Sentence examples for proof based on the from inspiring English sources

Gwyneth Paltrow is arriving as the star of Proof, based on the Pulitzer Prize-winning stage play in which she appeared in the West End.

We offer the following short proof based on the structure of the Alexandroff-Urysohn Square.

Here we give a proof based on the ideas developed in [25].

Here we give a short proof based on the structure of the Alexandroff-Urysohn Square.

A new functional proof based on the Riesz representation theorem [4, 5] is also given.

In the following, we give the proof of Theorem 1.3, and our proof based on the Ekeland's variational principle [22].

For completeness and comparison, we provide alternative proofs based on the transformation in Section 4.

The approach used in the proofs, based on the properties of the Poincaré map, guarantees that our results are stable with respect to small perturbations.

The scheme is simple and intuitive, and makes use of polynomial reductions and zero-knowledge proofs, based on the difficulty of factorization hypothesis.

We give a short proof based on properties of the row sum vectors of submatrices in an incidence matrix.

As Planet Terror took shape, Tarantino developed the story for Death Proof, based on his fascination for the way stuntmen would "death-proof" their cars.