Sentence examples for examples studied in the from inspiring English sources

We show that ifRcoE=PcoE(and two other hypotheses, named the segment property and the extreme points property) and ifϕ∈C1(Ω; Rm) is such thatDϕ(x)∈E∪int PcoE,  x∈Ωthen there exists (a dense set of u∈W1, ∞(Ω; Rm) such that[formula]We apply this existence theorem to some relevant examples studied in the literature, as well as to problems with (x, u) dependence.

As the examples studied in this paper show, the minor species can be better detected if the label is far from the interface.

This latter situation is the case in the prototype examples studied in this paper, where models for fluorescence emission in photosynthesis have been used.

Conclusions are drawn for the examples studied in this paper.

By employing results of the example studied in the previous section, computational comparisons of the ARD and the ARR with the classical one are made in terms of additions and multiplications.

The example studied in the present paper consists of a set of 23 chemical reactions involving 27 molecular species, and one or a combination of several criteria as mentioned above are used to drive the optimization.

Unlike trypanosomes, in which polycistronic messages contain a series of different genes, the few examples studied in dinoflagellates consist of tandemly arrayed copies of the same gene [ 37].

We analyze the same examples studied in Bayona et al. (2011) [2], both with structured and unstructured grids, and compare our new results with those obtained previously.

The Drosophila A data set is the example studied in [ 14], which was extracted from a larger Drosophila data set considered by Cotton and Page [ 32].

This is the example studied in [14, Section 3.1].

The three example systems studied in the first paper of this series are again employed to ascertain the anticipation.