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Extra info for An analytic counterexample to the KAM theorem

Example text

If the ratio of Dn/J might not be large enough before, it is large enough now. Therefore, the 1 H spectra can be interpreted as the first-order spectra in almost each case, that is, the spectra can be analyzed by using the n þ 1 rule. Of course, we should also pay attention to the second condition mentioned above, that is, magnetic equivalence. When we apply the n þ 1 rule, the nuclei group, which has the number of n, should have the same coupling constant. If they have different coupling constants, the n þ 1 rule should be applied several times.

2 for the calculation of the chemical shift values of a substituted benzene. T. 4 CH I 2. The relationship between the size of the substituent and the chemical shift value of the substituted carbon atom The larger the size of the substituent, the greater the increment in the chemical shift of the substituted carbon atom. In the following series, the chemical shift of the carbon atom marked at its upper-left with “Ã ” increases from the left side to the right side. Interpretation of 13C NMR Spectra 45 R----*CH3 ; R----*CH2 CH3 ; R----*CH2 CH2 CH3 ; R----*CH2 CHðCH3 Þ2 ; R----*CH2 CðCH3 Þ3 : This phenomenon can be explained as follows.

If a group of magnetically equivalent nuclei is split by several long-range coupling constants, the coupled splittings of the peak set of the group will not be clear. As a result, it is difficult to find the coupled splittings from related long-range coupling constants. To sum up, in a peak set, we find out first one or several equal distances, with every distance obtained from equally spaced peaks. Therefore, we can know by how many coupling constants the peak set is split. Then, we will find equal distances from related coupled peak sets.

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An analytic counterexample to the KAM theorem by Bessi U.


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