to be addressed of whether — accepting arguendo that torture in this situation is morally justified — states can torture in TBSs while limiting both torture and its direct and indirect harm to a morally acceptable level, or else must slide down an inevitable, and intolerable ‘slippery slope’. ‘Slippery surface’ dangers unique to the public sphere are also discussed.
Victor F. Petrenko and Robert W. Whitworth
- Published in print:
- 2002
- Published Online:
- February 2010
- ISBN:
- 9780198518945
- eISBN:
- 9780191707247
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198518945.001.0001
- Subject:
- Physics, Crystallography: Physics
Ice is one of the most abundant and environmentally important materials on Earth, and its unique and intriguing physical properties present fascinating areas of study. This book takes as its subject ...
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Ice is one of the most abundant and environmentally important materials on Earth, and its unique and intriguing physical properties present fascinating areas of study. This book takes as its subject the physics of ice: the properties of the material itself and the ways in which these properties are interpreted in terms of water molecules and crystalline structure. Although ice has a simple crystal structure its hydrogen bonding results in unique properties, which continue to be the subject of active research. An understanding of these properties is essential in fields such as glaciology, ice mechanics, ice adhesion, the dating of ice cores in Antarctica and Greenland, meteorology, thunderstorm electricity, and the study of comets or the icy moons of the outer planets in the solar system. In this book the physical principles underlying the properties of ice are carefully developed. Much work on important topics such as the current understanding of the electrical, mechanical, and surface properties of ice, or the occurrence of many different crystalline phases, are developed.Less
Ice is one of the most abundant and environmentally important materials on Earth, and its unique and intriguing physical properties present fascinating areas of study. This book takes as its subject the physics of ice: the properties of the material itself and the ways in which these properties are interpreted in terms of water molecules and crystalline structure. Although ice has a simple crystal structure its hydrogen bonding results in unique properties, which continue to be the subject of active research. An understanding of these properties is essential in fields such as glaciology, ice mechanics, ice adhesion, the dating of ice cores in Antarctica and Greenland, meteorology, thunderstorm electricity, and the study of comets or the icy moons of the outer planets in the solar system. In this book the physical principles underlying the properties of ice are carefully developed. Much work on important topics such as the current understanding of the electrical, mechanical, and surface properties of ice, or the occurrence of many different crystalline phases, are developed.
Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198566656
- eISBN:
- 9780191718014
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566656.003.0005
- Subject:
- Mathematics, Mathematical Physics
This chapter deals with the discretization issues raised by multifluid magnetohydrodynamics problems. The additional difficulty compared to those in Chapter 3, is the presence of one (or many) free ...
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This chapter deals with the discretization issues raised by multifluid magnetohydrodynamics problems. The additional difficulty compared to those in Chapter 3, is the presence of one (or many) free interface(s) separating the fluids. Numerically, one has also to resort to up-to-date techniques for the simulation of moving interfaces. In particular, the chapter presents a numerical method based on the Arbitrary Lagrangian Eulerian formulation, and lays emphasis on the stability of the time-advancing schemes. A short review of some other numerical methods to deal with moving interfaces is provided. Some numerical test cases illustrate the capabilities of the ALE method.Less
This chapter deals with the discretization issues raised by multifluid magnetohydrodynamics problems. The additional difficulty compared to those in Chapter 3, is the presence of one (or many) free interface(s) separating the fluids. Numerically, one has also to resort to up-to-date techniques for the simulation of moving interfaces. In particular, the chapter presents a numerical method based on the Arbitrary Lagrangian Eulerian formulation, and lays emphasis on the stability of the time-advancing schemes. A short review of some other numerical methods to deal with moving interfaces is provided. Some numerical test cases illustrate the capabilities of the ALE method.
Niels E. Henriksen and Flemming Y. Hansen
- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199203864
- eISBN:
- 9780191708251
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199203864.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This book deals with a central topic at the interface of chemistry and physics — the understanding of how the transformation of matter takes place at the atomic level. Building on the laws of ...
