Sentence examples for be a finite collection from inspiring English sources

Let ({mathcal {K}^{(i)}}_{iin I}) be a finite collection of disjoint simplicial complexes.

Let ( X, κ ) be a finite collection of digital m-simplices, 0 ≤ m ≤ d, for some nonnegative integer d.

Definition 2.5 Let ( X, κ ) be a finite collection of digital m-simplexes, 0 ≤ m ≤ d for some nonnegative integer d.

The parametrization provided by D is inconvenient near the directions tangent to ∂ M. Let H m be a finite collection of smooth hypersurfaces in M 1 int.

Let ({mathcal{A}_{lambda }}_{lambda in Lambda }) be a finite collection of algebras of sets given on a set X with (# (Lambda ) =n>0), and for each λ there exist at least (frac{10}{3}n+sqrt{frac{2n}{3}}) pairwise disjoint sets belonging to (mathcal{P}(X setminusmathcal{A}_{lambda }).

Finally, fix (m inmathbb{N}_{0}) such that n/m leqepsilon/2, and let Φ be a finite collection of Borel probability measures on S of the form Q = sum_{i=1}^{n+1} (k_{i}/m) delta_{x_{i}}, where the (k_{i}) range in ({0,ldots,m}) so that sum_{i=1}^{n + 1} k_{i} = m, and (delta_{x_{i}}) stands for the Dirac probability measure putting all its mass on (x_{i}).

A partition Y of [ a, b ] is a finite collection of points Y = { y 0, …, y N } such that a = y 0 ≤ y 1 ≤ y 2 ≤ ⋯ ≤ y N = b.

A function is absolutely continuous (or ) on if for each there exists such that whenever is a finite collection of nonoverlapping intervals that have endpoints in and satisfy while denotes the oscillation of over ; that is, (2.3).

A sub-semigroup H of G is said to have finite index if there is a finite collection of elements say (psi _1,psi _2,ldots,psi _ {m-1} in G) such that begin{aligned} G =Big (bigcup _{i=1}^{m-1} psi _i circ HBig ) cup H. end{aligned}The index of H in G is the smallest possible number m.

There is a finite collection of open bounded sets in R n ; Ω 1, Ω 2, …, Ω N with ⋃ { Ω j ∣ 1 ≤ i ≤ N } ⊃ ∂ Ω and corresponding ı j ∈ C m ( Q ; Ω j ) which are bijections satisfying Q, Q +, and Q 0 mapping onto Ω j, Ω j ∩ Ω, and Ω j ∩ ∂ Ω, respectively, and each Jacobian J ( ı j ) is positive.

A sub-semigroup H of a semigroup G of endomorphisms of (mathbb C^k) is of co-finite index if there is a finite collection of elements say (psi _1,psi _2,ldots,psi _{m-1} in G) such that either begin{aligned} psi circ psi _{j} in H ; text{ or }; psi in H end{aligned}for every (psi in G) and for some (1 le j le m-1).