Sentence examples for further derivations from inspiring English sources

Since the block RLS algorithm derived in (3), which minimizes (15) involves no approximations, (25) can be used for further derivations without restrictions.

In addition, once a phase derivation is completed, its complement will be transferred both to the phonological component PF and the semantic component LF and hence frozen in place in the narrow syntax, becoming inaccessible to any further operation; only the phase edge (i.e., the phase head and its specifier) is accessible to further derivations.

For further derivations of Fourier transforms, (a) uses the time-shift property as begin{array}{*{20}l} mathbb{F} left{delta left(t - left m-1right)frac{T_{mathrm{S}}}{Omega{M_{mathrm{R}}}} right) right} = e^{-j 2pi frac{(m-1) T_{mathrm{S}}}{Omega M_{mathrm{R}}} f}, end{array} (6).

Dependence of Pmed on Ys is therefore replaced by a linear function on F10.7, so that Pmed (LT, M, F10.7) is used for further derivations, with the source values of F10.7 linearly interpolated to appropriately obtain the solar radio flux values for any given M and YS.

Then, for further derivations, we define random variable ({Gamma ^{(e_{i},a_{i})}_{i}}) indicates SINR of the MS in the ith cell where the ith BS nullifies e i generated interference links to neighboring cells and a i received interference links of the MS in the ith cell are nullified by the neighboring BSs.

The new constants c and d in Eq.  7 are crucial for the further derivations (Fig.  2; Table  1).

Further derivation of 1a afforded J-111,225 (2a), J-114,870 (3and and J-114,871 (3b), which showed improved safety profiles and retained broad-spectrum antibacterial activities.

For all faculties of the soul, or capacities, are reducible to three, which do not admit of any further derivation from a common ground: the faculty of knowledge, the feeling of pleasure or displeasure, and the faculty of desire.

The religious and historical roles of madness in society are further reinforced with elaborations in these dictionaries of the stigmata, a further derivation of the word stigma in medicine, meaning a "mark that is a characteristic of a defect or disease" – hardly very progressive and politically challenging.

Further, derivation of reaction variables, i.e. substrate amount and enzyme dose through full-factorial central composite design led to enhanced degree of deacetylation with formation of 90% deacetylated chitosan.

We divide our further derivation into four steps.