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This book deals with a central topic at the interface of chemistry and physics — the understanding of how the transformation of matter takes place at the atomic level. Building on the laws of physics, the book focuses on the theoretical framework for predicting the outcome of chemical reactions. The style is highly systematic with attention to basic concepts and clarity of presentation. Molecular reaction dynamics is about the detailed atomic-level description of chemical reactions. Based on quantum mechanics and statistical mechanics or, as an approximation, classical mechanics, the dynamics of uni- and bi-molecular elementary reactions are described. The first part of the book is on gas-phase dynamics and it features a detailed presentation of reaction cross-sections and their relation to a quasi-classical as well as a quantum mechanical description of the reaction dynamics on a potential energy surface. Direct approaches to the calculation of the rate constant that bypasses the detailed state-to-state reaction cross-sections are presented, including transition-state theory, which plays an important role in practice. The second part gives a comprehensive discussion of basic theories of reaction dynamics in condensed phases, including Kramers and Grote–Hynes theory for dynamical solvent effects. Examples and end-of-chapter problems are included in order to illustrate the theory and its connection to chemical problems. The book has nine appendices with useful details, e.g. on statistical mechanics including the Boltzmann distribution, quantum mechanics, stochastic dynamics and various coordinate transformations including normal-mode and Jacobi coordinates.Less
This book deals with a central topic at the interface of chemistry and physics — the understanding of how the transformation of matter takes place at the atomic level. Building on the laws of physics, the book focuses on the theoretical framework for predicting the outcome of chemical reactions. The style is highly systematic with attention to basic concepts and clarity of presentation. Molecular reaction dynamics is about the detailed atomic-level description of chemical reactions. Based on quantum mechanics and statistical mechanics or, as an approximation, classical mechanics, the dynamics of uni- and bi-molecular elementary reactions are described. The first part of the book is on gas-phase dynamics and it features a detailed presentation of reaction cross-sections and their relation to a quasi-classical as well as a quantum mechanical description of the reaction dynamics on a potential energy surface. Direct approaches to the calculation of the rate constant that bypasses the detailed state-to-state reaction cross-sections are presented, including transition-state theory, which plays an important role in practice. The second part gives a comprehensive discussion of basic theories of reaction dynamics in condensed phases, including Kramers and Grote–Hynes theory for dynamical solvent effects. Examples and end-of-chapter problems are included in order to illustrate the theory and its connection to chemical problems. The book has nine appendices with useful details, e.g. on statistical mechanics including the Boltzmann distribution, quantum mechanics, stochastic dynamics and various coordinate transformations including normal-mode and Jacobi coordinates.
Mark Wilson
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199269259
- eISBN:
- 9780191710155
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269259.003.0006
- Subject:
- Philosophy, Philosophy of Language
Drawing upon the rich experience gathered within applied mathematics, various ‘facade patterns’ are examined that frequently develop when an originating usage enlarges its descriptive scope through ...
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Drawing upon the rich experience gathered within applied mathematics, various ‘facade patterns’ are examined that frequently develop when an originating usage enlarges its descriptive scope through patch-to-patch prolongation. The completed results can generate a global structure that is syntactically inconsistent as a whole, yet avoids logical ruination through simple restrictions upon data exportation from one patch to another (a ‘Riemann surface’ represents a standard mathematical prototype of the phenomenon). It is argued that not only do such facades often represent the natural end products of ordinary linguistic development, they often provide particularly effective forms of linguistic engineering. Philosophical puzzles sometimes arise when these alternative patterns of semantic design get mistaken for classical models, as the troubled history of ‘force’ effectively illustrates. The fact that we can rarely determine whether an initial collection of descriptive vocabulary is destined to develop into a facade rather than implementing a simpler pattern of word/world alignment provides a convenient indication of the degree to which a classical picture of conceptual grasp exaggerates our capacity to augur the fate of our descriptive words over time.Less
Drawing upon the rich experience gathered within applied mathematics, various ‘facade patterns’ are examined that frequently develop when an originating usage enlarges its descriptive scope through patch-to-patch prolongation. The completed results can generate a global structure that is syntactically inconsistent as a whole, yet avoids logical ruination through simple restrictions upon data exportation from one patch to another (a ‘Riemann surface’ represents a standard mathematical prototype of the phenomenon). It is argued that not only do such facades often represent the natural end products of ordinary linguistic development, they often provide particularly effective forms of linguistic engineering. Philosophical puzzles sometimes arise when these alternative patterns of semantic design get mistaken for classical models, as the troubled history of ‘force’ effectively illustrates. The fact that we can rarely determine whether an initial collection of descriptive vocabulary is destined to develop into a facade rather than implementing a simpler pattern of word/world alignment provides a convenient indication of the degree to which a classical picture of conceptual grasp exaggerates our capacity to augur the fate of our descriptive words over time.
Paula Tretkoff
- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.001.0001
- Subject:
- Mathematics, Geometry / Topology
This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. It emphasizes those finite coverings that ...
