Sentence examples for by substituting the expression from inspiring English sources

By substituting the expression of,,, and into (17), we have.

By substituting the expression of in (B.19) we find (B.20).

where the second result is obtained by substituting the expression of the transmission rate in (15) into the third constraint of problem (P1) and equaling the restriction.

The outage probability for DHS is obtained by substituting the expression for P o z) given by (18) for the quantity in the brackets of (7), i.e., (1-frac {1}{2pi i}int _{c-iinfty }^{c+iinfty }lambda _{k}(s,z) = P_{mathrm {o}} z)).

By substituting the expression for the energy function in Equation 8, we obtain the expression for our reliability to motion estimation as P ( v | F ( t ), F ( t − d t ) ) = 1 K exp ( − U ( v ( t ) | F ( t − d t ) ) − 1 2 ( ν L 2 + σ L 2 ) ∑ p = 1 P [ F L l l, t ) − F L l l − v, t − d t ) ] 2 − 1 2 ( ν D 2 + σ D 2 ) ∑ p = 1 P [ F D ( l, t ) − F D ( l − v, t − d t ) ] 2 ).

By substituting the expressions (24) for the into (30), we get after some manipulations the following inequality: (31).

By substituting the expressions for the functions and in (1.1), it can be shown that (1.11) holds.

The explicit expression for the ballistic light transmitted through a cell of length D can be obtained by substituting the expressions (2) and (6) in Equation 1: (8).

The minimum value for the MSE cost function given by Equation (25) can be obtained by substituting the expressions obtained for the optimum filters F MMSE THP and B MMSE THP, and for the gain factor g MMSE THP.

Assuming that the NA is at the center of the ITO, this equation can be obtained by substituting the expressions for y and A into the expressions for t and w; thus, E b t b + t I 2 t b w + E I 0 t b w − E 0 t 0 + t I 2 t 0 w = 0 (5).

In this case, the remaining two model parameters a and b can be calculated with low computational effort and online updated using the knowledge from the past N key frames by substituting the expressions for x and y in (5) into (6) (6).