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One such sorting technique is to sort the vectors b 1, b 2, …, b m according to the ascending order of their lengths, which will be referred to as ascending sorting and abbreviated by ASCE.
In the following one or two iterations, we sort the vectors b 1, b 2, …, b m according to the ascending order of the lengths of the orthogonalized vectors b 1 ∗, b 2 ∗, …, b m ∗.
Here, we implement two versions, one directly in ascending order of the lengths of the vectors and the other by perturbing the ascending sorting strategy in the first one or two iterations with the order of the lengths of the orthogonalized vectors; (b) the Gram-Schmidt orthogonalization process; and (c) a complete size reduction on the whole Gram-Schmidt coefficient matrix.
From sample 1# to 3#, both the diameter and length of nanowires are in the ascending order of increase.
Perhaps in ascending order of intelligence?
Here they are, in ascending order of importance.
I list them in ascending order of plausibility: 1.
That's in ascending order of horror, presumably.
As usual, they're ranked in ascending order of likelihood to win the Democratic nomination.
I was visiting my spas in ascending order of luxury and dedication.
They come in three types (in ascending order of expense): mechanical, hybrid and hydraulic.
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CEO of Professional Science Editing for Scientists @ prosciediting.com