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This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. It emphasizes those finite coverings that are free quotients of the complex 2-ball. The book also includes a background on the classical Gauss hypergeometric function of one variable, and a chapter on the Appell two-variable F1 hypergeometric function. The book began as a set of lecture notes, taken by the author, of a course given by Friedrich Hirzebruch at ETH Zürich in 1996. The lecture notes were then considerably expanded over a number of years. In this book, the author has expanded those notes even further, still stressing examples offered by finite covers of line arrangements. The book is largely self-contained and foundational material is introduced and explained as needed, but not treated in full detail. References to omitted material are provided for interested readers. Aimed at graduate students and researchers, this is an accessible account of a highly informative area of complex geometry.Less
This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. It emphasizes those finite coverings that are free quotients of the complex 2-ball. The book also includes a background on the classical Gauss hypergeometric function of one variable, and a chapter on the Appell two-variable F1 hypergeometric function. The book began as a set of lecture notes, taken by the author, of a course given by Friedrich Hirzebruch at ETH Zürich in 1996. The lecture notes were then considerably expanded over a number of years. In this book, the author has expanded those notes even further, still stressing examples offered by finite covers of line arrangements. The book is largely self-contained and foundational material is introduced and explained as needed, but not treated in full detail. References to omitted material are provided for interested readers. Aimed at graduate students and researchers, this is an accessible account of a highly informative area of complex geometry.
J. D. Moreland and S. Westland
- Published in print:
- 2003
- Published Online:
- April 2010
- ISBN:
- 9780198525301
- eISBN:
- 9780191584947
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525301.003.0028
- Subject:
- Psychology, Cognitive Neuroscience
Macular pigment (MP) is a natural filter with ‘notch’ transmission characteristics. This chapter examines the effects of MP on surface colours in Normal and Anomalous Trichromats for a database of ...
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Macular pigment (MP) is a natural filter with ‘notch’ transmission characteristics. This chapter examines the effects of MP on surface colours in Normal and Anomalous Trichromats for a database of 1782 reflectance spectra. The results show that increases in MP concentration produce a general clockwise rotation of chromaticity around the illuminant point for Normals and Anormals. The chromaticity shifts, associated with rotation, increase with distance from the illuminant point.Less
Macular pigment (MP) is a natural filter with ‘notch’ transmission characteristics. This chapter examines the effects of MP on surface colours in Normal and Anomalous Trichromats for a database of 1782 reflectance spectra. The results show that increases in MP concentration produce a general clockwise rotation of chromaticity around the illuminant point for Normals and Anormals. The chromaticity shifts, associated with rotation, increase with distance from the illuminant point.
Michael S. Landy, Yun-Xian Ho, Sascha Serwe, Julia Trommershäuser, and Laurence T. Maloney
- Published in print:
- 2011
- Published Online:
- September 2012
- ISBN:
- 9780195387247
- eISBN:
- 9780199918379
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195387247.003.0014
- Subject:
- Psychology, Cognitive Neuroscience, Cognitive Psychology
This chapter reviews experimental evidence concerning the use of pseudocues in the perception of 3D scene properties such as roughness and depth. In the first two experiments, observers judged ...
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This chapter reviews experimental evidence concerning the use of pseudocues in the perception of 3D scene properties such as roughness and depth. In the first two experiments, observers judged surface roughness of an irregular surface in which roughness was varied by scaling the range of depths of bumps and valleys. It is shown that observers did indeed use pseudocues, such as the amount of shadow, and as a result they misperceived surface roughness. A similar phenomenon occurred in the perception of surface gloss. Finally, a third study is summarized in which observers judged the depth of a single bump. This final experiment investigated how pseudocues might be learned and, in particular, how observers determine how much weight to give to a pseudocue in combining it with other depth cues.Less
This chapter reviews experimental evidence concerning the use of pseudocues in the perception of 3D scene properties such as roughness and depth. In the first two experiments, observers judged surface roughness of an irregular surface in which roughness was varied by scaling the range of depths of bumps and valleys. It is shown that observers did indeed use pseudocues, such as the amount of shadow, and as a result they misperceived surface roughness. A similar phenomenon occurred in the perception of surface gloss. Finally, a third study is summarized in which observers judged the depth of a single bump. This final experiment investigated how pseudocues might be learned and, in particular, how observers determine how much weight to give to a pseudocue in combining it with other depth cues.
Paula Tretkoff
- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0005
- Subject:
- Mathematics, Geometry / Topology
This chapter discusses complex algebraic surfaces, with particular emphasis on the Miyaoka-Yau inequality and the rough classification of surfaces. Every complex algebraic surface is birationally ...
