Sentence examples for use the representation from inspiring English sources

In the case (b), let us use the representation (39) for the matrix A cp.

It is easier to use the representation R = 1[A1] +⋯+ 1[An], where Ak denotes the event "the kth draw results in a red ball".

In the following results, we shall use the representation (3.1).

Thus, we can use the representation of Corollary 1.

That is why we use the representation ' min x max y max z ' and not use the representation ' min x max y, z '.

We use the representation of a delayed matrix cosine and, after putting, we obtain (3.29).

Our methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis.

These approaches, also known as coarse-grained simulations, use the representations of small groups of atoms by beads or particles with specified interaction potentials.

Defining probability and utility using the representation theorems thus weakens the traditional principle of expected utility.

Using the representation, we construct solutions for Dunkl-Poisson's equation.

Using the representation of (5.4), these corresponds to (beta_{4}=2) and (beta_{5}=1).