Sentence examples for if we endow from inspiring English sources

From [15, 17 19], it is clear that W 2 3 [ 0, 1 ] become a reproducing kernel Hilbert space if we endow it with suitable inner product.

On the other hand, if we endow with the discrete topology and denote by the one-point compactification of, then is isometrically contained in, where is a topological compact space which satisfies.

We show that the open unit ball of the space of operators from a finite-dimensional Hilbert space into a separable Hilbert space (we call it "operator ball") has a restricted form of normal structure if we endow it with a hyperbolic metric (which is an analogue of the standard hyperbolic metric on the unit disc in the complex plane).

By the Schwarz-Pick lemma, (phi mathbb{D}_{r}rightarrow U') is weakly contracting in the Poincaré metrics of (mathbb{D}_{r}) and (U'), hence strongly contracting if we endow (U') with the Poincaré metric of U. By Lemma 3.2 we have (|phi' z)|<1) for (zinmathbb{D}_{r}).

On the other hand, if we endow X with the standard metric d x, y) = |x - y| for all x, y ∈ X, we have d ( F ( x ), F ( y ) ) = | F ( x ) - F ( y ) | = 2 | x - y | > φ ( | x - y | ). for x ≠ y and for any φ : [0, +∞) → [0, +∞) satisfying φ(t) < t for t > 0. Therefore, Theorem 3.6 of O'Regan and Petruşel [29] is not applicable.

Note that if is a partially ordered set, then we endow the product with the following partial order: (253).

If ( X, ⪯ ) is a partially ordered set, we endow the product set X × X with the partial order ∇ defined by ( x, y ) ∇ ( u, v ) ⇔ x ⪯ u, v ⪯ y.

If (X, d) is a cone metric space, we endow the product set X × X by the cone metric ν defined by.

We endow G with the norm ?

"If we are endowed by our creator with rights, then why shouldn't those be attainable by gays and lesbians?" he wrote in a statement to The Tampa Bay Times.

"If we are endowed by our Creator with rights, then why shouldn't those be attainable by gays and lesbians?" Nelson told the Tampa Bay Times.