Discrete Energy on Rectifiable Sets (Hardcover, 1st ed. 2019)

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.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Springer Monographs in Mathematics
Release date:	November 2019
First published:	2019
Authors:	Sergiy V. Borodachov • Douglas P. Hardin • Edward B. Saff
Dimensions:	235 x 155 x 45mm (L x W x T)
Format:	Hardcover
Pages:	666
Edition:	1st ed. 2019
ISBN-13:	978-0-387-84807-5
Categories:	Books > Science & Mathematics > Physics > General Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Books > Science & Mathematics > Mathematics > Topology > General Books > Science & Mathematics > Mathematics > Number theory > General Books > Science & Mathematics > Mathematics > Applied mathematics > General
LSN:	0-387-84807-X
Barcode:	9780387848075

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