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The discretization will be sufficient provided that the set of admissible functions is complete and a sufficiently large number of functions is used.
In this paper, we prove that for every ρ∈U∞, the space of weighted pseudo almost automorphic functions is complete under the supremum norm.
Moreover, they proved that the space of P(Lambda Lambda) functions is complete; so they solve a key fundamental problem on this issue and pave the road to further study the applications of P(Lambda Lambda) functions.
A set of orthonormal wave functions is complete in the space of square-integrable functions if any wave function ψ can be expressed as a combination of the φn: : \psi = \sum c_n \phi_n, with c_n = \langle \phi_n | \psi \rangle.
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In the context of structural mechanics, it is established that the basis functions are complete with respect to affine transformations, meaning that all rigid body motions and constant strain states are exactly represented.
So at least implicitly, Kant's propositional logic of truth-functions is complete.
Lastly, it might be safer to perform adrenalectomy several weeks after the initial catastrophic presentation, once recovery of LV systolic function is complete.
Corollary 1.2 If an affine maximal surface given by a strictly convex function is complete with respect to α-metric with α > − 1, then it must be an elliptic paraboloid.
However, in the hippocampus, the Cux2 neo/neo mutation abolished all Cux2 immunoreactivity, demonstrating the loss of function is complete (Supporting Information Fig. S1).
Steroidal hormones are usually deactivated after their function is complete in the liver using biochemical transformations that modify chemically its structure.
Here are the Fourier transforms of functions being completed by zero up to the whole axis.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com