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Topics in Hyperplane Arrangements, Polytopes and Box-Splines / by Corrado De Concini, Claudio Procesi
(Universitext. ISSN:21916675)
版 | 1st ed. 2010. |
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出版者 | (New York, NY : Springer New York : Imprint: Springer) |
出版年 | 2010 |
大きさ | XXII, 381 p. 19 illus., 4 illus. in color : online resource |
著者標目 | *De Concini, Corrado author Procesi, Claudio author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis LCSH:Geometry LCSH:Algebra LCSH:Algebras, Linear LCSH:Differential equations LCSH:Approximation theory FREE:Analysis FREE:Geometry FREE:Algebra FREE:Linear Algebra FREE:Differential Equations FREE:Approximations and Expansions |
一般注記 | Preliminaries -- Polytopes -- Hyperplane Arrangements -- Fourier and Laplace Transforms -- Modules over the Weyl Algebra -- Differential and Difference Equations -- Approximation Theory I -- The Di?erentiable Case -- Splines -- RX as a D-Module -- The Function TX -- Cohomology -- Differential Equations -- The Discrete Case -- Integral Points in Polytopes -- The Partition Functions -- Toric Arrangements -- Cohomology of Toric Arrangements -- Polar Parts -- Approximation Theory -- Convolution by B(X) -- Approximation by Splines -- Stationary Subdivisions -- The Wonderful Model -- Minimal Models Several mathematical areas that have been developed independently over the last 30 years are brought together revolving around the computation of the number of integral points in suitable families of polytopes. The problem is formulated here in terms of partition functions and multivariate splines. In its simplest form, the problem is to compute the number of ways a given nonnegative integer can be expressed as the sum of h fixed positive integers. This goes back to ancient times and was investigated by Euler, Sylvester among others; in more recent times also in the higher dimensional case of vectors. The book treats several topics in a non-systematic way to show and compare a variety of approaches to the subject. No book on the material is available in the existing literature. Key topics and features include: - Numerical analysis treatments relating this problem to the theory of box splines - Study of regular functions on hyperplane and toric arrangements via D-modules - Residue formulae for partition functions and multivariate splines - Wonderful completion of the complement of hyperplane arrangements - Theory and properties of the Tutte polynomial of a matroid and of zonotopes Graduate students as well as researchers in algebra, combinatorics and numerical analysis, will benefit from Topics in Hyperplane Arrangements, Polytopes, and Box Splines HTTP:URL=https://doi.org/10.1007/978-0-387-78963-7 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9780387789637 |
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電子リソース |
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EB00203873 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000115252 |
ISBN | 9780387789637 |
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