Sentence examples similar to 1 lacunae from inspiring English sources

If (#(X) = aleph_{1}), then the situation is much simpler: each algebra (mathcal{A}_{k}) has (aleph_{1}) lacunae.

We note that here each algebra (mathcal{A}_{k}) has (aleph_{0}) lacunae.

Let ({mathcal{A}_{k}}_{k in mathbb{N}^) be a family of σ-algebras, and assume that for each k the algebra (mathcal{A}_{k}) has (4k-3) lacunae.

Let (mathcal{A}_{1}, ldots, mathcal{A}_{n}) be a finite family of algebras, and assume that for each (k in[1,n]) the algebra (mathcal{A}_{k}) has (4k-3) lacunae.

Using the notion of absolute introduced by Gleason in [11], we can construct a family of algebras ({mathcal{B}_{k}}_{k in mathbb{N}^) with the following properties: each algebra (mathcal{B}_{k}) has (aleph_{0}) lacunae, is not a σ-algebra, and (bigcup_{k in mathbb{N}^ mathcal{B}_{k} = mathcal{P}(X)) (see [2], Chapter 5).

Indeed, by definition (M in mathcal{A}) if and only if for each (k in[1,m]) either (A_{k} capoverline{M} = emptyset), or (A_{k} subseteqoverline{M}). Let us recall that an algebra which does not have (aleph_{0}) lacunae is called ω-saturated.

This represents approximately 200 lacunae per counting session.

Two-dimensional intensity plots of lacuna count with maximum intensity of 5 lacunae.

Global sensitivity analysis results for lacuna count capped at maximum of 5 lacunae.

Instead, 10 lacunae with intact full-depth structures were randomly chosen per animal from the region of cancellous bone.

The mean values ± SD represent measurements of 10 lacunae per zone, which were performed on three representative mid-sections per growth plate.