Uncoupling coupling efficiency

The value of rjmax depends only on the extent of coupling. When two reactions are completely uncoupled, the efficiency must be zero. When q = 1, we have the maximum efficiency of unity. 

The total angular momentum basis is thus computationally more efficient, even for collision problems in external fields. There is a price to pay for this. The expressions for the matrix elements of the collision Hamiltonian for open-shell molecules in external fields become quite cumbersome in the total angular momentum basis. Consider, for example, the operator giving the interaction of an open-shell molecule in a 51 electronic state with an external magnetic field. In the uncoupled basis (8.43), the matrix of this operator is diagonal with the matrix elements equal to Mg, where is the projection of S on the magnetic field axis. In order to evaluate the matrix elements of this operator in the coupled basis, we must represent the operator 5 by spherical tensor of rank 1 (Sj = fl theorem [5]... 

In the last two sections, we have applied increasingly tricky devices to solve what amounts to systems of equations, in order to make their solution efficient. Even the two-species uncoupled case involved the generation of the u and v vectors and the solution of small (2 x 2) systems to obtain the boundary values. In the case of coupled systems, the problems mount and matrix-vector equations had to be used. 

As the coupling reaction is not fully efficient, the star-branched copolymers contain a nonnegligible amount of uncoupled linear copolymer. To get the star-branched copolymers as pure as possible, a purification step where linear chains were extracted by fractional precipitation using different solvent or nonsolvent methods was necessary (J). 

Polylysine of 300 repeat units has been found to be the most useful for coupling. Some authors have stated that residual uncoupled polylysine can reduce the efficiency of specific receptor-mediated transfection in the final preparation unless more extensive purification is done, such as preparative acid-urea gel electrophoresis followed by cation-exchange HPLC (69). 

Thus, the osmotic coupling coefficient is the ratio of the actual volume flow observed with equal bathing media relative to the virtual volume flow that would be necessary for reabsorption to be isotonic. In the models we shall consider, 0 < y < 1. For tight couphng, Y 1 in an uncoupled system y = 0. y has also been termed the efficiency of osmotic transport [16]. 

Note that the first of the two equations has terms in both variables, Ca and Cb- This is not a problem when using an explicit method, but these are practically useless when hers are involved and implicit methods are normally chosen for their greater efficiency. However, while these produce tridiagonal systems of equations for single species or uncoupled multireactions, they produce more complicated systems for coupled reaction systems, which are not amenable to the usual solution techniques. This problem was solved recently by Rudolph [7] and references therein, who introduced the technique known as hlock-tridiagonal solution into electrochemical simulations, (see Ref. [2], 3rd edn. only) and Sect. 1.3.9. 

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