Sentence examples for matrices and substituting from inspiring English sources

So, considering these two matrices and substituting them into Eqs.

The Al2O3 crucible is more susceptible to corrosion than the MgO-Al2O3 crucible, which is attributed to the effect of the slag penetrating through the Al2O3 crucible matrix and substituting part of its matrix.

Finally, the exact natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions, respectively.

These tools ease the interpretation of model behavior by providing diagnostic visualizations of transition matrices, and allow substituting dense transition matrices with a sparse counterpart by applying an iterative approximation algorithm that is independent of model symmetry.

Note that the column vectors of the matrix in (15) are in fact the FFT vectors of a matrix, we thus have and Substituting (21 - 22 21 - 2226), we then obtaintohe variance of the weighted average estimation associated with, as.

Genomic estimated breeding values were obtained using the following mixed model and substituting the A matrix by the two G matrices estimated using the alternative methods.

Then, by replacing Σ n in Equation 26 with the identity matrix and by substituting it to Equation 34 and Equation 35, we obtain: {xi_{text{nr}}}(mathbf{H}_{n}) = frac{L}{sumlimits_{i=1}^{L} sumlimits_{j=1}^{L_{s}} mathbf{V}_{ n-1 L+i,j}^{ n-1 L+i(37).

Denoting (bar{lambda }_{text{m}}^) as the (lambda_{text{m}}^) evaluated average pressure in the matrix block and substitute (beta_{text{m}}^ = smallint bar{lambda }_{text{m}}^ {text{d}}t/t) into Eq. 5.

Ni is substitutionally doped in TiO2 matrix by substituting the Ti4+ lattice sites and the oxygen vacancy forms for Ti0.995Ni0.005O2.

Maintainability is evaluated from the tribo-maintainability index, obtained from SPF-t (i.e. permanent of the matrix) by substituting the numerical values of the features and their interdependence.

We have generated the commuting matrix by substituting with in (17).