Sentence examples for main equation of from inspiring English sources

Therefore, it is inconvenient to use (44) as a main equation of the inverse problem.

This equation is called the main equation of the inverse problem.

For spatial data over time, our main equation of interest (expressed in differences for spatial unit s between period t and t-1, denoted by the difference operator Δ) relates the crime rate to the immigrant/population ratio as: Δ Crime Population st = β 1 Δ Immigrants Population st + β 2 Δ X st + T t + ϵ st (1).

The method of spectral mappings is connected with the idea of the contour integration method and reduces the inverse problem to the so-called main equation of the inverse problem, which is a linear equation in the Banach space of bounded sequences.

For each fixed (x ge0), the following relation holds: tilde{varphi} x, lambda) = varphi x, lambda) + frac{1}{2 pi i} int_{gamma} varphi x, mu) tilde{r} x, lambda, mu),dmu, (18) which is called the main equation of Inverse problem 1.

Here, we will only summarize the main equations of this model when it is applied to the case of a transparent paint applied on a substrate.

(13) through (17) summarize the main equations of type C phase field models for void growth in irradiated solids (Rokkam et al., 2009; Millett et al., 2009; Millett et al., 2011c; Millett et al., 2011b), where a non-conserved order parameter η is considered to distinguish the void and matrix phases.

By reducing the singularity, the transformation of the main equation to the equivalent integral equations is performed in Section 3.

Let us rewrite the main equation (18) of the inverse problem in terms of the spectral data.

The non-linearity of the main equation (11) necessitates the use of a numerical method of integration.

Finally, the solvability of the main equation is proved and the unique recovery of the potential from the solution of the main equation is shown in Section 4.