Sentence examples for proof include from inspiring English sources

Key ingredients in the proof include a long-time Strichartz estimate and a frequency-localized interaction Morawetz inequality.

Main ideas in the proof include establishing pseudo-locality of the Fourier-integral operator and recent techniques from smoothed empirical processes.

New ingredients in our proof include an integration of Timorin's mixed Hodge Riemann bilinear relation and a mixed norm version of Hörmander's L2-estimate, which also implies a non-compact version of the Khovanskiĭ Teissier inequality.

Other challenges to proof include the likely time lag between infection and diagnosis, the ubiquity of many infections, the influence of age at infection, and the limitations in laboratory assays; small numbers of cases, inaccurate background leukemia rates, and difficulty tracking mobile populations further affect cluster investigations.

In court on Wednesday, a prosecutor, Edward Y . Kim said that the government's proof included Mr. Arbabsiar's "extensive" post-arrest statements.

But they promised even more proof, including video, a DNA test and, of course, a mission to capture one of the big guys.

Their published proof, including diagrams derived from more than 1,000 hours of calculations on a high-speed computer, was the first significant mathematical proof to rely heavily on artificial computation.

As proof includes photos of himself with Jimmy Carter, Queen Noor, Yasir Arafat and Bill Clinton.

This proof includes an explicit design instruction for the desired nonlinear control.

The second proof includes the Lipschitz summation formula following Luo's method in [3].

Now, the proof includes applying Theorem 2.10 to show that S ( x ) has an r-maximal element x ¯ ∈ S ( x ).