Sentence examples for extending factor from inspiring English sources

Let B be a C∗-subalgebra of A and ϑ a factor state on B. Due to the independent work of S. Popa and R. Longo the existence of a factor state extension of ϑ to A is assured in case of a separable B. However, the type of the extending factor state can't be determined according to their highly nonconstructive procedures.

Not all surface points are applied the extending factor.

On the other side, we introduce the candidate extended factor in the V-M algorithm to increase the ability to an anti-replay attack.

We stop extending an extended factor when we reach a black position which causes it to violate the threshold.

Given a weighted string x and a cumulative weight threshold 1/ z∈ 0,1], any valid factor of x occurs in at least one extended factor.

We recall an important lemma on how many black positions may be contained within any valid (or extended) factor of a weighted string.

The intuition behind extended factors is to generate a set of strings such that all the valid factors of the weighted string occur in at least one extended factor.

For the second part, it is enough to note that each suffix of an extended factor starting from i, which there is O (1 ) of, can only contain one square of a given period.

Given a weighted string x and a cumulative weight threshold 1/ z∈ 0,1], any valid repetition in x occurs in at least one extended factor. By Lemma 2, any valid factor of x occurs in at least one extended factor. By the definition of valid repetitions, any valid repetition is a valid factor.

These will then be extended to create the extended factors starting from that black position.

For some segment N i, each black position may generate 2 z ℓ extended factors.