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20140310151441.0 |
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100825s2010 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780387789637 |
|
978-0-387-78963-7 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA184-205 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.5 |
| Edition number |
23 |
| 264 #1 - |
|---|
| -- |
New York, NY : |
| -- |
Springer New York, |
| -- |
2010. |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
De Concini, Corrado. |
| Relator term |
author. |
| 245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
Topics in Hyperplane Arrangements, Polytopes and Box-Splines |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by Corrado De Concini, Claudio Procesi. |
| 250 ## - EDITION STATEMENT |
|---|
| Edition statement |
1. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XXII, 381p. 19 illus., 4 illus. in color. |
| Other physical details |
online resource. |
| 440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
|---|
| Title |
Universitext |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
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. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
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| Topical term or geographic name as entry element |
Matrix theory. |
|
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| Topical term or geographic name as entry element |
Topological Groups. |
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| Topical term or geographic name as entry element |
Differential Equations. |
|
|---|
| Topical term or geographic name as entry element |
Cell aggregation |
| General subdivision |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Linear and Multilinear Algebras, Matrix Theory. |
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| Topical term or geographic name as entry element |
Ordinary Differential Equations. |
|
|---|
| Topical term or geographic name as entry element |
Approximations and Expansions. |
|
|---|
| Topical term or geographic name as entry element |
Manifolds and Cell Complexes (incl. Diff.Topology). |
|
|---|
| Topical term or geographic name as entry element |
Topological Groups, Lie Groups. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Procesi, Claudio. |
| Relator term |
author. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9780387789620 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-0-387-78963-7 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
|
| Item type |
E-Book |
