Sentence examples for matrices in their from inspiring English sources
In 1858 the English mathematician Arthur Cayley began the study of matrices in their own right when he noticed that they satisfy polynomial equations.
Owing to their inert nature, the nanotubes tend to form bundles with each other and thus do not disperse well in organic matrices in their pristine state.
In particular, the source and the relay matrices, in their simplest forms, in the NAF scheme are defined as left{begin{aligned} mathbf{B}_{k}& = sqrt{P_{mathrm{s}}/N_{mathrm{s}}},mathbf{I}_{N_{mathrm{s}}},~~text{for }k = 1, dots, K, mathbf{F} &= sqrt{P_{mathrm{r}}/text{tr}({boldsymbol Psi})}, mathbf{I}_{N_{mathrm{r}}}. end{aligned}right.
Cells are surrounded by extracellular matrix in their natural environment2; nanoscale topography is observed on the extra cellular matrix (ECM) surface.
Bi Y, Ehirchiou D, Kilts TM, Inkson CA, Embree MC, Sonoyama W et al. Identification of tendon stem/progenitor cells and the role of the extracellular matrix in their niche.
In this study, multi-walled carbon nanotubes (MWCNTs) were incorporated into poly (ethylene terephthalate) (PET) matrix in their as-received (A-MWCNTs) and treated (T-MWCNTs) forms.
The uniformity and similarity between the synthesized particle forms of KT reaction products indicate the presence of homogeneous distributed matrix in their morphological phases.
This allows the introduction of the matrices R1 and R2 in Equation 19, so that all information bits have a random matrix in their corresponding block column in the parity-check matrix.
They have applied the concept of a transition matrix in their studies to analyse, for example, the probability of moving from one fixed-term contract to a permanent contract.
They compared an alignment calculated using their composition-adjusted matrix and the original BLOSUM62 matrix in their report.
They also estimated actual relationships from a finite number of markers and, occasionally, obtained a singular matrix in their simulated replicates [ 11].
