Sentence examples for calculations given by from inspiring English sources

In this section, we consider X as a digital simplicial group, and we use the method of calculations given by [14] and [9].

The next step is to estimate the noise variance, which requires an SVD decomposition and therefore an extra number of calculations given by 4 3 K 3 + 3 2 K 2 + 19 6 K − 6.

This would make the year of death correct according to the eclipse, but still leave a discrepancy on the specific day of death, for which Stenton asserted the length calculations given by Bede were more correct than the actual death date given.

Considering the calculations given by Kunz et al. [2] together with our very similar qPCR results it is sensible to assume that melanoma cells (and also immune cells) do not express functional receptor pairs that could transmit signals emanating from IL-24, a notion which is further substantiated by the lack of STAT3 activation in these cell types following IL-24 treatment.

A calculation given by Weissman conservatively estimates the diameter at 35 km; an estimated density of 0.6 g/cm3 then gives a cometary mass of 1.3×1019 g.

Based on the maximum observed ratio for B12/DPPC of around 1 3 (B12-rich domains) and considering the dimensions of the involved molecules, it is estimated that at least 7 molecules of B12 are arranged along each of the honeycomb walls; thus accommodating about 50 DPPC molecules in the hexagonal cells, as estimated by calculations given in the Supporting Information.

The results of experimental investigations and calculations given in this paper, their testing by different ways and comparison suggest that using ensembles of magnetic carriers as a superparamagnetic probe and Langevin's paramagnetism theory, one can evaluate the sizes of the components of complex shell structure of nanocomposites.

The results of the calculations are given by Table 1.

For water flow calculations, tables given by Bos (1976) and Hudson (1993) can be used.

The relative error for these calculations is given by Eq. 6, in which ( R t) ) denotes the observed traffic volume at time ( t ) and normalized ( S t) ) denotes the simulated traffic volume at time ( t ).

The initial conditions for the recursive calculations are given by (7) Although the covariance of the system noise,, isan unknown parameter, a Kalman filter gives the likelihood of the trend model for a given, so that the value of can be determined using an Akaike information criterion (AIC) minimization procedure (Kitagawa, 2010).