Sentence examples for using the new coefficients from inspiring English sources

One can then express the scattered field by the l th sphere in the coordinate system of j th sphere using the new coefficients, p mn lj and q mn lj, p mn lj = − ∑ v = 0 ∞ ∑ μ = − v v a μv l A mn μv l, j + b μv l B mn μv l, j q mn lj = − ∑ v = 0 ∞ ∑ μ = − v v a μv l B mn μv l, j + b μv l A mn μv l, j (4 where A μν mn and B μν mn are related to A 0 μν mn and B 0 μv mn as given in Ref. [36].

Besides, our methods incorporate the least squares principle, utilize a shrinkage estimation approach to adjust the coefficients of the regression model, and then use the new coefficients to estimate missing values.

Using the new lifting coefficients, the degradation of the filters is generally reduced (Figure 17 in comparison with Figure 16).

A new inbreeding coefficient is estimated by f = 1 − H obs / H exp. Using the new inbreeding coefficient values, genotype calling is repeated for the subset of SNPs.

For the resulting designs, factors of safety are computed using upper and lower bound strength reduction finite element analysis and it is concluded that the limit equilibrium approach, using the new earth pressure coefficients, is fairly accurate, albeit slightly unconservative.

Thus, by using the new method, the reaction coefficient of a reaction process can be accurately determined even if it is not reaction-limited.

Using the new accessibility indicator based on local coefficients, MARS model fits better with the real data in respect of the distribution of workplaces and residents, which are the key representatives of the land use sub-model.

The present study aim at: (i) analyzing the influence of the rotating magnetic field (RMF) on the aeration process of various types of liquids and (ii) quantifying the obtained liquid volumetric mass transfer coefficients (kLa) by using the new type of relationships.

The estimated permeability using the new model was plotted against the measured permeability and revealing high coefficient of correlation.

The procedure is as follows: compute the first coefficients of the regression model, then compute the residuals and weights, and finally compute the new coefficients using Equation (6).

It was shown that more accurate results were achieved by using this new coefficient in the Halpin-Tsai equation.