Sentence examples for derived by taking the from inspiring English sources

The Jacobian of these formulations is then derived by taking the directional derivative of the discrete weak forms with respect to displacement (and pressure).

The equation of the state sensitivity matrix can be derived by taking the first order partial derivative of Eq. (1) with respect to parameters p (3) S ˙ = ∂ f ∂ x S + ∂ f ∂ p where S = ∂ x ∂ p is the state sensitivity matrix.

Typically, ensemble response (climate response) is derived by taking the mean or median of ensemble members.

Further, the equations of motion of the wind turbine are derived by taking the variable rotor speed into account.

The higher order Laplacian is derived by taking the divergence of a particle-based gradient model (Monaghan, 1992) [18].

One would produce an unadjusted number, and the other would be derived by taking the results from a sample of 314,000 households and using that data to adjust the national, state and local population counts.

The sin.aspect and cos.aspect variables were derived by taking, respectively, the sine and cosine of the aspect measurement in degrees to enable inclusion of these data in distance-based redundancy models.

The exergy balance and the dimensionless exergy relationships are derived by taking into account the irreversibilities produced by the pressure drop in the flow of the working fluid through the collector.

This paper not only describes the measurement methods but also presents the theoretical formulations derived by taking into account the effect of adhesive bonds.

It is based on a novel regression equation which is derived by taking into account the nature of the underlying test signal.

Then, the LS solution is derived by taking a derivative to the term τ as follows: 0 = 6 ∑ l ( ω l 2 τ - ω l ξ E, d ( ω l ) ) + 4 π ∑ m = - 1 1 m ∑ l ω l. (9).