Sentence examples for correctness of the solutions from inspiring English sources

We have verified the correctness of the solutions obtained here by substituting them back into the system (1.1a) and (1.1b).

In addition to the correctness of the solutions, the semi-analytical approach is computationally more efficient than the numerical integration approach.

Note that in order to ensure the correctness of the solution in case of mistakes, messages are also sent to processes considered to be faulty.

After verifying the validity of T s to avoid the flooding of identical puzzles, the EMR-ARP node investigates the correctness of the solution contained in the field of c s.

The experimental results confirm that the island model with fission and fusion outperforms the sequential as well as the island models without fission and fusion in terms of correctness of the solution arrived and size of the trees evolved.

By using the KKT conditions, constraints (Equation 28) can be neglected, i.e., we can first solve P 3 without constraints (Equation 28) and then using (Equation 28) to examine the correctness of the solution.

If other existing EMR-ARP nodes retain an entry corresponding to the IP address of the voting request node in the long term table, then they first verify the correctness of the solution to the first-type puzzle and send voting reply packets after solving the second-type puzzle, only if the first puzzle solution is correct.

Good agreements in the results validate the correctness of the analytical solutions and accuracy of the proposed numerical algorithm.

The correctness of the design solutions and calculation assumptions is reflected in the fact that, after a period of more than three years, no damage to the repaired elements of the masonry dome occurred.

In this paper, a novel separation of variables is presented for solving the exact solutions for the free vibrations of thin orthotropic rectangular plates with all combinations of simply supported (S) and clamped (C) boundary conditions, and the correctness of the exact solutions are proved mathematically.

Furthermore, computational experiments with notably large amounts of simulation data are conducted to test the solution approach and validate the correctness of the approximate solution compared with the optimal all-permutation-based result.