Order of the resonance

The chemical shifts of in natural abundance have been measured for thiazole and many derivatives (257,258). They are given in Tables 1-37 and T38. These chemical shifts are strongly dependent on the nature of the substituent CNDO/2 calculations have shown (184) that they correlate well with the ((t+tt) net charge of the atom considered. As a consequence, the order of the resonance signals is the same for protons and for carbon atoms. 

This general expression for QSim(E) looks cumbersome unless B(E), and hence, the background S matrix Sb(E) is independent of E [64]. On the other hand, its trace has been shown to take a simple form (65). The trace is independent of the order of the resonances Sv, which it should be, but QSun itself is unfortunately not, since v- in Qv is not. 

The reactions of furansulfonyl chlorides with anilines (entry 11)123 in MeOH yield a linear Bronsted plot with fix =0.51, which indicates an Sw2 mechanism rather than a stepwise process. This value is quite similar to those found for the reactions of anilines with benzenesulfonyl chloride (0.63)117, with 2-thiophenesulfonyl chloride (0.53)124 and with 3-thiophenesulfonyl chloride (0.54)125. Thus their anilinolysis mechanism is also expected to be S/y2. The reaction rate therefore depends not only on the nucleophile basicity but also on the substrate reactivity. Comparison of the reaction rates leads to the following reactivity order for the Ar moiety benzene > 3-thiophene > 3-furan > 2-furan > 2-thiophene. This reactivity sequence follows the order of the resonance interaction between the... 

In this article we discuss the problem of understanding the long-term stability properties of a solution of a quasi-integrable Hamiltonian system by means of a Fourier analysis on a short observation time. Precisely, even for resonant chaotic motions, we will show how the combined use of Fourier analysis and Nekhoroshev theorem allows to understand the stability properties on a time T exp(T), where T is a suitable observation time, of the order of the resonant period. To be definite, we will refer to quasi-integrable Hamiltonian systems with Hamiltonian of the form ... 

The term non-linear resonance describes the resonant absorption of potential energy from higher-order trapping fields. Such absorption occurs when combinations of an ion s secular frequencies match harmonic sidebands of the RF drive frequency. Conditions for non-linear resonance exist in all QITs but the effect on ion motion is dependent upon the order, sign (+ or -) and strength of the superimposed non-linear fields. Due in large part to the work of Franzen and co-workers [87-92], the phenomenon of non-linear fields and their contribution to non-linear resonance effects in ion traps is now well understood. In addition to the quadrupolar resonance, there are a series of resonance conditions desaibed by Equations 9.11 and 9.12 where V is an integer 0 and n is the order of the multipole. The overall order of the resonance (AO is described by Equation 9.13. 

If in PM homopolymer, the different values of magnetic fields experienced by the a-Me group are due to the magnetic anisotropy of ( —C = 0), in PAM copolymer this magnetic anisotropy is enhanced by the presence of ( —C = N) groups of the two adjacent A units It seems reasonable to assume that, from low to high field, the order of the resonance lines are the same for PM (MMM triad) and PAM (AMA triad) ... 

Aldonic acids are found in many biological systems and are formed by the oxidation of sugars. The compounds have a hydroxyl group a to the carboxylic acid moiety. In a study of 17 aldonic acids, one example of which is 89, with Eu(pdta), enantiomeric discrimination of the Ha, Hp and H7 resonances was observed in the H NMR spectrum. Furthermore, the order of the resonances for the enantiomeri-cally discriminated Ha, Hp, and H-y atoms correlated with the absolute configuration of the a-carbon in each of the aldonic acids. ... 

Wlien resonances, or near resonances, are present in the 4WM process, the ordering of the field actions in the perturbative treatment (equation (Bl.3.1)), can be highly significant. Though the tliree-colour generators... 

The locations of the maxima of the -field and the E-field are different depending on the mode chosen for the EPR experuuent. It is desirable to design the cavity in such a way that the B field is perpendicular to the external field B, as required by the nature of the resonance condition. Ideally, the sample is located at a position of maxuuum B, because below saturation the signal-to-noise ratio is proportional to Simultaneously, the sample should be placed at a position where the E-field is a minimum in order to minimize dielectric power losses which have a detrimental effect on the signal-to-noise ratio. 

The main cost of this enlianced time resolution compared to fluorescence upconversion, however, is the aforementioned problem of time ordering of the photons that arrive from the pump and probe pulses. Wlien the probe pulse either precedes or trails the arrival of the pump pulse by a time interval that is significantly longer than the pulse duration, the action of the probe and pump pulses on the populations resident in the various resonant states is nnambiguous. When the pump and probe pulses temporally overlap in tlie sample, however, all possible time orderings of field-molecule interactions contribute to the response and complicate the interpretation. Double-sided Feymuan diagrams, which provide a pictorial view of the density matrix s time evolution under the action of the laser pulses, can be used to detenuine the various contributions to the sample response [125]. 

It will be seen that the second-order treatment leads to results which deviate more from the correct values than do those given by the first-order treatment alone. This is due in part to the fact that the second-order energy was derived without considerar-tion of the resonance phenomenon, and is probably in error for that reason. The third-order energy is also no doubt appreciable. It can be concluded from table 3 that the first-order perturbation calculation in problems of this type will usually lead to rather good results, and that in general the second-order term need not be evaluated. 

In the discussion of metallic radii we may make a choice between two immediate alternative procedures. The first, which I shall adopt, is to consider the dependence of the radius on the type of the bond, defined as the number (which may be fractional) of shared electron pairs involved (corresponding to the single, double, and triple bonds in ordinary covalent molecules and crystals), and then to consider separately the effect of resonance in stabilizing the crystal and decreasing the interatomic distance. This procedure is similar to that which we have used in the discussion of interatomic distances in resonating molecules.7 The alternative procedure would be to assign to each bond a number, the bond order, to represent the strength of the bond with inclusion of the resonance effect as well as of the bond type.8... 

In order to discuss the geometrical structures of electronically excited states, the same procedure as described above is used, except for the use of a different value 3.3 for exponent a in the exponential form of the resonance integral This value of a was determined so that the predicted fluorescence energy from the lowest singlet excited state CB2J in benzene may fit the experimental value. 

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