Duhamel procedure

Complications of Hirschsprung s disease include an enterocolitis with or without intraluminal air, intermittent dilatation after surgical treatment which may give a picture of pseudo-obstruction. Following a Duhamel procedure ( pull through procedure) there may be persistent narrowing at the anastomosis site. 

The first case has already been considered section 2.0 the second case leads to a strong classical spin-orbit coupling, which is reflected in a Hamiltonian nature of the classical combined dynamics. In both situations the procedure is to find a suitable approximate Hamiltonian Hq( ) that propagates coherent states exactly along appropriate classical spin-orbit trajectories (x(l,),p(t),n(l,)). (For problems with only translational degrees of freedom this has been suggested in (Heller, 1975) and proven in (Combescure and Robert, 1997).) Then one treats the full Hamiltonian as a perturbation of the approximate one and calculates the full time evolution in quantum mechanical perturbation theory (via the Dyson series), i.e., one iterates the Duhamel formula... 

In retrospect, the effect of the change of variables has been to deform the velocity field from axisymmetric stagnation flow over a sphere to linear shear flow along a flat plate. The main advantage of the new coordinates is that the coefficients of the derivatives in (32) are independent of X, and consequently Duhamel s theorem can be applied. Thus, the following procedure can be used (1) solve equation (32) subject to a uniform surface concentration (2) extend this solution to one valid for an arbitrary, nonuniform surface concentration by applying Duhamel s theorem (3) select the surface concentration which satisfies (33a). 

Since the seminal work of Lucette Duhamel [3] in 1976 describing what is the first direct asymmetric protonation of an enolate (in fact its enamine analogue), it is only in 1992 that Takeuchi et al. successfully used a cinchona alkaloid for the enantioselective protonation of a particular samarium enediolate under mild conditions [4], Samarium diodide reduced benzil 1 into the corresponding enediolate 2, which was then enantioselectively protonated by quinidine 3 at room temperature, affording (R)-benzoin 4 in 91% ee (Scheme 7.3). The presence of molecular oxygen was necessary to obtain high selectivities. However, the procedure was not catalytic as 3 equiv of quinidine 3 were needed. Moreover, only one substrate was described showing the limits of this procedure. 

Jean-Marie-Constant Duhamel (1797-1872) rounded off the basic theory by defining its limitations. Mathematical models of real situations could be constructed, but not necessarily solved. Duhamel identified tests for these insoluble forms, which would have to be tackled by other means, the iterative procedures and successive approximations that are suited to mechanical calculators. 

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