Sentence examples for maximal subset of from inspiring English sources

Let Λ be a locally maximal subset of M. In [8], Lee showed that if Λ is hyperbolic then it is limit shadowable.

8A strongly connected component is a maximal subset of nodes such that there is a directed path in both direcitons between every pair in the subset (Newman (2010), p. 144).

We consider the set Q = 2 ( T m ( B ∖ D ) ) ∩ H. Let Q ε ′ = { z 1, …, z N } be the maximal subset of Q such that ∥ z i − z j ∥ 1 ≥ ε ′ for all i ≠ j.

If (D=C_{M}(D)), then D is called a complete invariant set of descending flow relative to M. Clearly, (C_{M}(D supset D) and (C_{M}(D)) is the maximal subset of M which is retracted by D and (C_{M}(D)) is the minimal one of all complete invariant sets of descending flow containing D and contained in M. see [6].

(since otherwise d ( x, c ) > β 4, for each c ∈ C, which implies that x ∉ C, and therefore, C ∪ { x } ≠ C and d ( u, v ) > β 4 for every u, v ∈ C ∪ { x }, u ≠ v ; this contradicts the fact that C is a maximal subset of A having the property that d ( x, y ) > β 4 for every x, y ∈ C, x ≠ y ).

Lemma 2.1 Let Λ be a locally maximal subset of M. If f has the limit shadowing property on Λ then the shadowing points are taken from Λ. Proof Let δ > 0 be the number of the limit shadowing property of f, and let U be a locally maximal neighborhood of Λ. Suppose that f has the limit shadowing property on Λ.

In microarray analysis, biclustering is used to find the maximal subsets of rows and columns satisfying some coherence criteria.

Note that A⊥p is the set of maximal subsets of A that do not imply p, it is not sufficient that they do not contain p. Hence {p ∨ q, p ↔ q} ⊥p = {{p ∨ q}, {p ↔ q}}.

Next, we identify all compatibility classes in M (maximal subsets of compatible initial chemical graphs).

Thus this relation defines equivalence classes on the set of k-cliques, i.e., there are unique maximal subsets of k-cliques that are all k-clique-connected to each other.

In most cases, this results in positive examples that are identical to the benchmark SMISPs, but five training set PPIs have large benchmark SMISPs that are decomposed into all possible maximal subsets of residues that fit within a 12Å distance cutoff.