Sentence examples for be any dense set from inspiring English sources

Let D be any dense set in C 1.

Let { x i } i = 1 ∞ be any dense set in [ 0, 1 ] and Ψ x ( y ) = L ∗ r x ( y ), where L ∗ is the adjoint operator of L and r x is given by Remark 3.1.

We then show that the non-degenerate critical points of Φ can be chosen to be a dense set concluding the sketch of the proof of the theorem.

In particular, Buterin and Shieh [20, 22] derived the asymptotic expansion of nodal points of problem (1) with (p=2) and showed that α, β, (q_{0}), and (q_{1}) can be uniquely determined and reconstructed by any dense set of nodal points.

As Bill Tai, a partner at Charles River Ventures and a veteran investor, put it, "The social fabric of Silicon Valley is a dense set of overlapping spider webs, meaning everyone is connected".

Let us consider, which is a dense set in, let be a compact set in, and let.

We show that for given Cantor group and minimal translation, there is a dense set of continuous sampling functions such that the spectrum of the associated operators has zero Hausdorff dimension and all spectral measures are purely singular continuous.

Also A is the attractor of the IIFS (mathcal{S}_{B}= X, f_{a})_{ain B})) for any dense set B in A. If A is separable and B is a countable dense set in A, then A is the attractor of the CIFS (countable IFS) (mathcal {S}_{B}= X, f_{a})_{ain B})).

The intersection of these invariant manifolds may not be transverse within P, but it will be for a dense set of nearby vector fields.

end{aligned} Let (varepsilon > 0) and let (P_{varepsilon }) be a relatively dense set in ℝ for which the estimate (2.13) is fulfilled.

To this end, let be a countable dense set of.