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This chapter discusses complex algebraic surfaces, with particular emphasis on the Miyaoka-Yau inequality and the rough classification of surfaces. Every complex algebraic surface is birationally equivalent to a smooth surface containing no exceptional curves. The latter is known as a minimal surface. Two related birational invariants, the plurigenus and the Kodaira dimension, play an important role in distinguishing between complex surfaces. The chapter first provides an overview of the rough classification of (smooth complex connected compact algebraic) surfaces before presenting two approaches that, in dimension 2, give the Miyaoka-Yau inequality. The first, due to Miyaoka, uses algebraic geometry, whereas the second, due to Aubin and Yau, uses analysis and differential geometry. The chapter also explains why equality in the Miyaoka-Yau inequality characterizes surfaces of general type that are free quotients of the complex 2-ball.Less
This chapter discusses complex algebraic surfaces, with particular emphasis on the Miyaoka-Yau inequality and the rough classification of surfaces. Every complex algebraic surface is birationally equivalent to a smooth surface containing no exceptional curves. The latter is known as a minimal surface. Two related birational invariants, the plurigenus and the Kodaira dimension, play an important role in distinguishing between complex surfaces. The chapter first provides an overview of the rough classification of (smooth complex connected compact algebraic) surfaces before presenting two approaches that, in dimension 2, give the Miyaoka-Yau inequality. The first, due to Miyaoka, uses algebraic geometry, whereas the second, due to Aubin and Yau, uses analysis and differential geometry. The chapter also explains why equality in the Miyaoka-Yau inequality characterizes surfaces of general type that are free quotients of the complex 2-ball.
Ian P. Howard and Brian J. Rogers
- Published in print:
- 1996
- Published Online:
- January 2008
- ISBN:
- 9780195084764
- eISBN:
- 9780199871049
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195084764.003.0007
- Subject:
- Psychology, Cognitive Psychology
This chapter begins with a discussion of monocular and binocular coordinate systems, projection surfaces and camera calibration, and the concept of disparity. It then covers disparity on slanted ...
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This chapter begins with a discussion of monocular and binocular coordinate systems, projection surfaces and camera calibration, and the concept of disparity. It then covers disparity on slanted surfaces, perception of slant, disparities on inclined surfaces, perception of inclination, vertical disparity, disparity-defined shape, and types of disparity.Less
This chapter begins with a discussion of monocular and binocular coordinate systems, projection surfaces and camera calibration, and the concept of disparity. It then covers disparity on slanted surfaces, perception of slant, disparities on inclined surfaces, perception of inclination, vertical disparity, disparity-defined shape, and types of disparity.
Johanna Laybourn-Parry and Warwick F. Vincent
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199213887
- eISBN:
- 9780191707506
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213887.003.0017
- Subject:
- Biology, Ecology, Aquatic Biology
This concluding chapter identifies some of the emerging concepts and technologies that will drive future advances in polar limnology. These include the increased awareness of climate and related ...
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This concluding chapter identifies some of the emerging concepts and technologies that will drive future advances in polar limnology. These include the increased awareness of climate and related impacts in the polar regions, and the importance of high latitude lakes and rivers as sentinels of global change; the increased availability of wireless network technology to obtain high temporal resolution data sets from these remote sites; the emergence of new sensor technologies and underwater platforms, including robotic systems that may be used in the future to explore subglacial lakes and other polar waters; and the development of surface imagery approaches ranging from local-scale observations by unmanned aerial vehicles to circumpolar-scale measurements by satellite, for example by synthetic aperture radar. The chapter also examines the new opportunities provided by environmental genomics, including application towards bioprospecting for novel extremophiles and biomolecules of pharmaceutical and industrial interest.Less
This concluding chapter identifies some of the emerging concepts and technologies that will drive future advances in polar limnology. These include the increased awareness of climate and related impacts in the polar regions, and the importance of high latitude lakes and rivers as sentinels of global change; the increased availability of wireless network technology to obtain high temporal resolution data sets from these remote sites; the emergence of new sensor technologies and underwater platforms, including robotic systems that may be used in the future to explore subglacial lakes and other polar waters; and the development of surface imagery approaches ranging from local-scale observations by unmanned aerial vehicles to circumpolar-scale measurements by satellite, for example by synthetic aperture radar. The chapter also examines the new opportunities provided by environmental genomics, including application towards bioprospecting for novel extremophiles and biomolecules of pharmaceutical and industrial interest.
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/9780198564959.003.0011
- Subject:
- Mathematics, Geometry / Topology
This chapter describes Sasakian geometry in low dimensions. In dimension three there is a complete classification; dimension five is large enough to be interesting, yet small enough to hope for some ...
