Medial/skeletal linking structures for multi-region configurations:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
November 2017
|
| Series: | Memoirs of the American Mathematical Society
volume 250, number 1193 (sixth of 6 numbers) |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 163, 4 ungezählte Seiten |
| ISBN: | 9781470426804 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804178228949024768 |
|---|---|
| adam_text | Contents
Chapter 1. Introduction 1
Part 1. Medial/Skeletal Linking Structures 7
Chapter 2. Multi-Region Configurations in Mn+1 9
Local Models for Regions at Singular Points on Boundary 9
The Space of Equivalent Configurations via Mappings of a Model 10
Configurations Allowing Containment of Regions 11
Chapter 3. Skeletal Linking Structures for Multi-Region
Configurations in Mn+1 13
Skeletal Structures for Single Regions 13
Skeletal Linking Structures for Multi-Region Configurations 15
Linking Between Regions and Between Skeletal Sets 17
Chapter 4. Blum Medial Linking Structure for a Generic Multi-Region
Configuration 19
Blum Medial Axis for a Single Region with Smooth Generic Boundary 19
Structure of Maxwell Set Described by 7^+-Versai Unfoldings 19
Addendum to Generic Blum Structure for a Region
with Boundaries and Corners 22
Spherical Axis of a Configuration 24
Blum Medial Linking Structure 26
Existence of a Blum Medial Linking Structure 29
Addendum: Classification of Linking Types for Blum Medial Linking
Structures in M3 31
Chapter 5. Retracting the Full Blum Medial Structure to a
Skeletal Linking Structure 33
Example of Evolving Skeletal Linking Structure for Simple
Generic Transition 33
Retracting Full Blum Linking Structure via Smoothing 34
Part 2. Positional Geometry of Linking Structures 39
Chapter 6. Questions Involving Positional Geometry of a Multi-Region
Configuration 41
Chapter 7. Shape Operators and Radial Flow for a Skeletal Structure 45
The Radial Flow 45
Radial and Edge Shape Operators 45
V
CONTENTS
Curvature Conditions and Nonsingularity of the Radial Flow 46
Evolution of the Shape Operators Under the Radial Flow 48
Chapter 8. Linking Flow and Curvature Conditions 51
Nonsingularity of the Linking Flow 51
Special Möbius Transformations of Matrices and Operators 53
Evolution of the Shape Operators Under the Linking Flow 55
Chapter 9. Properties of Regions Defined Using the Linking Flow 57
Medial/Skeletal Linking Structures in the Unbounded Case 57
Medial/Skeletal Linking Structures for the Bounded Case 60
Chapter 10. Global Geometry via Medial and Skeletal Linking Integrals 63
Defining Medial and Skeletal Linking Integrals 63
Computing Boundary Integrals via Medial Linking Integrals 65
Computing Integrals as Skeletal Linking Integrals via the Linking Flow 67
Skeletal Linking Integral Formulas for Global Invariants 71
Chapter 11. Positional Geometric Properties of Multi-Region Configurations 75
Neighboring Regions and Measures of Closeness 75
Measuring Positional Significance of Objects Via Linking Structures 77
Properties of Invariants for Closeness and Positional Significance 78
Tiered Linking Graph 80
Higher Order Positional Geometric Relations via Indirect Linking 82
Part 3. Generic Properties of Linking
Structures via Transversality Theorems 85
Chapter 12. Multi-Distance and Height-Distance Functions and Partial
Multi-Jet Spaces 87
Multi-Distance and Height-Distance Functions 87
Partial Jet Spaces for Multi-Distance and Height-Distance Functions 90
Chapter 13. Generic Blum Linking Properties via Transversality Theorems 93
Transversality Theorem for Multi-Distance and Height-Distance Functions 93
Submanifolds Defining Generic Properties of Blum Linking Structures 94
Chapter 14. Generic Properties of Blum Linking Structures 101
Properties of Transversality and Whitney Stratified Sets 101
Consequences of Transversality for (Multi-) Distance Functions 102
Consequences of Transversality for Height-Distance Functions 107
Generic Properties of and M^ 109
Proof of Theorem 4.17 for a Residual Set of Embeddings 112
Chapter 15. Concluding Generic Properties of Blum Linking Structures 115
Blum Medial Structure Near Corner Points 115
Openness of the Genericity Conditions 117
Relation with Infinitesimally Stable Mappings 118
Openness of Generic Properties for General Configurations 122
