Sentence examples for by another solution from inspiring English sources

Similarly, as in the proof of Theorem 4.1, denote and let be a solution of (2.1) generated by another solution (linearly independent of ) of (1.1).

Denote by the associated solution of (2.1) and let be a solution of (2.1) generated by another solution (linearly independent of ) of (1.1).

In science, the best we can do is to come up with a provisional solution which could be overturned by another solution that explains more of the evidence: no matter how unlikely that might seem.

To stop the reaction the 2% KOH solution was replaced by another solution with 2% KOH and 25% glycerol (Sigma-Aldrich).

Expanding the use of letter-of-credit guarantees issued by banks is another solution.

Initially staff at the centre nursed it back to health by feeding it by hand but realised another solution was needed if the turtle was ever going to be able to fend for itself.

Putting the point in more modern terms, the laws of (Hamiltonian) mechanics are such that for every solution one can construct another solution by reversing all velocities and replacing $t$ by $-t$.

Rick Quino gave yet another solution, by removing walls between adjoining rooms — which, I have to say, was my original approach: by removing a wall, we get a bigger room, but still satisfy the requirements.

The interior problem has infinitely many solutions in general, in the sense that a solution can differ from another solution by an infinitely differentiable function [3].

We tend to think that we can deal with the challenge of carbon dioxide in the atmosphere by planting more vegetation, but it turns out that animals like sea otters are providing another solution by helping to keep forests growing.

The PS quantitative model was then tested by another series solution also with the composition as Table 1 shows.