Sentence examples for substituting the form from inspiring English sources

Hence, each point in time corresponds to a different surface and the time integration can be transformed to the volume integral: Now substituting the form of Γ given by Eq. (8), and assuming Γ 0 is spatially independent, Setting, without loss of generality, the observation point at the origin (r = 0 ), the PA response becomes where and.

Substitute the form of um,n into (23), we finally have R λ ≤ π − σ m, n · F − 1 1 − α 4 π sin π m − n M sin θ H (24). Therefore, in order to use the correlation interferometer algorithm based on dimension separation, the radius to wavelength ratio must satisfy (24).

Substituting the polar form A n ( T 1 ) = 1 2 a n ( T 1 ) e i β n ( T 1 ) (41).

We explored the feasibility of substituting the natural bilayer (formed on the lithium surface when lithium is in contact with water), for a thin polymeric film.

Let's substitute the factored form of our original expression for the expression in the numerator: (3(3x2 + 9x - 1))/3 Notice that now, both the numerator and the denominator share the coefficient 3. Dividing the numerator and denominator by 3, we get: (3x2 + 9x - 1)/1.

In order to simplify the equation, γ i is used to substitute the variables formed by the combination of α i and β i.

Substituting the (_{4}F_{3}(1)) by its reduced form in (10).

The idea consists of formulating the problem of optimal control under a variational problem form by substituting the control variable by its expression derived from the system model in the performance index.

Similarly, optimization of PS can be formed by substituting the objective function to the summation of service levels.

In the EIIP representation, a single EIIP indicator sequence [11, 12] is formed by substituting the EIIP of the nucleotides as C = 0.1340, G = 0.0806, A = 0.1260, and T = 0.1335 in a nucleotide sequence.

Interestingly, her anger at the thought of feeding her baby the "other person's milk" implies that supplying breast milk is in some ways equated with caring for one's baby and that she might be "replaced" by another person (though ironically, it was a real dairy cow that substituted, in the form of cow's-milk-based infant formula).