Sentence examples for be approximated using linear from inspiring English sources

The third order derivatives in (25) can be approximated using linear combinations of values of (u^{k}( x)) as follows: frac{partial^{3}u^{k} ( x ) }{partial x^{3}}bigg| _{x=x_{i}}=sum_{i=0}^{n} beta_{i}^{ ( k,i ) }u^{k} bigl( x_{i}^{ k)} bigr), (28) where ({ beta_{i}^{ ( k,i ) } } _{i=1}^{N}) is the RBF-FD coefficient corresponding to the third order derivatives.

The response waves can be approximated using linear response rules (Response Rules, Additional file 1: Figure S1) combined with the law of mass conservation, and this approach has been previously used to successfully model the TLRs and TRAIL signaling pathways [ 17- 20].

The state term is approximated using linear interpolation and second-degree Lagrange polynomial interpolation, achieving the first- and second-order HLFDM, respectively.

We tested for nonlinearity in these associations using fractional polynomials, and any nonlinear relationships were approximated using linear splines.

The sorption-desorption of DOC onto aquifer materials such as silicate minerals, ferric oxyhydroxides, and POC has been observed to be quasi-linear (Oren and Chefetz 2012) and can be approximated using a simple linear isotherm: (8 where is the concentration of DOC adsorbed to aquifer material and Kd is the distribution coefficient [L/M].

The simulation reveals that the contact angle distribution along the slug profile in the microchannel flow can be approximated using a piecewise linear function.

In fact, the relation between A and R can be approximated using a simple linear relation A = -R.

Log-linear models introduce bias terms that can be approximated using within-group variances (appendix 2).

Similar to the implementation given in the original paper, the driving input function was approximated by a spline interpolant, while the delay was approximated using a linear chain approximation (x5,…, x13).

Similar to the implementation given in the original article, the driving input function was approximated by a spline interpolant, while the delay was approximated using a linear chain approximation.

The highly nonlinear mass matrix because of the inertia coupling between the reference and the elastic displacements is approximated using the linear theory of elastodynamics.