Sentence examples for spaces we found from inspiring English sources

"It celebrates and builds on the loss of these somewhat sacred spaces we found growing up going to arcades at the mall," Mr. Miller, 39, said.

While GE is insensitive to effects of mechanical water entrapment variations in roughness spaces, we found that the viscoelastic model, a typical QCM-D model analysis approach, overestimates the mass of deposited TiO2NP.

In the case of tensor product spaces, we find under very general conditions bases of minimally founded functions although we show that, in contrast to the univariate case, they are no least founded bases.

In the framework of Hilbert spaces, we find the following.

In the framework of Hilbert spaces, we find from Theorem 3.1 the following result.

Using Hölder's inequality for the classical Lebesgue spaces we find that (4.24).

Then { x n } converges weakly to some point in F. In Hilbert spaces, we find from Theorem 2.1 the following.

Proof In Hilbert spaces, we find that J is the identity and ϕ ( x, y ) = ∥ x − y ∥ 2. We can immediately derive from Theorem 2.1 the desired conclusion.

If ∑ m = 1 N δ m T m is semicompact, then { x n } converges strongly to some point in F. In Hilbert spaces, we find from Theorem 2.1 the following.

Since Hilbert spaces are Opial's spaces, we find from (2.17) that lim inf i → ∞ ∥ y n i − w ∥ < lim inf i → ∞ ∥ y n i − W w ∥ = lim inf i → ∞ ∥ y n i − W y n i + W y n i − W w ∥ ≤ lim inf i → ∞ ∥ W y n i − W w ∥ ≤ lim inf i → ∞ ∥ y n i − w ∥, which derives a contradiction.

Then the sequence { x n } converges strongly to Proj Ω x 0, where Proj Ω is the metric projection from E onto Ω. Proof In the framework of Hilbert spaces, we find that ϕ ( x, y ) = ∥ x − y ∥ 2, J is reduced to the identity mapping and the generalized projection Π C is reduced to the metric projection Proj C.