Note that the detector has the form of the Radon-Wigner distribution, which ensures that the energy of the watermark is distributed over the hyper plane defined by ( is the phase function of the watermark).
As for the structure of the whole cell, it could be determined by analyzing the phase function of the outside surface of the cell.
(mathbb {V}) is the phase function defined by (mathbb{V} x,t)= int_{0}^{t}g (vert u x,s) vert^{2} ), ds).
From the normalization of the phase function given by Eq. (2), one obtains the normalization for F, {displaystyle {int}_{-1}^1 Fleft tau right) dtau =frac{1}{pi},} (24 and therefore a single-scattering intensity is normalized as 4 pi {displaystyle {int}_0^{vt}{I}_1left( r, tright){r}^2 dr=frac{vt}{l_s}{e}^{- vt/{l}_s}}, (25 which is consistent with the normalization obtained by Shendeleva [17].
The second phase function, D4, has a simple algebraic relation (in the range 0 < k < 1) between the anisotropy factor and the parameter of the phase function, as given by Eq. (40).
From Theorems 3.1-3.3 3.1-3.3 oneucanmore useful asymptotic stability theorems in terms of coefficients of (1.1) by choosing the phase functions as asymptotic solutions of the characteristic equation.
By different choices of the phase functions, we deduce stability theorems in terms of the auxiliary function of coefficients R A ( t ), which is invariant with respect to the lower triangular transformations.
In this study, the SFM was coupled to the Henyey Greenstein (HG) scattering phase function in order to assemble the model with a more accurate description of the scattering phenomenon provided by this phase function.
Structural shapes are represented by the phase field function defined in the design domain, and this function is optimized by solving a time-dependent reaction diffusion equation.
