Download PDF by Ramis E., Deschamps C., Odoux J.: Cours de mathematiques speciales: algebre

By Ramis E., Deschamps C., Odoux J.

ISBN-10: 2225815011

ISBN-13: 9782225815010

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Qn } where for each i, qi is allowed to take arbitrary values of Fi . A document Di is an exact partial match for a fuzzy query F if Q ⊆ Di , for some Q in this bunch of ordinary queries corresponding to F. If the Fi are pairwise disjoint, then F consists of n i=1 |Fi | ordinary queries. Although this number might grow rapidly, there are efficient algorithms to compute all matches, see Section 4. Finally, let us discuss a third alternative. Instead of notes [p, t] we now consider pairs of notes ([p, t], [p , t ]) as our basic objects.

1 Conics and Polars Let a1 , a2 , . . , an+1 ∈ IRp,q represent n + 1 = p + q linearly independent vectors in IRp,q . This means that I = a1 ∧a2 ∧ · · · ∧an+1 = 0. As an Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean 17 element in the projective space Πn , I represents the projective n-plane determined by the n + 1 non-co(n − 1)planar points a1 , . . , an+1 . Representing the points of Πn by homogeneous vectors x ∈ IRp,q , makes it easy to study the quadric hypersurface (conic) Q in Πn defined by Q := {x| x ∈ IRp+q , x = 0, and x2 = 0}.

As an example, a database of 180 GB of audio material can be indexed using about 50 MB only, while still allowing audio signals of only several seconds of length to be located within fractions of seconds ([Ribbrock and Kurth, 2002]). Index construction may be performed very efficiently. For the PROMS system, index construction takes only a few minutes, hence allowing for indexing on the fly. Indexing PCM audio data 32 COMPUTATIONAL NONCOMMUTATIVE ALGEBRA may be performed several times faster than real-time on standard PC hardware.

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Cours de mathematiques speciales: algebre by Ramis E., Deschamps C., Odoux J.

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