Sentence examples for spaces used in from inspiring English sources

For a complex-valued vector function u = (u1,..., u s ) defined on Q, we denote D u p = ( D u 1 p,..., D u s p ), u t j = ∂ j u ∂ t j = ( ∂ j u 1 ∂ t j, …, ∂ j u s ∂ t j ), | u | = ( ∑ j = 1 s | u j | 2 ) 1 2.. Let us introduce the following functional spaces used in this paper.

The Sobolev spaces used in the following belong to standard (see [20]).

This selective operation is repeated for all color spaces used in our application.

The ColorEdge CG275W comes with six preset color modes that reproduce common color spaces used in pre-press, digital photography, broadcasting and digital cinema: Adobe RGB, sRGB, Rec709, EBU, SMPTE-C, and DCI.

For the sake of completeness, we briefly recall some notions from the theory of fuzzy metric spaces used in this paper.

We recall that the Triebel-Lizorkin space is a unification of most of the classical function spaces used in partial differential equations such as Lebesgue space (L^{p}(mathbb{R}^{N})), Sobolev space (H_{p}^{s}(mathbb{R}^{N})) and Hölder space (C^{s}(mathbb {R}^{N})) for (s>0).

They have been employed in research into the polio vaccine, and into the effects of atomic warfare; they were shot into space, used in AIDS research.

Note: Because we couldn't precisely reproduce the spacing used in this poem here on our blog, please also view it on the Poetry Magazine page.

The basic space used in this paper is (E=C[0,1]).

The basic space used in this paper is (Q(I)).

The metabolic space used in model construction contains 314 reconstructed biochemical reactions and 287 compounds.