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The differential quantity dU can always be expanded in terms of its partial derivatives according to (29) where the subscripts denote the quantity being held constant when calculating derivatives.
Thus, any function f ∈ L 2 [ 0, 1 ] can be expanded in terms of ShLP.
For the inversion of the singular operators, all functions including the incident field should be expanded in terms of the Fourier series in φ.
An important point is that a general function can be expanded in terms of all the eigenfunctions of an operator, a so-called complete set of functions.
Thus the sinc function, which belongs to the space of band-limited signals, can be expanded in terms of the PSWFs as (4).
We show that the Schrödinger propagator can be expanded in terms of resonances at energy levels at which a barrier separates the interaction region from infinity.
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Klein also says that Kano intends to create integrations with the original Kano computer kit too — which, at least for now, continues to be the business' main revenue engine — and which he notes will soon be expanding in terms of retail availability, with the startup inking deals to stock its computer kits in ToysRUs and Barnes & Noble in the U.S. in time for the holiday season.
Both parts are expanded in terms of spherical harmonics.
All variables are expanded in terms of Fourier–Hermite basis functions.
They are expanded in terms of an integral transform associated to the sub-Laplacian.
The general forced solution is expanded in terms of these complex modes.
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