Sentence examples for spaces involved in from inspiring English sources

The proof follows from the fact that the zero sequence belongs to each of the classes the sequence spaces involved in the intersection.

Compared to these studies, we introduce other projection techniques applied in face recognition to the lipreading task and discuss and justify their use in the different feature spaces involved in the lipreading system: the images themselves, a smooth and compact representation of the images in the frequency domain or the final features used in the classifier.

Theorem 3.2 For any two sequences p = ( p k ) and t = ( t k ) of positive real numbers and for any two 2-norms ∥ ⋅, ⋅ ∥ 1 and ∥ ⋅, ⋅ ∥ 2 on X we have Z ( B ( m ) n, p, ∥ ⋅, ⋅ ∥ 1 ) ∩ Z ( B ( m ) n, p, ∥ ⋅, ⋅ ∥ 2 ) ≠ ∅, where Z = c ¯, c ¯ 0, m, m 0. Proof The proof follows from the fact that the zero element belongs to each of the sequence spaces involved in the intersection.

As usual, the only space involved in Mr. Serra's sculpture is space you can walk through.

The NCI descriptor enables visualizing regions of space involved in either attractive or repulsive interactions.

For eAch point of the grid, the correct detection and falsimilartives rates of the true red-eyes procedurethin the dataset wasemployeded.

In order to reduce the computational time and save the storage space involved in determining the effect of varying particle volume fractions on the flexural properties of HA/PLLA, a superelement technique was applied.

The appropriate carbon shell and void space involved in the yolk shell structure are considered to be the crucial factor in accommodating volume expansion as well as preserving the structural integrity of yolk shell ZnGa2O4@C.

Under physiological conditions neurons and astrocytes release purines into the extracellular space, involved in intercellular communication between neurons and astrocytes via activation of nucleotide receptors of the P2X- (ligand-gated ion channels) and the P2Y-subtype (G-protein coupled receptors) [5] [7].

This assumption is not always true because of the "activity space" involved in the daily travel patterns of individuals [ 11].

Conversely, considering pairs of genes/drugs for which the deletion mutant is resistant to treatment could assist in identifying those drug combinations which are unlikely to succeed, reducing the search space involved in an otherwise expensive combinatorial problem [ 49].