Sentence examples for characterize the cases from inspiring English sources

In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.

Finally, a substantial part of this work is devoted to the uniqueness of symmetrizing measures for L. We characterize the cases, where we have uniqueness, by the irreducibility of the associated (classical) Dirichlet forms.

We can fully characterize the cases, when the rotation displacements are next to each other.

If sensation has begun to characterize the case, so has mystery.

They will try to characterize the case as being politically motivated.

These conditions together characterize the case when a nonnegative functional becomes zero.

It can also be used to characterize the case of the zig-zag instability for the interface dynamics in liquid crystals; see Chevallard et al.[4].

In Section 4 we characterize the case (k x,y)= 1), which is essentially used in Section 5 with the main results of the paper.

Also, they gave an example to point out that to characterize the case whether there is a k-arc-connected digraph in (langlemathbf {d}rangle) may be very difficult.

T tests and Chi-square tests were used to characterize the case-control frequency distributions of the demographic information and potential risk factors for NPC.

While Mr. Ashcroft characterized the cases as the products of a coordinated action, they had a variety of origins.