Sentence examples for by direct computation using from inspiring English sources

By direct computation, using Matlab software package, we get (R_{0}=1.3281).

Above equalities can be obtained by direct computations using definition of operator and (2.3).

By using the chain rule, the formulas in (3.1) are obtained by direct computation, see [[25], p.129].

Note that for the case (a_{1} < a_{2}), OFF-BANG switching cannot be ruled out using this argument, and the synthesis has to be constructed by direct computation.

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).

The converse follows by direct computation.

By direct computation for, we have.