# scalar triple product

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## scalar triple product

[′skā·lər ′trip·əl ‚präd·əkt]
(mathematics)
The scalar triple product of vectorsv1,v2, andv3 from Euclidean three-dimensional space determines the volume of the parallelepiped with these vectors as edges; it is given by the determinant of the 3 × 3 matrix whose rows are the components ofv1,v2, andv3. Also known as triple scalar product.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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His topics include the q-binomial theorem, Heine's transformation, the Jacobi triple product identity, the Rogers-Fine identity, Bailey chains, WP-Bailey pairs and chains, further results on Bailey/WP-Bailey pairs and chains, bijective proofs of basic hypergeometric identities, q-continued fractions, Lambert series, and mock theta functions.
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At the end of Q1, penetration of triple product customers increased to 36% compared to 33% in the first quarter of 2013.
Equation (5) indicates [x.sub.k,n,p] as a sum of triple products, which is variably known as the trilinear model, trilinear decomposition, triple product decomposition, canonical decomposition, or parallel factor (PARAFAC) analysis.
With above notation, the celebrated Jacobi triple product identity can be expressed as follow
An invitation to q-series; from Jacobi's triple product identity to Ramanujan's "most beautiful identity".
Jacobi's triple product identity (JTP) is ubiquitous in various areas of mathematics and especially in analytical number theory.
Thanks to this triple product registration in the EU, Novus is confident that it will repeat the Brazilian and US successes of the MINTREX[R] range in Europe.
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In this paper, we obtain a new proof of Ramanujan's receprocity theorem using an Heine's transformation which is a generalization of Jacobi's triple product identity.
The lowest order I-violating combination of spins and momenta appears in the form of the mixed triple product. From the experimentally accessible quantities, four triple products can be formed: R J * (p X s), D J * (p X [p.sub.v]), V J * (P X s), L P * (p X s), where J is the spin of the parent system, s, p are the spin and momentum of the detected lepton, P denotes the momentum of the recoil system and [p.sub.v] stands for the momentum of the unobserved neutrino.
But the triple product of energy, confinement time and density--the three critical parameters -- is 10 to 20 times that of DCX-1, and none of the typical instabilities formed.

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