Sentence examples for using this fact we from inspiring English sources

Using this fact, we define the H-distance on Pe(G), which enables us to establish a transportation cost inequality on Pe G).

Using this fact, we replace the multi-commodity flow formulation with a tree formulation enhanced with Steiner cuts.

Using this fact, we show that perfect representation and reconstruction of a signal with a time encoding machine is possible whenever this device satisfies some density property.

Using this fact, we can bound.

Using this fact we prove the following theorems.

Using this fact we can prove the following.

Using this fact, if we consider U and T as before, being independent of ( X ( t ), t ≥ 0 ), for any absolutely continuous random variable Y, we have the following identity (cf. [[20], Prop. 4]): d d t E F Y ( X ( t ) ) = E f Y ( X ( t ) + U T ), t > 0, (17).

We note that the condition (3.2) implies that there is a constant N ≥ 0 such that | x ( t ) | 1 ≤ N exp ( λ t ), t ∈ J. Using this fact in (3.3), we observe that | x | E ≤ N. (3.4).

Using this fact, from (21) we get lambda_{max} bigl(X^{T}D+DX bigr) leq lambda_{max} bigl(A^{T}_{p}D+DA_{p} bigr) (22) for all (|X|preccurlyeq A_{p}), which proves (20).

Using this fact and (3.17), we have lim_{i toinfty}{biglVert x^{{k}_{i}}-y^{{k}_{i}} bigrVert } = 0. (3.18) Recall that (x^{k} rightharpoonup p), together with (3.18), implies that (y^{k_{i}} rightharpoonup p) as (i toinfty).

Using this fact and (2.3) in (2.1) we easily arrive at our required result.