Sentence examples for matrix by substituting from inspiring English sources

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

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.

Form a new matrix E' by substituting the endmember e k by the data vector x i.   ii.

For each endmember e k, k = 1,..., p: For each data vector x i, i = 1,..., N: Form a new matrix E' by substituting the endmember e k by the data vector x i. Calculate the volume of the simplex v' = V (E').

where, as can easily be verified (in view of the above-defined delayed matrix exponential) by substituting into (3.1), (3.5). is a normal fundamental matrix of the homogeneous system related to (3.1) (or (2.1)) with the initial data, and the Cauchy matrix has the form (3.6).

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).

Let M′ denote the matrix restored by substituting the modified eigenvalues into S such that M ′ = c 1 ′ c 2 ′ c 3 ′ c 4 ′ ⋯ ⋯ c N / 2 − 1 ′ c N / 2 ′ = U λ 1 ′ 0 0 λ 2 ′ 0 0 ⋯ ⋯ 0 0 V T. (20).

In order to overcome these limitations, a new class of composites has emerged under the name of fabric-reinforced-cementitious-matrix (FRCM) materials by substituting the organic resin of the FRP system with a cementitious-based binder.

The Fe-based single atomic chains are designed in the semiconductive CoTiSb matrix by continuously substituting Fe for Ti, Ti Sb or Co in [0 0 1] crystallographic direction.

Robust counterparts of the correlation matrix based detectors are obtained by substituting a robust correlation matrix estimate as it was discussed in Section 2 (12) mathbf{R}_{r} = left{ begin{array}{ll} mathbf{R},& text{if} mathbf{x} leq eta kappa eta,& text{otherwise} end{array} right.