Sentence examples for by direct computations from inspiring English sources

By direct computations, we get (2.35).

By direct computations we have (3).

Furthermore by direct computations we have (2.4).

By direct computations, one has that solves (3.5).

By direct computations, we get the following results.

Proof This can be verified by direct computations, so we omit it.

By direct computation, (6.4).

By direct computation, we have.

By direct computation, we get.

By direct computation, inequality (3.12) is obvious.

By direct computation, we also have (3.9).