Henceforth, the obtained products are described in relation to their dimensionality.
Henceforth, we obtain the feedback loop relationship between steering vector a S, diagonal loading level ρ, and weight vector w through (22), (23), (25), and (28).
It then follows from (16 ) and the first-order optimality condition that [∇ u F (u ∗, S ∗ )] T Δ u ≥ 0 and [∇ S F (u ∗, S ∗ )] T Δ S ≥ 0. Henceforth, we obtain that (17) F u ∗ + Δ u, S ∗ + Δ S F u ∗, S ∗ + ∇ u F u ∗, S ∗ T Δ u + ∇ S F u ∗, S ∗ T Δ S ≥ F u ∗, S ∗, which implies that (u ∗, S ∗ ) is a local minimizer of (5 ).
In contrast to constant-density incompressible flows, where the characteristics-based variables reconstruction leads to a single formulation, in the case of variable density flows three different schemes can be obtained henceforth labeled as: transport, conservative and hybrid schemes.
All data presented henceforth has been obtained from EPG recordings that have undergone minimal or no manual correction (see Methods).
For notational brevity, we shall henceforth refer to the obtained serially concatenated codes as diversified space-time (DST) codes.
Henceforth, the acid chlorides obtained above were refluxed with tert-butyl 3-aminopropyl carbamatee (1:1) for 4 h and respective tert-butyl (3-aminopropyl carbamatebamate derivatives were synthesized.
2-[Methoxy polyethyleneoxy propyl]-trichlorosilane (CH3O(C2-[Methoxy polyethyleneoxy propyl]-trichlorosilanebtained from Fluorochem (Hadfield, U.K).
By replacing the standardFoc with other standard salient in the context (e.g., rooms without garbage and with few stuff piled up) (henceforth, standardAlt), the alternatives are obtained, namely, the alternative judgments of the property cleanness, as in 44b.
In particular, the alternatives of the focused denotation (i.e., the denotation of the focus domain) (henceforth, fd) in 33a e are obtained by substituting the correspondent focus associate with other salient elements in the context, as in 34a e, respectively.
