Exact(7)
It achieves dimension reduction by a Petrov Galerkin projection associated with residual minimization; it delivers computational efficiency by a hyper-reduction procedure based on the 'gappy POD' technique.
This is due in part to difficulties arising from the fact that Galerkin techniques perform optimal projection associated with residual minimization at the time-continuous level, while LSPG techniques do so at the time-discrete level.
Denote by P i the spectral projection associated with F and the spectral set {μ i }.
Note that we can also express μu as μu(P) = Tr(P Pu), where Pu is the one-dimensional projection associated with the unit vector u.
Gleason's theorem can now be invoked to identify the states on A with the density operators on H: to each state ω in ω(AH) there corresponds a unique density operator W such that, for every unit vector x of H, ω(x) = = Tr WPx), Px being the one-dimensional projection associated with x.
Let μ n be a pole of the resolvent of A of order k n and P n the spectral projection associated with μ n P n = 1 2 π i ∫ Γ n ( μ - A ) - 1 d μ, where Γ n is a small circle centered at μ n such that it surrounds no point of σ(A) except μ n.
Similar(53)
The other one is for the spectral projections associated to the sub-Laplacian.
However, variance of wave-climate projections associated with study methodology dominates other sources of uncertainty (for example, climate scenario and model uncertainties).
Damage to a second putative white matter bottleneck in the left deep prefrontal white matter involving projections associated with ventral language pathways and thalamo-cortical projections has recently been proposed as a source of semantic deficits after stroke.
To balance locality and computational efficiency, the hash projection matrix of each instance is parameterized, with guaranteed approximation error bound, as a linear combination of basis hash projections associated with a small set of anchor points.
Let, let, and let be the sequence of projections associated with the basis, then it holds that (2.10).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com