Sentence examples for matrix is due from inspiring English sources

The equivalence of (a) and (b) for M a finite set (so A is a matrix) is due to Beurling Deny [54].

This high concentration of Er incorporated into the Sc2O3 matrix is due to the presence of Sc that creates concentration quenching.

We propose that the difference in the interfacial thermal resistance between the MWCNTs and the matrix is due to the difference of the MWCNT surface state caused by different treatment processes.

In principle, it might be possible to reparametrise model (27) in such a way that the single singularity of the information matrix is due to the score of one of the new parameters becoming identically 0. In that case, a square root transformation of this parameter should allow one to derive a joint extremum test of (H_{0}:psi _{x}=psi _{u}=0) along the lines of Sect.

Furthermore, Suzuki et al. documented that the increase in interstitial matrix is due to both increased production by activated fibroblasts and decreased matrix removal by MMPs [37].

Recent studies have suggested that the association of IGFBP-2 with the cell surface or the extracellular matrix is due to its ability to bind to proteoglycans [22], but the relative contributions of the HBD in vivo is unknown.

The accuracy of each classification was assessed by calculating the Kappa statistic, a common measure of classification accuracy that accounts for the extent to which correctly classified values in a confusion matrix are due to actual agreement and not to chance [11].

This strongly suggests that the differing rates in a substitution matrix are due to biophysical factors, rather than common ancestry (as first discussed by Zuckerkandl and Pauling [ 14]).

Most of the errors identified in the accuracy matrix were due to misclassification of the following classes: reeds/flooded reeds and Tugay forests/reeds.

The generalization of the above inequalities to matrices is due to Bhatia and Davis [1] as follows: 2 ⦀ A 1 2 X B 1 2 ⦀ ≤ ⦀ A ν X B 1 − ν + A 1 − ν X B ν ⦀ ≤ ⦀ A X + X B ⦀, (1.1).

These results suggest that the axonal regeneration seen in in vivo studies using fibronectin-based matrices is due to the molecule itself and not a consequence of secondary events such as cellular infiltration.