For FTIR experiments focusing in on the physiologically relevant range of glucose concentrations (50-400 mg/dL) in aqueous and serum solutions, a denser range of nominal concentration values was used.
Moral systems, McEwan writes, are "like peaks in a dense mountain range seen from a great distance, none obviously higher, more important, truer than another".
Let H be a complex, separable, infinite dimensional Hilbert space, and let (L(H)) denote the algebra of all linear bounded operators on H, (C(H)) the set of linear operators A with domain (D(A)) dense in H and range (R A)) contained in H and a graph (G A)) closed in (Htimes H). (K(H)) is the set of compact elements of (L(H)).
As another application of the construction of derivations, we show that ifAis aC*-algebra of the above type andα∈HInn(A) has the Rohlin property and comes fromϕ∈Hom K1(A), R) with dense range as in Kishimoto and Kumjian (preprint), then the crossed productA×αZis again of the same type; in particularA×αZis an AT algebra.
It says that if (A_n) is a family of self-adjoint operators, they have a srs limit for some A if and only if ((A_n-z)^{-1}) has a strong limit with dense range for one z in ({mathbb {C}}_+) and one z in ({mathbb {C}}_-).
Let Λ be an at most countable index set, define ℓ 2 ≔ x = (x λ ) λ ∈ Λ ⊂ R : ∑ λ ∈ Λ | x λ | 2 < ∞, and assume that F X X ≔ ℓ → Y is a bounded linear operator with dense range in the Hilbert space Y.
Suppose that (Ain mathcal{L}(H)) is a compact operator in Hilbert space, injective and with dense range.
One can show that it has zero null space and dense range in this case.
We consider the liquid-side mass transfer coefficient kL in a dense bubble swarm for a wide range of gas volume fraction (0.45%≤αG≤16.5%).
As we will see in the experimental sections, the described pairwise alignment pipeline, even compared to other solutions, presents good performance and is suitable for automatic alignment of dense range scans in terms of computational speed and robustness (successful alignment rate).
