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)
Resource Information
The item Discrete Energy on Rectifiable Sets, by Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Discrete Energy on Rectifiable Sets, by Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
- 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
- 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
- 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
- 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.--
- 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)
- 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)
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.eui.eu/portal/Discrete-Energy-on-Rectifiable-Sets-by-Sergiy-V./TFv-NsOPsJ4/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/Discrete-Energy-on-Rectifiable-Sets-by-Sergiy-V./TFv-NsOPsJ4/">Discrete Energy on Rectifiable Sets, by Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff, (electronic resource)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>