Sentence examples for write the set of from inspiring English sources

From assumption A2′ in this theorem, we can write the set of maximal element clusters of F ( b ) by { [ u 1 ], [ u 2 ], …, [ u m ] } ⊆ 2 F ( b ), for some positive integer m, with { u 1, u 2, …, u m } ⊆ F ( b ).

Proof Take an arbitrary chain { x α } ⊂ P satisfying that every element x β ∈ { x α } has an upper bound z β ∈ A. We write the set of maximal elements of A by { u 1, u 2, …, u m } ⊂ A, for some positive integer m.

For a cooperative network, we write the set of vertices of the corresponding graph as V = V O ∪ V A, where V A is the set of vertices corresponding to the anchors, and V O is the set of vertices associated with ordinary nodes.

If A = 0, then the problem (3.1) is reduced to the mixed equilibrium problem, that is, to find x ∈ C such that F ( x, y ) + φ ( y ) − φ ( x ) ≥ 0, for all y ∈ C. We shall write the set of solutions of the mixed equilibrium problem by MEP. 3. If φ = 0, A = 0, then the problem (3.1) is reduced to the equilibrium problem, which is to find x ∈ C such that F ( x, y ) ≥ 0,  .

We write the sets of those potentials as, and, respectively.

Let us write for the set of models of sentence φ.

We can write the new set of constraints as and.

Then, following Definition 1, one can write the following set of inclusions, ∀ k ∈ K, p k † ∈ BR k p − k †. (17).

The same thing happens to My Week with Marilyn, which is based on the diaries Colin Clark wrote on the set of The Prince and the Showgirl.

where the last line has been written using the set of nondimensional parameters.

In addition, notation (mathcal {B}^(H)) is written as the set of all positive operators in (mathcal{B}_{h}(H)).