Relaxation definition

Recently the following, more relaxed definition was accepted [5] ... 

The hydrogen-bonded complexes are characterized by several structural and spectroscopic properties that provide means of identifying the presence of such bonds. The most typical hydrogen bonds would exhibit all those properties. Some authors require that all the characteristics listed below should be present to classify dimers as hydrogen-bonded ones, but recently the more relaxed definition of the hydrogen bond given in section 1, which does not include this requirement, has become generally accepted. 

The conformations termed A, B, and Z DNA are derived from idealized DNA models based on X-ray diffraction data (Table 1.9). This implies that only broad and relaxed definitions should be applied to the DNA structures in solution. Perhaps more appropriately, local structures of DNA in solution should not be considered static. 

In another important class of cases, the matrix A is positive definite. When this is so, both the Gauss-Seidel iteration and block relaxation converge, but the Jacobi iteration may or may not. 

Unfortunately, even for low molecular weight material it is difficult to obtain clear experimental evidence for a roughening transition [71]. This is mainly due to the fact that during growth the interface generally assumes a metastable shape and relaxation times are long and increase with crystal size. Therefore we certainly cannot expect a definitive answer for macromolecules. We shall therefore just make several comments which hopefully will be of use when reading the literature. 

It is evident from Table 2 that the chemical shift data are very similar in both states of aggregation. Only the carbonyl carbon show a small but definite shifts, 2 ppm. In the solution state, in acetone -d6 solution the relaxation times T1 of the pyranose carbon atoms are very similar and only slightly smaller than those of the carbon atom of the methyl group in the acetyl substituent, while the T1-value of the carbon atom of the carbonyl group is considerably higher. 

Let us note that this definition of y breaks the limits of the Kielson-Storer model and can cause a few contradictions in interpretation of results. If the measured cross-section oj appears to be greater than oo, then, according to (3.45), the sought y does not exist. To be exact, this assertion is valid relative to the cross-section of the rotational energy relaxation oe = (1 — y2)oot since y2 is always positive. As to oj, taking into account the domain of negative values of y, corresponding to the anticorrelated case (see Chapter 2), formula (3.45) fails to define y when oj > 2co. 

Let us demonstrate that the tendency to narrowing never manifests itself before the whole spectrum collapses, i.e. that the broadening of its central part is monotonic until Eq. (6.13) becomes valid. Let us consider quantity x j, denoting the orientational relaxation time at ( = 2. If rovibrational interaction is taken into account when calculating Kf(t) it is necessary to make the definition of xg/ given in Chapter 2 more precise. Collapse of the Q-branch rotational structure at T = I/ojqXj 1 shifts the centre of the whole spectrum to frequency cog. It must be eliminated by the definition... 

The physical meaning of and f L.., is obvious they govern the relaxation of rotational energy and angular momentum, respectively. The former is also an operator of the spectral exchange between the components of the isotropic Raman Q-branch. So, equality (7.94a) holds, as the probability conservation law. In contrast, the second one, Eq. (7.94b), is wrong, because, after substitution into the definition of the angular momentum correlation time... 

Limiting ourselves to derivation of the Hubbard relation in the simplest case ( = 1 (for t = 2 see Appendix 9), we write out the definition of orientational relaxation time... 

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