Sentence examples similar to exists a dense set of 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.

There exist integrable functions (f) for which the sequence ({s_n f,x }) diverges for almost all (x), and a dense set of functions (fin C^*) for which ({s_n f,0)}) diverges.

Then U has a dense set of C∞-vectors.

The resulting geometric sequence therefore yielded a dense set of values, suitable for constructing a table.

Instead of using analytical reflectance models, we represent each BRDF as a dense set of measurements.

At a certain stage, a dense set of parallel Riedel shears forms at shallow depth.

This approach tends to provide a dense set of samples and has interesting theoretical convergence properties.

In some cases, a Biot medium presents a dense set of fractures oriented in preference directions.

On the other hand, detecting these differences could require a dense set of markers.

Typically such a dense set of knot points is not necessary.

Second, a dense set of markers from the public database was genotyped in a panel of 349 healthy women.