Sentence examples for matrix expressed by from inspiring English sources

The analytical solutions were obtained by computing the trace and the determinant of the stability matrix expressed by A[20].

The evaluation values of chemical and physical performance of seven repair material alternatives are arrayed in left matrix in Eq. (10), where right matrix is the global weight matrix expressed by relative weights between performance evaluation items.

and C in (9) is a diagonal matrix expressed by [21] begin{array}{*{20}l} boldsymbol{C}[varepsilon] =left(begin{array}{cccc} 1 & 0 & cdots & 0 0 &quad exp j2pivarepsilon/N) & cdots & 0 vdots & vdots & ddots & vdots 0 & 0 & cdots & ~exp j2pivarepsilon N-1)/N) end{array}right)!. end{array} (11).

The structure tensor J(∇ S) characterizes the geometry of local structures within S and can be defined as a symmetric positive definite matrix expressed by (1) J (∇ S ) = K * (∇ S ⋅ ∇ S T ), where K is a Gaussian kernel with a spread defined by σ, * is the convolution operator, and · is the dot product operator.

For the j th illuminator, the signals at the coarse-resolution cell and the fine-resolution cell can be associated by a transform matrix, expressed as r j = Φ j w j, j = 1, 2, ⋯, J, (12).

Runx2 regulates the expression of several major extracellular matrix genes expressed by osteoblasts including alkaline phosphatase and osteocalcin [ 29, 30].

Even distribution of vimentin, an extracellular matrix protein expressed by stellate cells, illustrates continuous connective tissue activity in liver spheroids during the 15-day co-culture.

The near-field steering matrix is expressed by combining (9), (16), (18), and (19) as A N = Y Ω B N ⊙ Y Φ N, (20).

The conjugate, transposition, and conjugate transposition of the matrix are expressed by three markers, T, and † respectively.

where KF p is the Kalman filter propagation, and the backward track state prediction and its covariance matrix are expressed by begin{array}{*{20}l} bar {boldsymbol{x}}_{k|k+1+}^{tau}&=boldsymbol{F}_{b} hat {boldsymbol{x}}_{k+1|k+1+}^{tau} bar{boldsymbol{P}}_{k|k+1+}^{tau}&=boldsymbol{F}_{b}hat{boldsymbol{P}}_{k+1|k+1+}^{tau}boldsymbol{F}_{b}^{T}+boldsymbol{Q}_{b} end{array} (13).

Chondroitin sulphate proteoglycan (CSPG) is an extracellular matrix protein expressed by cells in the pia, subplate and marginal zone (Sheppard et al., 1991).