Sentence examples for then, observing that from inspiring English sources

The proof of Theorem 2.1 entails showing that the metric space ( X, ℓ ) is complete, where ℓ is the path metric on X induced by d, and then observing that g is actually a global contraction on ( X, ℓ ).

Then, observing that Sendak had been sketching, Nicholas asked, "Can you make me a ferryboat?" Sendak did, and then drew other pictures at Nicholas's direction, including some of seagulls creatures that my son is very fond of.

We then observe that 0 < ω n ( i, j ) < 1 ( n ∈ N ).

We then observe that centering relocates a lot of the information included in postfire band 2 in the 2nd component (eigenvector increases from 0.53 in case A to 0.73 in case C).

Praeger then observes,"That doesn't make you a good person.

He then observes that ranking by the introduced empirical pvalues is equivalent to ranking by Weighted Node Connectivity alone (except for ties that arise from the limited number of shuffled samples).

We then observe that { F (u k, S k )} k ∈ K is bounded, which together with the monotonicity of { F (u k, S k )} implies that { F (u k, S k )} is bounded below and hence lim k → ∞ (u k, S k ) exists.

If K eq red denotes the equilibrium constant for the reduced network, then observe that K eq red = k f I k f II k r I k r II = K eq I K eq II For this example, our procedure yields a reduced model with 8 parameters while the original model has 12 parameters.

He then observes that with 8.3% unemployment, inflation is increasing.

Warne then observed that it must be because humans came from aliens.

Justice David H. Souter then observed that "if they had someone like Justice Scalia to go on the screen," there would be ample coverage.