Sentence examples for be applied to equations from inspiring English sources

The same principle can be applied to equations (4).

So the methods of QFT could be applied to equations resulting from the quantum mechanical (field like) treatment of particles like the electron (e.g., Dirac equation).

Moreover, they can be applied to equations for which the results obtained in some of the above mentioned papers could not be used (see Examples 1-3).

The results presented here have been successfully applied to some special classes of Eq. (1), see [16, 17] and can be applied to equations considered in [18 22].

It is obvious that the described decomposition methods may be applied to equations of any order and any degree in the variables, a detailed discussion of these more general cases will be given elsewhere; an algorithm for decomposing equations of any order into rational components has been given by Gao and Zhang [8].

From the laws of exponentiation: Multiplication: :: r_0 e^{i\varphi_0} \cdot r_1 e^{i\varphi_0}=r_0 r_1 e^{i(\varphi_0 + \varphi_1)} \, Division: :: \frac{r_0 e^{i\varphi_0}}{r_1 e^{i\varphi_1}}=\frac{r_0}{r_1}e^{i(\varphi_0 - \varphi_1)} \, Exponentiation (De Moivre's formula): :: (re^{i\varphi})^n=r^ne^{in\varphi} \, Calculus can be applied to equations expressed in polar coordinates.

Thus, Theorems A, B, and C all cannot be applied to Equation 10.

For this case, the main results of [18, 19] cannot be applied to equation (3.18).

Although any combination of weights can be applied to Equation 1, not all such combinations are actually logical or preferred.

Observe that the results reported in [7, 20] cannot be applied to equation (3.25) since (g(t)>t).

However, since equation (1.4) is anisotropic and with the variable exponents, the method of [6] seems difficult to be applied to equation (1.4).