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With scalar-variable application defined, we can lift the application of a substitution to general types with no difficulty.
This would reduce the problem once more to determining sequences of scalars and, if one chooses well, their number need not be prohibitively large.
Only 22 of the set of 30 scalar equations derived from (28) are independent.
The scalar potential in the continuity and momentum equations is taken as the linear combination of the electrostatic and self-gravitational potential.
The scalar organisation of these chorus melodies also offers an interesting contrast with their verses.
The other operations involve vector-vector dot products, scalar-vector multiplies, and in general, only operations involving vectors.
The operands considered mostly in engineering design include scalars and three-dimensional vectors.
The inner product of two vectors is equivalent to the standard scalar (dot) product.
Reversing any of these conventions on orientation may change local signs in the incidence function, but not the final, scalar results of computations.
The results apply to semi- and fully discrete approximations of scalar and systems of conservation laws.
But perhaps this claim is more controversial on the scalar than on the bivalent view.
This motivates scalar construal which systematically limits the licensing potential of polarity triggers.
Regularization of the stress-energy tensor for vector and scalar particles propagating in a general background metric.
Since the scalar potentials are matched at the reference surface, it follows that they are matched globally.
In the sections on the analysis of subdivision schemes, we consider only schemes with scalar masks.
