Exact(3)
The embedding yields distances between nodes that carry more semantics than plain hop counts, and can be used within further applications (search, recommendations).
For the preparation of sediments and colloidal suspension in nonmarine, low ionic strength aqueous environments, Nanoplast embedding yields high quality ultrathin sections free of extraction artifacts and salt precipitation with minimal handling disturbance to the structural integrity.
Once the joint dissimilarity and weighting matrices are specified, a d-dimensional BiFold embedding yields coordinates (X=(boldsymbol {x}_{1},boldsymbol {x}_{2},dots,boldsymbol{x}_{m})) and (Y=(boldsymbol{y}_{1},boldsymbol {y}_{2},dots,boldsymbol{y}_{n})) to denote the sets of points corresponding row objects and column objects.
Similar(57)
In the current situation, Sobolev's embedding theorem yields the existence of a constant C s depending only on s, n, and N such that we have sup B ρ + ( x 0 ) | g − g x 0, ρ ′ | ≤ C s ρ 1 − n s ∥ g ∥ H 1, s ( B ρ + ( x 0 ), R N ) (1.4).
Still, the semantics is not in conflict with (C): tautologies might differ structurally or in the meaning of their constituents, which could explain how their embedding can yield non-synonymous sentences; cf. Carnap (1947) and Lewis (1970).
Within the vicious thunderstorm line, embedded supercells yielded nearly a half dozen simultaneous tornadic circulations at times.
The embedded sensors yield the absolute liquid water content and enable an experimental, non-destructive monitoring of liquid water in porous materials.
Applying the Gronwall inequality and the Sobolev embedding theorem yields ∥ ρ φ N ∥ L 2 n ≤ e ( 4 M + λ ) t ∥ ρ 0 φ N ∥ L 2 n.
If l > n / q and u ∈ E q t ( D ) then the Sobolev embedding theorem yields sup ξ ∈ Ω | D s u | ≤ c max { 1, t, …, t l } t k ∥ u ∥ E q t ( D ) ≤ c 0 t k, | s | = k ∈ Z +, (21).
In the current situation the Sobolev embedding theorem yields the existence of a constant C s depending only on s, n and N such that there holds: sup B ρ + ( x 0 ) | g - g x 0, ρ ′ | ≤ C s ρ 1 - n s g H 1, s ( B ρ + ( x 0 ), R N ), (1.4).
The Sobolev embedding theorem yields the existence of a constant C s depending only on s, n and N such that sup B ρ + ( x 0 ) | g − g x 0, ρ ′ | ≤ C s ρ 1 − n s ∥ g ∥ H 1, s ( B ρ + ( x 0 ), R N ) (3.1).
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Justyna Jupowicz-Kozak
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