Quasilinearization

The quantum numbers tliat are appropriate to describe tire vibrational levels of a quasilinear complex such as Ar-HCl are tluis tire monomer vibrational quantum number v, an intennolecular stretching quantum number n and two quantum numbers j and K to describe tire hindered rotational motion. For more rigid complexes, it becomes appropriate to replace j and K witli nonnal-mode vibrational quantum numbers, tliough tliere is an awkw ard intennediate regime in which neitlier description is satisfactory see [3] for a discussion of tire transition between tire two cases. In addition, tliere is always a quantum number J for tire total angular momentum (excluding nuclear spin). The total parity (symmetry under space-fixed inversion of all coordinates) is also a conserved quantity tliat is spectroscopically important. 

Quasilinear first-order differential equations are like... 

The equations for flow and adsorption in a packed bed or chromatography column give a quasilinear equation. 

Some analytical solutions to the quasilinear heat conduction equation. ... 

As can readily be observed, they are not monotone, thus causing some ripple . This obstacle can be avoided by refining some suitable grids in time. When solving equations of the form (13) with a weak quasilinearity for the coefficients k = k x,t), f = f u) and c = c x,t), common practice involves predictor-corrector schemes of accuracy 0(r" -f /r). Such a scheme for the choice c = k = 1, f = f u) is available now ... 

Because of this, there is a real need for designing the general method, by means of which economical schemes can be created for equations with variable and even discontinuous coefhcients as well as for quasilinear non-stationary equations in complex domains of arbitrary shape and dimension. As a matter of experience, the universal tool in such obstacles is the method of summarized approximation, the framework of which will be explained a little later on the basis of the heat conduction equation in an arbitrary domain G of the dimension p with the boundary F... 

A quasilinear equation of parabolic type. The complete posing of problem (15) includes... 

In addition, Winnewisser et al. [36] have demonstrated quantum monodromy for the NCNCS molecule, not only in the (vb, Ka) eigenvalues but also in the Bes = B + C)/2 rotational constant, which varies smoothly with Ka, at fixed Vb for Vb = 0-2, but shows a kink for Vb = 3-5. This observation is a key to the assignment of the extremely congested rotational spectrum of this interesting quasilinear molecule. 

The nature of the monodromy within a given polyad was discussed. Two of the regimes allow no such monodromy one conforms to the type displayed by the swing spring, which has qualitative similarities with that in quasilinear molecules. Finally, the monodromy in the fourth regime is of the folded type, with close qualitative similarities to that observed for LiCN isomerization in Section lllB. 

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