This representation as a (sup ) allows to prove semicontinuity of the slope.4 It is also possible (see [2], for instance) to prove that the slope is an upper gradient.
Given the profusion of such measures, it is useful, for instance, to prove bounds for special graph classes or to study interrelations among them.
Israeli case law says that the Interior Ministry has to register citizens as they define themselves if they can show an official document supporting what they claim -- a marriage certificate from Cyprus, for instance, to prove they are married.
"The federal criminal justice system is still in the terrible state of placing the burden of proof on the defendant in many instances to prove his innocence, as opposed to the prosecution proving his guilt," Smith said.
To prove that CHORDAL- ( k,ℓ )-SP is NP-complete for k+ℓ≥ 3, k,ℓ positive integers, we proved first that (2,1) TRIANGULATING COLORED GRAPHS ((2,1) TCG) is NP-complete showing that the instance used to prove that the problem of Triangulating Colored Graphs (TCG) is NP-complete [19] is also a (2,1 -graph.
Instances that prove the strict inclusion can be found in Table 1.
We believe that such a number of obtained results and analyzed instances is enough to prove consistency of the proposed optimization concept.
Studies of lung cancer screening, for instance, have failed to prove that it prolongs life.
In other instances, they are charged to prove that they've memorized the order in which the fifty-two cards of a shuffled deck randomly fell.
This confirms literature reports maintaining that the relationship between food allergens and, for instance, asthma is difficult to prove.
