Sentence examples for by direct computation for from inspiring English sources

By direct computation for, we have.

By a direct computation, for, we obtain that (3.11).

By a direct computation, for, we have (4.11).

By a direct computation, for x ∈ Ω, 0 < t < c/b, we obtain that (3.17).

In view of Lemma 1 and Remark 1, by direct computation, we obtain explicit formulas for (S_{n,p}(t^{i};q;x)), (i=1,2) as follows.

By direct computation, we get (Deltaphi(t)=t 3t-3-6eta)), (Deltaphi (t geq0) for (t>1+2eta) and (Deltaphi(t)leq0) for (0< tleq 1+2eta).

By direct computation, the operator equation has only zero solution; then by Fredholm theorem, for any, the operator equation (3.8) has a unique solution in.

By direct computation, we know that ((e^{itheta}a,e^{itheta}b,e^{itheta}X)) is also a solution of (2.1) for (thetain 0,2pi)).

By direct computation, (6.4).

By direct computation, we have.

By direct computation, we get.