Sentence examples for we specialized to from inspiring English sources

The comparisons made with the calculations show that OpenFOAM's InterFoam solver, that we specialized to Euler's equations here, can successfully simulate the data in many cases.

In the third part of Section 4 we specialize to (1.1), (1.4), and (1.10).

Then we specialize to phase transformations of a solid sphere that is subjected to an all-round tension/pressure.

6 we specialize to the case of regular graphs and we investigate network dynamics using some explicit examples of anatomical connectivity.

We specialize to AQS that prepare ground or thermal states of quantum many-body models since these are the most common types of AQS currently under experimental development.

As before, we specialize to the case: n = 2 and leave the proof of the general case as an exercise for the reader.

Indeed, when we specialize to translations we get the usual autocorrelation, and by Plancherel theorem C q [ f ] ( ξ, 0 ) = | ∫ R 2 f ( x − ξ ) f ( x ) ¯ d x | 2 = | F ( | F f | 2 ) | 2 (15).

Moreover, the density is constant in each region, i.e., we specialize to the case of constant densities, which are defined as: ρ = ρ 1, z < 0, ρ = ρ 2, z > 0. (27).

We also consider measures μ that arise as fixed points (in the sense of Hutchinson) of iterated function systems (IFSs), and we specialize to the case when the function system in the IFS consists of affine and contractive mappings in Rn.

Finally, in Sect. 5 we specialize to Kobayashi-hyperbolic manifolds and give classifications for (dim mathrm{Bihol}(X)=N^2) and (dim mathrm{Bihol}(X)=N^2-1), withethe main result being a complete list of 2-dimensional manifolds whose automorphism groups have dimension 3. Let (X) be a topological space and ({mathcal H}(X)) the group of homeomorphisms of (X).

Here we test whether other strains have specialized to rely on citrate after 50,000 generations.