000			03793nam a22005295i 4500
001			978-0-387-78963-7
003			DE-He213
005			20251006084420.0
007			cr nn 008mamaa
008			100825s2010 xxu| s |||| 0|eng d
020			_a9780387789637
020			_a99780387789637
024	7		_a10.1007/978-0-387-78963-7 _2doi
082	0	4	_a512.5 _223
100	1		_aDe Concini, Corrado. _eauthor.
245	1	0	_aTopics in Hyperplane Arrangements, Polytopes and Box-Splines _h[electronic resource] / _cby Corrado De Concini, Claudio Procesi.
250			_a1.
264		1	_aNew York, NY : _bSpringer New York, _c2010.
300			_aXXII, 381p. 19 illus., 4 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext
505	0		_aPreliminaries -- 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			_aSeveral 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	_aMATHEMATICS.
650		0	_aMATRIX THEORY.
650		0	_aTOPOLOGICAL GROUPS.
650		0	_aDIFFERENTIAL EQUATIONS.
650		0	_aCELL AGGREGATION _xMATHEMATICS.
650	1	4	_aMATHEMATICS.
650	2	4	_aLINEAR AND MULTILINEAR ALGEBRAS, MATRIX THEORY.
650	2	4	_aORDINARY DIFFERENTIAL EQUATIONS.
650	2	4	_aAPPROXIMATIONS AND EXPANSIONS.
650	2	4	_aMANIFOLDS AND CELL COMPLEXES (INCL. DIFF.TOPOLOGY).
650	2	4	_aTOPOLOGICAL GROUPS, LIE GROUPS.
700	1		_aProcesi, Claudio. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387789620
830		0	_aUniversitext
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-78963-7 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59132 _d59132