Sentence examples for derivation holds from inspiring English sources
Note that this derivation holds even if the diagonal elements of Λ ε are not exactly equal to zero, which is more common in real-world situations.
Although the whole space is separated vertically in Figure 11 of Appendix for convenience, the following derivation holds for arbitrary separations.
The derivation holds in the case of more receivers.
The value of su produced by Eq. 4 is a best linear unbiased estimator of σu – provided the assumptions underlying its derivation hold.
An additive mapping is called a generalized -Jordan derivation in case holds for all where is a -Jordan derivation.
One derivation, the aperture card, holds a square of 35-millimeter film and is still widely used to archive technical drawings, especially those used by public utilities and aerospace companies like Boeing, which has an archive of 40 million cards.
A linear mapping (delta: mathcal {A}to mathcal {A}) is said to be a left Jordan derivation if (delta(x^{2})=2xdelta(x)) holds for all (x in mathcal {A}).
The method used was to distinguish between a derivation relation (the relation that holds between some premises and what can be got from them in a finite number of steps) and a consequence relation.
Following the similar derivation as Proposition 1, it holds that the mean perturbation of the steering vector of the FSBB is bounded by {fontsize{9.2pt}{9.6pt}selectfont{begin{aligned} &|mathbb{E}left{Deltamathbf{g} phi_{d},f,theta)right}|leq& sqrt{KNcdotunderset{phi_{d}in mathbf{Psi}}{max}left{frac{1-D^{2M}}{1-D^{2}}right} }{max}left{frac{1-D^{2M}}{1-D^{2}}right} }{max}left{frac{1-D^{2M}}{1-D^{2}}right}
Since the imputation index j holds across the derivation and validation datasets, predictions P4 as defined in Table 1 can be calculated and used to evaluate ideal model performance.
The advent of advanced molecular profiling techniques has enabled the derivation of molecular signatures that hold promise for more accurate, even individualized patient evaluation [ 1].
