LEADER 04835nam 22007575 450 001 9910349324903321 005 20230810140348.0 010 $a0-387-84808-8 024 7 $a10.1007/978-0-387-84808-2 035 $a(CKB)4100000009751189 035 $a(MiAaPQ)EBC5969412 035 $a(DE-He213)978-0-387-84808-2 035 $a(PPN)258059125 035 $a(EXLCZ)994100000009751189 100 $a20191031d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDiscrete Energy on Rectifiable Sets /$fby Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff 205 $a1st ed. 2019. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2019. 215 $a1 online resource (xviii, 666 pages) $cillustrations 225 1 $aSpringer Monographs in Mathematics,$x2196-9922 311 $a0-387-84807-X 327 $a0. 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. 330 $aThis book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations. Written by leading authorities on the topic, this treatise is designed with the graduate student and further explorers in mind. The presentation includes a chapter of preliminaries and an extensive Appendix that augments a course in Real Analysis and makes the text self-contained. Along with numerous attractive full-color images, the exposition conveys the beauty of the subject and its connection to several branches of mathematics, computational methods, and physical/biological applications. This work is destined to be a valuable research resource for such topics as packing and covering problems, generalizations of the famous Thomson Problem, and classical potential theory in Rd. It features three chapters dealing with point distributions on the sphere, including an extensive treatment of Delsarte?Yudin?Levenshtein linear programming methods for lower bounding energy, a thorough treatment of Cohn?Kumar universality, and a comparison of 'popular methods' for uniformly distributing points on the two-dimensional sphere. Some unique features of the work are its treatment of Gauss-type kernels for periodic energy problems, its asymptotic analysis of minimizing point configurations for non-integrable Riesz potentials (the so-called Poppy-seed bagel theorems), its applications to the generation of non-structured grids of prescribed densities, and its closing chapter on optimal discrete measures for Chebyshev (polarization) problems. . 410 0$aSpringer Monographs in Mathematics,$x2196-9922 606 $aConvex geometry 606 $aDiscrete geometry 606 $aMathematical physics 606 $aMeasure theory 606 $aNumber theory 606 $aTopology 606 $aComputer science$xMathematics 606 $aConvex and Discrete Geometry 606 $aMathematical Methods in Physics 606 $aMeasure and Integration 606 $aNumber Theory 606 $aTopology 606 $aMathematical Applications in Computer Science 615 0$aConvex geometry. 615 0$aDiscrete geometry. 615 0$aMathematical physics. 615 0$aMeasure theory. 615 0$aNumber theory. 615 0$aTopology. 615 0$aComputer science$xMathematics. 615 14$aConvex and Discrete Geometry. 615 24$aMathematical Methods in Physics. 615 24$aMeasure and Integration. 615 24$aNumber Theory. 615 24$aTopology. 615 24$aMathematical Applications in Computer Science. 676 $a518.25 700 $aBorodachov$b Sergiy V$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781828 702 $aHardin$b Douglas P$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSaff$b Edward B$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910349324903321 996 $aDiscrete Energy on Rectifiable Sets$92498804 997 $aUNINA