Sentence examples for by a direct calculation from inspiring English sources

By a direct calculation we have for (3.17).

The following statement can be proved by a direct calculation.

By a direct calculation from (1.6), we have (2.2).

If, then by a direct calculation we get.

By a direct calculation, (1.6) holds if (xi=eta).

end{aligned} (2.22) By a direct calculation, we obtain the result (2.20).

By considering (1.6), a direct calculation gives that (2.17).

In this paper, an innovative mesoscopic damage parameter is developed by following a unique calculation procedure in which the damage parameter is cumulatively computed from the minimum to the maximum by iterative cycles instead of using a direct calculation method.

By the definition of ϕ and a direct calculation we show that (i) holds.

(1) By the definition of ϕ and a direct calculation we can show (1).

(57) Furthermore, the approximation of the time derivative can be computed as Du_{r}(t) =sum _{j=0}^{K}a_{r,j}Dbigl(P^{(alpha_{3},beta_{3})}_{T,j}(t) bigr),quad r=1,ldots, R, (58) where the time derivative, (D(P^{(alpha_{3},beta_{3})}_{T,j}(t))), can be explicitly obtained by using (3) for (q=1), with a direct calculation at the points (t^{(alpha_{3},beta_{3})}_{T,K,i}).