Sentence examples for independent solutions from inspiring English sources

By Proposition 3.7, Eq. (3.12) has 1 + r independent solutions.

Obviously, and are two linearly independent solutions of (1.1).

The layered model allows independent solutions for each layer.

are two linear independent solutions of the difference equation (4.13).

have the same number of linearly independent solutions.

Both grid and time step were optimized to reach independent solutions.

Two independent solutions are obtained: the optimized Rayleigh Ritz method and the finite element algorithmic procedure.

Now let us construct the linearly independent solutions of equation (3) for (lambda=0).

We know that if then and are independent solutions of the Kummer's equation (2.1).

corresponding to the problem (3.11), (3.12) has exactly linearly independent solutions (3.28).

Mesh-independent solutions were achieved at mean cell volumes of 5 × 10−9 m3.