Sentence examples for this problem was proved from inspiring English sources

That this quadratic "speed-up" is also the optimal quantum "speed-up" possible for this problem was proved by Bennett, Bernstein, Brassard and Vazirani (1997).

Regular solvability of the Problem B with continuous gluing conditions ( α = 1, β = 0 ) have been proved, for the first time, in [27], and strong solvability of this problem was proved in the work [28].

This problem was proved by Gomez et al. [ 57], whose study confirms a correlation between drug addiction and an increase of abnormal occluso-muscle function.

First the #P-completeness of this problem was proven.

Although this problem was proven to be NP-hard [ 58], several algorithms have been developed for its solution.

The solvability of this problem is proved.

The theorem on the necessary and sufficient conditions to solve this problem is proved.

The existence of solutions to this problem is proved and the estimate for the regularity of solutions is given.

The well-posedness and long-time behaviour of this problem were proved in [9] under suitable assumptions on h.

A mixed problem with a boundary Dirichlet condition and nonlocal integral condition is considered for a two-dimensional elliptic equation.The existence and uniqueness of a weak solution of this problem are proved in a weighted Sobolev space.

The existence of global solutions for this problem is proved by constructing the stable sets and shows the asymptotic stability of the global solutions as time goes to infinity by applying the multiplier method.