Sentence examples for reduced words from inspiring English sources

Definewnas the set of all reduced words inFrof lengthn(the identity is a neutral element), and |wn| as the number of elements ofwn.

The relative standard normal forms of these groups found in [19, 20] are the reduced words for what was later called a relative GS basis [59].

As a result, since P E is obtained by using both unique reduced words (according to NFT) and the matrix ℳ as the endomorphism ψ M, polynomial (8) represents this presentation uniquely as a characteristic polynomial.

A group (or a monoid) presentation P = 〈 x ; r 〉 (1). is a pair where x is a set (generating symbols) and r is a set of non-empty, cyclically reduced words (relators) on x.

The substitution (sigma ) defined by begin{aligned} sigma (a) = aca,quad sigma (b) = d,quad sigma (c) = b,quad sigma (d) = c end{aligned}extends to reduced words, for example (sigma (abac) = acadacab), and the resulting map begin{aligned} sigma, :, mathfrak{G }_{-1} longrightarrow mathfrak{G }_{-1} end{aligned}is a group endomorphism.

Elements in (mathfrak{G }_{-1}) are in natural bijection with "reduced words" of the form begin{aligned} t_0 a t_1 a cdots a t_{k-1} a t_k end{aligned}with (k ge 0), (t_1, ldots, t_{k-1} in {b,c,d}), and (t_0, t_k in { emptyset, b,c,d }).

In the single-channel task, full batch processing reduced word error rate (WER) from 10.0 to 9.3 % on SimData as compared to utterance-based batch processing.

This reduced word-document set retained all 2,153,769 documents, but reduced the number of unique tokens from 272,926 to 65,776.

For example, the aforementioned study by Sinnett et al. (2006) showed reduced word recognition rates when attention was paid to a demanding stimulus stream, irrespective of whether the words and stream were presented in the same or different modalities.

Standard word delimiters are used to split multiple text strings to words and the Porter stemming algorithm [24] reduces words to common stems in order to map different forms of one word to their common stem.

The team used two electronic methods to distort the words: noise-vocoded (NV) synthesis, which makes words sound very raspy and breathy; the other, known as sine-wave (SW) synthesis, which reduces words to just three tones, is something like converting a rich color photograph into a stripped-down black and white version.