Sentence examples for proof exploits from inspiring English sources
Our proof exploits arguments from[31] with appropriate tailoring to our framework.
Our proof exploits a close relationship between complex-weighted degree-2 #CSPs and Holant problems, which are a natural generalization of complex-weighted #CSPs.
Kremer's proof exploits an intimate relationship between circular definitions understood revision-theoretically and circular definitions understood as inductive definitions: the theory of inductive definitions has been quite well understood for some time.
The proof exploits a simplification of a classical result by Rogers (1993) which characterizes the attainable joint laws for the supremum and the drawdown of a uniformly integrable martingale (not necessarily continuous), combined with classical convex duality results from Rockefellar (1974) using paired spaces with compatible locally convex topologies and the Hahn Banach theorem.
The proof exploits the Banach-Caccioppoli theorem applied on the space mathcal{E}=bigl{ y in Cbigl([0, 1]bigr) mid A^{2} u^{2} leq y u) leq B^{2} u^{2} text{ for every } u in[0, eta]bigr}, endowed with the norm (Vert y Vert=sup_{0 < t leqeta} frac{y(t)}{t}).
end{aligned} Their proof exploited extrapolation techniques for strongly continuous semigroups and an explicit solution representation formula.
A proof of the following lemma may be obtained from that of Lemma 2.1: we give here an independent proof, exploiting the additional information contained in the hypothesis.
Lambert's proof exploited a continued-fraction representation of the tangent function.
In [700], Yafaev found a proof that exploits smoothness ideas (as well as some of the tools Mourre estimates [177, 448, 482], Deift Simon wave operators [110], Enss type phase space analysis [139, 140] of the earlier approaches).
In Step 4 of his proof, Einstein exploited a symmetry known as scaling.
Hackers have always boasted of their work – leaving messages on their victims' servers, posting proof of their exploits on bulletin boards‚ so in a world where every criminal and his dog has a YouTube channel and a Facebook fan-page it's hardly surprising that LulzSec is obsessed with online publicity.
