Sentence examples for reduction equation from inspiring English sources

The proposed methodology also provides correlation information between all outputs, thus providing information not easily obtained using the traditional uncertainty process based on analyzing one data reduction equation (DRE /model at a time.

The DAS data reduction equation is a function of many parameters including the microphone locations, microphone transfer functions, temperature and the cross-spectral matrix (CSM), where each one of these parameters has a unique uncertainty associated with it.

For any function v in the even function space can be expressed as follows: v = ∑ k ≥ 1 x 2 k e 2 k, by the Lyapunov-Schmidt reduction method used in Step 3, we can deduce that the reduction equation of (1.1) is as follows: d x 2 d t = x 2 + A x 2 3 + O ( | λ − μ − α | 2 | x 2 | 3 ) + o ( | x 2 | 3 ), (4.6).

The fast variable x2 is equilibrated, and the equilibration equation corresponds to the classical notion of quasi-stationary approximation, as described in Section " Classical Michaelis-Menten reduction", equation 16.

The form (36) of the truncated equations and the conservation of x1+ x2 by the fast dynamics shows that this case corresponds to quasi-equilibrium of the first reaction in the Michaelis-Menten model, as described in Section " Classical Michaelis-Menten reduction", equation 17.

However, it is still very difficult to get exact solutions for infinitely many reduction equations.

It is shown that its reduction equations are Painleve I and II, respectively, which are the same as those of the KdV equations.

To get the exact form of the reduction equations, we need to obtain the expression of 〈 G ( u ), e 1 〉 and 〈 G ( u ), e 2 〉.

Let Φ be the center manifold function, in the neighborhood of ( u, λ ) = ( 0, μ + α ), we have u = y + Φ ( y ), where y = x 1 e 1 + x 2 e 2. Then the reduction equations of (3.2) are as follows: { d x 1 d t = x 1 + 〈 G ( u ), e 1 〉, d x 2 d t = x 2 + 〈 G ( u ), e 2 〉. (4.3).

In fact, we have used the electron-rich source of plasma region produced by a discharge between two titanium electrodes in HAuCl4 solution to reduce the HAuCl4 into Au nanoparticles according to these reduction equations: H A u C I 4 → H + + A u C I 4 - Open image in new window (1) A u C I 4 − + 3 e − → A u + 4 C I − Open image in new window (2).

As the first step for the reduction of Equation (27), we divide it into two equations for the r and θ components.