Sentence examples for by considering the convolution from inspiring English sources

In the following sections, we discuss the observed characteristics of the electron density enhancement after summarizing an overview of the lithium release experiment during the WIND campaign, and suggest that the observation can be reasonably explained by considering the convolution of very short-time intermittent releases using a simple spherical free expansion model.

The value of α i can be calculated for an individual voxel within a VOI, centred at x i,y i and z i, by considering the convolution with a 3D Gaussian kernel, g x,y,z,σ), integrated over the volume of the VOI.

Specifically, the integral convolution of the two-phase mixture is done by considering the special bi-exponential kernel.

In this paper, we consider the convolution operator given by T f ( x 1, x 2 ) = ∫ a b f ( x 1 − t, x 2 − ϕ ( t ) ) ω ( t ) d t (1.1).

This good agreement verifies the model calculation and indicates that the electron density enhancement observed using the NEI during the WIND campaign can be explained by considering a convolution of very short-time intermittent releases with the simple spherical free expansion model.

Although the assumptions (1) and (2) affect the estimated total amount and the altitude profile of the vaporized lithium in some degree, these assumptions do not deny the result that the observed electron density enhancement can be explained by considering a convolution of very short-time intermittent releases.

A simple model calculation performed under the assumption that the increased electron density equals the photoionized lithium ion density indicates that the observed electron density enhancements cannot be explained by considering each lithium release as an instantaneous one, but rather by considering a convolution of very short-time intermittent releases.

By comparing an altitude profile of the vaporized lithium calculated from the model described below and that of the luminosity shown in Fig. 5(b), we suggest that Δne can be reasonably explained by considering a convolution of very short-time intermittent releases.

Ca can be calculated at the relevant frequencies such as ± f p and ± f n by considering all the possible convolution relationships of the frequency components.

In Section 6, we present a generalization of Besge's formula by considering certain combinatorial convolution sums (see Theorem 6.3).

We consider the Mellin convolution integral representation of the third Appell function given in Erdélyi (1953) [8].