Sentence examples for proved separately from inspiring English sources

Since underactuated AUVs have no independent actuators in the sway direction, stability of the sway dynamics has been proved separately.

However, in this case the result does not follow automatically from the corresponding result in the continuous case but must be proved separately.

As regards their proofs, some common ideas have been involved especially in the proof of Theorem 3.1, but Theorems 4.1 and 4.3 themselves had to be proved separately.

Couples' futures together depend on proving separately to a skeptical bureaucrat that, as the law states, they did not marry "solely" for a green card.

Trivially, equation (1.3) amounts to the conjunction of begin{aligned} &mathbb{P}biggl(S_{n}-frac{a_{0}}{1-a_{1}}n mu >xbiggr)lesssimfrac{na_{0}}{1-a_{1}} overline{F}_{X}(x quad text{and} &mathbb{P}biggl(S_{n}-frac{a_{0}}{1-a_{1}}nmu >xbiggr gtrsim frac{na_{0}}{1-a_{1}} overline{F}_{X}(x), end{aligned} (3.1) which will be proven separately in the following two subsections.

This can avoid proving results separately.

Then (21) T ˆ ħ (z ) S ˆ = S ˆ T ˆ ħ (S − 1 z ) (see e.g. [21,23,44]); one easy way to derive this intertwining relation is to prove it separately for each generator J ˆ, M ˆ L, m, V ˆ P of the metaplectic group described in formulae (61), (62), (63).

The results of experiments to detect objects behind gypsum walls and concrete walls have been separately proved for human target detection.

If u x, y) reduce to u(x) in (2.1), then the inequality (2.1) and its particular case l ≥ 2, μ = λ = 2 with the right-hand side multiplied by l have been separately proved by Pachpatte in [17].

Probe based median centering normalization on FFPE and FF samples processed separately proved to be an excellent way of data normalization in our study and eliminated the systemic technical differences in signal intensity between FFPE and FF paired samples.

The SAS located the captive British soldiers from the latter's shouts of "British Army, British Army!", though Bangura had been held separately and proved more difficult to locate.