Sentence examples for matrix so it from inspiring English sources
The left-hand side is a non-negative power of a circulant matrix, so it is circulant.
(13) The presented operational matrix is a sparse matrix, so it can reduce the error of solving Eq. (1).
However, it was also found that for such high stiffness contrast viscoelastic composites, the ratio of their effective storage and loss shear moduli (the damping factor) remains essentially unchanged as compared to that of pure unfilled matrix so it is the invariability of the damping factor that can be viewed as a special signature of underlying micromechanical mechanism of reinforcement.
The femur is the strongest weight-bearing bone that contains large number of cells and huge amount of bone matrix, so it is the most affected bone by AEDs (Souverein et al. 2005; Mattson and Gidal 2001; Sheth et al. 2008).
The GBLUP procedure simply requires replacing the numerator relationship matrix with the realized genomic relationship matrix, so it is straightforward to model complex variance-covariance structures, such as genotype by environment interactions in plant breeding.
Human biomonitoring studies using adipose tissue are understandably quite limited because of the invasive procedures needed to isolate this biological matrix, so it is not likely that this study will be repeated with a larger sample size or a broader population.
It was important to measure the protein adsorption capacity of the material as well as its capacity to retain the adsorbed compound into polymer matrix so that it could be reusable.
In the companion paper (Part II), analytical formulae are derived for the posterior covariance matrix so that it can be evaluated without resorting to finite difference method.
This was due to the matrix flow in the miscible displacement process being slow during the pulse, although greater amounts of Cl− entered the matrix, so that it initially had no evident effect on the solute in the effluent.
It is assumed that the uniform distribution of the SiO2 units, as demonstrated by cryo-field emission scanning electron microscopy, causes the silica to act as nano-sized water reservoirs, which reduce the characteristic diffusion length of water in the PNIPAM matrix so that it can be transported faster within the hybrid PNIPAM nano-composite.
Following this approach, the Oaxaca-Blinder decomposition represents a special case of this generalized equation, in which Ω is a null matrix or the identity matrix, so that it assumes the following simplified form: {overline{Y}}^A-{overline{Y}}^B={beta}^Aleft({overline{X}}^A-{overline{X}}^Bright)+left {beta}^A-{beta}^Bright){overline{X}}^B (5).
