Sentence examples for by applying an argument from inspiring English sources

By applying an argument similar to that in the proof of [9, Theorem ] (see also the proof of [7, Lemma ]), it follows that is compact and there is a minimal element in the following sense: (3.4).

By applying an argument similar to that in the proof of [9, Theorem ], it follows that is compact (the topology on is that of weak pointwise convergence) and there is a minimal element in the following sense: (x2a).

The following result can be established by applying a similar argument as that in the proof of Theorem 3.2.

Then, by applying a similar argument to the proof of Theorem 2.4, we can obtain a global weak solution u of problem (1.1 - 1.3 1.1 - 1.3ng uin L^{infty} bigl( 0,T;H^{1} bigr), qquad u_{t} in L^{infty} bigl( 0,T;L^{2} bigr).

By applying an improved vacuum technique, Thomson was able to put forward a convincing argument that these rays were composed of particles.

Finish by applying an overglaze.

On the other hand, by applying a similar convex hull argument to the codimension j - 1 subspace, we know that.

The next fact [8] follows then by applying the argument principle to a circle of a sufficiently large radius, where (|p_n|gg |q_m|.) Let (h=p_n+overline{q_m}) be regular.

By applying the argument in Kakimura and Makino [6] for robustness in general independence systems, a (1/√μ -robust solution exists and is found in polynomial time, where μ is the exchangeability of the independence system.

This can also been seen directly, without invoking the existence of $M$, by applying the argument of the proof of Lemma 15.77.6 to the (defining) distinguished triangle $K \to \prod K_ n \to \prod K_ n \to K$.

Since and commute it follows, and, by applying the preceding argument to and, we conclude that has a nonempty fixed point set in.