球垛格點(diǎn)和群

前言

The main themes.  This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5,.... Given a large number of equal spheres, what is the most efficient （or densest） way to pack them together？ We also study several closely related problems: the kissing number problem, which asks how many spheres can be arranged so that they all touch one central sphere of the same size; the covering problem, which asks for thc least dense way to cover n-dimensional space with equal overlapping spheres; and the quantizing problem, important for applications to analog-to-digital conversion （or data compression）, which asks how to place points in space so that the average second moment of their Voronoi cells is as small as possible.  Attacks on these problems usually arrange the spheres so their centers form a lattice. Lattices are described by quadratic forms, and we study the classification of quadratic forms. Most of the book is devoted to these five problems.

內(nèi)容概要

本書為第三版，繼前兩版之后，接著探討“如何最有效地將大量等球放入n維的歐氏空間中？”這一核心問題。同時(shí)，作者仍在思考一些相關(guān)的問題，如：吻接數(shù)問題，覆蓋問題，量子化問題以及格分類與二次型。與前兩版相同的是，第三版也描述了以上這些問題與數(shù)學(xué)或自然科學(xué)中其他一些領(lǐng)域的聯(lián)系，這些領(lǐng)域包括：碼理論，數(shù)字通信，數(shù)論，群論，模擬數(shù)字轉(zhuǎn)換以及數(shù)據(jù)壓縮與n維晶體。值得特別注意的是，本書收錄了一篇介紹本領(lǐng)域的最新的一些研究成果的報(bào)告，并補(bǔ)充了1988-1998年間出版的超過800項(xiàng)的參考書目，相信這些珍貴的資料一定能夠引起讀者特殊的興趣。本書適用于數(shù)學(xué)專業(yè)的高年級(jí)本科生或研究生以及需要相關(guān)知識(shí)的科研人員。

作者簡(jiǎn)介

作者：(英國)康韋 (Conway.J.H)

書籍目錄

Preface to First EditionPreface to Third EditionList of SymbolsChapter 1 Sphere Packings and Kissing NumbersChapter 2 Coverings,Lattices and QuantizersChapter 3 Codes,Designs and GroupsChapter 4 Certain Important Lattices and Their PropertiesChapter 5 Sphere Packing and Error-Correcting CodesChapter 6 Laminated LatticesChapter 7 Further Connections Betwwen Codes and LatticesChapter 8 Algebraic Constructions for LatticesChapter 9 Bounds for Codes and Sphere PackingsChapter 10 Three Lectures on Exceptional GroupsChapter 11 The Golay Codes and the Mathieu GroupsChapter 12 A Characterization of the Leech LatticeChapter 13 Bounds on Kissing NumbersChapter 14 Uniqueness of Certain Spherical CodesChapter 15 On the Classification of Integral Quadratic FormsChapter 16 Enumeration of Unimodular LatticesChapter 17 The 24-Dimensional Odd Unimodular LatticesChapter 18 Even Unimodular 24-Dimensional LatticesChapter 19 Enumeration of Extremal Self-Dual LatticesChapter 20 Finding the Closest Lattice PointChapter 21 Voronoi Cells of Lattices and Quantization ErrorsChapter 22 A Bound for the Covering Radius of the Leech LatticeChapter 23 The Covering Radius of the Leech LatticeChapter 24 Twenty-Three Constructions for the Leech LatticeChapter 25 The Cellular Structure of the Leech LatticeChapter 26 Lorentzian Forms for the Leech LatticeChapter 27 The Automorphism Group of the 26-Dimensional Even Unimodular Lorentzian LatticeChapter 28 Leech Roots and Vinberg GroupsChapter 29 The Monster Group and its 196884-Dimensional SpaceChapter 30 A Monster Lie Algebra?BibliographySupplementary BibliographyIndex

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