Sentence examples for the formulation below from inspiring English sources

The formulation below is directly applicable and extensible to a wide range of groundwater dewatering and remediation problems.

(The literature on supervenience contains several other variations; see the entry on supervenience for an excellent introduction, from which this entry adopts some of the formulations below.

If links (_mathrm{new}) is less than the total number of nodes existing in the network at the time of introduction of a node, then the existing nodes are chosen for a link probabilistically according to the formulation explained below.

For each grid the probabilities are calculated via the formulation given below by Eqs. 1, 2, 3, and 4. For the 1st grid 20 binding energies are available, while for the remaining grid pairs 400 binding energies are available; the corresponding statistical weight matrix is given in Eq.1 and 2, respectively.

The robust formulation below tolerates noise in the sample measurements m i and subsequently in the reduced representations x i, improving the stability of these estimates.

The last equality is a consequence of the LS theory and will be used in the NLS formulation below.

In the formulation of the theorem given below, the following notion is used.

For this particular purpose, thermal stability tests were conducted to determine the threshold temperature below which the formulation is thermally stable.

The formulation is restricted to frequencies well below the cut-on of higher order fluid modes.

For this reason, in the formulation of an initial Cauchy problem below, we prescribe initial vectors for the solution and its first derivative.

with another assemblage requiring oxygen fugacities 10 log-units below this buffer motivates the formulation of a low-temperature hypothesis.