Sentence examples for start with the given from inspiring English sources

We must start with the given statement of the broader objective (see Exhibit II).

The second type includes a variety of operations that indicate particular matching processes; e.g., lines 5, 6, 7, and 12 use "$" to allow matching to all the terms in the citation that start with the given string.

Start with the given and then describe the proof as if you were explaining your steps to a friend.

Starting with the given grid, we consider the grid-averages of the numerical solution for a hierarchy of nested grids which is obtained by diadic coarsening, and we compute its equivalent multiresolution representation.

Second, we simulated bulk forsterite with 13,440 atoms (11 × 5 × 8 unit cells of forsterite), starting with the given experimental crystal structure, which was obtained by an experiment (Fujino et al. 1981) and with randomly generated atom velocities; then, we cut along the (010) surface.

Proof Starting with the given x 0, put x n = f n x 0. Since x 0 ⪯ f x 0 and f is an increasing function we obtain by induction that x 0 ⪯ f x 0 ⪯ f 2 x 0 ⪯ … ⪯ f n x 0 ⪯ f n + 1 x 0 ⪯ ⋯.

Proof Starting with the given x 0, define a sequence { x n } in X such that x n + 1 = f x n, for all n ≥ 0. Since x 0 ⪯ f x 0 = x 1 and f is nondecreasing, we have x 1 = f x 0 ⪯ x 2 = f x 1, and by induction x 0 ⪯ x 1 ⪯ ⋯ ⪯ x n ⪯ x n + 1 ⪯ ⋯.

Then, we listed all GPs within each county with a surname starting with the given letter.

The implementation of each scenario starts with the given remaining life expectancy in 2050.

To implement this strategy, TreeFix-DTL performs local search starting with the given ML gene tree and successively finds statistically equivalent gene trees that have a lower reconciliation cost.

The treatment started with the giving of the DSS drinking water.