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The Resource Discrete Energy on Rectifiable Sets, by Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff, (electronic resource)

Discrete Energy on Rectifiable Sets, by Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff, (electronic resource)

Creator
Author
Contributor
Summary
This book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations. Written by leading authorities on the topic, this treatise is designed with the graduate student and further explorers in mind. The presentation includes a chapter of preliminaries and an extensive Appendix that augments a course in Real Analysis and makes the text self-contained. Along with numerous attractive full-color images, the exposition conveys the beauty of the subject and its connection to several branches of mathematics, computational methods, and physical/biological applications. This work is destined to be a valuable research resource for such topics as packing and covering problems, generalizations of the famous Thomson Problem, and classical potential theory in Rd. It features three chapters dealing with point distributions on the sphere, including an extensive treatment of Delsarte–Yudin–Levenshtein linear programming methods for lower bounding energy, a thorough treatment of Cohn–Kumar universality, and a comparison of 'popular methods' for uniformly distributing points on the two-dimensional sphere. Some unique features of the work are its treatment of Gauss-type kernels for periodic energy problems, its asymptotic analysis of minimizing point configurations for non-integrable Riesz potentials (the so-called Poppy-seed bagel theorems), its applications to the generation of non-structured grids of prescribed densities, and its closing chapter on optimal discrete measures for Chebyshev (polarization) problems.--
Language
eng
Work
Publication
Edition
1st ed. 2019.
Extent
1 online resource (XVIII, 666 pages)
Contents
  • 0. An Overview: Discretizing Manifolds via Particle Interactions.-1. Preliminaries
  • 2. Basics of Minimal Energy
  • 3.-Introduction to Packing and Covering
  • 4. Continuous and Discrete Energy
  • 5. LP Bounds on the Sphere
  • 6. Asymptotics for Energy Minimizing Congurations on Sd
  • 7. Some Popular Algorithms for Distributing Points on S2
  • 8. Minimal Energy in the Hypersingular Case
  • 9. Minimal Energy Asymptotics in the "Harmonic Series" Case
  • 10. Periodic Riesz Energy
  • 11. Congurations with non-Uniform Distribution
  • 12. Low Complexity Energy Methods for Discretization
  • 13. Best-Packing on Compact Sets
  • 14. Optimal Discrete Measures for Potentials: Polarization (Chebyshev) Constants
  • Appendix
  • References
  • List of Symbols
  • Index
Isbn
9780387848082
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-0-387-84808-2
Instance
Label
Discrete Energy on Rectifiable Sets
Title
Discrete Energy on Rectifiable Sets
Statement of responsibility
by Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
Creator
Contributor
Author
Subject
Language
eng
Summary
This book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations. Written by leading authorities on the topic, this treatise is designed with the graduate student and further explorers in mind. The presentation includes a chapter of preliminaries and an extensive Appendix that augments a course in Real Analysis and makes the text self-contained. Along with numerous attractive full-color images, the exposition conveys the beauty of the subject and its connection to several branches of mathematics, computational methods, and physical/biological applications. This work is destined to be a valuable research resource for such topics as packing and covering problems, generalizations of the famous Thomson Problem, and classical potential theory in Rd. It features three chapters dealing with point distributions on the sphere, including an extensive treatment of Delsarte–Yudin–Levenshtein linear programming methods for lower bounding energy, a thorough treatment of Cohn–Kumar universality, and a comparison of 'popular methods' for uniformly distributing points on the two-dimensional sphere. Some unique features of the work are its treatment of Gauss-type kernels for periodic energy problems, its asymptotic analysis of minimizing point configurations for non-integrable Riesz potentials (the so-called Poppy-seed bagel theorems), its applications to the generation of non-structured grids of prescribed densities, and its closing chapter on optimal discrete measures for Chebyshev (polarization) problems.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Borodachov, Sergiy V
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Hardin, Douglas P
  • Saff, Edward B
Series statement
  • Springer Monographs in Mathematics,
  • Springer eBooks.
http://library.link/vocab/subjectName
  • Convex geometry
  • Discrete geometry
  • Physics
  • Measure theory
  • Number theory
  • Topology
  • Information theory
Label
Discrete Energy on Rectifiable Sets, by Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-0-387-84808-2
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
0. An Overview: Discretizing Manifolds via Particle Interactions.-1. Preliminaries -- 2. Basics of Minimal Energy -- 3.-Introduction to Packing and Covering -- 4. Continuous and Discrete Energy -- 5. LP Bounds on the Sphere -- 6. Asymptotics for Energy Minimizing Congurations on Sd -- 7. Some Popular Algorithms for Distributing Points on S2 -- 8. Minimal Energy in the Hypersingular Case -- 9. Minimal Energy Asymptotics in the "Harmonic Series" Case -- 10. Periodic Riesz Energy -- 11. Congurations with non-Uniform Distribution -- 12. Low Complexity Energy Methods for Discretization -- 13. Best-Packing on Compact Sets -- 14. Optimal Discrete Measures for Potentials: Polarization (Chebyshev) Constants -- Appendix -- References -- List of Symbols -- Index
Control code
978-0-387-84808-2
Dimensions
unknown
Edition
1st ed. 2019.
Extent
1 online resource (XVIII, 666 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9780387848082
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
62 illustrations, 53 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1126278829
Label
Discrete Energy on Rectifiable Sets, by Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-0-387-84808-2
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
0. An Overview: Discretizing Manifolds via Particle Interactions.-1. Preliminaries -- 2. Basics of Minimal Energy -- 3.-Introduction to Packing and Covering -- 4. Continuous and Discrete Energy -- 5. LP Bounds on the Sphere -- 6. Asymptotics for Energy Minimizing Congurations on Sd -- 7. Some Popular Algorithms for Distributing Points on S2 -- 8. Minimal Energy in the Hypersingular Case -- 9. Minimal Energy Asymptotics in the "Harmonic Series" Case -- 10. Periodic Riesz Energy -- 11. Congurations with non-Uniform Distribution -- 12. Low Complexity Energy Methods for Discretization -- 13. Best-Packing on Compact Sets -- 14. Optimal Discrete Measures for Potentials: Polarization (Chebyshev) Constants -- Appendix -- References -- List of Symbols -- Index
Control code
978-0-387-84808-2
Dimensions
unknown
Edition
1st ed. 2019.
Extent
1 online resource (XVIII, 666 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9780387848082
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
62 illustrations, 53 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1126278829

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