Sentence examples for approximation to define from inspiring English sources

We perform density functional theory calculations within the local density approximation to define the structures and energetics of sulphur in graphite, including its interactions with point defects and edges, in order to understand its role in the later stages of graphitization.

Now, using our conditions outlined in equations 2 5, we can make approximations to define the potential functions ψ 1 (inside the nanowire) and ψ 2 (outside the nanowire) as the following: ψ 1 = K 1 + ∑ n = 1 ∞ r n A n sin nθ + B n cos nθ (21) ψ 2 = K 2 − E o r cos θ + ∑ n = 1 ∞ 1 r n C n sin nθ + D n cos nθ (22).

We then use de-noised approximation coefficients to define boundaries where there is a transition from one copy number state to another.

We use vegetation types and their condition classes as a first approximation or surrogate to define and map the underlying ecosystems in terms of their regulating, supporting, provisioning and cultural services.

This shows that our notion of statistically significant noun phrases is a good approximation to manually defined term labels.

We are interested in situations where the approximations Yn allow to define a Dirichlet form in the space L2 PY) where PY is the law of Y.

In the formulation proposed here, the 1st- and 2nd- order Taylor approximations are employed to define the relation between the dimensionless normal stress and the sine of the instantaneous friction angle.

The local approximations are then used to define a series of explicit approximate optimization problems.

It is now necessary to define an approximation for the second boundary condition of (1.2).

All field equations are imposed in a weighted residual form and Legendre polynomials are used to define the approximation bases.

A novel scheme for locally enriching the solution in order to obtain a higher order solution is used to define this approximation to the error, which is then subtracted from the functional to improve it.