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Ramsey Methods in Analysis

Spiros A. Argyros Stevo Todorcevic

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Functional Analysis; Combinatorics

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2005 SpringerLink

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Tipo de recurso:

libros

ISBN impreso

978-3-7643-7264-4

ISBN electrónico

978-3-7643-7360-3

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

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© Birkhäuser Verlag 2005

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The Proof of the Finite Representability of

Spiros A. Argyros; Stevo Todorcevic

The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.

The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.

Part A - Saturated and Conditional Structures in Banach Spaces | Pp. 105-116

Bibliography

Spiros A. Argyros; Stevo Todorcevic

The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.

The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.

Part A - Saturated and Conditional Structures in Banach Spaces | Pp. 117-120

Introduction

Spiros A. Argyros; Stevo Todorcevic

The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.

The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.

Part B - High-Dimensional Ramsey Theory and Banach Space Geometry | Pp. 123-126

Finite-Dimensional Ramsey Theory: Finite Representability of Banach Spaces

Spiros A. Argyros; Stevo Todorcevic

The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.

The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.

Part B - High-Dimensional Ramsey Theory and Banach Space Geometry | Pp. 127-141

Ramsey Theory of Finite and Infinite Sequences

Spiros A. Argyros; Stevo Todorcevic

The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.

The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.

Part B - High-Dimensional Ramsey Theory and Banach Space Geometry | Pp. 143-196

Ramsey Theory of Finite and Infinite Block Sequences

Spiros A. Argyros; Stevo Todorcevic

The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.

The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.

Part B - High-Dimensional Ramsey Theory and Banach Space Geometry | Pp. 197-216

Approximate and Strategic Ramsey Theory of Banach Spaces

Spiros A. Argyros; Stevo Todorcevic

The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.

The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.

Part B - High-Dimensional Ramsey Theory and Banach Space Geometry | Pp. 217-246

Bibliography

Spiros A. Argyros; Stevo Todorcevic

The origin of the Moon 4.56 Gyr ago, its subsequent evolution, and the implications of both relative to the Earth remain subject to lively debate. Because the internal geochemistry and geophysics of the Moon does not appear consistent with an origin by the giant impact of a Mars-sized asteroid on the Earth, this hypothesis is challenged by one that proposes the capture of an independently formed planetesimal. The Moon—s internal structure also indicates that it and all the terrestrial planets initially had relatively cool, chondritic proto-cores prior to formation of metallic cores. Evidence exists that these proto-cores delayed formation of metallic cores for periods that correlate with the final mass of a planet.

The impact history of the inner solar system has been broadly outlined by the modern investigation of the Moon. First, soon after the formation of a coherent lunar crust and against an intense background of smaller cratering events, the Moon was subjected to extremely large impacts that formed basins up to 3200km in diameter. On Earth, the melt sheets from these continental-scale impacts may have been responsible for the formation of the first continental crust at ∼4.4 Gyr. Second, ∼50 impact basins >300 km in diameter formed between 4.5 and 3.8 Gyr probably by pulses of impactors produced during the migration and interaction of the giant planets within a structured solar disk of planetesimal rings. The last of these pulses at about 3.85 Gyr, producing the ∼14 mascon basins, resurfaced most of the Moon, and suggested an apparent “cataclysm” at that time. This period of 700 Myr may have been one of “punctuated cataclysm” as one or more giant planets encountered separate planetesimal rings and gaps during outward orbital migration. Finally, the implication of this violent impact history in the inner solar system prior to 3.8 Gyr relative to the surfaces of the hydrous terrestrial planets, that is, Earth, Mars and probably early Venus, is that clays were the dominant mineral species. These clays, as well as volcanic sulfides, may have provided the templates for the formation of complex organic precursors that made up the first living cells.

Part B - High-Dimensional Ramsey Theory and Banach Space Geometry | Pp. 247-252