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This chapter describes Sasakian geometry in low dimensions. In dimension three there is a complete classification; dimension five is large enough to be interesting, yet small enough to hope for some partial classification. We concentrate on the simply connected case, as there we can rely on the Smale-Barden classification. In terms of Sasakian structures, the main focus is on the case of positive Sasakian structures. The chapter describes several remarkable theorems of Kollfiar showing how positivity severely restricts the topology, in particular the torsion of a manifold which admits a positive Sasakian structure. The method heavily depends on the algebraic geometry of log del Pezzo surfaces with cyclic Du Val singularities.Less
This chapter describes Sasakian geometry in low dimensions. In dimension three there is a complete classification; dimension five is large enough to be interesting, yet small enough to hope for some partial classification. We concentrate on the simply connected case, as there we can rely on the Smale-Barden classification. In terms of Sasakian structures, the main focus is on the case of positive Sasakian structures. The chapter describes several remarkable theorems of Kollfiar showing how positivity severely restricts the topology, in particular the torsion of a manifold which admits a positive Sasakian structure. The method heavily depends on the algebraic geometry of log del Pezzo surfaces with cyclic Du Val singularities.
A.D. Neate and A. Truman
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199239252
- eISBN:
- 9780191716911
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199239252.003.0013
- Subject:
- Mathematics, Probability / Statistics, Analysis
This chapter summarises a selection of results on the inviscid limit of the stochastic Burgers equation emphasising geometric properties of the caustic, Maxwell set and Hamilton-Jacobi level surfaces ...
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This chapter summarises a selection of results on the inviscid limit of the stochastic Burgers equation emphasising geometric properties of the caustic, Maxwell set and Hamilton-Jacobi level surfaces and relating these results to a discussion of stochastic turbulence. It shows that for small viscosities there exists a vortex filament structure near to the Maxwell set. It is discussed how this vorticity is directly related to the adhesion model for the evolution of the early universe, and new explicit formulas for the distribution of mass within the shock are included.Less
This chapter summarises a selection of results on the inviscid limit of the stochastic Burgers equation emphasising geometric properties of the caustic, Maxwell set and Hamilton-Jacobi level surfaces and relating these results to a discussion of stochastic turbulence. It shows that for small viscosities there exists a vortex filament structure near to the Maxwell set. It is discussed how this vorticity is directly related to the adhesion model for the evolution of the early universe, and new explicit formulas for the distribution of mass within the shock are included.
Teresa Wilcox and Rebecca Woods
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780195301151
- eISBN:
- 9780199894246
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195301151.003.0005
- Subject:
- Psychology, Developmental Psychology
Increased attention has been given toward understanding the reasons that infants are more sensitive to some types of information than to others, and how infants come to identify new sources of ...
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Increased attention has been given toward understanding the reasons that infants are more sensitive to some types of information than to others, and how infants come to identify new sources of information as relevant to the individuation problem. One approach is to identify experiences that can alter infants' sensitivity to surface features. The conditions under which these experiences are most effective can reveal important information about the nature and content of infants' object representations, how infants' use these representations, and the cognitive and/or learning mechanisms that govern changes in infants' individuation capacities. This chapter focuses on this body of research.Less
Increased attention has been given toward understanding the reasons that infants are more sensitive to some types of information than to others, and how infants come to identify new sources of information as relevant to the individuation problem. One approach is to identify experiences that can alter infants' sensitivity to surface features. The conditions under which these experiences are most effective can reveal important information about the nature and content of infants' object representations, how infants' use these representations, and the cognitive and/or learning mechanisms that govern changes in infants' individuation capacities. This chapter focuses on this body of research.
Józef Ignaczak and Martin Ostoja‐Starzewski
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199541645
- eISBN:
- 9780191716164
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199541645.003.0010
- Subject:
- Mathematics, Applied Mathematics, Mathematical Physics
The tenth chapter, entitled “Moving discontinuity surfaces,” focuses on singular surfaces propagating in a thermoelastic medium, and studies the propagation of a plane shock wave in a thermoelastic ...
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The tenth chapter, entitled “Moving discontinuity surfaces,” focuses on singular surfaces propagating in a thermoelastic medium, and studies the propagation of a plane shock wave in a thermoelastic half‐space with one relaxation time, as well as the propagation of a plane acceleration wave in a thermoelastic half‐space with two relaxation times.Less
The tenth chapter, entitled “Moving discontinuity surfaces,” focuses on singular surfaces propagating in a thermoelastic medium, and studies the propagation of a plane shock wave in a thermoelastic half‐space with one relaxation time, as well as the propagation of a plane acceleration wave in a thermoelastic half‐space with two relaxation times.
