Sentence examples for problem which completes from inspiring English sources

Therefore, the optimal solution of problem P4 is the same as that of the PFPA problem, which completes the proof.

Therefore, by Lemma 2.5, we find (x^in E) such that (x^=Qx^), and so (x^) is a solution of problem (1.1), which completes the proof.

This show that if problem 1 has a solution, then it can be represented by Equation 6 and that every function of form Equation 6 is a solution of problem 1, which completes the proof.

This yields the existence of a nontrivial sign-changing solution of problem (1.1) satisfying which completes the proof.

The problems at Oregon, which completes its spring practice Saturday with its annual spring game, have not been confined to the police blotter.

Thus we have shown that the CORP-D problem is NP-complete, which completes the proof.

Moreover, u ( 0 ) = u ( T ) = 0. Consequently, u is a solution of problem (17a) and (17b) which completes the proof.

Thus we have shown that the problem CARP-D is NP-complete, which completes the proof.

Here \ \textbf{A}^{\textbf{B}}\) denotes the class of problems solvable by using an instance of the model of computation in terms of which the complexity class \ \textbf{A}\) is defined using oracle queries to some problem which is complete for the class \ \textbf{B}\).

From the control design point of view, the general idea is to apply the CSF to a given controller in order to set up a standard problem which can be completed to handle frequency-domain H2 or H∞ specifications.

Based on its similarity to distance-2 edge coloring problem which is NP-complete for K ≥ 4, the interference-range edge coloring problem is, therefore, also NP-complete.