Multichannel expansion

Reduction to direct and exchange amplitudes The antisymmetric multichannel expansion is... 

The antisymmetric multichannel expansion (7.3) of the collision state T S,+ (k)) has a serious difficulty. It is not unique. This is seen by considering the orbital-cofactor expansion (7.5) in the elements of the u Vk)) column. If we add A(xr a) to (xr u k)), where the orbital a) is occupied in all the determinants comprising ly), we are adding determinants with two identical columns, which are zero. Therefore u (k)) is ambiguous, at least with respect to the addition of a linear combination of occupied orbitals. 

Using (7.5) the antisymmetric multichannel expansion for M target states is... 

The integral equations corresponding to (7.117) are obtained by using the unsymmetrised multichannel expansion (7.27), considering (7.117) as a projection onto the channel state (k i of... 

Rigorous scale homogenization procedures lead to continuum models for the entire DPF (Bissett, 1984 Konstandopoulos et al., 2001, 2003) exploiting (as is common in continuum descriptions) a suitable scale disparity, namely the ratio of the channel hydraulic radius to the entire DPF diameter. The smallness of this parameter is invoked to formulate a perturbation expansion of the discrete multichannel equations. The continuum multichannel description of the DPF can accommodate various regeneration methods (thermal, catalytic and N02-assisted) and can provide spatio-temporal information of several quantities of interest (e.g. filter temperature, soot mass distribution, flow distribution, etc.) as illustrated in Fig. 38. 

M. Venuti, P. Decleva, Convergent multichannel continuum states by a general configuration interaction expansion in a B-spline basis Application to H photodetachment, J. Phys. B At. Mol. Opt. Phys. 30 (1997) 4839. 

Expansion of the original AutoAnalyzer concept resulted in the multichannel AutoAnalyzer dedicated to simultaneous determinations. For clinical analyses, the multiple, simultaneously recorded peaks can be combined to build up a multiple analysis chart [20], which has been recognised as a very important tool for clinical diagnosis. 

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