Sentence examples for for any ordered from inspiring English sources

For a digraph D, if for any ordered pair of vertices ((u,v)), there is a directed path from u to v, then D is said to be strongly connected.

A finitely generated group (G) is isolated if, for any ordered generating set (S = (s_1, ldots, s_k)) of (G), the point ((G,S)) is isolated in (mathcal{M }_k).

The arrows indicate the paths i → j for every nonzero entry ( D + P ) ( i, j ) of the matrix D + P. For any ordered pair of nodes i and j, there exists a direct path ( i, l 1 → ), ( l 1, l 2 → ), …, ( l k, j → ) connecting i to j.

If there is some individual J who is almost decisive for any ordered pair of alternatives, then a LTM satisfying conditions C1, C2, and C3 implies that J must be dominant.

There is an arc e = (v, v′) in the arc set E for this directed graph G = (V, E) for any ordered pair of 8-neighbors, that is, whenever (1) max (| x − x ′ |, | y − y ′ | ) = 1.

Observe that for any ordered pair (T x, T y ) satisfying condition (1) with respect to T, T x is the core tree of F and belongs to E. Further, T x and T y share a common prefix; thus, T y also belongs to E. The claim follows.

SZFDPC is known to asymptotically achieve the sum rate of DPC in the low and high SNR regimes, at low SNR with optimal ordering, and at high SNR for any ordering.

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