Sentence examples for replace equations from inspiring English sources

Therefore, it is necessary to replace equations as follows.

Just like with the SLLM, we use Chebyshev differentiation to replace equations (35) through (38) with the discrete form A 1 f r + 1 = B 1, f r + 1 ( ξ N ) = f w, (40).

(19) (20) Then, instead of the gene expression/TF activity indicators, the surrogate gene expression/TF activity indicators are used to determine the enzyme/TF status and thus reaction states via GPR associations and transcriptional regulation by equations (21 - 23 21 - 23replace equations (3),(4), and (7).

Before continuing, we replace equation (3) by the following: T ( x, C ( x ) ) ∈ A, x ∈ A. (4).

The PGFEM supposes that we may replace equation (18) with ∫ Ω ϕ i ( ∂ U ∂ X + ∂ V ∂ Y ) d Ω = − ϵ ∫ ϕ i P, (19).

The following slightly modified cost function was used to replace Equation 3 J x = y - Ax 2 2 + λ ∑ k = 1 K f k 2 + ε 1 / 2 (4).

If we replace Equation 22 in Equation 19, we find: C EE ( t ) = a 4 e 2 ∫ f r ⃗, v ⃗ e ⃗ r · e ⃗ mf ( r ( t ) ) d r ⃗ d v ⃗, Open image in new window (28).

We replace Equation 29 with Equation 33 to maximize the utility during T, taking into account the already downloaded data during T m. q ( s ) = ∑ t ∈ T m ∑ a ∈ A r ( a, s ) ∗ ( t ) + ∑ t ∈ T ∑ a ∈ A r ( a, s ) ( t ) ∑ t ∈ T m u s ( t ) + ∑ t ∈ T u s ( t ).

Here the usual methods of science are stretched to the limit -- and that is where an influential minority of scientists quietly agree on the kind of cure Dr. Wolfram is so loudly prescribing: replacing equations with a different kind of mathematical device called algorithms, simple little computer programs.

Equation (4) constitutes the necessary minimum set of constitutive equations for an isotropic material replacing Equations (1) and (2).

By replacing Equations 32 and 33 in 26, it can be shown similarly that no terms cancel out.