Sentence examples for classification of pairs from inspiring English sources

In this case, for (nge 5) there also exists a complete classification of pairs ((X,G)) as stated, for example, in [54], p. 54] (see [59, 70, 91]).

This section contains a complete biholomorphic classification of pairs ((X,G)) for (N^2+1le dim Gle N^2+2N) obtained independently of the facts presented in Sect.

Next, there exists an explicit classification of pairs ((X,G)) with ((n-1)(n-2)/2+2le dim Gle n n-1)/2) for (n n-1) (see [56] and [86]), which is for too lengehy to be reproduced here.

Studying proper actions becomes harder as the group dimension decreases, and there exists no complete classification of pairs ((X,G)) for any prescribed (dim G) not exceeding (N^2).

The most impressive contribution to the area was made by Kobayashi and Nagano who produced, among other results, a classification of pairs ((X,G)) for group dimension ((n-1)(n-2)/2+2), with (nge 6) (see [56]).

Next, if (n=3) and (dim G=4), then again arguing as in [54], we see that the action of (G) is transitive, and for a simply-connected (X) a classification of pairs ((X,G)) is then given by a theorem stated in [15], p. 303] (see also [73]).

Therefore, one cannot rely on the classifications of pairs ((X,G)) obtained in the smooth case to derive classifications in the complex setting simply by identifying (G -invariant complex structures on (X).

In general, the "size"and explicit form of the linear isotropy subgroups are rather essential for obtaining classifications of pairs ((X,G)) and will be a recurrent theme throughout the survey.

Traditional approaches mainly involve two steps: comparison of record pairs to generate comparison vectors, and classification of record pairs into three sets of true match, possible match, and true non-match based on the comparison vectors [ 9, 10].

For the evaluation of the model we also include a performance evaluation for the classification of drug target pairs into binding or non-binding, using the metrics AUC and AUPR.

On the automatic identification of question type involving the main concerns of the asker, Souza et al. [7] conducted an experimental study for the automated classification of Q&A pairs into three categories: how-to-do-it, conceptual, and seeking-something.