Suppose that A is an SAPD operator, condition (2) for coefficients is valid, (varphi,psi,zetain D(A cap D(A^{-frac{1}{2}})), and (f(t)in C_{0T}^{alpha,alpha}(H)).
Assume that (A^{x}) is defined by equation (47), condition (2) for coefficients is valid, (fin mathcal{C}_{0T}^{alpha,alpha}(L_{2} overline{Omega})) ) and (varphi,zeta,psiin D(A^{x} cap D ( ( A^{x} ) ^{-frac{1}{2} } ) ).
The new filter coefficients are valid within this new region.
In this respect, the mole fraction dependent pseudo-components delumping coefficients are valid for comprising components.
In this work we propose three different methods to compute optimized filter coefficients with the purpose of maximizing the array gain and minimizing distortions, and with the objective that these filter coefficients are valid for all users.
Therefore, the maximum likelihood estimates of the coefficients are valid in the analysis.
So, the maximum likelihood estimates of the coefficients are valid in the analysis.
Hence, the maximum likelihood estimates of the coefficients are valid in the analysis.
As such, the maximum likelihood estimates of the coefficients are valid in the analysis.
