Product diadic

Here I stands for the 3 x 3 unit matrix acting (as does the 3 x 3 diadic product <, m <8> eRmLm) on the vector parts of HOs in the quaternion form. 

The details of electron distribution in atoms characterized by higher multipoles (dipoles and quadrupoles) are defined by the deviations S P . As it has been already mentioned the vector parts of the HOs centered at each given atom vA transform as 3-vectors under the molecule/space rotations, and the hybrid densities sAvA transform as 3-vectors as well. On the other hand, the diadic products v,A vA under 3-dimensional rotations transform as a sum of a scalar and of the rank two tensor of the 3-dimensional space. The values of these momenta are obtained by averaging their standard definitions ... 

Catalyst performance has of course been a permanent theme in industry. For example, the catalytic activity of oxo catalysts (in hydroformylation) has improved in the past 50 years by a factor of 10 000 change from diadic and triadic process technology to continuous plant operation, replacement of cobalt by rhodium, tailoring of the ligand sphere (phosphines), change of phase application (from mono- to two-phase processes). At the same time, an improvement of selectivity has been achieved, apart from the ease of product/catalyst separation [132]. A similar development seems to occur in the Monsanto acetic acid process [49]. 

Here ij, etc., represent diadic products of the elementary Cartesian vectors. The unit vector is... 

The diadic product of two vectors is a second-rank tensor... 

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See also in sourсe #XX -- [ , ]

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