Discrete Energy on Rectifiable Sets

Released on by Sergiy V. Borodachov
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  • Discrete Energy on Rectifiable Sets Book Detail

  • Author : Sergiy V. Borodachov
  • Release Date : 2019-10-31
  • Publisher : Springer Nature
  • Genre : Mathematics
  • Pages : 666
  • ISBN 13 : 0387848088
  • File Size : 29,29 MB
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Discrete Energy on Rectifiable Sets by Sergiy V. Borodachov PDF Summary

Book Description: 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.

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This book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations. Written by leading authorities

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This package (book + CD-ROM) has been replaced by the ISBN 0321388410 (which consists of the book alone). The material that was on the CD-ROM is available for d