Sentence examples for given the ordering from inspiring English sources
Given the ordering π of 𝒳, we now have to compute two embeddings τ1 and τ2 for the forests ℱ(N1) and ℱ(N2) such that π is non-interleaving with respect to τ1 and τ2.
Given the ordering of the elements of the sets A ( 2 ) and P ( 2 ), the term (a1−a2)(p2−p1) is always non-negative, and hence (11) proves (i).
Since h ~ ∈ F ( m − 1 ), and because of (12), we have ∑ i = 1 m a i p h ( i ) ≥ ( a j − a m ) ( p m − p h ( m ) ) + a m p m + ∑ i = 1 m − 1 a i p i = ( a j − a m ) ( p m − p h ( m ) ) + ∑ i = 1 m a i p i. Finally, since (a j −a m )(p m −ph(m)) is non-negative given the ordering of the sets A ( m ) and P ( m ), we have ∑ i = 1 m a i p h ( i ) ≥ ∑ i = 1 m a i p i. which proves (ii).
Given the ordering C, for every clique C k, let c k be a coordinate such that c k belongs to all the intervals in C k but does not belong to any interval which is not in C k.
Given the orders the company handled on the Web last year, that amounts to about $1.1 million saved.
In fact, Duckenfield later admitted he had given the order for it to be opened.
