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The most compact way of writing these equations in the metre-kilogram-second (mks) system is in terms of the vector operators div (divergence) and curl.
In this way, one arrives at a notion of semantics based on metrics and operators in vector spaces, where vector operators can mimic Boolean operators in various ways (Gärdenfors 2000; Widdows 2004; Clarke 2012).
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The vector operator denotes the mirroring operation in which the vector indices are reversed, such that where for and for.
The vector operator, called "del".
The cross product of the vector operator with the vector w.
The divergence of the vector field w; it is the dot product of the vector operator with the vector w, or.
(Here the tangential gradient operator is the vector operator (delta =(delta _1, ldots, delta _n)) with (delta _i = (delta _{ij}-nu _inu _j D_j), where (delta _{ij}) is the usual Kronecker delta).
Since a vector operator is isomorphic, ( X 1 ∗, X 2 ∗, …, X q ∗ ) is the unique least Frobenius norm generalized reflexive solution group of the system of matrix equations (5).
The vector operator creates a vector from a matrix by stacking the columns of the matrix on top of each other.
The apozidation and zero-filling parameters in steps ii iv partially define a vector operator F͡ that can be applied identically to both the acquired FID and a model FID.
The apodization and zero-filling parameters associated with steps i-iv along each dimension d define a vector operator F ^ d that can be applied identically to both the acquired FID and the model FID along dimension d.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com