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Titlebook: Sphere Packings; Chuanming Zong,John Talbot Textbook 1999 Springer Science+Business Media New York 1999 Kabatjanski-Levenstein method.Latt

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发表于 2025-3-21 18:02:59 | 显示全部楼层 |阅读模式
书目名称Sphere Packings
编辑Chuanming Zong,John Talbot
视频video
丛书名称Universitext
图书封面Titlebook: Sphere Packings;  Chuanming Zong,John Talbot Textbook 1999 Springer Science+Business Media New York 1999 Kabatjanski-Levenstein method.Latt
描述Sphere Packings is one of the most attractive and challenging subjects in mathematics. Almost 4 centuries ago, Kepler studied the densities of sphere packings and made his famous conjecture. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with othe subjects found. Thus, though some of its original problems are still open, sphere packings has been developed into an important discipline. This book tries to give a full account of this fascinating subject, especially its local aspects, discrete aspects and its proof methods.
出版日期Textbook 1999
关键词Kabatjanski-Levenstein method; Lattice; Lattice packings; Sphere packing; sausage conjecture; combinatori
版次1
doihttps://doi.org/10.1007/b98975
isbn_softcover978-1-4757-8148-9
isbn_ebook978-0-387-22780-1Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer Science+Business Media New York 1999
The information of publication is updating

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发表于 2025-3-21 20:33:42 | 显示全部楼层
Lower Bounds for the Packing Densities of Spheres,ant and interesting. In 1905, by studying positive definite quadratic forms, Minkowski [6] proved . where . is the Riemann zeta function, and made a general conjecture for bounded .. Forty years later his conjecture was proved by Hlawka [1]. In this section we prove the Minkowski-Hlawka theorem for
发表于 2025-3-22 03:21:42 | 显示全部楼层
Sphere Packings Constructed from Codes,enience, we say that a codeword or point is of type [.∣.∣⋯] if . = ∣.∣ for . choices of ., . = ∣. for [itl} choices of ., etc. The . between two codewords . and . of . is the number of coordinates at which they differ, and is denoted by ‖., .‖.. The . of a codeword ., .(.), is the number of its nonz
发表于 2025-3-22 08:08:34 | 显示全部楼层
Upper Bounds for the Packing Densities and the Kissing Numbers of Spheres I,be a packing and let . be a number such that . > 1. Then, replace the spheres . + x, where x ∈ ., by . + x and fill each of these new spheres with a certain amount of mass, of variable density, such that the total mass at any point of . does not exceed 1. Hence, the total mass of the spheres . + x,
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Finite Sphere Packings,be a unit vector in .. Then, we define ., it can be regarded as a local density of . + . in .,.. By routine computation it follows that . Based on this observation, in 1975 L. Fejes Tóth [10] made the following conjecture about the volume case of the above problem.
发表于 2025-3-23 07:00:40 | 显示全部楼层
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