The matrices are, respectively, the connection weight matrix and the discretely delayed connection weight matrix.
The matrices H and S are respectively named the matrices of hard and soft limits, and they have the same dimensions of the matrix of bandwidths F. The entries on the main diagonals of such matrices are respectively the hard and soft limits for each node.
Based on Eq. (2), the output sensitivity matrices are, respectively, given by (5) ∂ y ∂ p = ∂ h ∂ x ∂ x ∂ p = − ∂ h ∂ x ∂ f ∂ x − 1 ∂ f ∂ p (6) ∂ y ∂ q = ∂ h ∂ q To ensure unique estimation of the parameters (i.e. all parameters to be identifiable), based on the measured data of y, it is necessary that the columns in the output sensitivity matrices ∂ y ∂ p, ∂ y ∂ q are linearly independent.
(Bone and blood are considered specialized connective tissues, in which the intercellular matrix is, respectively, hard and liquid).
In example calculations, the mechanical properties and the thermal expansion coefficients of carbon nanotubes and polymer matrix are, respectively, treated as the functions of temperature change.
Expression of lineage-specific markers and components of extracellular matrix was respectively quantified by RT-qPCR and immunohistochemistry.
We call these earlier models (B1) and (B2), and their 2×2 substitution-matrices are respectively where g, l are unknown transition rates that can be estimated and for the model (B1) g= l= c.
In the second step, for each g i and corresponding X i = [1| L| g i], the estimates of the effects and the variance-covariance matrix are respectively obtained as β ̭ i = (X i T M ̭ − 1 X i ) − 1 X i T M ̭ − 1 y, (1 ) and V a r (β ̭ i ) = σ ̭ 2 (X i T M ̭ − 1 X i ) − 1, with i = 1,..., m, where m is the number of genetic markers considered.
Low electrical percolation thresholds of 0.05 and 0.4 vol.% of carbon nanotubes in epoxy and HDPE matrices were found respectively.
The other materials considered for the matrix and reinforcement phases were, respectively, epoxy resin and E-glass.
