Sentence examples for we represented by from inspiring English sources

Excepting E. multilocularis, all isolates show sites with double-peaks within reads of high quality, which we represented by IUPAC ambiguity codes.

Currently, we represent by the shortest path distance (9).

For, we fix, and we represent by the norm of in.

Hereafter we represent by X α the space D ( ( − A ) α ) endowed with the norm ∥ ⋅ ∥ α.

In practice, the data is contaminated by noise, which we represent by the following data model (5).

We represent by (operatorname{PAP}(Y,Z)) the set of all pseudo almost periodic functions (g:mathbb{R}times Yto Z).

Moreover, we represent by ([D(A)]) the domain of A endowed with the graph norm (| x |_{A} = | x | + | Ax |), (x in D(A)).

For a linear operator A with domain (D(A)) and range (mathcal {R}(A)) in X, we represent by (sigma (A)) (resp.

As usual, we represent by (operatorname{PAP}(Y)) the set of all pseudo almost periodic functions (h:mathbb{R}to Y).

Therefore, we calculate probability distributions for the spread, which we represent by using pgfs.

Formally, we represent by { X i, Y i   (i = 1,2,…, m)} the training dataset with m examples.