Sentence examples for by evaluating the integral from inspiring English sources

By evaluating the integral in (D.1) by using [25, ], one can obtain the result given in (25).

The spatial variance of the E E fluctuations is estimated by evaluating the integral (int_{-infty}^{infty}[tilde {mathbf{G}}(q)]_{11},dq); meanwhile the spatial autocorrelation of these fluctuations is extracted from the inverse Fourier transform, ([mathbf{G}(x)]_{11} = mathcal{F}^{-1}[tilde {mathbf{G}}(q)]_{11}).

It is based on a global integral representation of the unknown function in the form of a potential, followed by evaluating the integrals in the resulting series solution using Monte Carlo simulation.

The focal volume is subsequently calculated by evaluating the diffraction integral in Eq. (1) with the modified wavefront.

The analysis is carried out by evaluating the related integrals in the wavenumber domain.

The theoretical method is hampered by the difficulty of evaluating the integrals.

Start by evaluating the relationship.

If in (A.13) is an integer, we evaluate the integral of (A.13) by using Theorem 3 and after some manipulations, (10) arises.

Background: This study was designed to evaluate the integral dose (ID) received by normal tissue from intensity-modulated radiotherapy (IMRT) for prostate cancer.

We have evaluated the integral in Eq. (16) by Trapezoidal rule for all the grains considered.

Inserting the values of A and B, we have evaluated the integral in Eq. (19) by Simpson's one-third rule for all the grain sizes considered.