CONTENTS vil
Part 4. Proofs and Calculations for the Transversality Theorems 125
Chapter 16. Reductions of the Proofs of the Transversality Theorems 127
Hybrid Transversality Theorem 128
Chapter 17. Families of Perturbations and their Infinitesimal Properties 133
Construction of the Families of Perturbations 133
Computation of Derivatives for Families of Perturbations 135
Multijet Properties Implying Stratification Properties on the Boundaries 137
Chapter 18. Completing the Proofs of the Transversality Theorems 143
Perturbation Transversality Conditions via Fiber Jet Extension Maps 143
Derivatives of Multi-Distance and Height-Distance Functions 146
Verifying the Perturbation Transversality Conditions 147
Concluding the Proofs 152
Appendix A. List of Frequently Used Notation 155
Bibliography 161
|
| any_adam_object | 1 |
| author | Damon, James 1945- Gasparovic, Ellen |
| author_GND | (DE-588)172036828 (DE-588)1141604116 |
| author_facet | Damon, James 1945- Gasparovic, Ellen |
| author_role | aut aut |
| author_sort | Damon, James 1945- |
| author_variant | j d jd e g eg |
| building | Verbundindex |
| bvnumber | BV044732092 |
| classification_rvk | SI 130 |
| ctrlnum | (OCoLC)1020569795 (DE-599)BVBBV044732092 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV044732092 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:00:39Z |
| institution | BVB |
| isbn | 9781470426804 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030128143 |
| oclc_num | 1020569795 |
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| physical | x, 163, 4 ungezählte Seiten |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Damon, James 1945- (DE-588)172036828 aut Medial/skeletal linking structures for multi-region configurations James Damon, Ellen Gasparovic Providence, Rhode Island American Mathematical Society November 2017 x, 163, 4 ungezählte Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 250, number 1193 (sixth of 6 numbers) Verallgemeinerter topologischer Raum (DE-588)4836917-2 gnd rswk-swf Modellierung (DE-588)4170297-9 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Kompakter Raum (DE-588)4164857-2 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Verallgemeinerter topologischer Raum (DE-588)4836917-2 s Kompakter Raum (DE-588)4164857-2 s Modellierung (DE-588)4170297-9 s 1\p DE-604 Gasparovic, Ellen (DE-588)1141604116 aut Memoirs of the American Mathematical Society volume 250, number 1193 (sixth of 6 numbers) (DE-604)BV008000141 1193 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030128143&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Damon, James 1945- Gasparovic, Ellen Medial/skeletal linking structures for multi-region configurations Memoirs of the American Mathematical Society Verallgemeinerter topologischer Raum (DE-588)4836917-2 gnd Modellierung (DE-588)4170297-9 gnd Differentialgeometrie (DE-588)4012248-7 gnd Kompakter Raum (DE-588)4164857-2 gnd |
| subject_GND | (DE-588)4836917-2 (DE-588)4170297-9 (DE-588)4012248-7 (DE-588)4164857-2 |
| title | Medial/skeletal linking structures for multi-region configurations |
| title_auth | Medial/skeletal linking structures for multi-region configurations |
| title_exact_search | Medial/skeletal linking structures for multi-region configurations |
| title_full | Medial/skeletal linking structures for multi-region configurations James Damon, Ellen Gasparovic |
| title_fullStr | Medial/skeletal linking structures for multi-region configurations James Damon, Ellen Gasparovic |
| title_full_unstemmed | Medial/skeletal linking structures for multi-region configurations James Damon, Ellen Gasparovic |
| title_short | Medial/skeletal linking structures for multi-region configurations |
| title_sort | medial skeletal linking structures for multi region configurations |
| topic | Verallgemeinerter topologischer Raum (DE-588)4836917-2 gnd Modellierung (DE-588)4170297-9 gnd Differentialgeometrie (DE-588)4012248-7 gnd Kompakter Raum (DE-588)4164857-2 gnd |
| topic_facet | Verallgemeinerter topologischer Raum Modellierung Differentialgeometrie Kompakter Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030128143&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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