Sentence examples for proof has been given from inspiring English sources

Lyapunov based stability proof has been given to analyze the zero dynamics stability of the MAV longitudinal dynamics during tracking.

The standard of proof has been given different interpretations.

However, this proof has been given to only the case where the two links suffer from independent block Rayleigh fading with the same average SNR.

Finally, an elegant and short proof has been given by Cabré in [30] using the properties of solutions of the Neumann problem for the Laplacian.

Lemma 2.2 Set Q ( u ) = ∫ R N | ∇ u | 2 d x, u ∈ E. Then Q is weakly lower semicontinuous on E. Proof The proof has been given by Lemma 2 in [16].

Although a shorter proof has been given later by Cicalese and Leonardi [45] using the regularity theory for area minimizing sets of finite perimeter, the proof by symmetrization uses no deep results from geometric and functional analysis, is geometrically intuitive and can be adapted to other situations where a complete regularity theory is not available.

"This is the first time that a mass number of Chechens have taken part in military actions abroad," said analyst Mairbek Vatchagayev, based in Paris, adding that claims were made that Chechens had fought with the Taliban in Afghanistan or in Iraq, but no definitive proof had been given.

Since his time, and possibly before, more elegant proofs have been given, and the mere existence of such proofs speaks about the beauty of the result.

In Section 3, the sufficient conditions for partial stochastic asymptotic stability have been obtained and proofs have been given.

The original proof of the Shapley Folkman lemma established only the existence of the representation, but did not provide an algorithm for computing the representation: Similar proofs have been given by Arrow and Hahn, Cassels, and Schneider, among others.

DR. MERKEL: Then how do you explain the ill-treatment and atrocities which actually took place in connection with interrogations, proof of which has been given by the Prosecution?